Flory equation gel point

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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 … 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 ...

Flory-Rehner equations - Big Chemical Encyclopedia

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. Webbiphasic system, a single glass transition, a miscible system following the Flory-Fox equation. Further support for miscibility would come from microscopy and scattering (neutron, x-ray and light can all be used to characterize miscibility). Generally, thermal analysis is the easiest and most available of techniques to apply to a sample and lithosphere width

Calculation of Swelling for a Gel - University of Cincinnati

WebJun 11, 2024 · The Carothers equation can be used to estimate the conversion needed to reach the gel point in condensation polymerization involving monomers with functionalities higher than 2. With the assumption that the gel point is reached when practically all molecules of the limiting monomer have reacted, the requisite fractional conversion of … WebThree-dimensional condensation of silicon-containing alcohols with tetrafunctional acid esters ☆ Webcases 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 lithospheric architecture andes

The gelation point of alkyd resins - Jonason - 1960 - Journal of ...

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 ... WebFeb 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 … lithosphere wikipediaWebJan 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). lithosphere word origin

"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. " - Flory equation gel point

Flory equation gel point

Gel Point - an overview ScienceDirect Topics

WebIf adipic or isophthalic acid is used as the dibasic acid, the gel point equation deduced by Flory's original method, which takes no account of reactivity differences, may be used. In such a case the difference between the observed and calculated gel point is about 5% when the polyhydric alcohol used is trifunctional and 8–9% when the ... 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 …

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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 ... WebFor the ν calculation Flory-Rehner equation is used: ... e.g. sol gel analysis, differential scanning calorimetry, ultrasonic, small angular neutrons scattering (SANS) in swelled cross-linked ...

Web2. Flory Theory. Flory treated the question of equilibrium conformation of real chains using a mean field approach. The equilibrium size is set by a balance between excluded volume which tends to expand the chain size, and a restoring force due to loss of conformational entropy due to swelling. The energetic contribution due to excluded volume ... 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 ...

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 ... 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 …

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 ...

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 … lithosphere worksheetWebFor 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 ... lithospheric cycle翻译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). lithospheric convection currentsFlory–Stockmayer theory is a theory governing the cross-linking and gelation of step-growth polymers. 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 … See more Gelation occurs when a polymer forms large interconnected polymer molecules through cross-linking. In other words, polymer chains are cross-linked with other polymer chains to form an infinitely large molecule, … See more In creating the Flory-Stockmayer Theory, Flory made three assumptions that affect the accuracy of this model. These assumptions were: 1. All functional groups on a branch unit are equally reactive 2. All reactions occur between A and B See more The Flory-Stockmayer Theory predicts the gel point for the system consisting of three types of monomer units linear units with two A-groups (concentration See more lithosphere where is it locatedWebThe weight fraction distribution is the fraction of x-mers in a system and the probability of finding them in terms of mass fraction. = = = Notes: M o is the molar mass of the repeat unit,; N o is the initial number of monomer molecules,; and N is the number of unreacted functional groups; Substituting from the Carothers equation = = We can now obtain: = … lithospheric crustWebJan 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 … lithospheric cycleWebFirst 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. lithospheric deformation