Liesegang Mechanism with a Gradual Phase Transition

We report a novel and generalized chemical model for the Liesegang mechanism that involves gradual phase transitions of macromolecules, unlike previous models that involved definite and discontinuous phase transitions. As a model system, an agarose gel medium doped with an initiator was contacted with a solution containing monomer 2-methoxyethyl acrylate (MEA), in which monomers diffused into the gel medium and initiated a polymerization reaction. As there is a monomer concentration gradient along the diffusion direction, the degree of polymerization and the corresponding degree of insolubility showed a similar spatial gradient in the reaction medium because molecular solubility gradually changes from soluble to insoluble with an increase in the degree of polymerization. Under this condition with such a spatial gradient in the degree of polymerization, multiple bands satisfying the spacing law were formed by repetitive precipitation and depletion of insoluble poly(2-methoxyethyl acrylate) (PMEA). In contrast to the Liesegang mechanism for salt formation reactions with definite transition points, such as the solubility product and nucleation threshold, our model involves a gradual transition with a nonzero transition width. The width of the transition point would be the governing parameter for the appearance and characteristics of periodic pattern formation. This model with a nonzero transition width is largely generalized and applicable to various processes involving any solubility transition and thus can be used as a generalized Liesegang model that can be applied to any system with both definite and gradual transitions.