Shear modulus of two-dimensional colloidal crystals

A new method for the determination of elastic constants of colloidal systems is described. We study super-paramagnetic microspheres confined by gravity to a two-dimensional layer at a water-air interface. Under an external vertical magnetic field the particles arrange in a crystalline triangular phase because of the repulsive dipole-dipole interaction. By use of an optical tweezer, one triangle formed by three spheres is rotated from its equilibrium position and the relaxation time measured using video-microscopy. We demonstrate that this time is directly related to the shear modulus mu of the crystal and study mu as a function of the magnetic particle interaction strength.