Markovian statistics and simplex algorithm for carbon-13 nuclear magnetic resonance spectra of ethylene-propylene copolymers

Cheng, H. N.

doi:10.1021/ac00248a040

Cited by 42 publications

(33 citation statements)

References 10 publications

(12 reference statements)

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“…Fitting of the experimental triad intensities to Markovian statistical models [26][27][28] and mixture models [29,30] was achieved with QuickBasic programs, as published earlier [26,27]. These were optimized through a simplex algorithm and could accommodate Markovian and Bernoullian reaction probability models and their mixtures.…”

Section: Model Calculationsmentioning

confidence: 99%

NMR analysis and triad sequence distributions of poly(3-hydroxybutyrate-co-3-hydroxyvalerate)

et al. 2020

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Polyhydroxyalkanoates (PHAs) are considered promising "green" alternatives to synthetic polymers because they are bio-derived, biodegradable and biocompatible. The properties of bacterial PHA copolymers depend on their microstructures, which can be modified with the use of different fermentation processes and feed materials. Thus, it is desirable to have an improved testing method for the determination of PHA microstructures. In this work, a detailed NMR analysis of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) microstructure was made. Previously only two of the hydroxyvalerate 13 C NMR peaks have been assigned at the triad level. In this work, three of the 13 C hydroxyvalerate peaks and two of the hydroxybutyrate peaks were found to be split into four peaks each due to comonomer sequence effects. Using eight copolymer samples with a wide compositional range, we were able to assign all these peaks to B-centered and V-centered triad sequences. Through curve deconvolution, the triad intensities were determined. These triad sequence intensities can then be analyzed via both the first-order Markovian and two-component Bernoullian models to obtain more in-depth information on copolymer composition and comonomer reactivities.

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Section: Model Calculationsmentioning

confidence: 99%

NMR analysis and triad sequence distributions of poly(3-hydroxybutyrate-co-3-hydroxyvalerate)

et al. 2020

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“…Markov chains have been widely applied to simulate geologic processes (Harbaugh and Bonham-Carter, 1970;Lin and Harbaugh, 1984;Davis, 1986), polymer formation (Lowry, 1970;Carman et al, 1977;Bruns et al, 1981;Cheng, 1982), and chemical kinetics (Formosinho and Miguel, 1979). Transition probabilities for a first-order Markov chain can be estimated from the aggregate data using the method of Kalbfleisch and Lawless (1984).…”

Section: Introductionmentioning

confidence: 99%

A First-Order Markov-Chain Model of Zeolite Crystallization

Hawkins

1989

Clays and clay miner.

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Abstraet--A method using a finite, first-order Markov chain is presented to estimate rate constants for zeolite formation from experimental nuclear magnetic resonance (NMR) data on the abundance of different silica oligomers. An experimental design is suggested by which this method can be implemented. The method uses weighted least squares to estimate transition probabilities from aggregate NMR data. Rate constants, equilibrium constants, and free energies of elementary zeolite-forming reactions can be estimated. Hypothetical zeolite-forming reactions can also be modeled. An example of modeling, using hypothetical data, shows how zeolite formation can result from reactions involving mainly silica cyclic tetramers.

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“…This spectrum clearly shows that, using the assignments of Cheng and others, the statistics of monomer incorporation into the copolymer can be determined to at least the triad level (Ref. 10 Structure and dynamics become particularly important when considering the blend of a homopolymer and a copolymer. case of such a blend the composition and dynamics of the two In the phases can dramatically affect the properties of the polymer product.…”

Section: Mas 1 3 Cmentioning

confidence: 78%

Dynamics of polypropene and propene‐ethylene copolymers at temperatures above ambient

Zeigler¹

1994

Macromolecular Symposia

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Several applications of solid‐state nuclear magnetic resonance (NMR) spectroscopy to studying polyolefin mobility at temperatures ranging from room temperature to above the polymer melt are described. 13C NMR can be used with magic‐angle spinning and high‐power proton decoupling to determine the fraction of mobile polymer in polypropene and to characterize the nature of the polymer chain motions as a function of sample temperature. Similar techniques can be used to characterize the local motions of complex copolymer systems such as heterophasic ethylene‐propene copolymers. The practicality of low‐speed magic angle spinning to observe quantitative high‐resolution NMR spectra of neat, molten polymer samples is also described.

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Markovian statistics and simplex algorithm for carbon-13 nuclear magnetic resonance spectra of ethylene-propylene copolymers

Cited by 42 publications

References 10 publications

NMR analysis and triad sequence distributions of poly(3-hydroxybutyrate-co-3-hydroxyvalerate)

NMR analysis and triad sequence distributions of poly(3-hydroxybutyrate-co-3-hydroxyvalerate)

A First-Order Markov-Chain Model of Zeolite Crystallization

Dynamics of polypropene and propene‐ethylene copolymers at temperatures above ambient

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