Potential energy surfaces configuration entropy

The Gibbs free energy G and the chemical potentials include contributions from the internal energy, vibrational free energy, and configurational entropy. Since most relevant stmctures will have a low surface free energy, we obtain from (5.4) that... 

We present an improved model for the flocculation of a dispersion of hard spheres in the presence of non-adsorbing polymer. The pair potential is derived from a recent theory for interacting polymer near a flat surface, and is a function of the depletion thickness. This thickness is of the order of the radius of gyration in dilute polymer solutions but decreases when the coils in solution begin to overlap. Flocculation occurs when the osmotic attraction energy, which is a consequence of the depletion, outweighs the loss in configurational entropy of the dispersed particles. Our analysis differs from that of De Hek and Vrij with respect to the dependence of the depletion thickness on the polymer concentration (i.e., we do not consider the polymer coils to be hard spheres) and to the stability criterion used (binodal, not spinodal phase separation conditions). 

If the dissociation of the ionizable groups on the particle surface is not complete, or the configurational entropy Sc of adsorbed potential-determining ions depends on N, then neither of ij/o nor of cr remain constant during interaction. This type of double--layer interaction is called charge regulation model. In this model, we should use Eqs. (8.35) and (5.44) for the double-layer free energy [ 11-13]. 

We derived this before, see [1.3.9.6 and 7. The configurational integral requires the computation of the potential energy of the system for all configurations of the system, that is for all x, y, z positions of all molecules (numbered 1, 2,. .. N) in a volume V. Equations [2.9.5 and 6] are exact for three-dimensional systems of monatomic fluids, be they ideal or non-ideal. Now we apply them to a surface phase and introduce approximations compatible with the energy-entropy de-coupling. 

There is a very large increase in interfacial surface area when an emulsion is formed from layers of two immiscible liquids. This can be a 7-8 order of magnitude increase. To accomplish this, work must be done, some of which remains in the system as potential energy and some of which is dissipated as heat. The free energy of formation, Gform-, is a function of the work done and the increase in configurational entropy ... 

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