Effect of molecular orientation distribution and crystallinity on the measurement of the crystal lattice modulus of nylon 6 by x-ray diffraction

The crystal lattice modulus of nylon 6 (-type) was measured by x-ray diffraction using nylon 6 films drawn up to five times. The measured crystal lattice modulus was 173–175 GPa for all specimens whose crystallinity and the Young's modulus were beyond 46% and 3.75 GPa, respectively. These results indicate that a state of homogenous stress can be achieved. In contrast, the values were scattered for the speciments whose crystallinity and Young's modulus are less than the above values. To study the origin, a numerical calculation of the crystal lattice modulus, as measured by x-ray diffraction, was carried out by considering effects on the orientation factors of molecular chains and crystallinity. In this calculation, a previously introduced model was employed, in which oriented crystalline layers are surrounded by oriented amorphous phases so that the strains of the two phases at the boundary are identical. The theoretical results calculated by the introduced model indicated that the crystal lattice modulus by x-ray diffraction is almost equal to the intrinsic crystal modulus if the morphology of the test specimen can be represented as a series model. In contrast, if a parallel model is more appropriate, the difference between the measured modulus and the intrinsic value can be pronounced. Such morphological dependence was found to be less pronounced with increasing high degree of molecular orientation and crystallinity.     

High-pressure phase of polytetrafluoroethylene

The effect of hydrostatic pressure on the crystal structure of PTFE has been studied up to pressures of ca. 25 kbar by x-ray diffraction. The experimental method uses opposed diamond anvils of small surface area as transmitters of pressure with MoKα x-radiation propagating through these anvils. A small specimen of oriented polymer is held in place with a molybdenum gasket. Pressures are measured by change in lattice spacing of sodium chloride included with some specimens. It is found that above 4.5 kbar the PTFE changes to a high-pressure phase in which the molecules have transformed from their normal helical arrangement to that of a planar zigzag and that the planes of the molecules all lie parallel to one another. Further changes in the diffraction pattern on increase in pressure are attributed to slip and twinning in the high-pressure phase rather than to another phase change.     

Application of Vegard's law to mixed cation sodalites: a simple method for determining the stoichiometry

Vegard’s law describes the empirical relationship between the crystal lattice parameter of a mixture and its components. This relationship holds for some sodalites, in particular those containing mixtures of Li, K and Na as the charge balancing cations. By utilizing previously published lattice parameters for Li/Na and K/Na mixed cation chloride sodalites, linear curves were drawn allowing the composition of the mixed cation sodalites to be determined from their lattice parameters. Further, by mathematical addition of the curves for Li/Na and K/Na mixed cation chloride sodalites, a linear curve was developed and tested for the mixed tri-cation Li/Na/K chloride sodalites. This provides a simple way to monitor the composition of mixed cation sodalites and has an application in monitoring the composition of multi-phase materials where the sodalite phase cannot be easily separated for elemental analysis.     

Crystal structure,morphology, and phase transitions in aromatic polyimide oligomers. 3. Poly(1,4-phenyleneoxy-1,3-phenylene pyromellitimide)

An aromatic polyimide oligomer, poly(1,4-phenyleneoxy-1,3-phenylene pyromellitimide) (PMDA-3,4'-ODA), was synthesized from pyromellitic dianhydride (PMDA) and 3,4'-oxydianiline (3,4'-ODA) via a melt-polymerization method. This method permits growth of PMDA-3,4'-ODA lamellar crystals and the crystal structure can be studied via electron diffraction (ED) and wide-angle x-ray diffraction (WAXD) experiments. Our structure analysis indicates that this polyimide possesses a two-chain orthorhombic crystal lattice with dimensions of a = 0.848, b = 0.562, and c = 3.365 nm. It has also been found that poly(amic acid) precursors with little imidization possess the same ab lateral lattice packing, but statistical departure from the ordered packing along the c-direction. Upon increasing the degree of imidization through annealing at elevated temperatures, the order along the c-axis was progressively enhanced. Increasing the annealing temperature caused the dimensions of the a- and the b-axes to expand while the crystal correlation lengths decreased laterally. Simultaneously the dimension of the c-axis shrinks with an increase of the crystal correlation length along the chain direction. Crystal morphological study via transmission electron microscopy (TEM) indicates a mainly lamellar crystal texture with different thicknesses depending upon the polymerization conditions. The end lamellar surface is usually smooth. After annealing at elevated temperatures, the lamellar end surfaces become rough, which may be due to chain motion along the c-axis. The annealed PMDA-3,4'-ODA lamellar crystals still show a large amount of defects. © 1994 John Wiley & Sons, Inc.     

Optical and swelling properties of macroscopic “single crystals” of an S–B–S copolymer. II. Samples possessing a cylindrical morphology

A study is reported of the anisotropic swelling behavior of “single crystal” samples of an S–B–S two-phase copolymer, Kraton K102, on imbibing a selective swelling agent. This material consists of a hexagonal array of polystyrene cylinders in a matrix of polybutadiene. Initially the material expands reversibly, perpendicular to the cylinders. Low-angle x-ray studies show that this corresponds to expansion of the hexagonal lattice and indicates lateral expansion of the matrix material. Birefringence changes can be broadly ascribed to the changes in form birefringence. Subsequently, irreversible expansion occurs along the rod direction. x-ray diffraction studies combined with electron microscopy indicate a transformation of the cylindrical microstructure into a more complex arrangement. This often appears to be an arrangement of spheres, packed on a hexagonal or square lattice, but this cannot completely account for the x-ray results. Some micrographs suggest the existence of a more complex network of the polystyrene microphase units.     

The determination of longitudinal crystal moduli in polymers by spectroscopic methods

Experimental methods for determining longitudinal crystal moduli of polymers were evaluated in light of recent proceesing methods that produced macroscopic Young's moduli which exceeded ultimate values as found by the x-ray diffraction method. The spectroscopic techniques of Raman and coherent inelastic neutron scattering yielded higher longitudinal crystal moduli than x-ray diffraction, and from calculations described herein it is concluded that these spectroscopic values are better estimates of the maximum Young's moduli in fully aligned and crystalline polymeric materials.     

Intermolecular interactions of globular proteins in the crystal state

The present work is devoted to investigation of thermal transitions in the crystals of seven proteins to compare the protein globule stability in crystal and solution. Calorimetry methods, electron and optical microscopy, as well as x-ray diffraction studies are used. It is found that protein crystals do not melt and that the destruction of the crystal lattice is a result of protein globule denaturation within the crystal. It is demonstrated that during the heating of pepsin and DF-trypsin crystals it is possible to observe phase transition of the first order. Equilibrium temperatures of protein denaturation in crystals and in solution coincide. The peculiarities of the crystal state are revealed in the increasing thermal transition cooperativity and the system relaxation period.     

Nuclear magnetic resonance and x-ray determination of the structure of poly(vinylidene fluoride)

In this study, wide-line NMR and x-ray diffraction have been used in conjunction to study the crystal structure of poly(vinylidene fluoride). Drawn poly(vinylidene fluoride) film was found to contain two crystal phases, the relative amounts of each depending on the draw temperature. Drawing at 50°C. yields a single phase, designated as phase I, while drawing at temperatures between 120 and 160°C. yields a mixture of phase I and a second phase (phase II). The fraction of phase II increases with increasing draw temperature, but this phase was never obtained without some phase I. A tentative orthorhombic unit cell is proposed for phase II. The structure of phase I has been determined from x-ray data. The unit cell is orthorhombic, space group Cm2m, having lattice constants a = 8.47, b = 4.90, and c (chain axis) = 2.56 A. There are two polymer chains in this unit cell. The conformation of the polymer chains is planar zigzag. The details of this structure have been confirmed by experimentally determining at ?196°C. the change in the NMR second moment with the angle between the magnetic field and the draw direction of phase I (drawn at 50°C.), and by comparing these results with a theoretical calculation of the second moments, based on the atomic positions obtained from the proposed structure.     

Calculation of crystal and molecular structures of carbon disulfide CS2

Crystal and molecular structures of carbon disulfide CS(2) were investigated by molecular packing analysis with a computed dynamical model. This model includes thermal motions, molecular deformations, and anisotropic atomic repulsive interactions. Several crystalline structures with orthorhombic symmetry Cmca have been found by the calculation. The lowest energy structure agrees with the experimental one. The temperature dependence of the crystal structure parameters reproduces the general features and the particular increase with decreasing temperature of the lattice parameter c (and orientational angle psi) as determined by x-ray diffraction or neutron scattering experiments. The pressure behavior of the crystal structure parameters up to 12 GPa at room temperature is also correctly reproduced.     

Phase transitions and structural properties of a thermotropic polyester

The phase transition behavior and the structural properties of a thermotropic polyester, poly-(chloro-1,4-phenylene-trans-1,4-cyclohexanedicarboxylate), were studied by differential scanning calorimetry, x-ray diffraction, polarized-light microscopy, and electron microscopy. The polyester shows two first-order transitions in heating, i.e., a crystal-crystal transition and a crystal-liquid-crystal transition at 190–220 and 300–330°C, respectively. The texture in the liquid-crystalline phase is very similar to that of nematic low-molecular-weight materials. Oriented films of the polyester can be obtained from the liquid-crystalline state. Many fibrils occur in a fractured lateral surface of the film. Bandlike structures 50–100 nm wide were observed in surfaces of both oriented and unoriented films. The direction of the polymer chain axis is almost perpendicular to that of band elongation. In the oriented film, the band structures are perpendicular to the direction of orientation.     

Thermal expansion of the crystal lattice of novel thermoplastic polyimides

Measurements of the coefficient of thermal expansion (CTE) of the crystalline lattice of two semicrystalline thermoplastic polyimides are reported. NEW-TPI and LARC-CPI polyimides were studied using elevated temperature wide-angle x-ray scattering (WAXS) from 25°C. To 325°C. To examine possible shifts in the c-axis, a novel approach developed in our lab was used to create highly oriented samples. Films were treated in 1-methyl-2-pyrrolidinone (NMP) at the reflux temperature, washed and then dried under constraint. The films treated in this manner were highly oriented, with c-axes preferentially aligned along the film normal. The advantage of this orientation is that it allows numerous reflections of type (00l) to be examined for temperature shifts of the c-axis using reflection mode WAXS. No systematic shift of the c-axis lattice parameter as a function of temperature was observed in either NEW-TPI or LARC-CPI. The c-axis thermal expansion is concluded to be smaller than 8 x 10^?6/°C for LARC-CPI, and for NEW-TPI may be weakly negative. From WAXS of unoriented films, systematic shifts in the a and b lattice parameters were deduced as a function of temperature. The linear CTEs relating these unit cell parameters at temperature T to their values at 0°C are: ©1995 John Wiley & Sons, Inc.     

Study of crystalline orientation in drawn ultra-high–molecular weight polyethylene films

A wide-angle x-ray diffraction (WAXD) study of the development of molecular orientation in the crystalline phase of ultra-high–molecular weight polyethylene films prepared by the gelation–crystallization method is presented. WAXD scans of the undrawn films show that the lamellae are oriented in the plane of the films. Upon drawing at 130°C, the orientation of the molecular chains changes from the direction normal to the film surface (ND) to the elongation direction. The decrease of the 200/020 intensity ratio at low draw ration (λ <10) indicates that double orientation develops during the transformation from the lamellar to the fibrillar morphology, with the a-axis oriented parallel to ND. The orientation distributions of the 110, 200, 020, and 002 planes of the orthorhombic unit cell of polyethylene were studied and characterized by the coefficients of a Legendre polynomial series. At a draw ratio of 4.5, the second-order coefficient, 〈P₂(cos χ〉, already gets close to its limiting value, but it is shown that higher order coefficients of the polynomial series can be used to describe the evolution of the orentation, even up to λ = 50. The coefficients relative to the molecular chain orientation, 〈P_n(cos χ)〉_c, can be calculated from different crystalline reflections. Curve-fitting calculations were made in order to improve the correlation between the results obtained from the orientation distribution of the 110, 020, and 002 planes. A Person VII function was found to give a better fit of the experimental curves than Gaussian or Lorentzian equations. © 1993 John Wiley & Sons, Inc.     

Crystal deformation in aromatic polyesters

A study has been carried out of the changes in the x-ray diffraction patterns which occur when oriented fibers or tapes of poly(trimethylene terephthalate) (3GT) and poly-(tetramethylene terephthalate) (4GT) are subjected to mechanical tensile stress. Although the polymers show very different behavior in detail, in both cases comparatively large reversible lattice strains are observed (～ several %). The diffraction pattern of 3GT changes monotonically with increasing macroscopic strain, suggesting that the lattice responds immediately to the applied stress, and deforms as though it were a coiled spring. In 4GT, on the other hand, there is no detectable change in the x-ray diffraction pattern at low macroscopic strains, i.e., low values of the applied stress. At higher stresses, changes in the pattern occur which suggest a definite change in the crystal structure. Finally at the highest values of applied stress, the lattice deformations cease to increase. A preliminary discussion is presented of the relationship of these x-ray diffraction results to the mechanical stress–strain behavior.     

Negative thermal expansion of polymer crystals: Lattice model

The lateral thermal motion of atoms in an inextensible polymer chain would cause a shortening along the chain direction. This effect could explain the observed negative thermal expansivity α along the chain direction of a polymer crystal. Using this idea, the expansivity α is calculated for a lattice of parallel linear chains. A value of ?1.3 × 10^?5 K is obtained for chains with a carbon backbone, in good agreement with data for polyethylene.     

Mechanism of ion transfer in structure-disordered copper and silver chalcogenides

Copper and silver selenides and tellurides and their solid solutions are studied. Parameters of ion transfer are measured; the solid solution structure is refined using x-ray and neutron diffraction analysis; the lattice dynamics is studied using the neutron inelastic scattering and NMR; and the short-range order is studied using EXAFS. Based on the summarizing of the experimental results obtained, in aggregate with literature data, a physical mechanism of ion transfer in mixed ion-electron conductors is suggested.     

Oriented crosslinked polyethylene pipes by a novel extrusion method

Crosslinking and stretching (2.5 times along the circumferential direction) of the molten polymer during extrusion produced pipes with dominantly circumferential orientation and a lower degree of axial chain orientation. Differential scanning calorimetry (crystallinity and crystal thickness), density measurements (crystallinity), X-ray diffraction (c-axis orientation), infrared dichroism measurements (crystalline and amorphous chain orientation) and contraction measurements (molecular draw ratio) assessed the microstructure of the pipe material. The mechanical properties of the oriented material were assessed by uniaxial tensile tests. The orientation was biaxial with the main orientation in the circumferential direction and a lesser orientation in the axial direction. The maximum degree of circumferential orientation was obtained at the inner wall of the pipe. The lower degree of crosslinking of the core material allowed slippage of chains during the stretching of the molten polymer and it is suggested that this is the cause of the lower degree of orientation of the core material. The oriented pipe material exhibited a 5-10% higher degree of crystallinity and higher crystal thickness than conventionally crosslinked material. The tensile modulus and the tensile strength of the oriented, cross-linked material was greater along the axial direction than along the circumferential direction. The circumferential and axial moduli for the oriented, crosslinked pipe were greater than the corresponding moduli of the non-oriented cross-linked pipe material. Another pipe based on crosslinked PE that were first circumferentially stretched 2.5 times and later axially stretched 10 times (in the molten state) showed, despite the fact that it exhibited pronounced axial orientation almost a balanced tensile modulus (4.3±0.2 GPa) in the axial-circumferential plane. Atomistic modelling showed that the orientational dependence of the density of the amorphous phase is small.     

Progress in crystal structure prediction

The results of the application of a density functional theory method incorporating dispersive corrections in the 2010 crystal structure prediction blind test are reported. The method correctly predicted four out of the six experimental structures. Three of the four correct predictions were found to have the lowest lattice energy of any crystal structure for that molecule. The experimental crystal structures for all six compounds were found during the structure generation phase of the simulations, indicating that the tailor-made force fields used for screening structures were valid and that the structure generation engine, which combines a Monte Carlo parallel tempering algorithm with an efficient lattice energy minimiser, was working effectively. For the three compounds for which the experimental crystal structures did not correspond to the lowest energy structures found, the method for calculating the lattice energy needs to be further refined or there may be other polymorphs that have not yet been found experimentally.     

A three-dimensional mesophase with rhombohedral structure formed by double-swallow-tailed compounds

In five double-swallow-tailed compounds a weakly birefringent high temperature phase occurs which exhibits a characteristic optical texture. On the basis of X-ray diffraction measurements on well oriented monodomains, the structure of this phase could be described by a rhombohedral lattice of space group R3c or R32/c; the lattice parameters are not far from a cubic lattice. In spite of the three dimensional superstructure with long range character, the lateral packing of the molecules is liquid-like - similar to the well known cubic mesophases.     

A three-dimensional mesophase with rhombohedral structure formed by double-swallow-tailed compounds

In five double-swallow-tailed compounds a weakly birefringent high temperature phase occurs which exhibits a characteristic optical texture. On the basis of X-ray diffraction measurements on well oriented monodomains, the structure of this phase could be described by a rhombohedral lattice of space group R3c or R32/c; the lattice parameters are not far from a cubic lattice. In spite of the three dimensional superstructure with long range character, the lateral packing of the molecules is liquid-like - similar to the well known cubic mesophases.