Use of Liquid-Droplet Model in Calculations of the Critical Exponentδ

Abstract

The liquid-droplet model is used to derive a formula relating the exponent $\delta$ and the compressibility factor $\frac{P_c}{k_{\mathrm{B}}{T}_c{\rho }_c}$ at the critical point of a fluid. For fluids (the van der Waals continuum, the Bragg-Williams lattice gas, and Ising lattice gases) where both these quantities are known, the proposed relation is in agreement with experiment and theoretical prediction. Therefore, in other cases this relation may be used to predict $\delta$ from the known $P_c$, $T_c$, and ${\rho }_c$. On this basis we predict a $\delta$ between 4.2 and 4.5 for nonpolar molecules, about 5 for hydrocarbons, and larger than 5 for polar molecules.