Effective charges along the melting line of colloidal crystals

The shear modulus G of charged colloidal crystals was measured at several constant particle densities n and varying salt concentrations c up to the melting salt concentration cM using torsional resonance spectroscopy. Far from the phase boundary the samples are polycrystalline and the shear modulus stays roughly constant as a function of c. Upon approaching the melting transition an increasing amount of wall based crystal material is formed surrounding a shrinking polycrystalline core and G drops nearly linearly. When the transition is complete G again stays constant. The morphologic transitions may be scaled upon a single master curve. For the polycrystalline morphology, the elastic data are evaluated in terms of a pairwise additive screened Coulomb interaction yielding a particle effective charge Z(G)*. Under de-ionized conditions Z(0,G)* is independent of n and significantly lower than expected from charge renormalization theory. With increasing salt concentration Z(G)* increases. The increase becomes more pronounced at larger n. By extrapolation we further obtain the melting line effective elasticity charge Z(M,G)*. Z(M,G)* shows a steplike increase with increasing nM and cM to values consistent with charge renormalization theory. Interestingly, the increase coincides semi-quantitatively with the one expected from the universal melting line for charged spheres, thus facilitating a consistent description of phase behavior and elasticity over an extended range of the phase diagram.