Transient response of an electrolyte to a thermal quench

Abstract

We study the transient response of an electrolytic cell subject to a small, suddenly applied temperature increase at one of its two bounding electrode surfaces. An inhomogeneous temperature profile then develops, causing, via the Soret effect, ionic rearrangements towards a state of polarized ionic charge density q and local salt density c. For the case of equal cationic and anionic diffusivities, we derive analytical approximations to q, c, and the thermovoltage VT for early (t τT ) and late (t τT ) times as compared to the relaxation time τT of the temperature. We challenge the conventional wisdom that the typically large Lewis number, the ratio a/D of thermal to ionic diffusivities, of most liquids implies a quickly reached steady-state temperature profile onto which ions relax slowly. Though true for the evolution of c, it turns out that q (and VT ) can respond much faster. Particularly when the cell is much bigger than the Debye length, a significant portion of the transient response of the cell falls in the t τT regime, for which our approximated q (corroborated by numerics) exhibits a density wave that has not been discussed before in this context. For electrolytes with unequal ionic diffusivities, VT exhibits a two-step relaxation process, in agreement with experimental data of Bonetti et al. [J. Chem. Phys. 142, 244708 (2015)].

On the time-dependent electrolyte Seebeck effect

“…( 2)-providing evidence that the "instantaneous" Seebeck coefficient is rather reached on the Debye timescale-though we did not realize this at the time of writing Ref. [51].…”

“…Yet, while the Poisson equation connects q(x, t) to V T (t), there is no such connection between c(x, t) and V T (t), which means that Bierlein's expression cannot be used to interpret V T (t). To solve this problem, one of us-with Biergeneralized Stout and Khair's model to an electrolyte for which D + = D − [51]. For this case, we showed that q(x, t) relaxes exponentially with both τ D and τ difand, because of Poisson's equation, so does V T (t) [see Fig.…”

A Molecular Dynamics Approach to Calculate the Thermodiffusion (Soret and Seebeck) Coefficients of Salts in Aqueous Solutions

“…where z i is the valence number, x is a space coordinate and E x is the hypothetical ad hoc thermoelectric field. Recently, it was shown that E x arises from two dynamical effects that are distant in at least 8 orders of magnitude in their transient times: 22 E 1 proportional to the difference of products α + D + − α − D − , which affect the fast response of the system that is much longer than the Debye transient and much shorter than the diffusive transient; and…”

“…E 2 proportional to the difference α + − α − , which affects the slow response of the system that is much longer than the diffusive transient. 22 The equations for amplitude modules of Seebeck coefficients related to both time transients are given by: 22,58…”

Molecular Dynamics Approach to Calculate the Thermodiffusion (Soret and Seebeck) Coefficients of Salts in Aqueous Solutions

“…The dependence of thermal diffusion coefficient D T on temperature, a broadly discussed topic in literature on thermodiffusion, shows a linear behavior with temperature as a consequence of the temperature independence of the single-ion Soret coefficient α i and a linear dependence of effective mass diffusion D(T )for all ions. For describing the thermoelectric effect, Seebeck coefficient was calculated using a recent theoretical expression, 22 with agreements in the same orders of magnitude for monovalent salt in aqueous solutions.…”