Lattice model for ideal and regular solutions

In this appendix, we present a very brief outline of the lattice theory of ideal and regular solutions, developed mainly by Guggenheim (1952). The main reason for doing so is to emphasize the first-order character of the deviations from SI, equation (M.12) below. 

The system consists of M lattice sites occupied by a mixture of NA molecules A and NB molecules B, such that NA + NB = M (figure M.l). It is assumed that A and B have roughly the same size and that they can exchange sites without disturbing the structure of the lattice. 

For each configuration of the system, the canonical partition function is written as 

Therefore, the energy level E is determined by the single parameters NAB. Hence, we can replace the sum over j in (M.l), by a sum over all possible Nab, i-e-  

Although g(NAB) is a very complicated function, we know that the sum over all g(NAB) must be the total number of configurations, i.e., 

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