Direct Determination of Cross-Link Density and Its Correlation with the Elastic Modulus of a Gel with Slidable Cross-Links

The universal relationship between the elastic modulus and the cross-link density of a conventional rubber/gel has been demonstrated experimentally to be inapplicable to gels with slidable cross-links. Herein, we describe the synthesis of slide-ring (SR) gel networks devoid of intramolecular cross-links by the cross-coupling of two differently functionalized polyrotaxanes. The cross-link density was determined from the characteristic UV absorption attributed to the asymmetric cross-linked moiety. The cross-link density was shown to correlate considerably more weakly with the Young's modulus than conventional gels and rubbers that follow a universal proportional dependence. In addition, even at a similar cross-link density, the modulus appeared to be lower due to a lower density of cyclic components along the threading chain, i.e., the "coverage", though the data were limited in the narrow cross-link density range. These results might suggest a considerably lower contribution from the conformational entropy of chains associated with sliding through the cross-links and the counteracting entropy attributed to ring arrangement, though effects of the different persistence length due to the coverage difference could affect the modulus.