Crosslink density fluctuations

In order to enable these fluctuations to occur, the network chains are assumed to be "phantom" in nature i.e. their material properties are dismissed and they act only to exert forces on the junctions to which they are attached. With common networks having tetrafunctional junctions, the results of the two approaches differ by a factor of two. Identical results are only obtained from both theories, when the functionality is infinite. From a practical viewpoint, however, a value of about 20 for f can already be equated to infinity because crosslink densities can hardly be obtained with an accuracy better than 10%. 

The computer-assisted modelling of formation of the epoxy-amine networks indicates that the density fluctuations of the crosslinks does not exceed the value predicted by the statistical theory, which is much lower than the size of the globules in... 

Critical Behavior of Gels. In 1977, the critical phenomena were discovered in the light scattered from an acrylamide gel in water [18]. As the temperature was lowered, both the scattered intensity and the fluctuation time of the scattered light increased and appeared to diverge at —17 °C. The phenomenon was explained as the critical density fluctuations of polymer networks although the polymers were crosslinked [19, 20]. 

It is important to note that in the inhomogeneous gel, the average crosslinking density is not a relevant parameter for determining the frictional pore size of the gel. It is the spatial correlation length of the density fluctuations that determines the bulk frictional behavior of water in the gel. 

It is not an easy task to define inhomogeneities in the structure of a polymer network. Every system will exhibit the presence of defects and fluctuations of composition in space when the scale of observation becomes smaller and smaller. A hierarchy of structures exists, from atomic dimensions to the macroscopic material. A scheme of different scale levels used to describe linear and crosslinked polymer structures is shown in Fig. 7.2. Inhomogeneities described in the literature for polymer networks are ascribed to permanent fluctuations of crosslink density and composition, with sizes varying from 10 nm up to 200 nm. This means that their size lies in the range of the macromolecular scale. 

Inhomogeneous open networks characterized by spatial fluctuations of the crosslink density (nodular/globular morphologies, microgels, see Chapter 7). 

One possible way of characterizing the network inhomogeneity linked to spatial fluctuations of the crosslink density (Chapter 7) could be to study the width of the a dissipation band in the DMTA or DS spectra. The comparison between tetraglycidyl methylene dianiline (TGMDA) DDS... 

The mean-square displacement of the chain segments of BR swollen with deuterated benzene was observed to be independent of diffusion time, indicating restricted diffusion around an attractive centre. The mean-squared displacement decreased with increasing crosslinking density and was approximately equal to the mean-squared collective fluctuations calculated for these polymers. 

In this approximation, Bueche (1970) has related the correlation function of the dielectric constant e (Equation 2.1-73) to the fluctuations in the crosslinks density in gel ( / — i/q) and obtained the relationship... 

The crosslinked organosilicon nanophase formed by the sol-gel procedure possesses a rather loose inner structure, characterized by an enhanced water diffusivity and by mean-square electron density fluctuations and dynamic elasticity moduli comparable to those of the pristine, glassy PI. 

Let us now consider the modulus in more detail. It was shown very early that fluctuations in crosslink density modify the modulus and this can be brought into a general context. The modulus is related to the structure of the material as we have seen in the section of network formation. The question raised from the structural point of view is whether there is any concept as to how to count the contribution of elastically effective chains to the modulus. This question is difficult to answer and the main problem is the inffuence of entanglements. 

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