Intermolecular and interparticle forces

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Intermolecular energies

3D Pressure-volume isotherms 2D Spreading pressure-area isotherms
Hirschfelder Fig 4-1-1.gif Gaines Fig 4-7.gif
Hisrshfelder, Fig. 4.1.1 Gaines, Fig. 4.7
The figure at left shows a sample pressure-volume isotherm. Note that the horizontal lines between the liquid and gas phases are an unstable state. The fluid discontinuously transforms from the intersection at one side of the dashed curve to the other (e.g. boiling water undergoes a sudden change from liquid to vapor). The figure on the right shows the spreading of a thin layer of myristic acid on the surface of a liquid. Since the system is two-dimensional, the pressure is replaced by a force per volume (dyne/cm). As the layer is compressed or the temperature is raised, it exerts more pressure along its boundary.

I've always thought that phase diagrams are rich with information that is often hard to glean without a basic introduction to what all of those lines and points mean. I found this tutorial very helpful when I was working at Corning: Phase Diagrams Explained --BPappas 19:34, 28 September 2008 (UTC)

Examples

Milk

The gastroscience of milk provides many insights into the interparticle forces in a colloid. On its own, fresh whole milk segregates into a cream layer floating on top of a fat-depleted liquid. However homogenization was developed in France around 1900 to overcome this problem. By forcing hot milk through a surface of small nozzles, turbulence in the fluid tears the 4-micron fat globules into smaller particles closer to a micron in size. The original membrane surrounding the globules is insufficient to cover the greatly increased surface area of the globules. Since they are hydrophobic, they attract casein proteins from the surrounding liquid, which weight them down. The combination of smaller particle size and greater density allows Brownian motion to keep the particles in suspension.

Aggregation is another phenomenon that can lead to phase separation in a colloid. In the case of milk, additional ingredients or a change in acidity can cause the globules to stick together and separate from the liquid. This can happen with the addition of an acid, such as lemon juice. The astringent tannins in beverages like tea and coffee make this process more likely (which could be why one rarely adds both milk and lemon juice to tea).

To read more about the gastroscience of milk, see On Food and Cooking by Harold McGee (in the section "Unfermented Dairy Products") or Chapter 4 ("Colloidal dispersions") of Soft Condensed Matter by Richard A. L. Jones.

Water

...the most "complex" fluid...

In contrast to the simple example presented in many introductory physics textbooks, water can actually be considered one of the most "complex" fluids. A leader in the field of understanding the intricacies of phase transitions in water is Prof. Gene Stanley at Boston University. In a recent presentation (September 24, 2008) in the "Squishy Physics" lecture series at Harvard, he explained that there are 63 recorded anomalies in the physical properties of water. Some of these may be due to the asymmetrical structure of the molecule, which allows two different packing structures. At very low temperatures (well below zero celsius), the water forms regions in which these different types of packing occur. As the water freezes, the correlation length between similar packing structures increases, until the entire material forms a solid.

  • Note on packing: Interestingly, ellipsoids pack more closely than spheres during random orienting - such as packing in a fluid such as water. See Packing in the Spheres for more information.

Gecko Adhesion

The toes of the gecko adhere to a wide variety of surfaces, without the use of liquids or surface tension. Recent studies of the spatula tipped setae on gecko footpads demonstrate that the attractive forces that hold geckos to surfaces are van der Waals interactions between the finely divided setae and the surfaces themselves. Every square millimetre of a gecko's footpad contains about 14,000 hair-like setae. Each seta has a diameter of 5 micrometres. Human hair varies from 18 to 180 micrometre, so a human hair could hold between 3 to 30 setae. Each seta is in turn tipped with between 100 and 1,000 spatulae.

These van der Waals interactions involve no fluids; in theory, a boot made of synthetic setae would adhere as easily to the surface of the International Space Station as it would to a living room wall, although adhesion varies with humidity and is dramatically reduced under water, suggesting a contribution from capillarity. The setae on the feet of geckos are also self cleaning and will usually remove any clogging dirt within a few steps. Teflon, which is specifically engineered to resist van der Waals forces, is the only known surface to which a gecko cannot stick

A gecko can support about eight times its weight hanging from just one toe on smooth glass.

Here is a great paper on the subject Evidence For van der Waals adhesion in Gecko Setae

Cell Adhesion



Flow properties from molecular energies

Vicosity at short times.png For short time scales and simple liquids, the viscosity η can be approximated by the product of the instantaneous modulus G0 and the relaxation time τ.
Erying model of flow.png Erying model: When the strain is generated molecules are "trapped" inside an energy barrier of size ε and "jump" to a relaxed state with the characteristic time τ. While inside the barrier, the molecule vibrates with the characteristic frequency ν of the solid. Relaxation time in Eyring model.png
Viscosity with Erying model.png Combining these equations yields the Arrhenius behavior. In this case, ε is the heat of vaporization of the liquid, which is the upper bound of the energy barrier. This behavior can be seen experimentally by plotting the logarithm of viscosity as a function of the reciprocal of the temperature.



Impact of Bond Type on Physical Properties of a Solid

Melting point: The melting point of solids has an almost monotonically increasing relation with the cohesive energy - e.g., the following substances are arranged in order of increasing melting temperature : Ne (VdW bond), Na (simple metal), Fe (transition metal), KCl (ionic bond), Si (covalent bond).

Electrical and Thermal conductivity: For conducting current, some of the valence electrons must be free to move in response to an electric field - only in metallic bonds are the valence electrons delocalised sufficiently for this to be possible. Hence metals are good electrical conductors. Thermal conductivity is related to electrical conductivity (Wiedemann-Franz relation, first observed in 1853) - hence metals are also good thermal conductors.

Optical properties: Metals reflect light, non-metals are transparent. (http://www.imsc.res.in/~sitabhra/teaching/cmp03/class3.html)


Forces near surfaces

  • Bulk phases are characterized by density, free energy and entropy – not by forces.
  • Molecular forces average out.
  • Not so at surfaces.

Galileo Surface Forces.png Galileo reference.png







(Modern) forces near sufaces

  • (a) This potential is typical of vacuum interactions but is also common in liquids. Both molecules and particles attract each other.
  • (b) Molecules attract each other; particles effectively repel each other.
  • (c) Weak minimum. Molecules repel, particles attract.
  • (d) Molecules attract strongly, particles attract weakly.
  • (e) Molecules attract weakly, particles attract strongly.
  • (f) Molecules repel, particles repel.

Israelachvili Fig 10-1.gif
Israelachivili Fig.10.1






Interactions from molecular attraction

H.C. Hamaker, More than just a constant. Langmuir, 7, 209 - 211, 1991. Karol J. Mysels and Piet C. Scholten

"Recently we had the privilege of spending an afternoon with Hamaker, now a tall vigorous 85-year-old widower lining in Eindhoven, The Netherlands, and learned a bit about his interesting life. Thus we can shed some light on this bit of C&CS history." Thus follows:

Hamaker was born in 1905, obtained a Master's degee (doctoandus) in physics at the University of Utrecht. With a thesis on "The reflectivity and Emissivity of Tungsten" he obtained his doctorate in 1934. He wished to work in oceanography but could not find position so he accepted a position at the Phillips Research Laboratory in Eindhoven.

Following a suggestion from his first boss, J.H. de Boer, he worked on the nature of electrodeposition and the nature of the deposits. From that work he began to consider interparticle interactions that depend on a distant-dependent attraction and a distance-dependent repulsion - something of a new idea. He consider various electrical forces and, following the lead of de Boer, considered van der Waals interaction for the interaction between spheres. This derivation led to a separation between material constants and the geometry of the problem. The collection of material constants is called the Hamaker constant to this day. (H.C. Hamaker, Physica, 4, 1058, 1937. He gradually became more and more interested in statistics, particularly in quality control.

"The busy statistician had not time to follow the development of colloid science and was quite surprised when in 1965 his second son, who studied soil science, asked him, 'Dad, there is something called a Hamaker constant. Is it named after some relative of ours?'!"


Eqn molecular attraction.png
Israelachvili Fig 10-2.gif
Israelachivili Fig.10.2

  • (a) A molecule near a flat surface.
  • (b) A sphere near a flat surface.
  • (c) Two flat surfaces.


Eqn Molecule surface attraction.png
Eqn Sphere Surface Attraction.png
Eqn Surface Surface Attraction.png






Effect of molecular weight

Polymers derive a lot of their properties from the fact that they are long, random coils; it is not surprising that the length of these coils plays an important role in surface forces as well. For a given polymer (e.g. polystyrene), molecular weight will undoubtedly have a significant effect on:

- viscosity

- surface tension [1]

- melting point

- friction [2]

...


All of these, to a certain extent, are linked to either surface or intermolecular forces in some way. Therefore, since molecular weight has a significant impact on so many different physical properties of polymers, it is essential that molecular weight be specified as clearly as possible. It is crucial especially when properties depend non-linearly on the molecular weight (e.g. viscosity, as seen in Repulsion_-_Steric(entropic)).

So, what are the different ways to characterize molecular weight of a polymer? First of all, it must be emphasized that because people often synthesize and work with polymer chains several thousands of monomers long, the error on the molecular weight is not so small in the absolute. Polydisperse polymer solutions can have variabilities of well over 10% on the actual length of polymer chains within a solution, which, for polymer chains of <math>10^6</math> or more monomers, amounts to an error greater than <math>10^5</math> monomers! Polymer solutions are considered quite good (monodisperse) when the variability or standard deviation of the molecular weight distribution is on the order of a couple of percent.


Sometimes, scientists use the polydispersity index [3] to describe the quality of a polymer solution. This is the ratio of the weight-averaged molecular weight <math>M_w</math> and the number-averaged molecular weight <math>M_n</math>. Because <math>M_w</math> uses molecular weight to weight the average, that number is always higher than <math>M_n</math>; as a consequence, the polydispersity index is always greater than 1. A perfect monodisperse solution would have a polydispersity index of 1.

Scientists also describe a polymer solution through the viscosity-weighted average molecular weight. It is usually situated in the same range as <math>M_w</math> and <math>M_n</math>, but is a better descriptor of the material's bulk viscous properties. In the ideal case, one has direct access to the molecular weight distribution; in many simple cases however, one number is enough to describe the system globally and allows for simple thinking to be done on experiments. But again, especially when modeling physical properties that depend strongly and nonlinearly on the molecular weight (e.g. viscosity, as seen in Repulsion_-_Steric(entropic)), it might be best to fully characterize the molecular weight distribution of the solution, e.g. using MALDI [4].


Molecular weight.gif

[5]

Derjaguin Force Approximation

Israelachvili Fig 10-3.gif
Israelachivili Fig.10.3
Eqn Derjaguin Force Equation.png
Eqn Derjaguin Force Equation-II.png

Where W(D)is the energy of interaction of two flat plates.


Derjaguin Force Approximation has been deemed fairly accurate from a number of experiments. One experiment measuring interaction forces between colloidal particles of different sizes were conducted to investigate the validity of the approximation. Forces between silica particles of 2.0, 4.8, and 6.8mm in diameter were measured by an atomic force microscope. In this investigtion, the Derjaguin approximation is confirmed at all distances investigated. This approximation holds even at small distances, which are comparable to the surface roughness or the characteristic distance of a heterogeneously charged substrate. To read more about the investigation, the research by Samuel Rentsch, et al. is uploaded to the wiki. Research pdf



Casimir Effect

Most forces that are usually taken into account in soft matter physics are electro- or magneto-static in nature. That means that the forces are specifically due to the electric or magnetic attraction or repulsion between charges. As distances become sufficiently smaller (on the order of 10's of nm) quantum effects begin to become apparent.

From another perspective, since radiation can be modeled by waves, then each object generates a boundary condition for the radiation in the surrounding space. Thus two objects, when close enough, create strict boundary conditions on the electromagnetic field that is contained between them. When changing the distance between the objects these boundary conditions change. Boundary conditions impose a quantization of the frequencies of radiation than can exist in the space between the two objects. According to quantum mechanics, all radiation can be modeled as a simple harmonic oscillator and each radiation state has a non-zero energy even when no photons occupy that state. Thus even the vacuum has a non-zero energy that is determined by summing this fundamental energy over all modes of the field. However, this fundamental energy changes with the boundary conditions. Thus as two objects are moved with the respect to eachother, the "vacuum-energy" contained changes. A change of energy with respect to position manifests itself as a force!

Thus when two objects get close enough that the vacuum energy between them starts to change appreciably with distance, once can observer a non-negligible force between the two objects called the "Casimir Effect"

For example, at around 10nm, the force can be as high as 1atm of pressure.



Back to Topics.

Repulsive Van Der Waals Forces

While we usually think of Van der Waals forces as being attractive, Hamaker predicted repulsive Van der Waals forces in 1937 and they have since been seen experimentally. Repulsive van der Waals forces have been used to explain the properties of liquid helium, and have been seen on thin liquid hydrocarbon films on alumina and quartz. They are of great interest to researchers, despite their rarity, because they can be measured more easily by AFM techniques than attractive Van der Waals forces. This paper describes the use of AFM to study repulsive forces between Teflon thin films and silica and alumina.

http://courses.washington.edu/overney/ChemE554_Course_Mat/course_material/AFM%20repulsiveVdW.pdf.pdf

Nanotube switch

Jae Eun Jang et. al. have applied Van Der Waals and electrostatic forces to make a mechanical nanotube switch.

051010.jpg

The device is composed of carbon nanotubes attached to 3 electrodes. Two carbon nanotubes act as the switch, with the on state occurring when they touch. One of these electrodes is grounded, while the other has a positive bias. The third electrode is the gate electrode, which pushes the positively biased electrode towards the sources, turning on the switch. Depending upon the conditions, Van der Waals interactions can then cause the two electrodes to stick even after the voltage is reduced, or the interaction may be too weak and the tubes will spring back.

http://physicsworld.com/cws/article/news/23337