Many-body interactions and the melting of colloidal crystals

Abstract

We study the melting behavior of charged colloidal crystals, using a simulation technique that combines a continuous mean-field Poisson-Boltzmann description for the microscopic electrolyte ions with a Brownian-dynamics simulation for the mesoscopic colloids. This technique ensures that many-body interactions between the colloids are fully taken into account, and thus allows us to investigate how many-body interactions affect the solid-liquid phase behavior of charged colloids.Using the Lindemann criterion, we determine the melting line in a phase-diagram spanned by the colloidal charge and the salt concentration. We compare our results to predictions based on the established description of colloidal suspensions in terms of pairwise additive Yukawa potentials, and find good agreement at high-salt, but not at low-salt concentration. Analyzing the effective pairinteraction between two colloids in a crystalline environment, we demonstrate that the difference in the melting behavior observed at low salt is due to many-body interactions. If the salt concentration is high, we find configuration-independent pair-forces of perfect Yukawa form with effective charges and screening constants that are in good agreement with well-established theories. At low added salt, however, the pair-forces are Yukawa-like only at short distances with effective parameters that depend on the analyzed colloidal configuration. At larger distances, in contrast, the pair-forces decay to zero much faster than they would following a Yukawa force law. This is explained with a screening effect of the macroions. Based on these findings, we suggest a simple model potential for colloids in suspension which has the form of a Yukawa potential, truncated after the first coordination shell of a colloid in a crystal. Using this potential in a one-component simulation, we find a melting line that shows good agreement with the one derived from the full PoissonBoltzmann-Brownian-dynamics simulation.2

Phase diagrams of hard-core repulsive Yukawa particles

“…one observes a sequence of fluid, FCC and again a fluid phase with increasing colloid volume fraction. Re-entrance is not seen in Yukawa systems [9][10][11][12] but has been observed in an earlier study on truncated Yukawa systems [3]. Although not studied here further, we expect that, because of the hard-core interaction, the fluid phase will freeze again to the FCC phase at high enough packing fractions, around η ≈ 0.5.…”

“…In section 2, we present the model and briefly discuss the methods used to calculate the phase diagram. In section 3, we present the results and make comparisons with the results of Dobnikar et al [3]. Finally, in section 4 we draw our conclusions.…”

“…With this value for x, both FCC and BCC have approximately equal numbers of neighbour interactions: 12 for FCC and 14 for BCC. A subtle difference between our model for the cut potential in equation (1) and the one used by Dobnikar et al [3] is that, while we truncate the pair potential, they truncate the force. Our motivation to truncate the potential instead of the force stems from the experiments [2] that suggest truncation in the pair potential.…”

“…The results of Dobnikar et al [3] were given in the so-called (λ,T ) representation, a typical way to represent phase diagrams of repulsive point Yukawa particles [11,12], while our results are given in (packing fraction η, Debye screening length 1/κσ ) representation. Therefore, in order to compare our results with those in [3], we need to define a mapping between the two systems.…”

“…Therefore, in order to compare our results with those in [3], we need to define a mapping between the two systems. The mapping that we present below is the same as in [9], where it was shown that, for sufficiently high β of the hard-core repulsive Yukawa potential, the phase boundaries are well described by those of point Yukawa particles by employing this mapping.…”