Melting of polydisperse colloidal crystals in nonequilibrium

Abstract

The influence of a time-dependent oscillatory external field on the melting transition of a polydisperse colloidal crystal is examined by theory and computer simulation. In a monodisperse crystal the field just induces an overall dynamical mode which does not affect the melting line. For a polydisperse sample, on the other hand, the field shifts the melting line towards smaller temperatures. Combining a solid cell approach and a Lindemann criterion in nonequilibrium, a simple theory is presented showing that the temperature shift scales with the square of the relative polydispersity. The theory is in reasonable agreement with nonequilibrium Brownian dynamics computer simulations.

Freezing and melting criteria in non-equilibrium

“…As has been shown earlier, the external field has no influence for a monodisperse system apart from adding a trivial overall dynamical mode [26]. Hence a finite polydispersity p Z > 0 is essential to drive the system into real non-equilibrium and the polydispersity itself measures the 'distance' from equilibrium.…”

“…Our model for non-equilibrium Brownian dynamics of charge-polydisperse colloids is defined as follows [26]: N colloidal particles confined to a volume (with a fixed number density ρ = N/ defining a mean interparticle spacing of a = ρ −1/3 ) are held at fixed temperature T . Two colloidal particles i and j are interacting via an effective screened Coulomb pair potential [29,30] …”

“…We have shown recently [26] that such a field shifts the freezing transition with respect to equilibrium freezing. The shift depends strongly on the field amplitude, scaling with the square of the relative polydispersity, and vanishes for very large field frequencies.…”

Melting of dusty plasma crystals in oscillating external fields

“…Such an approach was already applied to the completely overdamped Brownian dynamics in reference [16]. On average, the neighbour particles constitute a cage potential for which we assume no occupation correlations, i.e.…”

“…To access the solid melting curve we now use a generalized Lindemann rule [16,20]. According to this phenomenological criterion, a solid melts in equilibrium if the Lindemann parameter defined as…”