Derivation of the Matalon-Packter law for Liesegang patterns

TL;DR

This paper derives explicit formulas for Liesegang pattern spacing, compares competing theories, and finds that induced sol-coagulation best explains experimental data related to the Matalon-Packter law.

Contribution

It provides a derivation of the Matalon-Packter law with explicit concentration dependencies and evaluates different theories against experimental results.

Findings

Induced sol-coagulation theory aligns best with experimental data.

Derived formulas clarify how electrolyte concentrations influence pattern spacing.

Comparative analysis distinguishes the most accurate theoretical model.

Abstract

Theoretical models of the Liesegang phenomena are studied and simple expressions for the spacing coefficients characterizing the patterns are derived. The emphasis is on displaying the explicit dependences on the concentrations of the inner- and the outer-electrolytes. Competing theories (ion-product supersaturation, nucleation and droplet growth, induced sol- coagulation) are treated with the aim of finding the distinguishing features of the theories. The predictions are compared with experiments and the results suggest that the induced sol-coagulation theory is the best candidate for describing the experimental observations embodied in the Matalon-Packter law.