Hyperscaling of the correlation length, interfacial tension, and specific heat in two-dimensional and quasi-two-dimensional liquids.

Abstract

The line tension of two immiscible liquids under two-dimensional and quasi-two dimensional conditions is calculated as a function of temperature, using mesoscale numerical simulations, finding that it decays linearly. The liquid-liquid correlation length, defined as the thickness of their interface, is also predicted as the temperature is varied, and it diverges as the temperature becomes close to the critical temperature. These results are compared with recent experiments on lipid membranes and good agreement is obtained. The scaling exponents of the line tension (μ) and the spatial correlation length (ν) with temperature are extracted, finding that they fulfill the hyperscaling relationship, μ=d-1ν, where d is the dimension. The scaling of specific heat with temperature of the binary mixture is obtained as well. This is the first report of the successful test of the hyperscaling relation between μ and ν for d = 2 and for the non-trivial case of quasi-two dimensions. This work can help to understand experiments that test properties of nanomaterials using simple scaling laws, without needing to know specific chemical details of those materials.