Electrostatic Potentials and Fields in the Vicinity of Engineered Nanostructures Page: 4 of 40
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Abstract
We have developed a method of calculation of the electrostatic potentials and fields in the
vicinity of geometrically complex engineered nanostructures comprised of varying
materials in electrolytes of arbitrary pH and ionic strength. The method involves direct
summation of charged Debye-Hiickel spheres comprising the nanostructural surfaces and,
by including charge redistribution on the surface of conducting materials held at constant
potential, is applicable to mixed boundary conditions. The method is validated by
comparison to analytical solutions for an infinite plane (Gouy-Chapman), an infinite
cylinder (Bessel functions) and an infinite plane which contains a hole and which is held
at constant potential. Excellent agreement between the potentials obtained by our
numerical method and the closed form solutions is found for these conditions. The
method is applied to the calculation of the electric field enhancement in the vicinity of a
nanomembrane whose pore wall is held at constant charge and whose membrane surfaces
are held at constant potential. The electric field is found to be enhanced by the charge
buildup in the rim of the hole of the nanomembrane, which redistribution results from the
potential being held constant in the conducting region. Ion concentrations are also
calculated; positive ion rejection is found to be enhanced by this charge buildup in the
region of the rim when a constant positive potential is applied.
Keywords: Nanotechnology, membranes, Poisson-Boltzmann, electrostatic potentials
I. Introduction
Nanostructural engineering applied to membranes may lead to breakthrough
electrochemical separation technologies for the removal of toxins such as nitrates, dioxins2
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Schaldach, C; Bourcier, W; Paul, P & Wilson, W. Electrostatic Potentials and Fields in the Vicinity of Engineered Nanostructures, report, March 15, 2004; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc883850/m1/4/: accessed May 8, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.