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The local Coulombic Monte Carlo algorithm : applications to the electric double layer Thompson, David

Abstract

A reformulation of the Coulomb problem, using a local Coulomb algorithm based on auxiliary fields, has been extended to slab and quasi-2D geometries. It has been implemented using Metropolis Monte Carlo and Gaussian charge interpolation functions. We have established the accuracy of the algorithm by generating effective pair potentials. Using this implementation, the Gouy-Chapman problem was numerically resolved for constant potential slab boundaries. In the low coupling limit, we find excellent aggreement with analytic solutions. In the high coupling regime, we find agreement with the analytic theory in the limit of large wall separation. Using the contact value theorem, we calculate the pressure experienced by like-charged equipotential walls. The parameter space we consider pertains to many interesting biomaterials ranging from monovalent biomembranes to spermidine DNA. The numerical results show attractions mediated by counter-ions between the like-charged equipotential slab boundaries. We also extend the implementation to allow for inhomogeneous dielectric backgrounds. The effect of a thin adsorbed layer of solvent is considered for an electrolyte system bounded by isolated electrodes. We show that a reduction in the dielectric value of this adsorbed layer results in a depletion of ions near the electrodes, even though the electrodes carry zero total charge. The applications considered show the versatility and accuracy of our implementation.

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