Non-Isothermal Membrane Potentials

Abstract

ALTHOUGH the measurement of isothermal membrane potentials has received considerable attention, we know of no previous work in which the e.m.f. of a membrane-cell has been measured when the two halves of the cell are at different temperatures. Application of the methods of the thermodynamics of irreversible processes to a system consisting of two half-cells separated by a membrane yields the following equation for J_i, the flux of the ith component, through the membrane: where the L_ik's are the phenomenological coefficients obeying the Onsager reciprocal relations, L_ik = L_ki, V̄_k is the partial molar volume of the kth species, Q^*_k its heat of transfer, e_k (= z_kF) the charge, including sign, per mole of the kth species, and dP, dT, dμ_k (= R T d ln a_k) and dψ the differences in pressure, temperature, chemical potential of the kth species and electrical potential, between the two half-cells. If the half-cells are well stirred, the values of these parameters are uniform throughout each half-cell and all the above differences occur across the membrane. Previous theoretical treatments^1,2 have neglected the possibility of temperature as a variable, treating only the isothermal case.