Identification of thermodiffusion coefficients in an aqueous potassium ferri/ferrocyanide thermocell using open-circuit voltage data

Abstract

Ion thermodiffusion coefficients are crucial to analyse effects of thermodiffusion in thermocells and these values are difficult to measure experimentally. To determine these coefficients, this paper adopts parameter identification and studies their identifiability. Time dependence of open-circuit voltage is measured in an aqueous potassium ferri/ferrocyanide thermocell as data set. A one-dimensional numerical model is established according to theories of electrochemistry and non-equilibrium thermodynamics. Identification of thermodiffusion coefficients is conducted using genetic algorithm in eight parameter spaces, which are divided according to signs of three parameters. Thermodiffusion is suggested to induce a 9.38% drop in voltage. The best identification results are −8.30 × 10−12, −6.56 × 10−12, −3.48 × 10−12 m2/(s K) for ferricyanide, ferrocyanide and potassium ion, respectively. However, five optimal parameters in other parameter spaces have close fitness, implying multimodality of identification. And only one of these parameters is practically identifiable using this method. To improve identification results, more accurate estimation of inner temperature difference and determination of ion mobilities are necessary. Besides, electric current data has the potential to determine the actual combination of thermodiffusion coefficients from these six optimal results.