Field-induced ordering phenomena and non-local elastic compliance in two-dimensional colloidal crystals

Abstract

Ordering phenomena in colloidal dispersions exposed to external one-dimensional, periodic fields or under confinement are studied systematically by Monte Carlo computer simulations. Such systems are useful models for the study of monolayers on a substrate. We find that the interaction with a substrate potential completely changes the miscibility of a binary, hard disc mixture at low external field amplitudes. The underlying ordering mechanisms leading to this laser-induced de-mixing differ, depending on which components interact with the substrate potential. Generic effects of confinement on crystalline order in two dimensions are studied in a model system of point particles interacting via a potential ∝ r −12. The state of the system (a strip of width D) depends very sensitively on the precise boundary conditions at the two confining walls. Commensurate, corrugated boundary conditions enhance both orientational order and positional order. In contrast, smooth repulsive boundaries enhance only the orientational order and destroy positional (quasi-)long range order. As external fields have a strong impact on the elastic behaviour of colloidal crystals there is a need to analyse the elastic response in such systems for the field-free case first. To this aim we study the strain-strain correlation functions in a two-dimensional crystal formed by super-paramagnetic colloids, as monitored by standard video microscopy.

Coarse-graining microscopic strains in a harmonic, two-dimensional solid: Elasticity, nonlocal susceptibilities, and nonaffine noise

“…For this reason the corresponding correlation functionsG 22 andG 33 exhibit only a four-fold rotational symmetry. As was discussed in [18], the presence of defects, breaks the rotational symmetries of the strain correlation functions.…”

Crystallization in three- and two-dimensional colloidal suspensions

“…Furthermore, the nature of the substrate surface also has a strong effect. The effects of two kinds of walls have been studied in a system with an inter-particle potential ∝r −12 [187], where r is the distance between particles. When the wall is formed by a crystal of fixed particles, a crystal with long-range order forms on the surface.…”

“…In 2d systems, the application of an external potential can induce a transition from quasi-long-range to true longrange translational order, if the periodicity of the external field is comparable to that of the crystal [188,187]. The effect of periodic light fields on the phase behavior has been studied in detail for 2d colloidal systems of magnetic particles with repulsive dipole-dipole interaction.…”

“…Recently, a binary hard-disc system with size ratio α = 0.414 has been studied by MC simulations with an external field of spatially periodic attractive lines [194,187]. For a weak external potential, de-mixing of large and small particles in the binary suspension is observed, which leads to the coexistence of ordered structures of large particles and a fluid of small ones.…”

Heterogeneous crystallization near structured walls in quenched two-dimensional binary colloidal suspensions

“…A similar setup for a one-component two-dimensional system was studied in [36]. The wall pattern exactly corresponds to the equilibrium crystal structure after the quench which is an alternating binary equimolar square crystal S(AB).…”