Combinatorial excess entropy

In the models discussed hitherto, we have always assumed that the molar volumes of the two components of the solution were very similar, so that the imperfection of the solution was attributed solely to interactions between the molecules. This hypothesis, though, is clearly not true in all cases -particularly in solutions of a polymer in a solvent - e.g. a solution of polystyrene in acetone, where the difference between the molar volumes is very significant acetone has a molar volume of 73 cm /mole, whilst that of polystyrene is, on average, 3333 cmVmole. In order to take account of this fact, we introduce the concept of combinatorial excess entropy, which is linked to the distributions of the molecules in the space. 

Flory and Huggins, simultaneously but independently of one another, constructed a term representing the excess entropy known as the conformation term or the combinatorial excess entropy. We shall now present their reasoning process for a mixture of small molecules, of a solvent A, and large one-dimensional molecules making up the solute B. The hypothesis at the heart of the model is still the pseudo-lattice, whose mesh is defined as follows the molecule of component A (the smallest molecules) determines the acceptable dimension on each site of the lattice - its base volume. The larger molecules of polymer (component B) are virtually divided into sequences of the same voliune as the small molecule, so that the large molecule contains sequences such that is equal to the ratio of the molar volumes of the two pure components ... 

Next, in Chapters, we present a number of solution models with microscopic definition, including random distribution models and models integrating the concepts of local composition and combinatorial excess entropy. 

The fourth chapter deals with the modeling of ionic solutions combining the term due to the electrical effects, found using the Debye and Huckel model, with the terms of local composition and combinatorial excess entropy found in the previous chapter. 

The entropic interaction parameter (Xs) is obtained from the partial molar excess entropy change of mixing (ASjexc) (not including the combinatorial part) ... 

We may compare (17.6.2) with the corresponding expression (10.7.4) for monomer mixtures. Apart from the combinatorial entropy and factors qjqA and CA/iA, these formulae are exactly the same, when the mole fractions xa and xb are replaced by Xa and Xb- We must also notice that in our present model the configurational specific heat at constant volume cvA vanishes as a consequence of our assumption that the cell partition functions do not depend on the temperature. Therefore the detailed discussion of the effect of intermolecular forces on excess functions presented in Ch. IX-XI, applies also to polymer mixtures. For example p will again give rise to positive deviations from ideality, positive excess entropy and heat absorption. We shall not go into more detail. 

More sophisticated models for have been developed from molecular principles. For example, the universal quasi-chemical theory, UNIQUAC, is an extension of the Wilson equation. It divides the excess Gibbs energy into two parts, one due to entropy, the combinatorial part, and one due to ener, the residual part ... 

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