Abstract
Under special circumstances, Liesegang rings, which are normally associated with the periodic precipitation of inorganic salts, can be observed in emulsion polymerization systems. A quantitative theory is presented for the formation of these polymer rings, based on the numerical solution of coupled reaction-diffusion equations describing their temporal and spatial evolution. The autocatalytic step required for periodic phenomena is identified as arising from the coagulative nucleation mechanism for latex particle formation. In this mechanism, precursor particles, formed by either micellar entry or homogeneous nucleation, coagulate to give latex particles. An initial spatial inhomogeneity in the latex particle concentration grows and induces a depletion region adjacent to it. Another maximum in the latex concentration subsequently appears, separated from the initial one by a region where few latex particles have been nucleated. This type of periodic structure is shown to evolve only if the nucleation rate is an increasing function of time. Such a function is derived from extended Müller-Smoluchowski coagulation kinetics involving precursor and latex particles. Excellent agreement is obtained between the theory, using physically reasonable parameters, and the spacing between the two rings in unstirred emulsion polymerization systems.
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