Monte Carlo simulation of molecular weight distribution and copolymer composition in transamidation reaction of polyamides

Abstract

Melt mixing of polyamides results in exchange reaction and generation of copolymers. In this work, Monte Carlo method is used to simulate the time evolution of molecular weight distribution (MWD) and copolymer composition during the exchange reaction process between polyamides with AA and BC structure. The influences of initial composition and molecular weight have been investigated. Decrease in the difference between the average molecular weight of two kinds of polyamides results in faster approach of the MWD toward Flory's dis-tribution and higher probability of producing copolymers. When the ratio between the numbers of initial molecules of two homopolymers is increased, the number of generated copolymers is reduced and the wider MWD is obtained.

A multi-thread parallel computation method for dynamic simulation of molecular weight distribution of multisite polymerization

“…Several of methods have been proposed to compute MWD, including the molecular weight moment method (Timothy and Kyu, 1997), the lumping method (Arno et al, 1978), the continuous variable methods (Stanley and Gerald, 1967), the numerical Monte Carlo method (Al-Harthi et al, 2006, 2007Yao et al, 2012), the transformed domains method (Miller et al, 1996;Mills, 1986), the discrete Galerkin method (Deuflhard and Wulkow, 1989;Wulkow, 1996), the reduced stiffness via quasi-steady-state approximation method (Enrique et al, 2010;Zapata-Gonzales et al, 2012), the serial variable decoupling method (Chen et al, 2009), and Flory method (Flory, 1953;Soares, 2001;Soares and McKenna, 2012). Timothy and Kyu (1997) proposed a novel method that utilizes polymerization kinetic equations and molecular weight moment equations in conjunction with a function that describes the weight fraction of the polymer in a finite chain length interval; in this method, the entire range of molecular weight is divided into a finite number of intervals, and the weight fractions of the polymers in these intervals are calculated.…”

“…Disproportionation reactions and model probabilities were calculated from the polymerization kinetic parameters and reactor conditions; the model predicts monomer conversion, average molecular weight, polydispersity, and complete molecular weight distribution at any polymerization time or monomer conversion. Yao et al (2012) used the Monte Carlo method to simulate the time evolution of MWD and copolymer composition during the exchange reaction process between polyamides with AA and BC structure; they analyzed the influences of initial composition and molecular weight. Miller et al (1996) in chain length; ordinary differential equations (ODEs) were converted to a finite set of partial differential equations, which were solved by taking the Laplace transform with respect to the chain length; the procedure yielded the ordinary differential equations in time.…”

Molecular Weight Distribution Simulation in Equilibrium Ring‐Opening Polymerization: A New Macroscopic Model

“…Molecular weight (MW) and molecular weight distribution (MWD) are very important molecular parameters to describe the structure of polymers and key factors that affect their properties . Though examination methods such as gel permeation chromatography and small‐angle laser scattering are widely used, simulation has been extensively studied and becomes a near irreplaceable method to investigate MWD . The Monte Carlo method was adopted by former researchers to study kinetic parameters and MWD of various polymerizations, including free radical polymerization, polycondensation, and ionic polymerization .…”

“…[1,2] Though examination methods such as gel permeation chromatography and small-angle laser scattering are widely used, [3][4][5] simulation has been extensively studied and becomes a near irreplaceable method to investigate MWD. [6][7][8][9][10][11][12][13] The Monte Carlo method was adopted by former researchers to study kinetic parameters and MWD of various polymerizations, including free radical polymerization, polycondensation, and ionic polymerization. [6][7][8][9][10] MWD of mixtures that coincided well with experimental results was given as well.…”

“…[6][7][8][9][10][11][12][13] The Monte Carlo method was adopted by former researchers to study kinetic parameters and MWD of various polymerizations, including free radical polymerization, polycondensation, and ionic polymerization. [6][7][8][9][10] MWD of mixtures that coincided well with experimental results was given as well. However, simulations of polysiloxane, polyamide, and polylactic acid synthesis were rarely investigated and discussed according to current literature.…”