Two-dimensional melting revisited

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Abstract
The two-dimensional melting behaviour of the inverse-twelfth-power system and its dependence on boundary and initial conditions has been re-examined with long molecular dynamics simulation runs. The system consists of 1225 particles, which in a first series of runs is being simulated under standard periodic boundary conditions. It is feasible to reconcile some central simulation results with the experimental data of Murray et al., 1987, Phys. Rev. Lett., 58, 1200 for possible two-stage melting of submicron-sized charged colloidal spheres in liquid water. In another series of simulations, the particles are confined to a roughly rectangular cell with irregularly shaped walls. The energy as a function of density is found to be very sensitive to the choice of boundary conditions. The dependence on the initial conditions is studied by setting up the latter simulations with different sets of starting coordinates—some of them probably those of a hexatic phase—which were directly obtained from Murray et al.'s experimental data for colloidal suspensions. Using the short ranged r -12 potential, molecular dynamics simulations of these configurations were examined over five million time steps each. The initial order, even if experimentally found to be consistent with that of a hexatic phase, is not seen to undergo any rapid breakup. This suggests that kinetic bottlenecks limiting equilibration are still important, even for runs of this length.

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