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Analysis and spline approximation of surface charge and potential at planar electrochemical interfaces
Author(s) -
Bedin Luciano,
Bazán Fermín Sinforiano Viloche,
Giordani Flavia Tereza
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5753
Subject(s) - mathematics , surface (topology) , ode , charge density , planar , smoothing , surface charge , charge (physics) , spline (mechanical) , mathematical analysis , constant (computer programming) , geometry , physics , quantum mechanics , computer science , statistics , computer graphics (images) , thermodynamics , programming language
In this paper, we consider the Poisson‐Boltzmann theory to model the electrostatic potential of a bulk electrolyte containing a single planar charged surface. In the case of a constant surface charge density, we address the problem as a ODE system by using the stability theory for autonomous dynamical systems. By stating that the surface charge density and the surface potential are non‐linearly related through the Grahame equation, we give a description of the stable manifold of the system. To solve the Grahame equation and obtain an approximation for the stable manifold, we propose a smoothing collocation method based on cubic splines, including implementation details and numerical results.