Kinetic Gelation Modeling:  Structural Inhomogeneity during Cross-Linking Polymerization

Abstract

Kinetic gelation models simulate free-radical polymerization on fixed lattices, where propagation and termination reactions are restricted to occur only between nearest neighbors. Here such a model is used with bifunctional sites and with kinetics recast as a Markov process through a stochastic approach. The reaction time is calculated by employing the probability density function and associated Monte Carlo method devised originally by Gillespie. As polymerization proceeds, the evolution of structure is characterized by pair correlation functions of three typesof reacted sites, of doubly reacted sites, and of monomers. These show that as polymerization proceeds, reacted sites and doubly reacted sites come to be distributed more uniformly in space; monomers come to be distributed less uniformly. A higher initiation rate constant, a higher initiator concentration, and a lower propagation rate constant lead to more uniform distribution of reacted sites, of doubly reacted sites, and of monomers. These factors also lead to lower average connectivity between reacted sites. These trends are strongest at low conversions. In contrast, an enhanced primary cyclization leads to less uniform distribution of reacted sites but to more uniform distribution of monomers. It also leads to higher connectivity between reacted sites that are close together but to lower connectivity between reacted sites that are far apart. Finally, at high conversions it leads to a more uniform distribution of doubly reacted sites.

Structural Characterization of Protein‐Imprinted Gels Using Lattice Monte Carlo Simulation

“…[1,16] The kinetic gelation model (KGM) describes the chemistry of irreversible polymer gelation and relates to the rules of initiation, propagation, termination and radical trapping. [25][26][27] KGMs generally describe the formation of a rigid network without relating to the flexibility of the resulting structure. Verdier et al [28,29] present a MC method for studying polymer chain dynamics and equilibrium configurations.…”

Semibatch operation and primary cyclization effects in homogeneous free-radical crosslinking copolymerizations

“…Simultaneously with these experimental efforts, numerous computational studies have also been carried out in order to quantitatively describe free radical crosslinking copolymerizations: the well-known probabilistic approach [9], the method of the moments [10][11][12][13][14][15][16], Monte Carlo simulation [17][18][19][20][21][22][23][24][25] or statistical crosslinking methods [26] are some examples of techniques used in this context. 'Numerical fractionation' [27,28] and real chain-length domain calculation exploiting Galerkin finite elements method [29,30] are alternative techniques for dealing with non-linear free radical polymerizations.…”

Studies on dialkoxysilane hydrolysis kinetics under alkaline conditions

“…Cyclization plays an important role in silicate structure development in acidic systems. Compared with NMR spectra of alkoxysilane hydrolysis under acidic conditions, the concentration of cyclic tetramer in alkaline systems was much lower than that in a similar acid-catalyzed sample [5][6][7][8][9][10]. From Fig.…”

“…Many studies on alkoxysilane hydrolysis were often carried out in the system of alkoxysilane/alcohol/water [2][3][4][5][6][7][8][9][10]. Alcohol not only is a solvent but also causes hydrolysis reverse reaction since alcohol is one of the hydrolysis products.…”

“…There were many studies on the kinetics of alkoxysilane hydrolysis and condensation, but most of the cases focused on acid-catalyzed system [5][6][7][8][9][10], and few on alkaline-catalyzed system. Grubb studied silanol condensation reaction in alkaline-catalyzed system by Karl Fisher titration and found that the reaction rate is sensitive to steric factors [11].…”