Single crystals of four polyethylene fractions ranging in molecular weight from 3100 to 11 600 were grown isothermally from xylene solution by using the self-seeding technique. Growth rates of the crystals were measured as a function of solution concentration, molecular weight, and temperature of crystallization. The most interesting resulb concern the temperature dependence of the growth rates. For the higher molecular weight fractions the growth rate decreases monotonically when the crystallization temperature increases. In contrast for fractions in the molecular weight range of 3OOC-4OOO the growth curves show a notched appearance in which two branches can be distinguished. These branches intersect at a transition temperature where the temperature coefficient of the growth rates changes discontinuously. This behavior is interpreted to mean that the transition temperatures correspond to changes in the conformation of the chains deposited on the growth faces. Thus, as the crystallization temperature decreases, there is a transition from extended-to once-folded-chain growth, for a fraction with a molecular weight of 3100, and from once-folded to twice-folded for crystals with a molecular weight of 4050. This interpretation of the growth transitions is rationalized with the observed continuous temperature variation of the lamellar thickness by invoking a model of the growth process in which the chain ends are preferentially rejected to the exterior of the lamellae as cilia. With decreasing crystallization temperature the pendant cilia become longer and form a fold when their length becomes equal to the lamella thickness. In accordance with the kinetic theory of polymer crystal growth based on coherent surface nucleation, the growth rate data for the four fractions were analyzed by plotting log G vs. l/TAT, where G is the growth rate, Tis the crystallization temperature, and AT is the supercooling. Values of the basal surface free energies ue derived from the analysis are compared with those obtained by two independent methods and discussed in relation to the molecular structure of the crystals. It is shown that theory and experiment are consistent for crystals in which n (the average number of folds per molecule) > 1 and acceptable values of u, are obtained. Values of ue for once-folded-chain crystals are too low, possibly reflecting inadequacies in the theory. On the other hand, for extended-chain crystals the growth kinetics follow a completely different law in which G a AT. These results pose a challenge to derive the correct theory for the case of extended and once-folded chains and account for the transition between them.
Note that these matrix elements are appropriate to the case that the doublet-state species be sensitized to an excited state.
Melting and dissolution temperatures (I", and Td) and enthalpies of fusion ( A H ) have been measured as a function of crystallization temperature (TJ for solution-grown crystals of polyethylene fractions covering the molecular weight range 1000-11 600. Analysis of the data yields values of the basal surface free energies ue which increase with molecular weight and lie in the range 40-60 erg/cm2 for the molecular weights from 3100 to 11 600. Values of the equilibrium melting/dissolution temperatures obtained from the intercept of T, (Td) plots vs. the reciprocal lamellar thickness are in good agreement with those obtained from direct measurements on extended-chain crystals of large lateral dimensions and thickness. The enthalpies of fusion of the crystals of the various fractions generally increase monotonically with T, in parallel with their thickness.However, for samples with molecular weights of 3100 and 4050 sigmoidal curves are obtained when the enthalpies of fusion are plotted against crystallization temperature. This is interpreted to mean that in this molecular weight range there is a transition in the number of folds per molecule deposited on the growth faces as T, increases.
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