Monte Carlo Model for Arborescent Polyisobutylene Production in the Batch Reactor

Zhao, Yutian R.; McAuley, Kimberley B.; Puskás, Judit E.

doi:10.1002/mats.201300114

Cited by 15 publications

(89 citation statements)

References 37 publications

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“…As a result, only four apparent rate constants ( k pIMapp , k pMIapp , k pMMapp , and k pSMapp ,) were used in the model. Values of these parameters were estimated using experimental data and are reported in Table . Simulation results agreed well with experimental data corresponding to low average branching levels (about two branches per polymer chain), but were worse for polymers having higher branching levels …”

Section: Introductionsupporting

confidence: 56%

“…Figure shows a simplified reaction mechanism of “one‐pot” living copolymerization of IM and IB developed by Puskas et al The first step is an exchange reaction that converts 4‐(2‐methoxyisopropyl)styrene (MeOIM) to IM. A large excess of TiCl 4 , which is a Lewis acid (LA), is often used in the experiments to ensure that this exchange reaction goes to completion and that there is sufficient LA to initiate the living carbocationic polymerization.…”

Section: Introductionmentioning

confidence: 99%

“…The average branching level for the polymer chains that are produced is:

B_{kin} = \frac{{\overset{M}{true}}_{normaln}}{{\overset{M}{true}}_{n, theo}} - 1

{\overset{M}{true}}_{n, theo} = {normalM}_{IM} + \frac{{[IB]}_{normalo} - [IB]}{{[IM]}_{normalo} - [IM]} M_{IB}

where

{\overset{M}{true}}_{normaln}

, is the number average molecular weight for all polymers and

{\overset{M}{true}}_{n, theo}

is a theoretical molecular weight that would be obtained if IM were consumed as initiator only (i.e., if none of the V I groups could react and only linear PIB was produced).…”

Section: Introductionmentioning

confidence: 99%

“…Several research groups have developed mathematical models for SCVP and SCVCP systems. These models can be classified mainly into two different types: (i) dynamic material balance models and (ii) Monte Carlo (MC) models . These two areas are complementary in that each has advantages that the other does not.…”

Section: Introductionmentioning

confidence: 99%

“…For example, it is relatively straightforward to build individual material balance equations, especially using automated tools like PREDICI but not as easy to formulate and implement models using MC methods. However, MC models can provide very detailed information about the structure of polymer molecules, but dynamic material balance models may not be able to provide such detailed information unless a prohibitive number of differential equations is used …”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Advanced Monte Carlo Model for Arborescent Polyisobutylene Production in Batch Reactor

Zhao

McAuley

Iedema

et al. 2014

Macro Theory & Simulations

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An advanced Monte Carlo (MC) model is developed to predict the molecular weight distribution and branching level for arborescent polyisobutylene produced in a batch reactor via carbocationic copolymerization of isobutylene and an inimer. This new MC model uses differential equations and random numbers to determine the detailed structure of dendritic polymer molecules. Results agree with those from a traditional MC model for the same system, but the proposed model requires considerably less computational effort. The proposed MC model is also used to obtain information about polymer segments between branch points and dangling polymer segments.

show abstract

Section: Introductionsupporting

confidence: 56%

Section: Introductionmentioning

confidence: 99%

“…The average branching level for the polymer chains that are produced is:

B_{kin} = \frac{{\overset{M}{true}}_{normaln}}{{\overset{M}{true}}_{n, theo}} - 1

{\overset{M}{true}}_{n, theo} = {normalM}_{IM} + \frac{{[IB]}_{normalo} - [IB]}{{[IM]}_{normalo} - [IM]} M_{IB}

where

{\overset{M}{true}}_{normaln}

, is the number average molecular weight for all polymers and

{\overset{M}{true}}_{n, theo}

is a theoretical molecular weight that would be obtained if IM were consumed as initiator only (i.e., if none of the V I groups could react and only linear PIB was produced).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Advanced Monte Carlo Model for Arborescent Polyisobutylene Production in Batch Reactor

Zhao

McAuley

Iedema

et al. 2014

Macro Theory & Simulations

Self Cite

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Parallel models for arborescent polyisobutylene synthesized in batch reactor

2014

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A mathematical model is developed for estimating kinetic parameters that influence the production of arborescent polyisobutylene via carbocationic copolymerization of inimer (IM) and isobutylene. Six different propagation rate constants arise due to the two types of vinyl groups and three types of carbocations. These six parameters are estimated using parallel simulation systems in PREDICI that track (1) functional groups, (2) internal and dangling segments in the polymer, and (3) concentrations of IM and polymer molecules. Parameter estimates obtained using the proposed model result in a better fit to literature data than was obtained using a previous model that neglected two types of propagations reactions. Predictions from the proposed model are consistent with Monte Carlo simulations for molecular weight distribution of the internal and dangling segments.

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Statistical kinetic modeling procedure for cationic polymerization and its application to polyisobutylene

et al. 2023

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A statistical modeling procedure is established for carbocation polymerization with the characteristics of living with chain transfer. A single state model is suggested for cases of narrow molecular weight distribution, whereas a multi-state model is claimed for cases of broad distribution. In the multi-state case, it is demonstrated how the overall kinetics can be derived using the expectations and variances of the kinetic parameters rather than those of individual states, thereby simplifying the modeling step. Although the expectation and variance do not follow the relationship of the Arrhenius equation, a procedure is given for how to account for temperature dependence. The proposed statistical method minimizes the number of parameters to identify and therefore is expected to help establish a model with fewer experiments. The whole procedure is demonstrated through an experimental study of isobutylene polymerization.

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Monte Carlo Model for Arborescent Polyisobutylene Production in the Batch Reactor

Cited by 15 publications

References 37 publications

Advanced Monte Carlo Model for Arborescent Polyisobutylene Production in Batch Reactor

Advanced Monte Carlo Model for Arborescent Polyisobutylene Production in Batch Reactor

Parallel models for arborescent polyisobutylene synthesized in batch reactor

Statistical kinetic modeling procedure for cationic polymerization and its application to polyisobutylene

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