The Sol-Gel Transition in Chemical Gels

Martin, James E.; Adolf, David B.

doi:10.1146/annurev.pc.42.100191.001523

Cited by 187 publications

(200 citation statements)

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“…(2) and f v is the monomer volume fraction. Equation (1) is consistent with earlier studies 2,17 that indicated that the kinetic and percolation approaches can merge at the "critical growth stage" that occurs late in the aggregation process were the aggregate volume fraction approaches unity. There the aggregates become "huge monomers" with size R g,G that percolate to form the gel.…”

Section: Introductionsupporting

confidence: 88%

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Kinetic percolation

Heinson

Sorensen

2017

Phys. Rev. E

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Abstract.We demonstrate that kinetic aggregation forms superaggregates that have structures identical to static percolation aggregates, and these superaggregates appear as a separate phase in the size distribution. Diffusion limited cluster-cluster aggregation (DLCA) simulations were performed to yield fractal aggregates with a fractal dimension of 1.8 and superaggregates with a fractal dimension of D = 2.5 composed of these DLCA supermonomers. When properly normalized to account for the DLCA fractal nature of their supermonomers, these superaggregates have the exact same monomer packing fraction, scaling law prefactor, and scaling law exponent (the fractal dimension) as percolation aggregates; these are necessary and sufficient conditions for same structure. The size distribution remains mono-modal until these superaggregates form to alter the distribution. Thus the static percolation and the kinetic descriptions of gelation are now unified.

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Section: Introductionsupporting

confidence: 88%

“…Then the connectivity length scale diverges and a gel of "infinite" extent is formed. This is the kinetic description of the sol-gel transition [1][2][3][4] .…”

Section: Introductionmentioning

confidence: 99%

Kinetic percolation

Heinson

Sorensen

2017

Phys. Rev. E

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“…Thus, the averaged viscosity for general L ≥ 1 follows from (2.31), (3.31), the averaged viscosity (3.26) of the corresponding Brownian-particle case and the relation ∞ n=1 nτ n = 1, which is valid for all 0 < c < 1 2 . This gives rise to the exact result…”

Section: Network Of Polymers: General Lmentioning

confidence: 90%

Critical dynamics of gelation

et al. 2000

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Shear relaxation and dynamic density fluctuations are studied within a Rouse model, generalized to include the effects of permanent random crosslinks. We derive an exact correspondence between the static shear viscosity and the resistance of a random resistor network. This relation allows us to compute the static shear viscosity exactly for uncorrelated crosslinks. For more general percolation models, which are amenable to a scaling description, it yields the scaling relation k = φ − β for the critical exponent of the shear viscosity. Here β is the thermal exponent for the gel fraction and φ is the crossover exponent of the resistor network. The results on the shear viscosity are also used in deriving upper and lower bounds on the incoherent scattering function in the long-time limit, thereby corroborating previous results. 61.25.Hq, 64.60.Ht, 61.20.Lc

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“…29,30 It therefore corresponds to the limit of the curing depth, z c , in the photocuring process and is a characteristic of the photochemical system. 31,32 Substitution of Eqs. (9) and (10) into Eq.…”

Section: Theoretical Model For Photocuring Depthmentioning

confidence: 99%

Cure depth in photopolymerization: Experiments and theory

2001

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The depth of photocuring for a model resin system was investigated as a function of photoinitiator concentration. Direct measurements of gel thickness were made from thin films of cross-linked multifunctional methacrylate monomer. The monomer, 2,2-bis{4- [2-hydroxy-3-(methacryloxy)propoxy]phenyl}propane, was polymerized in a solution of trichloroethylene with an ultraviolet laser light source at 325 nm. The monomer solutions were photocured using varying levels of both photonic energy and photoinitiator concentration. An optimal photoinitiator concentration that maximized the gel cure depth was observed. Additionally, two regimes were shown to exist in which the shrinkage (upon solvent removal) was minimized or maximized. A model was developed to probe the physics of the system. Good agreement with experiment was obtained, and the model may be employed to predict both the existence and location of the optimal photoinitiator concentration and the corresponding cure depth. The study showed that photoinitiator plays a significant role in controlling the quality and performance of the formed gel network, with special regard to thickness of cured layers. This has potential application to fields as diverse as industrially cured coatings and dental fillings, and more generally, 3-dimensional rapid prototyping techniques.

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The Sol-Gel Transition in Chemical Gels

Cited by 187 publications

References 1 publication

Kinetic percolation

Kinetic percolation

Critical dynamics of gelation

Cure depth in photopolymerization: Experiments and theory

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