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Electrostatic and Entropic Interactions between Parallel Interfaces Separated by a Glassy Film
Author(s) -
Johnston Karen,
Finnis Michael W.
Publication year - 2002
Publication title -
journal of the american ceramic society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.9
H-Index - 196
eISSN - 1551-2916
pISSN - 0002-7820
DOI - 10.1111/j.1151-2916.2002.tb00496.x
Subject(s) - dlvo theory , ion , charge density , planar , electrostatics , poisson's equation , discretization , surface charge , materials science , nonlinear system , chemistry , physics , quantum mechanics , mathematical analysis , mathematics , colloid , computer graphics (images) , computer science
A simple classical density functional model is set up to describe the electrostatic and entropic interactions between two parallel planar charged interfaces separated by a thin film of a phase (the glass) containing a distribution of charged ions. The total charge in the system is zero. Three cases are treated: (1) the two interfaces carry a fixed surface charge; (2) the first interface carries a fixed surface charge, simulating a ceramic, while the second is held at zero potential, simulating a metal; and (3) both interfaces are held at zero potential. A discretized form of the nonlinear Poisson–Boltzmann equation is derived and solved by a Newton–Raphson method. The continuum approximation is compared with a model in which the ions are only allowed to occupy discrete planes. The effect of correlation among the ions is included within the local density approximation. Inserting parameters appropriate to the copper–alumina interface, we find that the attractive image force between the ceramic and metal dominates the entropic (DLVO) repulsive force in the 1–2 nm range.