Interaction free energy between two

Solution The free energy of interaction between a perfect sphere and a flat surface goes as [-(AHam/6)](R//) whereas the interaction free energy between two flats goes as -( Ham/127r/2) per area. What if the sphere flattens slightly ... 

A similar procedure can be used to calculate the interaction free energy between two undulating (or rough) surfaces. Assumingthat the separation distance between surfaces is normally distributed around H with a dispersion o, the interaction free energy is given by... 

In this appendix we provide the generalized equations for the mean-field potential and double layer interaction free energy between two surfaces having distinct but periodic nonuniform distributions. These results were taken from Ref. [78]. We denote by yL(s) the charge distribution on the left (L) surface at z = 0 and yR(s) that on the right (R) surface at z — h. As in the text the variable y represents either surface potential, T (s), or surface charge, periodic distribution represented by the Fourier expansions,... 

FIGURE 6.12 The scaled interaction free energy between two equal-sized spheres, with Ka = 10 a being the sphere radius) for several values of the dimensionless surface potential and at various ratios of the surface potentials. Results are shown for (a) constant potential interaction with 2/ 1 = (b) constant charge interaction with = 3. 

Figure 3.8 Non-retarded van der Waals interaction free energy between two perpendicular cylinders, w = —Aj (6Z)) with D the distance between the...

Saroff and Minton (1972) correctly pointed out that A unan s quantity, WY, defined in Eq. (5.8.1), cannot serve as an average interaction free energy between the ligands. It is easy to see that Wyman s quantity is the difference in the work associated with the following two processes, denoted and P, ... 

When the radius of the spherical colloidal particles a is much larger than the shortest distance between the surfaces of two colloidal particles, the free energy between two identical spherical particles, due to double-layer, steric, and depletion interactions, can be calculated using the Derjaguin approximation 2... 

Figure 3.2 Interaction between elements of volume dV containing qdV molecules, which on summation for all pairs oj volume elements gives the total-interaction free energy between the two bodies (a) particles oj arbitrary shape, (b) two parallel semi-infinite plates a distance H apart, (c) two spheres whose surfaces are a distance H apart.

The Rory-Huggins free energy of mixing, appropriately modified, is conveniently used for this purpose.(3,257) There are essentially two major contributions to the mixing free energy, the combinatorial entropy and the net interaction free energy between the polymer and diluent. The latter can be expressed as (258,259)... 

The interaction free energy per unit area between two planar double layers V(L) is just the difference between the change in free energy per unit area in charging up two surfaces at a distance L apart and that at infinite separation... 

Detailed numerical examples of the behaviour of the surface charge and surface potential when the electrical double layer of two identical amphoteric surfaces overlap and interact are available in the literature (8). Examples of the differences between the form of the interaction free energy under constant... 

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