Melting Of Colloidal Crystals Research Articles

Observation of two-step melting on a sphere

Melting in two-dimensional flat space is typically two-step and via the hexatic phase. How melting proceeds on a curved surface, however, is not known. Topology mandates that crystalline particle assemblies on these surfaces harbor a finite density of defects, which itself can be ordered, like the icosahedral ordering of 5-coordinated disclination defects on a sphere. Thus, melting even on a sphere, the simplest closed surface, involves the loss of both crystalline and defect order. Probing the interplay of these two forms of order, however, requires a system in which melting can be performed in situ, and this has not been achieved hitherto. Here, by tuning interparticle interactions in situ, we report an observation of an intermediate hexatic phase during the melting of colloidal crystals on a sphere. Remarkably, we observed a precipitous drop in icosahedral defect order in the hexatic phase where the shear modulus is expected to vanish. Furthermore, unlike in flat space, where disorder can fundamentally alter the nature of the melting process, on the sphere, we observed the signature characteristics of ideal melting. Our findings have profound implications for understanding, for instance, the self-assembly and maturation dynamics of viral capsids and also phase transitions on curved surfaces.

Many-body interactions and the melting of colloidal crystals

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 among 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 pair-interaction 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-type only at short distances with effective parameters that depend on the analyzed colloidal configuration. At larger distances, the pair-forces decay to zero much faster than they would following a Yukawa force law. 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 Poisson–Boltzmann–Brownian-dynamics simulation.

Theory of shear-induced melting of colloidal crystals.

We propose a theory of shear-induced melting of colloidal crystals based on a nonequilibrium generalization of first-order freezing theory. The results agree qualitatively with experiment.