Freezing potentials arising on solidification of dilute aqueous solutions of electrolytes

A theory of the Workman-Reynolds effect [E.J. Workman and S.E. Reynolds, Phys. Rev. 78 (1950) 254] - the difference in electric potentials between dilute aqueous solution (water with impurities) and an ice crystal growing from the solution - is developed. The effect arises from inequality between distribution coefficients for solute cations and anions. At the beginning of solidification, the predominantly trapped ions from in ice a space charge layer parallel to the ice-water interface. An excess of counterions accumulates in the water next to the interface. The impurity cations and anions in ice then are neutralized by highly mobile OH- and H3O+ groups (ionization defects) supplied by thermal dissociation of H2O molecules in ice. Uncompensated ionization defects remaining after neutralization are moved by the electric field to the growing interface, encountering and neutralizing ions of solute. Thus the space charge layer of impurity follows the growth front. At the same time the oppositely charged layer of counterions is pushed ahead of the interface. The potential difference between the two layers - here considered as "capacitor plates" - is the freezing potential. It is calculated taking into account a current of OH- and H3O+ ions from water to ice. Our theory predicts that the freezing potential arises only when the product of growth rate and impurity concentration at the front exceeds a critical value that depends on pH, at which point the potential increases with the growth rate up to tens and hundreds of volts. The calculations presented in this paper qualitatively explain the experimental dependence of the transient potential difference on crystal thickness, rate of crystal growth, initial solute concentration, and the pH of water. In the case of instability of the ice crystallization front the theory predicts a rapid neutralization of the electrical charge in ice, a decrease of the crystallization potential, and a substantial change in acidity of the water remaining unfrozen. This change in pH is proportional to the logarithm of the ratio of the total ice-water interface area and the unfrozen water volume. Chemical reactions caused by this change in pH are called freezing (crystallization) hydrolysis. The experiments described demonstrate freezing hydrolysis of potassium ferricyanide (a reduction of K3Fe(CN)6 to K4Fe(CN)6) in a frozen NaCl-K3Fe(CN)6-H2O solution.