The contact between a solid and an electrolyte

Abstract

The condition for equilibrium between a binary salt and an electrolyte is that the free-energy change accompanying the transfer of an ion from the interior of the crystal to its hydrated state in solution is zero. In an arbitrary electrolyte this condition can only be satisfied if the two phases are charged. The charge in the electrolyte occurs, at least in part, as a space charge of hydrated ions, the charge density being highest near the interface and falling exponentially to zero in the bulk of the electrolyte. This charged layer, which is well known in colloid science as a factor determining the electrokinetic behaviour of the solid, is usually assumed to be balanced by an opposite charge carried by the crystal in the form of ions adsorbed to the surface. If, however, lattice defects are present in the crystal in thermal equilibrium, the balancing charge may reside actually inside the crystal in the form of a space charge of lattice defects whose structure is similar, in many respects, to the charged layer in the electrolyte. The charge density is highest near the interface and falls exponentially to zero inside the crystal; only at the isoelectric point where the two phases are uncharged are the concentrations of defects uniform throughout the crystal. In any other electrolyte the equations governing the distribution of defects in the crystal are similar to the equations of the Gouy-Chapman theory of the space charge in the electrolyte. This theory of the double layer is developed for plate-like crystals, and equations are derived which relate the potential drop in each phase and the total charge on the double layer to the physical constants of the system. As the thickness of the crystal is reduced, the space charges at opposite faces begin to overlap in the interior of the crystal so that (except at the isoelectric point) there is no place in the crystal where the defect concentrations are identical with those which exist in thermal equilibrium in an isolated crystal. Because of this overlapping, the thickness of the crystal appears as a parameter in the argument. The theory is applied to silver bromide in contact with an electrolyte. The defects in the crystal are assumed to be of the Schottky type, so that the charge in the crystal arises through the presence of vacant cation and anion sites in unequal concentrations. On the silver side of the isoelectric point, vacant anion sites are in excess, whilst on the bromide side the reverse is true. c A 0 the silver-ion concentration at the isoelectric point, is given by 2 kT In (c A 0 /c 0 )= W B - W A , where c 0 is the silver (or bromide) ion concentration at the equivalence point, W A is the work to transfer a silver ion from the interior of the crystal to the electrolyte when the two phases are uncharged and W B is the corresponding quantity for bromide ions. The double­-layer potentials and the total charge are computed as functions of the P Ag for the case in which the electrolyte contains either added silver salts or added bromides only. The existence of the space charge of vacant sites means that the self-diffusion coefficients of the ions in the crystal are functions of position, and this has an important effect on the rates of exchange of radioactive silver and bromide ions between the electrolyte and the crystal. The rates of exchange are functions of the P Ag , and for silver ions the half-life of the exchange increases as the P Ag increases. For bromide ions the half-life decreases with in­creasing P Ag . Detailed calculation shows that this phenomenon becomes increasingly im­portant as the dimensions of the crystal are reduced below 10 -4 cm., and some experimental work with a bearing on this result is discussed.