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, S^±=α±kB for cations and anions, respectively, where kB is the Boltzmann constant, and analyze non-isothermal electric double layers in terms of the dimensionless Soret coefficients α±. Analytical solutions of the generalized Debye–Hückel equation show that, for α+=α−, the potential is exactly described by a modified Bessel function, while the marginal case α±=1 exhibits algebraic decay. An effective screening length, λeff, 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 α±−1. The differential capacitance is controlled by α± via λeff, 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.
Kazuhiko Seki (Thu,) studied this question.