Polypropylene during crystallization from the melt as a model for the rheology of molten-filled polymers

Abstract

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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“…2, higher frequencies produce higher moduli and the curves of different frequencies converge at the late stage of crystallization. The same behavior has been observed in the work of Boutahar et al [8] . After an induction period, G′(ω) grows more quickly than G″(ω) and then exceeds G″(ω).…”

Using rheometry to determine nucleation density in a colored system containing a nucleating agent

“…One could think of using other approaches by applying more simple models (Boutahar et al 1996(Boutahar et al , 1998Tanner 2002Tanner , 2003van Ruth et al 2006) or empirically based scaling laws between the space filling and the storage modulus (see Coppola et al 2006;Khanna 1993;Pogodina et al 1999). However, it was demonstrated in Steenbakkers and Peters (2008) that such approaches do perform less than the suspension model as used here, and therefore, we will not apply them to our results.…”

Suspension-like hardening behavior of HDPE and time-hardening superposition

“…Perhaps a network of physical crosslinks is formed (Boutahar et al 1996(Boutahar et al , 1998Coppola et al 2006;Peters et al 2002;Pogodina et al 1999a;Zuidema et al 2001). Subsequently, spherulites grow in this altered melt, the effect of which is well described by suspension-like behavior.…”

“…A slight difference in behavior in the two experiments might result in a large error in the hardening function. For instance, Steenbakkers and Peters (2008) found the experiments from Boutahar et al (1996Boutahar et al ( , 1998 showed suspension-like behavior but in order to get quantitative agreement between experiments and simulations, the space filling obtained from DSC measurements had to be adjusted significantly.…”