Experimental results from the literature and from this work show the reliability of the dynamic mechanical spectroscopy as a complementary tool to follow the crystallization of polymers from the melt. However the problem of the interrelation between the transformed fraction and the mechanical data is not simple and remains a topic open to discussion. To get a better understanding of these relations, the method was applied to the study of two polyolefins which show very different morphologies during their crystallization from the melt. Their morphological study has shown that, though they both crystallize in a well-defined spherulitic structure, because of the differences of size of the crystalline entities, one can be considered as a suspension of spherical particles in a liquid matrix whereas the other behaves as a colloid of small particles. The study of the rheological behavior of the suspension-like material shows the existence of two critical values of the volume fraction. In agreement with the percolation theory, the first value is related to the appearance of a yield effect and the second indicates the maximum packing. Moreover, in this case, throughout the crystallization, the relaxation times depend on the filler content and the zero-shear viscosity varies upon the −3/2 exponent of the volume fraction. The colloid-like material behaves in a completely different way since a yield effect appears in the earliest stage of the crystallization. For both materials, the use of an equilibrium modulus is able to characterize the yield effect, and in both cases, it is described by the same type of expression with a universal exponent equal to 3 in agreement with theories for physical gels. Unfortunately, these results show that a unique expression can hardly be used to relate the transformed fraction to the rheological data and that such a derivation always requires an additional investigation of the morphology.

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SYNOPSISPolarized light microscopy shows that polypropylene crystallizes from the melt into a welldistinguished spherulitic structure. Therefore, it provides a useful model for molten-filled polymers, where the growing spherulites are considered to be filler particles dispersed in a matrix fluid. Although spherulites are randomly dispersed in the space, two dispersion models (simple cubic and centered cubic) are discussed to correlate the transformed fraction a ( t ) with the volume fraction of filler q5 (t). The combination of these results with those of differential scanning calorimetry (DSC) shows that the transformed fraction a(t) is a direct indication of the volume fraction of filler q5(t). The rheological study, using oscillatory experiments coupled with DSC results, shows the relative sensitivity of the rheological functions to structural changes of the liquid during crystallization. Furthermore, they reveal the existence of a yield effect above a certain critical value of the filler content (& = 0.4). In the absence of this yield effect, a model is proposed to predict the variation of the rheological functions with the filler content. This model shows not only a variation of the plateau modulus, but also the modification of the characteristic times of relaxation of the polymer matrix, whereas the shape of the relaxation spectrum remains unchanged. 0 1996 John Wiley & Sons, Inc. INTRODUCTION Rheological BehaviorThe rheological behavior of filled polymers strongly depends on a large number of parameters such as volume fraction, shape and size of particles, fillerfiller and filler-matrix interactions. The influence of the volume fraction on the main flow functions such as viscosity and normal stress coefficients has been the most extensively discussed in the literat~r e . ' -~ In order to overcome problems arising from the shape or anisometry of the particles, several author^'^^-'^ have used spherical particles such as glass beads and metal spheres. In general, the models proposed are concerning the steady shear flow. They are derived from theories established for suspensions of elastic particles in a Newtonian fluid. LeonovZ0 has proposed another approach wherein he described the rheological behavior of filled polymers by a model in which the total mean stress 7 is represented by the following sum:where 7, represents the mean stress arising in a suspension of inactive particles in a matrix, and 7p is an additional mean stress due to the particle-toparticle interactions in the particulate phase. The matrix mode was described using viscoelastic equations known for pure polymers (Maxwellian modes). In this description, the dependencies of the rheological parameters on the particle loading 4 was included. For the particle mode, he took into account both the effect of finite elasticity and the dissipative effect. Therefore, assuming that the matrix parameters are independent of the particle size, only hydrodynamic interactions between particles of filler are assumed to have an effect on the behavior of the pol...

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