http://soft-matter.seas.harvard.edu/api.php?action=feedcontributions&user=Smagkir&feedformat=atomSoft-Matter - User contributions [en]2022-05-27T22:37:30ZUser contributionsMediaWiki 1.24.2http://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=25269Structure factor2012-10-03T15:28:01Z<p>Smagkir: </p>
<hr />
<div>Sofia Magkiriadou, AP225, Fall 2011<br />
<br />
<br />
<br />
The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
<br />
The structure factor is a very useful concept. A closer look at the defining formula reveals that it is the Fourier transform of the density distribution. Information regarding general properties of a material structure, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify in the structure factor than in the structure itself. For example, the structure factor for a one-dimensional crystal of characteristic spacing <math>d</math> will have a maximum at <math>q = \frac{2 \pi} {d}</math>, the corresponding spatial frequency, and the width of this peak will be a measure of the quality of the crystalline order, as expected from Fourier Theory. While this is a trivial example where the periodic feature is readily identifiable, the structure factor can be a very powerful quantity for studying more complex structures such as quasi-crystals.<br />
<br />
<br />
Moreover, it is closely related to the scattering intensity from a material <math>\sigma</math>. In the case of single elastic scattering and for a material comprised of only one type of particles, this relation is, up to constants, as follows:<br />
<br />
:<math>\sigma_{\mathbf{q}} = C \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where C is a constant and <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for an arbitrary number of particle types by a simple summation where each term has the corresponding form factor (see also [[scattering]]). Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres it may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering each scatterer acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from different points in space. Within this picture, which emphasizes the analogy between a scattering pattern and a Fourier Transform, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation of S(q) as the collective interference term.<br />
<br />
<br />
The structure factor is a key quantity in crystallography and materials science; all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Directed_self-assembly&diff=23547Directed self-assembly2011-12-10T02:47:01Z<p>Smagkir: </p>
<hr />
<div>== Definition ==<br />
<br />
See also: [[self-assembly]] <br />
<br />
Self-assembly is a bottom-up process during which particles of any kind come together to form a specific structure. Common examples of such a process include the three-dimensional formation of proteins from amino acids in a living organism and the often six-fold symmetric formation of crystals in snowflakes. <br />
<br />
Directed self-assembly refers to a self-assembly process where the initial particles and their environment have been engineered to promote the formation of a specific structure. <br />
<br />
Soft matter physics relates particularly to this subject since it provides a good model system for the study of self-assembly: colloidal suspensions of microspheres which can be used as the building blocks of more complex assemblies. The size range of microspheres can be as large as a few microns, which makes them fairly easy to image with conventional techniques such as [[optical microscopy]] and [[confocal microscopy]]; a recently introduced technique, [[digital holographic microscopy]], is also being used and under development for the study of dynamic processes.<br />
<br />
== Methods ==<br />
<br />
=== Thermodynamics ===<br />
<br />
Thermodynamics predicts that a system in equilibrium will relax in its lowest energy state. With that in mind, the game of directed self-assembly translates into engineering a system such that its ground state coincides with the desirable structure. It is possible for a system to be in a metastable state with a local energy minimum; if the lifetime of this state is long enough compared to the timescales relevant for the use of the self-assembled structure, this approach can also be used. <br />
<br />
Thermodynamics can be very helpful in designing systems for directed self-assembly, since it provides a theoretical toolcase for the prediction of the probability of occurrence of a certain configuration based on properties as general as the number of different types of interactions between particles and the range of the associated interparticle energies (see [[Design principles for self assembly with short ranged interactions]]).<br />
<br />
Thermodynamics underlies all physical processes, so in a sense all the methods described below can be eventually explained in terms of thermodynamical principles.<br />
<br />
=== Geometry and Surface Forces ===<br />
<br />
Geometry can set constraints on the motion of particles, making the desired structure more likely to self-assemble. Geometrical constraints are sometimes combined with surface forces which can be very strong at interfaces; in this case, the geometry of the space available to the particles is engineered so that the magnitude and direction of the associated surface forces will guide them in a desirable way. <br />
<br />
An example of how geometry can affect the yield of a self-assembly process is currently being explored for the creation of tetramers from a suspension of colloidal particles of two different sizes. The underlying idea is quite simple: a tetramer of particles can be formed by one small sphere in the center, on the surface of which are three larger spheres. If the larger spheres are too large compared to the small one, then it is impossible for three of them to fit, whereas if the larger spheres are too small compared to the small one, then it is highly likely that more than three of them will fit. It has been proven mathematically and shown experimentally that there is an optimal size ratio between the diameters of the two sphere types which results in the assembly of exactly three large spheres on the surface of one small sphere [[3]].<br />
<br />
The combination of geometry with capillary forces is commonly used for the directed self-assembly of thin films of crystals of particles on a flat surface. In such a process, a clean glass slide is immersed in a dense colloidal suspension and slowly pulled out. As the glass surface moves, a thin layer of the suspension full of particles protrudes from the liquid surface and carries the particles to the glass surface. If the surface moves slowly enough and the suspension is dense enough, this can result in the self-deposition of the spheres on a hexagonal lattice with the (1,1,1) plane parallel to the glass surface [1].<br />
<br />
=== Surface Functionalisation ===<br />
<br />
The interaction between two particles depends strongly on the properties of their surfaces. This can be used to engineer attractive or repulsive interactions. For example, in a colloidal system particles can be coated with surface charges. One of the simplest examples is the creation of colloidal crystals in a suspension where all particles have the same charge (see [[Photonic Properties of Strongly Correlated Colloidal Liquids]]). In this case the particles try to maintain the furthest distance from each other which is allowed by the volume of the surrounding medium and so they hover in the medium at periodically spaced locations. Even though electrostatics has only provided us with two types of electric charges, this technique can be surprisingly versatile with the addition of salt in the system, which allows control of the intensity of the electrostatic interactions since the concentration of free charges affects the [[Debye length]]. <br />
<br />
Such a system is currently being explored for the self-assembly of particle clusters with a specific number of constituents. Small negatively charged spheres are mixed with larger positively charged spheres; the large spheres are attracted to the small spheres and park on their surface, and due to the existence of free ions in the suspension large spheres attracted to the same small sphere are not repelled from each other, allowing for the attachment of more than one positively charged sphere on the surface of a negatively charged sphere [3].<br />
<br />
Another way to taylor interparticle interactions which offers greater variety relies on the use of DNA strands. By coating some spheres with half of a DNA strand and some with the complementary half, and assuming that the temperature of the system is higher than the binding energy between the DNA strands so that spheres can move Brownianly and find each other, it is possible to create a suspension where different pairs of particles are attracted to each other but indifferent to other particles which are coated with the half of another, non-complimentary DNA strand. This method is also being actively studied for the self-assembly of complex particle clusters [2].<br />
<br />
== Keyword in references: ==<br />
<br />
[[Design principles for self assembly with short ranged interactions]]<br />
<br />
== References ==<br />
<br />
[1] Jiang, Bertone, Hwang, and Colvin, Chem. Mater. 1999, 11, 2132-2140<br />
<br />
[2] Leunissen et al, Soft Matter, 2009, 5, 2422-2430<br />
<br />
[3] Schade et al, 2011 (in preparation)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Cooperative_motility&diff=23546Cooperative motility2011-12-10T02:46:30Z<p>Smagkir: </p>
<hr />
<div>Entry needed.<br />
<br />
<br />
<br />
<br />
<br />
== Keyword in references: ==<br />
<br />
[[Biofilms as Complex Fluids]]</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Directed_self-assembly&diff=23545Directed self-assembly2011-12-10T02:45:56Z<p>Smagkir: </p>
<hr />
<div>Entry needed - Sofia is on it, in progress.<br />
<br />
== Definition ==<br />
<br />
See also: [[self-assembly]] <br />
<br />
Self-assembly is a bottom-up process during which particles of any kind come together to form a specific structure. Common examples of such a process include the three-dimensional formation of proteins from amino acids in a living organism and the often six-fold symmetric formation of crystals in snowflakes. <br />
<br />
Directed self-assembly refers to a self-assembly process where the initial particles and their environment have been engineered to promote the formation of a specific structure. <br />
<br />
Soft matter physics relates particularly to this subject since it provides a good model system for the study of self-assembly: colloidal suspensions of microspheres which can be used as the building blocks of more complex assemblies. The size range of microspheres can be as large as a few microns, which makes them fairly easy to image with conventional techniques such as [[optical microscopy]] and [[confocal microscopy]]; a recently introduced technique, [[digital holographic microscopy]], is also being used and under development for the study of dynamic processes.<br />
<br />
== Methods ==<br />
<br />
=== Thermodynamics ===<br />
<br />
Thermodynamics predicts that a system in equilibrium will relax in its lowest energy state. With that in mind, the game of directed self-assembly translates into engineering a system such that its ground state coincides with the desirable structure. It is possible for a system to be in a metastable state with a local energy minimum; if the lifetime of this state is long enough compared to the timescales relevant for the use of the self-assembled structure, this approach can also be used. <br />
<br />
Thermodynamics can be very helpful in designing systems for directed self-assembly, since it provides a theoretical toolcase for the prediction of the probability of occurrence of a certain configuration based on properties as general as the number of different types of interactions between particles and the range of the associated interparticle energies (see [[Design principles for self assembly with short ranged interactions]]).<br />
<br />
Thermodynamics underlies all physical processes, so in a sense all the methods described below can be eventually explained in terms of thermodynamical principles.<br />
<br />
=== Geometry and Surface Forces ===<br />
<br />
Geometry can set constraints on the motion of particles, making the desired structure more likely to self-assemble. Geometrical constraints are sometimes combined with surface forces which can be very strong at interfaces; in this case, the geometry of the space available to the particles is engineered so that the magnitude and direction of the associated surface forces will guide them in a desirable way. <br />
<br />
An example of how geometry can affect the yield of a self-assembly process is currently being explored for the creation of tetramers from a suspension of colloidal particles of two different sizes. The underlying idea is quite simple: a tetramer of particles can be formed by one small sphere in the center, on the surface of which are three larger spheres. If the larger spheres are too large compared to the small one, then it is impossible for three of them to fit, whereas if the larger spheres are too small compared to the small one, then it is highly likely that more than three of them will fit. It has been proven mathematically and shown experimentally that there is an optimal size ratio between the diameters of the two sphere types which results in the assembly of exactly three large spheres on the surface of one small sphere [[3]].<br />
<br />
The combination of geometry with capillary forces is commonly used for the directed self-assembly of thin films of crystals of particles on a flat surface. In such a process, a clean glass slide is immersed in a dense colloidal suspension and slowly pulled out. As the glass surface moves, a thin layer of the suspension full of particles protrudes from the liquid surface and carries the particles to the glass surface. If the surface moves slowly enough and the suspension is dense enough, this can result in the self-deposition of the spheres on a hexagonal lattice with the (1,1,1) plane parallel to the glass surface [1].<br />
<br />
=== Surface Functionalisation ===<br />
<br />
The interaction between two particles depends strongly on the properties of their surfaces. This can be used to engineer attractive or repulsive interactions. For example, in a colloidal system particles can be coated with surface charges. One of the simplest examples is the creation of colloidal crystals in a suspension where all particles have the same charge (see [[Photonic Properties of Strongly Correlated Colloidal Liquids]]). In this case the particles try to maintain the furthest distance from each other which is allowed by the volume of the surrounding medium and so they hover in the medium at periodically spaced locations. Even though electrostatics has only provided us with two types of electric charges, this technique can be surprisingly versatile with the addition of salt in the system, which allows control of the intensity of the electrostatic interactions since the concentration of free charges affects the [[Debye length]]. <br />
<br />
Such a system is currently being explored for the self-assembly of particle clusters with a specific number of constituents. Small negatively charged spheres are mixed with larger positively charged spheres; the large spheres are attracted to the small spheres and park on their surface, and due to the existence of free ions in the suspension large spheres attracted to the same small sphere are not repelled from each other, allowing for the attachment of more than one positively charged sphere on the surface of a negatively charged sphere [3].<br />
<br />
Another way to taylor interparticle interactions which offers greater variety relies on the use of DNA strands. By coating some spheres with half of a DNA strand and some with the complementary half, and assuming that the temperature of the system is higher than the binding energy between the DNA strands so that spheres can move Brownianly and find each other, it is possible to create a suspension where different pairs of particles are attracted to each other but indifferent to other particles which are coated with the half of another, non-complimentary DNA strand. This method is also being actively studied for the self-assembly of complex particle clusters [2].<br />
<br />
== Keyword in references: ==<br />
<br />
[[Design principles for self assembly with short ranged interactions]]<br />
<br />
== References ==<br />
<br />
[1] Jiang, Bertone, Hwang, and Colvin, Chem. Mater. 1999, 11, 2132-2140<br />
<br />
[2] Leunissen et al, Soft Matter, 2009, 5, 2422-2430<br />
<br />
[3] Schade et al, 2011 (in preparation)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Confocal_microscopy&diff=23544Confocal microscopy2011-12-10T02:40:04Z<p>Smagkir: /* Advantages */</p>
<hr />
<div>== Definition ==<br />
<br />
Confocal microscopy is an optical technique that allows imaging with high resolution. It is a variation on [[optical microscopy]]. The underlying principle behind confocal microscopy relies on spatial filtering of the light coming from the sample, so that only photons from a specific point and narrow depth of field reach the observer at any given moment. This principle is schematically illustrated below:<br />
<br />
[[Image: confocal_basic_principle.jpg]]<br />
<br />
This picture shows a very basic microscope comprised of two lenses. On the right side is the illumination source, in the middle is the sample and on the left is the observer. To the immediate right of the observer is a pinhole. Light from points in the sample which lie on the focal plane of the microscope makes it through the pinhole to the observer, whereas light from points out of the focal plane is strongly attenuated by the pinhole and reaches the detector at a decreased intensity. The advantage of this setup is that it allows for clean imaging of only one point in the sample as the detector only collects light from a small volume around that point, confined by the depth of field, while the sample can be much thicker. In order to obtain a full two-dimensional image the sample needs to be scanned. This is usually done by translating the illumination beam with electrically orientable mirrors. Three-dimensional images of a structure can be obtained by additionally translating the focal plane (or the sample) along the optical axis. The name of this type of microscopy is a reminder of the fact that at any given moment the pinhole is in a plane of the same family of ''con''jugate planes as the focal point of the objective. <br />
<br />
Modern confocal microscopes can be operated in several different modes. As far as illumination options, the user can choose use either an incandescent lamp (and monitor transmission through the sample) or a laser - in which case one can additionally choose whether to monitor scattered laser light or emitted fluorescent light, if the sample has been stained with a fluorescent dye. This imaging method can further enhance the clarity of the images, since fluorescently emitted light has a different wavelength than the incident pumping light. Confocal microscopes are often equipped with color filters and dichroic mirrors (which reflect a specific bandwidth of light and transmit other wavelengths) which ensure that, when obtained in this way, the images have minimal background noise, since the illumination light is at a different wavelength and thus blocked from the detector.<br />
<br />
== Advantages ==<br />
<br />
A confocal microscope is a very powerful tool for the study of complex structures. It offers images of high quality and allows the user to observe different slices within the sample, which can later be superimposed to form a three-dimensional image. Besides the bulk of observations which can be made by simply looking at a three-dimensional image, this information can be the basis of further studies of the imaged structure. For instance, one can calculate the fourier transform of the captured images, in two or three dimensions, and obtain information analogous to the information obtainable from more cumbersome techniques such as [[small-angle neutron scattering]] (which may still be necessary, depending on exactly what information one is interested in).<br />
<br />
== Limitations ==<br />
<br />
Because of its key feature, the pinhole before the observer, the confocal microscope has a low light collection efficiency; of all photons emanating from the point being <br />
imaged only few make it to the detector. This usually necessitates the use of lasers as illumination sources (and was a technical limitation back when the confocal microscope was first introduced around 1955, when lasers were still an academic curiosity). While lasers are fairly commonplace nowadays, the high intensity required to illuminate the sample can sometimes damage it, either chemically by causing alterations to it, or optically by bleaching any fluorescent dyes that may be used to enhance imaging. <br />
<br />
Moreover, since it only images one point at a time, a confocal microscope is not suitable for capturing dynamic processes that happen in bulk and at timescales faster than the scanning rate. For such studies, a different imaging technique, [[digital holographic microscopy]], is more suitable. <br />
<br />
Finally, since this is an optical system that relies on light scattering for the identification of features in the sample, confocal microscopy has a resolution ultimately bound by the diffraction limit. <br />
<br />
== Keyword in references: ==<br />
<br />
[[A Blind Spot in Confocal Reflection Microscopy: The Dependence of Fiber Brightness on Fiber Orientation in Imaging Biopolymer Networks]]<br />
<br />
[[The Deformation of an Elastic Substrate by a Three-Phase Contact Line E. R. Jerison]]<br />
<br />
== References ==<br />
<br />
[1] ''Confocal Optical Microscopy, Robert H Webb, Rep. Prog. Phys. 59 (1996), 427–471''<br />
<br />
[2] ''How does a confocal microscope work?'' available at www.physics.emory.edu<br />
<br />
[3] http://www.microscopyu.com/articles/confocal/</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Confocal_microscopy&diff=23543Confocal microscopy2011-12-10T02:38:44Z<p>Smagkir: /* Advantages */</p>
<hr />
<div>== Definition ==<br />
<br />
Confocal microscopy is an optical technique that allows imaging with high resolution. It is a variation on [[optical microscopy]]. The underlying principle behind confocal microscopy relies on spatial filtering of the light coming from the sample, so that only photons from a specific point and narrow depth of field reach the observer at any given moment. This principle is schematically illustrated below:<br />
<br />
[[Image: confocal_basic_principle.jpg]]<br />
<br />
This picture shows a very basic microscope comprised of two lenses. On the right side is the illumination source, in the middle is the sample and on the left is the observer. To the immediate right of the observer is a pinhole. Light from points in the sample which lie on the focal plane of the microscope makes it through the pinhole to the observer, whereas light from points out of the focal plane is strongly attenuated by the pinhole and reaches the detector at a decreased intensity. The advantage of this setup is that it allows for clean imaging of only one point in the sample as the detector only collects light from a small volume around that point, confined by the depth of field, while the sample can be much thicker. In order to obtain a full two-dimensional image the sample needs to be scanned. This is usually done by translating the illumination beam with electrically orientable mirrors. Three-dimensional images of a structure can be obtained by additionally translating the focal plane (or the sample) along the optical axis. The name of this type of microscopy is a reminder of the fact that at any given moment the pinhole is in a plane of the same family of ''con''jugate planes as the focal point of the objective. <br />
<br />
Modern confocal microscopes can be operated in several different modes. As far as illumination options, the user can choose use either an incandescent lamp (and monitor transmission through the sample) or a laser - in which case one can additionally choose whether to monitor scattered laser light or emitted fluorescent light, if the sample has been stained with a fluorescent dye. This imaging method can further enhance the clarity of the images, since fluorescently emitted light has a different wavelength than the incident pumping light. Confocal microscopes are often equipped with color filters and dichroic mirrors (which reflect a specific bandwidth of light and transmit other wavelengths) which ensure that, when obtained in this way, the images have minimal background noise, since the illumination light is at a different wavelength and thus blocked from the detector.<br />
<br />
== Advantages ==<br />
<br />
A confocal microscope is a very powerful tool for the study of complex structures. It offers images of high quality and allows the user to observe different slices within the sample, which can later be superimposed to form a three-dimensional image. Besides the bulk of observations which can be made by simply looking at a three-dimensional image, this information can be the basis of further studies of the imaged structure. For instance, one can calculate the fourier transform of the captured images, in two or three dimensions, and obtain information analogous to the information obtainable from more cumbersome techniques such as small-angle neutron scattering ([[SANS]] - which may still be necessary, depending on exactly what information one is interested in).<br />
<br />
== Limitations ==<br />
<br />
Because of its key feature, the pinhole before the observer, the confocal microscope has a low light collection efficiency; of all photons emanating from the point being <br />
imaged only few make it to the detector. This usually necessitates the use of lasers as illumination sources (and was a technical limitation back when the confocal microscope was first introduced around 1955, when lasers were still an academic curiosity). While lasers are fairly commonplace nowadays, the high intensity required to illuminate the sample can sometimes damage it, either chemically by causing alterations to it, or optically by bleaching any fluorescent dyes that may be used to enhance imaging. <br />
<br />
Moreover, since it only images one point at a time, a confocal microscope is not suitable for capturing dynamic processes that happen in bulk and at timescales faster than the scanning rate. For such studies, a different imaging technique, [[digital holographic microscopy]], is more suitable. <br />
<br />
Finally, since this is an optical system that relies on light scattering for the identification of features in the sample, confocal microscopy has a resolution ultimately bound by the diffraction limit. <br />
<br />
== Keyword in references: ==<br />
<br />
[[A Blind Spot in Confocal Reflection Microscopy: The Dependence of Fiber Brightness on Fiber Orientation in Imaging Biopolymer Networks]]<br />
<br />
[[The Deformation of an Elastic Substrate by a Three-Phase Contact Line E. R. Jerison]]<br />
<br />
== References ==<br />
<br />
[1] ''Confocal Optical Microscopy, Robert H Webb, Rep. Prog. Phys. 59 (1996), 427–471''<br />
<br />
[2] ''How does a confocal microscope work?'' available at www.physics.emory.edu<br />
<br />
[3] http://www.microscopyu.com/articles/confocal/</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Confocal_microscopy&diff=23542Confocal microscopy2011-12-10T02:38:10Z<p>Smagkir: /* Advantages */</p>
<hr />
<div>== Definition ==<br />
<br />
Confocal microscopy is an optical technique that allows imaging with high resolution. It is a variation on [[optical microscopy]]. The underlying principle behind confocal microscopy relies on spatial filtering of the light coming from the sample, so that only photons from a specific point and narrow depth of field reach the observer at any given moment. This principle is schematically illustrated below:<br />
<br />
[[Image: confocal_basic_principle.jpg]]<br />
<br />
This picture shows a very basic microscope comprised of two lenses. On the right side is the illumination source, in the middle is the sample and on the left is the observer. To the immediate right of the observer is a pinhole. Light from points in the sample which lie on the focal plane of the microscope makes it through the pinhole to the observer, whereas light from points out of the focal plane is strongly attenuated by the pinhole and reaches the detector at a decreased intensity. The advantage of this setup is that it allows for clean imaging of only one point in the sample as the detector only collects light from a small volume around that point, confined by the depth of field, while the sample can be much thicker. In order to obtain a full two-dimensional image the sample needs to be scanned. This is usually done by translating the illumination beam with electrically orientable mirrors. Three-dimensional images of a structure can be obtained by additionally translating the focal plane (or the sample) along the optical axis. The name of this type of microscopy is a reminder of the fact that at any given moment the pinhole is in a plane of the same family of ''con''jugate planes as the focal point of the objective. <br />
<br />
Modern confocal microscopes can be operated in several different modes. As far as illumination options, the user can choose use either an incandescent lamp (and monitor transmission through the sample) or a laser - in which case one can additionally choose whether to monitor scattered laser light or emitted fluorescent light, if the sample has been stained with a fluorescent dye. This imaging method can further enhance the clarity of the images, since fluorescently emitted light has a different wavelength than the incident pumping light. Confocal microscopes are often equipped with color filters and dichroic mirrors (which reflect a specific bandwidth of light and transmit other wavelengths) which ensure that, when obtained in this way, the images have minimal background noise, since the illumination light is at a different wavelength and thus blocked from the detector.<br />
<br />
== Advantages ==<br />
<br />
A confocal microscope is a very powerful tool for the study of complex structures. It offers images of high quality and allows the user to observe different slices within the sample, which can later be superimposed to form a three-dimensional image. Besides the bulk of information which can be obtained by simply looking at a three-dimensional image, this information can be the basis of further studies of the imaged structure. For instance, one can calculate the fourier transform of the captured images, in two or three dimensions, and obtain information analogous to the information obtainable from more cumbersome techniques such as small-angle neutron scattering ([[SANS]] - which may still be necessary, depending on exactly what information one is interested in).<br />
<br />
== Limitations ==<br />
<br />
Because of its key feature, the pinhole before the observer, the confocal microscope has a low light collection efficiency; of all photons emanating from the point being <br />
imaged only few make it to the detector. This usually necessitates the use of lasers as illumination sources (and was a technical limitation back when the confocal microscope was first introduced around 1955, when lasers were still an academic curiosity). While lasers are fairly commonplace nowadays, the high intensity required to illuminate the sample can sometimes damage it, either chemically by causing alterations to it, or optically by bleaching any fluorescent dyes that may be used to enhance imaging. <br />
<br />
Moreover, since it only images one point at a time, a confocal microscope is not suitable for capturing dynamic processes that happen in bulk and at timescales faster than the scanning rate. For such studies, a different imaging technique, [[digital holographic microscopy]], is more suitable. <br />
<br />
Finally, since this is an optical system that relies on light scattering for the identification of features in the sample, confocal microscopy has a resolution ultimately bound by the diffraction limit. <br />
<br />
== Keyword in references: ==<br />
<br />
[[A Blind Spot in Confocal Reflection Microscopy: The Dependence of Fiber Brightness on Fiber Orientation in Imaging Biopolymer Networks]]<br />
<br />
[[The Deformation of an Elastic Substrate by a Three-Phase Contact Line E. R. Jerison]]<br />
<br />
== References ==<br />
<br />
[1] ''Confocal Optical Microscopy, Robert H Webb, Rep. Prog. Phys. 59 (1996), 427–471''<br />
<br />
[2] ''How does a confocal microscope work?'' available at www.physics.emory.edu<br />
<br />
[3] http://www.microscopyu.com/articles/confocal/</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Confocal_microscopy&diff=23541Confocal microscopy2011-12-10T02:37:34Z<p>Smagkir: /* Definition */</p>
<hr />
<div>== Definition ==<br />
<br />
Confocal microscopy is an optical technique that allows imaging with high resolution. It is a variation on [[optical microscopy]]. The underlying principle behind confocal microscopy relies on spatial filtering of the light coming from the sample, so that only photons from a specific point and narrow depth of field reach the observer at any given moment. This principle is schematically illustrated below:<br />
<br />
[[Image: confocal_basic_principle.jpg]]<br />
<br />
This picture shows a very basic microscope comprised of two lenses. On the right side is the illumination source, in the middle is the sample and on the left is the observer. To the immediate right of the observer is a pinhole. Light from points in the sample which lie on the focal plane of the microscope makes it through the pinhole to the observer, whereas light from points out of the focal plane is strongly attenuated by the pinhole and reaches the detector at a decreased intensity. The advantage of this setup is that it allows for clean imaging of only one point in the sample as the detector only collects light from a small volume around that point, confined by the depth of field, while the sample can be much thicker. In order to obtain a full two-dimensional image the sample needs to be scanned. This is usually done by translating the illumination beam with electrically orientable mirrors. Three-dimensional images of a structure can be obtained by additionally translating the focal plane (or the sample) along the optical axis. The name of this type of microscopy is a reminder of the fact that at any given moment the pinhole is in a plane of the same family of ''con''jugate planes as the focal point of the objective. <br />
<br />
Modern confocal microscopes can be operated in several different modes. As far as illumination options, the user can choose use either an incandescent lamp (and monitor transmission through the sample) or a laser - in which case one can additionally choose whether to monitor scattered laser light or emitted fluorescent light, if the sample has been stained with a fluorescent dye. This imaging method can further enhance the clarity of the images, since fluorescently emitted light has a different wavelength than the incident pumping light. Confocal microscopes are often equipped with color filters and dichroic mirrors (which reflect a specific bandwidth of light and transmit other wavelengths) which ensure that, when obtained in this way, the images have minimal background noise, since the illumination light is at a different wavelength and thus blocked from the detector.<br />
<br />
== Advantages ==<br />
<br />
A confocal microscope is a very powerful tool for the study of complex structures. It offers images of high quality and allows the user to capture images from different slices within the sample, which can later be superimposed to form a three-dimensional image. Besides the bulk of information which can be obtained by simply looking at a three-dimensional image, this information can be the basis of further studies of the imaged structure. For instance, one can calculate the fourier transform of the captured images, in two or three dimensions, and obtain information analogous to the information obtainable from more cumbersome techniques such as small-angle neutron scattering ([[SANS]] - which may still be necessary, depending on exactly what information one is interested in).<br />
<br />
== Limitations ==<br />
<br />
Because of its key feature, the pinhole before the observer, the confocal microscope has a low light collection efficiency; of all photons emanating from the point being <br />
imaged only few make it to the detector. This usually necessitates the use of lasers as illumination sources (and was a technical limitation back when the confocal microscope was first introduced around 1955, when lasers were still an academic curiosity). While lasers are fairly commonplace nowadays, the high intensity required to illuminate the sample can sometimes damage it, either chemically by causing alterations to it, or optically by bleaching any fluorescent dyes that may be used to enhance imaging. <br />
<br />
Moreover, since it only images one point at a time, a confocal microscope is not suitable for capturing dynamic processes that happen in bulk and at timescales faster than the scanning rate. For such studies, a different imaging technique, [[digital holographic microscopy]], is more suitable. <br />
<br />
Finally, since this is an optical system that relies on light scattering for the identification of features in the sample, confocal microscopy has a resolution ultimately bound by the diffraction limit. <br />
<br />
== Keyword in references: ==<br />
<br />
[[A Blind Spot in Confocal Reflection Microscopy: The Dependence of Fiber Brightness on Fiber Orientation in Imaging Biopolymer Networks]]<br />
<br />
[[The Deformation of an Elastic Substrate by a Three-Phase Contact Line E. R. Jerison]]<br />
<br />
== References ==<br />
<br />
[1] ''Confocal Optical Microscopy, Robert H Webb, Rep. Prog. Phys. 59 (1996), 427–471''<br />
<br />
[2] ''How does a confocal microscope work?'' available at www.physics.emory.edu<br />
<br />
[3] http://www.microscopyu.com/articles/confocal/</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Confocal_microscopy&diff=23540Confocal microscopy2011-12-10T02:36:55Z<p>Smagkir: /* Definition */</p>
<hr />
<div>== Definition ==<br />
<br />
Confocal microscopy is an optical technique that allows imaging with high resolution. It is a variation on [[optical microscopy]]. The underlying principle behind confocal microscopy relies on spatial filtering of the light coming from the sample, so that only photons from a specific point and narrow depth of field reach the observer at any given moment. This principle is schematically illustrated below:<br />
<br />
[[Image: confocal_basic_principle.jpg]]<br />
<br />
This picture shows a very basic microscope comprised of two lenses. On the right side is the illumination source, in the middle is the sample and on the left is the observer. To the immediate right of the observer is a pinhole. Light from points in the sample which lie on the focal plane of the microscope makes it through the pinhole to the observer, whereas light from points out of the focal plane is strongly attenuated by the pinhole and reaches the detector at a decreased intensity. The advantage of this setup is that it allows for clean imaging of only one point in the sample as the detector only collects light from a small volume around that point, confined by the depth of field, while the sample can be much thicker. In order to obtain a full two-dimensional image the sample needs to be scanned. This is usually done by translating the illumination beam with electrically orientable mirrors. Three-dimensional images of a structure can be obtained by additionally translating the focal plane (or the sample) along the optical axis. The name of this type of microscopy is a reminder of the fact that at any given moment the pinhole is in a plane of the same family of ''con''jugate planes as the focal point of the objective. <br />
<br />
Modern confocal microscopes can be operated in several different modes. As far as illumination options, the user can choose use either an incandescent lamp (and monitor transmission through the sample) or a laser - in which case one can additionally choose whether to monitor scattered laser light or emitted fluorescent light, if the sample has been stained with a fluorescent dye. This imaging method can further enhance the clarity of the images, since fluorescently emitted light has a different wavelength than the incident pumping light. Confocal microscopes are often equipped with color filters and dichroic mirrors (which reflect a specific bandwidth of light and transmit other wavelengths) which ensure that, when obtained in this way, the images have minimal background noise, since most of the illumination light has been blocked.<br />
<br />
== Advantages ==<br />
<br />
A confocal microscope is a very powerful tool for the study of complex structures. It offers images of high quality and allows the user to capture images from different slices within the sample, which can later be superimposed to form a three-dimensional image. Besides the bulk of information which can be obtained by simply looking at a three-dimensional image, this information can be the basis of further studies of the imaged structure. For instance, one can calculate the fourier transform of the captured images, in two or three dimensions, and obtain information analogous to the information obtainable from more cumbersome techniques such as small-angle neutron scattering ([[SANS]] - which may still be necessary, depending on exactly what information one is interested in).<br />
<br />
== Limitations ==<br />
<br />
Because of its key feature, the pinhole before the observer, the confocal microscope has a low light collection efficiency; of all photons emanating from the point being <br />
imaged only few make it to the detector. This usually necessitates the use of lasers as illumination sources (and was a technical limitation back when the confocal microscope was first introduced around 1955, when lasers were still an academic curiosity). While lasers are fairly commonplace nowadays, the high intensity required to illuminate the sample can sometimes damage it, either chemically by causing alterations to it, or optically by bleaching any fluorescent dyes that may be used to enhance imaging. <br />
<br />
Moreover, since it only images one point at a time, a confocal microscope is not suitable for capturing dynamic processes that happen in bulk and at timescales faster than the scanning rate. For such studies, a different imaging technique, [[digital holographic microscopy]], is more suitable. <br />
<br />
Finally, since this is an optical system that relies on light scattering for the identification of features in the sample, confocal microscopy has a resolution ultimately bound by the diffraction limit. <br />
<br />
== Keyword in references: ==<br />
<br />
[[A Blind Spot in Confocal Reflection Microscopy: The Dependence of Fiber Brightness on Fiber Orientation in Imaging Biopolymer Networks]]<br />
<br />
[[The Deformation of an Elastic Substrate by a Three-Phase Contact Line E. R. Jerison]]<br />
<br />
== References ==<br />
<br />
[1] ''Confocal Optical Microscopy, Robert H Webb, Rep. Prog. Phys. 59 (1996), 427–471''<br />
<br />
[2] ''How does a confocal microscope work?'' available at www.physics.emory.edu<br />
<br />
[3] http://www.microscopyu.com/articles/confocal/</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Confocal_microscopy&diff=23539Confocal microscopy2011-12-10T02:36:31Z<p>Smagkir: /* Definition */</p>
<hr />
<div>== Definition ==<br />
<br />
Confocal microscopy is an optical technique that allows imaging with high resolution. It is a variation on [[optical microscopy]]. The underlying principle behind confocal microscopy relies on spatial filtering of the light coming from the sample, so that only photons from a specific point and narrow depth of field reach the observer at any given moment. This principle is schematically illustrated below:<br />
<br />
[[Image: confocal_basic_principle.jpg]]<br />
<br />
This picture shows a very basic microscope comprised of two lenses. On the right side is the illumination source, in the middle is the sample and on the left is the observer. To the immediate right of the observer is a pinhole. Light from points in the sample which lie on the focal plane of the microscope makes it through the pinhole to the observer, whereas light from points out of the focal plane is strongly attenuated by the pinhole and reaches the detector at a decreased intensity. The advantage of this setup is that it allows for clean imaging of only one point in the sample as the detector only collects light from a small volume around that point, confined by the depth of field, while the sample can be much thicker. In order to obtain a full two-dimensional image the sample needs to be scanned. This is usually done by translating the illumination beam with electrically orientable mirrors. Three-dimensional images of a structure can be obtained by additionally translating the focal plane (or the sample) along the optical axis. The name of this type of microscopy is a reminder of the fact that at any given moment the pinhole is in a plane of the same family of ''con''jugate planes as the focal point of the objective. <br />
<br />
Modern confocal microscopes can be operated in several different modes. As far as illumination options, the user can choose use either an incandescent lamp (and monitor transmission through the sample) or a laser - in which case one can additionally choose whether to monitor scattered laser light or emitted fluorescent light, if the sample has been stained with a fluorescent dye. This imaging method can further enhance the clarity of the images, since fluorescently emitted light has a different wavelength than the incident pumping light. Confocal microscopes are often equipped with dichroic mirrors (which reflect a specific bandwidth of light and transmit other wavelengths) and color filters which ensure that, when obtained in this way, the images have minimal background noise, since most of the illumination light has been blocked.<br />
<br />
== Advantages ==<br />
<br />
A confocal microscope is a very powerful tool for the study of complex structures. It offers images of high quality and allows the user to capture images from different slices within the sample, which can later be superimposed to form a three-dimensional image. Besides the bulk of information which can be obtained by simply looking at a three-dimensional image, this information can be the basis of further studies of the imaged structure. For instance, one can calculate the fourier transform of the captured images, in two or three dimensions, and obtain information analogous to the information obtainable from more cumbersome techniques such as small-angle neutron scattering ([[SANS]] - which may still be necessary, depending on exactly what information one is interested in).<br />
<br />
== Limitations ==<br />
<br />
Because of its key feature, the pinhole before the observer, the confocal microscope has a low light collection efficiency; of all photons emanating from the point being <br />
imaged only few make it to the detector. This usually necessitates the use of lasers as illumination sources (and was a technical limitation back when the confocal microscope was first introduced around 1955, when lasers were still an academic curiosity). While lasers are fairly commonplace nowadays, the high intensity required to illuminate the sample can sometimes damage it, either chemically by causing alterations to it, or optically by bleaching any fluorescent dyes that may be used to enhance imaging. <br />
<br />
Moreover, since it only images one point at a time, a confocal microscope is not suitable for capturing dynamic processes that happen in bulk and at timescales faster than the scanning rate. For such studies, a different imaging technique, [[digital holographic microscopy]], is more suitable. <br />
<br />
Finally, since this is an optical system that relies on light scattering for the identification of features in the sample, confocal microscopy has a resolution ultimately bound by the diffraction limit. <br />
<br />
== Keyword in references: ==<br />
<br />
[[A Blind Spot in Confocal Reflection Microscopy: The Dependence of Fiber Brightness on Fiber Orientation in Imaging Biopolymer Networks]]<br />
<br />
[[The Deformation of an Elastic Substrate by a Three-Phase Contact Line E. R. Jerison]]<br />
<br />
== References ==<br />
<br />
[1] ''Confocal Optical Microscopy, Robert H Webb, Rep. Prog. Phys. 59 (1996), 427–471''<br />
<br />
[2] ''How does a confocal microscope work?'' available at www.physics.emory.edu<br />
<br />
[3] http://www.microscopyu.com/articles/confocal/</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Confocal_microscopy&diff=23538Confocal microscopy2011-12-10T02:35:26Z<p>Smagkir: /* Definition */</p>
<hr />
<div>== Definition ==<br />
<br />
Confocal microscopy is an optical technique that allows imaging with high resolution. It is a variation on [[optical microscopy]]. The underlying principle behind confocal microscopy relies on spatial filtering of the light coming from the sample, so that only photons from a specific point and narrow depth of field reach the observer at any given moment. This principle is schematically illustrated below:<br />
<br />
[[Image: confocal_basic_principle.jpg]]<br />
<br />
This picture shows a very basic microscope comprised of two lenses. On the right side is the illumination source, in the middle is the sample and on the left is the observer. To the immediate right of the observer is a pinhole. Light from points in the sample which lie on the focal plane of the microscope makes it through the pinhole to the observer, whereas light from points out of the focal plane is strongly attenuated by the pinhole and reaches the detector at a decreased intensity. The advantage of this setup is that it allows for clean imaging of only one point in the sample as the detector only collects light from a small volume around that point, confined by the depth of field, while the sample can be much thicker. In order to obtain a full two-dimensional image the sample needs to be scanned. This is usually done by translating the illumination beam with electrically orientable mirrors. Three-dimensional images of a structure can be obtained by additionally translating the focal plane (or the sample) along the optical axis. The name of this type of microscopy is a reminder of the fact that at any given moment the pinhole is in a plane of the same family of ''con''jugate planes as the focal point of the objective. <br />
<br />
Modern confocal microscopes can be operated in several different modes. As far as illumination options, the user can choose use either an incandescent lamp (and monitor transmission through the sample) or a laser - in which case one can additionally choose whether to monitor scattered laser light or emitted fluorescent light, if the sample has been stained with a fluorescent dye. This imaging method can further enhance the clarity of the images, since fluorescently emitted light has a different wavelength than the incident pumping light. Confocal microscopes are equipped with dichroic mirrors (which reflect a specific bandwidth of light and transmit other wavelengths) and color filters which ensure that, when obtained in this way, the images have minimal background noise, since most of the illumination light has been blocked.<br />
<br />
== Advantages ==<br />
<br />
A confocal microscope is a very powerful tool for the study of complex structures. It offers images of high quality and allows the user to capture images from different slices within the sample, which can later be superimposed to form a three-dimensional image. Besides the bulk of information which can be obtained by simply looking at a three-dimensional image, this information can be the basis of further studies of the imaged structure. For instance, one can calculate the fourier transform of the captured images, in two or three dimensions, and obtain information analogous to the information obtainable from more cumbersome techniques such as small-angle neutron scattering ([[SANS]] - which may still be necessary, depending on exactly what information one is interested in).<br />
<br />
== Limitations ==<br />
<br />
Because of its key feature, the pinhole before the observer, the confocal microscope has a low light collection efficiency; of all photons emanating from the point being <br />
imaged only few make it to the detector. This usually necessitates the use of lasers as illumination sources (and was a technical limitation back when the confocal microscope was first introduced around 1955, when lasers were still an academic curiosity). While lasers are fairly commonplace nowadays, the high intensity required to illuminate the sample can sometimes damage it, either chemically by causing alterations to it, or optically by bleaching any fluorescent dyes that may be used to enhance imaging. <br />
<br />
Moreover, since it only images one point at a time, a confocal microscope is not suitable for capturing dynamic processes that happen in bulk and at timescales faster than the scanning rate. For such studies, a different imaging technique, [[digital holographic microscopy]], is more suitable. <br />
<br />
Finally, since this is an optical system that relies on light scattering for the identification of features in the sample, confocal microscopy has a resolution ultimately bound by the diffraction limit. <br />
<br />
== Keyword in references: ==<br />
<br />
[[A Blind Spot in Confocal Reflection Microscopy: The Dependence of Fiber Brightness on Fiber Orientation in Imaging Biopolymer Networks]]<br />
<br />
[[The Deformation of an Elastic Substrate by a Three-Phase Contact Line E. R. Jerison]]<br />
<br />
== References ==<br />
<br />
[1] ''Confocal Optical Microscopy, Robert H Webb, Rep. Prog. Phys. 59 (1996), 427–471''<br />
<br />
[2] ''How does a confocal microscope work?'' available at www.physics.emory.edu<br />
<br />
[3] http://www.microscopyu.com/articles/confocal/</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Confocal_microscopy&diff=23537Confocal microscopy2011-12-10T02:33:54Z<p>Smagkir: </p>
<hr />
<div>== Definition ==<br />
<br />
Confocal microscopy is an optical technique that allows imaging with high resolution. It is a variation on [[optical microscopy]]. The underlying principle behind confocal microscopy relies on spatial filtering of the light coming from the sample, so that only photons from a specific point and narrow depth of field reach the observer at any given moment. This principle is schematically illustrated below:<br />
<br />
[[Image: confocal_basic_principle.jpg]]<br />
<br />
This picture shows a very basic microscope comprised of two lenses. On the right side is the illumination source, in the middle is the sample and on the left is the observer. To the immediate right of the observer is a pinhole. Light from points in the sample which lie on the focal plane of the microscope makes it through the pinhole to the observer, whereas light from points out of the focal plane is strongly attenuated by the pinhole and reaches the detector at a decreased intensity. The advantage of this setup is that it allows for clean imaging of only one point in the sample as the detector only collects light from a small volume around that point confined by the depth of field while the sample can be much thicker than that. In order to obtain a full two-dimensional image, the sample needs to be scanned. This is usually done by translating the illumination beam with the use of electrically orientable mirrors. Three-dimensional images of a structure can be obtained by additionally translating the focal plane (or the sample) along the optical axis. The name of this type of microscopy is a reminder of the fact that at any given moment the pinhole is in a plane of the same family of ''con''jugate planes as the focal point of the objective. <br />
<br />
Modern confocal microscopes can be operated in several different modes. As far as illumination options, the user can choose use either an incandescent lamp (and monitor transmission through the sample) or a laser - in which case one can additionally choose whether to monitor scattered laser light or emitted fluorescent light, if the sample has been stained with a fluorescent dye. This imaging method can further enhance the clarity of the images, since fluorescently emitted light has a different wavelength than the incident pumping light. Confocal microscopes are equipped with dichroic mirrors (which reflect a specific bandwidth of light and transmit other wavelengths) and color filters which ensure that, when obtained in this way, the images have minimal background noise, since most of the illumination light has been blocked.<br />
<br />
== Advantages ==<br />
<br />
A confocal microscope is a very powerful tool for the study of complex structures. It offers images of high quality and allows the user to capture images from different slices within the sample, which can later be superimposed to form a three-dimensional image. Besides the bulk of information which can be obtained by simply looking at a three-dimensional image, this information can be the basis of further studies of the imaged structure. For instance, one can calculate the fourier transform of the captured images, in two or three dimensions, and obtain information analogous to the information obtainable from more cumbersome techniques such as small-angle neutron scattering ([[SANS]] - which may still be necessary, depending on exactly what information one is interested in).<br />
<br />
== Limitations ==<br />
<br />
Because of its key feature, the pinhole before the observer, the confocal microscope has a low light collection efficiency; of all photons emanating from the point being <br />
imaged only few make it to the detector. This usually necessitates the use of lasers as illumination sources (and was a technical limitation back when the confocal microscope was first introduced around 1955, when lasers were still an academic curiosity). While lasers are fairly commonplace nowadays, the high intensity required to illuminate the sample can sometimes damage it, either chemically by causing alterations to it, or optically by bleaching any fluorescent dyes that may be used to enhance imaging. <br />
<br />
Moreover, since it only images one point at a time, a confocal microscope is not suitable for capturing dynamic processes that happen in bulk and at timescales faster than the scanning rate. For such studies, a different imaging technique, [[digital holographic microscopy]], is more suitable. <br />
<br />
Finally, since this is an optical system that relies on light scattering for the identification of features in the sample, confocal microscopy has a resolution ultimately bound by the diffraction limit. <br />
<br />
== Keyword in references: ==<br />
<br />
[[A Blind Spot in Confocal Reflection Microscopy: The Dependence of Fiber Brightness on Fiber Orientation in Imaging Biopolymer Networks]]<br />
<br />
[[The Deformation of an Elastic Substrate by a Three-Phase Contact Line E. R. Jerison]]<br />
<br />
== References ==<br />
<br />
[1] ''Confocal Optical Microscopy, Robert H Webb, Rep. Prog. Phys. 59 (1996), 427–471''<br />
<br />
[2] ''How does a confocal microscope work?'' available at www.physics.emory.edu<br />
<br />
[3] http://www.microscopyu.com/articles/confocal/</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Contact_electrification&diff=23536Contact electrification2011-12-10T02:32:40Z<p>Smagkir: </p>
<hr />
<div>Contact electrification is a process during which two materials acquire electric charges after being brought in contact with one another. The contact can be either simple touch of their surfaces or friction between them - in the latter case this phenomenon is called ''[[tribocharging]]''. This phenomenon has been known for thousands of years; the ancient Greeks were familiar with the fact that they could make objects attracted to amber by rubbing them on it. It was also exploited by Alessandro Volta when he made in the 18th century his [[voltaic pile]], the precursor to our batteries. <br />
<br />
Nonetheless, this phenomenon is poorly understood. While it seems obvious that it arises from the exchange of charges between the materials in contact, little can be said about whether it is the positive or negative charges moving, let alone why an ion in an overall neutral material would have the tendency to leave its balanced environment, hop across an interface, and end up in an environment which is now electrostatically imbalanced. <br />
<br />
Empirical observation over the last couple of centuries has led to the more-or-less agreed upon triboelectric series, a list of materials in order of decreasing amount of positive charge acquired upon contact (see also lecture notes on [[Charged Interfaces]]). More recently scientists have developed tools for the accurate measurement of the acquired charge by contact, such as the rolling sphere tool (ref: 11 in [[Controlling the Kinetics of Contact Electrification with Patterned Surfaces]]) which measures the charge accumulated on a magnetically controllable sphere rolling on a surface. <br />
<br />
From such and similar observations, it has been more or less concluded that when it comes to contact electrification between two different metals, the charges accumulated on each side correlate with the work function of the electrons - i.e. the energy required to remove an electron from inside the metal to just outside of it. This, in turn, seems to indicate that in the case of metals it is the electrons that move [3]. <br />
<br />
The case of dielectrics seems to be a bit more complicated, as there is disagreement between experimenters regarding any correlation of the accumulated charges with quantities that one would think relevant, such as electronegativity or ionization energy. It is possible that such experiments are very sensitive to ambient conditions (ex. humidity, which would affect the conductivity of the air between the surfaces), surface roughness, and the exact manner by which two materials are brought in contact and then taken apart, making the results of these studies hard to systematize. One fact which seems to be generally accepted is a correlation between accumulated charge and acidity or basicity [3].<br />
<br />
The fundamental understanding of contact electrification and subsequent understanding of ways to control it has a lot of potential applications. Learning how to prevent contact electrification may provide solutions to associated problems, such as explosions due to sparking (for example in silos containing powders) or damage in electronic circuits. Learning how to engineer a system where known amounts of charge can be exchanged between particles may be a new tool for [[directed self-assembly]]. Moreover, this knowledge may lead to the development of novel materials that can maintain a permanent charge, by analogy to permanent magnets, which could be used in their stead as an alternative with longer-range interaction strength.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Controlling the Kinetics of Contact Electrification with Patterned Surfaces]]<br />
<br />
[[The Determination of the Location of Contact Electrification-Induced Discharge Events]]<br />
<br />
== References ==<br />
<br />
[1] ''Charged Interfaces'', Ian Morrison, lecture notes for Introduction to Soft Matter<br />
<br />
[2] ''Triboelectric Generation: Getting Charged'', available at www.esdjournal.com/techpapr/ryne/ryntribo.doc<br />
<br />
[3] ''Electrostatic Charging Due to Separation of Ions at Interfaces: Contact Electrification of Ionic Electrets'', Logan S. McCarty and George M. Whitesides, Angewandte<br />
Chemie, Angew. Chem. Int. Ed. 2008, 47, 2188 – 2207</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Contact_electrification&diff=23535Contact electrification2011-12-10T02:32:23Z<p>Smagkir: /* References */</p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
<br />
CONTACT ELECTRIFICATION<br />
<br />
reference: paper1: Electrostatic Charging Due to Separation of Ions at<br />
Interfaces: Contact Electrification of Ionic Electrets<br />
Logan S. McCarty and George M. Whitesides*<br />
Angewandte<br />
Chemie, Angew. Chem. Int. Ed. 2008, 47, 2188 – 2207<br />
<br />
curiosities:<br />
<br />
1. nonpolar materials develop strong charges<br />
2. polar materials become positive, nonpolar ones negatives<br />
<br />
====================================================================<br />
<br />
Contact electrification is a process during which two materials acquire electric charges after being brought in contact with one another. The contact can be either simple touch of their surfaces or friction between them - in the latter case this phenomenon is called ''[[tribocharging]]''. This phenomenon has been known for thousands of years; the ancient Greeks were familiar with the fact that they could make objects attracted to amber by rubbing them on it. It was also exploited by Alessandro Volta when he made in the 18th century his [[voltaic pile]], the precursor to our batteries. <br />
<br />
Nonetheless, this phenomenon is poorly understood. While it seems obvious that it arises from the exchange of charges between the materials in contact, little can be said about whether it is the positive or negative charges moving, let alone why an ion in an overall neutral material would have the tendency to leave its balanced environment, hop across an interface, and end up in an environment which is now electrostatically imbalanced. <br />
<br />
Empirical observation over the last couple of centuries has led to the more-or-less agreed upon triboelectric series, a list of materials in order of decreasing amount of positive charge acquired upon contact (see also lecture notes on [[Charged Interfaces]]). More recently scientists have developed tools for the accurate measurement of the acquired charge by contact, such as the rolling sphere tool (ref: 11 in [[Controlling the Kinetics of Contact Electrification with Patterned Surfaces]]) which measures the charge accumulated on a magnetically controllable sphere rolling on a surface. <br />
<br />
From such and similar observations, it has been more or less concluded that when it comes to contact electrification between two different metals, the charges accumulated on each side correlate with the work function of the electrons - i.e. the energy required to remove an electron from inside the metal to just outside of it. This, in turn, seems to indicate that in the case of metals it is the electrons that move [3]. <br />
<br />
The case of dielectrics seems to be a bit more complicated, as there is disagreement between experimenters regarding any correlation of the accumulated charges with quantities that one would think relevant, such as electronegativity or ionization energy. It is possible that such experiments are very sensitive to ambient conditions (ex. humidity, which would affect the conductivity of the air between the surfaces), surface roughness, and the exact manner by which two materials are brought in contact and then taken apart, making the results of these studies hard to systematize. One fact which seems to be generally accepted is a correlation between accumulated charge and acidity or basicity [3].<br />
<br />
The fundamental understanding of contact electrification and subsequent understanding of ways to control it has a lot of potential applications. Learning how to prevent contact electrification may provide solutions to associated problems, such as explosions due to sparking (for example in silos containing powders) or damage in electronic circuits. Learning how to engineer a system where known amounts of charge can be exchanged between particles may be a new tool for [[directed self-assembly]]. Moreover, this knowledge may lead to the development of novel materials that can maintain a permanent charge, by analogy to permanent magnets, which could be used in their stead as an alternative with longer-range interaction strength.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Controlling the Kinetics of Contact Electrification with Patterned Surfaces]]<br />
<br />
[[The Determination of the Location of Contact Electrification-Induced Discharge Events]]<br />
<br />
== References ==<br />
<br />
[1] ''Charged Interfaces'', Ian Morrison, lecture notes for Introduction to Soft Matter<br />
<br />
[2] ''Triboelectric Generation: Getting Charged'', available at www.esdjournal.com/techpapr/ryne/ryntribo.doc<br />
<br />
[3] ''Electrostatic Charging Due to Separation of Ions at Interfaces: Contact Electrification of Ionic Electrets'', Logan S. McCarty and George M. Whitesides, Angewandte<br />
Chemie, Angew. Chem. Int. Ed. 2008, 47, 2188 – 2207</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Contact_electrification&diff=23534Contact electrification2011-12-10T02:32:06Z<p>Smagkir: /* == */</p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
<br />
CONTACT ELECTRIFICATION<br />
<br />
reference: paper1: Electrostatic Charging Due to Separation of Ions at<br />
Interfaces: Contact Electrification of Ionic Electrets<br />
Logan S. McCarty and George M. Whitesides*<br />
Angewandte<br />
Chemie, Angew. Chem. Int. Ed. 2008, 47, 2188 – 2207<br />
<br />
curiosities:<br />
<br />
1. nonpolar materials develop strong charges<br />
2. polar materials become positive, nonpolar ones negatives<br />
<br />
====================================================================<br />
<br />
Contact electrification is a process during which two materials acquire electric charges after being brought in contact with one another. The contact can be either simple touch of their surfaces or friction between them - in the latter case this phenomenon is called ''[[tribocharging]]''. This phenomenon has been known for thousands of years; the ancient Greeks were familiar with the fact that they could make objects attracted to amber by rubbing them on it. It was also exploited by Alessandro Volta when he made in the 18th century his [[voltaic pile]], the precursor to our batteries. <br />
<br />
Nonetheless, this phenomenon is poorly understood. While it seems obvious that it arises from the exchange of charges between the materials in contact, little can be said about whether it is the positive or negative charges moving, let alone why an ion in an overall neutral material would have the tendency to leave its balanced environment, hop across an interface, and end up in an environment which is now electrostatically imbalanced. <br />
<br />
Empirical observation over the last couple of centuries has led to the more-or-less agreed upon triboelectric series, a list of materials in order of decreasing amount of positive charge acquired upon contact (see also lecture notes on [[Charged Interfaces]]). More recently scientists have developed tools for the accurate measurement of the acquired charge by contact, such as the rolling sphere tool (ref: 11 in [[Controlling the Kinetics of Contact Electrification with Patterned Surfaces]]) which measures the charge accumulated on a magnetically controllable sphere rolling on a surface. <br />
<br />
From such and similar observations, it has been more or less concluded that when it comes to contact electrification between two different metals, the charges accumulated on each side correlate with the work function of the electrons - i.e. the energy required to remove an electron from inside the metal to just outside of it. This, in turn, seems to indicate that in the case of metals it is the electrons that move [3]. <br />
<br />
The case of dielectrics seems to be a bit more complicated, as there is disagreement between experimenters regarding any correlation of the accumulated charges with quantities that one would think relevant, such as electronegativity or ionization energy. It is possible that such experiments are very sensitive to ambient conditions (ex. humidity, which would affect the conductivity of the air between the surfaces), surface roughness, and the exact manner by which two materials are brought in contact and then taken apart, making the results of these studies hard to systematize. One fact which seems to be generally accepted is a correlation between accumulated charge and acidity or basicity [3].<br />
<br />
The fundamental understanding of contact electrification and subsequent understanding of ways to control it has a lot of potential applications. Learning how to prevent contact electrification may provide solutions to associated problems, such as explosions due to sparking (for example in silos containing powders) or damage in electronic circuits. Learning how to engineer a system where known amounts of charge can be exchanged between particles may be a new tool for [[directed self-assembly]]. Moreover, this knowledge may lead to the development of novel materials that can maintain a permanent charge, by analogy to permanent magnets, which could be used in their stead as an alternative with longer-range interaction strength.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Controlling the Kinetics of Contact Electrification with Patterned Surfaces]]<br />
<br />
[[The Determination of the Location of Contact Electrification-Induced Discharge Events]]<br />
<br />
== References ==<br />
<br />
[1] ''Charged Interfaces'', Ian Morrison, lecture notes for Introduction to Soft Matter<br />
[2] ''Triboelectric Generation: Getting Charged'', available at www.esdjournal.com/techpapr/ryne/ryntribo.doc<br />
[3] ''Electrostatic Charging Due to Separation of Ions at Interfaces: Contact Electrification of Ionic Electrets'', Logan S. McCarty and George M. Whitesides, Angewandte<br />
Chemie, Angew. Chem. Int. Ed. 2008, 47, 2188 – 2207</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Contact_electrification&diff=23533Contact electrification2011-12-10T02:30:16Z<p>Smagkir: /* == */</p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
<br />
CONTACT ELECTRIFICATION<br />
<br />
reference: paper1: Electrostatic Charging Due to Separation of Ions at<br />
Interfaces: Contact Electrification of Ionic Electrets<br />
Logan S. McCarty and George M. Whitesides*<br />
Angewandte<br />
Chemie, Angew. Chem. Int. Ed. 2008, 47, 2188 – 2207<br />
<br />
curiosities:<br />
<br />
1. nonpolar materials develop strong charges<br />
2. polar materials become positive, nonpolar ones negatives<br />
<br />
====================================================================<br />
<br />
Contact electrification is a process during which two materials acquire electric charges after being brought in contact with one another. The contact can be either simple touch of their surfaces or friction between them - in the latter case this phenomenon is called ''[[tribocharging]]''. This phenomenon has been known for thousands of years; the ancient Greeks were familiar with the fact that they could make objects attracted to amber by rubbing them on it. It was also exploited by Alessandro Volta when he made in the 18th century his [[voltaic pile]], the precursor to our batteries. <br />
<br />
Nonetheless, this phenomenon is poorly understood. While it seems obvious that it arises from the exchange of charges between the materials in contact, little can be said about whether it is the positive or negative charges moving, let alone why an ion in an overall neutral material would have the tendency to leave its balanced environment, hop across an interface, and end up in an environment which is now electrostatically imbalanced. <br />
<br />
Empirical observation over the last couple of centuries has led to the more-or-less agreed upon triboelectric series, a list of materials in order of decreasing amount of positive charge acquired upon contact (see also lecture notes on [[Charged Interfaces]]). More recently scientists have developed tools for the accurate measurement of the acquired charge by contact, such as the rolling sphere tool (ref: 11 in [[Controlling the Kinetics of Contact Electrification with Patterned Surfaces]]) which measures the charge accumulated on a magnetically controllable sphere rolling on a surface. <br />
<br />
From such and similar observations, it has been more or less concluded that when it comes to contact electrification between two different metals, the charges accumulated on each side correlate with the work function of the electrons - i.e. the energy required to remove an electron from inside the metal to just outside of it. This, in turn, seems to indicate that in the case of metals it is the electrons that move [3]. <br />
<br />
The case of dielectrics seems to be a bit more complicated, as there is disagreement between experimenters regarding any correlation of the accumulated charges with quantities that one would think relevant, such as electronegativity or ionization energy. It is possible that such experiments are very sensitive to ambient conditions (ex. humidity, which would affect the conductivity of the air between the surfaces), surface roughness, and the exact manner by which two materials are brought in contact and then taken apart, making the results of these studies hard to systematize. One fact which seems to be generally accepted is a correlation between accumulated charge and acidity or basicity [3].<br />
<br />
The fundamental understanding of contact electrification and subsequent understanding of ways to control it has a lot of potential applications. Learning how to engineer a system where known amounts of charge can be exchanged between particles may be a new tool for [[directed self-assembly]]. Learning how to prevent contact electrification may provide solutions to many associated problems, such as explosions and fires due to sparking (for example in silos storing powders such as flour) or damage in electronic circuits. Moreover, it may lead to the development of novel materials that can maintain a permanent charge, by analogy to permanent magnets, which could be used in their stead as an alternative with longer-range interaction strength.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Controlling the Kinetics of Contact Electrification with Patterned Surfaces]]<br />
<br />
[[The Determination of the Location of Contact Electrification-Induced Discharge Events]]<br />
<br />
== References ==<br />
<br />
[1] ''Charged Interfaces'', Ian Morrison, lecture notes for Introduction to Soft Matter<br />
[2] ''Triboelectric Generation: Getting Charged'', available at www.esdjournal.com/techpapr/ryne/ryntribo.doc<br />
[3] ''Electrostatic Charging Due to Separation of Ions at Interfaces: Contact Electrification of Ionic Electrets'', Logan S. McCarty and George M. Whitesides, Angewandte<br />
Chemie, Angew. Chem. Int. Ed. 2008, 47, 2188 – 2207</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Contact_electrification&diff=23532Contact electrification2011-12-10T02:29:39Z<p>Smagkir: /* == */</p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
<br />
CONTACT ELECTRIFICATION<br />
<br />
reference: paper1: Electrostatic Charging Due to Separation of Ions at<br />
Interfaces: Contact Electrification of Ionic Electrets<br />
Logan S. McCarty and George M. Whitesides*<br />
Angewandte<br />
Chemie, Angew. Chem. Int. Ed. 2008, 47, 2188 – 2207<br />
<br />
curiosities:<br />
<br />
1. nonpolar materials develop strong charges<br />
2. polar materials become positive, nonpolar ones negatives<br />
<br />
====================================================================<br />
<br />
Contact electrification is a process during which two materials acquire electric charges after being brought in contact with one another. The contact can be either simple touch of their surfaces or friction between them - in the latter case this phenomenon is called ''[[tribocharging]]''. This phenomenon has been known for thousands of years; the ancient Greeks were familiar with the fact that they could make objects attracted to amber by rubbing them on it. It was also exploited by Alessandro Volta when he made in the 18th century his [[voltaic pile]], the precursor to our batteries. <br />
<br />
Nonetheless, this phenomenon is poorly understood. While it seems obvious that it arises from the exchange of charges between the materials in contact, little can be said about whether it is the positive or negative charges moving, let alone why an ion in an overall neutral material would have the tendency to leave its balanced environment, hop across an interface, and end up in an environment which is now electrostatically imbalanced. <br />
<br />
Empirical observation over the last couple of centuries has led to the more-or-less agreed upon triboelectric series, a list of materials in order of decreasing amount of positive charge acquired upon contact (see also lecture notes on [[Charged Interfaces]]). More recently scientists have developed tools for the accurate measurement of the acquired charge by contact, such as the rolling sphere tool (ref: 11 in [[Controlling the Kinetics of Contact Electrification with Patterned Surfaces]]) which measures the charge accumulated on a magnetically controllable sphere rolling on a surface. <br />
<br />
From such and similar observations, it has been more or less concluded that when it comes to contact electrification between two different metals, the charges accumulated on each side correlate with the work function of the electrons - i.e. the energy required to remove an electron from inside the metal to just outside of it. This, in turn, seems to indicate that in the case of metals it is the electrons that move [3]. <br />
<br />
The case of dielectrics seems to be a bit more complicated, as there is disagreement between experimenters regarding any correlation of the accumulated charges with quantities that one would think relevant, such as electronegativity or ionization energy. It is possible that such experiments are very sensitive to ambient conditions (ex. humidity, which would affect the conductivity of the air between the surfaces), surface roughness, and the exact manner by which two materials are brought in contact and then taken apart, making the results of these studies hard to systematize. One fact which seems to be generally accepted is a correlation between accumulated charge and acidity or basicity [3].<br />
<br />
The fundamental understanding of contact electrification and subsequent understanding of ways to control it has a lot of potential applications. Learning how to engineer a system where known amounts of charge can be exchanged between particles may be a new tool for [[directed self-assembly]]. Learning how to prevent contact electrification will prevent a lot of associated problems, such as explosions and fires due to sparking (for example in silos storing powders such as flour) or damage in electronic circuits. Moreover, it may lead to the development of novel materials that can maintain a permanent charge, by analogy to permanent magnets, which could be used in their stead as an alternative with longer-range interaction strength.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Controlling the Kinetics of Contact Electrification with Patterned Surfaces]]<br />
<br />
[[The Determination of the Location of Contact Electrification-Induced Discharge Events]]<br />
<br />
== References ==<br />
<br />
[1] ''Charged Interfaces'', Ian Morrison, lecture notes for Introduction to Soft Matter<br />
[2] ''Triboelectric Generation: Getting Charged'', available at www.esdjournal.com/techpapr/ryne/ryntribo.doc<br />
[3] ''Electrostatic Charging Due to Separation of Ions at Interfaces: Contact Electrification of Ionic Electrets'', Logan S. McCarty and George M. Whitesides, Angewandte<br />
Chemie, Angew. Chem. Int. Ed. 2008, 47, 2188 – 2207</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Contact_electrification&diff=23531Contact electrification2011-12-10T02:29:09Z<p>Smagkir: /* == */</p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
<br />
CONTACT ELECTRIFICATION<br />
<br />
reference: paper1: Electrostatic Charging Due to Separation of Ions at<br />
Interfaces: Contact Electrification of Ionic Electrets<br />
Logan S. McCarty and George M. Whitesides*<br />
Angewandte<br />
Chemie, Angew. Chem. Int. Ed. 2008, 47, 2188 – 2207<br />
<br />
curiosities:<br />
<br />
1. nonpolar materials develop strong charges<br />
2. polar materials become positive, nonpolar ones negatives<br />
<br />
====================================================================<br />
<br />
Contact electrification is a process during which two materials acquire electric charges after being brought in contact with one another. The contact can be either simple touch of their surfaces or friction between them - in the latter case this phenomenon is called ''[[tribocharging]]''. This phenomenon has been known for thousands of years; the ancient Greeks were familiar with the fact that they could make objects attracted to amber by rubbing them on it. It was also exploited by Alessandro Volta when he made in the 18th century his [[voltaic pile]], the precursor to our batteries. <br />
<br />
Nonetheless, this phenomenon is poorly understood. While it seems obvious that it arises from the exchange of charges between the materials in contact, little can be said about whether it is the positive or negative charges moving, let alone why an ion in an overall neutral material would have the tendency to leave its balanced environment, hop across an interface, and end up in an environment which is now electrostatically imbalanced. <br />
<br />
Empirical observation over the last couple of centuries has led to the more-or-less agreed upon triboelectric series, a list of materials in order of decreasing amount of positive charge acquired upon contact (see also lecture notes on [[Charged Interfaces]]). More recently scientists have developed tools for the accurate measurement of the acquired charge by contact, such as the rolling sphere tool (ref: 11 in [[Controlling the Kinetics of Contact Electrification with Patterned Surfaces]]) which measures the charge accumulated on a magnetically controllable sphere rolling on a surface. <br />
<br />
From such and similar observations, it has been more or less concluded that when it comes to contact electrification between two different metals, the charges accumulated on each side correlate with the work function of the electrons - i.e. the energy required to remove an electron from inside the metal to just outside of it. This, in turn, seems to indicate that in the case of metals it is the electrons that move [3]. <br />
<br />
The case of dielectrics seems to be a bit more complicated, as there is disagreement between experimenters regarding any correlation of the accumulated charges with quantities that one would think relevant, such as electronegativity or ionization energy. It is possible that such experiments are very sensitive to ambient conditions (ex. humidity, which would affect the conductivity of the air between the surfaces), surface roughness, and the exact manner by which two materials are brought in contact and then taken apart, making the results of these studies hard to systematize. One fact which seems to be generally accepted is a correlation between accumulated charge and acidity or basicity (red: Whitesides review).<br />
<br />
The fundamental understanding of contact electrification and subsequent understanding of ways to control it has a lot of potential applications. Learning how to engineer a system where known amounts of charge can be exchanged between particles may be a new tool for [[directed self-assembly]]. Learning how to prevent contact electrification will prevent a lot of associated problems, such as explosions and fires due to sparking (for example in silos storing powders such as flour) or damage in electronic circuits. Moreover, it may lead to the development of novel materials that can maintain a permanent charge, by analogy to permanent magnets, which could be used in their stead as an alternative with longer-range interaction strength.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Controlling the Kinetics of Contact Electrification with Patterned Surfaces]]<br />
<br />
[[The Determination of the Location of Contact Electrification-Induced Discharge Events]]<br />
<br />
== References ==<br />
<br />
[1] ''Charged Interfaces'', Ian Morrison, lecture notes for Introduction to Soft Matter<br />
[2] ''Triboelectric Generation: Getting Charged'', available at www.esdjournal.com/techpapr/ryne/ryntribo.doc<br />
[3] ''Electrostatic Charging Due to Separation of Ions at Interfaces: Contact Electrification of Ionic Electrets'', Logan S. McCarty and George M. Whitesides, Angewandte<br />
Chemie, Angew. Chem. Int. Ed. 2008, 47, 2188 – 2207</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Contact_electrification&diff=23530Contact electrification2011-12-10T02:28:15Z<p>Smagkir: /* == */</p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
<br />
CONTACT ELECTRIFICATION<br />
<br />
reference: paper1: Electrostatic Charging Due to Separation of Ions at<br />
Interfaces: Contact Electrification of Ionic Electrets<br />
Logan S. McCarty and George M. Whitesides*<br />
Angewandte<br />
Chemie, Angew. Chem. Int. Ed. 2008, 47, 2188 – 2207<br />
<br />
curiosities:<br />
<br />
1. nonpolar materials develop strong charges<br />
2. polar materials become positive, nonpolar ones negatives<br />
<br />
====================================================================<br />
<br />
Contact electrification is a process during which two materials acquire electric charges after being brought in contact with one another. The contact can be either simple touch of their surfaces or friction between them - in the latter case this phenomenon is called ''[[tribocharging]]''. This phenomenon has been known for thousands of years; the ancient Greeks were familiar with the fact that they could make objects attracted to amber by rubbing them on it. It was also exploited by Alessandro Volta when he made in the 18th century his [[voltaic pile]], the precursor to our batteries. <br />
<br />
Nonetheless, this phenomenon is poorly understood. While it seems obvious that it arises from the exchange of charges between the materials in contact, little can be said about whether it is the positive or negative charges moving, let alone why an ion in an overall neutral material would have the tendency to leave its balanced environment, hop across an interface, and end up in an environment which is now electrostatically imbalanced. <br />
<br />
Empirical observation over the last couple of centuries has led to the more-or-less agreed upon triboelectric series, a list of materials in order of decreasing amount of positive charge acquired upon contact (see also lecture notes on [[Charged Interfaces]]). More recently scientists have developed tools for the accurate measurement of the acquired charge by contact, such as the rolling sphere tool (ref: 11 in [[Controlling the Kinetics of Contact Electrification with Patterned Surfaces]]) which measures the charge accumulated on a magnetically controllable sphere rolling on a surface. <br />
<br />
From such and similar observations, it has been more or less concluded that when it comes to contact electrification between two different metals, the charges accumulated on each side correlate with the work function of the electrons - i.e. the energy required to remove an electron from inside the metal to just outside of it. This, in turn, seems to indicate that in the case of metals it is the electrons that move (ref: whitesides review). <br />
<br />
The case of dielectics seems to be a bit more complicated, as there is disagreement between experimenters regarding any correlation of the accumulated charges with quantities that one would think relevant, such as electronegativity or ionization energy. It is possible that such experiments are very sensitive to ambient conditions (ex. humidity, which would affect the conductivity of the air between the surfaces), surface roughness, and the exact manner by which two materials are brought in contact and then taken apart, making the results of these studies hard to systematize. One fact which seems to be generally accepted is a correlation between accumulated charge and acidity or basicity (red: Whitesides review).<br />
<br />
The fundamental understanding of contact electrification and subsequent understanding of ways to control it has a lot of potential applications. Learning how to engineer a system where known amounts of charge can be exchanged between particles may be a new tool for [[directed self-assembly]]. Learning how to prevent contact electrification will prevent a lot of associated problems, such as explosions and fires due to sparking (for example in silos storing powders such as flour) or damage in electronic circuits. Moreover, it may lead to the development of novel materials that can maintain a permanent charge, by analogy to permanent magnets, which could be used in their stead as an alternative with longer-range interaction strength.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Controlling the Kinetics of Contact Electrification with Patterned Surfaces]]<br />
<br />
[[The Determination of the Location of Contact Electrification-Induced Discharge Events]]<br />
<br />
== References ==<br />
<br />
[1] ''Charged Interfaces'', Ian Morrison, lecture notes for Introduction to Soft Matter<br />
[2] ''Triboelectric Generation: Getting Charged'', available at www.esdjournal.com/techpapr/ryne/ryntribo.doc<br />
[3] ''Electrostatic Charging Due to Separation of Ions at Interfaces: Contact Electrification of Ionic Electrets'', Logan S. McCarty and George M. Whitesides, Angewandte<br />
Chemie, Angew. Chem. Int. Ed. 2008, 47, 2188 – 2207</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Directed_self-assembly&diff=23529Directed self-assembly2011-12-10T02:25:01Z<p>Smagkir: /* References - to be added */</p>
<hr />
<div>Entry needed - Sofia is on it, in progress.<br />
<br />
== Definition ==<br />
<br />
See also: [[self-assembly]] <br />
<br />
Self-assembly is a bottom-up process during which particles of any kind come together to form a specific structure. Common examples of such a process include the three-dimensional formation of proteins from amino acids in a living organism and the often six-fold symmetric formation of crystals in snowflakes. <br />
<br />
Directed self-assembly refers to a self-assembly process where the initial particles and their environment have been engineered to promote the formation of a specific structure. <br />
<br />
Soft matter physics relates particularly to this subject since it provides a good model system for the study of self-assembly: colloidal suspensions of microspheres which can be used as the building blocks of more complex assemblies. The size range of microspheres can be as large as a few microns, which makes them fairly easy to image with conventional techniques such as [[optical microscopy]] and [[confocal microscopy]]; a recently introduced technique, [[digital holographic microscopy]], is also being used and under development for the study of dynamic processes.<br />
<br />
== Methods ==<br />
<br />
=== Thermodynamics ===<br />
<br />
Thermodynamics predicts that a system in equilibrium will relax in its lowest energy state. With that in mind, the game of directed self-assembly translates into engineering a system such that its ground state coincides with the desirable structure. It is possible for a system to be in a metastable state with a local energy minimum; if the lifetime of this state is long enough compared to the timescales relevant for the use of the self-assembled structure, this approach can also be used. <br />
<br />
Thermodynamics can be very helpful in designing systems for directed self-assembly, since it provides a theoretical toolcase for the prediction of the probability of occurrence of a certain configuration based on properties as general as the number of different types of interactions between particles and the range of the associated interparticle energies (see [[Design principles for self assembly with short ranged interactions]]).<br />
<br />
Thermodynamics underlies all physical processes, so in a sense all the methods described below can be eventually explained in terms of thermodynamical principles.<br />
<br />
=== Geometry and Surface Forces ===<br />
<br />
Geometry can set constraints on the motion of particles, making the desired structure more likely to self-assemble. Geometrical constraints are sometimes combined with surface forces which can be very strong at interfaces; in this case, the geometry of the space available to the particles is engineered so that the magnitude and direction of the associated surface forces will guide them in a desirable way. <br />
<br />
An example of how geometry can affect the yield of a self-assembly process is currently being explored for the creation of tetramers from a suspension of colloidal particles of two different sizes. The underlying idea is quite simple: a tetramer of particles can be formed by one small sphere in the center, on the surface of which are three larger spheres. If the larger spheres are too large compared to the small one, then it is impossible for three of them to fit, whereas if the larger spheres are too small compared to the small one, then it is highly likely that more than three of them will fit. It has been proven mathematically and shown experimentally that there is an optimal size ratio between the diameters of the two sphere types which results in the assembly of exactly three large spheres on the surface of one small sphere [[Nick Schade's paper]].<br />
<br />
The combination of geometry with capillary forces is commonly used for the directed self-assembly of thin films of crystals of particles on a flat surface. In such a process, a clean glass slide is immersed in a dense colloidal suspension and slowly pulled out. As the glass surface moves, a thin layer of the suspension full of particles protrudes from the liquid surface and carries the particles to the glass surface. If the surface moves slowly enough and the suspension is dense enough, this can result in the self-deposition of the spheres on a hexagonal lattice with the (1,1,1) plane parallel to the glass surface [1].<br />
<br />
=== Surface Functionalisation ===<br />
<br />
The interaction between two particles depends strongly on the properties of their surfaces. This can be used to engineer attractive or repulsive interactions. For example, in a colloidal system particles can be coated with surface charges. One of the simplest examples is the creation of colloidal crystals in a suspension where all particles have the same charge (see [[Photonic Properties of Strongly Correlated Colloidal Liquids]]). In this case the particles try to maintain the furthest distance from each other which is allowed by the volume of the surrounding medium and so they hover in the medium at periodically spaced locations. Even though electrostatics has only provided us with two types of electric charges, this technique can be surprisingly versatile with the addition of salt in the system, which allows control of the intensity of the electrostatic interactions since the concentration of free charges affects the [[Debye length]]. <br />
<br />
Such a system is currently being explored for the self-assembly of particle clusters with a specific number of constituents. Small negatively charged spheres are mixed with larger positively charged spheres; the large spheres are attracted to the small spheres and park on their surface, and due to the existence of free ions in the suspension large spheres attracted to the same small sphere are not repelled from each other, allowing for the attachment of more than one positively charged sphere on the surface of a negatively charged sphere [[Nick Shade's paper]].<br />
<br />
Another way to taylor interparticle interactions which offers greater variety relies on the use of DNA strands. By coating some spheres with half of a DNA strand and some with the complementary half, and assuming that the temperature of the system is higher than the binding energy between the DNA strands so that spheres can move Brownianly and find each other, it is possible to create a suspension where different pairs of particles are attracted to each other but indifferent to other particles which are coated with the half of another, non-complimentary DNA strand. This method is also being actively studied for the self-assembly of complex particle clusters [2].<br />
<br />
== Keyword in references: ==<br />
<br />
[[Design principles for self assembly with short ranged interactions]]<br />
<br />
== References - to be added ==<br />
<br />
[1] Jiang, Bertone, Hwang, and Colvin, Chem. Mater. 1999, 11, 2132-2140<br />
<br />
[2] Leunissen et al, Soft Matter, 2009, 5, 2422-2430</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Directed_self-assembly&diff=23528Directed self-assembly2011-12-10T02:24:45Z<p>Smagkir: /* References - to be added */</p>
<hr />
<div>Entry needed - Sofia is on it, in progress.<br />
<br />
== Definition ==<br />
<br />
See also: [[self-assembly]] <br />
<br />
Self-assembly is a bottom-up process during which particles of any kind come together to form a specific structure. Common examples of such a process include the three-dimensional formation of proteins from amino acids in a living organism and the often six-fold symmetric formation of crystals in snowflakes. <br />
<br />
Directed self-assembly refers to a self-assembly process where the initial particles and their environment have been engineered to promote the formation of a specific structure. <br />
<br />
Soft matter physics relates particularly to this subject since it provides a good model system for the study of self-assembly: colloidal suspensions of microspheres which can be used as the building blocks of more complex assemblies. The size range of microspheres can be as large as a few microns, which makes them fairly easy to image with conventional techniques such as [[optical microscopy]] and [[confocal microscopy]]; a recently introduced technique, [[digital holographic microscopy]], is also being used and under development for the study of dynamic processes.<br />
<br />
== Methods ==<br />
<br />
=== Thermodynamics ===<br />
<br />
Thermodynamics predicts that a system in equilibrium will relax in its lowest energy state. With that in mind, the game of directed self-assembly translates into engineering a system such that its ground state coincides with the desirable structure. It is possible for a system to be in a metastable state with a local energy minimum; if the lifetime of this state is long enough compared to the timescales relevant for the use of the self-assembled structure, this approach can also be used. <br />
<br />
Thermodynamics can be very helpful in designing systems for directed self-assembly, since it provides a theoretical toolcase for the prediction of the probability of occurrence of a certain configuration based on properties as general as the number of different types of interactions between particles and the range of the associated interparticle energies (see [[Design principles for self assembly with short ranged interactions]]).<br />
<br />
Thermodynamics underlies all physical processes, so in a sense all the methods described below can be eventually explained in terms of thermodynamical principles.<br />
<br />
=== Geometry and Surface Forces ===<br />
<br />
Geometry can set constraints on the motion of particles, making the desired structure more likely to self-assemble. Geometrical constraints are sometimes combined with surface forces which can be very strong at interfaces; in this case, the geometry of the space available to the particles is engineered so that the magnitude and direction of the associated surface forces will guide them in a desirable way. <br />
<br />
An example of how geometry can affect the yield of a self-assembly process is currently being explored for the creation of tetramers from a suspension of colloidal particles of two different sizes. The underlying idea is quite simple: a tetramer of particles can be formed by one small sphere in the center, on the surface of which are three larger spheres. If the larger spheres are too large compared to the small one, then it is impossible for three of them to fit, whereas if the larger spheres are too small compared to the small one, then it is highly likely that more than three of them will fit. It has been proven mathematically and shown experimentally that there is an optimal size ratio between the diameters of the two sphere types which results in the assembly of exactly three large spheres on the surface of one small sphere [[Nick Schade's paper]].<br />
<br />
The combination of geometry with capillary forces is commonly used for the directed self-assembly of thin films of crystals of particles on a flat surface. In such a process, a clean glass slide is immersed in a dense colloidal suspension and slowly pulled out. As the glass surface moves, a thin layer of the suspension full of particles protrudes from the liquid surface and carries the particles to the glass surface. If the surface moves slowly enough and the suspension is dense enough, this can result in the self-deposition of the spheres on a hexagonal lattice with the (1,1,1) plane parallel to the glass surface [1].<br />
<br />
=== Surface Functionalisation ===<br />
<br />
The interaction between two particles depends strongly on the properties of their surfaces. This can be used to engineer attractive or repulsive interactions. For example, in a colloidal system particles can be coated with surface charges. One of the simplest examples is the creation of colloidal crystals in a suspension where all particles have the same charge (see [[Photonic Properties of Strongly Correlated Colloidal Liquids]]). In this case the particles try to maintain the furthest distance from each other which is allowed by the volume of the surrounding medium and so they hover in the medium at periodically spaced locations. Even though electrostatics has only provided us with two types of electric charges, this technique can be surprisingly versatile with the addition of salt in the system, which allows control of the intensity of the electrostatic interactions since the concentration of free charges affects the [[Debye length]]. <br />
<br />
Such a system is currently being explored for the self-assembly of particle clusters with a specific number of constituents. Small negatively charged spheres are mixed with larger positively charged spheres; the large spheres are attracted to the small spheres and park on their surface, and due to the existence of free ions in the suspension large spheres attracted to the same small sphere are not repelled from each other, allowing for the attachment of more than one positively charged sphere on the surface of a negatively charged sphere [[Nick Shade's paper]].<br />
<br />
Another way to taylor interparticle interactions which offers greater variety relies on the use of DNA strands. By coating some spheres with half of a DNA strand and some with the complementary half, and assuming that the temperature of the system is higher than the binding energy between the DNA strands so that spheres can move Brownianly and find each other, it is possible to create a suspension where different pairs of particles are attracted to each other but indifferent to other particles which are coated with the half of another, non-complimentary DNA strand. This method is also being actively studied for the self-assembly of complex particle clusters [2].<br />
<br />
== Keyword in references: ==<br />
<br />
[[Design principles for self assembly with short ranged interactions]]<br />
<br />
== References - to be added ==<br />
<br />
[1] Jiang, Bertone, Hwang, and Colvin, Chem. Mater. 1999, 11, 2132-2140<br />
[2] Leunissen et al, Soft Matter, 2009, 5, 2422-2430</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Directed_self-assembly&diff=23527Directed self-assembly2011-12-10T02:23:04Z<p>Smagkir: /* Surface Functionalisation */</p>
<hr />
<div>Entry needed - Sofia is on it, in progress.<br />
<br />
== Definition ==<br />
<br />
See also: [[self-assembly]] <br />
<br />
Self-assembly is a bottom-up process during which particles of any kind come together to form a specific structure. Common examples of such a process include the three-dimensional formation of proteins from amino acids in a living organism and the often six-fold symmetric formation of crystals in snowflakes. <br />
<br />
Directed self-assembly refers to a self-assembly process where the initial particles and their environment have been engineered to promote the formation of a specific structure. <br />
<br />
Soft matter physics relates particularly to this subject since it provides a good model system for the study of self-assembly: colloidal suspensions of microspheres which can be used as the building blocks of more complex assemblies. The size range of microspheres can be as large as a few microns, which makes them fairly easy to image with conventional techniques such as [[optical microscopy]] and [[confocal microscopy]]; a recently introduced technique, [[digital holographic microscopy]], is also being used and under development for the study of dynamic processes.<br />
<br />
== Methods ==<br />
<br />
=== Thermodynamics ===<br />
<br />
Thermodynamics predicts that a system in equilibrium will relax in its lowest energy state. With that in mind, the game of directed self-assembly translates into engineering a system such that its ground state coincides with the desirable structure. It is possible for a system to be in a metastable state with a local energy minimum; if the lifetime of this state is long enough compared to the timescales relevant for the use of the self-assembled structure, this approach can also be used. <br />
<br />
Thermodynamics can be very helpful in designing systems for directed self-assembly, since it provides a theoretical toolcase for the prediction of the probability of occurrence of a certain configuration based on properties as general as the number of different types of interactions between particles and the range of the associated interparticle energies (see [[Design principles for self assembly with short ranged interactions]]).<br />
<br />
Thermodynamics underlies all physical processes, so in a sense all the methods described below can be eventually explained in terms of thermodynamical principles.<br />
<br />
=== Geometry and Surface Forces ===<br />
<br />
Geometry can set constraints on the motion of particles, making the desired structure more likely to self-assemble. Geometrical constraints are sometimes combined with surface forces which can be very strong at interfaces; in this case, the geometry of the space available to the particles is engineered so that the magnitude and direction of the associated surface forces will guide them in a desirable way. <br />
<br />
An example of how geometry can affect the yield of a self-assembly process is currently being explored for the creation of tetramers from a suspension of colloidal particles of two different sizes. The underlying idea is quite simple: a tetramer of particles can be formed by one small sphere in the center, on the surface of which are three larger spheres. If the larger spheres are too large compared to the small one, then it is impossible for three of them to fit, whereas if the larger spheres are too small compared to the small one, then it is highly likely that more than three of them will fit. It has been proven mathematically and shown experimentally that there is an optimal size ratio between the diameters of the two sphere types which results in the assembly of exactly three large spheres on the surface of one small sphere [[Nick Schade's paper]].<br />
<br />
The combination of geometry with capillary forces is commonly used for the directed self-assembly of thin films of crystals of particles on a flat surface. In such a process, a clean glass slide is immersed in a dense colloidal suspension and slowly pulled out. As the glass surface moves, a thin layer of the suspension full of particles protrudes from the liquid surface and carries the particles to the glass surface. If the surface moves slowly enough and the suspension is dense enough, this can result in the self-deposition of the spheres on a hexagonal lattice with the (1,1,1) plane parallel to the glass surface [1].<br />
<br />
=== Surface Functionalisation ===<br />
<br />
The interaction between two particles depends strongly on the properties of their surfaces. This can be used to engineer attractive or repulsive interactions. For example, in a colloidal system particles can be coated with surface charges. One of the simplest examples is the creation of colloidal crystals in a suspension where all particles have the same charge (see [[Photonic Properties of Strongly Correlated Colloidal Liquids]]). In this case the particles try to maintain the furthest distance from each other which is allowed by the volume of the surrounding medium and so they hover in the medium at periodically spaced locations. Even though electrostatics has only provided us with two types of electric charges, this technique can be surprisingly versatile with the addition of salt in the system, which allows control of the intensity of the electrostatic interactions since the concentration of free charges affects the [[Debye length]]. <br />
<br />
Such a system is currently being explored for the self-assembly of particle clusters with a specific number of constituents. Small negatively charged spheres are mixed with larger positively charged spheres; the large spheres are attracted to the small spheres and park on their surface, and due to the existence of free ions in the suspension large spheres attracted to the same small sphere are not repelled from each other, allowing for the attachment of more than one positively charged sphere on the surface of a negatively charged sphere [[Nick Shade's paper]].<br />
<br />
Another way to taylor interparticle interactions which offers greater variety relies on the use of DNA strands. By coating some spheres with half of a DNA strand and some with the complementary half, and assuming that the temperature of the system is higher than the binding energy between the DNA strands so that spheres can move Brownianly and find each other, it is possible to create a suspension where different pairs of particles are attracted to each other but indifferent to other particles which are coated with the half of another, non-complimentary DNA strand. This method is also being actively studied for the self-assembly of complex particle clusters [2].<br />
<br />
== Keyword in references: ==<br />
<br />
[[Design principles for self assembly with short ranged interactions]]<br />
<br />
== References - to be added ==<br />
<br />
[1] Jiang, Bertone, Hwang, and Colvin, Chem. Mater. 1999, 11, 2132-2140</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Directed_self-assembly&diff=23526Directed self-assembly2011-12-10T02:21:18Z<p>Smagkir: /* References - to be added */</p>
<hr />
<div>Entry needed - Sofia is on it, in progress.<br />
<br />
== Definition ==<br />
<br />
See also: [[self-assembly]] <br />
<br />
Self-assembly is a bottom-up process during which particles of any kind come together to form a specific structure. Common examples of such a process include the three-dimensional formation of proteins from amino acids in a living organism and the often six-fold symmetric formation of crystals in snowflakes. <br />
<br />
Directed self-assembly refers to a self-assembly process where the initial particles and their environment have been engineered to promote the formation of a specific structure. <br />
<br />
Soft matter physics relates particularly to this subject since it provides a good model system for the study of self-assembly: colloidal suspensions of microspheres which can be used as the building blocks of more complex assemblies. The size range of microspheres can be as large as a few microns, which makes them fairly easy to image with conventional techniques such as [[optical microscopy]] and [[confocal microscopy]]; a recently introduced technique, [[digital holographic microscopy]], is also being used and under development for the study of dynamic processes.<br />
<br />
== Methods ==<br />
<br />
=== Thermodynamics ===<br />
<br />
Thermodynamics predicts that a system in equilibrium will relax in its lowest energy state. With that in mind, the game of directed self-assembly translates into engineering a system such that its ground state coincides with the desirable structure. It is possible for a system to be in a metastable state with a local energy minimum; if the lifetime of this state is long enough compared to the timescales relevant for the use of the self-assembled structure, this approach can also be used. <br />
<br />
Thermodynamics can be very helpful in designing systems for directed self-assembly, since it provides a theoretical toolcase for the prediction of the probability of occurrence of a certain configuration based on properties as general as the number of different types of interactions between particles and the range of the associated interparticle energies (see [[Design principles for self assembly with short ranged interactions]]).<br />
<br />
Thermodynamics underlies all physical processes, so in a sense all the methods described below can be eventually explained in terms of thermodynamical principles.<br />
<br />
=== Geometry and Surface Forces ===<br />
<br />
Geometry can set constraints on the motion of particles, making the desired structure more likely to self-assemble. Geometrical constraints are sometimes combined with surface forces which can be very strong at interfaces; in this case, the geometry of the space available to the particles is engineered so that the magnitude and direction of the associated surface forces will guide them in a desirable way. <br />
<br />
An example of how geometry can affect the yield of a self-assembly process is currently being explored for the creation of tetramers from a suspension of colloidal particles of two different sizes. The underlying idea is quite simple: a tetramer of particles can be formed by one small sphere in the center, on the surface of which are three larger spheres. If the larger spheres are too large compared to the small one, then it is impossible for three of them to fit, whereas if the larger spheres are too small compared to the small one, then it is highly likely that more than three of them will fit. It has been proven mathematically and shown experimentally that there is an optimal size ratio between the diameters of the two sphere types which results in the assembly of exactly three large spheres on the surface of one small sphere [[Nick Schade's paper]].<br />
<br />
The combination of geometry with capillary forces is commonly used for the directed self-assembly of thin films of crystals of particles on a flat surface. In such a process, a clean glass slide is immersed in a dense colloidal suspension and slowly pulled out. As the glass surface moves, a thin layer of the suspension full of particles protrudes from the liquid surface and carries the particles to the glass surface. If the surface moves slowly enough and the suspension is dense enough, this can result in the self-deposition of the spheres on a hexagonal lattice with the (1,1,1) plane parallel to the glass surface [1].<br />
<br />
=== Surface Functionalisation ===<br />
<br />
The interaction between two particles depends strongly on the properties of their surfaces. This can be used to engineer attractive or repulsive interactions. For example, in a colloidal system particles can be coated with surface charges. One of the simplest examples is the creation of colloidal crystals in a suspension where all particles have the same charge (see [[Photonic Properties of Strongly Correlated Colloidal Liquids]]). In this case the particles try to maintain the furthest distance from each other which is allowed by the volume of the surrounding medium and so they hover in the medium at periodically spaced locations. Even though electrostatics has only provided us with two types of electric charges, this technique can be surprisingly versatile with the addition of salt in the system, which allows control of the intensity of the electrostatic interactions since the concentration of free charges affects the [[Debye length]]. <br />
<br />
Such a system is currently being explored for the self-assembly of particle clusters with a specific number of constituents. Small negatively charged spheres are mixed with larger positively charged spheres; the large spheres are attracted to the small spheres and park on their surface, and due to the existence of free ions in the suspension large spheres attracted to the same small sphere are not repelled from each other, allowing for the attachment of more than one positively charged sphere on the surface of a negatively charged sphere [[Nick Shade's paper]].<br />
<br />
Another way to taylor interparticle interactions which offers greater variety relies on the use of DNA strands. By coating some spheres with half of a DNA strand and some with the complementary half, and assuming that the temperature of the system is higher than the binding energy between the DNA strands so that spheres can move Brownianly and find each other, it is possible to create a suspension where different pairs of particles are attracted to each other but indifferent to other particles which are coated with the half of another, non-complimentary DNA strand. This method is also being actively studied for the self-assembly of complex particle clusters, such as octahedra [[reference]].<br />
<br />
== Keyword in references: ==<br />
<br />
[[Design principles for self assembly with short ranged interactions]]<br />
<br />
== References - to be added ==<br />
<br />
[1] Jiang, Bertone, Hwang, and Colvin, Chem. Mater. 1999, 11, 2132-2140</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Directed_self-assembly&diff=23525Directed self-assembly2011-12-10T02:20:27Z<p>Smagkir: /* Geometry and Surface Forces */</p>
<hr />
<div>Entry needed - Sofia is on it, in progress.<br />
<br />
== Definition ==<br />
<br />
See also: [[self-assembly]] <br />
<br />
Self-assembly is a bottom-up process during which particles of any kind come together to form a specific structure. Common examples of such a process include the three-dimensional formation of proteins from amino acids in a living organism and the often six-fold symmetric formation of crystals in snowflakes. <br />
<br />
Directed self-assembly refers to a self-assembly process where the initial particles and their environment have been engineered to promote the formation of a specific structure. <br />
<br />
Soft matter physics relates particularly to this subject since it provides a good model system for the study of self-assembly: colloidal suspensions of microspheres which can be used as the building blocks of more complex assemblies. The size range of microspheres can be as large as a few microns, which makes them fairly easy to image with conventional techniques such as [[optical microscopy]] and [[confocal microscopy]]; a recently introduced technique, [[digital holographic microscopy]], is also being used and under development for the study of dynamic processes.<br />
<br />
== Methods ==<br />
<br />
=== Thermodynamics ===<br />
<br />
Thermodynamics predicts that a system in equilibrium will relax in its lowest energy state. With that in mind, the game of directed self-assembly translates into engineering a system such that its ground state coincides with the desirable structure. It is possible for a system to be in a metastable state with a local energy minimum; if the lifetime of this state is long enough compared to the timescales relevant for the use of the self-assembled structure, this approach can also be used. <br />
<br />
Thermodynamics can be very helpful in designing systems for directed self-assembly, since it provides a theoretical toolcase for the prediction of the probability of occurrence of a certain configuration based on properties as general as the number of different types of interactions between particles and the range of the associated interparticle energies (see [[Design principles for self assembly with short ranged interactions]]).<br />
<br />
Thermodynamics underlies all physical processes, so in a sense all the methods described below can be eventually explained in terms of thermodynamical principles.<br />
<br />
=== Geometry and Surface Forces ===<br />
<br />
Geometry can set constraints on the motion of particles, making the desired structure more likely to self-assemble. Geometrical constraints are sometimes combined with surface forces which can be very strong at interfaces; in this case, the geometry of the space available to the particles is engineered so that the magnitude and direction of the associated surface forces will guide them in a desirable way. <br />
<br />
An example of how geometry can affect the yield of a self-assembly process is currently being explored for the creation of tetramers from a suspension of colloidal particles of two different sizes. The underlying idea is quite simple: a tetramer of particles can be formed by one small sphere in the center, on the surface of which are three larger spheres. If the larger spheres are too large compared to the small one, then it is impossible for three of them to fit, whereas if the larger spheres are too small compared to the small one, then it is highly likely that more than three of them will fit. It has been proven mathematically and shown experimentally that there is an optimal size ratio between the diameters of the two sphere types which results in the assembly of exactly three large spheres on the surface of one small sphere [[Nick Schade's paper]].<br />
<br />
The combination of geometry with capillary forces is commonly used for the directed self-assembly of thin films of crystals of particles on a flat surface. In such a process, a clean glass slide is immersed in a dense colloidal suspension and slowly pulled out. As the glass surface moves, a thin layer of the suspension full of particles protrudes from the liquid surface and carries the particles to the glass surface. If the surface moves slowly enough and the suspension is dense enough, this can result in the self-deposition of the spheres on a hexagonal lattice with the (1,1,1) plane parallel to the glass surface [1].<br />
<br />
=== Surface Functionalisation ===<br />
<br />
The interaction between two particles depends strongly on the properties of their surfaces. This can be used to engineer attractive or repulsive interactions. For example, in a colloidal system particles can be coated with surface charges. One of the simplest examples is the creation of colloidal crystals in a suspension where all particles have the same charge (see [[Photonic Properties of Strongly Correlated Colloidal Liquids]]). In this case the particles try to maintain the furthest distance from each other which is allowed by the volume of the surrounding medium and so they hover in the medium at periodically spaced locations. Even though electrostatics has only provided us with two types of electric charges, this technique can be surprisingly versatile with the addition of salt in the system, which allows control of the intensity of the electrostatic interactions since the concentration of free charges affects the [[Debye length]]. <br />
<br />
Such a system is currently being explored for the self-assembly of particle clusters with a specific number of constituents. Small negatively charged spheres are mixed with larger positively charged spheres; the large spheres are attracted to the small spheres and park on their surface, and due to the existence of free ions in the suspension large spheres attracted to the same small sphere are not repelled from each other, allowing for the attachment of more than one positively charged sphere on the surface of a negatively charged sphere [[Nick Shade's paper]].<br />
<br />
Another way to taylor interparticle interactions which offers greater variety relies on the use of DNA strands. By coating some spheres with half of a DNA strand and some with the complementary half, and assuming that the temperature of the system is higher than the binding energy between the DNA strands so that spheres can move Brownianly and find each other, it is possible to create a suspension where different pairs of particles are attracted to each other but indifferent to other particles which are coated with the half of another, non-complimentary DNA strand. This method is also being actively studied for the self-assembly of complex particle clusters, such as octahedra [[reference]].<br />
<br />
== Keyword in references: ==<br />
<br />
[[Design principles for self assembly with short ranged interactions]]<br />
<br />
== References - to be added ==</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Directed_self-assembly&diff=23524Directed self-assembly2011-12-10T02:19:15Z<p>Smagkir: /* Geometry and Surface Forces */</p>
<hr />
<div>Entry needed - Sofia is on it, in progress.<br />
<br />
== Definition ==<br />
<br />
See also: [[self-assembly]] <br />
<br />
Self-assembly is a bottom-up process during which particles of any kind come together to form a specific structure. Common examples of such a process include the three-dimensional formation of proteins from amino acids in a living organism and the often six-fold symmetric formation of crystals in snowflakes. <br />
<br />
Directed self-assembly refers to a self-assembly process where the initial particles and their environment have been engineered to promote the formation of a specific structure. <br />
<br />
Soft matter physics relates particularly to this subject since it provides a good model system for the study of self-assembly: colloidal suspensions of microspheres which can be used as the building blocks of more complex assemblies. The size range of microspheres can be as large as a few microns, which makes them fairly easy to image with conventional techniques such as [[optical microscopy]] and [[confocal microscopy]]; a recently introduced technique, [[digital holographic microscopy]], is also being used and under development for the study of dynamic processes.<br />
<br />
== Methods ==<br />
<br />
=== Thermodynamics ===<br />
<br />
Thermodynamics predicts that a system in equilibrium will relax in its lowest energy state. With that in mind, the game of directed self-assembly translates into engineering a system such that its ground state coincides with the desirable structure. It is possible for a system to be in a metastable state with a local energy minimum; if the lifetime of this state is long enough compared to the timescales relevant for the use of the self-assembled structure, this approach can also be used. <br />
<br />
Thermodynamics can be very helpful in designing systems for directed self-assembly, since it provides a theoretical toolcase for the prediction of the probability of occurrence of a certain configuration based on properties as general as the number of different types of interactions between particles and the range of the associated interparticle energies (see [[Design principles for self assembly with short ranged interactions]]).<br />
<br />
Thermodynamics underlies all physical processes, so in a sense all the methods described below can be eventually explained in terms of thermodynamical principles.<br />
<br />
=== Geometry and Surface Forces ===<br />
<br />
Geometry can set constraints on the motion of particles, making the desired structure more likely to self-assemble. Geometrical constraints are sometimes combined with surface forces which can be very strong at interfaces; in this case, the geometry of the space available to the particles is engineered so that the magnitude and direction of the associated surface forces will guide them in a desirable way. <br />
<br />
An example of how geometry can affect the yield of a self-assembly process is currently being explored for the creation of tetramers from a suspension of colloidal particles of two different sizes. The underlying idea is quite simple: a tetramer of particles can be formed by one small sphere in the center, on the surface of which are three larger spheres. If the larger spheres are too large compared to the small one, then it is impossible for three of them to fit, whereas if the larger spheres are too small compared to the small one, then it is highly likely that more than three of them will fit. It has been proven mathematically and shown experimentally that there is an optimal size ratio between the diameters of the two sphere types which results in the assembly of exactly three large spheres on the surface of one small sphere [[Nick Schade's paper]].<br />
<br />
The combination of geometry with capillary forces is commonly used for the directed self-assembly of thin films of crystals of particles on a flat surface. In such a process, a clean glass slide is immersed in a dense colloidal suspension and slowly pulled out. As the glass surface moves, a thin layer of the suspension that carries particles protrudes from the liquid surface and carries the particles to the glass surface. If the surface moves slowly enough and the suspension is dense enough, this can result in the self-deposition of the spheres on a hexagonal lattice with the (1,1,1) plane parallel to the glass surface [[paper reference]].<br />
<br />
=== Surface Functionalisation ===<br />
<br />
The interaction between two particles depends strongly on the properties of their surfaces. This can be used to engineer attractive or repulsive interactions. For example, in a colloidal system particles can be coated with surface charges. One of the simplest examples is the creation of colloidal crystals in a suspension where all particles have the same charge (see [[Photonic Properties of Strongly Correlated Colloidal Liquids]]). In this case the particles try to maintain the furthest distance from each other which is allowed by the volume of the surrounding medium and so they hover in the medium at periodically spaced locations. Even though electrostatics has only provided us with two types of electric charges, this technique can be surprisingly versatile with the addition of salt in the system, which allows control of the intensity of the electrostatic interactions since the concentration of free charges affects the [[Debye length]]. <br />
<br />
Such a system is currently being explored for the self-assembly of particle clusters with a specific number of constituents. Small negatively charged spheres are mixed with larger positively charged spheres; the large spheres are attracted to the small spheres and park on their surface, and due to the existence of free ions in the suspension large spheres attracted to the same small sphere are not repelled from each other, allowing for the attachment of more than one positively charged sphere on the surface of a negatively charged sphere [[Nick Shade's paper]].<br />
<br />
Another way to taylor interparticle interactions which offers greater variety relies on the use of DNA strands. By coating some spheres with half of a DNA strand and some with the complementary half, and assuming that the temperature of the system is higher than the binding energy between the DNA strands so that spheres can move Brownianly and find each other, it is possible to create a suspension where different pairs of particles are attracted to each other but indifferent to other particles which are coated with the half of another, non-complimentary DNA strand. This method is also being actively studied for the self-assembly of complex particle clusters, such as octahedra [[reference]].<br />
<br />
== Keyword in references: ==<br />
<br />
[[Design principles for self assembly with short ranged interactions]]<br />
<br />
== References - to be added ==</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Directed_self-assembly&diff=23523Directed self-assembly2011-12-10T02:18:46Z<p>Smagkir: /* Geometry and Surface Forces */</p>
<hr />
<div>Entry needed - Sofia is on it, in progress.<br />
<br />
== Definition ==<br />
<br />
See also: [[self-assembly]] <br />
<br />
Self-assembly is a bottom-up process during which particles of any kind come together to form a specific structure. Common examples of such a process include the three-dimensional formation of proteins from amino acids in a living organism and the often six-fold symmetric formation of crystals in snowflakes. <br />
<br />
Directed self-assembly refers to a self-assembly process where the initial particles and their environment have been engineered to promote the formation of a specific structure. <br />
<br />
Soft matter physics relates particularly to this subject since it provides a good model system for the study of self-assembly: colloidal suspensions of microspheres which can be used as the building blocks of more complex assemblies. The size range of microspheres can be as large as a few microns, which makes them fairly easy to image with conventional techniques such as [[optical microscopy]] and [[confocal microscopy]]; a recently introduced technique, [[digital holographic microscopy]], is also being used and under development for the study of dynamic processes.<br />
<br />
== Methods ==<br />
<br />
=== Thermodynamics ===<br />
<br />
Thermodynamics predicts that a system in equilibrium will relax in its lowest energy state. With that in mind, the game of directed self-assembly translates into engineering a system such that its ground state coincides with the desirable structure. It is possible for a system to be in a metastable state with a local energy minimum; if the lifetime of this state is long enough compared to the timescales relevant for the use of the self-assembled structure, this approach can also be used. <br />
<br />
Thermodynamics can be very helpful in designing systems for directed self-assembly, since it provides a theoretical toolcase for the prediction of the probability of occurrence of a certain configuration based on properties as general as the number of different types of interactions between particles and the range of the associated interparticle energies (see [[Design principles for self assembly with short ranged interactions]]).<br />
<br />
Thermodynamics underlies all physical processes, so in a sense all the methods described below can be eventually explained in terms of thermodynamical principles.<br />
<br />
=== Geometry and Surface Forces ===<br />
<br />
Geometry can set constraints on the motion of particles, making the desired structure more likely to self-assemble. Geometrical constraints are sometimes combined with surface forces which can be very strong at interfaces; in this case, the geometry of the space available to the particles is engineered so that the magnitude and direction of the associated surface forces will guide them in a desirable way. <br />
<br />
An example of how geometry can affect the yield of a self-assembly process is currently being exploited for the creation of tetramers from a suspension of colloidal particles of two different sizes. The underlying idea is quite simple: a tetramer of particles can be formed by one small sphere in the center, on the surface of which are three larger spheres. If the larger spheres are too large compared to the small one, then it is impossible for three of them to fit, whereas if the larger spheres are too small compared to the small one, then it is highly likely that more than three of them will fit. It has been proven mathematically and shown experimentally that there is an optimal size ratio between the diameters of the two sphere types which results in the assembly of exactly three large spheres on the surface of one small sphere [[Nick Schade's paper]].<br />
<br />
The combination of geometry with capillary forces is commonly used for the directed self-assembly of thin films of crystals of particles on a flat surface. In such a process, a clean glass slide is immersed in a dense colloidal suspension and slowly pulled out. As the glass surface moves, a thin layer of the suspension that carries particles protrudes from the liquid surface and carries the particles to the glass surface. If the surface moves slowly enough and the suspension is dense enough, this can result in the self-deposition of the spheres on a hexagonal lattice with the (1,1,1) plane parallel to the glass surface [[paper reference]].<br />
<br />
=== Surface Functionalisation ===<br />
<br />
The interaction between two particles depends strongly on the properties of their surfaces. This can be used to engineer attractive or repulsive interactions. For example, in a colloidal system particles can be coated with surface charges. One of the simplest examples is the creation of colloidal crystals in a suspension where all particles have the same charge (see [[Photonic Properties of Strongly Correlated Colloidal Liquids]]). In this case the particles try to maintain the furthest distance from each other which is allowed by the volume of the surrounding medium and so they hover in the medium at periodically spaced locations. Even though electrostatics has only provided us with two types of electric charges, this technique can be surprisingly versatile with the addition of salt in the system, which allows control of the intensity of the electrostatic interactions since the concentration of free charges affects the [[Debye length]]. <br />
<br />
Such a system is currently being explored for the self-assembly of particle clusters with a specific number of constituents. Small negatively charged spheres are mixed with larger positively charged spheres; the large spheres are attracted to the small spheres and park on their surface, and due to the existence of free ions in the suspension large spheres attracted to the same small sphere are not repelled from each other, allowing for the attachment of more than one positively charged sphere on the surface of a negatively charged sphere [[Nick Shade's paper]].<br />
<br />
Another way to taylor interparticle interactions which offers greater variety relies on the use of DNA strands. By coating some spheres with half of a DNA strand and some with the complementary half, and assuming that the temperature of the system is higher than the binding energy between the DNA strands so that spheres can move Brownianly and find each other, it is possible to create a suspension where different pairs of particles are attracted to each other but indifferent to other particles which are coated with the half of another, non-complimentary DNA strand. This method is also being actively studied for the self-assembly of complex particle clusters, such as octahedra [[reference]].<br />
<br />
== Keyword in references: ==<br />
<br />
[[Design principles for self assembly with short ranged interactions]]<br />
<br />
== References - to be added ==</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Directed_self-assembly&diff=23522Directed self-assembly2011-12-10T02:17:49Z<p>Smagkir: /* Thermodynamics */</p>
<hr />
<div>Entry needed - Sofia is on it, in progress.<br />
<br />
== Definition ==<br />
<br />
See also: [[self-assembly]] <br />
<br />
Self-assembly is a bottom-up process during which particles of any kind come together to form a specific structure. Common examples of such a process include the three-dimensional formation of proteins from amino acids in a living organism and the often six-fold symmetric formation of crystals in snowflakes. <br />
<br />
Directed self-assembly refers to a self-assembly process where the initial particles and their environment have been engineered to promote the formation of a specific structure. <br />
<br />
Soft matter physics relates particularly to this subject since it provides a good model system for the study of self-assembly: colloidal suspensions of microspheres which can be used as the building blocks of more complex assemblies. The size range of microspheres can be as large as a few microns, which makes them fairly easy to image with conventional techniques such as [[optical microscopy]] and [[confocal microscopy]]; a recently introduced technique, [[digital holographic microscopy]], is also being used and under development for the study of dynamic processes.<br />
<br />
== Methods ==<br />
<br />
=== Thermodynamics ===<br />
<br />
Thermodynamics predicts that a system in equilibrium will relax in its lowest energy state. With that in mind, the game of directed self-assembly translates into engineering a system such that its ground state coincides with the desirable structure. It is possible for a system to be in a metastable state with a local energy minimum; if the lifetime of this state is long enough compared to the timescales relevant for the use of the self-assembled structure, this approach can also be used. <br />
<br />
Thermodynamics can be very helpful in designing systems for directed self-assembly, since it provides a theoretical toolcase for the prediction of the probability of occurrence of a certain configuration based on properties as general as the number of different types of interactions between particles and the range of the associated interparticle energies (see [[Design principles for self assembly with short ranged interactions]]).<br />
<br />
Thermodynamics underlies all physical processes, so in a sense all the methods described below can be eventually explained in terms of thermodynamical principles.<br />
<br />
=== Geometry and Surface Forces ===<br />
<br />
Geometry can set constraints on the motion of particles, making the desired structure more likely to self-assemble. Geometrical constraints are sometimes combined with surface forces, which can be very strong at interfaces; in this case, the geometry of the space available to the particles is engineered so that the magnitude and direction of the associated surface forces will guide them in a desirable way. <br />
<br />
An example of how geometry can affect the yield of a self-assembly process is currently being exploited for the creation of tetramers from a suspension of colloidal particles of two different sizes. The underlying idea is quite simple: a tetramer of particles can be formed by one small sphere in the center, on the surface of which are three larger spheres. If the larger spheres are too large compared to the small one, then it is impossible for three of them to fit, whereas if the larger spheres are too small compared to the small one, then it is highly likely that more than three of them will fit. It has been proven mathematically and shown experimentally that there is an optimal size ratio between the diameters of the two sphere types which results in the assembly of exactly three large spheres on the surface of one small sphere [[Nick Schade's paper]].<br />
<br />
The combination of geometry with capillary forces is commonly used for the directed self-assembly of thin films of crystals of particles on a flat surface. In such a process, a clean glass slide is immersed in a dense colloidal suspension and slowly pulled out. As the glass surface moves, a thin layer of the suspension that carries particles protrudes from the liquid surface and carries the particles to the glass surface. If the surface moves slowly enough and the suspension is dense enough, this can result in the self-deposition of the spheres on a hexagonal lattice with the (1,1,1) plane parallel to the glass surface [[paper reference]].<br />
<br />
=== Surface Functionalisation ===<br />
<br />
The interaction between two particles depends strongly on the properties of their surfaces. This can be used to engineer attractive or repulsive interactions. For example, in a colloidal system particles can be coated with surface charges. One of the simplest examples is the creation of colloidal crystals in a suspension where all particles have the same charge (see [[Photonic Properties of Strongly Correlated Colloidal Liquids]]). In this case the particles try to maintain the furthest distance from each other which is allowed by the volume of the surrounding medium and so they hover in the medium at periodically spaced locations. Even though electrostatics has only provided us with two types of electric charges, this technique can be surprisingly versatile with the addition of salt in the system, which allows control of the intensity of the electrostatic interactions since the concentration of free charges affects the [[Debye length]]. <br />
<br />
Such a system is currently being explored for the self-assembly of particle clusters with a specific number of constituents. Small negatively charged spheres are mixed with larger positively charged spheres; the large spheres are attracted to the small spheres and park on their surface, and due to the existence of free ions in the suspension large spheres attracted to the same small sphere are not repelled from each other, allowing for the attachment of more than one positively charged sphere on the surface of a negatively charged sphere [[Nick Shade's paper]].<br />
<br />
Another way to taylor interparticle interactions which offers greater variety relies on the use of DNA strands. By coating some spheres with half of a DNA strand and some with the complementary half, and assuming that the temperature of the system is higher than the binding energy between the DNA strands so that spheres can move Brownianly and find each other, it is possible to create a suspension where different pairs of particles are attracted to each other but indifferent to other particles which are coated with the half of another, non-complimentary DNA strand. This method is also being actively studied for the self-assembly of complex particle clusters, such as octahedra [[reference]].<br />
<br />
== Keyword in references: ==<br />
<br />
[[Design principles for self assembly with short ranged interactions]]<br />
<br />
== References - to be added ==</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Small-angle_neutron_scattering&diff=23521Small-angle neutron scattering2011-12-10T02:16:24Z<p>Smagkir: </p>
<hr />
<div>Small-angle neutron scattering is a technique for probing the internal structure of a material by measuring how a beam of neutrons scatters from it when incident at small angles with respect to the plane normal to the beam. <br />
<br />
<br />
There are several scattering techniques which share the same operating principle: X-ray scattering, neutron scattering, and even optical scattering all come down to illuminating a sample with a beam of particles/waves and recording the resulting scattering pattern. Which one is most appropriate depends on the required resolution and the specific type of information required. <br />
<br />
Treating all particles (and photons) as waves, the resolution of these techniques depends linearly on the wavelength, which, in turn, depends, for massive particles, on their momentum, according to de Broglie:<br />
<br />
:<math>\lambda = \frac{h}{p} = \frac{h}{{m}{v}}</math><br />
<br />
where <math>\lambda</math> is the wavelength, <math>h</math> is the Planck constant, <math>m</math> is the particle's mass and <math>v</math> its velocity.<br />
<br />
By Bragg's law, the distance d resolvable by radiation of wavelength <math>\lambda</math> incident on a material with refractive index <math>n</math> at an angle <math>\theta</math> with respect to the plane perpendicular to the beam is <br />
<br />
:<math>d = \frac{{n}{\lambda}}{2\sin\theta}\!</math>.<br />
<br />
Typical values for the wavelength of neutrons in a beam are between 1-1000 angstrom; by changing the angle and the energy of the neutron beam, the resolution of this technique can be tuned in the 1-1000nm regime. Small angle scattering is used when larger lengthscales are of interest, for example to study polymer molecules or biological macromolecules. <br />
<br />
<br />
Neutrons are not electrically charged and so they interact very weakly with matter. This has the advantage that neutron scattering is elastic, which means that the resulting scattering pattern is not convoluted with secondary processes and can be used to extract purely structural information (see [[structure factor]]). Moreover, they can penetrate deeply into a material - sometimes as much as several centimeters - and so they can be used to obtain information about its bulk. The scattering cross-section of atoms to neutron radiation is somewhat constant across the periodic table, so even when a complex material comprised of atoms with varying sizes is probed, all of its constituents have more or less the same chance of being identified. Particularly sensitive to neutrons are hydrogen atoms, so SANS is frequently used for the study of materials made of organic molecules, including biological molecules. At the same time, the weakness of the neutron-matter interaction means that high intensity beams are required, which is a technical challenge. <br />
<br />
Neutrons mostly interact with the nucleus, but they also have a small magnetic moment which sometimes induces them to interact with electrons at large orbits. This property is sometimes used to study the electronic structure. <br />
<br />
Finally, an interesting aspect of neutrons is that the energies at which they are available is of the same order as phonons in atomic crystals, molecular vibrational modes, and diffusive processes (~1μeV - eV). This makes it possible to study these processes in experiments involving energy exchange between neutrons and the sample.<br />
<br />
<br />
Neutrons can be obtained from nuclear reactors, where they are a byproduct of fission of Uranium-235, or from particle accelerators, as the byproduct of collisions between protons and atoms with heavy nuclei. There are only a few such facilities in the world; the highest-flux neutron beam is maintained at the Institut Laue-Langevin in Grenoble, France, while other SANS facilities are located in Oak Ringe National Lab and Brookhaven National Lab.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== References ==<br />
http://www.ill.eu/science-technology/why-use-neutrons/<br />
<br />
www.wikipedia.org<br />
<br />
International Atomic energy Agency, ''Small angle neutron scattering: Report of a coordinated research project 2000–2003'', March 2006</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Small-angle_neutron_scattering&diff=23520Small-angle neutron scattering2011-12-10T02:16:13Z<p>Smagkir: </p>
<hr />
<div>Entry needed - IN PROGRESS by Sofia.<br />
<br />
<br />
Small-angle neutron scattering is a technique for probing the internal structure of a material by measuring how a beam of neutrons scatters from it when incident at small angles with respect to the plane normal to the beam. <br />
<br />
There are several scattering techniques which share the same operating principle: X-ray scattering, neutron scattering, and even optical scattering all come down to illuminating a sample with a beam of particles/waves and recording the resulting scattering pattern. Which one is most appropriate depends on the required resolution and the specific type of information required. <br />
<br />
Treating all particles (and photons) as waves, the resolution of these techniques depends linearly on the wavelength, which, in turn, depends, for massive particles, on their momentum, according to de Broglie:<br />
<br />
:<math>\lambda = \frac{h}{p} = \frac{h}{{m}{v}}</math><br />
<br />
where <math>\lambda</math> is the wavelength, <math>h</math> is the Planck constant, <math>m</math> is the particle's mass and <math>v</math> its velocity.<br />
<br />
By Bragg's law, the distance d resolvable by radiation of wavelength <math>\lambda</math> incident on a material with refractive index <math>n</math> at an angle <math>\theta</math> with respect to the plane perpendicular to the beam is <br />
<br />
:<math>d = \frac{{n}{\lambda}}{2\sin\theta}\!</math>.<br />
<br />
Typical values for the wavelength of neutrons in a beam are between 1-1000 angstrom; by changing the angle and the energy of the neutron beam, the resolution of this technique can be tuned in the 1-1000nm regime. Small angle scattering is used when larger lengthscales are of interest, for example to study polymer molecules or biological macromolecules. <br />
<br />
<br />
Neutrons are not electrically charged and so they interact very weakly with matter. This has the advantage that neutron scattering is elastic, which means that the resulting scattering pattern is not convoluted with secondary processes and can be used to extract purely structural information (see [[structure factor]]). Moreover, they can penetrate deeply into a material - sometimes as much as several centimeters - and so they can be used to obtain information about its bulk. The scattering cross-section of atoms to neutron radiation is somewhat constant across the periodic table, so even when a complex material comprised of atoms with varying sizes is probed, all of its constituents have more or less the same chance of being identified. Particularly sensitive to neutrons are hydrogen atoms, so SANS is frequently used for the study of materials made of organic molecules, including biological molecules. At the same time, the weakness of the neutron-matter interaction means that high intensity beams are required, which is a technical challenge. <br />
<br />
Neutrons mostly interact with the nucleus, but they also have a small magnetic moment which sometimes induces them to interact with electrons at large orbits. This property is sometimes used to study the electronic structure. <br />
<br />
Finally, an interesting aspect of neutrons is that the energies at which they are available is of the same order as phonons in atomic crystals, molecular vibrational modes, and diffusive processes (~1μeV - eV). This makes it possible to study these processes in experiments involving energy exchange between neutrons and the sample.<br />
<br />
<br />
Neutrons can be obtained from nuclear reactors, where they are a byproduct of fission of Uranium-235, or from particle accelerators, as the byproduct of collisions between protons and atoms with heavy nuclei. There are only a few such facilities in the world; the highest-flux neutron beam is maintained at the Institut Laue-Langevin in Grenoble, France, while other SANS facilities are located in Oak Ringe National Lab and Brookhaven National Lab.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== References ==<br />
http://www.ill.eu/science-technology/why-use-neutrons/<br />
<br />
www.wikipedia.org<br />
<br />
International Atomic energy Agency, ''Small angle neutron scattering: Report of a coordinated research project 2000–2003'', March 2006</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Small-angle_neutron_scattering&diff=23519Small-angle neutron scattering2011-12-10T02:14:52Z<p>Smagkir: </p>
<hr />
<div>Entry needed - IN PROGRESS by Sofia.<br />
<br />
<br />
Small-angle neutron scattering is a technique for probing the internal structure of a material by measuring how a beam of neutrons scatters from it when incident at small angles with respect to the plane normal to the beam. <br />
<br />
There are several scattering techniques which share the same operating principle: X-ray scattering, neutron scattering, and even optical scattering all come down to illuminating a sample with a beam of particles/waves and recording the resulting scattering pattern. Which one is most appropriate depends on the required resolution and the specific type of information required. <br />
<br />
Treating all particles (and photons) as waves, the resolution of these techniques depends linearly on the wavelength, which, in turn, depends, for massive particles, on their momentum, according to de Broglie:<br />
<br />
:<math>\lambda = \frac{h}{p} = \frac{h}{{m}{v}}</math><br />
<br />
where <math>\lambda</math> is the wavelength, <math>h</math> is the Planck constant, <math>m</math> is the particle's mass and <math>v</math> its velocity.<br />
<br />
By Bragg's law, the distance d resolvable by radiation of wavelength <math>\lambda</math> incident on a material with refractive index <math>n</math> at an angle <math>\theta</math> with respect to the plane perpendicular to the beam is <br />
<br />
:<math>d = \frac{{n}{\lambda}}{2\sin\theta}\!</math>.<br />
<br />
Typical values for the wavelength of neutrons in a beam are between 1-1000 angstrom; by changing the angle and the energy of the neutron beam, the resolution of this technique can be tuned in the 1-1000nm regime. Small angle scattering is used when larger lengthscales are of interest, for example to study polymer molecules or biological macromolecules. <br />
<br />
<br />
Neutrons are not electrically charged and so they interact very weakly with matter. This has the advantage that neutron scattering is elastic, which means that the resulting scattering pattern is not convoluted with secondary processes and can be used to extract purely structural information (see [[structure factor]]). Moreover, they can penetrate deeply into a material - sometimes as much as several centimeters - and so they can be used to obtain information about its bulk. The scattering cross-section of atoms to neutron radiation is somewhat constant across the periodic table, so even when a complex material comprised of atoms with varying sizes is probed, all of its constituents have more or less the same chance of being probed and identified. Particularly sensitive to neutrons are hydrogen atoms, so SANS is frequently used for the study of materials made of organic molecules, including biological molecules. At the same time, the weakness of the neutron-matter interaction means that high intensity beams are required, which is a practical challenge. <br />
<br />
Neutrons mostly interact with the nucleus, but they also have a small magnetic moment which sometimes induces them to interact with electrons at large orbits. This property is sometimes used to study the electronic structure. <br />
<br />
Finally, an interesting aspect of neutrons is that the energies at which they are available is of the same order as phonons in atomic crystals, molecular vibrational modes, and diffusive processes (~1μeV - eV). This makes it possible to study these processes in experiments involving energy exchange between neutrons and the sample.<br />
<br />
<br />
Neutrons can be obtained from nuclear reactors, where they are a byproduct of fission of Uranium-235, or from particle accelerators, as the byproducts of collisions between protons and atoms with heavy nuclei. There are only a few such facilities in the world; the highest-flux neutron beam is maintained at the Institut Laue-Langevin in Grenoble, France, while other SANS facilities are located in Oak Ringe National Lab and Brookhaven National Lab.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== References ==<br />
http://www.ill.eu/science-technology/why-use-neutrons/<br />
<br />
www.wikipedia.org<br />
<br />
International Atomic energy Agency, ''Small angle neutron scattering: Report of a coordinated research project 2000–2003'', March 2006</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Small-angle_neutron_scattering&diff=23518Small-angle neutron scattering2011-12-10T02:14:22Z<p>Smagkir: </p>
<hr />
<div>Entry needed - IN PROGRESS by Sofia.<br />
<br />
<br />
Small-angle neutron scattering is a technique for probing the internal structure of a material by measuring how a beam of neutrons scatters from it when incident at small angles with respect to the plane normal to the beam. <br />
<br />
There are several scattering techniques which share the same operating principle: X-ray scattering, neutron scattering, and even optical scattering all come down to illuminating a sample with a beam of particles/waves and recording the resulting scattering pattern. Which one is most appropriate depends on the required resolution and the specific type of information required. <br />
<br />
Treating all particles (and photons) as waves, the resolution of these techniques depends linearly on the wavelength, which, in turn, depends, for massive particles, on their momentum, according to de Broglie:<br />
<br />
:<math>\lambda = \frac{h}{p} = \frac{h}{{m}{v}}</math><br />
<br />
where <math>\lambda</math> is the wavelength, <math>h</math> is the Planck constant, <math>m</math> is the particle's mass and <math>v</math> its velocity.<br />
<br />
By Bragg's law, the distance d resolvable by radiation of wavelength <math>\lambda</math> incident on a material with refractive index <math>n</math> at an angle <math>\theta</math> with respect to the plane perpendicular to the beam is <br />
<br />
:<math>d = \frac{{n}{\lambda}}{2\sin\theta}\!</math>.<br />
<br />
Typical values for the wavelength of neutrons in a beam are between 1-1000 angstrom; by changing the angle and the energy of the neutron beam, the resolution of this technique can be tuned in the 1-1000nm regime. Small angle scattering is used when larger lengthscales are of interest, for example to study polymer molecules or biological macromolecules. <br />
<br />
<br />
Neutrons are not electrically charged and so they interact very weakly with matter. This has the advantage that neutron scattering is elastic, which means that the resulting scattering pattern is not convoluted with secondary processes and can be used to extract purely structural information (see [[structure factor]]). Moreover, they can penetrate deeply into a material - sometimes as much as several centimeters - which means that they can be used to obtain information about its bulk. The scattering cross-section of atoms to neutron radiation is somewhat constant across the periodic table, so even when a complex material comprised of atoms with varying sizes is probed, all of its constituents have more or less the same chance of being probed and identified. Particularly sensitive to neutrons are hydrogen atoms, so SANS is frequently used for the study of materials made of organic molecules, including biological molecules. At the same time, the weakness of the neutron-matter interaction means that high intensity beams are required, which is a practical challenge. <br />
<br />
Neutrons mostly interact with the nucleus, but they also have a small magnetic moment which sometimes induces them to interact with electrons at large orbits. This property is sometimes used to study the electronic structure. <br />
<br />
Finally, an interesting aspect of neutrons is that the energies at which they are available is of the same order as phonons in atomic crystals, molecular vibrational modes, and diffusive processes (~1μeV - eV). This makes it possible to study these processes in experiments involving energy exchange between neutrons and the sample.<br />
<br />
<br />
Neutrons can be obtained from nuclear reactors, where they are a byproduct of fission of Uranium-235, or from particle accelerators, as the byproducts of collisions between protons and atoms with heavy nuclei. There are only a few such facilities in the world; the highest-flux neutron beam is maintained at the Institut Laue-Langevin in Grenoble, France, while other SANS facilities are located in Oak Ringe National Lab and Brookhaven National Lab.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== References ==<br />
http://www.ill.eu/science-technology/why-use-neutrons/<br />
<br />
www.wikipedia.org<br />
<br />
International Atomic energy Agency, ''Small angle neutron scattering: Report of a coordinated research project 2000–2003'', March 2006</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Small-angle_neutron_scattering&diff=23517Small-angle neutron scattering2011-12-10T02:13:32Z<p>Smagkir: </p>
<hr />
<div>Entry needed - IN PROGRESS by Sofia.<br />
<br />
<br />
Small-angle neutron scattering is a technique for probing the internal structure of a material by measuring how a beam of neutrons scatters from it when incident at small angles with respect to the plane normal to the beam (see also [[structure factor]]). <br />
<br />
There are several scattering techniques which share the same operating principle: X-ray scattering, neutron scattering, and even optical scattering all come down to illuminating a sample with a beam of particles/waves and recording the resulting scattering pattern. Which one is most appropriate depends on the required resolution and the specific type of information required. <br />
<br />
Treating all particles (and photons) as waves, the resolution of these techniques depends linearly on the wavelength, which, in turn, depends, for massive particles, on their momentum, according to de Broglie:<br />
<br />
:<math>\lambda = \frac{h}{p} = \frac{h}{{m}{v}}</math><br />
<br />
where <math>\lambda</math> is the wavelength, <math>h</math> is the Planck constant, <math>m</math> is the particle's mass and <math>v</math> its velocity.<br />
<br />
By Bragg's law, the distance d resolvable by radiation of wavelength <math>\lambda</math> incident on a material with refractive index <math>n</math> at an angle <math>\theta</math> with respect to the plane perpendicular to the beam is <br />
<br />
:<math>d = \frac{{n}{\lambda}}{2\sin\theta}\!</math>.<br />
<br />
Typical values for the wavelength of neutrons in a beam are between 1-1000 angstrom; by changing the angle and the energy of the neutron beam, the resolution of this technique can be tuned in the 1-1000nm regime. Small angle scattering is used when larger lengthscales are of interest, for example to study polymer molecules or biological macromolecules. <br />
<br />
<br />
Neutrons are not electrically charged and so they interact very weakly with matter. This has the advantage that neutron scattering is elastic, which means that the resulting scattering pattern is not convoluted with secondary processes and can be used to extract purely structural information. Moreover, they can penetrate deeply into a material - sometimes as much as several centimeters - which means that they can be used to obtain information about its bulk. The scattering cross-section of atoms to neutron radiation is somewhat constant across the periodic table, so even when a complex material comprised of atoms with varying sizes is probed, all of its constituents have more or less the same chance of being probed and identified. Particularly sensitive to neutrons are hydrogen atoms, so SANS is frequently used for the study of materials made of organic molecules, including biological molecules. At the same time, the weakness of the neutron-matter interaction means that high intensity beams are required, which is a practical challenge. <br />
<br />
Neutrons mostly interact with the nucleus, but they also have a small magnetic moment which sometimes induces them to interact with electrons at large orbits. This property is sometimes used to study the electronic structure. <br />
<br />
Finally, an interesting aspect of neutrons is that the energies at which they are available is of the same order as phonons in atomic crystals, molecular vibrational modes, and diffusive processes (~1μeV - eV). This makes it possible to study these processes in experiments involving energy exchange between neutrons and the sample.<br />
<br />
<br />
Neutrons can be obtained from nuclear reactors, where they are a byproduct of fission of Uranium-235, or from particle accelerators, as the byproducts of collisions between protons and atoms with heavy nuclei. There are only a few such facilities in the world; the highest-flux neutron beam is maintained at the Institut Laue-Langevin in Grenoble, France, while other SANS facilities are located in Oak Ringe National Lab and Brookhaven National Lab.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== References ==<br />
http://www.ill.eu/science-technology/why-use-neutrons/<br />
<br />
www.wikipedia.org<br />
<br />
International Atomic energy Agency, ''Small angle neutron scattering: Report of a coordinated research project 2000–2003'', March 2006</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Small-angle_neutron_scattering&diff=23516Small-angle neutron scattering2011-12-10T02:12:45Z<p>Smagkir: </p>
<hr />
<div>Entry needed - IN PROGRESS by Sofia.<br />
<br />
<br />
Small-angle neutron scattering is a technique for probing the internal structure of a material by measuring how a beam of neutrons scatters from it when incident at small angles with respect to the plane normal to the beam (see also [[structure factor]]). <br />
<br />
There are several scattering techniques which share the same operating principle: X-ray scattering, neutron scattering, and even optical scattering all come down to illuminating a sample with a beam of particles/waves and recording the resulting scattering pattern. Which one is most appropriate depends on the required resolution and the specific type of information required. <br />
<br />
Treating all particles (and photons) as waves, the resolution of these techniques depends linearly on the wavelength, which, in turn, depends, for massive particles, on their momentum, according to de Broglie:<br />
<br />
:<math>\lambda = \frac{h}{p} = \frac{h}{{m}{v}}</math><br />
<br />
where <math>\lambda</math> is the wavelength, <math>h</math> is the Planck constant, <math>m</math> is the particle's mass and <math>v</math> its velocity.<br />
<br />
By Bragg's law, the distance d resolvable by radiation of wavelength <math>\lambda</math> incident on a material with refractive index <math>n</math> at an angle <math>\theta</math> with respect to the plane perpendicular to the beam is <br />
<br />
:<math>d = \frac{{n}{\lambda}}{2\sin\theta}\!</math>.<br />
<br />
Typical values for the wavelength of neutrons in a beam are between 1-1000 angstrom; by changing the angle, the resolution of this technique can be varied in the 1-1000nm regime. Small angle scattering is used when larger lengthscales are of interest, for example to study polymer molecules or biological macromolecules. <br />
<br />
Neutrons are not electrically charged and so they interact very weakly with matter. This has the advantage that neutron scattering is elastic, which means that the resulting scattering pattern is not convoluted with secondary processes and can be used to extract purely structural information. Moreover, they can penetrate deeply into a material - sometimes as much as several centimeters - which means that they can be used to obtain information about its bulk. The scattering cross-section of atoms to neutron radiation is somewhat constant across the periodic table, so even when a complex material comprised of atoms with varying sizes is probed, all of its constituents have more or less the same chance of being probed and identified. Particularly sensitive to neutrons are hydrogen atoms, so SANS is frequently used for the study of materials made of organic molecules, including biological molecules. At the same time, the weakness of the neutron-matter interaction means that high intensity beams are required, which is a practical challenge. <br />
<br />
Neutrons mostly interact with the nucleus, but they also have a small magnetic moment which sometimes induces them to interact with electrons at large orbits. This property is sometimes used to study the electronic structure. <br />
<br />
Finally, an interesting aspect of neutrons is that the energies at which they are available is of the same order as phonons in atomic crystals, molecular vibrational modes, and diffusive processes (~1μeV - eV). This makes it possible to study these processes in experiments involving energy exchange between neutrons and the sample.<br />
<br />
Neutrons can be obtained from nuclear reactors, where they are a byproduct of fission of Uranium-235, or from particle accelerators, as the byproducts of collisions between protons and atoms with heavy nuclei. There are only a few such facilities in the world; the highest-flux neutron beam is maintained at the Institut Laue-Langevin in Grenoble, France, while other SANS facilities are located in Oak Ringe National Lab and Brookhaven National Lab.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== References ==<br />
http://www.ill.eu/science-technology/why-use-neutrons/<br />
<br />
www.wikipedia.org<br />
<br />
International Atomic energy Agency, ''Small angle neutron scattering: Report of a coordinated research project 2000–2003'', March 2006</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Small-angle_neutron_scattering&diff=23515Small-angle neutron scattering2011-12-10T02:12:11Z<p>Smagkir: </p>
<hr />
<div>Entry needed - IN PROGRESS by Sofia.<br />
<br />
<br />
Small-angle neutron scattering is a technique for probing the internal structure of a material by measuring how a beam of neutrons scatters from it when incident at small angles with respect to the plane normal to the beam (see also [[structure factor]]). <br />
<br />
There are several scattering techniques which share the same operating principle: X-ray scattering, neutron scattering, and even optical scattering all come down to illuminating a sample with a beam of particles/waves and recording the resulting scattering pattern. Which one is most appropriate depends on the required resolution and the specific type of information required. <br />
<br />
Treating all particles (and photons) as waves, the resolution of these techniques depends linearly on the wavelength, which, in turn, depends, for massive particles, on their momentum, according to de Broglie:<br />
<br />
:<math>\lambda = \frac{h}{p} = \frac{h}{{m}{v}}</math><br />
<br />
where <math>\lambda</math> is the wavelength, <math>h</math> is the Planck constant, <math>m</math> is the particle's mass and <math>v</math> its velocity.<br />
<br />
By Bragg's law, the distance d resolvable by radiation of wavelength <math>\lambda</math> incident on a material with refractive index <math>n</math> at an angle <math>\theta</math> with respect to the plane perpendicular to the beam is <br />
<br />
:<math>d = \frac{{n}{\lambda}}{2\sin\theta}\!</math>.<br />
<br />
Typical values for the wavelength of neutrons in a beam are ~ angstrom; by changing the angle, the resolution of this technique can be varied in the 1-1000nm regime. Small angle scattering is used when larger lengthscales are of interest, for example to study polymer molecules or biological macromolecules. <br />
<br />
Neutrons are not electrically charged and so they interact very weakly with matter. This has the advantage that neutron scattering is elastic, which means that the resulting scattering pattern is not convoluted with secondary processes and can be used to extract purely structural information. Moreover, they can penetrate deeply into a material - sometimes as much as several centimeters - which means that they can be used to obtain information about its bulk. The scattering cross-section of atoms to neutron radiation is somewhat constant across the periodic table, so even when a complex material comprised of atoms with varying sizes is probed, all of its constituents have more or less the same chance of being probed and identified. Particularly sensitive to neutrons are hydrogen atoms, so SANS is frequently used for the study of materials made of organic molecules, including biological molecules. At the same time, the weakness of the neutron-matter interaction means that high intensity beams are required, which is a practical challenge. <br />
<br />
Neutrons mostly interact with the nucleus, but they also have a small magnetic moment which sometimes induces them to interact with electrons at large orbits. This property is sometimes used to study the electronic structure. <br />
<br />
Finally, an interesting aspect of neutrons is that the energies at which they are available is of the same order as phonons in atomic crystals, molecular vibrational modes, and diffusive processes (~1μeV - eV). This makes it possible to study these processes in experiments involving energy exchange between neutrons and the sample.<br />
<br />
Neutrons can be obtained from nuclear reactors, where they are a byproduct of fission of Uranium-235, or from particle accelerators, as the byproducts of collisions between protons and atoms with heavy nuclei. There are only a few such facilities in the world; the highest-flux neutron beam is maintained at the Institut Laue-Langevin in Grenoble, France, while other SANS facilities are located in Oak Ringe National Lab and Brookhaven National Lab.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== References ==<br />
http://www.ill.eu/science-technology/why-use-neutrons/<br />
<br />
www.wikipedia.org<br />
<br />
International Atomic energy Agency, ''Small angle neutron scattering: Report of a coordinated research project 2000–2003'', March 2006</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Small-angle_neutron_scattering&diff=23514Small-angle neutron scattering2011-12-10T02:11:29Z<p>Smagkir: </p>
<hr />
<div>Entry needed - IN PROGRESS by Sofia.<br />
<br />
<br />
Small-angle neutron scattering is a technique for probing the internal structure of a material by measuring how a beam of neutrons scatters from it when incident at small angles with respect to the plane normal to the beam (see also [[structure factor]]). <br />
<br />
There are several scattering techniques which share the same operating principle: X-ray scattering, neutron scattering, and even optical scattering all come down to illuminating a sample with a beam of particles/waves and recording the resulting scattering pattern. Which one is most appropriate depends on the required resolution and the specific type of information required. <br />
<br />
Treating all particles (and photons) as waves, the resolution of these techniques depends linearly on the wavelength, which, in turn, depends, for massive particles, on their momentum, according to de Broglie:<br />
<br />
:<math>\lambda = \frac{h}{p} = \frac{h}{{m}{v}}</math><br />
<br />
where <math>\lambda</math> is the wavelength, <math>h</math> is the Planck constant, <math>m</math> is the particle's mass and <math>v</math> its velocity.<br />
<br />
By Bragg's law of diffraction, the distance d resolvable by radiation of wavelength <math>\lambda</math> incident on a material with refractive index <math>n</math> at an angle <math>\theta</math> with respect to the plane perpendicular to the beam is <br />
<br />
:<math>d = \frac{{n}{\lambda}}{2\sin\theta}\!</math>.<br />
<br />
Typical values for the wavelength of neutrons in a beam are ~ angstrom; by changing the angle, the resolution of this technique can be varied in the 1-1000nm regime. Small angle scattering is used when larger lengthscales are of interest, for example to study polymer molecules or biological macromolecules. <br />
<br />
Neutrons are not electrically charged and so they interact very weakly with matter. This has the advantage that neutron scattering is elastic, which means that the resulting scattering pattern is not convoluted with secondary processes and can be used to extract purely structural information. Moreover, they can penetrate deeply into a material - sometimes as much as several centimeters - which means that they can be used to obtain information about its bulk. The scattering cross-section of atoms to neutron radiation is somewhat constant across the periodic table, so even when a complex material comprised of atoms with varying sizes is probed, all of its constituents have more or less the same chance of being probed and identified. Particularly sensitive to neutrons are hydrogen atoms, so SANS is frequently used for the study of materials made of organic molecules, including biological molecules. At the same time, the weakness of the neutron-matter interaction means that high intensity beams are required, which is a practical challenge. <br />
<br />
Neutrons mostly interact with the nucleus, but they also have a small magnetic moment which sometimes induces them to interact with electrons at large orbits. This property is sometimes used to study the electronic structure. <br />
<br />
Finally, an interesting aspect of neutrons is that the energies at which they are available is of the same order as phonons in atomic crystals, molecular vibrational modes, and diffusive processes (~1μeV - eV). This makes it possible to study these processes in experiments involving energy exchange between neutrons and the sample.<br />
<br />
Neutrons can be obtained from nuclear reactors, where they are a byproduct of fission of Uranium-235, or from particle accelerators, as the byproducts of collisions between protons and atoms with heavy nuclei. There are only a few such facilities in the world; the highest-flux neutron beam is maintained at the Institut Laue-Langevin in Grenoble, France, while other SANS facilities are located in Oak Ringe National Lab and Brookhaven National Lab.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== References ==<br />
http://www.ill.eu/science-technology/why-use-neutrons/<br />
<br />
www.wikipedia.org<br />
<br />
International Atomic energy Agency, ''Small angle neutron scattering: Report of a coordinated research project 2000–2003'', March 2006</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=23513Structure factor2011-12-10T02:09:51Z<p>Smagkir: </p>
<hr />
<div>The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
<br />
The structure factor is a very useful concept. A closer look at the defining formula reveals that it is the Fourier transform of the density distribution. Information regarding general properties of a material structure, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify in the structure factor than in the structure itself. For example, the structure factor for a one-dimensional crystal of characteristic spacing <math>d</math> will have a maximum at <math>q = \frac{2 \pi} {d}</math>, the corresponding spatial frequency, and the width of this peak will be a measure of the quality of the crystalline order, as expected from Fourier Theory. While this is a trivial example where the periodic feature is readily identifiable, the structure factor can be a very powerful quantity for studying more complex structures such as quasi-crystals.<br />
<br />
<br />
Moreover, it is closely related to the scattering intensity from a material <math>\sigma</math>. In the case of single elastic scattering and for a material comprised of only one type of particles, this relation is, up to constants, as follows:<br />
<br />
:<math>\sigma_{\mathbf{q}} = C \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where C is a constant and <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for an arbitrary number of particle types by a simple summation where each term has the corresponding form factor (see also [[scattering]]). Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres it may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering each scatterer acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from different points in space. Within this picture, which emphasizes the analogy between a scattering pattern and a Fourier Transform, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation of S(q) as the collective interference term.<br />
<br />
<br />
The structure factor is a key quantity in crystallography and materials science; all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=23512Structure factor2011-12-10T02:09:18Z<p>Smagkir: </p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
<br />
The structure factor is a very useful concept. A closer look at the defining formula reveals that it is the Fourier transform of the density distribution. Information regarding general properties of a material structure, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify in the structure factor than in the structure itself. For example, the structure factor for a one-dimensional crystal of characteristic spacing <math>d</math> will have a maximum at <math>q = \frac{2 \pi} {d}</math>, the corresponding spatial frequency, and the width of this peak will be a measure of the quality of the crystalline order, as expected from Fourier Theory. While this is a trivial example where the periodic feature is readily identifiable, the structure factor can be a very powerful quantity for studying more complex structures such as quasi-crystals.<br />
<br />
<br />
Moreover, it is closely related to the scattering intensity from a material <math>\sigma</math>. In the case of single elastic scattering and for a material comprised of only one type of particles, this relation is, up to constants, as follows:<br />
<br />
:<math>\sigma_{\mathbf{q}} = C \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where C is a constant and <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for an arbitrary number of particle types by a simple summation where each term has the corresponding form factor (see also [[scattering]]). Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres it may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering each scatterer acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from different points in space. Within this picture, which emphasizes the analogy between a scattering pattern and a Fourier Transform, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation of S(q) as the collective interference term.<br />
<br />
<br />
The structure factor is a key quantity in crystallography and materials science; all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=23511Structure factor2011-12-10T02:06:39Z<p>Smagkir: </p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
<br />
The structure factor is a very useful concept. A closer look at the defining formula reveals that it is the Fourier transform of the density distribution. Information regarding general properties of a material structure, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify in the structure factor than in the structure itself. For example, the structure factor for a one-dimensional crystal of characteristic spacing <math>d</math> will have a maximum at <math>q = \frac{2 \pi} {d}</math>, the corresponding spatial frequency, and the width of this peak will be a measure of the quality of the crystalline order, as expected from Fourier Theory. While this is a trivial example where the periodic feature is readily identifiable, the structure factor can be a very powerful quantity for studying more complex structures such as quasi-crystals.<br />
<br />
<br />
Moreover, it is closely related to the scattering intensity from a material <math>\sigma</math>. In the case of single elastic scattering and for a material comprised of only one type of particles, this relation is, up to constants, as follows:<br />
<br />
:<math>\sigma_{\mathbf{q}} = C \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where C is a constant and <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for arbitrary number or particle types by a simple summation over all of them, where each term has the corresponding form factor (see also [[scattering]]). Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres it may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering each scatterer acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from different points in space. Within this picture, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation arising from the formula for the cross-section.<br />
<br />
The structure factor is a key quantity in crystallography and materials science; all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=23510Structure factor2011-12-10T02:06:10Z<p>Smagkir: </p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
<br />
The structure factor is a very useful concept. A closer look at the defining formula reveals that it is the Fourier transform of the density distribution. Information regarding general properties of a material structure, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify in the structure factor than in the structure itself. For example, the structure factor for a one-dimensional crystal of characteristic spacing <math>d</math> will have a maximum at <math>q = \frac{2 \pi} {d}</math>, the corresponding spatial frequency, and the width of this peak will be a measure of the quality of the crystalline order, as expected from Fourier Theory. While this is a trivial example where the periodic feature is readily identifiable, the structure factor can be a very powerful quantity for studying more complex structures such as quasi-crystals.<br />
<br />
<br />
Moreover, it is closely related to the scattering intensity from a material <math>\sigma</math>. In the case of single elastic scattering and for a material comprised of only one type of particles, this relation is, up to constants, as follows:<br />
<br />
:<math>\sigma_{\mathbf{q}} = C \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for arbitrary number or particle types by a simple summation over all of them, where each term has the corresponding form factor (see also [[scattering]]). Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres it may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering each scatterer acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from different points in space. Within this picture, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation arising from the formula for the cross-section.<br />
<br />
The structure factor is a key quantity in crystallography and materials science; all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=23509Structure factor2011-12-10T02:05:29Z<p>Smagkir: </p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
<br />
The structure factor is a very useful concept. A closer look at the defining formula reveals that it is the Fourier transform of the density distribution. Information regarding general properties of a material structure, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify in the structure factor than in the structure itself. For example, the structure factor for a one-dimensional crystal of characteristic spacing <math>d</math> will have a maximum at <math>q = \frac{2 \pi} {d}</math>, the corresponding spatial frequency, and the width of this peak will be a measure of the quality of the crystalline order, as expected from Fourier Theory. While this is a trivial example where the periodic feature is readily identifiable, the structure factor can be a very powerful quantity for studying more complex structures such as quasi-crystals.<br />
<br />
<br />
Moreover, it is closely related to the scattering intensity from a material. In the case of single elastic scattering and for a material comprised of only one type of particles, this relation is, up to constants, as follows:<br />
<br />
:<math>\sigma_{\mathbf{q}} \prop V \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for arbitrary number or particle types by a simple summation over all of them, where each term has the corresponding form factor (see also [[scattering]]). Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres it may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering each scatterer acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from different points in space. Within this picture, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation arising from the formula for the cross-section.<br />
<br />
The structure factor is a key quantity in crystallography and materials science; all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=23508Structure factor2011-12-10T02:05:13Z<p>Smagkir: </p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
<br />
The structure factor is a very useful concept. A closer look at the defining formula reveals that it is the Fourier transform of the density distribution. Information regarding general properties of a material structure, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify in the structure factor than in the structure itself. For example, the structure factor for a one-dimensional crystal of characteristic spacing <math>d</math> will have a maximum at <math>q = \frac{2 \pi} {d}</math>, the corresponding spatial frequency, and the width of this peak will be a measure of the quality of the crystalline order, as expected from Fourier Theory. While this is a trivial example where the periodic feature is readily identifiable, the structure factor can be a very powerful quantity for studying more complex structures such as quasi-crystals.<br />
<br />
<br />
Moreover, it is closely related to the scattering intensity from a material. In the case of single elastic scattering and for a material comprised of only one type of particles, this relation is, up to constants, as follows:<br />
<br />
:<math>\sigma_{\mathbf{q}} \eq V \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for arbitrary number or particle types by a simple summation over all of them, where each term has the corresponding form factor (see also [[scattering]]). Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres it may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering each scatterer acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from different points in space. Within this picture, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation arising from the formula for the cross-section.<br />
<br />
The structure factor is a key quantity in crystallography and materials science; all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=23507Structure factor2011-12-10T02:05:02Z<p>Smagkir: </p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
<br />
The structure factor is a very useful concept. A closer look at the defining formula reveals that it is the Fourier transform of the density distribution. Information regarding general properties of a material structure, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify in the structure factor than in the structure itself. For example, the structure factor for a one-dimensional crystal of characteristic spacing <math>d</math> will have a maximum at <math>q = \frac{2 \pi} {d}</math>, the corresponding spatial frequency, and the width of this peak will be a measure of the quality of the crystalline order, as expected from Fourier Theory. While this is a trivial example where the periodic feature is readily identifiable, the structure factor can be a very powerful quantity for studying more complex structures such as quasi-crystals.<br />
<br />
<br />
Moreover, it is closely related to the scattering intensity from a material. In the case of single elastic scattering and for a material comprised of only one type of particles, this relation is, up to constants, as follows:<br />
<br />
:<math>\sigma_{\mathbf{q}} \prop V \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for arbitrary number or particle types by a simple summation over all of them, where each term has the corresponding form factor (see also [[scattering]]). Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres it may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering each scatterer acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from different points in space. Within this picture, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation arising from the formula for the cross-section.<br />
<br />
The structure factor is a key quantity in crystallography and materials science; all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=23506Structure factor2011-12-10T02:04:36Z<p>Smagkir: </p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
<br />
The structure factor is a very useful concept. A closer look at the defining formula reveals that it is the Fourier transform of the density distribution. Information regarding general properties of a material structure, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify in the structure factor than in the structure itself. For example, the structure factor for a one-dimensional crystal of characteristic spacing <math>d</math> will have a maximum at <math>q = \frac{2 \pi} {d}</math>, the corresponding spatial frequency, and the width of this peak will be a measure of the quality of the crystalline order, as expected from Fourier Theory. While this is a trivial example where the periodic feature is readily identifiable, the structure factor can be a very powerful quantity for studying more complex structures such as quasi-crystals.<br />
<br />
<br />
Moreover, it is closely related to the scattering intensity from a material. In the case of single elastic scattering and for a material comprised of only one type of particles, this relation is, up to constants, as follows:<br />
<br />
:<math>\sigma_{\mathbf{q}} ~ V \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for arbitrary number or particle types by a simple summation over all of them, where each term has the corresponding form factor (see also [[scattering]]). Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres it may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering each scatterer acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from different points in space. Within this picture, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation arising from the formula for the cross-section.<br />
<br />
The structure factor is a key quantity in crystallography and materials science; all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=23505Structure factor2011-12-10T02:03:39Z<p>Smagkir: </p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
<br />
The structure factor is a very useful concept. A closer look at the defining formula reveals that it is the Fourier transform of the density distribution. Information regarding general properties of a material structure, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify in the structure factor than in the structure itself. For example, the structure factor for a one-dimensional crystal of characteristic spacing <math>d</math> will have a maximum at <math>q = \frac{2 \pi} {d}</math>, the corresponding spatial frequency, and the width of this peak will be a measure of the quality of the crystalline order, as expected from Fourier Theory. While this is a trivial example where the periodic feature is readily identifiable, the structure factor can be a very powerful quantity for studying more complex structures such as quasi-crystals.<br />
<br />
<br />
Moreover, it is closely related to the scattering intensity from a material. In the case of single elastic scattering and for a material comprised of only one type of particles, this relation is, up to constants, as follows:<br />
<br />
:<math>\sigma~V \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for arbitrary number or particle types by a simple summation over all of them, where each term has the corresponding form factor (see also [[scattering]]). Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres it may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering each scatterer acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from different points in space. Within this picture, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation arising from the formula for the cross-section.<br />
<br />
The structure factor is a key quantity in crystallography and materials science; all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=23504Structure factor2011-12-10T02:01:49Z<p>Smagkir: </p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
The structure factor is a very useful concept. A closer look at the defining formula reveals that it is the Fourier transform of the density distribution. Information regarding general properties of a material structure, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify in the structure factor than in the structure itself. For example, the structure factor for a one-dimensional crystal of characteristic spacing <math>d</math> will have a maximum at <math>q = \frac{2 \pi} {d}</math>, the corresponding spatial frequency, and the width of this peak will be a measure of the quality of the crystalline order, as expected from Fourier Theory. While this is a trivial example where the periodic feature is readily identifiable, the structure factor can be a very powerful quantity for studying more complex structures such as quasi-crystals.<br />
<br />
Moreover, it is closely related to the scattering intensity from a material. In the case of single elastic scattering and for a material comprised of only one type of particles, this relation can be phrased mathematically as follows:<br />
<br />
:<math>\sigma=V \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for arbitrary number or particle types by a simple summation over all of them, where each term has the corresponding form factor (see also [[scattering]]). Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres it may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering each scatterer acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from different points in space. Within this picture, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation arising from the formula for the cross-section.<br />
<br />
The structure factor is a key quantity in crystallography and materials science; all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=23503Structure factor2011-12-10T02:01:31Z<p>Smagkir: </p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
The structure factor is a very useful concept. A closer look at the defining formula reveals that it is the Fourier transform of the density distribution. Information regarding general properties of a material structure, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify in the structure factor than in the structure itself. For example, the structure factor for a one-dimensional crystal of characteristic spacing <math>d<\math> will have a maximum at <math>q = \frac{2 \pi} {d}</math>, the corresponding spatial frequency, and the width of this peak will be a measure of the quality of the crystalline order, as expected from Fourier Theory. While this is a trivial example where the periodic feature is readily identifiable, the structure factor can be a very powerful quantity for studying more complex structures such as quasi-crystals.<br />
<br />
Moreover, it is closely related to the scattering intensity from a material. In the case of single elastic scattering and for a material comprised of only one type of particles, this relation can be phrased mathematically as follows:<br />
<br />
:<math>\sigma=V \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for arbitrary number or particle types by a simple summation over all of them, where each term has the corresponding form factor (see also [[scattering]]). Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres it may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering each scatterer acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from different points in space. Within this picture, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation arising from the formula for the cross-section.<br />
<br />
The structure factor is a key quantity in crystallography and materials science; all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=23502Structure factor2011-12-10T02:00:48Z<p>Smagkir: </p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
The structure factor is a very useful concept. A closer look at the defining formula reveals that it is the Fourier transform of the density distribution. Information regarding general properties of a material structure, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify in the structure factor than in the structure itself. For example, the structure factor for a one-dimensional crystal of characteristic spacing <math>d<\math> will have a maximum at <math>q = \frac{2 \pi} {d}<\math>, the corresponding spatial frequency, and the width of this peak will be a measure of the quality of the crystalline order, as expected from Fourier Theory. While this is a trivial example where the periodic feature is readily identifiable, the structure factor can be a very powerful quantity for studying more complex structures such as quasi-crystals.<br />
<br />
Moreover, it is closely related to the scattering intensity from a material. In the case of single elastic scattering and for a material comprised of only one type of particles, this relation can be phrased mathematically as follows:<br />
<br />
:<math>\sigma=V \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for arbitrary number or particle types by a simple summation over all of them, where each term has the corresponding form factor (see also [[scattering]]). Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres it may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering each scatterer acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from different points in space. Within this picture, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation arising from the formula for the cross-section.<br />
<br />
The structure factor is a key quantity in crystallography and materials science; all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=23501Structure factor2011-12-10T01:52:55Z<p>Smagkir: </p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
The structure factor is a very useful concept. A closer look at the defining formula reveals that it is the Fourier transform of the density distribution. Information regarding general properties of a material structure, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify from the structure factor than from the structure itself. <br />
<br />
Moreover, it is closely related to the scattering intensity from a material. In the case of single elastic scattering, for a material comprised of only one type of particles, this relation can be phrased mathematically as follows:<br />
<br />
:<math>\sigma=V \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for arbitrary number or particle types by a simple summation over all of them, where each term has the corresponding form factor. Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres is may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering of radiation from a material each scattering element acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from each scatterer. Within this picture, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation arising from the formula for the cross-section.<br />
<br />
Crystallography and materials science rely heavily on S(q); all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=23500Structure factor2011-12-10T01:51:55Z<p>Smagkir: </p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
The structure factor is a very useful concept. A closer look at the defining formula reveals that it is the Fourier transform of the density distribution. As such, information regarding some general properties of a material, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify from the structure factor than from the structure itself. <br />
<br />
Moreover, it is closely related to the scattering intensity from a material. In the case of single elastic scattering, for a material comprised of only one type of particles, this relation can be phrased mathematically as follows:<br />
<br />
:<math>\sigma=V \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for arbitrary number or particle types by a simple summation over all of them, where each term has the corresponding form factor. Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres is may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering of radiation from a material each scattering element acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from each scatterer. Within this picture, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation arising from the formula for the cross-section.<br />
<br />
Crystallography and materials science rely heavily on S(q); all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkirhttp://soft-matter.seas.harvard.edu/index.php?title=Structure_factor&diff=23499Structure factor2011-12-10T01:51:42Z<p>Smagkir: </p>
<hr />
<div>Entry needed - Sofia is working on it, IN PROGRESS.<br />
<br />
The (static) structure factor is a mathematical expression unique to every structure related to the density distribution of its ingredients. Mathematically, it is<br />
defined as follows:<br />
<br />
:<math> S_{\mathbf{q}}= 1/V \sum_{i,j} e^{-i\mathbf{q} \cdot {(\mathbf{r}_i-\mathbf{r}_j)}}</math><br />
<br />
where V is the volume, the sum over i,j is a sum over all constituent particles and q is spatial frequency measured in units of inverse length. The particles can be atoms, molecules, or larger entities like polystyrene spheres arranged to form a specific structure. Note that this quantity only depends on the positions of the constituent particles and does not depend on their nature or interactions; <math> S_{\mathbf{q}}</math><br />
is a purely structural quantity. <br />
<br />
The structure factor is a very useful concept. A closer look at the formula reveals that it is the Fourier transform of the density distribution. As such, information regarding some general properties of a material, such as the existence of characteristic length scales, periodicity along some axis, and symmetries, can be easier to identify from the structure factor than from the structure itself. <br />
<br />
Moreover, it is closely related to the scattering intensity from a material. In the case of single elastic scattering, for a material comprised of only one type of particles, this relation can be phrased mathematically as follows:<br />
<br />
:<math>\sigma=V \int d\Omega S_{\mathbf{q}} F_{\mathbf{q}}</math><br />
<br />
where <math>F_{\mathbf{q}}</math> is the form factor, a quantity representing the way each constituent particle scatters. This expression can be generalized for arbitrary number or particle types by a simple summation over all of them, where each term has the corresponding form factor. Note that the notions of form factor and structure factor are somewhat relative and depend on the length scale that is considered "fundamental": for example, in order to study scattering from a structure made of 1μm polystyrene spheres is may be convenient to use the form factor of the sphere, however each such sphere is made of atoms and its form factor depends, in turn, on the form factors of its constituent atoms and the way they arranged in space, i.e. the sphere's structure factor. <br />
<br />
From this expression for scattering an alternate interpretation of the structure factor arises: it is the quantity representing how waves scattered from each structural feature interfere with each other. Adopting the Rayleigh principle, during elastic scattering of radiation from a material each scattering element acts as a point source of a spherical wave and the resulting pattern is the sum of all these waves originating from each scatterer. Within this picture, the interpretation of S(q) as the Fourier transform of the density becomes synonymous to the interpretation arising from the formula for the cross-section.<br />
<br />
Crystallography and materials science rely heavily on S(q); all scattering experiments, such as (small-angle) X-ray scattering and [[small-angle neutron scattering]], measure S(q). This data can either be used directly or inverted to obtain the density distribution. It is also of fundamental importance in the study of [[photonic crystals]]: any peak in the structure factor corresponds to strong scattering of light carrying momentum corresponding to the momentum vector q where the peak is located, and may thus signal the onset of a photonic stop band or band gap.<br />
<br />
== Keyword in references: ==<br />
<br />
[[Photonic Properties of Strongly Correlated Colloidal Liquids]]<br />
<br />
== Reference ==<br />
''Principles of Condensed Matter Physics'', Chaikin and Lubensky, Cambridge University Press (1995)</div>Smagkir