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In the prevailing thermodynamics associated with Gibbsian surface physics of a century ago, the surface of a crystal has an associated surface energy and surface stress that influences properties and morphology. This work uses molecular mechanics to investigate the surface energy and epitaxial packing of chain folds on the surfaces of adjacent crystals. It is shown that there are lower energy juxtapositions of the crystals resulting from energetically favorable epitaxial arrangements. These lower the excess surface energy with respect to the melt, but do not completely eliminate the discrepancy between the values of the surface energy from computational results and analysis of experimental data. The epitaxial arrangements are consistent with the experimentally observed rotational displacement of successive layers in multi-layer polyethylene crystals. Thus, they might influence the rotation of the successive layers resulting from screw dislocations.

Silk from 3-molted, 4-molted and sex-limited Bombyx mori, Antheraea pernyi and Antheraea yamamai have been investigated using Atomic Force Microscopy and Low Voltage High Resolution Scanning Electron Microscopy. Nanofibrils, bundles of nanofibrils, helical features and a layered structure with a cross angle between nanofibrils in different layers were observed for all silks. Similar log-normal distributions of fibril widths were obtained from all silks with the geometric mean fibril widths covering the range of 90–170 nm. There is no correlation of the fibril width with the fiber size from different types of silkworm. Similar normal distributions of cross angles were observed in 30% of the images with the arithmetic means covering the range of 30–50°. There is an apparent correlation of cross angle with fiber size. The larger fibers for which the crystals are primarily alanine exhibit a greater average cross angle, 46°, than do those of the smaller fibers for which the crystals are primarily alanine and glycine, 36°. Initial wide angle X-ray diffraction measurements on a single fiber of A. pernyi are consistent with the fraction of fibrils at different cross angles being 28%. A simplified computer calculation method and molecular modeling were used in a search for packing angles which minimize the interaction energy of packing between beta sheets. Initial results revealed no definitive evidence of epitaxy to account for the cross angles. It is proposed that a multifibrillar fiber offers a number of mechanical advantages over a solid fiber with the same cross sectional area.

Over a wide crystallization temperature (Tc) range, elongated rectangular lamellar single crystals of syndiotactic polypropylene (s-PP) grown from the melt of thin films exhibit sectorization along both diagonal directions to form the (010) [with the (010) free edge] and the (100) [with the (100) free edge] sectors. They can be observed by transmission electron and atomic force microscopy (TEM and AFM). Electron diffraction experiments show that the crystals in both sectors are form III orthorhombic structure, as recently proposed.1-4 The observation of this sectorization is due to the thickness difference between these two sectors with different fold planes. In situ observations of the single-crystal growth are monitored using an AFM coupled with a hot stage. The Tc-dependent crystal growth rates along both the (100) and (010) normal can be measured, and they are anisotropic. This leads to a large aspect ratio of the rectangular single crystal. AFM results also show that the thickness difference between ...

Highly faceted, regular, lathlike lamellar single crystals of syndiotactic polypropylene (s-PP) fractions have been investigated through transmission electron microscopy (TEM), atomic force microscopy (AFM), and electron diffraction (ED). Single crystals of s-PP over 1 μm in size can be grown from the melt in thin films. ED results obtained from the s-PP single crystals indicate a unit cell III with a = 1.450 nm, b = 1.120 nm, and c = 0.740 nm as proposed by Lovinger and Lotz. At high crystallization temperatures, relatively low molecular weight s-PP fractions can grow lamellar single crystals with microsectors. The polyethylene decoration method has been used to identify the chain folding direction, and no preferred orientation has been observed on the nonsectorized lamellar crystals. Sectorized lamellar single crystals show two different regions. In the sectors along the long axis (the b-axis), the chain folding is found to be parallel to the 010 direction. In the sectors along the short axis (the a-axi...

A normal coordinate approach was used to generate crystallographic packing candidates of a multitorsional polyimide synthesized from 3,3`,4,4`-benzophenonetetracarboxylic acid (BTDA) and 2,2-dimethyl-1,3-(4-aminophenoxy) propane (DMDA) (PI-2). Candidates were obtained under conditions of fixed axial advance of 24.6 {Angstrom} per monomer, and imposed 2/1 helical or 1/0 translational symmetry, consistent with the observed WAXD meridional layer line spacing. The ability of combinatorially generated torsional states to adopt the desired geometry was examined. Necessary corrections to the conformational parameter equations have been made. The procedure described allowed crystallographic conformations satisfying explicit geometric and MM3 intramolecular energy criteria to be generated for a linear multitorsional polyimide prior to the application of crystallographic screening or refinement procedures. 20 refs., 7 figs., 1 tab.

Energy analysis is used to determine the low energy crystal structure for poly(tetrafluoroethylene) in the 15 7 conformation. It is also used to determine the energies of various conformational defects. The perfect structure has a motif of two left- and two right-handed molecular stems in a triclinic unit cell with parameters, a , b , and γ of 1.102 nm, 1.142 nm, and 121 degrees, respectively. A variety of other perfect structures with higher energies exist. None of these corresponds to the experimentally observed metrically hexagonal cell containing one rotationally disordered stem. Excess energies were calculated for rotationally disordering defects such as molecules with the 15 7 conformation in a crystal of 54 25 molecules (and vice versa ), rotated setting angle, reversed hand, and the 2 1 conformation. Subject to the model and the minimization techniques used, these energies ranged in order from near zero to approximately 2 kcal/mol defect CF 2 with those for the 54 25 crystal being about 38 percent greater than those for the 15 7 crystal. The intramolecular ‘interfacial’ energies for these defects ranged from near zero to approximately 2 kcal/mol interfaces. These numbers are approximately 33 percent greater in the 54 25 crystal. The defects decrease the specificity of packing of the molecules. They also increase the volume, energy, rotational disorder and equality of the dimensions of the unit cell. They drive the structure toward the experimentally observed one.

Semi-empirical energy calculations are reported for methyl branched hydrocarbon molecules in orthorhombic and monoclinic crystalline arrays of linear molecules. The 19 molecules in the array are flexible and twenty methylene units long. Two modes of packing the defect molecule in the crystals are found and for each the mechanical relaxation criterion of there being two or more sites available to the molecule is met. However, there is no significant relaxation strength because the differences in site energies are too large. This result holds for all cases because the unfavourable orientation of the molecular stem in one of the sites makes the energy much greater than in the other for which the stem has a favourable orientation. For the case with the lowest defect energy, the unit cell dimensions are comparable to those found experimentally for the same methyl group concentration. Drawings showing the molecular distortion are presented.

Energy analysis is used to determine the low energy crystal structure for polytetrafluoroethylene molecules in the 13 6 and 54 25 conformations. The structure for the 54 25 conformation contains an ordered repeating pattern of a left- and right-handed pair of molecules in a unit cell having projected parameters, a′, b′, and γ′, of 9.60 A, 5.62 A, and 91.4 degrees, respectively. These results, the relative orientations of the molecules, and the relative translations of the molecules are in good agreement with results obtained in a concurrent and independent analysis of diffraction data. Energies calculated for rotational and translational displacements in various modes suggest that a range of structures and a fairly large amount of disorder may be present, also in agreement with experiment.

X-ray diffraction patterns for oriented and unoriented copolymers of tetrafluoroethylene and hexafluoropropylene are presented. They show a transition between 229 and 243K for a copolymer with about 3.4 CF 3 per hundred main chain carbon atoms. The lower temperature phase (II) appears to be similar to that of the homopolymer. A primary difference is the presence in the copolymer crystals of small longitudinal displacements of the molecules caused by the randomly located CF 3 groups. The displacements increase with increasing CF 3 concentration. The higher temperature phase (I) is similar to that of the homopolymer with a difference again being the longitudinal disorder of the copolymer. The difference disappears at higher temperatures as longitudinal disorder is introduced thermally in the homopolymer. At 296K (phase I) the molecular stems in a copolymer with about 3.4 CF 3 per hundred main chain carbon atoms are at an angle of 37.1 degrees with respect to the normal to the basal plane of the lamellas. In phase II, this number is the same within the limits of error.

The unit‐cell dimensions of a given polyethylene have previously been shown to vary nearly linearly with the reciprocal of lamella thickness. Data obtained at 153.2 and 296.2°K are presented to show that the slope of this dependence is different for crystals of orthorhombic n ‐paraffins, melt‐crystallized polyethylene, and solution‐crystallized polyethylene. Within the limits of error, all extrapolate to the same basal area at infinite lamella thickness, and this agrees with the measured value for a sample crystallized from the melt under high pressure to yield a long period of about 3500 A. Since the effect is a surface one, it is proposed that these differences result from the differences between methyl interactions, fold interactions, different fold planes, domains, etc. It is shown that the variation of cell dimension with lamella thickness leads to a quadratic term in the variation of macroscopic density. This term permits the separation of the thickness and density of a lower‐density surface layer in a two‐phase model.

An electron diffraction pattern from polytetrafluoroethylene in Phase II was analysed to determine a chain conformation of 2.1598 CF2 units per turn of the helix. A structure was established from a combination of electron and X-ray diffraction data. The structure contains an ordered repeating pattern of a left- right-handed pair of chain stems. Although the structure is ordered in three dimensions, it cannot be described meaningfully in terms of classical space group nomenclature because very small changes in the structure result in very large changes in the cell parameters. The structure has a volume of 0.03542 nm3 per CF2 group, corresponding to a density of 2344 kg m−3.

X-ray diffraction has been used to measure the separation of the molecular axes as a function of temperature, lamella thickness, and comonomer concentration in copolymers of tetrafluoroethylene and hexafluoropropylene. These data show that the increase of separation with increasing concentration of perfluoromethyl groups is a consequence of inclusion of the groups in the crystals and not an artifact associated with lamella thickness or crystal transition temperature. This conclusion is supported by the fact that diffuseness of some of the x-ray reflections in the copolymers indicates the presence of molecular disorder which might be expected from inclusion of the perfluoromethyl groups in the crystals. The lamellas in the copolymers are thinner than those in the typical homopolymer and this aspect of the structure is the primary cause of the lower density in the copolymers. Analysis of the available data indicates that this is also the situation in copolymers of ethylene and propylene. For both copolymer series, the density of the lamellas is apparently increased by the inclusion of the methyl groups in the crystals as defects.