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| 3D Pressure-volume isotherms
|| 2D Spreading pressure-area isotherms
| 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.
Flow properties from molecular energies
|| 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: 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.
|| 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.
(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.
Interactions from molecular attraction
- (a) A molecule near a flat surface.
- (b) A sphere near a flat surface.
- (c) Two flat surfaces.
Derjaguin Force Approximation
Where W(D)is the energy of interaction of two flat plates.
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