Flory stockmayer equation

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August undefined, 2024

WebIn this respect, Flory [20,21,22] and Stockmayer [27,28,29] derived an equation to predict the gel point, i.e., the point at which a polymer network is formed, resulting in an … WebIt is shown that three basic models of the Flory-Stockmayer theory of polymerization may all be described directly by means of a kinetic rate equation of a form first discussed by Smoluchowski, and correspond to the three known classes of solutions to this equation. The kinetics of gelation are discussed from the rate equation; the nature of both the …

Flory-Stockmayer Theory Spectroom

WebMar 27, 2013 · The Flory-Stockmayer theory for the polycondensation of branched polymers, modified for finite systems beyond the gel point, is applied to the connection (synapses) of neurons, which can be considered highly branched “monomeric” units. Initially, the process is a linear growth and tree-like … WebIt is shown that three basic models of the Flory-Stockmayer theory of polymerization may all be described directly by means of a kinetic rate equation of a form first discussed by … markoff law ri

A NOTE ON THE KINETIC EQUATIONS 0. Introduction. 1, 2 3

WebJul 22, 2024 · Going Beyond the Carothers, Flory and Stockmayer Equation by Including Cyclization Reactions and Mobility Constraints Polymers (Basel). 2024 Jul 22;13 (15):2410. ... Flory and Stockmayer, assuming constant reactivities and ignoring intramolecular reactions, is very approximate, and the use of asymptotic limits is biased. … It is important to be able to predict the onset of gelation, since it is an irreversible process that dramatically changes the properties of the system. According to the Carothers equation number-average degree of polymerization is given by where is the extent of the reaction and is the average functionality of reaction mixture. For the gel can be considered to be infinite, thus the critical extent of the reaction at the gel point is found as WebMay 9, 2024 · Tavares et al. recently developed a generalization of the Flory-Stockmayer theory to describe patchy colloids [51,63], which can be understood as polyfunctional … markoff law chicago

Chemistry:Flory–Stockmayer theory - HandWiki

WebJul 22, 2024 · We showcase that a conventional approach based on equations derived by Carothers, Flory and Stockmayer, assuming constant reactivities and ignoring intramolecular reactions, is very approximate, and the use of asymptotic limits is biased. ... Flory and Stockmayer Equation by Including Cyclization Reactions and Mobility … WebFlory–Stockmayer theory is a theory governing the cross-linking and gelation of step-growth polymers. The Flory-Stockmayer theory represents an advancement from the … navy federal credit union taxWeb3) i) The (low shear rate) viscosity becomes infinite for a gel as shown in Flory's Plot. ii) Carothers: n1 => infinity Miller/Macosko: nw => infinity Flory/Stockmayer: α => 1 where α is a way to measure when you have reached the percolation threshold, that is when the network connects across the sample. navy federal credit union tax center

"WebJul 22, 2024 · We showcase that a conventional approach based on equations derived by Carothers, Flory and Stockmayer, assuming constant reactivities and ignoring … " - Flory stockmayer equation

Flory stockmayer equation

[PDF] Going Beyond the Carothers, Flory and Stockmayer Equation …

http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/stockmayer-walter.pdf WebThis Flory–Stockmayer, or classical, theory plays a role in gelation similar to that of the van der Waals equation for the gas-to-liquid transition or the molecular field approximation for the ferromagnetic Curie point. In particular, all three examples predict a sharp phase transition; that is, a qualitative change takes place in the system ...

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WebDec 29, 2004 · The status of the gel point equation, advanced by Flory, Stockmayer, and Walling for polyfunctional reactions, is briefly discussed. Two complicating factors in the chain polymerization of divinyl compounds, to which this equation has been applied, are reviewed: the admixture of a monovinyl compound of comparable reactivity, and the … WebFlory-Stockmayer Theory is a theory governing the cross-linking and gelation of step-growth polymers. The Flory-Stockmayer theory represents an advancement from the …

WebFlory-Stockmayer equations of coagulation. 0. Introduction. Models of cluster growth appear in a wide variety of applications. One well-known example is the Smoluchowski … Webwhere Ni is the weight average molecular weight and the equation is written for a polymer blend. For a polymer solution N 1 = 1, φ 1 ~ 1 and S D(q,R g1) ~ 1 so equation (7) can be rewritten, € φ 2 S(q) = 1 N 2 S D (q,R g2) +φ 2 (1−2χ) (8) (RPA Solution) Equation (8) bears resemblance to equation (6). The difference is that the inverse Debye

WebThe comparison shows that the results from the MC simulations based on Equation agree with the Flory-Stockmayer theory, while those based on Equation do not. It indicates that Equation ( 18 ) is consistent with the assumption made by the Flory-Stockmayer theory, i.e., all the active functional groups have the same probability to react with ... Webequation as a model for the growth of an antigen-antibody aggregate. The models themselves are coupled infinite systems of ordinary dif ferential equations (in the discrete case) or a single integro-differential equation (in the continuous case). In this note I reconsider the classi cal Smoluchowski-Flory-Stockmayer discrete equations and ...

WebAccording to Flory1, the criterion for gelation of a stoichiometric mixture containing branching units of functionality fis given by αc= 1 / (f- 1) Thus for f= 3, an infinite network …

WebApr 4, 2024 · The Flory-Stockmayer theory predicts that (2) where (3) (4) (5) Equation ( 2) is called the Stockmayer formula, which gives the number of molecules of any monomer … markoff meaningWebFlory–Stockmayer theory is a theory governing the cross-linking and gelation of step-growth polymers. The Flory-Stockmayer theory represents an advancement from the … markoff law office mark of fordring classicWebby Flory and Stockmayer. At the end of this lecture we will brie y describe the Flory-Stockmayer Theory. Many other elds have also approached this fascinating problem … mark of fordring questWebcients in the equation of state for multicomponent systems. While obtaining the experimental data, Stockmayer was trying to learn statistical ... They had a productive conversation, and Flory encouraged Stockmayer to write up his results, which he did in two articles published in the Journal of Chemical Physics in 1943 and 1944.3 All this ... mark-off lineWebJul 14, 2008 · ABSTRACT. The kinetics of polymer growth and especially gelation are discussed for a system of reacting f ‐functional monomeric units. The gelation models of … navy federal credit union tempe azWebThe PMC website is updating on 03/21/2024. Try out this update now on PMC Labs or Learn more. navy federal credit union teen debit card