Two simple approaches to sol–gel transition

Olemskoĭ, A. I.; Krakovský, Ivan

doi:10.1016/s0378-4371(00)00501-x

Cited by 5 publications

(5 citation statements)

References 13 publications

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“…Above a certain critical concentration of activated cross-links ( N c ), a macroscopic cluster appears. Its mass fraction, which is essentially our quantity F i , is found to vary linearly with the distance from N c , which is the normalized cross-links number above the critical value ( N − N c )/ N c . The system's shear modulus G , on the other hand, varies like the cube of this distance …”

Section: Resultsmentioning

confidence: 96%

“…30 The system's shear modulus G, on the other hand, varies like the cube of this distance. 30 Taken together, this predicts G to vary as F i 3 , which is in good agreement with eq 3. Note that the critical cross-link number will be reached at F i ) 0.…”

Section: Resultsmentioning

confidence: 99%

“…Its mass fraction, which is essentially our quantity F i , is found to vary linearly with the distance from N c , which is the normalized cross-links number above the critical value (N -N c )/N c . 30 The system's shear modulus G, on the other hand, varies like the cube of this distance. 30 Taken together, this predicts G to vary as F i 3 , which is in good agreement with eq 3.…”

Section: E ) 3gmentioning

confidence: 99%

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Swelling Behavior and Structural Characteristics of Wheat Gluten Polypeptide Films

et al. 2004

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Wheat gluten films were subjected to controlled thermomechanical treatments to increase the percentage of aggregated sodium dodecyl sulfate (SDS)-insoluble gluten protein, the aggregation reaction being disulfide bonding. The rheological properties of the films were measured under immersion in water, where wheat gluten films are stable and show only slight swelling. The equilibrium swelling of the gluten films in water decreased with the increase of the percentage of SDS-insoluble protein aggregates, and the frequency the independent shear modulus increased sharply with increasing percentage of SDS-insoluble aggregates. Both findings confirm that disulfide bonding between gluten proteins is the predominant cross-linking reaction in the system. A relationship between shear modulus and aggregated protein compatible with a power law (of exponent 3) suggests the existence of a protein network at a molecular scale. However, the classical Flory-Rehner model failed to describe the relationship between the plateau modulus and the gluten volume fraction (a very drastic increase, compatible with a power law of an exponent of about 14). This result shows that gluten cannot be described as an entangled polymer network. The interpretation of both relationships is a network of mesoscale particles which in turn have a fractal inner structure (with a fractal dimension close to 3).

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Section: Resultsmentioning

confidence: 96%

Section: Resultsmentioning

confidence: 99%

Section: E ) 3gmentioning

confidence: 99%

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Swelling Behavior and Structural Characteristics of Wheat Gluten Polypeptide Films

et al. 2004

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“…Below some critical degree of cross-linking the probability that a hydrogen bond formation leads to a finite size chain is one, i.e., υ h = 1 or υ o = 1, whereas above this point there is a gel formed by either direct PEO−PEO hydrogen bonds or through a single water-molecule cross-link (PEO−water−PEO) and υ h < 1, υ o < 1. The critical point can be defined by considering a small deviation from the critical “conversion” and expanding υ h , υ o in the power series of ε : …”

Section: Resultsmentioning

confidence: 99%

Influence of End Groups on Phase Behavior and Properties of PEO in Aqueous Solutions

2004

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The influence of the different terminal groups (hydroxyl, methyl) on the properties and phase behavior of PEO in aqueous solutions has been studied analytically. We have generalized our previous model to account for the competition for proton donors and acceptors among four types of hydrogen bonding (donors are mentioned first): water−PEO, water−water, PEO−water, and PEO−PEO. We found that for PEO terminated at both ends by methyl groups the influence of the end groups is minor, similar to infinitely long PEO. Termination of PEO by hydroxyl groups results in hydration enhancement in the poor hydration regions, i.e., at high polymer concentration (low water content) and at high temperature. The contribution of end groups to overall hydration is especially strong for short polymer chains and decreases with chain length as 1/N, but it remains larger than 1% for chains with N ≲ 250 (for equal fraction of polymer and solvent, Φ = 0.5) or with N ≲ 460 (for Φ = 0.9). For a polymer volume fraction less than about 0.886, the contribution of end group to hydration increases with temperature and for polymer solutions of higher concentration it decreases with temperature (due to competition with PEO−PEO hydrogen bonding). We also discuss the possibility of physical cross-linking of PEO either via direct PEO−PEO hydrogen bonds or via a single water molecule acting as a cross-linking agent. We found that the degree of cross-linking considerably increases with chain length and also is strongly enhanced for hydroxyl-terminated short chains. Hydration via end groups also results in a chain length dependence of the second virial coefficient, A 2. For one- or two-end hydroxyl-terminated PEO, the second virial coefficient decreases with a chain length increase whereas for the methyl-terminated PEO A 2 increases with an increase in chain length, tending to the same constant limit for infinitely long chains. The phase diagram calculated accounting for hydration via terminal hydroxyl groups features considerably improved agreement between theoretical predictions and experimental observations for short PEO chains: theoretical curves become more centered around experimental data and the chain lengths used for calculations are close to the molecular weight of experimental samples. Theoretical predictions become more consistent for the whole range of chain lengths studied. As a result the lower (LCST) and upper critical solution temperatures (UCST) for hydroxyl-terminated PEO agree very well with different experimental data. Comparing the critical points (UCST and LCST) for polymer chains terminated by different end groups we found that while all curves merge in the long chain limit (N > 300 for LCST and N > 500 for UCST), for shorter chain lengths curves deviate from each other considerably, reaching double critical points (where the UCST merges with the LCST) at different N. Termination of PEO by one hydroxyl group improves the solubility of PEO chains to an extent that it is equivalent to decreasing of chain length by 10 monomer units...

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“…Note that this operation does not modify the phantom modulus of the network . The elastically active material is defined by all network junctions that offer at least three independent connections to the gel and all strands (that can be linear sets of junctions and chains) that connect a pair of these junctions. , Analytical predictions for ξ are available in the literature. − Each independent cycle is assumed to contribute k B T of energy to the modulus where V denotes the volume of the sample.…”

Section: Shear Modulusmentioning

confidence: 99%

Elasticity of Tendomer Gels

2022

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We investigate the formation and the elastic properties of tendomer networks (i.e., slide-ring gels with “ storage chains” containing free sliding rings) with computer simulations. An analysis of the gel point shows that network formation is only possible up to a limiting number of slide rings per tendomer. Tendomer networks are super soft and quasi-entanglement-free model systems with extreme stretchability. The elastic properties of tendomers are dominated by the phantom contribution to modulus, which develops significant deviations from the mean field prediction. These can be explained with corrections from the formation of finite loops, differences between mean field behavior, and critical scaling near the gel point and additional contributions due to prestrain at high extents of reaction. A strong enhancement of the modulus by 2 orders of magnitude can be achieved by preparation in a selective solvent that is poor only for the slide rings. With this procedure, also the limit in the number of slide rings for network formation can be increased. The deformation of the chains is neither linear nor uniform since the force-elongation behavior of individual tendomers contains a critical force beyond which chains can be deformed at almost no increase in the applied force. Deformation of a network, thus, splits the tendomer units into two populations: those beyond and below the critical force that are either largely stretched or remain in a subcritical extension. This splitting causes a continuous strain softening for larger deformations even in the absence of entanglements and prior to the onset of finite extensibility effects. This observation contrasts the strain hardening originally observed for conventional slide ring gels and agrees with more recent experimental data on these gels.

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Two simple approaches to sol–gel transition

Cited by 5 publications

References 13 publications

Swelling Behavior and Structural Characteristics of Wheat Gluten Polypeptide Films

Swelling Behavior and Structural Characteristics of Wheat Gluten Polypeptide Films

Influence of End Groups on Phase Behavior and Properties of PEO in Aqueous Solutions

Elasticity of Tendomer Gels

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