Flory equation gel point

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August undefined, 2024

WebJan 1, 2002 · Abstract. Recent developments in gel research are reviewed with emphasis on the gel point problem. We will describe in due course how the gel point equation can be deduced from first principles. First we review briefly the industrial development of gel science in Japan (Sect. 1) and a central aspect of the classical theory of gelation (Sect. 2). WebJan 1, 2004 · That equation can also be used to estimate the gel point (state of conversion at which crosslinks begin to form) in polymerization of monomers with more than two functional groups per molecule. If the monomers are bifunctional and statistical growth can be assumed, the mole fractions of successive polymer molecules (with increasing …

The gelation point of alkyd resins Semantic Scholar

WebA branched oligomer becomes a crosslinked polymer when the reactive extent reaches the gel point Pc, and the formula used to calculate the gel point Pc is well described by Flory-Stockmayer Theory. We have therefore derived the formula to calculate the Pc for our own case, Where the parameters are: Pc: The gel point, at which the gel forms. WebJan 1, 2001 · Flory proposed the concept of “infinite molecular weight with respect to the weight average molecular weight,” which is the concept still in use. ... Therefore, from Eq. (lb), the following equation is derived: Pnp.gel • Pgel-2 (at gelation) (3) Consequently, it becomes apparent that the concept of the necessity of two crosslink points ... simple past tense of dive

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Web• Flory solvent eqn. uses χ = 0.3; V1/V2 = 0.241; parameters for typical PE solvent systems. • Flory copolymer; Tm° = 145°C; ∆ Hf° = 72 cal/gm. • Experimental data extrapolates to ≈ 135°C and has a slope that is ≈ 3x that seen for the Flory copolymer equation. • In general, Experimental melting data is LOWER WebThe specimen was cured at 145°C for 30 min. The cross-link density was measured by allowing it to swell in toluene and calculated to be 1.47 X 10 mol cm using the Flory-Rehner equation. The average number of... As pointed out earlier, an elastomer cross-linked above its gel point will not dissolve in a solvent, but will absorb it and swell. WebMay 12, 2014 · The conversion at the gel point can be calculated using the following equation: where: Take the simple diepoxy-diamine system with equal stoichiometry, where in the above equation: a1 = conversion of amine. a2 = conversion of epoxide. f 1 = functionality of amine = 4. f 2 = functionality of epoxy = 2. equal stoichiometry then … simple past tense of hit

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Chemistry:Flory-Stockmayer Theory - HandWiki

WebIt is important to realize that the value for the gel point predicted by Carothers is always larger than that of Flory and Stockmayer, i.e. 2/ϕ ≥ 1/(ϕ − 1), ∀ ϕ ≥ 2. Another consequence from this inequality is given by the comparison of … WebAug 31, 1998 · The Ferry–Eldridge equation has been used to determine the enthalpy of the melting of the gel structure (ΔH g) which is equal to (30±2.0) kcal mol −1. The gelation temperature T g is correlated to Flory’s statistical model of gelation, which gives the enthalpy of melting of pure gelatin crystallites (Δ H v ) as Δ H v =(35±2.0) kcal ... ray ban edith glassesWebFeb 21, 2024 · The description of gel swelling by Flory and Rehner using the original Flory–Huggins interaction parameter for the polymer–solvent interaction cannot be applied to most smart microgels. Here, we compare descriptions of the swelling curves of such microgels using series expansions of the Flory–Huggins parameter $$\\chi$$ χ with the … simple past tense of jump

"WebJan 10, 2024 · The Flory-Stockmayer theory represents an advancement from the Carothers equation, allowing for the identification of the gel point for polymer synthesis not at stoichiometric balance. The theory was initially conceptualized by Paul Flory in 1941 [1] and then was further developed by Walter Stockmayer in 1944 to include cross-linking … " - Flory equation gel point

Flory equation gel point

WebDec 14, 2024 · Abstract and Figures. The number-average functionality is proposed a simplified equation which can be used to predict the reaction progress of the stepwise polymerization expediently. According to ... Weboccurs in excess of Flory−Stockmayer gel point; the excesses are 0.09−0.15 in extent of reaction. λ 0 is determined from the gel point data through the p c−λ 0 relationship developed in the ﬁrst part of this study, where the schemes of unequal reactivity and the states of reaction for POP diamine unit are incorporated.

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WebMar 1, 2024 · Eventually, the gel point is reached when there is enough of a skeletal structure to allow strain transfer, provided an interface is also established [12]. As the reaction continues, the polymer will be subject to thermal expansions and contractions and the curing process will usually lead to an overall shrinkage as the covalent bonds are … Webpare a gel. The gel in the glass tube was heated at ca. 0.3 Cmin−1, while the height of the steel ball placed on the surface of gel layer was recorded by a cathetome-ter as a function of ...

WebThe Flory-Stockmayer theory represents an advancement from the Carothers equation, allowing for the identification of the gel point for polymer synthesis not at stoichiometric balance. [1] The theory was initially conceptualized by Paul Flory in 1941 [1] and then was further developed by Walter Stockmayer in 1944 to include cross-linking with ... WebAug 6, 2003 · reaction at the gel point is given by the following equation [15–17]: ... While the theory of Flory underestimates the gel point, the theory of Carothers over-estimates it. For example, for the ...

WebFlory’s theory treated these two entropic terms in the Gibbs free energy on an equal ... forward osmosis, (4) the antifouling characteristics of hydrogels, and (5) melting point suppression and boiling point elevation, and solubility of salts in hydrogels. ... Most applications of these thermodynamic models focused on the gel swelling ratio ... WebSep 17, 2024 · To explore the physical properties of hydrogels in terms of statistical thermodynamics, the mean-field Flory–Huggins–Rehner theory has long been used with various analytical and numerical modifications. Here, we suggest a novel mathematical model on the phase transition of a biological hybrid gel that is sensitive to ambient …

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WebThe Flory–Huggins theory plays an important role in assessing the mutual miscibility of the polymer and the plasticizer. The so-called Flory–Huggins parameter of mutual interaction is the criterion defining the miscibility of PVC with plasticizers. It allows for a quantification of the affinity of the plasticizer with the polymer. simple past tense of knowWebFirst proposed in 1950 by Paul J. Flory and Thomas G. Fox while at Cornell University. Proper noun . Flory-Fox equation In polymer chemistry, a simple empirical formula that relates molecular weight to the glass transition temperature of a polymer system. simple past tense of findWebFor S ≃ which is close to the gel point, the Flory-Stockmayer theory overestimates the fraction of low molecular weight polymers and underestimates the ... P.H.M.; Reyniers, M.F.; D’hooge, D.R. Going beyond the Carothers, Flory and Stockmayer equation by including cyclization reactions and mobility constraints. Polymers 2024, 13, 2410 ... rayban edithWebUsing Flory's basic method, an equation is derived for the gelation point of oil-modified alkyd resins in which account is taken of the different reactivities of the various carboxyl groups. The resultant modified equation is useful when phthalic anhydride is used as the dibasic acid because of the widely differing carboxyl group reactivities which occur in this … simple past tense of invitehttp://polymerdatabase.com/polymer%20chemistry/Gelation.html simple past tense of interruptWebSep 12, 2024 · KP2. Kinetics of Step-Growth Polymerization. It is important to understand how reactions proceed over time. This information can tell us how long it will take for a polymer to reach an optimum length. It can also provide insight into how the polymerization occurs, just as kinetics can provide insight into other reaction mechanisms. ray ban emblemWebcases is de ned as the gel point: p c = 1 f 1: (1) Below the gel point p < p c there are only soluble branched polymers and above the gel point p > p c there exists at least one in nite polymer, called the gel. One major consideration is to calculate the sol fraction P sol and gel fraction P gel as a function of p. To simple past tense of forgive