On the growth rate of spherulites and axialites from the melt in polyethylene fractions: Regime I and regime II crystallization
Year: 1975
Type: article
Abstract: The growth rate G of the crystalline bodies appearing in each of a set of 35 characterized polyethylene fractions ranging from 3600 to 807,000 in molecular weight has been measured as a function of the undercooling ?T. In isothermal crystallization, only axialites were found from Mw = 3600 to 18 ,000. (For these runs, ?T < 17.5 C.) From Mw = 18,000 to Mw = 115,000 coarse-grained non-banded spherulites were found for ?T > 17.5 C, and axialites for ?T < 17.5 C; a rather sharp break occurred in the log10 G versus T data at ?T = 17.5 C. The morphological changes were more gradual. Above Mw = 115,000, only nearly structureless "irregular" spherulites were found at all undercoolings corresponding to isothermal growth. Typical ringed spherulites were obtained only on quenching. Wide-angle x-ray data showed that the usual orthorhombic subcell predominated in all the morphologies encountered. Low-angle x-ray data showed that the specimens exhibited lamellar crystallization irrespective of the particular gross morphology involved. The growth rate data on each fraction were analyzed using G = Go exp [-U*/R(T - T8)] exp [-Kg/T(?T)f] where f = 1 to obtain values of Kg and G0. The value of Y in Kg = Ybsse/(?hf)k was obtained for each morphology by applying the "Z" test of Lauritzen. Y = 4 for regime I crystallization (single surface nucleus leads to completion of substrate) and Y = 2 for regime II crystallization (numerous surface nuclei involved in substrate completion). It was found that the axialites obeyed regime I kinetics (Y = 4), the coarse-grained spherulites regime II kinetics (Y = 2), and the irregular spherulites "mixed" kinetics (Y ~ 3). The assumption that the substrate length L in Lauritzen's regime theory was ~5 m led to the prediction of a rather sharp regime I ? regime II transition (corresponding to a break in the log10 G versus T data) at ?T = 17.5 C, in accord with experiment. The sse value calculated from Kg and Y for Mw = 20,000 was approximately constant with molecular weight and independent of morphology; the limiting value of sse from kinetic measurements was about 1285 erg2/cm4, corresponding to se(8) = 90.5 erg/cm2 and s = 14.2 erg/cm2. (This value of se(8) compares favorably with se(eq) = 93 8 erg/cm2 from melting point experiments.) The increase of sse and se that took place at low molecular weights on up to ~20,000 was treated using an expression given by Hoffman, viz, se = se(8) [(? + i) / (? + 1)] where ? = number of folds per molecule, i = se(cilium)/se(8). Intermittent high and low values of se were found experimentally in this region, showing that i varied with increasing molecular weight between 0.15 and ~0.7. Theoretical estimates of these upper and lower bounds for i are given. The variation of se between its upper and lower bounds was tentatively explained in terms of the alternate appearance of short and long terminal cilia. Estimates of the initial lamellar thickness I*g were made from se, and compared with the appropriate low-angle x-ray spacings. A theoretical estimate of the ratio of the pre-exponential factors Go(I) and Go(II) for regimes I and II was compared with experiment with satisfactory results. The value of Go is not strongly dependent upon the viscosity of the melt. The work of chain folding deduced from the growth rate data is close to 4.1 kcal/mol, which is in good agreement with other estimates.
Institution: National Institute of Standards and Technology
Language: English
Subfield: Polymers and Plastics
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2314753372