Application of Irreversible Thermodynamics to Mass Transport in Ionic Conductors

  • Frederick H. Horne
Part of the NATO Advanced Science Institutes Series book series (volume 92)


Despite the almost universal acceptance of the non-equilibrium, or irreversible, thermodynamics (NET) of Onsager1 and his followers,2,3 most of the published research concerning ion transport relies on the Nernst-Planck equations.4 The Nernst-Planck equations ignore cross-effects due to both equilibrium and non-equilibrium interactions. Cross-effects cannot be ignored in complete treatments of ion transport, as others5–9 have also noted. For an ion of concentration ci, charge zi, and velocity vi, the one dimensional Nernst-Planck equation is
$$ {{c}_{i}}{{v}_{i}}=-{{D}_{i}}\left( \frac{\partial {{c}_{i}}}{\partial x}-{{c}_{i}}{{z}_{i}}\frac{F}{RT}E \right) $$
where Di is a diffusion coefficient, F is the Faraday constant, R the gas constant, T the temperature, and E the electric field. The principal inaccuracy in Eq. (1.1) is the omission of terms which represent the effects upon civi of interactions among ions of different kinds. The NET equation corresponding to (1.1) is, for n solute components,
$$ {{c}_{i}}{{v}_{i}}={{c}_{i}}{{v}_{0}}-\underset{j}{\mathop{\Sigma }}\,{{D}_{ij}}\frac{\partial {{c}_{j}}}{\partial x}+\frac{\lambda {{t}_{i}}}{F{{Z}_{i}}}E,i,j=1,\cdots ,n, $$
where v0 is the velocity of the solvent (usually vanishingly small), λ is the specific conductance (often denoted σ by solid state physicists), and ti is the Hittorf transference number for ion i in the particular solution. Eq. (1.2) reduces to Eq. (1.1) for very dilute solutions.


Specific Conductance Planck Equation Irreversible Thermodynamic European Economic Community Onsager Equation 
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Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • Frederick H. Horne
    • 1
  1. 1.Department of ChemistryMichigan State UniversityEast LansingUSA

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