J. L. Valentín, J. Carretero-González, I. Mora-Barrantes, W. Chassé, K. Saalwächter.
Uncertainties in the Determination of Cross-Link Density by Equilibrium Swelling
Experiments in Natural Rubber.
Macromolecules 41, 4717-4729 (2008). DOI
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.