A decreasing‐table technique to increase the efficiency of monte carlo simulations of polymer modification reactions

Harwood, H. James; Landoll, L. M.; Kempf, Karl G.

doi:10.1002/pol.1978.130160206

Cited by 12 publications

(1 citation statement)

References 3 publications

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“…Theoretical [~4-4lJ~ numerical [42] and Monte Carlo methods [43][44][45][46][47] have been developed for calculating these various quantities from values of k o , kl and k z . In addition~ convenient methods for deducing k o , kl and kz from nmr spectral information are available [48,49].…”

Section: Utilization Of N-add Distributions Measured By Nmrmentioning

confidence: 99%

NMR Analysis of Stereo Regular Copolymers

Harwood

1979

Preparation and Properties of Stereoregular Polymers

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Stereoregular copolymers are formed by the chemical modification of stereoregular polymers, by copolymerizations of ~-olefins in the presence of stereoregulating catalysts and by ring opening copolymerizations of chiral monomers. Also appropriate for consideration are polydienes containing cis-l,4-and trans-l,4-units as well as those containing 1,2-{or 3,4-) and 1,4-units. Analysis of such copolymers by NMR spectroscopy provides information about their compositions and the arrangement of monomer units along their chains. Such information is valuable for understanding the chemical behavior of stereoregular polymers and the mechanisms of stereoregular polymerization processes. STRUCTURAL FEATURES PRESENT IN STEREOREGULAR COPOLYMERSIf a stereoregular copolymer containing A and B monomer units is considered, then some of its structural features that can be measured by NMR spectroscopy can be listed as follows.

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Section: Utilization Of N-add Distributions Measured By Nmrmentioning

confidence: 99%

NMR Analysis of Stereo Regular Copolymers

Harwood

1979

Preparation and Properties of Stereoregular Polymers

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Computer simulation of the steady state in reversible polymer‐analogous reactions, 2. Simulation of the statistics in detailed balance

Krieger¹,

Klesper²

1987

Makromol. Chem.

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The steady state of reversible polymer-analogous reactions is simulated by Monte Carlo methods. Two types of sets of relative rate constants were investigated, first, Kl = K, = K3, K, . K3 = (K,),, and second, Kl 9 K,, K, * K3, K, 9 K3, Kl . K3 = (K,)'. For both cases a detailed balance was found. The sequence probabilities depend on dimensionless relative rate constants K, only, while the rates of sequence flow depend on reaction probabilities p and ordinary rate constants k. For the first case, the sequence probabilities obey a Bernoullian statistics, while for the second case a first-order Markov statistics is found. and the reverse reactions are to be considered. These are written kl = k(AAA), & = k(AAB+), & = k(BAB), k4 = k(BBB), k, = k(ABB+), and & = k(ABA), whereby the central monomeric unit A or B within the triad in parenthesis is the reacting monomeric unit, and the sign + indicates the inclusion of both mirror image forms, i. e. AAB + includes AAB and BAA. For the purpose of simulation, the k ( X X X ) ( X = A or B) have been replaced by the reaction probabilities p ( X X X ) , possessing values between 0 and 1, all p ( X X X ) of a set of reaction probabilities differing from their corresponding k(XXX) by the same factor. Important for the results of the a) Part I: ~f .~) .

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Computer simulation of the steady state in reversible polymer‐analogous reactions, 3. Flows and statistics in detailed balance

Krieger¹,

Klesper²

1988

Makromol. Chem.

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The steady state of reversible polymer-analogous reactions was simulated by Monte Carlo calculations. The length of the simulated copolymer chains was chosen large enough to yield data with an acceptable degree of statistical fluctuation. Two types of sets of relative rate constants K were investigated, first K , = K , = K , , and second K, # K 2 , K , # K , , K2 # K , , with K, . K, = K i . The relative rate constants K are defined as K, = k(AAA)/k(ABA), K , = k(AAB+)/k(ABB+), and K, = k(BAB)/k(BBB), where k is the ordinary rate constant pertaining to the reaction of the central monomeric unit in the triad given in parentheses, with two different types of monomeric units A and B in the binary copolymer. For both types of sets of relative rate constants the simulation showed a detailed balance to prevail for the kinetics in the steady state. It was also shown that the same kinetics and statistics were obtained in the steady state when starting the simulation first from a homopolymer consisting of A-monomeric units, and then from a homopolymer of B-monomeric units. Based on the finding of a detailed balance and on the definition of K, it could be shown by analysis that the first type of the sets of K leads to a Bernoullian statistics of the copolymers in the steady state, while the second type leads to a first-order Markov statistics. Correspondingly, equations are given which allow to calculate the relative rate constants from statistics and vice versa.

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A decreasing‐table technique to increase the efficiency of monte carlo simulations of polymer modification reactions

Cited by 12 publications

References 3 publications

NMR Analysis of Stereo Regular Copolymers

NMR Analysis of Stereo Regular Copolymers

Computer simulation of the steady state in reversible polymer‐analogous reactions, 2. Simulation of the statistics in detailed balance

Computer simulation of the steady state in reversible polymer‐analogous reactions, 3. Flows and statistics in detailed balance

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