The rate of recombination of ions in a weak-electrolyte solution is often controlled by the rate at which the ions collide with one another. The rate of collision has been previously treated in the literature, resulting in a classic expression for the rate constant. A derivation is presented here employing the methodology of Onsager and Fuoss. This methodology makes use of a distribution function to track the relative average positions of the two reactants. The reactants are assumed to undergo movement that follows a Nernst-Planck Equation for the migration and diffusion components of the flux. The potential of interaction of the ions is assumed to be a coulomb potential screened by an ion cloud formed by a supporting electrolyte. The resulting expression for the rate constant is the same as that of Debye.

The dissociation of weak electrolytes is increased by an applied electric field. Lars Onsager's classic treatment of this increase in dissociation determines the effect of an applied electric field upon the movement of a pair of ions formed by dissociation. To obtain an analytic expression, Onsager approximates that the pair of ions form a chemical bond when they are at a separation distance of zero. This approximation is poor when long chemical bonds are involved, such as the dissociation of an electrolyte occurring via charge transport along a hydrogen-bond wire.

Here, the work of Onsager is extended to the case of dissociation via long chemical bonds. For bond lengths greater than zero, the results predict the recombination rate constant of a collision-controlled reaction will increase with an applied electric field. Additionally, results predict that the dissociation of a weak electrolyte will increase with an applied electric field. The increase in dissociation is predicted to vary by orders of magnitude with small changes in the length of the chemical bond.

A 1-d continuum model of a bipolar membrane is shown. The model accounts for the diffusion and migration of species, electrostatics, and chemical reaction. The bipolar membrane model is seen to rectify current and undergo breakdown. This is the first model to use a model of water splitting at large electric fields to predict the breakdown of the junction. A layer of weak base is included in the junction of the membrane as a catalyst layer. Model results show agreement with published experimental results. The effect of the catalyst layer is seen to be negligible. The ineffectiveness of the catalyst is attributed to the greater increase in water dissociation due to the electric field than by the catalyst mechanism. Results are shown for a bipolar membrane immersed in a neutral pH solution as well as a bipolar membrane separating a solution with a pH of 2 from a solution with a pH of 12.