Viscoelastic Relaxation of Rubber Vulcanizates Between the Glass Transition and Equilibrium
Authors: Chasset R. , Thirion P. 
Published: February 2011

Abstract
In agreement with the results of dynamic experiments of Stratton and Ferry, this study of relaxation of rubber vulcanizates entirely confirms the existence of peculiar, slow, viscoelastic processes in high polymer networks. Characteristic differences with the rheological behavior of unvulcanized polymers are best reflected by the shape of the end of the distribution functions of relaxation times. The box distribution found for free chains is replaced, for crosslinked polymers, by a long incline extending during several decades of time. The slope of this linear part of the spectrum is only slightly dependent on nature of the polymer and type of vulcanizate. On the other hand, the position of the incline along the time scale is very sensitive to the mean molecular weight Mc of the vulcanizates, by far the most important factor controlling the phenomenon. The downward deviations observed at the end of the incline also occur later for larger values of Mc. A useful step towards theoretical understanding of this behavior should be a quantitative knowledge of the effect of molecular weight in a broader range of Mc than studied here. If the chain entanglements are of primary importance, as considered probable by Ferry it seems that some singularity should occur for a critical molecular weight fitting the corresponding value for the viscosity of free chains. The role of crosslink mobility might be tested by comparing the relaxation of ordinary random vulcanizates with that of eventually more regular polybutadiene networks prepared by end group crosslinking of carboxy-terminated and mono-disperse chains. In fact, the displacement of a crosslink away from its affine position requires, apart from the Brownian fluctuations, an unbalance between the forces exerted by the four radiating chains. This implies that the lengths of the strands present large differences and that the shortest chains are approaching their limit of extensibility. As the latter condition can hardly be fullfilled at small deformations, it seems doubtful that this mechanism may be predominant either for dynamic properties or the relaxation experiments reported here. Another cause sometimes invoked is the presence of free chains attached to the networks and we are presently studying their effect on viscoelastic relaxation. At this stage, it is already apparent that they do not have a large effect, as might be expected on theoretical grounds. In our opinion, special attention should be paid to the reason why the experimentally found relaxation times are so large, in spite of the relatively short average length of the network strands. If the usual notion of entanglements developed for free chains, as an extension of the Rouse theory, should fail in this respect, it would be necessary to reconsider the non-equilibrium statistics of single chains with fixed ends, taking into account the proper inter- and intramolecular forces hindering their motion. This more direct approach to the problem, already outlined by Kirkwood, ought to express mathematically the fact that the presence of crosslinks tends to prevent longitudinal slippage of large parts of the chains. The slow changes of configuration should occur therefore rather through lateral motions to which the neighboring medium opposes a much greater resistance.