Three-body interactions, scaling variables, and singular diameters in the coexistence curves of fluids.

Abstract

Evidence is presented that the pair-potential model of fluids is insufficient in the critical region. In particular, data on the critical properties of Ne, ${\mathrm{N}}_{2}$, ${\mathrm{C}}_{2}$${\mathrm{H}}_{4}$, ${\mathrm{C}}_{2}$${\mathrm{H}}_{6}$, and ${\mathrm{SF}}_{6}$ are shown to exhibit well-defined trends in the variation of certain nonuniversal critical amplitudes with the critical temperature ${T}_{c}$. Both the slope of the coexistence-curve diameter far from the critical point, and the deviations from linear behavior which appear closer to ${T}_{c}$, increase systematically with ${T}_{c}$, and are directly correlated with the molecular polarizability. These trends are explained on the basis of the increasing importance of three-body dispersion (Axilrod-Teller) forces in the more polarizable systems, and a simple mean-field theory is developed which accounts for the observed correlations. The possibility of incorporating the effects of three-body interactions into an effective pair potential is explored within the context of perturbation theory in the grand canonical ensemble, and it is shown that such an interaction is explicitly a function of fugacity. In the critical region, this is equivalent to a thermal scaling field which depends on the bare chemical potential of the system, and ultimately leads to a breakdown in the classical law of the rectilinear diameter. The magnitude of this field mixing, and hence of the diameter anomaly, scales with the product of the particle polarizability and the critical number density, in agreement with experiment.