Role of reptation in the rate of crystallization of polyethylene fractions from the melt

Abstract

The theory of polymer crystallization with chain folding is extended to include the effect of reptation in the melt on the rates of crystallization G I and G II in régimes I and II. The result is that the pre-exponential factors for G I and G II contain a factor 1 n , Where n is the number of monomer units in the pendant chain being reeled onto the substrate by the force of crystallization; n is proportional to the molecular weight. The predicted fall in growth rate with increasing molecular weight is found experimentally in nine polyethylene fractions M z =2.65 × 10 4 to M z =2.04 × 10 5, corresponding to n z =1.90 × 10 3 to 1.45 × 10 4. The data on these fractions are analysed to find the reptation or ‘reeling’ rate r and the substrate completion rate g. The values g nuc ∼0.5/ n z cm s −1 and r nuc ∼21/ n z cm s −1 at 400K are obtained from the data in conjunction with nucleation theory adapted to account for reptation assuming a substantial degree of regular folding. These results are consistent with a melting point in the range of ∼142° to ∼145°C. (The analysis using T° m (∞)=145°C gives values of such quantities as σ σ e and α that are quite similar to those deduced in earlier studies.) An estimate of g (denoted g expt ) that is independent of the molecular details of nucleation theory gives g expt ∼0.4/ n z cm s −1 and r∼17/ n z cm s −1 at 400K. Calculations of the reptation rate from r 1,2 = (force of crystallization ÷ friction coefficient for reptation in melt), where the friction coefficient is determined from diffusion data on polyethylene melts, leads to r 1,2∼17/ n z to 34/n z cm s −1 at at 400K, or g 1,2∼0.4/ n z to 0.8/n z cm s −1. The conclusion is that the reptation rate characteristic of the melt is fast enough to allow a significant degree of adjacent re-entry or ‘regular’ folding during substrate completion at the temperature cited, and that the substrate completion process is governed jointly by the activation energy for reptation Q∗ D and the work of chain folding q. The nucleation theory and the friction coefficient theory approaches are compared, and the formulations found to be essentially equivalent; the ‘reeling’ rate r is found to be proportional to ( 1 n )A 0(Δf)v 0 exp[− (Q∗ D+q) RT ] , where v 0 is a frequency factor, and A 0( Δf) is the force of crystallization on the pendant chain. The data analysis on the fractions confirms the detailed applicability of régime theory. The growth rate theory presented allows the possibility that the growth front may be microfaceted in régime I.