Temperature-Gradient Effects on Electric Double Layer Screening in Electrolytes

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.