The Heat and Free Energy of Mixing

If in a uniquely specified arrangement of the molecules in the solution there are pi2 pairs of unlike neighbors, i.e., 1,2 contacts, the heat of formation of that particular configuration from the pure components is 

This is just the well-known van Laar expression for the heat of mixing in any two-component system. Thus, within the limits of the approximations used, the polymeric character of the solute does not alter the form of the heat of mixing expression. To generalize somewhat, let the solvent molecule contain Xi segments instead of only one. Eq. (19) is then replaced by 

If the configurational entropy A Sm is assumed to represent the total entropy change LSm on mixing, the free energy of mixing is simply obtained by combining Eqs. (10) and (20). That is, 

In the case of a heterogeneous polymer comprising molecular species differing in size but otherwise equivalent chemically, substitution of Eq. (12) for ASm gives 

Expressions for the entropy and heat of mixing which are appropriate in the light of the above revision may be obtained from AFm through use of the standard thermodynamic relations 

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