Explicit stochastic modeling of termination chain length dependencies for all disparate radical pairs in single phase free radical induced grafting

A Comprehensive Monte Carlo Model of the Grafting of Maleic Anhydride onto Polypropylene with Experimental Validation

“…Previous studies have conducted a comparative analysis to assess the advantages of including phase differentiation in order to enhance the depiction of the grafting process. [25,31,38,39] We found that for our system the use of a pseudo-homogeneous model was enough to accurately portray the grafting process, as we will discuss in detail later. Diffusional limitations have not been specially considered in this model.…”

“…Diffusional limitations have not been specially considered in this model. Although there are studies that highlight the importance of diffusional effects in grafting processes, [39] the approach adopted in this work represents the behavior of the system well, as evidenced by the comparison with experimental data. The influence of variables such as reaction time and reactant concentrations on the final properties, including the degree of grafting (DG), number-average molecular weight (M n ), and weight average molecular weight (M w ), is still a matter of debate.…”

Simulation of mass transfer and kinetics during double‐network formation using a heterogeneous model

“…In addition, the following simplifications are adopted: (a) all types of elementary reactions of PU are equal reactivity; 44 (b) the reactivity of TRIM is considered to be three times higher than that of MMA ( k p 22 = 3 k p 11 ); 47 (c) the reactivity of midchain radicals are equal to that of chain‐end radicals on the TRIM ( k p 3 i = k p 2 i , i = 1 or 2); 48 (d) the reactivity of chain‐end radicals towards PDBs is proportional to that towards TRIM ( k pip = f p k pi 2 , i = 1 or 2); and (e) the chain length dependencies are ignored. Although different radical types have an impact on reactivity, 49 the method with less parameters known is more defendable in the scope of the present work. Thus, propagation and termination rate coefficients are independent of the type of chain‐end radical ( k p 11 = k p 21 , k p 12 = k p 22 , k tc 11 = k tc 12 = k tc 22 , and k td 11 = k td 12 = k td 22 ) 48 …”

“…Although different radical types have an impact on reactivity, 49 the method with less parameters known is more defendable in the scope of the present work. Thus, propagation and termination rate coefficients are independent of the type of chain-end radical 48 The gel effect is introduced to elucidate the effect of viscosity on the termination rate coefficients.…”

Simulation of Molecular and Particle Properties of Polypropylene Produced in Multizone Circulating Reactors

“…In recent years, applying versatile modeling methods to investigate complicated polymerizations has received extensive attention with the rapid development of computer technology. In the polymer reaction engineering (PRE) field, the method of mapping the polymerization mechanism is mainly divided into two categories. − One is the stochastic modeling approach based on discrete reaction probabilities, in which the kinetic Monte Carlo technique is widely used. ,− This approach is free from computational stiffness issues and can track the individual polymer chains, but it demands a high cost of computation. The other is the deterministic method based on a series of differential equations, − where the most prominently employed one is the method of moments (MoM).…”