Elastic Properties of 2D Colloidal Crystals from Video Microscopy

Elastic constants of two-dimensional (2D) colloidal crystals are determined by measuring strain fluctuations induced by Brownian motion of particles. Paramagnetic colloids confined to an air-water interface of a pendant drop are crystallized under the action of a magnetic field, which is applied perpendicular to the 2D layer. Using video microscopy and digital image processing we measure fluctuations of the microscopic strain obtained from random displacements of the colloidal particles from their mean (reference) positions. From these we calculate system-size dependent elastic constants, which are extrapolated using finite-size scaling to obtain their values in the thermodynamic limit. The data are found to agree rather well with zero-temperature calculations.