Kinetics of structural relaxation of poly(ethylene terephthalate)

The results of an experimental study of the kinetics of structural relaxation of amorphous poly(ethylene terephthalate) are reported. Samples were prepared by ultraquenching the melt on rotating stainless-steel discs. Two types of measurements by differential scanning calorimetry were made: (1) the dependence of the “fictive” (or “structural”) temperature T_f(q^?) introduced by Tool, on the cooling rate q^? and (2) the dependence of the glass transition temperature T_g on the heating rate q⁺. In this way the value x = 0.47 was obtained for the dimensionless parameter proposed by Narayanaswamy.     

A theoretical investigation of electron correlation and relaxation in organometallic polymers

The importance of many-body interactions beyond the mean-field approximation of the Hartree–Fock (HF ) self-consistent-field crystal orbital formalism is analyzed in one-dimensional (lD) transition-metal (3d) polymers with extended organic π ligands. The correlation energies are expressed in a quasiparticle picture. They are divided into long-range contributions that are coordinated with the basis of spatially uncorrelated Bloch orbitals and into short-range correlations derived for local rearrangement processes that are described in terms of a one-electron basis which breaks the translational symmetry of the lD system. Both contributions (long-range and short-range correlations) are fragmented into elements of physical significance (hole and electron self-energies for the former interactions; relaxation, pair-relaxation and pairremoval terms for the local virtual excitations). The magnitude of these elements is analyzed as a function of the characters of the one-electron states in the HF bands, the occupation patterns at the 3d centers, the available particle and hole channels in the elementary fluctuations and the energies and shapes of the various bands. The broad spectrum of possible amplifications and compensations leading to the quasiparticle shifts in metallomacrocycles is discussed. The different mechanisms to change the dispersions and to modify the width of the ?(k) curves are studied. It is shown that electron correlation and relaxation in transition-metal polymers can lead even to a broadening of the energy bands. This behavior is in contrast to the influence of many-body effects in simpler homogeneous materials where electron correlation is in any case accompanied by a narrowing of the dispersions (i.e., detraction of the group velocities of particles and holes). Possible modifications in the shapes of the one-particle curves and the quasiparticle bands are also considered in the text [transition from a “normal ?(k) dispersion” to an energy band with a negative slope as a result of electron correlation]. Simplified formulas are derived that allow for a rough assessment of the various correction terms even in structurally complicated transition-metal stacks with extended organic ligands. The approximate relations are used to correct the HF band structures of complex onedimensional metallomacrocycles as well as simpler crystalline materials by means of the quasiparticle approximation.     

Third-order energy derivative corrections to the Kohn-Sham orbital hardness tensor

The third term in the Taylor expansion of the total energy functional around the number of electronsN is evaluated as the second-order derivative of orbital Kohn-Sham energies with respect to orbital occupancy. Present approach is an extension of an efficient algorithm to compute densityfunctional based orbital reactivity indices. Various energy derivatives used to approximate orbital reactivity indices are defined within the space spanned by the orbital occupation numbers and the Kohn-Sham one-electron energies. The third-order energy functional derivative has to be considered for singular hardness tensor ([η]). On the contrary, this term has negligible influence on the reactivity index values for atomic or molecular systems with positively defined hardness tensors. In this context, stability of a system in equilibrium state estimated through the eigenvalues of [η] is discussed. Numerical illustration of the Kohn-Sham energy functional derivatives in orbital resolution up to the third order is shown for benchmark molecules such as H₂O, H₂S, and OH⁻.     

Self-Consistent APW–k · p method. II. Application to NaCl

The self-consistent APW – k · p method is utilized to obtain the band structure of NaCl in the “muffin-tin” approximation. Qe have investigated the convergence of many intermediate results, e.g., crystalline potential, matrix elements of the momentum operator, and energy eigenvalues at the Γ point. The summation in reciprocal space, included in the definition of the matrix D of the theory, is performed by direct sum and also by a special points technique. For the convergence criteria used, the results converged after five iterations.     

Density functionals from many-body perturbation theory: the band gap for semiconductors and insulators

Theoretically the Kohn-Sham band gap differs from the exact quasiparticle energy gap by the derivative discontinuity of the exchange-correlation functional. In practice for semiconductors and insulators the band gap calculated within any local or semilocal density approximations underestimates severely the experimental energy gap. On the other hand, calculations with an "exact" exchange potential derived from many-body perturbation theory via the optimized effective potential suggest that improving the exchange-correlation potential approximation can yield a reasonable agreement between the Kohn-Sham band gap and the experimental gap. The results in this work show that this is not the case. In fact, we add to the exact exchange the correlation that corresponds to the dynamical (random phase approximation) screening in the GW approximation. This accurate exchange-correlation potential provides band structures similar to the local density approximation with the corresponding derivative discontinuity that contributes 30%-50% to the energy gap. Our self-consistent results confirm substantially the results for Si and other semiconductors obtained perturbatively [R. W. Godby et al., Phys. Rev. B 36, 6497 (1987)] and extend the conclusion to LiF and Ar, a wide-gap insulator and a noble-gas solid.     

Maximum-entropy analysis of atomic compton profiles

The maximum-entropy formalism is used to obtain approximations to the atomic Compton profile, ??(q), in terms of the first few radial expectation values 〈Pⁿ〉 of the momentum density γ(p). This method leads to the least-biased results by the information not used. In particular, analytical and numerical approximations to the kinetic energy T and to the height of the peak ??(O) and the half-width q_0.5 of the Compton profile are obtained. Our results generalize and improve some approximations to ??(q) previously obtained by other authors. For illustration, the accuracy of these approximations are studied by means of near-Hartree–Fock wave functions. © 1995 John Wiley & Sons, Inc.     

Theoretical investigations of the electronic states of porphyrins. II. Normal and hyper phosphorus porphyrins

Ab initio methods have been used to calculate the ground and excited states of “normal” and “hyper” porphyrins. Perturbation theory and CI methods were used to determine differential ground and excited-state correlation effects for [P^v(P)F₂]⁺ and [P^III(P)]⁺. A comparison is made to the INDO /S /CI predicted wavefunctions and spectra and to the experimental spectra of closely related molecules. The “hyper” [P^III(P)]⁺ calculations show some very low energy electronic transitions which provide an explanation for an anomalous “red” band in the spectrum and for the lack of fluorescence. Ab initio calculations also predict that (1) the lowest energy ¹A₁ state is a two-configuration wavefunction which can be described as a diradical, (2) the two lowest-energy singlet excited states are double excitations from the closed shell SCF configuration, and (3) a ³B₂ state is very close in energy to the lowest ¹A₁ state.     

The Flipping of CO Ligand Groups in Metal Carbonyl Compounds and its Frequency in Fe(CO)5

It has been proven qualitatively by a number of authors using variable temperature NMR experiments that most metal carbonyl complexes are nonrigid. A quantitative determination of the ligand exchange frequency v_e is often achieved by a line shape analysis or by measurement of the transverse relaxation time T₂ using the Carr-Purcell method. In the case of a “very fast” exchange, however, both methods prove unsuccessful. It is shown in this study that a simultaneous fit of IR or Raman spectra on the one hand and NMR spectra on the other can make possible the determination of v_e for the “very fast” exchange and can also facilitate the determination of v_e in “slow” and “medium” exchange cases considerably. The ligand exchange frequency thus found for Fe(CO)₅, 1.1 × 10¹⁰s^?1, is unexpectedly high; comparison with variable temperature measurements on solid Fe(CO)₅, yields similar energy barriers. A mechanism of exchange closely related to the “Berry mechanism” is proposed. Finally the consequences of this surprisingly large ligand exchange rate are discussed with respect to IR band assignments for molecular “fragments” M(CO)^x (where x=coordination number, and M is a transition metal, typically lanthanoid or actinoid).     

Remote Effect from Boron Cluster: Tunable Photophysical Properties of o-Carborane-Based Luminogens

We proposed a new molecular design strategy that the o-carboranyl group is attached as “an innocent unit” to the remote side of luminogens to tune photophysical properties. To verify this strategy, two o-carborane-based compounds with asymmetric molecular geometry were designed and synthesized. Photophysical properties of o-carborane-based luminogens were investigated on the basis of UV-Vis spectra, photoluminescence spectra, crystal structure analysis and theoretical calculations. The results indicate that the o-carboranyl group has a slight effect on the energy gap between the ground state (S₀) and the first excited state (S₁) in the solution state but a significant effect on the energy gap between S₀ and S₁ in the solid state. Besides, the radiative and non-radiative transition processes are modulated by the o-carboranyl unit. This leads to emission quenching in the solution state but an enhanced luminous efficiency in the aggregate state with a typical aggregation-induced emission (AIE) property.     

Investigation of the mechanism of chlorination of poly(vinyl chloride) as influenced by chain microstructure

Samples of poly(vinyl chloride) polymerized at different temperatures (+30, 0, ?30, and ?78°C) and a commercial sample were chlorinated by a photoinitiated, free-radical method in o-dichlorobenzene at ambient temperature. The chlorine content was determined by difference by using a carbon-hydrogen analyzer. High-resolution infrared analysis revealed a selective attack on the methylene hydrogens along with a concomitant decrease in intensity of the isotactic methylene deformation band and the syndiotactic carbon-chlorine stretching band. Graphical representation of the relative intensities of the _v(CH), δ(CH₂), and _v(C? CI) modes indicate that the chlorine radical preferentially attacks the middle carbon of the heterotactic triad. The increased “stiffness” of this unit causes the rotational energy of the system to be transferred to the syndiotactic portion of the chain. It is proposed that this additional energy causes the TTTT conformer of the syndiotactic unit to rotate into the less-preferred TTGG conformation, which would be more reactive. Facile chlorination of this latter conformer is predicted. This mechanism is in accord with the reported equilibrium composition of the different conformers.     

Dynamic light scattering and rheology studies of aqueous solutions of amphiphilic sodium maleate containing copolymers

Light scattering techniques, video particle‐tracking microrheology, and bulk rheology were employed to examine the structure and dynamics of a series of alternating sodium maleate copolymers with moderately hydrophobic comonomers (diisobutylene, styrene, and isobutylene) in aqueous solutions. The scaling dependence of the specific viscosity (η_sp) on the polyelectrolyte concentration (c) was studied with and without added salt; similar trends were found in both conventional rheology and particle‐tracking microrheology measurements, showing good performance of the technique with flexible polyelectrolytes. Furthermore, with dynamic light scattering performed in high added salt conditions, we examined the behavior of the amplitude of the fast mode, which is in agreement with scaling predictions. In contrast, the slow modes are not understood and display three separate behaviors for the wavevector q dependence of the decay rate (Γ), depending on the comonomer; superdiffusive (Γ ～ q^2.7, isobutylene) possibly because of sticky aggregates, wavevector independent (Γ ～ q⁰, styrene) most likely because of coupled polyion‐ion diffusion and diffusive (Γ ～ q^2.0, diisobutylene) presumably because these aggregates are not sticky. The hydrophobicity of the comonomer appears to switch the aggregation process between “open,” “closed,” and “non” association for isobutylene, diisobutylene, and styrene respectively. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 774–785, 2007     

Rheological Measurements in Titania Gels Synthesized from Reverse Micelles

Abstract

TiO₂ sol and gel systems have been synthesized by hydrolysis of titanium butoxide in microemulsions W/O. Different systems compositions were prepared at constant W _o = [H₂O]/[AOT] and changing R = [H₂O]/[Ti(BuO)₄]. Experimental measurements show a progressive increase of the viscosity with time, characteristic of a sol-gel transition. The rheology of the transition was studied by following the behavior of viscoelastic parameters (G′, G″ and η?) as a function of time at different frequencies.

The possibility to apply standard percolation theory was discussed. The application of two alternative growth models-either “fractal growth model” or “nearly linear growth model”-has been analysed.     

Electron correlation and the compton profile of atomic neon

The radial momentum distribution I_o(p) and the Compton profile J_o(q) are determined for atomic neon from several restrictid Hartree-Fock (RHF) wavefunctions and two configuration interaction (CI) wavefunctions. The CI functions are the well correlated (full“second-order”) function of Viers, Schaeffer and Harris, and the Ahlrichs-Hinze multi-configuration Hartree-Fock (MCHF) function which includes only L-shell correlation. It is found for this completely closed shell system that the effects of electron correlation are quite small. This contrasts with the results for systems such as Be(²S) and B(²P) where the semi-internal and internal correlation effects were responsible for significant discrepancies between the RHF and CI results. These results indicate that a wavefunction which carefully includes the semi-internal, orbital polarization, and internal correlations beyond the RHF wavefunction (i.e., a “first-order” or “charge-density” function), should account for the principal correlation effects on the Compton profiles and momentum distributions.     

Structure of the optimized effective Kohn—Sham exchange potential and its gradient approximations

An analysis of the structure of the optimized effective Kohn-Sham exchange potential v_x and its gradient approximations is presented. The potential is decomposed into the Slater potential v_s and the response of v_s to density variations, v_resp. The latter exhibits peaks that reflect the atomic shell structure. Kohn—Sham exchange potentials derived from current gradient approaches for the exchange energy are shown to be quite reasonable for the Slater potential, but they fail to approximate the response part, which leads to poor overall potentials. Improved potentials are constructed by a direct fit of v_x with a gradient-dependent Padé approximant form. The potentials obtained possess proper asymptotic and scaling properties and reproduce the shell structure of the exact v_x. © 1996 John Wiley & Sons, Inc.     

Tris (methylidene)-cyclopropane (“[3]Radialene”). Part 2. Electronic states of the molecular cation and revised UV.-absorption spectrum of the parent neutral

The photoelectron spectrum of tris (methylidene)-cyclopropane 1 (“[3]radialene”) is reported and the electronic states of 1 ⁺ assigned. Jahn-teller activity in the degenerate states of 1 ⁺is discussed. Differences in the Franck-Condon profile of the first PE band and the Rydberg series in the Vacuum-UV./UV. absorption spectrum indicate for the Rydberg series (n=3) a ¹A″₂-species, which supports earlier tentative proposals. The high intensity absorption in the 5.5 eV-6 eV energy range of the latter spectrum recorded earlier are definitely due to impurities. The vibrational fine structure of a weak band system around 5.5 eV in our spectrum suggests for this transition S₀→S₂(¹A′₁), which is dipole forbidden but borrows intensity from S₁(¹E′) trough vibronic coupling via an e′-mode. From vapor pressure measurements ε(λ_max=289 nm) = 9390± 1170 for gaseous 1 was found.     

Obtaining self–consistent wave functions which satisfy the virial theorem

The virial theorem has played an important role in applying quantum mechanics to chemical problems. It has served as one criterion of a satisfactory wave function and its consequences on chemical bonding, molecular structure, and substituent effects have been analyzed extensively. A common method of gaining compliance with the virial theorem is to introduce a “scale” factor which adjusts all distances by a factor η. Optimizing the scale factor through the variational principle produces a wave function satisfying the virial theorem. In the present paper it is shown that when this “scaling” procedure is applied to self-consistent wave functions, the virial theorem can be satisfied, but self-consistency is lost. Scaling generally has a small effect on the total energy, but the effects on the energy components (T, V_ne, V_ee, V_nn) can be two to three orders of magnitude larger and in the range of tens to hundreds of kcal. Consequently, for applications where the energy components are useful, it is highly desirable to obtain wave functions which satisfy the virial theorem and are self-consistent. In the present paper, a simple, inexpensive extrapolation technique is reported which requires one integral evaluation and two SCF cycles to achieve convergence. Applications to atoms and small molecules are reported.     

Switch From Pauli-Lowering to LUMO-Lowering Catalysis in Brønsted Acid-Catalyzed Aza-Diels-Alder Reactions

Brønsted acid-catalyzed inverse-electron demand (IED) aza-Diels-Alder reactions between 2-aza-dienes and ethylene were studied using quantum chemical calculations. The computed activation energy systematically decreases as the basic sites of the diene progressively become protonated. Our activation strain and Kohn-Sham molecular orbital analyses traced the origin of this enhanced reactivity to i) “Pauli-lowering catalysis” for mono-protonated 2-aza-dienes due to the induction of an asynchronous, but still concerted, reaction pathway that reduces the Pauli repulsion between the reactants; and ii) “LUMO-lowering catalysis” for multi-protonated 2-aza-dienes due to their highly stabilized LUMO(s) and more concerted synchronous reaction path that facilitates more efficient orbital overlaps in IED interactions. In all, we illustrate how the novel concept of “Pauli-lowering catalysis” can be overruled by the traditional concept of “LUMO-lowering catalysis” when the degree of LUMO stabilization is extreme as in the case of multi-protonated 2-aza-dienes.     

SI-traceable certification of the IMEP-12 water sample combining contributions from different reference laboratories

In the International Measurement Evaluation Programme (IMEP-12) comparison, a synthetically prepared water sample was offered to the analytical laboratories to perform measurements of As, B, Cd, Cr, Cu, Fe, Mg, Mn, Ni and Pb. The choice of elements to be measured was based on EU legislation, which the comparison was aiming to support. As to the IMEP policy, the laboratories’ results were presented according to the certified/assigned reference values established by several reference laboratories all around the world. The performed certification campaign is described in detail in this paper. Isotope dilution mass spectrometry (IDMS) was applied as a primary method of measurement (PMM), whenever possible, to achieve SI-traceable results. Apart from IDMS for reference measurements of some elements, k _o-neutron activation analysis (k _o-NAA) and external calibration (Ext-Calib) using inductively coupled plasma-mass spectrometry (ICP-MS) were applied. The reference values were characterised as “certified” (for B, Cd, Cr, Cu, Fe, Mg, Ni and Pb) or “assigned” (for As and Mn) according to the IMEP policy. Measurement uncertainty of the certified/assigned reference values was calculated according to the ISO/BIPM guide using the specialised software GUM Workbench.

     

Model calculation of weak and medium strong linear hydrogen bonded systems

The model hamiltonian with two coupling constants between the low and high frequency vibrations of a linear AH?B system is studied. The results show that the wave functions and energy levels of this hamiltonian obtained by exact diagonalisation can be adequately approximated by the wave functions and energy levels of a harmonic “effective hamiltonian”. The experimental spectrum of (CH₃)O?HCl in the stretching region was reconstituted by means of this model.