TY - THES
AU - Thompson, David
PY - 2007
TI - The local Coulombic Monte Carlo algorithm : applications to the electric double layer
KW - Thesis/Dissertation
LA - eng
M3 - Text
AB - 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.
N2 - 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.
UR - https://open.library.ubc.ca/collections/831/items/1.0084913
ER - End of Reference