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arXiv · 0902.3363

Derivation of the phase field crystal model for colloidal solidification

Sven van Teeffelen·Rainer Backofen·Axel Voigt·Hartmut Löwen
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Abstract

The phase-field crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field crystal dynamics can be derived from the microscopic Smoluchowski equation via dynamical density functional theory. The different underlying approximations are discussed. In particular, a variant of the phase-field crystal model is proposed which involves less approximations than the standard phase-field crystal model. We finally test the validity of these phase-field crystal models against dynamical density functional theory. In particular, the velocities of a linear crystal front from the undercooled melt are compared as a function of the undercooling for a two-dimensional colloidal suspension of parallel dipoles. Good agreement is only obtained by a drastic scaling of the free energies in the phase-field crystal model in order to match the bulk freezing transition point.

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Sven van Teeffelen, Rainer Backofen, Axel Voigt, Hartmut Löwen. 2009-05-28. Derivation of the phase field crystal model for colloidal solidification. https://doi.org/10.1103/physreve.79.051404

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