Extra meridional reflections of drawn polyoxymethylene

Extra meridional reflections (00l: l = 3, 5, 13, 15, 21) were observed in drawn polyoxymethylene (POM). The 003, 0015, and 0021 x-ray diffraction intensities increase on annealing, while the 005 and 0013 intensities decrease. It is concluded that crystalline regions are of two kinds: in the first, which generates the 003, 0015, and 0021 reflections, the molecular conformation is slightly distorted from the uniform helix by intermolecular steric hindrance between the CH₂ groups; and in the second, which generates 005 and 0013 reflections, the molecular conformation is distorted in another way. The second form is converted into the first by annealing. The displacements in the c direction of the CH₂ groups and the oxygen atoms from the uniform helix in the first form are about 1.0% and 0.75% of the interval between a CH₂ group and an oxygen atom along helix axis of the POM crystal; thus the correct conformation in the stable state is known. The nature of distortion in the second region is not clarified but several characteristics are offered.     

Dynamics of nematic point defects in a capillary with tilted boundary conditions

The motion of a single point defect in a cylindrical cavity filled with a nematic liquid crystal is described by solving numerically the simplified equations of nematodynamics. Perfect homeotropic anchoring for the director on the lateral boundary would result in the creation of domains with equal elastic energy, escaped upwards or downwards along the cavity axis and separated by point defects of strength ± 1. Defects do not move as long as they are sufficiently far apart. However, small deviations from homeotropic anchoring remove this degeneracy and the energetically favourable domains start to expand at the expense of the others, thus setting the defects in motion along the tube. We present a new numerical approach, which neglects the backflow, for studying the influence of both the pretilt and the elastic anisotropy (K ₃₃ ≠ K ₁₁) on the motion of a defect. We show how even very small pretilt angles (≈1°) result in speeds observed in experiments. For a moderate elastic anisotropy, the velocity of a +1 defect equals the velocity of a -1 defect, whereas for K ₃₃?K ₁₁ a + 1 defect moves faster than a -1 defect. For small pretilts we confirm a good qualitative agreement with an existing analytical approach, which proves inaccurate for large pretilts.     

Structure of a poly(2,5‐benzimidazole)/phosphoric acid complex

As‐cast films of poly(2,5‐benzimidazole) exhibit uniplanar orientation in which the planes of the aromatic rings lie parallel to the film surface. Upon doping with phosphoric acid, the original crystalline order is lost, but the doped film can be stretched to produce films with uniaxial orientation. After thermal annealing at 540 °C, nine Bragg reflections are resolved in the fiber diagram, and these are indexed by an orthorhombic unit cell with the dimensions a = 18.1 Å, b = 3.5 Å, and c = 11.4 Å, containing four monomer units of two chains. The absence of odd‐order 00l reflections points to a 2₁ chain conformation, which is probably planar so that the aromatic units can be stacked along the b axis. The water and phosphoric acid contents of the crystalline structure cannot be determined exactly because of the presence of extensive amorphous regions that probably have different solvation. The best agreement between the observed and calculated intensities is for an idealized structure containing two phosphoric acids and two water molecules per unit cell. However, the phosphoric acid is probably present mainly in the form of pyrophosphoric acid and its higher oligomers. In addition, the X‐ray data are consistent with a more disordered structure containing chains with random (up and down) polarity and a lack of c‐axis registry. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2576–2585, 2004     

Elastic modulus of the crystalline regions of polyimide derived from poly(amic acid)–biphtalic dianhydride and p-phenylene diamine

The elastic modulus E_l of the crystalline regions in the direction parallel to the chain axis was measured by X-ray diffraction for polyimide derived from polyamic acid (biphthalic dianhydride and p-phenylene diamine). These specimens were cured by two different routes: curing at 200 °C, and at 400 °C for 1 h, respectively (2STEPS), and curing from 80 °C to 400 °C stepwise (nine steps) for 1 h at each step (STEPWISE). The E_l values of 54–169 GPa were obtained for the STEPWISE specimen and 80–178 GPa for the 2STEPS specimen, depending on the meridional reflection employed for measurement of the E_l value. A linear relationship between the E_l value and the fiber identity period was obtained from each meridional diffraction, such that the E_l value increased with an increase in the fiber identity period. The E_l value of the fully extended structure was estimated to be 210 GPa. These are considered to be due to the coexistence of polymorphs with different skeletal structures. The crystalline regions of the 2STEPS specimen seems to consist of a more extended skeleton than those of the STEPWISE specimen. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3294–3301, 1999     

A study of the dilation of the unit cell of metallocene isotactic poly(propylenes): The monoclinic form

The lattice parameters of a series of monoclinic metallocene poly(propylenes) of constant molecular weight are measured as a function of defect content, that vary between 0.3 and 2.35 total defects per 100 monomeric units. The parameters are also measured as a function of molecular weight for a fixed defect content and as a function of the crystallization temperature. The b axis is found to increase with decreasing isothermal crystallization temperature whereas only small changes are found for samples rapidly crystallized. The a and c axis showed basically no variation with crystallization temperature. The parameters of the unit cell were essentially constant with varying defect content in the poly(propylene) chain. Lack of observed effect on the dilation of the unit cell by increasing defects is a consequence of the rapid crystallization required to ensure formation of monoclinic crystals. The unit cell parameters increased as a mild function of the molecular weight. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2511–2521, 1997     

Elastic modulus of the crystalline regions of chitin and chitosan

The elastic moduli E_l of the crystalline regions of α‐chitin and chitosan in the direction parallel to the chain axis were measured by X‐ray diffraction. The E_l values were 41 GPa for α‐chitin, and 65 GPa for chitosan, respectively, at 20°C. The contracted skeletons of α‐chitin and chitosan are the key factor for the low E_l values compared with that (138 GPa) of cellulose I. The E_l value of α‐chitin was constant at 41 GPa both at −190°C and 150°C, which indicates that the molecular chain of α‐chitin is stable against heat within the temperature and stress range studied. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1191–1196, 1999     

Membrane Structure of Substance P. I. Prediction of Preferred Conformation,Orientation, and Accumulation of Substance P on Lipid Membranes

Preferred conformation, orientation, and accumulation of substance P on a neutral hydrophilic-hydrophobic interface was estimated and extrapolated to interactions with neutral and anionic lipid bilayer membranes according to our general procedure. Nine residues at the C-terminus were predicted to be transferred to the hydrophobic phase as an α-helical domain, oriented quite perpendicularly on the membrane surface. The N-terminal residues remained in the aqueous phase with their charges exposed to H₂O. The molecular amphiphilic moment vector was strong (338 arbitrary units) and pointed its hydrophilic end towards the N-terminus, only 15° away from the helix axis. The molecular electric dipole moment vector was also strong (124 debye) and pointed its positive end towards the N-terminus, only 9° away from the helix axis. Thus, it reinforced the effect of the amphiphilic moment of a peptide intruding into the membrane dipole layer. The estimated dissociation constant for the equilibrium between membrane-bound and free substance P was K_d ≈? 46 mM for neutral membranes, and K_d ≈?0.43 mM for anionic membranes with a Gouy-Chapman surface potential of ?40 mV. Thus, substance P behaved similarly to dynorphin A and adrenocorticotropin peptides which insert their N-terminal message segments as perpendicularly oriented helical domains into membranes, whereas their C-terminal address segments remain in the aqueous phase as random coils. Substance P is the first instance of a neuropeptide which is expected to insert a C-terminal message into lipid membranes.     

Axial X-ray scattering on high-performance polymeric fibers

High-temperature polymers were spum from liquid-crystalline solutions into fibers of superior thermal stability and mechanical properties. Fibers of two extended-chain polymers poly(p-phenyleneterephthalamide), PPTA, and poly-2,5-benzoxazole, ABPBO, as well as a rod-like polymer poly(p-phenylenebenzobisoxazole), PBO, were examined by axial x-ray scattering. Both wide-angle scattering and small-angle scattering were performed with CuKα radiation aiming along the fiber axis (c-axis) for structural information on the a-b lattice plane. In addition to previously reported lattice structure, the PPTA fibers (Kevlar® 29, 49, and 149) showed strong [004] and a [022] reflections suggesting that segments of the PPTA molecules were transverse to the fiber axis. This unique fiber structure is more prominent and the void content is less for the PPTA fibers with higher tensile modulus, (i.e., Kevlar® 149 > Kevlar® 49 > Kevlar® 29). Similar measurements on thermally annealed ABPBO and PBO fibers showed no [00l], [h0l], or [0kl] reflection indicative of a truly uniaxial molecular orientation. Evidence of microfibrillar order was discovered for the Kevlar® fibers and the ABPBO fiber. Results of conventional x-ray scattering on these fibers were compared and reconciled. © 1994 John Wiley & Sons, Inc.     

Structure and thermochromic solid-state phase transition of poly (3-alkylthiophene)

In order to clarify the structural changes that occur in the thermochromic phase transition of poly (3-dodecylthiophene) [P3DT] and poly (3-hexylthiophene) [P3HT], the temperature dependence of x-ray diffraction and Fourier transform infrared spectra was measured. (1) Orthogonal unit-cell parameters were determined at room temperature: a=25.83 Å, b=7.75 Å, c (fiber axis)=7.77 Å for P3DT and a=16.63 Å, b=7.75 Å, and c=7.77 Å for P3HT. A large variation of the a-axis length between P3DT and P3HT indicates the extended trans conformation for the alkyl side chains which are oriented along the lateral a-axis direction. (2) The interplanar spacing, intensity, and integral width of the x-ray (h00) and (00l) reflections were found to change drastically in the transition region. (3) Polarized infrared measurements at high temperature revealed a marked increase of the gauche band intensity for the alkyl side group modes followed by a decrease in the band intensity of the thiophene ring modes. (4) The layer reflections of the x-ray fiber diagram become diffuse at high temperatures, indicating that the transition occurs in a liquidcrystalline manner with the orientation of the main chain axes preserved but with almost no axial correlation between the neighboring main chains. These results provide experimental support for the structural model proposed earlier: as the temperature increases, the trans-type side chains begin to disorder by introduction of gauche bonds. This disordering disrupts the regularity of the main chain conformation and decreases the effective length of the polythiophene conjugated system.     

Structural studies on polymer whiskers by transmission electron microscopy. II. Unit cell of poly(p‐hydroxybenzoic acid) whisker crystal at room temperature

A set of conspicuous reflections, which are not indexed using the cell constants reported so far for poly(p‐hydroxybenzoic acid), were found in the electron diffraction (ED) patterns of its whisker crystal. A new unit cell [a = 1.487 nm, b = 0.572 nm, and c (chain axis) = 1.258 nm, α = β = γ = 90°] was proposed to explain the reflections in question, based on a set of the ED patterns viewed along the different zone axes, which were obtained by tilting the whisker around its long axis. The density of the whisker was experimentally measured to be 1.500 g/cm³, showing that four molecular stems are running through the new unit cell. From the extinction rule, the highest space group was assumed to be Pbca. In this case, the projection of the new unit cell onto the ab‐plane gives a two‐dimensional unit cell with pgm and is basically in agreement with those proposed so far. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2456–2462, 1999     

Neutron crystal structure analysis of polyethylene‐d4: The application of a neutron imaging plate

Neutron diffraction provides a more detailed structure than X‐ray diffraction. In this study, a neutron crystal structure analysis of polyethylene‐d₄ was carried out with a neutron imaging plate. This was the first crystal analysis of the crystalline polymer with the neutron fiber pattern. The procedure was almost the same as that in a previous work, in which the neutron structure analysis was carried out on the basis of the equatorial reflections. The azimuthal angle of the molecule with respect to the a axis was estimated to be 46.3°. This corresponded well to the value of 45° estimated in the previous work within the accuracy of the standard deviations. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3836–3839, 2004     

HELFIT: Helix fitting by a total least squares method

The problem of fitting a helix to data arises in analysis of protein structure, in nuclear physics, and in engineering. A continuous helix is described by five parameters: helix axis, helix radius, and helix pitch. One of these helix parameters is frequently predefined in the helix fitting. Other algorithms find only the helix axis or determine separately the helix axis, the helix radius, or the helix pitch. Here we describe a total least squares method, HELFIT, for helix fitting. HELFIT enables one to calculate simultaneously all five of the helix parameters with high accuracy. The minimum number of data points required for the analysis is only four. HELFIT is very insensitive to noise even in short helices. HELFIT also calculates a parameter, p = rmsd/(N − 1)^1/2, which estimates the regularity of helical structures independent of the number of data points, where rmsd is the root mean square distance from the best-fit helix to data points and N is the number of data points. It should become a basic tool of structural bioinformatics.     

Director configurations in nematic droplets with tilted surface anchoring

The polymer dispersed nematic liquid crystal (LC) with the tilted surface anchoring has been studied. The droplet orientational structures with two point surface defects – boojums and the surface ring defect – are formed within the films. The director tilt angle α = 40° ± 4° at the droplet interface and LC surface anchoring strength W_s ~ 10^–6 (J m^?2) have been estimated. The bipolar axes within the studied droplets of oblate ellipsoidal form can be randomly oriented are oriented randomly relatively to the ellipsoid axes as opposed to the droplets with homeotropic and tangential anchoring.     

Structural analysis of minimized models for syndiotactic polypropylene

In previous work we have shown that the stable form of syndiotactic polypropylene (sPP) adopts a fully antichiral packing in its crystalline lattice. At the same time, we had also discovered a number of prohibited reflections from crystallographic planes with a c-axis component, indicating distortions or defects along the molecular-chain direction and possible departures from the ideal Ibca unit-cell structure. Three studies that appeared in 1996 have proposed a number of possible minimized structures to explore the energetics of departure from such an ideal Ibca symmetry and to account for the prohibited reflections. Two of the studies were based upon energy minimization of the unit cell using empirical or spectroscopically derived force fields. The third model was based upon Rietveld refinement of the bulk X-ray diffractogram combined with ad hoc choices of space groups selected to reproduce the prohibited reflections, and results in a structure with minimal departures from Ibca. In the present article we examine the structural implications of all these models on various reciprocal-lattice sections of sPP by comparing calculated electron-diffraction patterns for appropriate zones with those we obtained experimentally from single crystals. We find that none of the proposed models fully accounts for the experimental data. One of the energy-minimized models (involving translation along the molecular axis) and the Rietveld-refined structure reproduce some of the observed reflections but are not in agreement with observed intensities and introduce additional unobserved reflections or other artifacts. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2523–2533, 1997     

Interaction of water with DNA single and double helix in the B conformation

The interaction energy between water and B-DNA in the single and double helix is computed at a number of planar cross sections perpendicular to the helix long axis and for a few cylindrical surfaces enclosing the helix. In addition, Monte Carlo simulations are presented for a small cluster of water around regions of energy minima. On the base of these simulations the structure of water for B-DNA in solution, the quaternary structure of B-DNA, is proposed and discussed. The intermolecular interaction used in the Monte Carlo computation has been derived from ab initio computations of complexes between water and the DNA bases, diethylphosphate, a ribose derivative, and other model compounds.     

Folded chain crystallization of poly(N-vinylcarbazole)

A study of the morphology of thermally induced crystallization in poly(N-vinylcarbazole) has shown the formation of folded chain lamellae. Diffraction analysis of multiple and single lamellae indicates a paracrystalline structure with hexagonal symmetry about the chain axis and an interchain spacing of 12.00 Å. No sharp reflections due to chain axis periodicity were observed and the chain axis period was calculated from the crystalline density extrapolated to 100% crystallinity. This gave a chain axis period/monomer unit of 2.16 Å consistent with an isotactic 3/1 screw axis and a basic trigonal structure with a = 12.00 Å and c = 6.47 Å.     

Crystal structure of isotactic poly(4-methyl-1-pentene)

The crystal structure of isotactic poly(4-methyl-1-pentene) was determined by x-ray analysis. The unit cell is tetragonal, P4 b2, with α = 18.70 Å and c (fiber axis) = 13.68 Å; it contains four molecular chains each consisting of seven monomeric units in the fiber period. The molecular conformation is essentially a (7/2) helix, but deviates slightly from the uniform (7/2) helix. The unusual low density is discussed from the structural point of view.     

Phase modulation and ellipticity of the light transmitted through a smectic C* layer with short helix pitch

A chiral ferroelectric smectic C* liquid crystal (FLC) with the helix pitch p ₀?=?330 nm was developed to avoid any scattering of visible light when the helix is not unwound over a certain limit. Planar cells with different FLC layer thickness (16 and 44 μm) have been assembled with helix axis parallel to the glass plates and aligned along the rubbing direction. The ellipticity of the light passing through the cells vs. the electric field was investigated, and a method for evaluating the electrically controlled birefringence via ellipticity measurements has been established. We have found that the FLC cell is an optical retardation layer driven by the electric field, the effective birefringence being proportional to the square electric field. The physical origin of the electrically controlled phase shift of the light passing through the FLC layer has been analysed.     

Energy calculations on helical polypeptides: Structure of polyglycine II

Single chain and packing energy calculations have been made on polyglycine (threefold and fourfold helical structures) with interchain NH…?O hydrogen bonds. In conformation A of polyglycine, in which the NH groups point away from the helix axis and the CO groups are nearer to the helix axis, the conformational energy is nearly the same for threefold and fourfold structures. However, the minimum energy conformation corresponds to a threefold structure of polyglycine with peptide configurations in conformation B in which the CO groups point away from the helix axis and NH groups are nearer to the helix axis. This structure is consistent with the polyglycine II x-ray diffraction data.     

Electronic structures around the local defects in all-trans-polyacetylene: An analysis by the cluster-series model

A new approach to analyze the electronic structure around the local defects in a polymer chain is developed based on the cluster-series model. In this approach, by extending the cluster molecule to both sides of the defect, the size effect on electronic structure can be estimated systematically and efficiently. Moreover, through the extension process, the periodicity of electronic structure can be extracted in the form of the periodic pattern of stationary orbitals, which are molecular orbitals unaltered by the extension of the cluster. Such periodic orbitals characterize the bulk states of periodic polymer and the energy band structure can be reconstructed from them. Illustrative analyses of some kinds of local defects in all-trans-polyacetylene are presented at the ab initio STO -3G level. The effects of local defects can be detected by the deviation from periodic bulk states. © 1993 John Wiley & Sons, Inc.