Mayer-Montroll expansion

Figure 6.1 Mayer-Montroll expansion for the insertion probability p(0 X"). The notation here is fairly standard (see, for example, Hansen and McDonald, 1976 Andersen, 1977). The solid lines indicate factors of Mayer / functions introduced in Eq. (6.2) and are further discussed as Ursell functions beginning on p. 126. The inclusion-exclusion interpretation for hard-core cases is that the second term - assesses the m molecular volumes excluded to the...

The idea for the potential distribution theorem, and consequently the Mayer-Montroll expansion Eq. (6.3), is to consider a distinguished, additional molecule. The idea for the Kirkwood-Salsburg expansion is to consider a distinguished, additional, p h atom conditional upon the locations of (p — 1) others. We will consider the p = 2 case specifically. 

A depiction of these results is shown in Fig. 6.3. Notice that the Mayer-Montroll expansion for is obtained for large separations where both... 

The Mayer-Montroll (Mayer and Montroll, 1941) and Kirkwood-Salsburg (Kirkwood and Salsburg, 1953) expansions are storied parts of basic statistical thermodynamics (Stell, 1985), but have been neglected for practical purposes because of a lack of recognition of how simple and simplifying they can be. 

---