Kinetics of polymer gelation

Ziff, Robert M.; Stell, G.

doi:10.1063/1.440502

Cited by 227 publications

(164 citation statements)

References 4 publications

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“…This type of modeling has been used for other aggregation processes in blood such as the formation of red cell rouleaux (Samsel and Perelson 1982;Samsel and Perelson 1984) and platelet-neutrophil aggregation (Laurenzi and Diamond 1999). In Section 2.1 we discuss gelation resulting from an initial distribution of polymers when there are no sources or sinks of polymers (Ziff and Stell 1980). There have been many reviews on models of coagulation and gelation, see for example Leyvraz (2003).…”

Section: Gelationmentioning

confidence: 99%

“…The expression (n − 2) i + 2 is the number of available binding sites on an i-mer. Ziff and Stell (1980) used this kernel and expressed (2.1) as…”

Section: Kinetic Gelation Modelmentioning

confidence: 99%

“…In the remainder of this paper, we review an analysis of an existing model of gelation for the case that the total amount of polymers is fixed (Hendriks, Ernst, and Ziff 1983;Ziff and Stell 1980). If polymer is removed from this system, gelation may not occur (Hendriks 1984).…”

mentioning

confidence: 99%

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Fibrin gel formation in a shear flow

Guy

Fogelson²,

Keener³

2007

Mathematical Medicine and Biology: A Journal of the IMA

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Blood clots are made up of platelets and fibrin gel, and the relative amount of fibrin is strongly influenced by the shear rate. In order to explore this phenomenon, this paper presents a model of fibrin gel formation over the surface of an injured blood vessel in a shear flow. A condition for gelation including source and sink terms of polymer is derived. A simplified model of coagulation, involving activation and inhibition of the enzyme thrombin and thrombinmediated production of fibrin monomer, is combined with the model of gelation to explore how the shear rate and other parameters control the formation of fibrin gel. The results show that the thrombin inhibition rate, the gel permeability, and the shear rate are key parameters in regulating the height of the fibrin gel.

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Section: Gelationmentioning

confidence: 99%

“…The expression (n − 2) i + 2 is the number of available binding sites on an i-mer. Ziff and Stell (1980) used this kernel and expressed (2.1) as…”

Section: Kinetic Gelation Modelmentioning

confidence: 99%

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Fibrin gel formation in a shear flow

Guy

Fogelson²,

Keener³

2007

Mathematical Medicine and Biology: A Journal of the IMA

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“…The class of coagulation kernels, K/j = sis j, has been discussed in the literature. For s k = Ak + B explicit solutions are known, (3)(4)(5)(6)(7)(8)(9)(10)(11)(12) including postgelation solutions. (7-9'4) Before proceeding we review what is known about the existence and uniqueness of solutions to the initial-value problem (the initial solutions) of the coagulation equation:…”

Section: Ck(tc) "" Ck-"mentioning

confidence: 99%

Coagulation equations with gelation

1983

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Smoluchowski's equation for rapid coagulation is used to describe the kinetics of gelation, in which the coagulation kernel Kij models the bonding mechanism. For different classes of kernels we derive criteria for the occurrence of gelation, and obtain critical exponents in the pre-and postgelation stage in terms of the model parameters; we calculate bounds on the time of gelation to, and give an exact postgelation solution for the model K,j = (/j)'~ (~0 > 1/2) and Kq = a i+j

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“…Their effect, in the general case is the total mass conservation equation ( ). Described equations are also used for modeling the processes polycondensation polymerization [14], and in meteorology for the calculation of the formation of atmospheric precipitation [15].…”

Section: International Letters Of Chemistry Physics and Astronomy Vomentioning

confidence: 99%

Simulation of Hardening Processes, in Silicate Systems

Kudryavtsev

Figovsky²

2015

ILCPA

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In this paper we consider the Quasi-homogeneous Approximation to Describe the Properties of Disperse Systems. We have used the statistical polymer method is based on the consideration of averaged structures of all possible macromolecules of the same weight. One has derived equations allowing evaluation of all additive parameters of macromolecules and their systems. The statistical polymer method allows modeling of branched crosslinked macromolecules and their systems in equilibrium or non-equilibrium. The fractal consideration of statistical polymer allows modeling of all kinds of random fractal and other objects studied by fractal theory. The statistical polymer method is applicable not only to polymers but also to composites, gels, associates in polar liquids and other aggregates. In this paper Description of the state of colloidal solutions of silicon oxide from the viewpoint of statistical physics is based on the idea lies in the fact that a colloidal solution of silicasilica sol consists of a very large number of interacting with each other particles that are in continuous motion. It is devoted to the study of an idealized system of colliding, but non-interacting particles of sol. Analysis was conducted of the behavior of silica sol, in terms of Maxwell-Boltzmann distribution and was calculated the mean free path of the colloidal particles. Based on these data, it was calculated the number of particles capable to overcome the potential barrier in a collision. To modeling of the solgel transition kinetics had considered various approaches.

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Kinetics of polymer gelation

Cited by 227 publications

References 4 publications

Fibrin gel formation in a shear flow

Fibrin gel formation in a shear flow

Coagulation equations with gelation

Simulation of Hardening Processes, in Silicate Systems

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