Effective molecular polarizabilities and crystal refractive indices estimated from x-ray diffraction data

Although it was proposed some time ago that (hyper)polarizabilities might be estimated from the results of x-ray charge density refinements, early results were unconvincing. In this work we show that the one particle density obtained from the usual multipole refinement model does not contain sufficient information to determine these response properties and instead pursue the "constrained wave function" approach of fitting to x-ray structure factors. Simplified sum-over-states expressions are derived for determining the dipole polarizability from these wave functions, and these clearly show that the earlier work ignored important two-electron expectation values for the dipole polarizability, and two- and three-electron terms for Beta, etc. Correction factors for the simplified sum-over-states polarizability tensors from the constrained wave function are obtained by calibration against coupled Hartree-Fock ab initio results to yield in-crystal effective polarizability tensors. Results obtained for benzene, urea, and 2-methyl-4-nitroaniline demonstrate that the effective molecular polarizabilities clearly include the effects of intermolecular interactions and electron correlation, especially for urea where the effects on the polarizability are known to be quite large. We also carefully consider the way in which the linear bulk susceptibility, chi((1)), and refractive indices are determined from the x-ray fitted polarizabilities, employing three models based on a rigorous treatment of the local field. Incorrect results are obtained for the sort of molecules that are of interest in nonlinear optical applications if the molecules are approximated by single point dipoles. In contrast, the use of Lorentz-factor tensors averaged over several sites yields excellent results, with refractive indices obtained using this model in remarkably good agreement with optical measurements extrapolated to zero frequency.     

TGA-DTA,infrared and x-ray powder diffraction studies on strontium nitroprusside and its hydrates

Dehydration data for the tetra-, di- and monohydrate of strontium nitroprusside and the vibrational behaviour of the water molecules in normal and deuterated samples agree with crystal data previously reported (for the di- and tetrahydrate as single crystals) and in this paper (monohydrate as a powder). Four distinct types of water molecules are present in the three hydrates with one type (oxygen bonded to Sr²⁺) in common. Other types are a non hydrogen-bonded molecule (dihydrate), a molecule bonded by a single hydrogen atom to the nitrogen atom of a cyanide group and a set of two molecules similarly bonded to the oxygen atom of the previous type (tetrahydrate). The spatial orientation of the NO groups of the nitroprusside ions in the tetrahydrate is confirmed by the observed dichroism of the corresponding stretching band.     

An investigation of the smectic-isotropic transition in a side-chain liquid crystal polymer by synchrotron radiation x-ray diffraction

In this work we have used synchrotron x-radiation diffraction to follow in real-time the isotropic-smoetic phase transition of a side-chain liquid crystalline polymer. The analysis of the x-ray data indicated that the transition occurs within a very narrow biphasic region. As the transition takes place, the size of the smectic regions, as indicated by the width of the diffraction peaks, changed only very slightly before impingement, suggesting a two-dimensional growth pattern. A thermal investigation of the polymer paralleling the x-ray experiments was undertaken and a kinetic analysis applied to the resulting data. Qualitative agreement with a disk-like growth of the smectic regions was found. We have shown that the overall kinetics of the isotropic-smectic transition of a side-chain polymer can be studied by x-ray diffraction permitting the evaluation of several structural parameters. © 1993 John Wiley & Sons, Inc.     

Polymorphism in alternating polyketones studied by x-ray diffraction and calorimetry

Differential scanning calorimetry and high temperature x-ray diffraction were used to study the perfectly alternating copolymer of ethene and carbon monoxide (polyketone; POKC2). It was found that oriented POK-C2 fibers show a crystalline phase transition at a temperature between 110–125°C with a 10% change in crystalline density. At this temperature, the crystal structure reported recently (POK-α) is transformed to a crystal structure that was reported in the past for room temperature imperfectly alternating polyketone. The latter structure will be designated as POK-β. The influence of chain defects on the crystal structure was studied by synthesizing terpolymers (POK-C2/C3), in which small amounts of propylene-CO units are incorporated into the polymer backbone. The resulting terpolymers differ from the copolymer by the presence of methyl groups randomly distributed along the polyketone backbone chain. Evidence is presented that indicates that the methyl groups are built into the crystal lattice as defects. With more than 5 mole-% propene the terpolymer fibers crystallize exclusively in the β-modification. Below this level the α/β ratio (at room temperature) increases with decreasing amounts of propene. Both as-synthesized and as-spun POK-C2 were found to consist of both POK-α and POK-β; the α/β ratio depends on the method of preparation. Because the drawn POK-C2 fibers studied here consist exclusively of POK-α, the process of spinning and drawing leads to the transformation of unoriented β-rich material into oriented POK-α. © 1995 John Wiley & Sons, Inc.     

Determination of the stereochemistry of isomeric steroidal 3-spiro-isoxazolidine-[2,3-d]-oxadiazoline by circular dichroism and x-ray diffraction

The absolute configuration of four isomeric steroidal molecules containing the isoxazolidine-[2,3-d]-oxadiazoline moiety has been determined by circular dichroism and X-ray diffraction methods. This heterocyclic system adopts a cis fused structure in which the mean planes passing through the two rings form a dihedral angle of 111°.     

Rheology and sensory texture of biopolymer gels

Sensory texture perception is based on food structure and the mastication process. Real-time observations of crack growth and rheological measurements have shown different patterns of microstructural fracture. This has allowed for a reductive approach in consolidating a range of gels into characteristic microstructures and fracture patterns that can be linked to sensory texture.     

Linear infrared dichroism by a double modulation technique

In the first part of this paper an experimental setup using Fourier-transform infrared spectroscopy (FTIR) in combination with a photoelastic modulator (PEM) for linear dichroism measurements is described. The second part shows the influence of PEM-amplitude and scan-velocity on the sensitivity of the instrument. The third part deals with the fringe-problem in the baselines of absorbance spectra and its influence on the determination of the linear dichroic ratio.     

Impulsive solvent heating probed by picosecond x-ray diffraction

The time-resolved diffraction signal from a laser-excited solution has three principal components: the solute-only term, the solute-solvent cross term, and the solvent-only term. The last term is very sensitive to the thermodynamic state of the bulk solvent, which may change during a chemical reaction due to energy transfer from light-absorbing solute molecules to the surrounding solvent molecules and the following relaxation to equilibrium with the environment around the scattering volume. The volume expansion coefficient alpha for a liquid is typically approximately 1 x 10(-3) K(-1), which is about 1000 times greater than for a solid. Hence solvent scattering is a very sensitive on-line thermometer. The decomposition of the scattered x-ray signal has so far been aided by molecular dynamics (MD) simulations, a method capable of simulating the solvent response as well as the solute term and solute/solvent cross terms for the data analysis. Here we present an experimental procedure, applicable to most hydrogen containing solvents, that directly measures the solvent response to a transient temperature rise. The overtone modes of OH stretching and CH3 asymmetric stretching in liquid methanol were excited by near-infrared femtosecond laser pulses at 1.5 and 1.7 microm and the ensuing hydrodynamics, induced by the transfer of heat from a subset of excited CH3OH* to the bulk and the subsequent thermal expansion, were probed by 100 ps x-ray pulses from a synchrotron. The time-resolved data allowed us to extract two key differentials: the change in the solvent diffraction from a temperature change at constant density, seen at a very short time delay approximately 100 ps, and a term from a change in density at constant temperature. The latter term becomes relevant at later times approximately 1 mus when the bulk of liquid expands to accommodate its new temperature at ambient pressure. These two terms are the principal building blocks in the hydrodynamic equation of state, and they are needed in a self-consistent reconstruction of the solvent response during a chemical reaction. We compare the experimental solvent terms with those from MD simulations. The use of experimentally determined solvent differentials greatly improved the quality of global fits when applied to the time-resolved data for C2H4I2 dissolved in methanol.     

Determination of protein-dye association by near infrared fluorescence-detected circular dichroism

Near-infrared (NIR) squarylium dye spectral properties were evaluated by absorption, fluorescence, circular dichroism (CD), and fluorescence-detected circular dichroism (FDCD). Substituents of the two NN dyes differed at R₁ and R₂, located symmetrically on the chromophore. The side chains of NN525 are R₁=hexanoic acid, R₂=butyl sulfonate and R₁=R₂=ethyl for NN127. FDCD signals were first confirmed by denaturing BSA with 2–8 M urea showing a diminution of dye FDCD peaks, but no change occurred in spectral properties of the dyes in urea. This indicated that the observed cotton effects occurred by noncovalent interactions with the secondary structure of the protein. The average BSA–dye association constants found by fluorescence, absorbance, and FDCD were 1.27×10⁶ (n=1) and 3.3×10⁶ M⁻¹ (n=1) for NN127 and NN525 respectively. These values were in good agreement when calculated by the three spectroscopic methods validating the use of NIRFDCD for optical parameter calculations. These results are useful to describe NIR squarylium dye labeling of BSA.     

Determination of mineral filler orientation in reinforced thermoplastics by x-ray diffraction

Orientation of mica and talc platelets in injection-molded polyamide 6.6 was investigated by X-ray diffraction (diffractometry, pole figures). The platelets are nearly perpendicular to the plane of the molded plaque in the core, and parallel to it in the skin. These orientations are related to the shear and elongation rate distribution in the thickness of the molding.     

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.     

Analyzing solution-phase time-resolved x-ray diffraction data by isolated-solute models

Extracting transient structural information of a solute from time-resolved x-ray diffraction (TRXD) data is not trivial because the signal from a solution contains not only the solute-only term as in the gas phase, but also solvent-related terms. To obtain structural insights, the diffraction signal in q space is often Fourier sine transformed (FT) into r space, and molecular dynamics (MD) simulation-aided signal decomposition into the solute, cage, and solvent terms has so far been indispensable for a clear-cut assignment of structural features. Here we present a convenient method of comparative structural analysis without involving MD simulations by incorporating only isolated-species models for the solute. FT is applied to both the experimental data and candidate isolated-solute models, and comparison of the correlation factors between the experimental FT and the model FTs can distinguish the best candidate among isolated-solute models for the reaction intermediates. The low q region whose influence by solvent-related terms is relatively high can be further excluded, and this mode of truncated Fourier transform (TFT) improves the correlation factors and facilitates the comparison. TFT analysis has been applied to TRXD data on the photodissociation of C(2)H(4)I(2) in two different solvents (methanol and cyclohexane), HgI(2) in methanol, and I(3) (-) in methanol excited at 267 nm. The results are consistent with previous conclusions for C(2)H(4)I(2) in methanol and HgI(2) in methanol, and the new TRXD data reveal that the C(2)H(4)I transient radical has a bridged structure in cyclohexane and I(3) (-) in methanol decomposes into I+I(2) (-) upon irradiation at 267 nm. This TFT method should greatly simplify the analysis because it bypasses MD simulations.     

Transcrystallinity and x-ray diffraction in trans-1,4-polyisoprene

Middle range fractions of mimusops balata, a natural trans-1,4-polyisoprene, exhibit transcrystallinity when crystallized in the 35–40°C range. The presence of transcrystallinity was established by x-ray diffraction and optical microscopy. Diffraction peak intensities change due to transcrystallinity, suggesting x-rays be used to detect transcrystallinity and that caution be exercised in using x-ray diffraction techniques to determine the phases present in bulk material and in calculating the degree of crystallinity. The tendency toward transcrystallinity may depend upon molecular weight.     

Segmental orientation and chain relaxation of polymers by fourier transform infrared dichroism

Fourier transform infrared dichroism has been used to investigate molecular orientation in polymeric materials. It is first applied to characterize network behavior in some elastomeric systems such as model networks of poly(dimethylsiloxane). The strain dependence of segmental orientation is analyzed through networks of known degree of cross-linking and experimental results are compared with calculation predictions based on the rotational isomeric state formalism. Infrared dichroism spectroscopy has also been used to analyze orientational relaxation in binary blends of long and short polystyrene chains. The effect of short deuterated chains (M_w = 3000 to 72000) on the orientational relaxation of long entangled chains (Mw = 2 000 000) is examined in the bidisperse melts uniaxially deformed above the glass transition temperature. While the long chain relaxation is found to be dependent on the short-chain concentration, the local orientational order of the latter is molecular weight dependent in agreement with the classical relaxation theories.