Frozen capillary waves on glass surfaces: an AFM study

TL;DR

This study uses atomic force microscopy to demonstrate that the surface roughness of melted glass can be explained by frozen capillary waves, allowing measurement of physical parameters like interface tension and freezing temperature.

Contribution

It provides a quantitative analysis linking surface roughness to frozen capillary waves and introduces a method to measure interface tension and freezing temperature from surface spectra.

Findings

Roughness follows a logarithmic scaling law.

Interface tension and freezing temperature can be estimated from surface analysis.

Surface treatments affect the roughness spectrum measurable by AFM.

Abstract

Using atomic force microscopy on silica and float glass surfaces, we give evidence that the roughness of melted glass surfaces can be quantitatively accounted for by frozen capillary waves. In this framework the height spatial correlations are shown to obey a logarithmic scaling law; the identification of this behaviour allows to estimate the ratio $kT\_F/\pi\gamma$ where $k$ is the Boltzmann constant, $\gamma$ the interface tension and $T\_F$ the temperature corresponding to the ``freezing'' of the capillary waves. Variations of interface tension and (to a lesser extent) temperatures of annealing treatments are shown to be directly measurable from a statistical analysis of the roughness spectrum of the glass surfaces.