Calculation of the gel-point for non-equilibrium polycondensation taking into account the “substitution effect”

Кучанов, С.И.; Povolotskaya, Ye.S.

doi:10.1016/0032-3950(82)90125-3

Cited by 18 publications

(20 citation statements)

References 2 publications

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“…The magnitude of the approximation arising from the absence of connectivity correlations in the structure growth, Equation (13), was tested against the exact solution by the kinetic theory. [25][26][27] Except of cases of large differences between rate constants k ij and their unusual combinations, the differences between the values of gel point conversions obtained by kinetic and statistical theories (Equation (13)) are small, i.e., the statistical generation described by distribution (13) is a good approximation.…”

Section: Single-component System With Substitution Effectmentioning

confidence: 98%

Applicability of Statistical Theories of Network Formation

Dusˇek

2007

Macromolecular Symposia

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Summary: The basis of the statistical method of generation of branched and crosslinked structures as a Markov process is analyzed with special emphasis on the effect of differences in reactivities of functional groups. For irreversible reactions, it is important that the transition probabilities are calculated kinetically and that bonds once formed are not allowed to be reformed. The statistical methods are often a good approximation of real situation even if not all approximations used in the model are fulfilled. Cyclization is still a serious problem in modeling; For practical application it is recommended to rescale calculated ring-free dependences against the experimental gel point.

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Section: Single-component System With Substitution Effectmentioning

confidence: 98%

Applicability of Statistical Theories of Network Formation

Dusˇek

2007

Macromolecular Symposia

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“…(10) can be found using the method of characteristics [11,13]. That solution can be recast in such a way that the results obtained by this rigorous kinetic treatment of irreversible polymerizations can be interpreted in terms of the TBP, provided that each monad A i is labelled with the times q 0 ; .…”

Section: The Statistics Of the Configurational Structure Of Branched mentioning

confidence: 99%

Prediction of mean square radius of gyration of tree-like polymers by a general kinetic approach

Costa

Dias

2007

Polymer

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This paper describes a kinetic method to predict the z-average molecular mean square radius of gyration of tree-like polymers formed by irreversible reactions, assuming Gaussian chains. It is based on the population balance equations for the two-sided molecular distributions of pendant chains associated with every chemically distinguishable kind of bonds. An automated method for the solution of those equations is valid both before as well as after gelation for complex kinetic schemes. Examples of its use are presented with polycondensation systems leading to hyperbranched polymers, the anionic polymerization of mono-and divinyl monomers and a radical polymerization with terminal branching and transfer to polymer.

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“…Nonequivalence of statistical and kinetic methods of modeling was shown by Kuchanov and Povolotskaya [15] for a system with varying reactivities of substrates. Later, Spouge [16] and Faliagas [17] clarified that the statistical models, in fact, generate equilibrium distributions, whereas the kinetic methods are more suitable for modeling the systems with kinetically controlled reaction steps.…”

Section: Introductionmentioning

confidence: 97%

Forced Gelation in an Off‐Stoichiometric Copolymerization of A₂ and B₃ Monomers

Lechowicz

Galina

2010

Macromolecular Symposia

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Summary: A step-growth alternating copolymerization of monomers A 2 and B 3 was studied by an off-lattice Monte-Carlo simulation. In the random systems, i.e. with no substitution effect, the polymerization leads to gel formation provided the molar ratio of monomers is not very far from the stoichiometric one (A 2 : B 3 3: 2) and the reaction is carried out in one batch. A substantial deviation from the stoichiometric ratio may halt gelation altogether, even at conversions of the minority functional groups approaching unity. We demonstrate that in these non-gelling off-stoichiometric systems, one can force the system to gel, after all, without altering the kinetics or diffusion parameters of the reaction. The clue is to carry out the reaction in steps.

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Calculation of the gel-point for non-equilibrium polycondensation taking into account the “substitution effect”

Cited by 18 publications

References 2 publications

Applicability of Statistical Theories of Network Formation

Applicability of Statistical Theories of Network Formation

Prediction of mean square radius of gyration of tree-like polymers by a general kinetic approach

Forced Gelation in an Off‐Stoichiometric Copolymerization of A₂ and B₃ Monomers

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Calculation of the gel-point for non-equilibrium polycondensation taking into account the “substitution effect”

Cited by 18 publications

References 2 publications

Applicability of Statistical Theories of Network Formation

Applicability of Statistical Theories of Network Formation

Prediction of mean square radius of gyration of tree-like polymers by a general kinetic approach

Forced Gelation in an Off‐Stoichiometric Copolymerization of A2 and B3 Monomers

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Product

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Forced Gelation in an Off‐Stoichiometric Copolymerization of A₂ and B₃ Monomers