Asymmetric Fluid Criticality

Abstract

This work investigates features of critical phenomena in fluids. The canonical description of critical phenomena, inspired by the Ising model, fails to capture all features observed in fluid systems, specifically those associated with the density or compositional asymmetry of phase coexistence. A new theory of fluid criticality, known as "complete scaling", was recently introduced. Given its success in describing experimental results, complete scaling appears to supersede the previous theory of fluid criticality that was consistent with a renormalization group (RG) analysis of an asymmetric Landau-Ginzburg-Wilson (LGW) Hamiltonian. In this work, the complete scaling approach and the equation of state resulting from the RG analysis are shown to be consistent to order ε, where ε = 4 - d with d being the spatial dimensionality. This is accomplished by developing a complete scaling equation of state, and then defining a mapping between the complete scaling mixing-parameters and the coefficients of the asymmetric LGW Hamiltonian, thereby generalizing previous work [Phys. Rev. Lett. 97, 025703 (2006)] on mean-field equations of state. The seemingly different predictions of these approaches are shown to stem from an intrinsic ambiguity in the interpretation of the ε-expansion at fixed order. To first order in ε it is found that the asymmetric correction-to-scaling exponent θ5 predicted by the RG calculations can be fully absorbed into the 2β exponent of complete scaling.

Complete scaling is then extended to spatially inhomogeneous fluids in the approximation η=0, where η is the anomalous dimension. This extension enables one to obtain a fluctuation-modified asymmetric interfacial density profile, which incorporates effects from both the asymmetry of fluid phase coexistence and the associated asymmetry of the correlation length. The derived asymmetric interfacial profile is used to calculate Tolman's length, the coefficient of the first curvature correction to the surface tension. The previously predicted divergence of Tolman's length at the critical point is confirmed and the amplitude of this divergence is found to depend nonuniversally on the asymmetry of the correlation length.