Charge Transport in Polymer Ion Conductors: a Monte Carlo Study

Diffusion of ions through a fluctuating polymeric host is studied both by Monte Carlo simulation of the complete system dynamics and by dynamic bond percolation (DBP) theory. Comparison of both methods suggests a multiscale-like approach for calculating the diffusion coefficients of the ion

Dynamic percolation theory for particle diffusion in a polymer network

Tracer-diffusion of small molecules through dense systems of chain polymers is studied within an athermal lattice model, where hard core interactions are taken into account by means of the site exclusion principle. An approximate mapping of this problem onto dynamic percolation theory is proposed. This method is shown to yield quantitative results for the tracer correlation factor of the molecules as a function of density and chain length provided the non-Poisson character of temporal renewals in the disorder configurations is properly taken into account

Capture numbers and islands size distributions in models of submonolayer surface growth

The capture numbers entering the rate equations (RE) for submonolayer film growth are determined from extensive kinetic Monte Carlo (KMC) simulations for simple representative growth models yielding point, compact, and fractal island morphologies. The full dependence of the capture numbers on island size, and on both the coverage and the D/F ratio between the adatom diffusion coefficient D and deposition rate F is determined. Based on this information, the RE are solved to give the RE island size distribution (RE-ISD). The RE-ISDs are shown to agree well with the corresponding KMC-ISDs for all island morphologies. For compact morphologies, however, this agreement is only present for coverages smaller than about 5% due to a significantly increased coalescence rate compared to fractal morphologies. As found earlier, the scaled KMC-ISDs as a function of scaled island size approach, for fixed coverage, a limiting curve for D/F going to infinity. Our findings provide evidence that the limiting curve is independent of the coverage for point islands, while the results for compact and fractal island morphologies indicate a dependence on the coverage.Comment: 13 pages, 12 figure

Melt viscosities of lattice polymers using a Kramers potential treatment

Kramers relaxation times $\tau_{K}$ and relaxation times $\tau_{R}$ and $\tau_{G}$ for the end-to-end distances and for center of mass diffusion are calculated for dense systems of athermal lattice chains. $\tau_{K}$ is defined from the response of the radius of gyration to a Kramers potential which approximately describes the effect of a stationary shear flow. It is shown that within an intermediate range of chain lengths N the relaxation times $\tau_{R}$ and $\tau_{K}$ exhibit the same scaling with N, suggesting that N-dependent melt-viscosities for non-entangled chains can be obtained from the Kramers equilibrium concept.Comment: submitted to: Journal of Chemical Physic

Loss of control in pattern-directed nucleation: a theoretical study

The properties of template-directed nucleation are studied close to the transition where full nucleation control is lost and additional nucleation occurs beyond the pre-patterned regions. First, kinetic Monte Carlo simulations are performed to obtain information on a microscopic level. Here the experimentally relevant cases of 1D stripe patterns and 2D square lattice symmetry are considered. The nucleation properties in the transition region depend in a complex way on the parameters of the system, i.e. the flux, the surface diffusion constant, the geometric properties of the pattern and the desorption rate. Second, the properties of the stationary concentration field in the fully controlled case are studied to derive the remaining nucleation probability and thus to characterize the loss of nucleation control. Using the analytically accessible solution of a model system with purely radial symmetry, some of the observed properties can be rationalized. A detailed comparison to the Monte Carlo data is included