Molecular orbital study of the selective hydrogenation of acetylene in aqueous metalcatalyzed tetrahydroborate systems

A computer program for geometry optimization based on a multivariate regression method is discussed. The configuration of the adsorbed species of acetylene on copper, silver and gold catalysts were obtained at the usual CNDO level. The adsorbed species of acetylene on copper and gold catalysts are M(ν² - C₂H₂) complexes, whereas that on silver is of vinyl form. The electronic-charge distribution, energy partitions and total Mulliken overlap population suggested that acetylene is effectively activated in these systems.     

Electronic quantum motions in hydrogen molecule ion

The hydrogen molecule ion is a two‐center force system expressed under the prolate spheroidal coordinates, whose quantum motions and quantum trajectories have never been addressed in the literature before. The momentum operators in this coordinate system are derived for the first time from the Hamilton equations of motion and used to construct the Hamiltonian operator. The resulting Hamiltonian comprises a kinetic energy T and a total potential V_Total consisting of the Coulomb potential and a quantum potential. It is shown that the participation of the quantum potential and the accompanied quantum forces in the force interaction within H₂⁺ is essential to develop an electronic motion consistent with the prediction of the probability density function |Ψ|². The motion of the electron in H₂⁺ can be either described by the Hamilton equations derived from the Hamiltonian H = T_K + V_Total or by the Lagrange equations derived from the Lagrangian H = T_K ? V_Total. Solving the equations of motion with different initial positions, we show that the solutions yield an assembly of electronic quantum trajectories whose distribution and concentration reconstruct the σ and π molecular orbitals in H₂⁺. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Effect of temperature and molecular weight on enthalpy relaxation in polystyrene

Isothermal enthalpy relaxation in polystyrene was measured as a function of temperature and molecular weight on a differential scanning calorimeter. Relaxation spectra were derived from the data and expressed as a distribution of relaxation times. For a given molecular weight the relaxation spectra at different temperatures could not be superimposed by a shift in time. The relaxation curves of samples of different molecular weights could be superimposed only when the difference between the temperature at which the relaxation was monitored (T_a) and their respective T_g was the same. The relaxation spectrum at any temperature for a given molecular weight was also expressed as a distribution of energies. The average energy represented by this distribution was associated with an activation energy required for the motion of a chemical repeat unit. The activation energy extracted from the temperature shift in the relaxation spectra corresponded to the motion of a statistical unit (Kuhn's segment) in polystyrene.     

Component analysis of proton NMR spectra of linear polyethylene in the α-transition temperature range and phase distribution

Broad-line ¹H NMR spectra of linear polyethylene at temperatures in the α-transition range can be analyzed in terms of contributions from the crystalline and noncrystalline components provided molecular motion in the crystalline region is adequately considered. The spectrum of solid n-C₃₂H₆₆ or n-C₄₄H₉₀ prior to melting is used to take account of the contribution of the crystalline region of the polymer to molecular motions. The temperature dependence of the component distribution in the polymer is briefly discussed for a wide range of temperatures, together with previously reported results at low temperatures. The noncrystalline component is in a rigid glassy state at very low temperatures but with rising temperature it transforms to a mobile glassy state with restricted molecular motion, and transforms partially to the rubbery state at high temperature. The crystalline component remains rigid at low temperature, but some molecular motion is associated with it at higher temperatures in the α-transition range.     

Phenylene motion in polycarbonate and polycarbonate/additive mixtures

Pulsed deuteron NMR line shapes have been analysed to characterize type and time scale of the phenylene group motion in glassy bisphenol-A polycarbonate. The motional mechanism involves-flips about theC ₁ C ₄ axis augmented by small angle fulctuations about the same axis, reaching a rms amplitude of ±35 at 380 K. The distribution of correlation times for the-flips is heterogeneous in nature and can be described either by a log-Gaussian or an asymmetric distribution with a more rapid decay at high correlation times comparable to the Williams-Watts distribution. From both distributions essentailly the same mean activation energy of 37 kJ/mol is obtained, whereas the temperature dependent width of the highly asymmetric distribution is somewhat smaller compared to the log-Gaussian distribution. Time scale and activation energy of the-flip motion are correlated to secondary mechanical relaxations. Low molecular mass additives, which suppress the mechanical relaxation, also hinder the phenylene motion for a substantial fraction of phenylene groups. The effect of additives is not only to shift the mean value of the distribution of correlation times to higher values but also to increase drastically the width of the distribution. The results of this work strongly suggest that the secondary mechanical relaxation and the large amplitude motions of the phenylene groups in polycarbonate are related.     

Pulsed NMR study of molecular motion in the uncured diglycidyl ether of bisphenol-A

The diglycidyl ether of bisphenol-A, an uncured epoxy resin, has been studied by pulsed NMR. Values of the proton relaxation times T₁, T_1p, and T₂ have been measured over the temperature range from ?160 to 200°C. The resin was studied in its monomeric form and in two mixtures containing higher oligomers. The relaxation times are interpreted in terms of the molecular motion in the resins. The motion responsible for relaxation in the solid monomer form is thought to be methyl group reorientation at low temperatures and general molecular motion at high temperatures. The motions are characterized by activation energies of 5 kcal/mole and 33 kcal/mole, respectively. The solid mixtures exhibit similar effects to the monomer, but an additional relaxation mechanism is observed which is attributed to segmental motion. This motion is characterized by an activation energy of 12–15 kcal/mole. The self-diffusion coefficient was measured in the liquid monomer, and the activation energy for self-diffusion is found to be 11 kcal/mole.     

Structure formation of surfactants in concentrated sulphuric acid: a light scattering study

A common cationic surfactant,n-hexadecylammonium hydrogensulphate, dissolved in concentrated sulphuric acid, has been studied by static and dynamic light scattering. Micelle formation has been observed even in this unusual solvent. An apparent molar mass of 45 500±4.5% was found for the aggregates. A translational diffusion coefficientD ₀=5.5×10^–9 cm²/s was measured which gave a hydrodynamically effective radius ofR _h=17.7 nm. The geometric radius of gyration wasR _g=76.2 nm. The ratioR _g/R _h=4.33 is indicative for rodlike structures. Assuming a polydispersity ofL _w/L _n=2 this corresponds to a cylinder ofL _w=152 nm. An axial ratiop _w=(L _w/d)=60.4 nm was estimated which leads to a cylinder diameter of 2.53 nm. At surfactant concentrations higher than 5% (w/vol) the rod-like micelles aggregate to form more globular structures. The time correlation function, recorded by dynamic light scattering, exhibited a two-step decay which indicates a bimodal distribution of particle sizes. The fast motion coincides with that of the micelles at low concentrations while the other is slower than the fast one by three orders of magnitude and corresponds to the translational motion of large clusters.     

Frequency and molecular-mass-dependent nonexponential proton NMR relaxation in polymer melts

A theoretical treatment of the nonexponential relaxation behavior of the different proton nuclear magnetic resonance (NMR) relaxation processes in polymer melts is presented. Formulas are derived for a three-component model given by two versions and a homogeneous distribution of correlation times. The theoretical results were tested with measurements of T₁, T_2e, and T₂ as functions of frequency and molecular mass in linear fractionated polyethylene samples. While the T₁ relaxation always yields exponential magnetization decays, the T_2e and T₂ measurements show biexponential relaxation behavior. From the calculations it was found that the correlation time of the local motion is independent of the molecular mass, whereas the correlation time of the slowest motional process increases with M^2.8_w for the three-component model and with M^2.2_w for the distribution of correlation times, respectively. © 1992 John Wiley & Sons, Inc.     

Crystal transition and structure of poly (γ-n-alkyl glutamate)s

The nature of the crystal transition of the α-helical forms of poly (γ-n-alkyl glutamate)s (alkyl = ethyl, propyl, and butyl) is described. The transition is thermally reversible, and its temperature T₂ is much higher than the glasslike transition temperature T₁ associated with the side-chain motion. The main chains undergo large-scale motion (librational about the chain axis and translational along the axis) above T₃ ≈ 200°C. The structure observed below T₂ is anomalously disordered compared with that observed between T₂ and T₃. The crystal structure emerging above T₂ is analyzed for a typical sample of poly(γ-n-propyl L -glutamate). The trigonal unit cell contains three α-helices so that each helix is surrounded by other helices in the same fashion, but the helices are not interrelated by a crystallographic symmetry element. The side chains suffer no particular change at T₂. The main-chain motion gives rise to the T₂ transition by inducing attractive forces between interpenetrating side chains.     

Photon correlation spectroscopy of syndiotactic poly (n-butyl methacrylate) near the glass transition

Slow relaxing longitudinal density fluctuations in bulk syndiotactic poly (n-butyl methacrylate) [PBMA] were studied by photon correlation spectroscopy as a function of temperature from 70 to 90°C. The shape of the light-scattering relaxation function broadened as the temperature approached the glass transition (T_g = 55°C). The average relaxation time shifted with temperature, consistent with previous studies of PBMA. The relaxation functions were analyzed in terms of a distribution of relaxation rates. The calculated distribution was clearly bimodal and the shape altered with temperature. The higher frequency peak in the distribution corresponds well with previous mechanical and dielectric relaxation studies of the intramolecular relaxation of the acrylate ester side chain. The resolution of the distribution into two modes is due to a well-defined side-chain motion with relaxation strength comparable to the primary glass-rubber relaxation. © 1994 John Wiley & Sons, Inc.     

Viscoelasticity of crosslinked epoxy polymer in the transition region

The dynamic mechanical properties of highly crosslinked epoxyamine polymer networks with nonrandomly distributed crosslinks were investigated. The transition temperatures of these polymers can be correlated with the number of CH₂ groups between crosslink junctions in the aliphatic amine portions of the network. The steepness of the modulus-temperature curve is also a function of crosslink density. This is in contrast with the case of natural rubber crosslinked by sulfur or by electron irradiation, where the modulus-temperature curves have similar shapes although the glass transition temperature increases with the degree of crosslinking. An empirical distribution function, similar to the one used by Tobolsky for stress relaxation distributions, was used to describe the temperature dispersion of the dynamic moduli. Two parameters, h_g and h_r, are used to characterize the steepness of the dispersion curve below and above the transition temperature, respectively. It is tentatively concluded that h_g correlates with the length of the CH₂ sequences in the amine portion of the polymer. The quantity h_r may be related perhaps to the motion involving the trifunctional nitrogen junction.     

Twiston vs. random fluctuation as the source of the rapid motion of polyethylene in the inclusion complex with perhydrotriphenylene

Recently molecular dynamics simulations were performed for polyethylene in the inclusion complex with perhydrotriphenylene. The system contained ninety molecules of perhydrotriphenylene, arranged in six stacks of fifteen molecules each, and one molecule of n-tetracontane, C₄₀H₈₂. The internal CH₂-CH₂ bonds in n-tetracontane have a very strong preference for the trans state. Nevertheless, the chain exhibits a high degree of internal flexibility. This motion produces a characteristic pattern in δ|ψ N + i ψi| vs. N, where ψ_i describes the instantaneous angle of a C-H bond vector at carbon atom i about the axis defined by the channel, and δ denotes the fluctuation. The pattern expected for δ|ψ N + i ψi| vs. N is derived for the case where the rapid internal motion is produced by a twiston. It is compared with the results from the simulation and from the expectation for the case where the rapid motion arises from uncorrelated internal fluctuations within the trans state at each CH₂-CH₂ bond.     

Reciprocating Motion of a Self‐Propelled Object on a Molecular Layer

The mode change of a simple autonomous motor depending on the nature of a monolayer on water is investigated. A camphor disk is floated on a molecular layer of N‐stearoyl‐p‐nitroaniline (C₁₈ANA), which gives a surface‐pressure (π)–area per molecule (A) isotherm with a local maximum and a local minimum. The nature of the camphor motion changes depending on A, and in particular, reciprocating motion is observed at a lower A while cutting out its own trajectory of motion. The characteristic motion of a camphor disk depending on A is discussed in relation to the π–A isotherm of C₁₈ANA and the influence of the molecular interaction between molecules on the driving force of motion.     

Theory of the instability and failure of viscoelastic materials in tension

In a tensile test of a bar or fiber formed from a transversely isotropic viscoelastic material, the initial motion in regions away from the clamps is a homogeneous uniaxial extension. If the applied tensile load is “tame” in the sense that it is given by a piecewise smooth function of time, then during the early stages of loading, the homogeneous extension of the specimen is also tame. It is, however, often the case that at a time t_c, previous to the instant of fracture, the motion departs from a tame homogeneous extension. The critical time t_c is the “failure time” of the specimen, i.e., the time at which the motion first changes character; t_c precedes, often by a constant factor, the time at which neck-down is easily visible. The problem of calculating t_c for a given loading program is here treated within the framework of the general theory of nonlinear simple materials with fading memory. For such materials the instantaneous tensile modulus, i.e., the derivative of the immediate change in tensile stress with respect to a sudden change in tensile strain, depends upon the previous history of the strain. Reasons are presented here for identifying t_c with the earliest time t₀ at which the instantaneous tensile modulus becomes zero. It is shown that at a time at which the instantaneous modulus vanishes one cannot arbitrarily assign the rate of change of tensile stress and have the motion remain in the class of tame homogeneous extensions.     

Relation of the decay of free radicals in irradiated polyethylene to the molecular motion of the polymer and the configurations of the free radicals

Decay reactions of the free radicals produced in irradiated polyethylene (high-density and low-density materials) were examined in connection with the molecular motion of the matrix polymer. Three temperature regions, in which the free radicals decay very rapidly, at around 120, 200, and 250°K, were designated T_A, T_L, and T_B, respectively. The decay of the free radicals at these temperatures had activation energies in high-density polyethylene of 0.4 kcal/mole for T_A, 9.4 kcal/mole for T_L, and 18.4 kcal/mole for T_B. In low-density polyethylene these quantities were 0.7 kcal/mole for T_A, 23.1 kcal/mole for T_L, and 24.8 kcal/mole for T_B. Comparison of time constants for the decay reactions and for molecular motion of the matrix polymer indicate that the decay in T_A and T_B is closely related to molecular motion in the amorphous regions of the polymer. The decay of the free radicals at T_L in high-density polyethylene is due to molecular motion associated with local mode relaxation at lamellar surfaces, while that of low-density polyethylene is due to local mode relaxation in the completely amorphous region. Steric configurations of the free radicals which decay in the respective temperature regions were also investigated.     

Piezoelectricity and viscoelastic crystalline dispersion in highly oriented poly(vinylidene fluoride)

The effects of poling temperature on piezoelectricity and its thermal stability were investigated on the basis of the thermal molecular motion associated with the crystalline region. This was done by using a film of highly oriented poly(vinylidene fluoride) containing form-I crystals. The film was prepared by a zone-drawing apparatus of the forced-quenching type. The piezoelectric stress constant e₃₁ is a monotonically increasing function of the poling temperature which becomes steeper above ca. 320 K and again at ca. 400 K. The degree of orientation of the crystal b axis generated by poling also increases more steeply with poling temperature above ca. 320 K and again at 400 K. These temperatures correspond, respectively, to the crystalline dispersion temperature at 11 Hz, designated as α_c, and the initiation temperature T_pm of large-scale molecular motion corresponding to premelting of form-I crystals. Thus the effect of poling temperature on piezoelectricity closely reflects the moleculer motion in form-I crystals. The annealing temperature T'_a at which e₃₁ decreases to 70% of that of unannealed sample by annealing a poled sample increases with the poling temperature and again this increase is steeper above poling temperatures of ca. 320 K and ca. 400 K. Thus the decay of piezoelectricity depends on both the α_c temperature and T_pm.     

Effects of diluent on molecular motion and glass transitions in polymers. II. The system polyvinylchloride–tetrahydrofuran

Dielectric measurements, differential thermal analyses, and density measurements are reported on concentrated solutions of polyvinylchloride in tetrahydrofuran. The relaxation processes observed between 80 and 400°K have been classified into four types. From the analysis of experimental data, the primary process at the highest temperature and the process at the lowest temperature are assigned, respectively, to segmental motion of the polymer and motion of the solvent. Activation plots for the primary process conform to the Vogel–Tamman equation. The dielectric glass-transition temperature T'_g (defined as the temperature at which the dielectric relaxation time is 100 sec) determined with this equation agrees well with the glass-transition temperature T_g from thermal analysis. Therefore, T_g can be represented by an expression of the form The parameters of the Vogel–Tamman equation A and B are nearly independent of concentration, whereas T_o depends strongly on concentration. The dipole moment per monomeric unit calculated from the experimental data changes with concentration and exhibits steep increments around 30% and 90% by weight. The width of the distribution of the relaxation time also increases with the concentration. The results were compared with those for the system polystyrene–toluene studies in the same way.     

Collision between polymeric radicals for termination rate constants

The motion of each polymeric radical during a collision between the polymeric radicals with the same radius is treated as completely random motion. The result obtained is: k_t = 0.250k_s (where k_t is the chain-termination rate constant and k_s is the reaction rate constant between radical chain ends). On taking the motion of the primary radical during a collision between a primary radical and a large polymeric radical to be completely random, the result obtained is: k_ti = 0.250k_si (where k_ti is the primary radical termination rate constant and k_si is the reaction rate constant between primary radical and radical chain end). On substituting k_s for k_si in the second equation, the rate constant obtained becomes the chain termination rate constant between the very small polymeric radical and the very large polymeric radical, and identical to the former equation. This identity indicates that the effect of the difference of the size of the polymeric radicals on the collision process relating to the chain termination rate constant should not be large.     

Studies of the amorphous region of polymers. I. Relationship between the change of structure and glass-transition temperature in drawn poly(ethylene terephthalate)

The effect of drawing on the glass-transition temperature of amorphous poly(ethylene terephthalate) has been studied. The T_g decreases to a minimum at a draw ratio of 1.5, then increases to a maximum at a draw ratio of about 2.0, and again decreases with increasing draw ratio. The relationship between the change of structure and T_g is discussed in terms of the configurational entropy and the rate of molecular motion in local-mode relaxation. On the basis of configurational entropy, the decrease of T_g at the beginning of drawing depends on the increase of configurational entropy, while at draw ratios above 2.0 it depends on the increase of entropy associated with intermolecular interaction. From the point of view of molecular motion, it is concluded that the change of T_g is determined by local oscillations in the amorphous region.     

Molecular Reorientational Dynamics of the Neat Ionic Liquid 1‐Butyl‐3‐methylimidazolium Hexafluorophosphate by Measurement of 13C Nuclear Magnetic Relaxation Data

The reorientational dynamics of the ionic liquid 1butyl‐3‐methylimidazolium hexafluorophosphate ([BMIM]PF₆) were studied over a wide range of temperatures by measurement of ¹³C spin–lattice relaxation rates and NOE factors. The reorientational dynamics were evaluated by performing fits to the experimental relaxation data. Thus, the overall reorientational motion was described by a Cole–Davidson spectral density with a Vogel–Fulcher–Tammann temperature dependence of the correlation times. The reorientational motion of the butyl chain was modelled by a combination of the latter model for the overall motion with a Bloembergen–Purcell–Pound spectral density and an Arrhenius temperature dependence for the internal motion. Except for C2 in the aromatic ring, an additional reduction of the spectral density by the Lipari–Szabo model had to be employed. This reduction is a consequence of fast molecular motions before the rotational diffusion process becomes effective. The C2 atom did not exhibit this reduction, because the librational motion of the corresponding C2? H vector is severely hindered due to hydrogen bonding with the hexafluorophosphate anion. The observed dynamic features of the [BMIM]⁺ cation confirm quantum‐chemical structures obtained in a former study.