The frequency dispersion of dynamic transfer coefficients and elastic moduli of magnetic liquids

The analytic equations for viscosity coefficients and the corresponding elastic moduli obtained in [3] were used to calculate these values over a wide range of reduced frequency values (ω* ≈ 10^?7?10). The volume η _v (ω) and shear η _s (ω) viscosity coefficients decreased as the frequency increased. The dispersions η _v (ω) and K _r (ω) were only caused by the contribution of structural relaxation, and the dispersions η _s (ω) and μ(ω), by translational and structural relaxation. The shear elastic modulus μ(ω) and relaxation volume elastic modulus K _r (ω) increased as the frequency grew. The results obtained were in satisfactory agreement with the conclusions from general relaxation theory.     

Numerical Calculation of Permittivity and Dielectric Loss of Aqueous KF Solution Depending on State Parameters

Based on the analytical expressions for permittivity ε₁(ω) and dielectric loss ε₂(ω) are obtained by the kinetic equation method, the frequency spectra of these coefficients are analyzed for an aqueous KF solution in a wide variation range of the density ρ, the concentration C, and the temperature T. With a certain choice of the solution model, the potential interaction energy Φab(|r|), and the radial distribution function g_ab(|r|) of a- and b-type ions, ε₁(ω) and ε₂(ω) of an aqueous KF solution are numerically calculated depending on ρ, C, T, and ω.     

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.     

Molecular structures of acetyl fluoride and acetyl iodide

The molecular structures of acetyl fluoride and acetyl iodide have been determined by making use of the average distances obtained in the present study together with the moments of inertia reported in the literature. The large amplitude theory for a molecule with an internal top was used in the joint analysis. The thermal-average values of internuclear distances r_g and the bond angles in the zero-point average structure Φ_z are as follows: r_g(C-O) = 1.185 ±0.002 $\text{}\text{?}$rA, r_g(C-F) = 1.362± 0.002 Å, r_g(C-C) = 1.505±0.002 Å, r_g(C-H) = 1.101 ±0.004 Å, Φ_z(OCF) = 120.7°±0.4°,Φ_z(CCF) = 110.5° ± 0.5°, Φ_z(HCH) = 109.3°±0.6° tilt(CH₃) = 0.1°±1°, for acetyl fluoride; r_g(C=O) = 1.198±0.013 $\text{}\text{?}$rA, r_g(C-I) = 2.217±0.009 Å, r_g(C-C) = 1.492±0.015 $\text{}\text{?}$rA, r_g(C-H) = 1.101 ± 0.004 Å, Φ_z(OCI) = 119.5°± 0.8°,Φ_z(CCI) = 111.7°±0.9°, Φ_z(HCH) = 110.8°±0.8° and tilt(CH₃) = 1.7°+5.4° for acetyl iodide. The uncertainties represent the estimated limits of error. The barriers V₃ to internal rotation have been reanalyzed making use of the effective moments of inertia of the methyl top estimated on the basis of the large amplitude theory and resulted in 1039 and 1176 cal mol^?1 for acetyl fluoride and acetyl iodide, respectively. The structure parameters have been compared with those of other CH₃COX (X = Cl, Br, H, CH₃) type molecules.     

Internal dynamics of the LaI3 molecule. II. Thermal average structure of the molecule and mean square vibration amplitudes

The structural parameters of the effective r _g configuration of the LaI₃ molecule were calculated using the DFT/B3LYP method. The difference between the calculated values of r _e (La-I) and r _g (La-I) is mostly due to the anharmonicity of the ν₁ and ν₂ vibrations and does not exceed the error in determining the distance r _g (La-I) in the electron diffraction experiment. Inclusion of the anharmonicity of the ν₂ and ν₄ deformation vibrations in calculations leads to decreased amplitudes l(I…I) and shrinking effect δ(I…I) compared to the respective values obtained in the harmonic approximation. The LaI₃ molecule proved to be more rigid than predicted by B3LYP calculations.     

The geometry of the propynol cation,HC3O+

The geometry of a potential interstellar molecule, the propynol cation, HC₃O⁺, is determined by split-valence plus polarization (6-31G*) SCF method with the inclusion of electron correlation effects by third order Møller—Plesset perturbation theory (MP3). The 6-31G* MP3 geometry is: r_e(CO) = 1.125, r_e(CC) = 1.351, r_e(CC) = 1.214, r_e(CH) = 1.078 A, and thus a B_e of 4.421 GHz.     

Electron-diffraction study of hydrogen isotope effects in cyclohexane

The electron-diffraction data for cyclohexane and perdeuterated cyclohexane were analyzed and the results were compared. It was found that r_g(C-C) = 1.535 Å (±0.002) for both compounds; r_g (C-H) = 1.116 Å (±0.004) and r_g(C-D) = 1.109 Å (±0.003). Observed hydrogen isotope effects in mean amplitudes agree very well with calculated ones. The C-C bond distance of cyclohexane is in good agreement with some of the previous studies, which is of importance in view of a recent scaling controversy involving this parameter.     

Molecular structure of Pt(PF3)4 by gas-phase electron diffraction

The structure of Pt(PF₃)₄ was reinvestigated making use of a new theory of intramolecular dynamic scattering. Derived molecular parameters were insensitive to the dynamic corrections. Refinements for this tetrahedral molecule yielded r_g(Pt-P) = 2.229(5) Å, r_g(P-F) = 1.550(4) Å, and ∠PtPF = 118.9°(0.4), with the indicated uncertainties representing 2.5σ. Amplitudes of vibration were also determined. Diffraction patterns were consistent with freely rotating PF₃ groups.     

The molecular structure and conformation of acetamides in the vapour phase: Part II. 2-Iodoacetamide

2-Iodoacetamide has been studied by electron diffraction, utilizing a new nozzle construction. A skew conformation with a dihedral angle of 126.3(1.1)° from syn (C-I bond eclipsing the C-N bond), and a gauche conformation with a dihedral angle of 42.3(1.6) both fit the experimental data almost equally well. However, comparison with the X-ray structure and the results for the two models indicate a slight preference for the skew form.The most important structural parameters are: r_g(CO) = 1.222(3)Å, r_g(C-N) = 1.370(3)Å, r_g(C-C) = 1.515(4) Å, r_g(C-I) = 2.160(4) Å, ∠_αOCC = 120.0(6)°, ∠_αNCC = 116.9(4)° and ∠_αCCl = 117.3(4)°. Parenthesized values are one standard deviation.     

Stationary perturbation theory for non-Hamiltonian eigenvalue equations

Second-order perturbation theory is developed for equations of the Klein-Gordon typeK(E, V, ?²) Ψ=0, in which the eigenvalueE occurs in various powers. The result is a simple generalization of Schrödinger's.     

An electron diffraction determination of the molecular structures of phosphoryl bromide and thiophosphoryl bromide

Gas-phase electron diffraction structures have been determined for phosphoryl bromide (OPBr₃ thiophosphoryl bromide (SPBr₃Normal coordinate analyses were carried out for the two molecules using a valence force field, and the resulting amplitude terms used for transformations between r_a and r_ga. An unconstrained refinement of the OPBr₃ intensities gives the parameters r_g(PO) = 1.455(7) Å and r_g(PBr) = 2.175(3) Å. The weighted average, geometrically-consistent valence angles derived from the four internuclear distances, r_α, are θ_α(OPBr) = 114.4(2)° and θ_α(BrPBr) = 104.1(2)°. For SPBr₃ a constrained fit to a self-consistent rα structure gives the parameters r_g(PS) = 1.895(4) Å, r_g(PBr) = 2.193(3) Å, θ_α(SPBr) = 116.2(2)°, and θ_α(BrPBr) = 101.9(2)°. Electron diffraction and spectroscopic vibrational amplitudes are reported for both molecules. The electron diffraction structures are compared with those predicted by simple models previously developed to describe main group V trihalides and trihalogen oxides and sulfides. Treatment of valence angles in four-coordinate molecules is found to be the least satisfactory feature of these models.     

Molecular structures of propene and 3,3,3-trifluoropropene determined by gas electron diffraction

The structures of propene and 3,3,3-trifluoropropene have been studied by electron diffraction intensities measured in the present study and rotational constants reported in the literature. The following average structures have been determined: For propene, r_g(CC) = 1.342 ± 0.002 Å, r_g(C-C) = 1.506 ± 0.003 Å, r_g(C-H)_vinyl = 1.104 ± 0.010 Å, r_g(C-H)_methyl = 1.117 ± 0.008 Å, ∠(C-CC) = 124.3 ± 0.4°, ∠(CC-H) = 121.3 ± 1.4°, and ∠(C-C-H) = 110.7 ± 0.9°; for trifluoropropene, r_g(CC) = 1.318 ± 0.008 Å, r_g(C-C) = 1.495 ± 0.006 Å, r_g(C-H)= 1.100 ± 0.018 Å, r_g(C-F) = 1.347 ± 0.003 Å, ∠(C-CC) = 125.8 + 1.1°, ∠(C-C-F) = 112.0 ± 0.2°, where the valence angles refer to the r_av structure, and the uncertainties represent estimated limits of experimental error. A simple set of quadratic force constants for each molecule has been estimated. Regular trends have been observed in the CC and C-C bond distances and the C-CC angles in these and related molecules. Significant differences between the CC, C-C and C-F distances and the C-C-F angle in trifluoropropene and in hexafluoroisobutene reported by Hilderbrandt et al. have been indicated.     

The structure of bis(1,1,1,5.5,5-hexafluoro-2,4. pentadionato) copper(II) as determined by gas phase electron diffraction

The r_g structure of bis(1,1,1,5,5,5-hexafluoroacetylacetonato) copper(II) has been determined by gas phase electron diffraction. The experimental data were found to be consistent with a D_2h model in which the oxygens from the two ligands are arranged in an essentially square planar configuration about the copper atom (∠OCuO = 90.6° ± 1.2°). It was possible to obtain a precise value for the copper oxygen bond length, r_g = 1.919 ± 0.008 Å, since this distance appeared as an isolated peak in the radial distribution curve. Structural parameters for the ligand (r_g(C-O) = 1.276 ± 0.009 Å, r_g(C-C_ring) = 1.392 ± 0.015 Å, r_g(C-CF₃)= 1.558 ± 0.009 Å and r_g(C-F) = 1.339 ± 0.003 Å), while less precisely determined are, nevertheless, consistent with reported values for related molecules. A model for the rotational isomerism of the four CF₃ groups was invoked in order to explain various features in the radial distribution curve in a region from 2.5 to 5.5 Å.     

Electronic Correlation Functions in Liquid Metals

Abstract

To determine experimentally the three pair correlation functions g_ii(r), g_ie(r) and g_ee(r) in a pure liquid metal, i denoting ions and e electrons, requires three independent diffraction measurements. A brief review will be given in this difficult area, but progress is quite slow. One can make headway by confronting available experimental diffraction data with the results of computer experiments, and in particular on g_ie(r). This will be illustrated with specific reference to recent computer simulations on liquid Mg and liquid Bi. for Mg, analytic modelling is also possible and this will be discussed.

Quite independently, computer experiments have recently appeared which describe the effects of isochoric heating on dense fluid hydrogen over a wide temperature range. This prompts again reference to analytic models, both caged atomic and molecular hydrogen being considered. Finally, though the electrical conductivity of the H plasma above has not yet been studied, a brief discussion of a possible mechanism of electronic transport in strongly coupled plasma will be presented.     

Molecular structure of bis(acetylacetonato)nickel(II) in the gas phase as determined from electron diffraction data

The molecular structure of bis(acetylacetonato)nickel(II) has been determined by a sector-microphotometer gaseous electron-diffraction method. The experimental data were found to be consistent with a monomeric square-planar structure. The structural parameters of the chelate were determined as follows: ∠ ONiO = 93.6 ± 1.1°, r_g(Ni-O) = 1.876±0.005A Å, r_g(C-0) = 1.273± 0.007 Å, r_g(C-C_ring) = 1.401 ± 0.010 Å, r_g(C-C_methyl) = 1.504 ± 0.013 Å. The mean amplitudes of vibration and the shrinkage effects were calculated from normal-vibration treatment using the Urey-Bradley force field.     

An improved electron diffraction—microwave and molecular orbital study of the structure of SF5Cl

A new study of the structure of SF₅Cl is reported. Previously-obtained electron diffraction data have been corrected for multiple scattering, and newly-reported microwave rotational constants have been combined in the analysis. Structural parameters, with estimated limits of error, were found to be r_g (S-Cl) 2.055(1) Å, r_g (S-F)_mean 1.570(1) Å, r_g (S-F_ax) - r_g(S-F_eq) 0.001(8) Å, r_g(S-F_eq) 1.571(3) Å, r_g (S-F_ax) 1.571(8) Å, ∠α Cl-S-F_eq 90.4(0.1)°. The new data are more self-consistent than was previously the case. Ab initio molecular calculations using three different basis sets are reported and discussed.     

The thermoelastic properties and structural relaxation of magnetic liquids

The kinetic equations for one-and two-particle distribution functions were used to study the thermoelastic properties of magnetic liquids in the presence of an external not uniform magnetic field. Dynamic equations for the heat conductivity coefficient λ(ω) and thermal elastic modulus Z(ω) over a wide reduced frequency range were obtained. The asymptotic behavior of λ(ω) and Z(ω) was studied at low and high frequencies; the results were in agreement with those obtained for classic liquids by the method of molecular dynamics. The λ(ω) and Z(ω) values were calculated for a magnetic liquid based on kerosene and Fe₃O₄ magnetic particles. The numerical data on transfer coefficients and elastic properties of magnetic liquids were on the whole in agreement with the general conclusions of the statistical theory of liquids.     

Problems in electron propagator calculations of the correlation energy

Approximations to the one-electron propagator, G(ω), are discussed asa basis for correlation energy calculations. The random-phase approximation (RPA) and second-order perturbation theory estimates of the self-energy are used to determine G(ω). Correlation energy expressions, resulting from contour integration, are compared with the standard perturbation expansion. We suggest that some of the simpler approximations to the electron propagator may be unsuited to calculations of the correlation energy.     

Molecular structure and conformation of gaseous 2-chloro-3-fluoro-1-propene

2-Chloro-3-fluoro-1-propene has been studied by electron diffraction, and the molecule was found to exist in equilibrium between a syn and a gauche conformation, with the syn conformation as the most stable. The most important structure parameters with standard deviation are: r_g(CC) = 1.338(6) Å,r_g(C—C) = 1.505(5) Å, r_g(C—F) = 1.378(4) Å, r_g(C-Cl) = 1.743(3) Å, ∠CC—Cl = 123.0(7)°, ∠CC—C = 125.6(6)° and ∠C—C—F = 111.2(8)°.A force field was determined by a least-squares refinement to vibrational frequencies. Mean square amplitudes of vibration and perpendicular amplitude correction coefficients have been calculated. The mean square amplitudes of vibration from the electron diffraction data are in very good agreement with the values calculated from the spectroscopic data.     

Molecular structure and force field of cerium tetrafluoride

Combined interpretation of electron diffraction and spectroscopic data for the CeF₄ molecule is reported. It is shown that the diffraction pattern corresponds to a tetrahedral structure of the molecule with the following effective configuration parameters (T=1180(50) K): r_g(Ce-F)=2.036(5) Å, r_g(F-F)=3.312(25) Å, l(Ce-F)=0.074(3) Å, l(F-F)=0.261(17) Å. The total force field of the CeF₄ molecule is found in a harmonic approximation. Possible participation of the Ce f-electrons in chemical bonding is discussed.