From density to interface fluctuations: the origin of wavelength dependence in surface tensions

TL;DR

This paper derives a general expression for wavelength-dependent surface tension of fluctuating interfaces using equilibrium properties of density correlations, avoiding effective Hamiltonians or pressure differences.

Contribution

It introduces a new framework linking interface fluctuations to density correlations, generalizing previous surface tension concepts without relying on effective Hamiltonians.

Findings

Provides a general formula for $ ext{γ}( ext{q})$ based on density correlations.

Clarifies the relation between interface fluctuations and microscopic density properties.

Reconciles previous criticisms of the Mecke/Dietrich surface tension.

Abstract

The height-height correlation function for a fluctuating interface between two coexisting bulk phases is derived by means of general equilibrium properties of the corresponding density-density correlation function. A wavelength-dependent surface tension $\gamma(\mathbf{q})$ can be defined and expressed in terms of the direct correlation function $c(\mathbf{r},\mathbf{r}')$, the equilibrium density profile $\rho_{\circ}(\mathbf{r})$ and an operator which relates density to surface configurations. Neither the concept of an effective interface Hamiltonian nor the difference in pressure is needed to determine the general structure of the height-height correlations or $\gamma(\mathbf{q})$, respectively. This result generalizes the Mecke/Dietrich surface tension $\gmd$ (Phys. Rev. E {\bf 59}, p. 6766 (1999)) and modifies recently published criticism concerning $\gmd$ (P. Tarazona, R. Checa and, E.Chac\'{o}n: Phys. Rev. Lett. {\bf 99}, p. 196101 (2007)).