Evidence for a Linear NMR−Elasticity Interrelationship in Polymeric Gels

Addad, J. P. Cohen; Thanh, and B. Phan; Montès, H.

doi:10.1021/ma961589i

Cited by 13 publications

(17 citation statements)

References 15 publications

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“…Note that very good linear relationships between NMR-based cross-link density determinations, and elastic moduli have been reported for different polymer systems, 91,92 demonstrating the qualitative validity of the models used for the interpretation of NMR results (mainly eq 12) and supporting the use of NMR as a proper reference. Correlating NMR with swelling results, we also found good linear dependencies in most cases.…”

Section: Methodsmentioning

confidence: 77%

Uncertainties in the Determination of Cross-Link Density by Equilibrium Swelling Experiments in Natural Rubber

et al. 2008

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Equilibrium swelling is a feasible and simple experiment to determine the cross-link density of networks. It is the most popular and useful approach; however, in most of the cases, the given values are highly uncertain if not erroneous. The description of the complex thermodynamics of swollen polymer networks is usually based on the Flory-Rehner model. However, experimental evidence has shown that both the mixing term described by the Flory-Huggins expression and the elastic component derived from the affine model are only approximations that fail in the description and prediction of the rubber network behavior. This means that the Flory-Rehner treatment can only give a qualitative evaluation of cross-link density because of its strong dependence on the thermodynamic model. In this work, the uncertainties in the determination of the cross-link density in rubber materials by swelling experiments based on this model are reviewed. The implications and the validity of some of the used approximations as well as their influence in the relationship of the cross-link densities derived from swelling experiments are discussed. Importantly, swelling results are compared with results of a completely independent determination of the cross-link density by proton multiple-quantum NMR, and the correlation observed between the two methods can help to validate the thermodynamic model.

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Section: Methodsmentioning

confidence: 77%

Uncertainties in the Determination of Cross-Link Density by Equilibrium Swelling Experiments in Natural Rubber

et al. 2008

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“…Further insight to this interrelation is gained from the NMRbased estimates of the microgel crosslinking density, related to the observable D res . A linear relationship of this molecularscale parameter to the macroscopic parameter m eff or to the elastic modulus is commonly observed in homogeneous bulk elastomers, [56][57][58][59][60] provided that samples are compared at identical polymer concentration; 61 however, even though this is the case for the given sample series (all 140 g L 21 ), we see that only the more homogeneous gels among them follow such a linear trend, whereas the most inhomogeneous ones swell more and thus have lower m eff than expected from D res , as shown in Figure 2. In contrast, the gels prepared by controlled polymer-analogous photogelation exhibit considerably less swelling in water (swollen microgel diameter 200 mm at 25 8C) than those prepared by uncontrolled free-radical crosslinking copolymerization (swollen microgel diameter 220-250 mm at 25 8C), especially if this is done at high microgel preparation temperature.…”

Section: Resultsmentioning

confidence: 92%

Critical fluctuations and static inhomogeneities in polymer gel volume phase transitions

Habicht

Schmolke

Goerigk

et al. 2015

J Polym Sci B Polym Phys

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Thermoresponsive polymer gels exhibit pronounced swelling and deswelling upon changes in temperature, accompanied by dynamic concentration fluctuations that have been interpreted as critical opalescence. These fluctuations span lengthscales similar to that of static structures in the gels, such as the gel polymer-network meshsize (1-10 nm) and static polymer-network crosslinking inhomogeneities (10-1000 nm). To systematically investigate this overlay, we use droplet-based microfluidics and fabricate submillimeter-sized gel particles with varying static heterogeneity, as revealed on a molecular scale by proton NMR. When these microgels are probed by small-angle neutron scattering, the detection of dynamic fluctuations during the volume phase transitions is strongly perturbed by the co-existing static inhomogeneity. Depending of the type of data analysis employed, the temperature-dependent evolution of the correlation length associated to the dynamic fluctuations does or does not agree with predictions by the critical scaling theory. Only the most homogeneous sample of this study, prepared by controlled polymer crosslinking in droplet microfluidics, shows a diverging correlation length in agreement to the critical scaling theory independent of the specific approach of data analysis. These findings suggest that care must be taken about polymernetwork heterogeneity when gel volume phase transitions are evaluated as critical phenomena.

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“…42 This is to be compared with the case of unswollen elastomers that always show a linear correspondence between the modulus and the NMR observable. 36,[45][46][47][48][49] Here, one of course has to take into account that the network fraction A as well as the overall polymer volume fraction both increase over the sample series. The apparent contradiction can thus be explained because the modulus is inversely proportional to the volume fraction of polymer.…”

Section: Resultsmentioning

confidence: 99%

Gelation as Studied by Proton Multiple-Quantum NMR

et al. 2007

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A novel NMR approach for the study of gelation in flexible polymer systems is presented, and the data are compared to results from rheological and light scattering experiments. Proton multiple-quantum NMR, also applicable at low field and amenable to high-throughput experimentation, represents a simple and robust yet powerful method that allows one to detect the topological gel point, quantify the gelation kinetics, and characterize composition, microstructure, and dynamics of the forming and the final gel. Applications to end-linked and statistically cross-linked poly(dimethylsiloxane) chains in the bulk, as well as statistically cross-linked poly-(styrene) chains in solution are presented, and good agreement as well as complementarity between the results from the different methods is found.

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Evidence for a Linear NMR−Elasticity Interrelationship in Polymeric Gels

Cited by 13 publications

References 15 publications

Uncertainties in the Determination of Cross-Link Density by Equilibrium Swelling Experiments in Natural Rubber

Uncertainties in the Determination of Cross-Link Density by Equilibrium Swelling Experiments in Natural Rubber

Critical fluctuations and static inhomogeneities in polymer gel volume phase transitions

Gelation as Studied by Proton Multiple-Quantum NMR

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