Strain-induced crystallization, Part III: Theory

Abstract

A nucleation theory for strain-induced crystallization is formulated to explain and to predict the effects of molecular strain on crystallization kinetics and crystallite size. Unlike any current theories that have based their formulations on some assumed extended-chain line nuclei or folded-chain crystals, the present theory avoids all assumptions concerning the crystal morphology. It is based on experimental findings which indicate limited crystal growth in the strain direction, following a reciprocal dependence of crystal thickness on supercooling ΔT. (ΔT = T m o , − T , where the equilibrium melting temperature, T m o , is a variable dependent on degree of molecular strain prior to strain-induced crystallization.) It is predicted that the logarithm of the nucleation rate, N o , is dependent on ( T m o ) 2 / T (Δ T ) or T m o / T (Δ T ), and that the critical nucleus thickness l * o is shown to be proportional to T m o /Δ T . In addition, expressions are also presented, including examples, to show the dependence of N o , l * o and T o m on degree of molecular strain, ε, or melt entropy reduction, Δs′. Our analysis predicts that, on comparing a polyethylene crystallized in the presence of strain to one crystallized in the absence of strain at 130°C, an increase in “coil” dimension of less than about 50 percent can bring about a 10 4 fold increase in heterogeneous nucleation rate, a 30–40 percent reduction in critical nucleus thickness and a 10°C increase in equilibrium melting temperature. These results will be discussed and compared with available experimental evidence.