Loss in configurational entropy

In other words, the loss in configurational entropy is due to a loss in molecular... 

Flocculation into a minimum of the type depicted in figure 7 will be opposed by the loss in configurational entropy of the particles. We may formally express this by the equation (30,31),... 

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). 

This arises from the loss in configurational entropy of the chains on the approach of a second particle. As a result of such an approach the volume available for the chains becomes restricted, which results in a loss of the number of configurations. This can be illustrated by considering a simple molecule, represented by a rod that rotates freely in a hemisphere across a surface (Figure 8.3). When the two surfaces are separated by an infinite distance, 00, the number of configurations of the rod is 2(oo), which is proportional to the volume of the hemisphere. When a second... 

Entropic, volume restriction or elastic interaction, G p This results from the loss in configurational entropy of the chains on significant overlap. Entropy loss is unfavourable and, therefore, G j is always positive. A combination of G,. with G gives the total energy of interaction Gj (theory of steric stabilisation). 

By way of contrast, the segments are mutually repulsive in a good solvent since, by definition, contacts with solvent molecules are enthalpically favoured. This tends to cause the polymer chains to swell, a process that is counteracted by the loss in configurational entropy as the chains expand. Nonetheless, the polymer molecules are mutually repulsive so that the volume available in the polymer solution is effectively reduced below the nominal volume. This causes the effective polymer concentration to be greater than that expected for an ideal system and results in positive deviations from ideality. 

The second repulsive effect resulting from the presence of the adsorbed layers is the loss in configurational entropy of the chains when significant overlap occurs. This effect, which is always repulsive, is referred to as an entropic, volume-restriction or elastic interaction, Gei. 

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