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.

The influence of several factors (temperature, elongation, swellihg or dilution ratio, cross-link density, nature of the polymers and cross-linking agents) on the dynamic properties, creep and relaxation of polymer networks is surveyed in the terminal region of the spectrum.Whereas the deformation does not change the relaxation kinetics in large ranges of extension, the cross-link density acts as a reduced variable apparently accelerating uniformly the viscoelastic processes beyond the glass transition. The other possible reductions time--temperature' and 'time-swelling' do not necessarily seem related to the variations of free volume.From the view point of the explanation of the relaxation mechanisms in the terminal zone, the fact that the equilibrium of loosely cross-linked elastomers would only virtually be reached after several years at room temperature seem in better agreement with chain entanglement effects, either trapped or not by the permanent network, than with the dissociation of secondary linkages. INTRODUCTJONi\ series of recent studies originating mainly from the laboratory of Professor J. D. Ferry has disclosed that polymer networks display peculiar loss mechanisms at low frequencies, thus giving rise to a new interest for the study of dynamic or transient properties which previously did not seem essentially different from those found in the glass transition zone Many obstacles, however, remain to be overcome in a field where experimental as well as theoretical difficulties abound A primary one, for example.concerns the poor precision of measurements made near the equilibrium state, either owing to the decrease of the dynamic losses at low frequencies1, or because eventually aging always masks the residual viscoelasticity in the course of static tests, whatever precautions are taken2 On the other hand, the interpretation of transient phenomena requires a thorough knowledge of the networks structure. Yet, their topology seems far from being completely defined by a unique criterium: the cross-link density. the present methods of determination of which may be vitiated by the drawbacks of the statistical elasticity theory and too rough an assimilation of labile chains entanglements with chemical cross-links3.In return, reduced variables methods widely used in other fields of polymer rheology4 have already provided, in particular for elastomer networks, much information on the kind of influence on the viscoelasticity of networks of such factors as temperature, deformation, swelling or dilution ratio and crosslink density. It is this broad approach which has been chosen here, in the 183

The influence of several factors (temperature, elongation, swellihg or dilution ratio, cross-link density, nature of the polymers and cross-linking agents) on the dynamic properties, creep and relaxation of polymer networks is surveyed in the terminal region of the spectrum.Whereas the deformation does not change the relaxation kinetics in large ranges of extension, the cross-link density acts as a reduced variable apparently accelerating uniformly the viscoelastic processes beyond the glass transition. The other possible reductions time--temperature' and 'time-swelling' do not necessarily seem related to the variations of free volume.From the view point of the explanation of the relaxation mechanisms in the terminal zone, the fact that the equilibrium of loosely cross-linked elastomers would only virtually be reached after several years at room temperature seem in better agreement with chain entanglement effects, either trapped or not by the permanent network, than with the dissociation of secondary linkages. INTRODUCTJONi\ series of recent studies originating mainly from the laboratory of Professor J. D. Ferry has disclosed that polymer networks display peculiar loss mechanisms at low frequencies, thus giving rise to a new interest for the study of dynamic or transient properties which previously did not seem essentially different from those found in the glass transition zone Many obstacles, however, remain to be overcome in a field where experimental as well as theoretical difficulties abound A primary one, for example.concerns the poor precision of measurements made near the equilibrium state, either owing to the decrease of the dynamic losses at low frequencies1, or because eventually aging always masks the residual viscoelasticity in the course of static tests, whatever precautions are taken2 On the other hand, the interpretation of transient phenomena requires a thorough knowledge of the networks structure. Yet, their topology seems far from being completely defined by a unique criterium: the cross-link density. the present methods of determination of which may be vitiated by the drawbacks of the statistical elasticity theory and too rough an assimilation of labile chains entanglements with chemical cross-links3.In return, reduced variables methods widely used in other fields of polymer rheology4 have already provided, in particular for elastomer networks, much information on the kind of influence on the viscoelasticity of networks of such factors as temperature, deformation, swelling or dilution ratio and crosslink density. It is this broad approach which has been chosen here, in the 183

Relaxation in relatively stable, gum natural rubber vulcanizates has been studied to determine the effects of viscoelasticity and aging, respectively, using a dark, air-oven. A quantitative analysis of experimental results shows that, in the case of a dicumyl peroxide vulcanizate at 100° C, relaxation is caused by aging, except in its initial stages. Stress decreases as a linear function of time, in agreement with theoretical assumptions. Conversely, at 30° C, the effect of aging is negligible. At this temperature the difference between actual stress and stress extrapolated to infinite time, is proportional to a negative power of time. At intermediate temperatures, both phenomena occur simultaneously over a time interval ranging from. 3 minutes to 150 hours.

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