Polymerization-Induced Phase Separation. 2. Morphological Analysis

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.

Deformation and dewetting of thin liquid films induced by moving gas jets

“…Here, N c is the areal density of nodes on the Voronoi grid [19,54] based on the centers of the dry-spots. These are illustrated in Fig.…”

Theory and simulation of polymerization-induced phase separation in polymeric media

“…[4,5] The growth rate of the reactive component, N B in Eq. (9) and (10) is determined by solving the following kinetic rate equation:…”

“…The particle size of the PB phase can be controlled by a proper choice of the processing conditions to obtain the desired properties. However, despite practical importance of PIPS in producing multi-component composite materials, relatively few theoretical [4][5][6][7][8][9] and experimental [10][11][12][13][14] studies have been performed. In particular, no model has yet been developed, as done here, to describe monomer polymerization in the presence of a non-reactive polymer, taking into account phase separation.…”

“…In the previous studies, [4][5][6] coupled phase separation and polymerization processes have been modeled using the time dependent non-linear Cahn-Hilliard (C-H) theory, the Flory-Huggins (F-H) theory for phase separation, and a reaction kinetic equation for polymerization. The mobility and interfacial parameter in the C-H theory are dependent on both the polymer molecular chain lengths and local concentration in the PIPS process.…”

“…The interfacial parameter can be assumed to be concentration independent in the absence of any accurate information about its behavior, however, the mobility is known to be highly sensitive to ceoncentration changes. [15] Chan and Rey [4,5] solved the non-linear fourth-order C-H equation to study the effects of diffusion coefficient and polymerization rate constant on the phase-separated morphology for polymer solutions in the PIPS process. Their system described polymerizing monomers in the presence of non-reactive low molar mass solvents.…”