Two-dimensional Colloidal Fluids Research Articles

Two-dimensional colloidal fluids exhibiting pattern formation.

Fluids with competing short range attraction and long range repulsive interactions between the particles can exhibit a variety of microphase separated structures. We develop a lattice-gas (generalised Ising) model and analyse the phase diagram using Monte Carlo computer simulations and also with density functional theory (DFT). The DFT predictions for the structures formed are in good agreement with the results from the simulations, which occur in the portion of the phase diagram where the theory predicts the uniform fluid to be linearly unstable. However, the mean-field DFT does not correctly describe the transitions between the different morphologies, which the simulations show to be analogous to micelle formation. We determine how the heat capacity varies as the model parameters are changed. There are peaks in the heat capacity at state points where the morphology changes occur. We also map the lattice model onto a continuum DFT that facilitates a simplification of the stability analysis of the uniform fluid.

Cross-over between central and non-central conservative effective forces in a modulated colloidal fluid

We study by Monte Carlo simulations the effective forces between two particles dispersed in a two-dimensional colloidal fluid, modulated in one direction by a spatially periodic external potential. When the modulation strength exceeds the strength of interaction between the dispersed and dispersing particles, the anisotropic effective forces, show cross-over between central and non-central nature, although the effective forces remain conservative. The non-central nature of the effective forces depends on the orientation of the separation vector between the dispersed particles with respect to the modulation direction.

On the interplay between sedimentation and phase separation phenomena in two-dimensional colloidal fluids

Colloidal particles that are confined to an interface effectively form a two-dimensional fluid. We examine the dynamics of such colloids when they are subject to a constant external force, which drives them in a particular direction over the surface. Such a situation occurs, for example, for colloidal particles that have settled to the bottom of their container, when the container is tilted at an angle, so that they ‘sediment’ to the lower edge of the surface. We focus in particular on the case when there are attractive forces between the colloids which causes them to phase separate into regions of high density and low density and we study the influence of this phase separation on the sedimentation process. We model the colloids as Brownian particles and use both Brownian dynamics computer simulations and dynamical density functional theory (DDFT) to obtain the time evolution of the ensemble average one-body density profiles of the colloids. We consider situations where the external potential varies only in one direction so that the ensemble average density profiles vary only in this direction. We solve the DDFT in one-dimension, by assuming that the density profile only varies in one direction. However, we also solve the DDFT in two dimensions, allowing the fluid density profile to vary in both the x- and y-directions. We find that in certain situations the two-dimensional DDFT is clearly superior to its one-dimensional counterpart when compared with the simulations and we discuss this issue.

Long-time behavior of the shear-stress autocorrelation function in two-dimensional colloidal fluids

Brownian dynamics simulations of two-dimensional Yukawa particles have been performed over a range of fluid densities in order to study the long-time behavior of the stress autocorrelation function in simple models for colloidal liquids. The system size and the trajectory length dependence of the shear stress autocorrelation function have been investigated in detail for simulation trajectories of length in excess of 1600${\mathrm{\ensuremath{\sigma}}}^{2}$/${\mathrm{D}}_{0}$. The results indicate that the decay of the shear-stress autocorrelation function has a fractional exponential form and is not algebraic in time, certainly up to times \ensuremath{\sim}${\mathrm{\ensuremath{\sigma}}}^{2}$/${\mathrm{D}}_{0}$ at which time the correlation function has decayed statistically to zero.

Cross-correlation intensity fluctuation spectroscopy applied to colloidal suspensions

The method of cross-correlation intensity fluctuation spectroscopy (CCIFS) is presented and contrasted with other scattering techniques. While standard scattering techniques monitor structure factors which are related to particle pair correlation functions, the CCIFS technique is sensitive to higher-order correlation functions and may be used to monitor the local particle order in condensed phases. To demonstrate the CCIFS technique, cross-correlation data for scattering from a two-dimensional colloidal monolayer is presented. These cross-correlation data indicate a local hexagonal structure in the fluid phase. A model calculation is presented which treats the two-dimensional colloidal fluid phase as a randomly oriented hexagonal solid with large lattice vibrations. The results of this calculation are in qualitative agreement with experimental observation.