Elastic Behavior of a Two-dimensional Crystal near Melting

TL;DR

This study measures the elastic properties of 2D colloidal crystals near melting, confirming the KTHNY theory's prediction that Young's modulus approaches 16π at the transition.

Contribution

It provides experimental validation of the KTHNY theory's universal melting criterion using video-microscopy data.

Findings

Young's modulus approaches 16π at melting

Elastic moduli decrease with temperature

Experimental data supports KTHNY predictions

Abstract

Using positional data from video-microscopy we determine the elastic moduli of two-dimensional colloidal crystals as a function of temperature. The moduli are extracted from the wave-vector-dependent normal mode spring constants in the limit $q\to 0$ and are compared to the renormalized Young's modulus of the KTHNY theory. An essential element of this theory is the universal prediction that Young's modulus must approach $16 \pi$ at the melting temperature. This is indeed observed in our experiment.