Shape and effective spring constant of liquid interfaces probed at the nanometer scale: finite size effects

TL;DR

This study explores the shape and mechanical properties of liquid interfaces at nanometer scales using AFM and SEM, revealing how size and confinement influence the effective spring constant and confirming the meniscus shape with high-resolution imaging.

Contribution

It provides a comprehensive analysis of nanometer-scale liquid interfaces, linking the spring constant to surface tension and lateral confinement effects, validated by experimental and theoretical models.

Findings

Spring constant proportional to surface tension, independent of frequency.

Meniscus shape confirmed as catenary through electron microscopy.

Lateral confinement affects spring constant logarithmically.

Abstract

We investigate the shape and mechanical properties of liquid interfaces down to nanometer scale by atomic force microscopy (AFM) and scanning electron microscopy (SEM) combined with in situ micromanipulation techniques. In both cases, the interface is probed with a cylindrical nanofiber with radius R of the order of 25-100 nm. The effective spring constant of the nanomeniscus oscillated around its equilibrium position is determined by static and frequency-modulation (FM) AFM modes. In the case of an unbounded meniscus, we find that the effective spring constant k is proportional to the surface tension {\gamma} of the liquid through k = (0.51 +- 0.06) {\gamma}, regardless of the excitation frequency from quasistatic up to 450 kHz. A model based on the equilibrium shape of the meniscus reproduces well the experimental data. Electron microscopy allowed to visualize the meniscus profile around the fiber with a lateral resolution of the order of 10 nm and confirmed its catenary shape. The influence of a lateral confinement of the interface is also investigated. We showed that the lateral extension L of the meniscus influences the effective spring constant following a logarithmic evolution k ~ 2{\pi}{\gamma}/ln(L/R) deduced from the model. This comprehensive study of liquid interface properties over more than four orders of magnitude in meniscus size, shows that advanced FM-AFM and SEM techniques are promising tools for the investigation of mechanical properties of liquids down to nanometer scale.