Configurational elastic interaction

Phase transitions in two-dimensional (adsorbed) layers have been reviewed. For the multicomponent Widom-Rowlinson model the minimum number of components was found that is necessary to stabilize the non-trivial crystal phase. The effect of elastic interaction on the structures of an alloy during the process of spinodal decomposition is analyzed and results in configurations similar to those found in experiments. Fluids and molecules adsorbed on substrate surfaces often have phase transitions at low temperatures where quantum effects have to be considered. Examples are layers of H2, D2, N2, and CO molecules on graphite substrates. We review the PIMC approach, to such phenomena, clarify certain experimentally observed anomahes in H2 and D2 layers and give predictions for the order of the N2 herringbone transition. Dynamical quantum phenomena in fluids are also analyzed via PIMC. Comparisons with the results of approximate analytical theories demonstrate the importance of the PIMC approach to phase transitions, where quantum effects play a role. 

Fig. 4.8. Elastic interaction of of crowdion with vacancy in metals (a) and F, H centres in alkali halides (b). Configuration 1 is energetically the most favourable with Eml = -0.043 eV.

The second contribution to the steric interaction arises from the loss of configurational entropy of the chains on significant overlap. This effect is referred to as entropic, volume restriction, or elastic interaction, Gei. The latter increases very sharply with a decrease in h when the latter is less than 8. A schematic representation of the variation of Gmix, Gei, G, and Gj =G X + Gei + Ga) is given in Fig. 10. The total energy-distance curve shows only one minimum, at h 25, the depth of which depends on 5, R, and A. At a given R and A, G decreases with an increase in 5. With small particles and thick adsorbed layers (5 > 5 nm), G, becomes very small (approaches thermodynamic stability. This shows the importance of steric stabilization in controlling the flocculation of emulsions and suspensions. 

A reduction of the configurational entropy of the chains in the interaction zone this entropy reduction results from the decrease in the volume available for the chains when these are either overlapped or compressed. This is referred to as volume restriction interaction, entropic or elastic interaction, and is described by a free energy of interaction, G j. 

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). 

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. 

Swelling of a polyelearolyte chain in salt solutions is one of the classical problems of polymer physics. The first attempt to account for the effect of the electrostatic interactions on conformations of a polyelectrolyte chain was made over 60 years ago by Kuhn, Kunzle, and Katchalsky and by Hermans and Overbeek (K3HO) by implementing a method that later became known as the Flory-like calculations of the chain size. In the framework of this approach, a free energy of polyelectrolyte chain consists of the chain s configurational (elastic) free energy... 

It may be shown that when the polymer concentration is large, the perturbation tends to be less. In particular, in a bulk polymer containing no diluent a = l for the molecules of the polymer. Thus the distortion of the molecular configuration by intramolecular interactions is a problem which is of concern primarily in dilute solutions. In the treatment of rubber elasticity—predominantly a bulk polymer problem—given in the following chapter, therefore, the subscripts may be omitted without ambiguity. 

Prior to a discussion of the theory of rubber elasticity, it is important to review how isolated polymer chains behave as this will provide a picture of the size and shape of a polymer. Clearly a polymer chain in a vacuum will collapse into a dense unit, but when in a solution the molecule will take on a conformation which is a function of the interaction with the surrounding molecules and the balance between the entropically driven tendency to maximise the spatial configuration and the connectivity of the monomer units. This is the case whether the chain is surrounded by small molecules (solvent) or other macromolecules that may or may not act like a solvent. 

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