The occurrence of head-to-head butene units in ethylene-butene copolymers and corresponding ethyl branches in low-density (branched) polyethylenes

A high resolution carbon-13 NMR study of an ethylene-butene copolymer has yielded a spectrum whose resonances could be assigned to isolated ethyl branches, 1,3-diethyl branching as well as 1,2-diethyl branches resulting from head-to-head butene polymerization. All these structures are present in the same sample. An examination of all the published spectra of low-density (branched) polyethylenes has revealed many examples of heretofore unassigned resonances which can be associated with this latter type of diethyl branching in these polymers. Spin-lattice relaxation times have been determined, when feasible, for the carbon atoms in each of the three branched structures.     

Morphology of melt-crystallized linear polyethylene fractions and its dependence on molecular weight and crystallization temperature

Replicas and thin-section electron microscopic studies were made of fractions of linear polyethylene covering the molecular weight range 2.78 × 10⁴ to 6.0 × 10⁶ for a variety of crystallizing conditions. Lamellar crystallites were found under all circumstances; and the supermolecular structure, or crystalline morphology, is in agreement with that previously reported from an analysis of the small-angle light-scattering patterns of the same samples under similar crystallization conditions. Details of the crystalline microstructure are also described, which range from truncated hollow pyramids which degenerate as the molecular weight or the undercooling are increased. From these results, it is possible to describe the mechanism of formation of polyethylene spherulites.     

Crystallization kinetics of stretched natural rubber

Studies of the crystallization kinetics of natural rubber networks held in simple extension are reported. In these experiments the length of the specimen was held constant, and the crystallization process was followed by the decay in stress that occurred. A wide range of extension ratios and crystallization temperatures was encompassed by these experiments. From an analysis of the shapes of the crystallization isotherms, it can be concluded that major changes take place in the nucleation and growth processes as the extension ratio is increased. This conclusion is in accord with reports in the literature of changes in the crystallite morphology with extension ratio. Analysis of the temperature coefficient of crystallization, by means of nucleation theory, indicates a substantial increase in apparent interfacial free energies with increased deformation. This latter observation is interpreted to indicate a departure from a correlated crystallization process to one where isolated crystallites are formed.     

On the use of Raman-active longitudinal acoustic modes in the study of polyethylene lamellar structures

The first-, third-, and fifth-order low-frequency, Raman-active, longitudinal acoustical modes of the n-alkane C₉₄H₁₉₀ and different morphological forms of semicrystalline polyethylene have been obtained. An analysis of the results shows that the correction needed to obtain the extended planar-zigzag ordered sequence length is maximum for the n-alkane and very small for the polymer systems. These represent solution crystals as well as bulk-crystallized material. For the latter, samples were prepared so that the crystallite thickness is either comparable to or very much smaller than the extended chain length. An approximate method is also developed which enables the natural linewidth to be determined.     

The thermal expansion of the monoclinic unit cell of isotactic polypropylene

The lattice parameters of a highly stereoregular metallocene polypropylene crystallized at 145°C were obtained after cooling and heating cycles in a temperature interval between 25°C and 165°C. The b dimension undergoes a large thermal expansion with temperature (0.6 Å) while the change of the a axis is relatively small (0.1 Å). The unit cell dimension along the molecular (c) axis appears less sensitive to temperature than are the intermolecular distances. The difference in dimensions between the a and c axis at low and high crystallization temperatures is small, varying from 2.3 to 3.5%. This small difference allows the formation of daughter, crosshatched lamellae in the complete interval of crystallization temperatures. The thermal expansion coefficient of the unit cell specific volume is also reported. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2945–2949, 1997     

Open subspaces of locally compact metric spaces

Although classically every open subspace of a locally compact space is also locally compact, constructively this is not generally true. This paper provides a locally compact remetrization for an open set in a compact metric space and constructs a one-point compactification. MSC: 54D45, 03F60, 03F65.     

Unit-cell dimensions of bulk- and solution-crystallized linear polyethylene

The unit-cell dimensions and density, at room temperature, of bulk- and solution-crystallized linear polyethylene have been determined. The macroscopic measured densities for the bulk-crystallized samples ranged from 0.917 to 0.993 g/cc, and the lattice parameters were found to be independent of the sample density. In contrast, for solution-formed crystals, despite the limited range in macroscopic densities that can be attained, there is a systematic variation in the a and b dimensions with the measured density and the crystallite thickness. The implication of these results for the calculation of the degree of crystallinity and the interpretation of certain infrared bands are discussed.     

Gelation and precipitation of copolymers from solution

There are several reports in the literature to the effect that when isotactic polystyrene crystallizes from moderately dilute solution, lamellas (precipitate) form at high crystallization temperatures and gels at low temperatures. We report here the occurrence of a very similar phenomenon during the crystallization of ethylene-butene-1 copolymers. The observations for the latter system can be given a straightforward explanation based on the demonstrated compositional fractionation that occurs on crystallization. Low co-unit content copolymers are associated with lamellas. Gels invariably contain much higher co-unit content. A generalization of these findings is invoked to explain the previous polystyrene results. A new resonance detected by ¹³C NMR experiments in this polymer can be ascribed to head–head sequences.     

Crystallization kinetics of dilute polyethylene solutions

The crystallization kinetics of a high molecular weight fraction of linear polyethylene was studied in dilute solutions of p-xylene, n-hexadecane, and decalin by dilatometric methods. For all solvents and temperatures, the experimental isotherms could be quantitatively described by the Avrami formulation for the complete transformation. This result is unique in the realm of polymer crystallization, since marked deviations from this theory are usually observed in more concentrated systems. The Avrami exponent is found to be n = 4 in all cases. The temperature coefficients of the rate constants are indicative of a nucleation controlled process. The data fit either a two-dimensional or three-dimensional nucleation mode, and a discrimination can not be made between these two cases. The interfacial free energies are found to be independent of the solvent medium. It is also shown that, irrespective of the type of nucleation control governing the kinetics, the same type governs the crystallite thickness of the lamella-like crystals that are formed.     

Light scattering studies of narrow fractions of polyethylene

Small-angle light scattering experiments were conducted on thin films of linear polyethylene fractions over a very wide range of molecular weights. Spherulitic structures were found in all samples with molecular weight 9 × 10⁵ or less. A rodlike morphology predominates for molecular weights between 1 × 10⁶ and 2 × 10⁶. Still higher fractions yield a very disordered superstructure. These results can be correlated with previous studies of the overall crystallization rates and the resulting properties.