Liquid-Gas Asymmetry and the Wavevector-Dependent Surface Tension

TL;DR

This paper investigates the challenges in extending capillary-wave theory to microscopic wavelengths by analyzing a density functional model, revealing the importance of a microscopic length scale $ \zeta(q)$ in understanding surface tension at the liquid-gas interface.

Contribution

It introduces a new scheme for separating microscopic observables into background and interfacial parts, emphasizing the role of a $q$-dependent length scale $ \zeta(q)$ in interpreting surface tension.

Findings

Identification of a $q$-dependent length $ \zeta(q)$ crucial for consistent interpretation.

Explicit illustration of the impact of $ \zeta(q)$ on the uncertainty of $ \sigma_ ext{eff}(q)$.

Highlighting the implications for experimental and simulation studies.

Abstract

Attempts to extend the capillary-wave theory of fluid interfacial fluctuations to microscopic wavelengths, by introducing an effective wave-vector ($q$) dependent surface tension $\sigma_\text{eff}(q)$, have encountered difficulties. There is no consensus as to even the shape of $\sigma_\text{eff}(q)$. By analysing a simple density functional model of the liquid-gas interface, we identify different schemes for separating microscopic observables into background and interfacial contributions. In order for the backgrounds of the density-density correlation function and local structure factor to have a consistent and physically meaningful interpretation in terms of weighted bulk gas and liquid contributions, the background of the total structure factor must be characterised by a microscopic $q$-dependent length $\zeta(q)$ not identified previously. The necessity of including the $q$ dependence of $\zeta(q)$ is illustrated explicitly in our model and has wider implications, i.e. in typical experimental and simulation studies, an indeterminacy in $\zeta(q)$ will always be present, reminiscent of the cut-off used in capillary-wave theory. This leads inevitably to a large uncertainty in the $q$ dependence of $\sigma_\text{eff}(q)$.