Periodic and aperiodic patterns in non-equilibrium PbI2/PbF2 precipitate systems

Abstract

Precipitate systems display a variety of beautiful patterns. Of particular interest are those patterns formed by more than one insoluble salt. Guided by a prior theoretical model, we present here experiments on two precipitate patterning using PbI2 and PbF2 as the precipitating salts, in agar gel medium. Throughout the study, a solution of Pb2+ is allowed to diffuse into a homogeneous solution of the two halides and not the reverse. Two major categories of patterns are obtained: periodic, in which the band locations follow a rigorous spacing law, and aperiodic, where the bands occupy erratic spatial positions. The former patterns are obtained at large values of the mean concentration difference Δ [≡(ΔI + ΔF)/2, where ΔI = [Pb2+]0 − 1/2[I−]0 and similarly for ΔF], while the latter are formed at relatively low values of Δ. The periodic patterns show two different types of behaviour. When ΔI = ΔF, one type of bands containing the two precipitates is obtained, obeying the spacing law rigorously. When ΔI ≠ ΔF, two types of bands are observed with two distinct spacing laws. A chemical analysis of the bands shows that in both cases, the latter consist of a complete overlap of PbI2 and PbF— (i.e. no alternation) consistent with the initial ratio of concentrations (of I− to F−). Different observations favour the mechanism of post-nucleation patterning. Some special features indicate the role of the kinetics of particle growth in deciding whether we obtain one or two types of bands (and hence one or two spacing laws).