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Abstract

A model composed of the nonlinear Cahn−Hilliard and Flory−Huggins theories for spinodal decomposition (SD) and a second-order rate equation for polymerization for the self-condensation of a trifunctional monomer is used to study the polymerization-induced phase separation (PIPS) phenomena. The numerical results are consistent with experimental observations. These observations include the formation and evolution of a droplet-type morphology. In addition, the time evolution of the maximum value of the structure factor S(km,t) exhibits an exponential growth during the early stage but saturates during the intermediate stage of SD. Moreover, the dominant dimensionless wavenumber km* decreases during the intermediate stage. The numerical results, however, also indicate that km* increases during the early stage, which has not yet been observed experimentally. Furthermore, the morphological analysis is also consistent with experimental observations. The droplet size and shape distributions indicate that the average droplet size and shape prevail during the PIPS phenomena, and statistical analysis of the Voronoi polygons indicates that the droplets are randomly positioned within the matrix. Lastly, the characteristic time τ, average dimensionless equivalent droplet diameter 〈d*〉, and droplet number density Nd depend on the magnitudes of a scaled diffusion coefficient D for phase separation and a scaled rate constant K1 for polymerization. Consistent with experimental observations, τ and 〈d*〉 decrease while Nd increases as K1 increases. Similarly, as D increases, τ and 〈d*〉 decrease while Nd increases. The parameters K1 and D have no effect on the average shape factor.

Polymerization-Induced Phase Separation. 2. Morphological Analysis

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