Hyperscaling relationship between the interfacial tension of liquids and their correlation length near the critical point

Abstract

Interfaces involving coexisting phases in condensed matter are essential in many phenomena: wetting, nucleation, morphology, phase separation kinetics, membranes, phase coexistence in nanomaterials, etc. The majority of analytical theories available use concepts derived from mean field artifacts which do not describe adequately these systems. Satisfactory numerical simulation of interfaces at the atomistic to mesoscopic scale is still a challenge. In the present work, the interfacial tension between mixtures of organic solvents and water is obtained from mesoscopic computer simulations. The temperature dependence of the interfacial tension is found to obey a scaling law with an average critical exponent μ = 1.23. Additionally, we calculate the evolution of the correlation length, defined as the thickness of the interface between the immiscible fluids, as a function of temperature and find that it obeys also a scaling law with an average critical exponent being ν = 0.67. Finally, we show that the comparison of μ and ν for these binary mixtures constitutes the first test of Widom's hyperscaling relationship between these exponents in 3d, expressed as μ = ν (d – 1). Based on these values and those for the 3d Ising model it is argued that both systems belong to the same universality class, which opens up the way for the calculation of new scaling exponents.