Lamellar and interlamellar structure in melt‐crystallized polyethylene. II. Lamellar spacing, interlamellar thickness, interlamellar density, and stacking disorder

Abstract

Measurements of the small‐angle scattering power and the degree of crystallinity in melt‐crystallized high‐density polyethylene have been used to evaluate the “amorphous” density in situ by the relation, where V is the irradiated volume and ḡ(S) is the “slit‐smeared” absolute intensity. The amorphous density is a function of sample history and is always higher than the extrapolated melt density. After slit‐height correction, and within the experimental error, the ratio of the two observed long periods is 2:1 at all temperatures (25‐‐126°C). The lamellar thickness and the average interlamellar spacing are obtained from the degree of crystallinity and the first corrected long period. At increasing temperatures between 25°C and 110°C, the lamellae become thinner while the interlamellar zone expands by almost half. Over this range the changes are reversible with temperature. Above 110°C, both the lamellae and the interlamellar region expand with temperature. The thickening is partially reversible upon recooling. Other results obtained include measurements of stacking disorder and of microstructural changes with crystallization temperature and with time at ambient temperature.

Density functional calculations on the structure of crystalline polyethylene under high pressures

“…The GGA geometry for this simulated single chain is also listed in Table I. In that table we verify that LDA grossly underestimates the interchain distances and the lattice constants, but that GGA corrects most of the LDA deficiencies and predicts interchain parameters and the cell volume in good agreement with the x-ray 33,34 and neutron 35 scattering results. Both GGA and LDA give good results for intrachain geometry, the errors being smaller than a few percent.…”

“…In each unit cell, there are four (CH) 2 groups situated in two polymer chains. The LDA and GGA optimized geometrical parameters, including the bond lengths, the bond angles and the setting angle of the chain as well as the lattice vectors are listed in Table I together with the experimental results [33][34][35] and the other theoretical predictions 36,37,21,24 for both the single chain and the crystalline system. For reasons of numerical stability that will be discussed below, the GGA geometry is actually obtained at a pressure of 0.1 GPa which is sufficiently small in comparison with the pressure steps of 2 GPa used in this article.…”

The degree of crystallinity of monoclinic isotactic poly(propylene)

“…These include, among others, measurements of density, 9 enthalpy of fusion, 10 small-and wide-angle X-ray scattering, 7,[11][12][13][14] vibrational spectroscopy, 1,[15][16][17][18][19] and NMR using different techniques and nuclei. 20 -24 Properties correlate directly with the degree of crystallinity.…”

Small‐angle x‐ray scattering of semicrystalline polymers. II. Analysis of experimental scattering curves

“…This effect is most pronounced in samples with large identity periods; Iiavesh and Schultz report that slit-height cororection $ecrcascd the apparent long period of a PE sample from 900 A to 500 A. 4 We found that Lorentz correction with isotropic samples further increases the scattering angle by 5-15'%, while Burmester reports 25%.3 Care must be taken with this correction to insure that the pattern is not radially broadened duc to slit width or beam diameter. This failure to account for the geometry of the beam and sample orientation will generally lead to identity periods which are 35% too large.…”