Gelation and critical phenomena

Stauffer, Dietrich; Coniglio, Antonio; Adam, M.

doi:10.1007/3-540-11471-8_4

Cited by 923 publications

(635 citation statements)

References 103 publications

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“…In the present study, the value of χ c was larger for the solvent in which the increase in both θ/θ 0 and G' was more significant, in agreement with the study of Gornall et al In the percolation model on lattice, the threshold value p c is relevant with the coordination number z in the lattice; typically, p c decreases with z [18]. In the sol-gel transition, the coordination number may correspond to functionality, or the number of reaction sites on which the cross-linking bonds can be formed in a molecules [19]. The increase in χ c by the addition of sugars may be attributed to the decrease in effective number of sites on which the junction zones can be formed in a gelatin molecule.…”

Section: Resultssupporting

confidence: 87%

Effect of sugars on aging of gelatin gels by vacuum-ultraviolet circular dichroism and rheological measurements

et al. 2014

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Many food products based on gelatin contain sugar. Although the effect of sugars on physical properties of gelatin gels has been intensively investigated, aging of gelatin gels containing sugars has not been studied in detail. In the present study, vacuum-ultraviolet circular dichroism (VUVCD) was applied to the study of the aging of gelatin gels with and without sugars and the aging process measured by VUVCD was compared with that measured by rheology and polarimetry. The storage modulus G' and reduced ellipticity θ/θ 0 in the aging process were correlated with each other, indicating VUVCD is a useful tool for detecting the conformation change of gelatin molecules. On the other hand, the behavior of optical rotation Δα was different with that of either G' or θ/θ 0 , suggesting that the optical rotation does not represent the conformation change accurately in the case of gelatin gels containing sugars. The relationship between G' and a fraction χ of helix amount estimated from VUVCD data showed that the critical helix fraction χ c for gelation is slightly increased by the addition of sugars, suggesting a change in the network structure.

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Section: Resultssupporting

confidence: 87%

Effect of sugars on aging of gelatin gels by vacuum-ultraviolet circular dichroism and rheological measurements

et al. 2014

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“…The early statistical theories of gelation of Flory (1941) and Stockmayer (1943) identified the onset of gelation as the weight-average molecular weight of polymers becoming unbounded. These early theories underlie percolation theory (Stauffer and Aharony 1992), which has been used to derive more detailed descriptions of the sol-gel transition (de Gennes 1976;Stauffer 1976;Stauffer, Coniglio, and Adam 1982). These models assume that bonds form randomly among some set of binding sites, and ignore the time evolution of the underlying kinetic processes.…”

Section: Gelationmentioning

confidence: 99%

Fibrin gel formation in a shear flow

Guy

Fogelson²,

Keener³

2007

Mathematical Medicine and Biology: A Journal of the IMA

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Blood clots are made up of platelets and fibrin gel, and the relative amount of fibrin is strongly influenced by the shear rate. In order to explore this phenomenon, this paper presents a model of fibrin gel formation over the surface of an injured blood vessel in a shear flow. A condition for gelation including source and sink terms of polymer is derived. A simplified model of coagulation, involving activation and inhibition of the enzyme thrombin and thrombinmediated production of fibrin monomer, is combined with the model of gelation to explore how the shear rate and other parameters control the formation of fibrin gel. The results show that the thrombin inhibition rate, the gel permeability, and the shear rate are key parameters in regulating the height of the fibrin gel.

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“…The scaling postulate states that ck(t ) for large clusters in the close vicinity of the gel point has the form (16) …”

Section: K~~oez(t ) -= M3(t)/m2(t)~lp -Pcl-1/~ -Tc1-1/~ (17)mentioning

confidence: 99%

“…This is reminiscent of the older Fisher droplet model, (28) where an effective surface area with to __-0.815 is considered. This effective surface should not be identified with the fine-grained external perimeter, which penetrates the whole cluster, (29) and is therefore proportional to k. To obtain an estimate of to we consider the mean radius of gyration Rk~k ~ as k~ oo, (16) What are the predictions of this model? Scaling holds for t < t c, as shown by Leyvraz and Tschudi, (4) but not for t > tc due to the absence of sol-gel interactions in the coagulation equations (see Section 2.3).…”

Section: Conclusionmentioning

confidence: 99%

Coagulation equations with gelation

1983

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Smoluchowski's equation for rapid coagulation is used to describe the kinetics of gelation, in which the coagulation kernel Kij models the bonding mechanism. For different classes of kernels we derive criteria for the occurrence of gelation, and obtain critical exponents in the pre-and postgelation stage in terms of the model parameters; we calculate bounds on the time of gelation to, and give an exact postgelation solution for the model K,j = (/j)'~ (~0 > 1/2) and Kq = a i+j

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Gelation and critical phenomena

Cited by 923 publications

References 103 publications

Effect of sugars on aging of gelatin gels by vacuum-ultraviolet circular dichroism and rheological measurements

Effect of sugars on aging of gelatin gels by vacuum-ultraviolet circular dichroism and rheological measurements

Fibrin gel formation in a shear flow

Coagulation equations with gelation

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