Advanced Monte Carlo Modeling Using Weight‐Based Selection of Arborescent Polyisobutylene Molecules in a Batch Reactor

Abstract

and copolymerization with one or more different vinyl monomers, which is called self-condensing vinyl copolymerization (SCVCP). [5][6][7][8][9][10][11][12][13] Puskas and Grasmüller have developed a "one-pot" living carbocationic copolymerization of IM and isobutylene (IB) to produce arborescent polyisobutylene ( arb PIB), [ 14,15 ] which greatly reduced the labor required compared with previous multi-step processes. [16][17][18] This one-pot living copolymerization system is illustrated in Figure 2 , where there are two types of vinyl groups, i.e., V I and V M , and three types of chloride end groups, i.e., C I , C M , and C S . V I is the vinyl group on the IM and V M is the vinyl group on the IB monomer. C I is an unreacted chloride group on the IM; C M is a chloride group formed after a reaction with V M , and C S is a chloride group formed after a reaction with V I . Each type of chloride group can be uncapped to form an active carbocation that can react with either type of vinyl group. As a result, there are six different propagation rate constants, which are named k pII , k pIM , k pMI , k pMM , k pSI and k pSM . The fi rst subscript letter after k p is the type of chloride group that is uncapped to produce the reactive carbocation and the second subscript is the type of vinyl group that is consumed. The corresponding propagation reactions are summarized in Table 1 , along with estimated values of the corresponding apparent rate constants. The apparent rate constants in An advanced Monte Carlo (MC) method is developed, using weight-based selection of polymer chains, to predict the molecular weight distribution (MWD) and branching level for arborescent polyisobutylene ( arb PIB) at the end of a batch reaction. This new weight-based MC method uses differential equations and random numbers to determine the detailed structure of arb PIB molecules. Results agree with those from an advanced number-based MC method. The proposed weight-based algorithm requires approximately twice the computation time of the numberbased method, but produces more accurate results in the high-molecular-weight portion of the MWD when the same number of polymer chains is assembled.

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

“…These propagation rate constants arise from three different types of chloride end groups and two different types of vinyl groups. It is a great advantage that the model does not take much computational effort (<1 s for each simulation in Matlab and ≈15 s in PREDICI) compared with traditional Monte Carlo methods which take many days for each simulation and our advanced Monte Carlo methods which take several hours . Simulation results agree with those from Monte Carlo simulation.…”

“…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.…”

Hyperbranched Polymers Formed through Irreversible Step Polymerization of AB2‐Type Monomer in a Continuous Flow Stirred‐Tank Reactor (CSTR)

“…Random selection of a unit means that the polymer molecule is selected on the weight basis. Because each molecule contains only one unreacted A group, the number‐based selection can also be done by choosing one unreacted A group randomly, although the weight‐based selection process is employed in the present MC simulation.…”