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Modelling the Static and Dynamic Behaviour of Electrolytes: A Modified Poisson-Nernst-Planck Approach
[Thesis]. Manchester, UK: The University of Manchester; 2014.
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Abstract
In this thesis a method is presented for the modelling the effects of the excluded volume (ion-ion) and ion excess polarisability (ion-solvent) interactions in an electrolyte at a smooth planar electrode. The impact of these interactions is studied in terms of the equilibrium state of single and mixed electrolytes, the dynamic response of single electrolytes to a time-dependent applied potential, and their effect on the reaction rate, for both steady and time-dependent applied potentials. For reacting systems, the reaction rate is modelled using a modified form of the Frumkin-Butler-Volmer equation, in which the interactions are explicitly accounted for.At equilibrium, the model offers improvement over models which only account for the excluded volume interaction, in terms of both the predicted electrolyte structure and the electrical properties of the electrode. For example accounting for the polarisability interaction is shown to limit and then reverse the growth in the differential capacitance at the point of zero charge as the bulk concentration increases, an effect is not seen when only the excluded volume interaction is accounted for. Another example is for mixed electrolytes, in which accounting for the polarisability interaction leads to better agreement with experimental data regarding the composition of the double layer.For the response of an electrolyte to a potential step, the two interactions both lead to peaks in the time taken to reach equilibrium as a function of the potential. The effect of the domain length on the equilibration time is qualitatively discussed, together with the differences between the two interaction models. The response to a time-dependent potential is analysed through simulated electrochemical impedance spectroscopy and consideration of the capacitance dispersion effect. Between this and the potential step response data it is shown that the interactions themselves have little direct effect on the dynamic processes beyond the way in which they limit the ion concentrations in the double layer and alter the differential capacitance of the system.The investigation of the effect of the ion interactions on the reaction rate shows that both terms can either increase or decrease the rate, relative to a system with no interactions, depending on the details of the reaction and the applied potential. This is linked to the changes in the electric field within the double layer, which are caused by the interactions, and how this affects the reactant flux in that region. In terms of simulated EIS, deviations are observed relative to the equivalent circuit for the system, the reasons for which are discussed.Geraint Minton, Modelling the Static and Dynamic Behaviour of Electrolytes: A Modified Poisson-Nernst-Planck Approach, Degree of Doctor of Philosophy, The University of Manchester, September 2013