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Linear sweep and cyclic voltammetry techniques are important tools forelectrochemists and have a variety of applications in engineering. Voltammetryhas classically been treated with the Randles-Sevcik equation, which assumes anelectroneutral supported electrolyte. In this paper, we provide a comprehensivemathematical theory of voltammetry in electrochemical cells with unsupportedelectrolytes and for other situations where diffuse charge effects play a role,and present analytical and simulated solutions of the time-dependentPoisson-Nernst-Planck (PNP) equations with generalized Frumkin-Butler-Volmer(FBV) boundary conditions for a 1:1 electrolyte and a simple reaction. Usingthese solutions, we construct theoretical and simulated currentvoltage curvesfor liquid and solid thin films, membranes with fixed background charge, andcells with blocking electrodes. The full range of dimensionless parameters isconsidered, including the dimensionless Debye screening length (scaled to theelectrode separation), Damkohler number (ratio of characteristic diffusion andreaction times) and dimensionless sweep rate (scaled to the thermal voltage perdiffusion time). The analysis focuses on the coupling of Faradaic reactions anddiffuse charge dynamics, although capacitive charging of the electrical doublelayers (EDL) is also studied, for early time transients at reactive electrodesand for non-reactive blocking electrodes. Our work highlights cases wherediffuse charge effects are important in the context of voltammetry, andillustrates which regimes can be approximated using simple analyticalexpressions and which require more careful consideration.

Theory of linear sweep voltammetry with diffuse charge: unsupported electrolytes, thin films, and leaky membranes