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

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 $c(\mathbf{r},{\mathbf{r}}^{\prime })$, 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.Chacón: Phys. Rev. Lett. {\bf 99}, p. 196101 (2007)).

8 pages, 1 figure

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