Temperature-Gradient Effects on Electric Double Layer Screening in Electrolytes

Abstract

Temperature gradients drive asymmetric ion distributions via thermodiffusion (the Soret effect), leading to deviations from the classical Debye--Hückel potential.We introduce the Eastman entropy of transfer, ${\hat{S}}_{\pm }=\hat{I}{\pm }_{\pm }{k}_{\mathrm{B}}$ for cations and anions, respectively, where $k_{\mathrm{B}}$ is the Boltzmann constant, and analyze non-isothermal electric double layers in terms of the dimensionless Soret coefficients $\hat{I}{\pm }_{\pm }$. Analytical solutions of the generalized Debye--Hückel equation show that, for $\hat{I}{\pm }_{+}=\hat{I}{\pm }_{-}$, the potential is exactly described by a modified Bessel function, while the marginal case $\hat{I}{\pm }_{\pm }=1$ exhibits algebraic decay. An effective screening length, $\hat{I}{»}_{\mathrm{eff}}$, 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 $\hat{I}{\pm }_{\pm }>-1$. The differential capacitance is controlled by $\hat{I}{\pm }_{\pm }$ via $\hat{I}{»}_{\mathrm{eff}}$, 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.

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