A frequency-dependent effective medium model for the rheology of crystallizing polymers

The rheology of crystallizing polymers is critical to polymer processing, but our current understanding of how crystallinity affects rheology during crystallization is lacking. The challenge is twofold: first, we must measure rheology simultaneously with crystallinity, and then we must develop models that can describe those measurements as well as prior phenomenological observations. Here, we further develop a generalized effective medium model to describe the frequency-dependent shear modulus of a crystallizing polymer. Through a simple model system, we show that the percolation transition in the effective medium model recovers the relaxation dynamics of a critical gel with a relaxation spectrum that can be approximated as the power mean of the initial melt and final semicrystalline material. We demonstrate the success of this model on the isothermal crystallization of polycaprolactones. From the generalized effective medium model, we can calculate the percolation fraction and power law relaxation exponent at the critical point, even when the measurement frequency range is dominated by shear thinning of the melt phase.