X‐Ray Study of Isothermal Thickening of Lamellae in Bulk Polyethylene at the Crystallization Temperature

A new method of estimating the equilibrium melting temperature, T m , of a polymer is described, and applied to polychlorotrifluoroethylene (PCTFE). Experimentally determined values of the so-called observed melting point, T m ′ ( obs ) , are plotted as a function of the isothermal crystallization temperature, T x . When freed of secondary effects, such as recrystallization, the data fit a straight line of positive slope on a T m ′ ( obs ) versus T x plot, T x being the abscissa. This line is then extrapolated to its intersection with the line T m ′ ( obs ) = T x . The temperature at this intersection is T m . This intersection is at 224 °C for PCTFE, and T m is quoted as 224 ± 1 °C. (The highest melting point actually attained for a specimen was 218.2 °C.) The value of T m estimated using the extrapolation procedure is compared with that estimated using the customary method of slow stepwise warming. A theoretical justification is given for making the type of plot mentioned above. The most important assumption used in the theory is that one of the dimensions of the growing crystal retains a value rather close to that of the appropriate growth nucleus during an isothermal crystallization, the other two dimensions being large in comparison. Combination of this with the fact that the relevant dimension of the growth nucleus will vary as the reciprocal of the degree of supercooling leads to the prediction of melting points that increase linearly with crystallization temperature. The assumption that one of the dimensions of the crystal retains a value fairly close to that of a growth nucleus can readily be justified on the basis of polymer crystal growth with chain folds. Its justification in the case of the customary bundlelike mode of crystallization is less clear. It is demonstrated experimentally that even the largest detectible crystals in PCTFE are only about 70 percent thicker than a primary nucleus, when secondary effects are minimized. The application of the theory to systems other than PCTFE is discussed briefly, and some preliminary measurements on polyethylene mentioned. Some points relating to the shape of the melting curves of highly crystalline polymers are also brought out.

A detailed interpretation of the kinetics of homogeneous nucleation and growth of crystals of a linear homopolymer from dilute solution is given. The probability of forming both nuclei with folded chains, and conventional bundlelike nuclei, from dilute solution is analyzed. It is predicted that at sufficiently high dilution, critical nuclei of length l p * will be formed from single polymer molecules by sharp folding of the chain backbone. The step height of the nucleus is given approximately by l p * = 4 σ e / Δ f . Here σ e is the free energy required to form a unit area of the loop-containing end surfaces, and Δf is the free energy difference per unit volume of crystal between the crystalline and solution states. The quantity Δf is approximately proportional to the degree of supercooling ΔT. The growth of these nuclei is then analyzed. After growth, the resulting crystal is flat and platelike, the loops formed by the chain folds being on the upper and lower surfaces. Kinetic factors determine that the distance between the flat surfaces in the grown crystal will vary over only a narrow range about a value that is in the vicinity of 1*=4σ e /Δf. (Neglecting effects due to edge free energies, the theoretical upper and lower limits are 1*=4σ e /Δf and 1*=2σ e /Δf, respectively.) In some cases the predicted temperature dependence of the step height of the grown crystal, 1* = const./ΔT, may be modified by the existence of a constant term resulting from the presence of an edge free energy ϵ p . A grown loop-type crystal is predicted to be stable in comparison with a bundlelike crystal of the same shape and volume in a sufficiently dilute solution. The logarithm of the nucleation rate is approximately proportional to 1/(ΔT)2 near the melting point. The exponent n in the free growth rate law is predicted under various assumptions. To the extent that comparison is possible, the predictions given agree with the experimental results obtained by Keller and O’Connor and others on single crystals of unbranched polyethylene grown from dilute solution. A survey is given of homogeneous nucleation in bulk polymers, where the conventional bundlelike nucleus containing segments from many different molecules is valid, and the essential results compared with those calculated for the dilute solution case. The theory given for loop nuclei is both general and precise enough at the critical points to suggest that, on crystallization from sufficiently dilute solution, crystals of a definite step height are commonly to be expected for other crystallizable linear polymers than polyethylene, provided loop formation is sterically possible.