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We present a Brownian dynamics simulation study of static and dynamic properties of quasi-two-dimensional dispersions of colloidal spheres interacting by long-range screened electrostatic and by dipolar magnetic forces, respectively. The calculated van Hove real-space dynamic correlation functions, mean squared displacements, and hydrodynamic functions are shown to obey a dynamic scaling behavior in terms of a characteristic relaxation time related to the geometrical mean particle distance. Hydrodynamic interactions introduce a second characteristic length scale, and they lead to a more restricted scaling behavior with an enhancement of self-diffusion. As a consequence of dynamic scaling, the dynamical criterion of Lowen @Phys. Rev. E 53, R29 ~1996!# for the onset of colloidal freezing is shown to be equivalent to a two-dimensional freezing criterion related to the static structure factor. © 2001 American Institute of Physics. @DOI: 10.1063/1.1366637# I. INTRODUCTION During the last several years, a lot of experimental and theoretical effort has been devoted to studying the static and dynamic properties of quasi-two-dimensional ~Q2D! disper- sions of colloidal particles. Experimentally well-studied ex- amples of such dispersions are charged colloidal particles confined between two narrow glass plates, 1-3 and superpara- magnetic colloidal particles suspended in water at a water- air interface ~hanging-drop geometry! and interacting via re- pulsive dipolar magnetic forces due to an applied magnetic field. 4 Part of the interest in these systems arises from the fact that, contrary to low-molecular liquids, the range, strength, and even the sign of the particle interactions can be experimentally controlled. Moreover, the particle trajectories of micron-sized colloidal particles can be directly tracked using video microscopy imaging.2 One area of intensive research is concerned with the na- ture of two-dimensional freezing and melting. Contrary to three-dimensional freezing, which is a first-order phase tran- sition, two-dimensional freezing may be a two-stage process of continuous phase transitions with an intermediate hexatic phase of long-range orientational order. 5 Strong experimental evidence for such a two-stage transition scenario has indeed been found very recently for magnetic particle monolayers with long-range dipolar repulsion.4

Brownian dynamics study of dynamic scaling and related freezing criteria in quasi-two-dimensional dispersions