Flory stockmayer equation
WebThe PMC website is updating on 03/21/2024. Try out this update now on PMC Labs or Learn more. 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
Flory stockmayer equation
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http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/stockmayer-walter.pdf 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 ...
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 … 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 …
WebSep 21, 2024 · In this work, we present an analytical mean field model, using the Flory-Stockmayer theory of gelation, to understand how different actin-binding proteins … 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 …
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. …
WebIn step-growth polymerization, the Carothers equation (or Carothers' equation) gives the degree of polymerization, Xn, for a given fractional monomer conversion, p. There are several versions of this equation, proposed by Wallace Carothers who invented nylon in 1935. 11 relations. ... Flory-Stockmayer Theory is a theory governing the cross ... two tone shower wallsWebStockmayer s equation As in so many things in this field, if you want to work through the arguments yourself, you cannot do better than go to Flory— see Principles of Polymer Chemistry, Chapter EX.Stockmayer s equation illustrates the point we wish to make with dazzling simplicity as f the number of branches, increases, the polydispersity decreases. tall woody plants crossword clueWebFlory-Stockmayer equation for ATRP systems Derivation of the equation 2 after Gao and Matyjaszewski1,2 is reproduced here for reader’s convenience. From the Flory-Stockmayer theory: 𝑣𝑐=𝜌𝑝𝑐( 𝑃𝑤−1)=1 where is v c is the weight-average … tall wool belted shacket coatWebExperimental stoichiometric gelation boundaries of a set of branched thiol to acrylate Michael addition polymerization systems were investigated, and the observed limits were compared to theoretical critical molar ratio (CMR) intervals. These CMR intervals were calculated via the Flory–Stockmayer equation (for the upper limit) and via a formula … two tone sterling silver ringsWebNational Center for Biotechnology Information tall woodworking projectsWebJan 1, 2001 · While the reason why the Flory-Stockmayer model ignores cyclization is to simplify analysis, it can also be interpreted based on classical kinetic theory. In a bulk … tall woody grassWebThe gel point temperature, as determined by rheometry using the Winter-Chambón criterion, was 92°C. corresponding to a gel-point conversion of 71%, consistent with the Flory-Stockmayer equation. The scaling exponents for the complex moduli, viscosity, and plateau modulus, in the vicinity of the gel-point, were determined and compared with ... tall woodworking projects crossword