Statistical mechanics McMillan-Mayer theory

The distinguishing feature of MM-level models is that the solvent molecules do not appear explicitly in the Hamiltonian. The potential function is the potential of the forces among the ions after averaging over solvent coordinates, i.e., the forces on the ions at any fixed locations in the solvent. The rigorous foundation for the use of such models is given by the McMillan-Mayer theory described in Section 4. This theory permits all of the statistical-mechanical apparatus and approximation methods developed for the calculation of equilibrium properties of BO-level models to be applied to MM-level models. For the calculation of dynamical properties the situation is not so satisfactory. A new set of forces, not derivable from a potential, must be taken into account the fluctuating forces exerted by the solvent on the ions and the... 

Much of the theory underlying the Pitzer equations was developed for gases and extended to electrolyte solutions largely by Joseph Mayer (Mayer and Mayer, 1940 Mayer, 1950), and especially McMillan and Mayer (1945). For a brief summary see McQuarrie (2000, Chapter 15) and for a comprehensive summary see Friedman, (1962). If you do consult these references, your knowledge of statistical mechanics had better be pretty good. Mazo and Mou (1991) describe the technical details in McMillan and Mayer as rather intricate. ... 

The primitive model of electrolytes constitutes a Arm basis for statistical-mechanical description of solutions of charged colloids. This model will be adopted throughout, and it originates from the more general McMillan-Mayer solution theory [62,63]. 

The complete analogy between various expansions in the total density in the gaseous phase, and expansions in the solute density in solution, has been developed by McMillan and Mayer (1945). In this chapter, we will be interested in the expansion (8.2) up to only the second-order term. For this purpose, we use the statistical mechanical expression for as obtained from the Kirkwood-Buff theory in Section 4.9 ... 

This is essentially the result of the McMillan-Mayer solution theory from statistical mechanics. 

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