Perturbation theory Mayer function

Thermodynamic perturbation theory is used to expand the Boltzmann distribution in the dipolar interaction, keeping it exact in the magnetic anisotropy (see Section II.B.l). A convenient way of performing the expansion in powers of is to introduce the Mayer functions fj defined by 1 +fj = exp( cOy), which permits us to write the exponential in the Boltzmann factor as... 

The theoretical techniques used most frequently in this context are perturbation theories of the type discussed in Section III.C based upon spherical reference systems. Thompson et al. focus upon perturbation expansions of the molecular density, p(r, pair potential or the Mayer function to parametrize the expansion. If the pair potential is used, then to first order they obtain... 

As we stated at the beginning of this section, most of the work in this area has focused upon the study of molecular orientation at the liquid-vapor interface and how this is affected by details of the intermolecular forces. Thompson and Gubbins have carried out molecular dynamics simulations of the vapor-liquid interface for homonuclear 12-6 diatomic molecules and for such molecules with point-charge quadrupoles. They find that in the case of the nonpolar molecules, there is a tendency for molecules in the liquid to align perpendicular to the surface and those in the vapor to align parallel to the surface. The addition of a quadrupole to the 12-6 diatomic " reverses this effect. A study of the vapor-liquid interface for an interaction site model of -octance leads to similar conclusions as for the nonpolar diatomic. These effects are reproduced qualitatively by all the theoretical approximations, with the exception of the influence of the quadrupole, which can only be predicted at first order within the context of the perturbation theory based upon division of the Mayer function Eq. (3.5.2). 

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