Temperature-Gradient Effects on Electric Double Layer Screening in Electrolytes

TL;DR

This paper investigates how temperature gradients influence electric double layer screening in electrolytes, revealing the coupling between thermodiffusion and electrostatics through analytical solutions and effective screening length analysis.

Contribution

It introduces the Eastman entropy of transfer and derives analytical solutions for non-isothermal electric double layers, expanding understanding of temperature effects on electrostatic screening.

Findings

Effective screening length increases with temperature, weakening screening on hot side.

Differential capacitance depends on Soret coefficients and peaks at zero charge potential.

Potential decay transitions from exponential to algebraic depending on Soret coefficient equality.

Abstract

Temperature gradients drive asymmetric ion distributions via thermodiffusion (the Soret effect), leading to deviations from the classical Debye--H\"uckel potential.We introduce the Eastman entropy of transfer, $\hat{S}_\pm = \alpha_\pm k_{\rm B}$ for cations and anions, respectively, where $k_{\rm B}$ is the Boltzmann constant, and analyze non-isothermal electric double layers in terms of the dimensionless Soret coefficients $\alpha_\pm$. Analytical solutions of the generalized Debye--H\"uckel equation show that, for $\alpha_+ = \alpha_-$, the potential is exactly described by a modified Bessel function, while the marginal case $\alpha_\pm = 1$ exhibits algebraic decay. An effective screening length, $\lambda_{\rm eff}$, characterizes the near-electrode potential and increases with temperature, resulting in weaker screening on the hot side and stronger screening on the cold side for $\alpha_\pm > -1$. The differential capacitance is controlled by $\alpha_\pm$ via $\lambda_{\rm eff}$, with its minimum coinciding with the potential of zero charge (PZC) even in the presence of a temperature gradient. These findings highlight the fundamental coupling between electrostatics and thermodiffusion in non-isothermal electrolytes.