Phase field modeling of electrochemistry. I. Equilibrium
Abstract
A diffuse interface (phase field) model for an electrochemical system is developed. We describe the minimal set of components needed to model an electrochemical interface and present a variational derivation of the governing equations. With a simple set of assumptions: mass and volume constraints, Poisson’s equation, ideal solution thermodynamics in the bulk, and a simple description of the competing energies in the interface, the model captures the charge separation associated with the equilibrium double layer at the electrochemical interface. The decay of the electrostatic potential in the electrolyte agrees with the classical GouyChapman and DebyeHückel theories. We calculate the surface free energy, surface charge, and differential capacitance as functions of potential and find qualitative agreement between the model and existing theories and experiments. In particular, the differential capacitance curves exhibit complex shapes with multiple extrema, as exhibited in many electrochemical systems.
 Publication:

Physical Review E
 Pub Date:
 February 2004
 DOI:
 10.1103/PhysRevE.69.021603
 arXiv:
 arXiv:condmat/0308173
 Bibcode:
 2004PhRvE..69b1603G
 Keywords:

 81.15.Aa;
 73.30.+y;
 82.45.Mp;
 82.45.Jn;
 Theory and models of film growth;
 Surface double layers Schottky barriers and work functions;
 Thin layers films monolayers membranes;
 Surface structure reactivity and catalysis;
 Condensed Matter  Materials Science
 EPrint:
 v3: To be published in Phys. Rev. E v2: Added link to condmat/0308179 in References 13 pages, 6 figures in 15 files, REVTeX 4, SIUnits.sty. Precedes condmat/0308179