Note on the Kinetics of Systems Manifesting Simultaneous Polymerization-Depolymerization Phenomena

Blatz, P. J.; Tobolsky, A. V.

doi:10.1021/j150440a004

Cited by 160 publications

(104 citation statements)

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“…Such equations play an important role in reversible polymerization processes and in related aggregation and fragmentation processes. [30][31][32][33][34][35] In our model, the variable window sizes for the chain fusion/fragmentation processes and for the irreversible mechanical breakage of chains imposes somewhat intricate constraints on the corresponding fusion/fragmentation and breakage kernels which must be accounted for correctly as many detailed features, revealed by the subsequent numerical simulations, depend non-linearly on these window sizes themselves. The details of how these window size constraints are handled are explained in the Appendix.…”

Section: Modelmentioning

confidence: 99%

Mechanically Induced Homochirality in Nucleated Enantioselective Polymerization

2017

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Section: Modelmentioning

confidence: 99%

Mechanically Induced Homochirality in Nucleated Enantioselective Polymerization

2017

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“…In Table I we have compared the size distribution and its moments for all addition models. Physically, the large time behavior of addition models is not so important, as they should be replaced by condensation models, and also fragmentation terms should be included (16)(17)(18)(19)(20).…”

Section: U(t) ~-Lht (T ~ ~)mentioning

confidence: 99%

“…The kinetic equations for reversible coagulation (2,(16)(17)(18)(19)(20) yield more realistic size distributions for large times; e.g., the "most probable solutions" in the Flory-Stockmayer theory of polymerization (12,21) for a given extent of reaction can be found as the stationary solution of the kinetic equations of reversible polymerization (20).…”

Section: Introductionmentioning

confidence: 99%

Exactly soluble addition and condensation models in coagulation kinetics

Hendriks¹,

Ernst²

1984

Journal of Colloid and Interface Science

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The kinetics of clustering through addition (ak + al ~ ak+l) and condensation (aj + ak ~ aj+k, j v ~ 1, k ~ 1) for a model of cylindrically shaped monomeric units a~ are studied, using Smoluchowski's coagulation equation, and analytic solutions for several limiting cases (fiat disks and needles) with and without condensation reactions, were given. The condensation models of flat disks and needles include, respectively, the linear polymer model RA 2 and the branched polymer model A2RB~ (with a gelation transition). If condensation reactions are inhibited, we obtain exactly soluble addition models with a monomer-cluster rate constant independent of or proportional to the cluster size. The monomers are (i) supplied in a given amount at the initial time; (ii) generated by a steady source; or (iii) supplied by an infinite reservoir that keeps the concentration of monomers, cz(t), constant in time.

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“…The former system (with its generalization in [14]) models the coagulation (or coalescence) and fragmentation of polymers consisting of monomeric units, represented by the chemical equations…”

Section: Modeling Molecular Assemblymentioning

confidence: 99%

“…From these chemical equations, mathematical equations may be derived with additional assumptions. For example, use of the Law of Mass Action and the corresponding rate equations have been thoroughly studied for these models [13][14][15][16][17]. However, this approximation requires a large number of particles to be valid and fails to capture mesoscopic effects [18].…”

Section: Modeling Molecular Assemblymentioning

confidence: 99%

Initial condition of stochastic self-assembly

Davis

Sindi

2016

Phys. Rev. E

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The formation of a stable protein aggregate is regarded as the rate limiting step in the establishment of prion diseases. In these systems, once aggregates reach a critical size the growth process accelerates and thus the waiting time until the appearance of the first critically-sized aggregate is a key determinant of disease onset. In addition to prion diseases, aggregation and nucleation is a central step of many physical, chemical and biological process. Previous studies have examined the first-arrival time at a critical nucleus size during homogeneous self-assembly under the assumption that at time t = 0 the system was in the all-monomer state. However, in order to compare to in vivo biological experiments where protein constituents inherited by a newly born cell likely contain intermediate aggregates, other possibilities must be considered. We consider one such possibility by conditioning the unique ergodic size distribution on sub-critical aggregate sizes -this "least-informed" distribution is then used as an initial condition. We make the claim that this initial condition carries fewer assumptions than an all-monomer one and verify that it can yield significantly different, averaged waiting times relative to the all-monomer condition under various models of assembly. *

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Note on the Kinetics of Systems Manifesting Simultaneous Polymerization-Depolymerization Phenomena

Cited by 160 publications

References 1 publication

Mechanically Induced Homochirality in Nucleated Enantioselective Polymerization

Mechanically Induced Homochirality in Nucleated Enantioselective Polymerization

Exactly soluble addition and condensation models in coagulation kinetics

Initial condition of stochastic self-assembly

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