Flory-Huggins Lattice-graph Models

Much of the progressive development of lattice-graph theories is charted in the form attached to the final, excess free energy , term in equation (4) initially added to extend the compass of the model to systems in which the enthalpy of mixing, while small, is not zero. That is, various arrangements of the system do not have the same energy as was assumed by Flory and Huggins. The interaction function, g, taken by them to be a function of temperature alone, was shown later to require a concentration dependence also. Since then, power series representations  

For ternary, quasi-temary, etc., systems, equation (4) is generalized in obvious ways (see also p. 320). For sample, for a polymer (p) in two solvents (1,2)  

In a similar vein, Scott extended the lattice-graph argument to mixtures of random copolymers to obtain  

Cohen has noted, from the general thermodynamics of phase transitions, that partial derivatives at constant pressure and at constant temperature show quite different divergence characteristics along spinodal and critical loci. This important effect disappears in lattice-graph models where no allowance is made for volume changes on mixing. Furthermore, density (volume) fluctuations which 

There is growing interest in what have been called lattice gas (fluid) models. These envisage a fluid to be a mixture of molecules and holes. In essence they are lattice-graph models in which some of the lattice sites are occupied while others remain empty (holes). Originally introduced by Sanchez and Lacombe they have been more recently developed by them - in terms of an equation-of-state approach (see p. 305). Such models offer an attractive and combinatorially transparent alternative to free volume (holes) extensions of corresponding states theories (see next section), which have been much described by Dayantis. Thornley and Shepherd comment that preliminary results using this model indicate that it might be the most accurate so far . 

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