Solid State Ordering of Wholly Aromatic Copolyesters of Random Monomer Sequence

1993 ◽  
Vol 321 ◽  
Author(s):  
J. Blackwell ◽  
A.-I. Schneider ◽  
C. M. McCullagh
Keyword(s):  
Random Sequence ◽  
Hexagonal Lattice ◽  
Three Dimensional ◽  
X Ray Diffraction ◽  
Molecular Mechanics Calculations ◽  
Polymer Systems ◽  
X Ray ◽  
Monomer Sequence ◽  
Naphthoic Acid ◽  
Diffraction Patterns

ABSTRACTX-ray diffraction and computer molecular modeling Methods are being used to investigate the ordering of random sequence copolyesters when cooled for the nematic Melt. Data will be presented for the copolymers prepared from p-hydroxybenzoic acid (HBA) and 6-hydroxy-2-naphthoic acid. The non-periodic diffraction patterns arising from the random monomer sequences are also indicative of the presence of limited three dimensional order. For both polymer systems, we can generate the qualitative feature of the x-ray data using models in which short non-identical segments of 10–12 Monomers on adjacent chains are approximately in register at their center. Molecular Mechanics calculations show that mese non-identical sequences can be packed on the observed hexagonal lattice with only small energy differences when compared to analogous homopolymer structures. Data will also be presented showing how x-ray diffraction can be used to follow transesterification of copoly (HBA/HNA) in the nematic MelL

A new model for packing of type-I collagen molecules in the native fibril

1981 ◽  
Vol 1 (10) ◽  
pp. 801-810 ◽  
Author(s):  
Karl A. Piez ◽  
Benes L. Trus
Keyword(s):  
Type I Collagen ◽  
Hexagonal Lattice ◽  
Three Dimensional ◽  
Equatorial Region ◽  
Type I ◽  
X Ray Diffraction ◽  
X Ray ◽  
Left Handed ◽  
Crystal Model ◽  
Collagen Molecules

A specific fibril model is presented consisting of bundles of five-stranded microfibrils, which are usually disordered (except axially) but under lateral compression become ordered. The features are as follows (where D = 234 residues or 67 nm): (1) D-staggered collagen molecules 4.5 D long in the helical microfibril have a left-handed supercoil with a pitch of 400–700 residues, but microfibrils need not have helical symmetry. (2) Straight-tilted 0.5-D overlap regions on a near-hexagonal lattice contribute the discrete x-ray diffraction reflections arising from lateral order, while the gap regions remain disordered. (3) The overlap regions are equivalent, but are crystallographically distinguished by systematic displacements from the near-hexagonal lattice. (4) The unit cell is the same as in a recently proposed three-dimensional crystal model, and calculated intensities in the equatorial region of the x-ray diffraction pattern agree with observed values.

2D X-ray diffraction and molecular modelling of the crystalline structure of polyesters under uniaxial stress

2021 ◽  
pp. 096739112199822
Author(s):  
Ahmed I Abou-Kandil ◽  
Gerhard Goldbeck
Keyword(s):  
Crystalline Structure ◽  
Molecular Modelling ◽  
Three Dimensional ◽  
Uniaxial Stress ◽  
X Ray Diffraction ◽  
X Ray ◽  
Wide Range ◽  
Modelling Techniques ◽  
Diffraction Patterns

Studying the crystalline structure of uniaxially and biaxially drawn polyesters is of great importance due to their wide range of applications. In this study, we shed some light on the behaviour of PET and PEN under uniaxial stress using experimental and molecular modelling techniques. Comparing experiment with modelling provides insights into polymer crystallisation with extended chains. Experimental x-ray diffraction patterns are reproduced by means of models of chains sliding along the c-axis leading to some loss of three-dimensional order, i.e. moving away from the condition of perfect register of the fully extended chains in triclinic crystals of both PET and PEN. This will help us understand the mechanism of polymer crystallisation under uniaxial stress and the appearance of mesophases in some cases as discussed herein.

Algorithms for the calculation of X-ray diffraction patterns from finite element data

2010 ◽  
Vol 43 (6) ◽  
pp. 1287-1299 ◽  
Author(s):  
E. Wintersberger ◽  
D. Kriegner ◽  
N. Hrauda ◽  
J. Stangl ◽  
G. Bauer
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Point Of View ◽  
X Ray Diffraction ◽  
Displacement Fields ◽  
X Ray ◽  
Si Substrates ◽  
Diffraction Patterns ◽  
Simulation Point ◽  
Ccd Detectors

A set of algorithms is presented for the calculation of X-ray diffraction patterns from strained nanostructures. Their development was triggered by novel developments in the recording of scattered intensity distributions as well as in simulation practice. The increasing use of two-dimensional CCD detectors in X-ray diffraction experiments, with which three-dimensional reciprocal-space maps can be recorded in a reasonably short time, requires efficient simulation programs to compute one-, two- and three-dimensional intensity distributions. From the simulation point of view, the finite element method (FEM) has become the standard tool for calculation of the strain and displacement fields in nanostructures. Therefore, X-ray diffraction simulation programs must be able to handle FEM data properly. The algorithms presented here make use of the deformation fields calculated on a mesh, which are directly imported into the calculation of diffraction patterns. To demonstrate the application of the developed algorithms, they were applied to several examples such as diffraction data from a dislocated quantum dot, from a periodic array of dislocations in a PbSe epilayer grown on a PbTe pseudosubstrate, and from ripple structures at the surface of SiGe layers deposited on miscut Si substrates.

Incorporating particle symmetry into orientation determination in single-particle imaging

2018 ◽  
Vol 74 (5) ◽  
pp. 512-517
Author(s):  
Miklós Tegze ◽  
Gábor Bortel
Keyword(s):  
Three Dimensional ◽  
Symmetric Case ◽  
X Ray Diffraction ◽  
X Ray ◽  
Coherent Diffraction Imaging ◽  
Diffraction Imaging ◽  
Diffraction Patterns ◽  
Particle Imaging ◽  
Single Particle Imaging ◽  
Orientation Determination

In coherent-diffraction-imaging experiments X-ray diffraction patterns of identical particles are recorded. The particles are injected into the X-ray free-electron laser (XFEL) beam in random orientations. If the particle has symmetry, finding the orientation of a pattern can be ambiguous. With some modifications, the correlation-maximization method can find the relative orientations of the diffraction patterns for the case of symmetric particles as well. After convergence, the correlation maps show the symmetry of the particle and can be used to determine the symmetry elements and their orientations. The C factor, slightly modified for the symmetric case, can indicate the consistency of the assembled three-dimensional intensity distribution.

Collagen: the organic matrix of bone

1984 ◽  
Vol 304 (1121) ◽  
pp. 455-477 ◽  
Keyword(s):  
Self Assembly ◽  
Hexagonal Lattice ◽  
Three Dimensional ◽  
Organic Matrix ◽  
Calcium Hydroxyapatite ◽  
Collagen Molecule ◽  
Crystalline Region ◽  
X Ray ◽  
Molecular Arrangement ◽  
Diffraction Patterns

Collagen is the principal organic matrix in bone. The triple helical region of the molecule is 1014 amino acids long. In fibrils these molecules are staggered axially by integers of 234 residues or 68 nm ( D ). This axial shift occurs by self-assembly and can be understood in terms of a periodicity in the occurrence of apolar and polar residues in the amino acid sequence. Because the molecular length L = 4.47 D , there are gaps 1.5 x 36.5 nm regularly arrayed throughout the fibrils. The three-dimensional molecular arrangement is a quasi-hexagonal lattice with three distinct values for the principal interplanar spacings. Analysis of the intensity distribution in the medium-angle X -ray diffraction patterns from tendons has produced the following picture of the molecular arrangement in fibrils (Fraser et al . 1983). The molecular helices have a coherent length of 32 nm and are tilted parallel to a specific place within the lattice. A regular azimuthal interaction exists between these helices. This crystalline region could be the overlap region with a non-crystalline gap region. However, the gap is still regular axially and the molecular helices retain their structure; their lateral packing is perturbed although they retain a ‘gap’. Neutron and X -ray scattering experiments have shown that calcium hydroxyapatite crystals occur in the gap and are nucleated at a specific though unknown location within the gap. The c -axis of the apatite crystals is parallel to the fibril axis and its length c = 0.688 nm is close to the axial periodicity in a protein with an extended β-conformation. If the telopeptides at the end of a collagen molecule do have this conformation they would either have a highly heterogeneous conformation or exist in a folded manner because the overall length of the telopeptides is shorter than a regular collagen repeat of 0.029 nm would allow.

A complex pseudo-decagonal quasicrystal approximant, Al37(Co,Ni)15.5, solved by rotation electron diffraction

2014 ◽  
Vol 47 (1) ◽  
pp. 215-221 ◽  
Author(s):  
Devinder Singh ◽  
Yifeng Yun ◽  
Wei Wan ◽  
Benjamin Grushko ◽  
Xiaodong Zou ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Single Crystal ◽  
Diffraction Data ◽  
Three Dimensional ◽  
Basic Structure ◽  
Electron Diffraction Data ◽  
Dimensional Electron ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Patterns

Electron diffraction is a complementary technique to single-crystal X-ray diffraction and powder X-ray diffraction for structure solution of unknown crystals. Crystals too small to be studied by single-crystal X-ray diffraction or too complex to be solved by powder X-ray diffraction can be studied by electron diffraction. The main drawbacks of electron diffraction have been the difficulties in collecting complete three-dimensional electron diffraction data by conventional electron diffraction methods and the very time-consuming data collection. In addition, the intensities of electron diffraction suffer from dynamical scattering. Recently, a new electron diffraction method, rotation electron diffraction (RED), was developed, which can overcome the drawbacks and reduce dynamical effects. A complete three-dimensional electron diffraction data set can be collected from a sub-micrometre-sized single crystal in less than 2 h. Here the RED method is applied forab initiostructure determination of an unknown complex intermetallic phase, the pseudo-decagonal (PD) quasicrystal approximant Al37.0(Co,Ni)15.5, denoted as PD2. RED shows that the crystal is F-centered, witha= 46.4,b= 64.6,c= 8.2 Å. However, as with other approximants in the PD series, the reflections with oddlindices are much weaker than those withleven, so it was decided to first solve the PD2 structure in the smaller, primitive unit cell. The basic structure of PD2 with unit-cell parametersa= 23.2,b= 32.3,c= 4.1 Å and space groupPnmmhas been solved in the present study. The structure withc= 8.2 Å will be taken up in the near future. The basic structure contains 55 unique atoms (17 Co/Ni and 38 Al) and is one of the most complex structures solved by electron diffraction. PD2 is built of characteristic 2 nm wheel clusters with fivefold rotational symmetry, which agrees with results from high-resolution electron microscopy images. Simulated electron diffraction patterns for the structure model are in good agreement with the experimental electron diffraction patterns obtained by RED.

Three-dimensional optical transforms

1961 ◽  
Vol 264 (1318) ◽  
pp. 339-354 ◽  
Keyword(s):  
Fourier Transforms ◽  
Three Dimensional ◽  
Polarized Light ◽  
Continuous Phase ◽  
Optical Diffraction ◽  
X Ray Diffraction ◽  
Circularly Polarized Light ◽  
X Ray ◽  
Half Wave ◽  
Diffraction Patterns

In recent years optical diffraction patterns have been used to assist in the solution of certain X-ray diffraction problems. The most useful technique—which is based partly on the properties of Fourier transforms and partly on optical experiments—is usually known as the optical-transform technique. It has, however, so far been confined to problems involving the projection of crystal structures on to a plane. The present work is aimed at extending the application to full three-dimensional structures. It is shown that this is most simply achieved by controlling the relative phases of beams of light; a method of phase control using circularly polarized light and half-wave plates of mica is described. The theory of the method, experimental details, and the demonstration of its validity are given. In order to gain experience in the use of three-dimensional optical transforms for solving X-ray diffraction problems a known structure has been examined, and the results of this work are included. Although this work has been primarily concerned with applications to X-ray diffraction, it is thought that the method of continuous phase changing, which is simple and linear, may find uses in other fields.

scholarly journals Femtosecond X-ray diffraction from two-dimensional protein crystals

IUCrJ ◽  
2014 ◽  
Vol 1 (2) ◽  
pp. 95-100 ◽  
Author(s):  
Matthias Frank ◽  
David B. Carlson ◽  
Mark S. Hunter ◽  
Garth J. Williams ◽  
Marc Messerschmidt ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Bragg Diffraction ◽  
Protein Crystal ◽  
Protein Crystals ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
X Ray ◽  
Linac Coherent Light Source ◽  
Diffraction Patterns ◽  
Better Than

X-ray diffraction patterns from two-dimensional (2-D) protein crystals obtained using femtosecond X-ray pulses from an X-ray free-electron laser (XFEL) are presented. To date, it has not been possible to acquire transmission X-ray diffraction patterns from individual 2-D protein crystals due to radiation damage. However, the intense and ultrafast pulses generated by an XFEL permit a new method of collecting diffraction data before the sample is destroyed. Utilizing a diffract-before-destroy approach at the Linac Coherent Light Source, Bragg diffraction was acquired to better than 8.5 Å resolution for two different 2-D protein crystal samples each less than 10 nm thick and maintained at room temperature. These proof-of-principle results show promise for structural analysis of both soluble and membrane proteins arranged as 2-D crystals without requiring cryogenic conditions or the formation of three-dimensional crystals.

The crystal structure of schairerite and its relationship to sulphohalite

1975 ◽  
Vol 40 (310) ◽  
pp. 131-139 ◽  
Author(s):  
L. Fanfani ◽  
A. Nunzi ◽  
P. F. Zanazzi ◽  
A. R. Zanzari ◽  
C. Sabelli
Keyword(s):  
Crystal Structure ◽  
Diffraction Data ◽  
Hexagonal Lattice ◽  
Three Dimensional ◽  
Chemical Formula ◽  
X Ray Diffraction ◽  
Cell Content ◽  
X Ray ◽  
Structural Framework ◽  
Unequal Number

SummaryThe crystal structure of schairerite from Searles Lake, California, has been determined employing X-ray diffraction data collected on a single-crystal diffractometer. The crystal structure was refined by least-squares methods employing isotropic thermal parameters to a final R index of 0·07 for 2536 independent observed reflections. The cell content is 3[Na21(SO4)7F6Cl]. The space group is P31m with a 12·197 A and c 19·259 Å. Schairerite exhibits a marked sub-cell (a 7·042 Å, the same c axis and P3m1 symmetry), which may be related to the unit cell of sulphohalite when described in a hexagonal lattice.The crystal structure of schairerite may be considered as consisting of seven sheets of Na+ ions perpendicular to the c axis. These sheets are connected to each other .building up a three-dimensional framework. The Na+ ions in these sheets are arranged in an array built up of hexagons and triangles. Sulphur atoms lie in the sheets at the centres of each hexagon, the halogen atoms lying between the sheets midway between the centres of two triangles. A comparison with sulphohalite shows that the close lattice analogies may be related to a similar atomic arrangement. Apart from the differences in chemical formula (F:C1 ratio 1:1 in sulphohalite), the main difference in the structural framework consists of the unequal number of Na+ sheets (six in sulphohalite) and in the SO42− tetrahedra orientation.

Systematic studies on side-chain structures of phthalocyaninato-polysiloxanes: Polymerization and self-assembling behaviors

2015 ◽  
Vol 19 (01-03) ◽  
pp. 160-170 ◽  
Author(s):  
Satoru Yoneda ◽  
Tsuneaki Sakurai ◽  
Toru Nakayama ◽  
Kenichi Kato ◽  
Masaki Takata ◽  
...  
Keyword(s):  
Hexagonal Lattice ◽  
Side Chain ◽  
Electron Systems ◽  
X Ray Diffraction ◽  
Strong Electron ◽  
Covalent Bonds ◽  
One Dimensional ◽  
X Ray ◽  
Self Assembling ◽  
Diffraction Patterns

A series of dihydroxysilicon phthalocyanines having soluble side chains were synthesized and their bulk-state polymerization capability was investigated. Detailed spectroscopic study of the obtained phthalocyaninato-polysiloxanes revealed that strong electron donating ability and small steric hindrance of the peripheral substituents are the dominant factors to afford high-molecular weight polymers. The polymers show the behaviors of columnar liquid crystal (LC), which is clarified by the presence of clear X-ray diffraction patterns with a hexagonal lattice and birefringent textures in polarized optical microscopy. Because of the siloxane covalent bonds through central silicon atoms, phthalocyaninato-polysiloxanes accommodate one-dimensional phthalocyanine arrays with strong π-electronic couplings, thus exhibiting colmnar LC property even for the derivatives carrying short peripheral chains and leading to the relatively higher density of π-electron systems in the materials. This tendency is different from typical discotic small molecules that require optimum side chain structures for LC formation.

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