S. J. Mitchell

Dynamics of Br electrosorption on single-crystal Ag(100): a computational study

Abstract We present dynamic Monte Carlo simulations of a lattice-gas model for bromine electrodeposition on single-crystal silver (100). This system undergoes a continuous phase transition between a disordered phase at low electrode potentials and a commensurate c (2×2) phase at high potentials. The lattice-gas parameters are determined by fitting simulated equilibrium adsorption icsotherms to chronocoulometric data, and free-energy barriers for adsorption/desorption and lateral diffusion are estimated from ab-initio data in the literature. Cyclic voltammograms in the quasi-static limit are obtained by equilibrium Monte Carlo simulations, while for nonzero potential scan rates we use dynamic Monte Carlo simulation. The butterfly shapes of the simulated voltammograms are in good agreement with experiments. Simulated potential-step experiments give results for the time evolution of the Br coverage, as well as the c (2×2) order parameter and its correlation length. During phase ordering following a positive potential step, the system obeys dynamic scaling. The disordering following a negative potential step is well described by random desorption with diffusion. Both ordering and disordering processes are strongly influenced by the ratio of the time scales for desorption and diffusion. Our results should be testable by experiments, in particular cyclic voltammetry and surface X-ray scattering.

Halide adsorption on single-crystal silver substrates: dynamic simulations and ab initio density functional theory

We investigate the static and dynamic behaviors of a Br adlayer electrochemically deposited onto single-crystal Ag(100) using an off-lattice model of the adlayer. Unlike previous studies using a lattice-gas model, the off-lattice model allows adparticles to be located at any position within a two-dimensional approximation to the substrate. Interactions with the substrate are approximated by a corrugation potential. Using density functional theory (DFT) to calculate surface binding energies, a sinusoidal approximation to the corrugation potential is constructed. A variety of techniques, including Monte Carlo and Langevin simulations, are used to study the behavior of the adlayer. The lateral root-mean-square (rms) deviation of the adparticles from the binding sites is presented along with equilibrium coverage isotherms, and the thermally activated Arrhenius barrier-hopping model used in previous dynamic Monte Carlo simulations is tested.

Scaling analysis of polyacrylamide gel surfaces synthesized in the presence of surfactants

Surfaces of polyacrylamide hydrogels synthesized in the presence of surfactants were imaged by atomic force microscopy (AFM), and the surface morphology was studied by numerical scaling analysis. The gels were formed by polymerizing acrylamide plus a cross-linker in the presence of surfactants, which were then removed by soaking in distilled water. Gels formed in the presence of over 20% surfactant (by weight) formed clear, but became opaque upon removal of the surfactants. Other gels formed and remained clear. The surface morphology of the gels was studied by several one- and two-dimensional numerical scaling methods. The surfaces were found to be self-affine on short length scales, with a roughness (Hurst) exponent in the range from 0.85 to 1, crossing over to a constant root-mean-square surface width at long scales. Both the crossover length between these two regimes and the saturation value of the surface width increased significantly with increasing surfactant concentration, coincident with the increase in opacity. We propose that the changes in the surface morphology are due to a percolation transition in the system of voids formed upon removal of the surfactants from the bulk.

First-Principles Parameter Estimation for Dynamic Monte Carlo of a Lattice-Gas Model

We present preliminary results demonstrating how dynamic Monte Carlo transition rates for lateral diffusion can be found from quantum ab initio calculations. As an example, we consider the specific problem of Br electrosorption onto Ag(100), and we use density functional theory (DFT) to calculate the Br binding energy at the four-fold hollow, bridge, and on-top sites. From these energies, we develop a simplified corrugation potential. Using Langevin simulations, we analyze the motion of a single particle in this corrugation potential and study the transition rates between lattice-gas states. We further test the corrugation potential by comparing results of an off-lattice equilibrium simulation with the previous results for a lattice-gas model. We find that our DFT barrier estimates are consistent with a lattice-gas treatment of the statics and dynamics of the system.

Frustrated Spring-Network Model for Crosslinked Polymer Surfaces

We present a simplified model to study the surface structure of a crosslinked polymer gel. The model consists of a two-dimensional spring network on a triangular lattice. The nodes represent the crosslinkers, and the equilibrium length of the harmonic springs between nodes is associated with the random length of a polymer chain between crosslinkers. Our preliminary results show that this model qualitatively reproduces some characteristics of surfaces of polyacrylamide gels into which holes are introduced through templating with surfactant micelles, recently observed by Atomic Force Microscopy. There is a length scale above which the surface width reaches a saturation value. This saturation value appears to be independent of the system size but changes significantly when holes are introduced in the system.

Hysteresis in an Electrochemical System: Br Electrodeposition on Ag(100)

We examine hysteresis in cyclic voltammetry of Br electrosorption onto single-crystal Ag(100) by dynamic Monte Carlo simulations. At room temperature, this system displays a second-order phase transition from a low-coverage disordered phase to a doubly degenerate c(2x2) phase. The electrochemical potential is ramped back and forth across the phase transition, linearly in time, and the phase lag between the response of the adlayer and the potential is observed to depend on the sweep rate. The hysteresis in this system is caused by slow ordering/disordering kinetics and critical slowing-down.