Advanced Monte Carlo Model for Arborescent Polyisobutylene Production in Batch Reactor

Abstract

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.

Applying Multidimensional Method of Moments for Modeling and Estimating Parameters for Arborescent Polyisobutylene Production in Batch Reactor

“…Based on the research of Puskas and Lanzendörfer, there are two different paths for LA to initiate the reaction (See Figure ), and path A is dominant when [LA] 0 < [IM] 0 , while path B is dominant when [LA] 0 > [IM] 0 . Similar to our previous research, we combine the rates from the two different paths and express the six different rates of propagation using the apparent rate constants in Table . Because the number and type of end groups on the polymer molecules are important for determining the rates at which they react, four different indexes are used to track individual polymer molecules in arb PIB system.…”

“…To address this computational issue, two new advanced MC algorithms were developed, which combine dynamic material balances and stochastic calculations. One of these new MC models constructs polymer molecules selected on a number basis, whereas the other selects the molecules on a weight basis, providing more accurate simulation results for the high molecular weight tail of the MWD for arb PIB . These two advanced MC models can achieve the same results as our traditional MC model, but with much less computational effort (hundreds of times faster).…”

“…Three MC‐based models exist that could provide reliable predictions of the entire MWD and branching levels, if accurate values of the apparent rate constants were available. Unfortunately, the MC methods are all prohibitively slow to be suitable for parameter estimation . On the other hand, dynamic material balance models that have been used for preliminary parameter estimation studies require substantially less computational effort.…”

Branching determination from radius of gyration contraction factor in radical polymerization

“…This is due to the 'conditional' character of the procedure to generate architectures, meaning that the computational effort is fully spent on molecules of the desired dimensions: number of monomer units, number of branch points and number of combination points. Using other stochastic methods like kinetic Monte Carlo (Gillespie [34], Zhao et al [35]) to detect the effect of topological variation would require the generation of whole populations of molecules, very few of which satisfy the predefined dimensions. This may be quantified by exploring Fig.…”

Molecular Architecture Manipulation in Free Radical Copolymerization: An Advanced Monte Carlo Approach to Screening Copolymer Chains with Various Comonomer Sequence Arrangements

“…[ 14,15 ] Considering the fact that in copolymerizations macromolecules with various architectural features are produced, an appropriate identifi cation card capable of storing maximum possible topological characteristics of the generated chains should be defi ned and issued. In addition, the data storage algorithm and corresponding computer code are of vital importance and must be designed to improve the calculation speed of the KMC simulator.…”