Monte–Carlo Simulation of Ester Exchange Reactions in PET/PEN Blends

Abstract

Monte–Carlo kinetic simulations are performed to study exchange reactions in PET/PEN blends. Chain distribution of the blend is simulated at various mixing conditions. The average length of PET and PEN repeating units decreases with increasing exchange reactions. Derivative of heat flow is modeled at Tg region during mixing. Two peaks are observed on the derivative of heat flow curve at the early stages of mixing, indicating formation of an immiscible blend. With increasing mixing time, miscibility between two phases increasea and the peaks converge toward each other and finally form a single peak. The Monte–Carlo simulation results are in fine agreement with experimental data obtained from different systems. magnified image

Importance of Statistical Factors in the Description of Kinetics of a Segmental Exchange in Polyester Systems. Re‐Analysis of Reshuffling in PET/PEN Blends

“…Results of fitting of rate constants of reshuffling to the experimental points: the “degree of randomness” and the average lengths of PET and PEN blocks (RD, L T , L N ), and the simulated molar contributions of copolymer dyads. System properties: PET/PEN blending, PET 25 wt%, temperature 280 °C, experimental points from ref . The estimated rate constants: k TTNN = 3.26 · 10 −5 , k TNTN = 4.98 · 10 −5 mol −1 · L · s −1 .…”

“…The results show that reshuffling of copolymer segments involving only internal units belongs to quite a large group of reactions in which statistical factors have to be taken into account while analyzing their kinetics. Re‐analysis of the experimental results of Mahjub et al allowed estimation of the rate constants of transformation of two different homo‐dyads into hetero‐dyads ( k TTNN ) and of the reverse reaction of transformation of hetero‐dyads into homo‐dyads ( k TNTN ). The determined rate constant of formation of homo‐dyads appeared to be almost twice higher than the rate constant of the reverse reaction of formation of hetero‐dyads, what results in a slight increase of homo‐dyads in the eventual product in comparison to random copolymer.…”

“…Recently Mahjub et al published a paper in which they assumed equal rate constants of reactions between homo‐ and hetero‐dyads in PET/PEN blends (TT + NN and TN + NT dyads, where T and N denote residues of terephthalic and naphthalic acids, respectively). However, the Monte Carlo simulation of the segmental exchange gave the final copolymer with the “degree of randomness” RD (defined as the ratio of half of the fraction of hetero‐dyads to the product of fractions of copolymer units; Equation ) of the final product equal to about 0.9 …”

“…At this stage of discussion the statistical factors are neglected but it is worth already mentioning that taking them into account results in the apparent rate coefficients for such reverse reactions being not equal. Recently Mahjub et al [2] published a paper in which they assumed equal rate constants of reactions between homoand hetero-dyads in PET/PEN blends (TT þ NN and TN þ NT dyads, where T and N denote residues of terephthalic and naphthalic acids, respectively). However, the Monte Carlo simulation of the segmental exchange gave the final copolymer with the ''degree of randomness'' RD (defined as the ratio of half of the fraction of hetero-dyads to the product of fractions of copolymer units; Equation 1) of the final product equal to about 0.9…”

Monte Carlo simulation of the dispersion polymerization of styrene

“…In the second stage, particles grow by absorbing polymer and monomer from the media followed by polymerization within the particles. 14,15 Several studies have been performed on the kinetics of dispersion polymerization process but none of them are capable to simulate the entire process and predict the particle size without using experimental data throughout the reaction. Paine 11 developed a multibin kinetic model for the coalescence of unstabilized particles and quantied the role of stabilizer molecules in the particle formation step.…”