Vibrational analysis of a rate-slowing conformational kinetic isotope effect

An enthalpy-entropy approach to analyzing a rate-slowing conformational kinetic isotope effect (CKIE) in a deuterated doubly-bridged biaryl system is described. The computed isotope effect (k_H/k_D?=?1.075, 368?K) agrees well with the measured value (k_H/k_D?=?1.06, 368?K). The rate-slowing (normal isotope effect) nature of the computed CKIE is shown to originate from a vibrational entropy contribution defined by the twenty lowest frequency normal modes in the ground state and transition state structures. This normal entropy contribution is offset by an inverse vibrational enthalpy contribution, which also arises from the twenty lowest frequency normal modes. Zero point vibrational energy contributions are found to be relatively small when all normal modes are considered. Analysis of the H_ZPE, H_vib, and S_vib energy terms arising from the low frequency vibrational modes reveals their signs and magnitudes are determined by larger vibrational energy differences in the labeled and unlabeled ground state structures.     

Differential double-layer capacitance of a mercury-drop electrode attached to a platinum wire: Frequency dispersion due to the measuring bridge and to the geometry at pendant and sessile electrodes

The frequency dependence of the double-layer capacitance has been studied at the interface Hg/0.116 M KCl in water at ?1.200 V vs. a reversible calomel electrode at 25°C. Two drop electrodes attached to 0.1-mm platinum wire have been used, one sessile with a narrow wedge, the other pendant with a widely open wedge between drop surface and support. The operation of the a.c. resistor-ratio arms bridge has been analysed in a manner generally applicable to series-R, C measurements. On that basis the effect of stray capacitances could be compensated and the frequency dispersion due to the measuring system reduced to a minimum. Both electrodes show a low-frequency dispersion of the measured series capacitance C(ω) and resistance R(ω), ω being the angular frequency. This dispersion has been analysed with a simple R, C network. In series with the bulk resistance R₃ this network has two mutually parallel series R, C's: R₁, C₁ of the drop itself and R₂, C₂ of its edge (neck). From the actual C(ω), R(ω) data follow correct capacitance data C₁, while R₂ and C₂ show a relatively stronger dependence on frequency and kind of electrode (pendant or sessile). Moreover, a sessile electrode exhibits a wedge or shielding effect above a much smaller ω (=ω_h >ω₁, the frequency above which the edge effect becomes insignificant) than a pendant electrode. Conclusions drawn from this information are: in the frequency domain (ω_h?ω₁) diffusive mass transport may be studied without interference from any geometric effect, which is probably also true at small electrolyte concentrations. This study should be performed with a pendant electrode, since it has the largest (ω_h?ω₁) domain.     

AC conductivity studies and relaxation behaviour in (LiX) y [(Li2O)0.6(P2O5)0.4](1 − y) glasses

The electrical conductivity of (LiX) _y [(Li₂O)_0.6(P₂O₅)_0.4]_(1???y) (X?=?Cl, Br, y?=?0, 0.1, 0.15, 0.2) glasses has been determined over a wide range of temperature and frequency by means of impedance spectroscopy. The real part of the frequency-dependent conductivity exhibits a simple power law feature, and the dimensionless frequency exponent n has been determined. The conductivity spectra show scaling behaviour when the conductivity spectra are scaled by ω/(σ _dc T) and ω/ω _p . The conductivity relaxation time and activation energy have been estimated from the modulus spectra. Increases of ionic conductivity values with addition of LiX content are in line with the decrease of activation energy and relaxation time.     

Density and temperature effects on relative Raman intensities in liquid toluene

Raman spectra of toluene at pressures up to 4.1 kbar and temperatures up to 100°C, have been studied. The frequency and intensity changes of the symmetric (ν_6a) and antisymmetric (ν_6b) ring breathing vibrations have been related principally to changes in density. Increasing density at constant temperature increases I(ν_6b/ν6a) and increases the frequency of (ν_6a) but has little effect on the frequency of ν_6b. Increasing temperature at constant density decreases I(ν_6b/ν_6a) and increases the frequency of ν_6a but has little effect on the frequency of ν_6b. An explanation of the different intensity changes with density for these two bands is suggested in terms of the contrasting volume changes associated with the two modes.     

Infrared and Raman spectra of lithium trihorate: Vibrational assignments and a correlation with its nonlinear optical activity

Infrared and polarized single crystal Raman spectra of lithium triborate (LBO; LiB₃O₅) are reported and analysed. All four (A₁, A₂, B₁ and B₂) symmetry species of the C_2v, point group isomorphic to the C_2v⁹(Pna2₁) space group are Raman active in distinct crystal polarization experiments. A complete set of symmetry assignments based on a factor group analysis is presented. The internal and external vibrations are separated on the basis of frequency and the observation that the magnitude of the correlation splitting for the internal modes is very small. A comparison of the internal frequencies of various borate species suggests a correlation between the B-O stretching frequency and the nonlinear optical efficiency of the material.     

The oscillation frequency of a quartz resonator in contact with liquid

A simple relationship is derived which expresses the change in oscillation frequency of a quartz crystal in contact with a fluid in terms of material parameters of the fluid and the quartz. The relationship is Δf = ?f^{$\text{3}\text{2}$}₀(η_L?_L/πμ_Q?_Q)^{$\text{1}\text{2}$}, where f₀ is the oscillation frequency of the free (dry) crystal, η_L and ?_L are the absolute viscosity and density of the liquid, respectively, and μ_Q and ?_Q are the elastic modulus and density of the quartz. This relation is obtained from a simple physical model which couples the shear wave in the quartz to a damped shear wave in the fluid. Quantitative comparisons with two test cases, aqueous solutions of glucose and ethanol at various concentrations, demonstrate the accuracy of this model.     

Low frequency Raman spectra of barium borate glasses in the system (BaCl2)y[(BaO)x(B2O3)1-y-x]1-y for various x and y

Low frequency Raman spectra of glasses of the types (BaO)_x·(B₂O₃)_1−x and (BaCl₂)_y·[(BaO)_x·(B₂O₃)₁-_y-_x]₁-_y have been reported. The temperature reduced Raman spectra show peaks at 67, 116 and 140 cm⁻¹ for the binary glass. The bands at 116 and 140 cm⁻¹ are ascribed to the librational motions of the borate groups and the 67 cm⁻¹ band arises because of the limited structural correlation range (SCR) of the glass network, causing a maximum of the frequency dependent Raman coupling coefficient. Due to addition of BaO in v-B₂O₃, the oxygen are mostly incorporated in the formation of BO₄ units; however large Ba²⁺ ions also enhance the number of non-bridging oxygen at higher concentrations of dopant. These barium ions as well as chlorine ions are accomodated in the interstitial vacancies of the glass network which leads to an expansion of the network structure.     

Electrical properties of LiBBaTe glass doped with Nd2O3

The dc and ac electrical conductivity of barium tellurite borate glass doped with Nd₂O₃ in the composition 50 B₂O₃- (20-X) BaO- 20TeO₂ 10 LiF or Li₂O where x = 0.5, 1, 1.5 and 2 Nd₂O₃ were measured in the temperature range 303–648 K and in the frequency range 0.1–100 kHz. The dc and ac conductivities values increase, whereas the activation energy of conductivities decreases with increasing Nd₂O₃ content in the glasses containing LiF and by the replacement of LiF by Li₂O the conductivity was found to decrease with addition of Nd₂O₃. The electrical conduction has been observed to be due to small polaron hopping at high temperatures. The frequency dependence of the ac conductivity follows the power law σ_AC (ω) = A ω^s. The frequency exponent (s) values (in the range 0.94 and 0.33) decreases with increasing temperature. The dielectric constant and dielectric loss increased with increasing temperature and decreased with increase in frequency for all glasses studied. In LiF glasses, it is observed that, the values of ?^\ and tan δ are observed to increase with the addition of Nd₂O₃ whereas they decrease in the glasses containing Li₂O. The electrical modulus formalism has been used for studying electrical relaxation behavior in studied glasses. It is for first time that the Nd₂O₃ doped barium tellurite borate glasses have been investigated for dc and ac conductivities and dielectric properties over a wide range of frequency and temperature.     

Ranges of frequency dispersion for the shear viscosity coefficients of aqueous solutions of electrolytes

The range of frequency dispersion for dynamic coefficient of shear viscosity η _S (ω) of electrolyte solutions obtained through kinetic equations under the condition of recovering the steady-state structure of a liquid exponentially or according to the diffusion law is considered. Numerical calculations of η _S (ω) are performed for an aqueous solution of NaCl depending on density ρ, temperature T, concentration C, and frequencies ω to select the potential of intermolecular interaction Φ _ab (|r|) and equilibrium radial distribution function g _ab (|r|). It is noted that the calculated theoretical results of η _S (ω) are in quantitative accordance with the experimental data. It is shown that the range of frequency dispersion η _S (ω) based on the diffusion mechanism is broad (～10⁵ Hz) and is narrow in the case of exponential attenuation of the viscous stress tensor (～10² Hz); this corresponds to both acoustic measurements and results from phenomenological theory.     

A new molecular electronic emission spectrum observed in the reaction of F2 with CS2

A novel emission spectrum extending from 5500 to 8600 Å has been observed during the gas-phase reaction of F₂ with CS₂. Long progressions in the lower-state (presumably the ground-state) bending frequency and shorter progressions in a ground-state stretching frequency were observed. A partial vibrational analysis is reported, from which two new frequencies are obtained: v″₂ = 356 ± 5 and v″₃ = 8 31 ± 8 cm⁻¹ .The electronic origin lies near 18500 ± 1200 cm⁻¹. The spectrum is tentatively assigned to the FCS radical.     

An analysis of semi-finite linear diffusion in the long-time limit: A clarification of the response to periodic sinusoidal and square-wave perturbations

Low-frequency peturbation of the surface concentration in a system exhibiting semi-finite diffusion can be modeled by an equivalent circuit comprising a resistor (R_s) and capacitor (C_s) connected in series. Mathematical analyses of other workers (supported by our own computer simulations) of sinusoidal and square-wave perturbations show that the values of R_s and C_s, though frequency independent (in the low frequency domain), depend upon the nature of the perturbation. This apparent paradox is resolved by noting that even a low-frequency square wave has high frequency components which modify the composition of the system; a sine wave is pure frequency.     

Coherence transfer processes in vibrational relaxation of polyatomic molecules in condensed media

The vibrational relaxation of a polyatomic molecule in a condensed host is studied by a consideration of two molecular vibrations. Relaxation processes, intermode coupling terms and vibrational frequency fluctuation contributions are retained. Population decay (T₁), dephasing (T₂), and coherence transfer rates are evaluated through second order in the limit where the host bath dynamics are rapid compared to these molecular timescales. The rates are expressed in terms of temperature and frequency dependent bath correlation functions. For the special case of a three level system (the ground state and ones where one of the two vibrational modes is excited) the important effects of anharmonicity are incorporated. It is shown that certain coherence transfer terms involve zero frequency bath correlation functions, so they should be larger than the high frequency ones which obey modified energy gap laws. A discussion is presented of the types of interactions which may contribute to these coherence transfer processes.     

Nuclear spin—lattice relaxation and molecular motions in the thermotropic mesophases of p-alkoxybenzylidene—p-n-alkylanilines

Experimental results of an investigation of the proton spin—lattice relaxation in a well-known homologous series exhibiting smectic polymorphism, are presented. Explanations for striking features of T₁ and T_1D dependences on temperature, frequency and molecular orientation in terms of molecular motions are proposed.     

Oscillating frequency of piezoelectric quartz crystal in solutions

Oscillating frequencies of a piezoelectric crystal were measured in various solutions. One side of the crystal surface was coated with a silicon sealant. This coating was useful for measuring the oscillation of crystals in solutions for a wide range of products of density (?) and viscosity (η) and in electrolyte solutions. For measurement in solutions, the frequency change depended on the circuit used, whereas for measurements in air the circuit did not influence the frequency change. All experimental data showed that the frequency change from pure water, ΔF_w, followed ΔF_w = ? K(√?η ? √?_wη_w) except for electrolyte and polymer solutions, where K is a proportionality constant, η_w the density of pure water and η_w the viscosity of water.     

Estimation of the kinetics of anion transfer across the liquid/liquid interface,by means of Fourier transformed square-wave voltammetry

A novel method of Fourier transformed square-wave voltammetry (FT-SWV) in combination with thin-film modified electrode was employed to investigate the kinetics of anion transfer across the liquid/liquid interface using a conventional three-electrode arrangement. Other than traditional SWV in which currents are sampled only at the end of each pulse, FT-SWV continuously collects the current response and then transforms it into frequency domain. Even harmonic frequencies, which are derived from the faradaic current response, will emerge in the power spectrum. The profile of the even harmonic power spectrum is parabolic and shows a maximum at a certain frequency. The maximum and the corresponding frequency are equivalent to the well-known “quasireversible maximum” and “critical frequency” (f_max) in traditional SWV, respectively. The rate constant and ion transfer coefficient α can be estimated by the obtained f_max. Compared with traditional SWV, FT-SWV is much simpler and faster in ion transfer kinetics estimation.     

Dependence of the mixed alkali effect on temperature and total alkali oxide content in y[xLi2O·(1−x)Na2O]·(1−y)B2O3 glasses

The complex conductivity spectra of mixed alkali borate glasses of compositions y [xLi₂O·(1−x)Na₂O]·(1−y)B₂O₃ (with x=0.0, 0.2, 0.4, 0.6, 0.8, 1.0; y=0.1, 0.2, 0.3) in a frequency range between 10⁻² Hz and 3 MHz and at temperatures ranging from 298 to 573 K have been studied. For each glass composition the conductivities show a transition from the dc values into a dispersive regime where the conductivity is found to increase continuously with frequency, tending towards a linear frequency dependence at sufficiently low temperatures. Mixed alkali effects (MAEs) in the dc conductivity and activation energy are identified and discussed. It has been for the first time found that the strength of the MAE in the logarithm of the dc conductivity linearly increases with the total alkali oxide content, y, and the reciprocal temperature, 1/T.     

Synthesis,structure and ionic conductivity of the molybdenum arsenate: Ag12.4Na1.6Mo18As4O71

The syntheses, structure and ionic conductivity of Ag_12.4Na_1.6Mo₁₈As₄O₇₁ are reported. Crystals and polycrystalline powders are synthesized by solid state reaction. It crystallized in the monoclinic space group C2/c with a = 20.032 Å, b = 16.872 Å, c = 19.373 Å and β = 112.14°. The structure can be described by the assemblage of Mo₈As₂O₃₄ ribbons interconnected through Mo₂O₇ groups. Monovalent cations are located around these ribbons. The ionic conductivities have been measured, on pellets of polycrystalline powders, between 423 and 663 K in the frequency range 1–13000 Hz, using diagrams of complex impedance. Impedance analysis suggests the presence of a dependent electrical relaxation temperature process in the material. Activation energy was obtained from Arrhenius plots (log σT versus 1000/T) and found to be 0.6 eV. The activation energies obtained from impedance and loss spectra are close. It suggests that the ionic transport in the elaborated material is due to a hopping mechanism. The dependence in frequency of the ac conductivity is found to obey Jonsher's relation.     

H-bonds of imidazole crystals. II. Determination of the magnitudes of the various anharmonic couplings of vs modes

In this article results given in a previous paper (part I), concerning the spectra of NH and ND species recorded with a polarization parallel to the c axis are analyzed, the necessary corrections on the raw data performed, v_s bands and their first moments are then compared with corresponding quantities predicted from a simple theory which describes quantitatively the anharmonic interactions of a single H-bond with a low frequency vibration of the same H-bond and with binary combinations of modes (Fermi resonances). This allows us to determine the magnitudes of the various anharmonic interactions involved. It appears that the low frequency vibration which modulates v_s is a bending mode of the H-bond (NH ↑ … N), a finding somewhat unexpected, as this low frequency vibration is usually thought to be the stretching vibration v_σ of the H-bond

     

Electrical conduction of bis(1,2-diondioximato)metals(II) and their partially oxidized complexes at high pressures

The resistivity of one-dimensional d⁸-metal complexes with various kinds of 1,2-diondioxime(dimethylglyoxime, nioxime, and diphenylglyoxime) ligands has been measured at high pressures. The resistivity of M(dmg)₂ and M(niox)₂ decreased with increasing pressure. The resistivity of M(dmg)₂ is much lower than that of M(niox)₂ at high pressure, though M-M distances and optical energy gaps in both salts are almost the same at atmospheric pressure. An anomalous low resistivity has been observed in Pt(dmg)₂ at about 40 kbar. The electrical resistivity of M(niox)₂ and M(dmg)₂, oxidized by oxidizing agents, decreased with increasing pressure. The resistivity of partially oxidized Pt complexes is significantly higher than that of the parent compounds at high pressure. On the contrary, partially oxidized Ni and Pd complexes are more conductive than unoxidized compounds at high pressures. The electrocal resistivity of unoxidized and partially oxidized Pt complexes increased with increasing pressure at higher pressures. The resistivity minimum at high pressure has been observed only in Pt complexes. The infrared spectra of the d⁸-metal complexes and their partially oxidized complexes have been investigated. The frequency of the CN stretching vibration in M(dmg)₂ and M(niox)₂ salts increases in the order Ni > Pd > Pt; on the other hand, the frequency of M(niox)₂X_n increases in the order Ni < Pd < Pt. The frequency of the CN stretching vibration is closely related to the effect of metal-ligand π1 back bonding in d⁸-metal complexes. Some anomalies in the resistance-pressure curve have been found in Ni(dpg)₂, Ni(dpg)₂I, Ni(dpg)₂I_0.5, and Ni(dpg)₂I_0.14. The anomalies are explained by new pressure-induced phase transitions.