Periodic trends in precipitate patterning schemes involving two salts

Abstract

Competitive particle growth (CPG) theory and linear stability analysis are combined to study the potential patterning trends of two-salt Liesegang systems. The pattern formation is treated as a post-nucleation phenomenon. Experimental investigations show that some systems mainly give patterns where the bands of the two salts essentially alternate, while others (such as typically the PbI₂–PbF₂ system) yield patterns where the bands completely overlap. We report on observations in a variety of two-salt systems, where we find a spectrum of patterning trends which generally fall into either of two categories: “correlated” patterns (with band overlap) or “anti-correlated” (with band alternation). The systems considered are Co(OH)₂–Mg(OH)₂, Ni(OH)₂–Mg(OH)₂, PbI₂–PbF₂, Ag₂Cr₂O₇–PbCr₂O₇, MnS–CuS and MnS–CdS. The analysis of the reaction–diffusion equations shows that the simple precipitation scheme would predominantly yield an alternation of bands of the two salts. To resolve this disagreement between theory and experiment in the PbI₂–PbF₂ case (and some other cases), another scenario involving the complex ions PbI⁺ and PbF⁺ was also considered. The analysis here yields a dominant overlap between the PbI₂ and PbF₂ bands conformly to the experimental result. This study on two-precipitate pattern formation gives clues on the possible reaction schemes actually involved in the precipitation process and suggests interesting experiments for eventual elucidations. The results and conclusions are revisited in the Discussion section.