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)

An Example: 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.

Another Example: 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.

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.

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

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

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

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