General matrix formula for the weight-average molecular weights of crosslinked polymer systems

Tobita, Hidetaka

doi:10.1002/(sici)1099-0488(19980930)36:13<2423::aid-polb17>3.0.co;2-5

Cited by 16 publications

(20 citation statements)

References 14 publications

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“…For example, the weight-average degree of polymerization, P w can be obtained by simply taking the arithmetic average of the sample. Incidentally, the analytic representation of P w can always be obtained by using the random sampling technique [20][21][22][23][24].…”

Section: Simulation Methodsmentioning

confidence: 99%

Model-Based Reactor Design in Free-Radical Polymerization with Simultaneous Long-Chain Branching and Scission

Tobita

2015

Processes

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Polymers are the products of processes and their microstructure can be changed significantly by the reactor systems employed, especially for nonlinear polymers. The Monte Carlo simulation technique, based on the random sampling technique, is used to explore the effect of reactor types on the branched polymer structure, formed through free-radical polymerization with simultaneous long-chain branching and scission, as in the case of low-density polyethylene synthesis. As a simplified model for a tower-type multi-zone reactor, a series of continuous stirred-tank reactors, consisting of one big tank and the same N-1 small tanks is considered theoretically. By simply changing the tank arrangement, various types of branched polymers, from star-like globular structure to a more randomly branched structure, can be obtained, while keeping the following properties of the final products, the monomer conversion to polymer, the average branching and scission densities, and the relationship between the mean-square radius of gyration and molecular weight.

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Section: Simulation Methodsmentioning

confidence: 99%

Model-Based Reactor Design in Free-Radical Polymerization with Simultaneous Long-Chain Branching and Scission

Tobita

2015

Processes

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“…The weight-average DP within all sol molecules, P w sol , can be obtained from the matrix formula developed for the pregelation period 20,23 :…”

Section: Number-average and Weight-average Molecular Weights Within Tmentioning

confidence: 93%

“…Markovian statistics can be used for this problem, and a general solution for the weight-average molecular weight in the pregelation period was developed as a matrix formula. 20,23 The gel point is simply described as a point at which the largest eigenvalue of the matrix Q, which defines the chain-connection statistics, reaches unity.…”

Section: Introductionmentioning

confidence: 89%

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Postgel properties in the statistical crosslinking of heterochains. I. Systems withN types of chains

Tobita

Sakai

Tani

2000

J. Polym. Sci. B Polym. Phys.

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“…By utilizing the Markovian model for the chain connection statistics, the random sampling technique can be used to obtain the analytic solution of the weight-average chain length of the nonlinear polymer systems, in a matrix formula. [15][16][17][18][19] Although the matrix approach is limited to the average properties, it can give more accurate values compared with the MC simulation. The matrix approach and the MC simulation method are nicely complementary.…”

Section: Introductionmentioning

confidence: 99%

Free‐Radical Polymerization with Long‐Chain Branching and Scission: Markovian Solution of the Weight‐Average Molecular Weight

Tobita

2014

Macro Theory & Simulations

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Analytic solution for the weight‐average chain length in a matrix formula, trueP¯w=wboldsboldw+wF(I−M)−1s, is derived for free‐radical polymerization with simultaneous long‐chain branching and scission. Illustrative calculations are conducted for a batch polymerization. With bimolecular termination by combination, gelation could be observed. Assuming the same polymerization kinetics for branching and scission in the post‐gel period, the formed gel molecule could be degenerated into sol molecules again, i.e., degelation might occur. Both the gelation and degelation points are defined as the point when the largest eigenvalue of M is unity. The matrix formula is suitable to determine accurate values, while the Monte‐Carlo simulation can give much more detailed information. These two approaches are nicely complementary.

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General matrix formula for the weight-average molecular weights of crosslinked polymer systems

Cited by 16 publications

References 14 publications

Model-Based Reactor Design in Free-Radical Polymerization with Simultaneous Long-Chain Branching and Scission

Model-Based Reactor Design in Free-Radical Polymerization with Simultaneous Long-Chain Branching and Scission

Postgel properties in the statistical crosslinking of heterochains. I. Systems withN types of chains

Free‐Radical Polymerization with Long‐Chain Branching and Scission: Markovian Solution of the Weight‐Average Molecular Weight

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