Studies of short-range order in amorphous polymers by radial distribution functions derived from X-ray diffraction

Interatomic and intermolecular ordering in amorphous polymers can be characterized by radial distribution functions (RDF) derived from radiation scattering measurements (X-rays, neutrons, etc.). The type of information which may be derived from RDF data in monatomic systems is illustrated by measurements on a sample of vitreous carbon, which is shown to consist of graphite-like sheets of hexagonally packed carbon atoms with no true graphitic registration between the sheets. As an example of the type of information available in polyatomic systems, an RDF study of aluminum phosphate is given to show that the basic atomic arrangement is very similar to vitreous silica with aluminum and phosphorous stoms occupying positions in aluminum phosphate similar to silicon atoms in silica.

RDF methods have been applied to investigate short-range ordering in amorphous bisphenol A polycarbonate which has been reported to exhibit a grainy or nodular structure under electron microscopy. Two samples with different thermal histories were examined. Both had been rapidly quenched from the melt, and subsequently one was annealed below Tg to produce a marked change in impact properties. Most of the intramolecular distances in the polymer repeat unit were successfully resolved in the RDF patterns in the region 1< r< 6 Å. However, there were only suggestions of broad peaks at r < 5.5 Å and r < 10 Å, attributable to inter-molecular ordering, indicating that little intermolecular ordering had occurred in either sample. The RDF patterns were virtually identical, indicating that the short-range order (0 to 10 Å) in the samples has been essentially unaffected by the annealing procedures. In order to assess the sensitivity of the RDF method to short-range intermolecular ordering, a more highly annealed sample was examined. In addition to the intramolecular distances which were very similar to those resolved in the previous samples, the RDF plot showed a marked periodicity peaking at intervals of ～ 5.5 Å which was attributable to intermolecular ordering, thus confirming the sensitivity of the RDF technique to intermolecular ordering in amorphous polymers.

Similar studies have been made on polyethylene terephthalate films, both “quenched amorphous” and one annealed near Tg (100 hr at 65[ddot]C) to provide complementary structural information on structures reported in electron micrographs under similar conditions. Again, all intramolecular peaks of the polymer repeat unit were resolved in the RDF's for both samples for r < 6 Å. However, there were only suggestions of broad peaks at ～5 and ～8 Å which might be attributed to intermolecular ordering, and there was no detectable increase in intermolecular ordering on annealing.

It is not necessary to assume intermolecular ordering over much greater than ～ 10 Å to explain the RDF data for either polycarbonate or polyethylene terephthalate, and the relevance of this finding to proposed models of polymer structure is discussed.     

Diffuse X-ray scattering and order-disorder effects in the iodide chain compounds N,N′-diethyl-N,N′-dihydrophenazinium iodide,E2PI1.6, and N,N′-diebenzyl-N,N′-dihydrophenazinium iodide,B2PI1.6

Crystals of E₂PI_1.6(C₁₆H₁₈I_1.6N₂) and B₂PI_1.6(C₂₆H₂₂I_1.6N₂) contain stacks of the organic cations which form an array of parallel channels filled with iodide anions. These anions are mainly “ordered” in channel direction. The structure of the iodine chain was derived from a quantitative analysis of the X-ray diffuse scattering. It consists of linear symmetric triiodide anions with intramolecular distances of 2.99 Å and average intermolecular distances of 3.72 Å. There is no long range order along the channel direction and the triiodide chains behave like a one-dimensional liquid or an amorphous body. The fluctuation of distances between the center of gravity of 1st neighbour I^?₃ molecules is well reproduced by a gaussian distribution law of 0.30 Å mean deviation. However, at room temperature, short range interchain transverse correlations exist between the average iodine positions in E₂PI_1.6, and between the triiodide sites in B₂PI_1.6. Longitudinal and transverse correlations increase at lower temperatures. The triiodide units of B₂PI_1.6 present also a displacive modulation of their positions with a long periodicity in channel direction.     

A neutron-diffraction study of liquid acetonitrile

Neutron-diffraction studies on liquid acetonitrile CD₃C¹⁵N at 20°C were carried out at neutron wavelengths of 0·5 Å and 0·7 Å. The data were corrected for background, absorption, multiple scattering and inelastic effects (Placzek correction) and then were normalized to absolute differential cross section by comparison with vanadium standard. The absolute coherent distinct differential cross section was separated into intermolecular and intramolecular contributions. From the latter the molecular structure in the liquid was determined.     

Microwave spectrum,structure, and dipole moment of 7-oxabicyclo[2.2.1]heptane

The microwave spectrum of 7-oxabicyclo[2.2.1]heptane has been assigned in the ground and two excited vibrational states. Relative intensity measurements indicate that these two vibrations have wavenumbers of 120(30) and 330(30) cm^?1. The dipole moment obtained from Stark effect measurements is 1.621(10) D. The molecule is shown to have C_2v symmetry and the assignment of the two singly substituted ¹³C species gives the following skeletal structure: C₁-C₂ = 1.537(5) Å; C₂-C₃ = 1.551(5) Å; C₁-O = 1.452(10) Å; ?C₁OCC₄ = 95.3(10)° φ = 113.1(5)°.     

A neutron diffraction study of liquid chloroform

Neutron diffraction studies of the isotopes of chloroform CD³⁵Cl₃ and CD³⁷Cl₃ in liquid phase were carried out at 20°C and a wavelength of 0·7 Å. The data were corrected for background, absorption, multiple scattering and inelastic effects. The coherent distinct differential cross section was separated into intramolecular and intermolecular contributions. The latter, together with intermolecular contributions from neutron scattering data on chloroform of natural isotopic chlorine composition and from X-ray data, was employed to determine four expansion coefficients of the molecular pair correlation function.     

Microwave spectrum,structure, and dipole moment of bicyclo[3.1.0]hex-2-ene

The microwave spectra of the normal and four monosubstituted ¹³C isotopic species of bicyclo[3.1.0]hex-2-ene have been observed and analyzed. For the normal species the rotational constants (in megahertz) are: Λ = 6306.121 ± 0.006, B = 4516.667 ± 0.004, C = 3208.823 ± 0.002. From the complete data set, a partial r_s heavy-atom structure has been obtained as well as a complete effective structure. The r_s distances are found to be C₁C₅ = 1.521 ± 0.001 Å, C₁C₂ = 1.494 ± 0.010 Å, C₅C₆ = 1.482 ± 0.006 Å, C₁C₆ = 1.522 ± 0.007 Å. The overall effective structure shows the five-membered ring to be only slightly nonplanar (by ca. 6°), and the three-membered ring to be rather sharply inclined with respect to the five-membered ring (dihedral angle C₁C₅C₆-C₁C₅C₄ = 113.5°). Dipole moment measurements for the symmetryless molecule yielded values of |μ_a| = 0.166 ± 0.009, |μ_b| = 0.209 ± 0.015, |μ_c| = 0.119 ± 0.001, |μ_T| = 0.292 ± 0.012 D.     

A quantum-chemical study of intermediates of the 1O2 photogeneration sensitized by buckminsterfullerene and accompanying photochemical reactions

The intermediates of hypothetical photochemical reactions that accompany the quenching of the ³C ₆₀ ^* triplet state by triplet oxygen are studied by the (U)PBE0 quantum-chemical method. The diradical C₆₀-O-O formed from ³O₂ and photoexcited buckminsterfullerene ³C ₆₀ ^* is characterized by a negative binding energy ?1.11 eV (with respect to C₆₀ and ³O₂), the singlet-triplet splitting ΔE _ST of 0.07 eV, and the dipole moment of 3.2 D at the equilibrium internuclear separations 1.522 Å (CO) and 1.294 Å (OO). Its decay produces ¹O₂. The formation of a dioxetane circle lowers the energy by 0.8 eV. The ground-state energy of diketone C₅₈(C=O)₂ is 2.0 eV lower than the energy of C₆₀-O-O. The metastable centrosymmetric diradical C₆₀-C₆₀, formed upon ineffective light absorption by clusters (C₆₀)_N, has a single interpolyhedral C-C bond (1.657 Å). Its triplet state T ₁ lies 0.16 eV higher than the S ₁ singlet. The S ₁ → S ₀ relaxation leads to the formation of a stable C₆₀-C₆₀ dimer with a shorter (1.584 Å) bis-single exothermic (+0.24 eV) bond of polyhedra. The photoexcited C₆₀-C₆₀ dimer is able to form isomeric metastable diradicals C₆₀-C₆₀-O-O.     

Nuclear Overhauser Effect Spectroscopy (NOESY) and 3JHH Coupling Measurements in the Determination of the Conformation of the Sesquiterpene Antimalarial Arteether in Solution

The twisting of the A-, B-, and D- rings of β-arteether were determined from dihedral angles derived from ³J_HH coupling constants and a Karplus-type equation that takes into account heteroatom substitution. The angles obtained by NMR were also compared to the angles obtained by molecular modeling and to those obtained from the methyoxyl analog (artemether) using x-ray crystallography. The NMR results showed that the A-ring was a relatively undistorted chair conformation with the 14-methyl group in an equatorial position. The NMR data indicated that the B-ring was very distorted and the D-ring was twisted outward because of the steric interactions with the ethoxy group. Two-dimensional NOESY data was used to measure selected proton-proton distances for arteether in solution and these distances were also compared to those obtained by molecular modeling and from the x-ray data for artemether. The NOESY data also indicated that the conformation of the A-ring was fairly normal, the B-ring was twisted, and the ethoxy group was in an extended conformation (C₁₁-C₁₂-O-C₁₆=+170°, and C₁₂-O-C₁₆-C₁₇=+169°)     

Templating a face-centered cubic (110) termination of C60

Scanning tunneling microscopy has been used to study C₆₀ overlayers on TiO₂(100)-(1 × 3). Initial adsorption preferentially occurs on O vacancies (Ti³⁺), evidencing a site-specific interaction dominated by substrate-adsorbate charge transfer. At saturation coverage the molecules are incommensurate with Ti³⁺ sites along [001], suggesting a delicate balance between intermolecular and substrate interactions. The unit cell of the C₆₀ overlayer is 13.8Å× 10.0 ± 0.5Å, consistent with the first layer of fcc C₆₀(110); molecules also adopt sites in the troughs of the (1 × 3) structure to form the second layer.     

Structural relaxation investigations of glassy polystyrene by radial distribution functions

The structural relaxation of an atactic polystyrene under sub-T _g annealing at 50°C and at 70°C was investigated by the radial distribution function (RDF) derived from its wide-angle x-ray scattering (WAXS). By recording the changes in RDF (i.e., ΔH(r), where r is the radial distance from an arbitrary reference atom) after it had been annealed for a certain period of days, and taking the integration of ΔAH(r) ²dr, we found that the atom density within structural domains in a size below 15 Å was changed dramatically, but that the tendency leveled off as annealing proceeded. However, the atom density outside the domains is barely changed by sub-T _g annealing. The size of the domain is similar to the statistical segment length reported in the literature. The behavior of the domains—that the segmental relaxation inside the domains in the initial sub-T _g annealing is unconstrained by their neighbors outside the domains—is also similar to the behavior of the statistical segments. The domains are believed to be composed of a statistical segment across the center, which has about 6 styrene repeat units, and 6 equal-distanced parallel segments tangent to the edge of the domain. On the other hand, as the annealing temperature is closer to the glass transition temperature, the frozen unstable chain segments reach equilibrium sooner and with less disturbance in their conformation.     

Titanium local structure in tektite probed by X‐ray absorption fine structure spectroscopy

The local structure of titanium in tektites from six strewn fields was studied by Ti K‐edge X‐ray absorption near edge structure (XANES) and extended X‐ray absorption fine structure (EXAFS) in order to provide quantitative data on Ti—O distance and Ti coordination number. The titanium in tektites possessed different coordination environment types. XANES spectra patterns revealed resemblance to high‐temperature TiO₂–SiO₂ glass and TiO₂ anatase. All samples showed that the valence of Ti is 4+. Based on the Ti—O distances, coordination numbers and radial distribution function determined by EXAFS analyses, the tektites were classified into three types: type I, Ti occupies a four‐coordinated tetrahedral site with Ti—O distances of 1.84–1.79 Å; type II, Ti occupies a five‐coordinated trigonal bipyramidal or tetragonal pyramidal site with Ti—O distances of 1.92–1.89 Å; type III, Ti occupies a six‐coordinated octahedral site with Ti—O distances of 2.00–1.96 Å. Although Ti occupies the TiO₆ octahedral site in most titanium minerals under ambient conditions, some tektites have four‐ and five‐coordinated Ti. This study indicated that the local structure of Ti might change in impact events and the following stages.     

The geometry and forcefield of acetylene

The variational method has been used to determine the geometry and ground state potential surface of acetylene. All the parameters were refined through a least-squares fit to J = 0, 1 levels for C₂H₂ and C₂D₂. A new program was written to evaluate the rovibrational energy levels; in particular, primitive basis sets were developed for all values of J taking into account the singularity for linear geometries. Thus Σ, II, δ states can be refined. The full theory for tetraatomic linear molecules is presented. In this refinement 150 observed levels were used as data, below 10 000cm^?1. The geometry was refined and gives R_e(CC) = 1.2028 Å, R_e(CH) = 1.0618 Å, to be compared with the best experimentally derived values of 1.2027 ± 0.0005 Å, 1.062 ± 0.001 Å, respectively. The zero point energies are 5771.1cm^?1 for C₂H₂ and 4571.1cm^?1 for C₂D₂.     

Ab initio potential energy surface and intermolecular vibrational frequency of C3-He complex

The intermolecular potential energy surface for C₃–He complex has been constructed using supermolecular CCSD(T) and MP4 methods. The potential surfaces have been calculated for 27 values of R ranging from 2.8 to 8.0 Å and 19 values of θ equally spaced between 0° and 180°. Both CCSD(T) and MP4 potentials have similar global behaviors. The global minimum in each of the potentials corresponds to the slightly distorted T-shaped geometry. On the basis of these two potentials, the intermolecular vibrational energies and wavefunctions were calculated. The energy level pattern of the vdW vibrational states was predicted for C₃–He complex. The zero point bending motion of this complex has a range of 180°. The calculated fundamental frequency of vdW bending is 3.16 cm^?1 at CCSD(T) level, and 5.38 cm^?1 at the MP4 level. In addition, we have also constructed the intermolecular potential energy surface with C₃ bending coordinate of 160° by using supermolecular CCSD(T) method. Two local minima including arrow-shaped and Y-shaped configurations were determined. The rotational constants of three C₃–He structures including T-shaped, arrow-shaped and Y-shaped configurations at CCSD(T) level were also reported.     

The structure of the water molecule in liquid water

The slow neutron scattering measurements of Walford, Clarke and Dore for liquid heavy water at 21°C for incident neutron wavelengths of 0·694 Å and 0·347 Å [7] have been reinterpreted using a sophisticated correction for recoil and detector effects [10] for the molecular contribution to the scattering cross-section. For momentum transfer greater than 6 Å^-1 the liquid structure contribution is negligible and a very good agreement between theory and experiment is obtained. It is concluded that the intramolecular oxygen nucleus-deuteron distance is 0·98₃±0·00₈ Å, and that the deuteron-deuteron distance is 1·55±0·02 Å. This molecular structure is nearer to that of the molecule in the vapour than that in ice I for the conventional interpretation for ice I. It is concluded that there is an environmental effect on the molecular internuclear distances at most of order 0·01 Å for the molecule in the orthobaric liquid near the triple point.     

Unusual spin transitions

New heterospin complexes of Cu(hfac)₂ (hfac, hexafluoroacetylacetonate) with pyrazole-substituted nitronyl nitroxides have been found that in the solid state exhibit thermally induced spin transitions analogous to spin crossover. For the first complex, [Cu(hfac)₂L^i-Pr], at room temperature, the Cu—O_L distances, where O_L is the oxygen atom of the nitroxyl group, are very short (2.143 Å). This leads to a strong antiferromagnetic exchange (～-120cm^?1) in the > N—^·O—Cu²⁺—O^·—N < exchange clusters. The CuO₆ coordination units formed by four O atoms of the two hfac anions and by the nitroxyl O atoms of the two bridging nitroxides have a rare form of flattened octahedra, transformed at low temperatures into elongated octahedra with shorter Cu—O_L distances (2.143 Å→2.002Å) and two longer Cu—O_hfac distances (2.130 Å→2.293 Å). For the second complex, [Cu(hfac)₂L^Bu·0.5C₆H₁₄], unusual low temperature structural dynamics of heterospin systems have been found. It is characterized by the formation of two types of CuO₆ unit. The axial Cu—O_L distances are lengthened in one unit (2.250 Å→2.347 Å) and shortened in the other (2.250 Å → 2.006 Å). This leads to a sophisticated μ_eff(T) dependence with μ_eff drastically decreased at 163 K as a result of full coupling of two spins in half of all >N—^·O—Cu²⁺—O^·—N < exchange clusters and to a shift from antiferromagnetic to ferromagnetic exchange in the other half.     

N2- and O2-broadening coefficients of C2H2 IR lines

Pressure-broadening parameters of six lines belonging to the ν₅ band of C₂H₂ in collision with N₂ have been measured with a tunable diode-laser spectrometer in order to complete up to J = 33 our earlier measurements (D. Lambot, G. Blanquet, and J. P. Bouanich, J. Mol. Spectrosc.136, 86–92 (1989)) on the broadening of C₂H₂ by N₂ and O₂ at 297 K. These N₂- and O₂-broadening coefficients have been first calculated on the basis of the Anderson-Tsao-Curnutte theory; in this approach, we show that the short-range interactions which contribute significantly to the linewidths are not correctly treated. Next, we consider the improved semiclassical model proposed by Robert and Bonamy. The intermolecular potential consists in the addition of the atom-atom interaction model to the quadrupolar interactions. The limited radial spherical harmonics expansion of the atom-atom potential, from which expressions for the differential cross section were derived, appears to be quite insufficient at short intermolecular distances. Therefore, we use a more accurate representation of this potential, avoiding an inadequate truncation and keeping the analytic expressions obtained by Bonamy and Robert. In the calculations we take into account the contributions derived from the radial functions U₀₀₀(r), U₂₀₀(r), and U₂₂₀(r), as well as from U₄₀₀(r). A theoretical expression is obtained for the U₄₀₀ contribution to the differential cross section. The results of the calculations arising from the exact radial expansion of the atom-atom potential appear to be significantly larger for high J lines than those arising from the truncated expansion. The latter results, which do not include adjustable atom-atom parameters, are in good agreement with experimental broadening coefficients for C₂H₂---O₂ and in reasonable agreement (except at large J values) for C₂H₂---N₂. It is also shown that the contributions to the linewidths derived from U₄₀₀ are rather small for C₂H₂---N₂ and more important for C₂H₂---O₂. Finally, by calculating the collisional linewidths of C₂H₂---N₂ and C₂H₂---O₂ at 200 K, we have predicted their temperature dependences.     

Extended X‐ray absorption fine structure and multiple‐scattering simulation of nickel dithiolene complexes Ni[S2C2(CF3)2]2n (n = −2, −1, 0) and an olefin adduct Ni[S2C2(CF3)2]2(1‐hexene)

A series of Ni dithiolene complexes Ni[S₂C₂(CF₃)]₂ⁿ (n = ?2, ?1, 0) ( 1 , 2 , 3 ) and a 1‐hexene adduct Ni[S₂C₂(CF₃)₂]₂(C₆H₁₂) ( 4 ) have been examined by Ni K‐edge X‐ray absorption near‐edge structure (XANES) and extended X‐ray absorption fine‐structure (EXAFS) spectroscopies. Ni XANES for 1 – 3 reveals clear pre‐edge features and approximately +0.7 eV shift in the Ni K‐edge position for `one‐electron' oxidation. EXAFS simulation shows that the Ni—S bond distances for 1 , 2 and 3 (2.11–2.16 Å) are within the typical values for square planar complexes and decrease by ～0.022 Å for each `one‐electron' oxidation. The changes in Ni K‐edge energy positions and Ni—S distances are consistent with the `non‐innocent' character of the dithiolene ligand. The Ni—C interactions at ～3.0 Å are analyzed and the multiple‐scattering parameters are also determined, leading to a better simulation for the overall EXAFS spectra. The 1‐hexene adduct 4 presents no pre‐edge feature, and its Ni K‐edge position shifts by ?0.8 eV in comparison with its starting dithiolene complex 3 . Consistently, EXAFS also showed that the Ni—S distances in 4 elongate by ～0.046 Å in comparison with 3 . The evidence confirms that the neutral complex is `reduced' upon addition of olefin, presumably by olefin donating the π‐electron density to the LUMO of 3 as suggested by UV/visible spectroscopy in the literature.     

Measurement of the oscillator strengths of transitions of titanium(I) in the region 3600–4500 Å

The emission spectrum of an arc discharge stabilized by a rotating radial magnetic field, operated at high pressure in an Ar-TiCl₄ mixture, has been analyzed under the assumption that local thermodynamic equilibrium is established in the arc. The temperature distribution was determined from absolute radial emission coefficients of the 4158 Å-4200 Å Ar(I) lines.Relative transition probabilities of 52 titanium lines have been obtained in the range 3600–4500 Å and converted to an absolute scale using absolute values for the three resonance transitions at 3635, 3981 and 3998 Å.     

Photoinduced energy and electron transfer in oligo(<Emphasis Type="Italic">p</Emphasis>-phenylene vinylene)-fullerene dyads

The intramolecular photoinduced charge separation within an oligo(p-phenylene vinylene)–fulleropyrrolidine dyad with four phenyl rings (OPV4-C₆₀) has been investigated with femtosecond pump-probe spectroscopy in solvents of different polarity and in the solid state. In solution, photoexcitation of the OPV4 moiety of OPV4-C₆₀ results in an ultrafast (<190 fs) singlet energy transfer reaction, creating the fullerene singlet excited state. In polar solvents, the ultrafast energy transfer is followed in the picosecond time domain by an intramolecular electron transfer. In accordance with Marcus theory, the rates for forward and backward intramolecular electron transfer in OPV4-C₆₀ are influenced by the polarity of the solvent. In the solid state the photophysics of OPV4-C₆₀ is dramatically different. In thin films, the forward electron transfer proceeds within 500 fs, irrespective of which chromophore is photoexcited. The increased rate for charge separation in the solid state is attributed to a more favorable orientation of the donor and acceptor that results in an intermolecular electron transfer. In the films, energy and electron transfer processes compete at the earliest moments after photoexcitation. In the solid state, the photogenerated electrons and holes have long lifetimes as a result of migration of these charges to thermodynamically more favorable sites in the film. PACS 78.47.1+p; 34.30.+h; 33.50.-j     

Coupled cluster calculations for the interstellar molecule HC3NH+

An accurate equilibrium structure has been established for the linear interstellar molecular cation HC₃NH⁺: r _1e(CH) = 1.0703Å, R _1e(C₍₁₎C₍₂₎) = 1.2097 Å, R _2e(C₍₂₎C₍₃₎) = 1.3509Å, R _3e(C₍₃₎N) = 1.1448 Å and r _2e(NH) = 1.0079Å. Ground-state rotational constants for less abundant isotopomers are predicted with an uncertainty of about 0.02 MHz. The equilibrium dipole moment of HC₃NH⁺ is calculated to be 1.61 D.