Polymerization in catalyst particles: Calculation of molecular weight distribution

Abstract

Factors which affect and broaden molecular weight distributions are investigated for polymerizations in catalyst particles which are accumulating polymer, such as Ziegler polymerizations of olefins. Expressions for the Q value, or ratio of weight‐average to number‐average molecular weight, are derived for simple, but important linear models. These expressions are of the form Q = FSX for a kinetic scheme in which polymer chains have an infinite growing lifetime, and Q = 2FGSX for a kinetic scheme in which termination by hydrogen is dominant and each site produces many chains. The factors F, G, S, and X are equal to or greater than unity: F depends on particle geometry and the nature of diffusion and reaction; G depends on environmental history of the particle; S depends on the distribution of site activities; and X depends on the distribution of particle sizes. Effects of reactor type are also studied quantitatively.

Effect of reactor residence time distribution on the size distribution of polymer particles made with heterogeneous Ziegler‐Natta and supported metallocene catalysts. A generic mathematical model

“…catalyst deactivation rate parameters, see Eq. (17) amount (in mol) of active sites in the particle concentration of active sites on the catalyst particle, in mol/cm3 initial concentration of unstable active sites on the catalyst, in mol/cm3 initial concentration of stable active sites on the catalyst, in mol/cm3 diameter of catalyst/polymer particle, in cm adjustable parameter for non-ideal RTD, defined in Fig. 12 residence time distribution adjustable parameter for non-ideal RTD, defined in Fig…”

“…Another incentive for supporting metallocenes is the enhancement of stereochemical and regiochemical control to make poly(propy1ene) with properties closer to those obtained with conventional heterogeneous Ziegler-Natta cataSome researchers advocate that, due to diffusion resistances, catalyst fragments in different radial position within the polymer particle are exposed to different concentrations of monomer, comonomer, and chain transfer agent (generally hydrogen). If these diffusion resistances are significant, one should observe a decrease in the polymerization rate (as compared to the polymerization rate in absence of monomer diffusion resistances), and broadening of the molecular weight and copolymer chemical composition distributions [16][17][18][19][20][21][22][23][24][25][26][27].…”

Multiscale modeling of syndiospecific styrene polymerization

“…Schmeal [8,9] and Nagel et al [10], used the SCM model for olefins polymerization over Ziegler-Natta catalysts. They concluded that with a single active site catalyst; this model could not predict the MWD.…”

“…This model is extended mainly from PMGM model and MGM model by taking the effect of monomer diffusion at both the macro-and microparticle levels. It has also been noticed that the model can give higher values of PDI, (PDI about [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Fractal approach for modeling the morphology evolution of olefin polymerization with heterogeneous catalysts

“…Moreover, many polymerization models have been developed, such as the solid pore model,1 the polymeric core model,2 the polymeric flow model,3–5, the multigrain model,6, 7 the improved multigrain model,8, 9 and the multiactive center model 10, 11. Of these models, the multigrain model is relatively close to the reality of particle growth and has widely been accepted.…”