Structure and dynamics of two-dimensional colloidal hard spheres

Abstract

The structural and dynamic behaviour of quasi-two-dimensional monodisperse and bidisperse colloidal hard spheres are studied by optical microscopy. Firstly, a full characterisation of the equilibrium structure is presented through a consideration of structural correlation functions and number fluctuations. Comparison to fundamental measure theory and Monte Carlo simulations confirms both the behaviour of the system as a model for hard disks and the equation of state. The differing structural behaviour of binary systems at different size ratios is also discussed in relation to the nonadditivity. Next, the short- and long-time self-diffusion of particles is considered. Results for the long-time diffusion coefficient are again compared to Monte Carlo simulations, which demonstrates that at long times the dynamic behaviour is effectively not affected by hydrodynamic interactions. Additionally, simple theoretical expressions for the area fraction dependence of the short- and long-time diffusion coefficients are discussed. The selfdynamic properties of particles are probed further using the self-intermediate scattering function and the self-van Hove correlation function. In particular, the extent to which these quantities may be described by the Gaussian approximation is considered in relation to the relevant hydrodynamic limits for colloidal systems. A scaling relation to describe the crossover between these limits at short and long times is also developed. The consideration of dynamic behaviour is then extended to collective phenomena and, in particular, to the process of interdiffusion. Here, the thermodynamic and kinetic drives for this process are explored for binary systems at two different size ratios. The differing interdiffusive effects seen in the two systems are considered in light of the predictions of the Darken equation. Finally, the melting of quasi-two-dimensional colloidal hard spheres is studied by considering a monolayer of particles in sedimentation-diffusion equilibrium. Density profiles and the equation of state are used to characterise the system. These quantities display a discontinuity, indicating a coexistence gap and hence an interface. This interface is located and analysed using capillary wave theory, from which both the size of the coexistence gap and the anisotropic stiffness of the interface are determined.</p