Characterization of Polymer Networks and Gels

Usually, crosslink density is expressed in terms of the average molecular weight between crosslinks, M. There are several experimental techniques available for measurement of crosslink density, such as DMA, equilibrium swelling, NMR spectroscopy, and dielectric measurements, among other methods. Reviews on these experimental techniques are available in the literature (e.g.. Ref. [42]). Some aspects about three of the most important techniques are briefly highlighted here. 

The extent of swelling is inversely proportional to network crosslink density and is highly dependent on the 

When the junctions (crosslinks) are allowed to fluctuate (phantom model), the Hory-Rhener equation takes form shown in Equation 9.9  

The actual swollen behavior of polymer networks lies in between the extremes calculated with the affine deformation and phantom network models [48, 49]. The sources of error/uncertainties during swelling equilibrium measurements, related to the estimation of the volumetric fraction of polymer, the interaction parameter, and the selection of the Hory-Rehner model (affine deformation or phantom network model), have been reviewed recently 

The total transverse relaxation function M(t) for inter-crosslinked chains and dangling chain ends follows an exponential correlation function [58], as shown in Equation 9.10  

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