Consequences of the renormalization group for the thermodynamics of fluids near the critical point

Abstract

We have obtained expressions including corrections to scaling terms for a number of thermodynamic properties of fluids near the critical point by specializing the appropriate derivatives of the logarithm of the grand partition function to trajectories of experimental interest. Our justification for applying Wegner's general predictions, for the functional form of the free energy, to this thermodynamic potential is that it is the potential for a fluid most closely analogous to the Helmholtz free energy for the Ising model. It is found that the average of the coexisting densities, the so-called rectilinear diameter, is a nonlinear function of the temperature with a temperature derivative which diverges like the constant volume specific heat, at the critical point, with a system-dependent coefficient. The second-temperature derivative of the chemical potential, along either the coexistence curve or the critical isochore, is found to be nondivergent at the critical point and its value is the same above and below $T_c$. The corrections due to the irrelevant scaling fields are found to be as important as those due to higher-order terms in the expansion of the scaling fields around the critical point. Using the parametric representation of the linear model, we have been able to obtain expressions for the elements of the matrix relating relevant scaling fields and physical variables in linear form, in terms of experimentally measurable quantities.