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

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 $\text{1}\text{n}$, 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 × 10⁴ to M_z=2.04 × 10⁵, corresponding to n_z=1.90 × 10³ to 1.45 × 10⁴. 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 $\text{Q1}{}_{\mathrm{D}}$ 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 $\text{(}\text{1}\text{n}\text{)A}{}_0\text{(Δf)v}{}_0\text{exp}\text{[?}\text{(Q1}{}_{\mathrm{D}}\text{+q)}\text{RT}\text{]}$, where v₀ is a frequency factor, and A₀(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.