We study the static and dynamic properties of bromine electrosorption onto single-crystal silver (100) electrodes by Monte Carlo simulation. At room temperature the system displays a second-order phase transition between a low-coverage disordered phase at more negative electrode potentials and a c(2 × 2) ordered phase with bromine coverage 1/2 at more positive potentials. We explore the phase diagram and demonstrate that the broad shoulder observed in room-temperature cyclic voltammograms is due to local fluctuations resembling ordered phases with coverage 1/4, which exist in the model at much lower temperatures. We construct a dynamic Monte Carlo algorithm using a thermally activated stochastic barrier-hopping model for the microscopic dynamics. We use this algorithm to study the phase ordering and disordering processes following sudden potential steps between the disordered phase and the c(2 × 2) phase, and to study the sweep-rate dependence in simulated cyclic-voltammetry experiments.

We report results from a numerical study of a two-dimensional model for the surface-directed spinodal decomposition in a critical mixture. We explicitly add a long-range surface interaction term to the bulk free-energy functional leading to preferential attraction of one of the components of the mixtures to a free surface. We find that, for sufficiently long-range interactions, the thickness of the wetting layer 1(t ) varies as l(t ) -t ' '. We also find that the magnitudes of the average domain sizes in the parallel and perpendicular directions are di6'erent. However, the exponent (n ) characterizing the asymptotic growth of domains in these two directions is found to be the same (n =1/3). As well, the density profile and the pair correlation functions satisfy dynamical scaling behavior.

Surface-induced ordering in block copolymer melts is studied numerically. For symmetric copolymers, the thickness of the surface-enrichment layer is found to scale as Req∼Nθ with θ≊0.6, suggesting the system is undergoing a surface-induced strong segregation. The density profile perpendicular to the interacting surface is described quite well by the form predicted by Fredrickson in a mean-field analysis. In asymmetric copolymers, the surface is found to have a profound effect on domain formation. For some off-critical compositions, domains were found to form near the surface with a geometry different from that in the bulk; while for stronger asymmetry in composition, minority domains were nucleated near the wall only, long before any formed in the bulk. These interesting pattern formation processes should be observable in experiments using a depth profiling technique.

The statistical properties of coherent radiation scattered from phase-ordering materials are studied in detail using large-scale computer simulations and analytic arguments. Specifically, we consider a two-dimensional model with a nonconserved, scalar order parameter ͑model A͒, quenched through an order-disorder transition into the two-phase regime. For such systems it is well established that the standard scaling hypothesis applies, consequently, the average scattering intensity at wave vector k and time is proportional to a scaling function which depends only on a rescaled time, tϳ͉k͉ 2 . We find that the simulated intensities are exponentially distributed, and the time-dependent average is well approximated using a scaling function due to Ohta, Jasnow, and Kawasaki. Considering fluctuations around the average behavior, we find that the covariance of the scattering intensity for a single wave vector at two different times is proportional to a scaling function with natural variables ␦tϭ͉t 1 Ϫt 2 ͉ and tϭ(t 1 ϩt 2 )/2. In the asymptotic large-t limit this scaling function depends only on zϭ␦t/ t 1/2 . For small values of z, the scaling function is quadratic, corresponding to highly persistent behavior of the intensity fluctuations. We empirically establish that the intensity covariance ͑for k 0) equals the square of the spatial Fourier transform of the two-time, two-point correlation function of the order parameter. This connection allows sensitive testing, either experimental or numerical, of existing theories for twotime correlations in systems undergoing order-disorder phase transitions. Comparison between theoretical scaling functions and our numerical results requires no adjustable parameters. ͓S1063-651X͑97͒05112-X͔