Flory equation gel point
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 ... 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
Flory equation gel point
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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 … 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.
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. WebThree-dimensional condensation of silicon-containing alcohols with tetrafunctional acid esters ☆
WebGelation in Polymerization. The classical theories of Carothers, Flory and Stockmayer 1-5 describe the conversion of growing polymers to insoluble gels which occurs through crosslinking. All three theories use a statistical approach and assume that polymers approach infinite size at the gel point, i.e. they become one gigantic molecule. 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 …
http://www.personal.psu.edu/irh1/PDF/Copolymer%20Melting.pdf how many company are listed in nepseFlory–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 how many company holidays in a yearWebCalculation of Swelling for a Gel. The Flory-Rehner Equation (Flory's first book) describes swelling of network polymers as a function of the enthalpic interaction parameter between the polymer unit and the solvent, c, the molar volume of the solvent, V 1, and the molecular weight between crosslink sites, n. where v 2 is the volume fraction of polymer … high school schedulingWebThe 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. high school scheduling optionsWebIf 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 ... high school scheduling softwareWebMar 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 … high school scheduling ideasWebJan 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 ... high school scheduling boards