The role of charge separation in the response of electrochemical systems

Abstract

To elucidate the effect of charge layers on the behaviour of electrochemical systems comprising microgeometries, we investigate microhemisphere and microdisc electrodes. A binary electrolyte is examined, consistent with virtually all battery and fuel-cell electrolytes. The transport-controlled current density response is shown to be governed by two dimensionless groups: the first group, δ, corresponds to a Debye length divided by the electrode radius, while the second,σ, characterizes the charge density on the electrode surface relative to the salt concentration. In many cases of practical interest, δ is very small, and the modelling equations approach a singularity; the resulting equation system is thus not amenable to numerical solution. We have used an asymptotic analysis to deal with this problem, so that our model calculations cover the full range of δ-values that are of interest. The asymptotics are given for more general electrode shapes, including hemispheres and discs.

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

“…Matched asymptotic expansions were first applied to steady-state PNP transport in the 1960s without considering FBV reaction kinetics [86][87][88][89] and used extensively in theories of ion transport [24] and electro-osmotic fluid instabilities [90,91] in electrodialysis, involving ion-exchange membranes rather than electrodes. Baker and Verbrugge [92] analyzed a simplified problem with fast reactions, where the active species concentration vanishes at the electrode. Bazant and co-workers first used matched asymptotic expansions to treat Faradaic reactions using the PNP-FBV framework, applied to steady conduction through electrochemical thin films [12,13].…”

Time-dependent modelling and asymptotic analysis of electrochemical cells

“…Note that the non-dimensionalisation applied above is essentially the same as (10) (that applied to the dilute model) provided we take 0 , the reference ion concentration, equal to that of pure water 0 = 1/H w . Applying (94) to (83-93) leads to…”

“…All three investigate steady-state problems; reference [7] looks at the passage of a steady current through an electrode, reference [8] investigates the potential adjacent to an electrode (in the presence of an advective flow normal to the electrode) and [9] performs a matched asymptotic analysis about a membrane carrying a fixed charge. There has recently been a revival of interest in the use of matched asymptotic expansions in this context, exemplified by Baker and Verbrugge [10]; Bonnefant et al [11]; Bazant et al [12,13]. Baker and Verbrugge [10] investigate the scenario in which the electrode reaction is extremely fast, so that the concentration of the reacting ion species is zero on the electrode, and look for steady-state solutions for various geometries of electrode.…”

“…There has recently been a revival of interest in the use of matched asymptotic expansions in this context, exemplified by Baker and Verbrugge [10]; Bonnefant et al [11]; Bazant et al [12,13]. Baker and Verbrugge [10] investigate the scenario in which the electrode reaction is extremely fast, so that the concentration of the reacting ion species is zero on the electrode, and look for steady-state solutions for various geometries of electrode. 2 In Bonnefant et al [11] the behaviour of a three-species electrolyte is investigated in proximity to an electrode.…”

Stress fields in hollow core–shell spherical electrodes of lithium ion batteries

“…Lithium ion batteries are the choices of diverse applications, such as electronics and electric cars because of their high capacity, high voltage and long lifetime, and therefore attracted wide research interests [1][2][3][4][5][6]. During the process of discharge/charge, lithium ions insert into/extract from electrodes, which will cause cyclic deformation.…”