Asymmetry in the Liquid and Vapor Density Fluctuations at the Critical Point

Abstract

Recent theoretical evidence has suggested that in general the temperature derivative of the diameter of the liquid-vapor coexistence curve should diverge at the critical point at least as fast as the constant-volume specific heat. This evidence implies with equal force that the difference across the coexistence curve in the density fluctuations in the two phases, $\Delta {\left(\frac{\partial \rho }{\partial \mu }\right)}_T={\left(\frac{\partial \rho }{\partial \mu }\right)}_T^L-{\left(\frac{\partial \rho }{\partial \mu }\right)}_T^V$, should in general diverge at least as fast as the temperature derivative of the liquid-vapor density difference: $\Delta {\left(\frac{\partial \rho }{\partial \mu }\right)}_T\sim \left(\frac{d}{\mathrm{dT}}\right)\Delta \rho \sim {(T_c-T)}^{\beta -1\mathrm{}}$. Experimental estimates of this quantity would provide an alternative test of those hypotheses that currently predict a singular diameter.