Kinetic model of hyperbranched polymers formed by the polymerization of AB2 monomer with a substitution effect

Cheng, Kuo‐Chung; Don, Trong‐Ming; Guo, Wenjeng; Chuang, Tsu-Hwang

doi:10.1016/s0032-3861(02)00545-1

Cited by 24 publications

(31 citation statements)

References 36 publications

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“…[28][29][30]34,37 The X w calculated by the exact kinetic model are identical to those determined in the present study, showing that the kineticprobability minimal model provides accurate and significant information on these hyperbranched polymerizations.…”

Section: Ab-branching Factor δ Ab δ Ab Simplifies Tosupporting

confidence: 74%

First Shell Substitution Effects in Hyperbranched Polymers: Kinetic−Recursive Probability Analysis

Fradet

Tessier

2007

Macromolecules

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The kinetic-probability approach taking into account first shell substitution effects (FSSE) is applied to hyperbranched condensation polymerizations. Simple explicit relationships giving the mass-average molar mass (M w ) and mass-average degree of polymerization (X w ) as a function of conversion, of initial monomer mixture composition and of polymer architecture at a given reaction time are derived using the "in-out" recursive probability approach. Three experimentally available parameters, the A-, B-, and AB-branching factors (δ A , δ B , and δ AB ) are introduced to describe polymer branching. δ B generalizes Frey's degree of branching to polymerizations involving any type of monomer mixture and can directly be used to calculate polymer M w . δ AB characterizes the substitution effects induced on A-group reactivity by the reaction of B-groups (and vice versa). This effect, generally neglected in hyperbranched polymerization studies, may exert a dramatic influence on hyperbranched polymer dispersity (M w /M n ). Two systems, AB f polymerizations and AB f + B g polymerizations, are taken as examples and discussed to illustrate the method. The polymerizations of 2,2-bis(hydroxymethyl)propanoic acid (BMPA) (AB 2 polymerization) and of BMPA with Pentaerythritol (AB 2 + B 4 polymerization) are more specifically studied. The results are compared to experimental data, showing that negative FSSE involving both OH and COOH groups take place, leading to much lower dispersities and branching factors than expected for ideal (random) polymerizations. The method can be extended to any type of condensation polymerizations.

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Section: Ab-branching Factor δ Ab δ Ab Simplifies Tosupporting

confidence: 74%

First Shell Substitution Effects in Hyperbranched Polymers: Kinetic−Recursive Probability Analysis

Fradet

Tessier

2007

Macromolecules

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“…As regards the AB 2 problem with substitution, significant progress has been achieved in studies by Galina [5,8], Cheng [6] and Zhou [7,9]. Here, the behaviour in time of the degree of branching [5,6], the dendritic and linear units [6] and the fraction of cyclized molecules [5] has been obtained. In the work by Galina [5] and Cheng [6] the average microstructural properties have been computed using the generating functions approach.…”

Section: Introductionmentioning

confidence: 98%

“…In other words, all B groups in the AB 2 monomer units in the polymer have the same reactivity. Yet, the equal reactivity is questioned if a substitution effect is taken into account [6].…”

Section: Introductionmentioning

confidence: 99%

“…Here, the behaviour in time of the degree of branching [5,6], the dendritic and linear units [6] and the fraction of cyclized molecules [5] has been obtained. In the work by Galina [5] and Cheng [6] the average microstructural properties have been computed using the generating functions approach. More recently, the 2-dimensional chain-length/degree-of-branching distribution was obtained in the form of an analytical expression by Zhou [7] under the assumption that no cyclization reaction takes place.…”

Section: Introductionmentioning

confidence: 99%

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Predicting multidimensional distributive properties of hyperbranched polymer resulting from AB2 polymerization with substitution, cyclization and shielding

Kryven

Iedema

2013

Polymer

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A deterministic mathematical model for the polymerization of hyperbranched molecules accounting for substitution, cyclization, and shielding effect has been developed as a system of nonlinear population balances. The solution obtained by a novel approximation method shows perfect agreement with the analytical solution in limiting cases and provides, for the first time in this class of polymerization problems, full multidimensional results.

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“…While the slope (i.e., the scaling exponent) nearly coincides with the theoretical value 1.176 for linear chains, 211, (1.178), in case of the 655 system a value 1.196 is found near to Flory's original exponent 1.2. Mean‐field theory and Monte Carlo simulations of lattice and off‐lattice dendrimers as well as experiments gave similar results, i.e., an exponent near 6/5 for various spacer lengths. Obviously, short‐chain effects are slightly more pronounced for higher functionalities.…”

Section: Resultsmentioning

confidence: 54%

Monte Carlo Simulation Studies of the Size and Shape of Regular Three Generation Dendrimers

Wawrzyńska

Eisenhaber

Parzuchowski

et al. 2014

Macro Theory & Simulations

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By the use of a dynamic Monte Carlo method, three‐generation dendrimers of type F1F2F2 with functionalities F1 = 3 to 6 and F2 = 2 to F1–1 are simulated and investigated as functions of spacer lengths, with a total chain length up to 200 000 segments. Highly diluted athermal and theta solutions are studied as well as properties of non‐reversal random walk dendrimers for comparison. For athermal conditions mean square dimensions obey the same scaling law regarding the total number of bonds as linear chains, irrespective of functionality and complexity. Likewise the theta parameter is the same for all systems investigated. Dimensions of theta systems are slightly expanded as compared to non‐reversal random walk data, the effect increasing with increasing F1 and F2 while shape data near to theta conditions fairly well coincide with those of non‐reversal random walks.

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Kinetic model of hyperbranched polymers formed by the polymerization of AB2 monomer with a substitution effect

Cited by 24 publications

References 36 publications

First Shell Substitution Effects in Hyperbranched Polymers: Kinetic−Recursive Probability Analysis

First Shell Substitution Effects in Hyperbranched Polymers: Kinetic−Recursive Probability Analysis

Predicting multidimensional distributive properties of hyperbranched polymer resulting from AB2 polymerization with substitution, cyclization and shielding

Monte Carlo Simulation Studies of the Size and Shape of Regular Three Generation Dendrimers

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