Mechanism of chemical instability for periodic precipitation phenomena

Abstract

A mechanism of chemical instability of autocatalytic reactions coupled with diffusion is proposed for spatially periodic precipitation phenomena (such as Liesegang rings or bands). We postulate that precipitation is preceded by colloid formation; electric double layers surround the colloid particles, and at sufficient concentration of colloid, autocatalytic growth of particles and formation of new particles occur owing to an increased product of ion concentrations within the double layer with an increased colloid concentration. A linear stability analysis of the reaction-diffusion equations for this mechanism predicts (1) formation of macroscopic inhomogeneities (spatial structures) due to the onset of instability in the absence of imposed external gradients and prior to the appearance of any visible bands; (2) ranges of the characteristic length scales and time scales of the initial structure pattern; (3) phase relations of concentrations of ionic species and colloid; (4) variation of characteristic length scales with initial concentrations, and rate and diffusion coefficients of ions and colloid; (5) a mechanism for secondary structure of precipitation bands; (6) the possibility of revert structure (decreasing distance between bands away from the origin of an imposed gradient); and (7) the suggestion that the imposition of a concentration gradient, as in a Liesegang experiment, polarizes and may alter the shape of the periodic precipitation structure but is not the basic cause of that structure. The quantitative nature of the structure requires solution of the nonlinear reaction-diffusion equations which is not attempted. The predictions of the proposed mechanism are in substantial agreement with experiments. We report on some experiments which provide evidence for items (1), (6), and (7); for the remaining items we refer to experiments reported in the literature. We conclude with a critique of the Ostwald theory of Liesegang rings, which does not predict revert spacing nor secondary structure. We provide additional experimental evidence against the requirements of this theory of an imposed concentration gradient that in time brings about supersaturation followed by precipitation.