Experimental criterion for the crystallization regime in polymer crystals grown from dilute solution: Possible limitation due to fractionation

By integration of equations previously derived by Frank, the growth rate of polymer crystals is shown to be dependent on their size, provided that the persistence length L_p or the kinetic length L_k = (2g/i)^1/2 are significantly larger than the primary nucleus. A new method of decorating the fold surface (isochronous decoration) allows the measurement of the quasi-instantaneous growth rate of very small crystals obtained from dilute xylene solution of a sharp polyethylene fraction of moderate molecular weight (M_w = 17,000, M_w/M_n = 1.11). Although the theory predicts that the growth rate increases with the size of the crystals as long as its dimension is smaller than the persistence length and/or the kinetic length, such an increase is not observed experimentally with the sharp PE fraction presently used. Therefore it appears that both the kinetic length and the (hypothetical) persistence length are beyond the resolution limit of electron microscopy and that crystallization occurs in the polynucleation regime. An upper bound is obtained for the rate g at which a locally new layer spreads in two directions on the substrate. The rate is lower than is estimated by the commonly Accepted theories. These theories lead also to an abnormally high value for the lateral surface free energy. The possibility that the observed initial linearity of the growth-rate curve may results from a balance of opposite effects (an increase with the size of the crystals on the one hand, a decrease with decreasing concentration and possible fractionation on the other) is thoroughly examined and ruled out. In fact, it must be stressed that at the early beginning of crystallization, negligible parts of the sample are crystallized and it is only at the end of crystallization that these effects appear. The fall in the growth rate as crystallization ends is due neither to progressive exhaustion of the solution alone nor to a depletion of the concentration by diffusion for this sharp fraction of low-molecular-weight PE. The major effect comes from fractionation. This segregation of the various molecular weights is predicted on the basis of a simple model and is verified by gel permeation chromatography (GPC). The fact that in such a sharp fraction significant fractionation occurs precludes any accurate determination of the supercooling and of the concentration of the polymer actually crystallizing. Subtle differences in the molecular weight distributions may result in significant variation of the growth rate. In conclusion, as the data used in the first part of this work were obtained with only a small percentage of the dissolved polymer sample crystallized, the observed constancy of the growth rate does not result from mutual compensation of opposite effects, and our conclusions about crystallization regime, order of magnitude of the kinetic and persistence lengths, and value of the rate of lateral spreading of a secondary nucleus are well founded.