Theory of the Single-Ion Heat of Transport in Nonisothermal Electrolytic Solutions

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Abstract
The single-ion heat of transport is determined formally by considering the Soret effect in dilute electrolytic solutions. Specifically considered is the contribution of ion—ion interactions. That part of the contribution depending on nonequilibrium distribution functions is shown to vanish through order κ by means of a direct determination of the nonequilibrium distribution functions. In determining the distribution functions, the statistical mechanical basis of the classical isothermal limiting laws is first considered. They result from the Liouville equation when a superposition approximation for ion triplets is introduced and ensemble-average ion—solvent forces are treated phenomenologically according to the linear laws of the thermodynamics of irreversible processes. The superposition approximation is equivalent to the usual Debye—Hückel approximation at equilibrium. The nonisothermal case is treated by using the same superposition equation and generalizing the phenomenological ion—solvent force equations. The results agree with those of Helfand and Kirkwood who considered a reciprocal isothermal experiment, and therefore they constitute a direct verification of the heat—matter Onsager reciprocity relation.