Analysis of the transport coefficients for simple dense fluids: The diffusion and bulk viscosity coefficients

The analysis of transport coefficients based on the modified Enskog theory (MET), discussed in a previous publication, has been extended to include the self-diffusion coefficient (D) and the bulk viscosity coefficient (η_v). Specifically, calculated values according to the MET are compared with experiment over the range for which data are available. Fluids considered are argon, nitrogen and methane. Agreement between theory and experiment for densities less than about twice the critical density (ρ_c) is generally within about 10%. However, much of the data was taken at densities well in excess of 2_ρc in which case agreement is still not unsatisfactory. Deviations exceeding 10% between theoretical and experimental self-diffusion coefficients were observed for densities in the approximate range 0.9 ? _ρ/ρc ? 2.0. It is possible that these deviations are due to long range correlated molecular motions which are not present in the MET. The sound absorption is also briefly considered. Finally, the behavior of η_v and D at low densities is discussed.     

Thermal conductivity of two binary mixtures of gases of equal molecular weight

The paper reports new measurements of the thermal conductivity of two binary mixtures at a nominal temperature of 27.5°C but over a pressure range. The two systems, N₂-CO (three compositions up to 12MPa) and N₂O-CO₂ (four mixtures up to 4.2 MPa) have been chosen because they consist of molecules of similar structure and equal molecular weight (28.01 and 44.01, respectively). Moreover, the zero-density viscosity is identical within each mixture.The results have been extrapolated and fitted to equations in the usual way. The zero-density thermal conductivity in each system varies systematically with composition and differs by about 4% for the pure components in each case. This is a measure of the effect of the internal degrees of freedom on thermal conductivity.In the absence of a reliable theory, it is shown that the equations of kinetic theory can be used to represent the composition-dependence of zero-density thermal conductivity with a judicious choice of two quantities which cannot be calculated independently.In both systems, both the excess thermal conductivity λ(T,?) - λ(T, 0) and the ratio λ(T, ?)?λ(T, 0) are sole functions of density with a remarkable degree of precision.The variation of the thermal conductivity with density could be predicted quit accurately with the aid of the theory due to Mason.     

Investigation of the mass dependence of self-diffusion coefficients by molecular dynamics calculations: comparison with the Enskog theory

The dependence of the Enskog self-diffusion coefficients D_i,E on mass ratios m_i* = m_i/m₁ in hard sphere mixtures is described by exponential expressions of the form D_i,E = D⁰ _i,E(m*₂)eX_i,E in the case of binary mixtures and D_i,E = D⁰ _iE (m*₂)eX_i,E(m*₃)eXt_i,E in the case of ternary mixtures. D⁰ _i,E are the self-diffusion coefficients in reference mixtures with m*₂ = m*₃ = 1. ex_i,E (i = 1,2) and ext_i,E (i = 1,2,3) are the so called Enskog exponents of binary and ternary mixtures, respectively. Their dependence on particle mass and diameter, mole fraction, density and temperature is discussed and compared with corresponding results of molecular dynamics calculations.     

Thermal conductivity of fluids with steeply repulsive potentials

We consider the thermal conductivity of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, φ(r) = ε(σ/r)ⁿ. The time correlation function for the heat flux, C_λ(t), and the time average, C_λ(0) are calculated numerically by molecular dynamics simulations, and accurate expressions for these are also derived for the SRP fluid. We show, by molecular dynamics simulations, that close to the hard-sphere limit this time correlation function has the same analytic form as for the shear and pressure correlation functions for the shear and bulk viscosity, i.e. C_λ(t)/C_λ(0) = 1 ?T* (nt*)² + 0((nt*)⁴), where T* = k _B T/ε, is the reduced temperature, k _B is Boltzmann's constant and t* = (ε/σ²)^1/2 t is the reduced time. The thermal conductivity for the limiting case of hard spheres is numerically very close to that given by the traditional Enskog relation. At low densities the normalized relaxation times are typically largest for the thermal conductivity, followed by shear and then bulk viscosity. Close to the maximum fluid density, the latter two increase rapidly with density (especially for the shear) but continue a monotonic decline for the thermal conductivity. This reflects the relative insensitivity of the thermal conductivity to the approach to the fluid-solid phase boundary.     

The vibrational contribution to the thermal conductivity of a polyatomic fluid

A simple analytical expression is proposed in this article to calculate the vibrational contribution to the thermal conductivity of a polyatomic fluid. The analytic expression was obtained based on the assumption that the self-diffusion process is the major mechanism in the transport of vibrational energy. The proposed expression is validated by comparing the thermal conductivity of CO₂ calculated by molecular dynamics (MD) simulations to experimental data over a wide range of temperature and pressure. It is also demonstrated that the proposed analytic expression greatly increases the accuracy of calculated thermal conductivity for CO₂ at the supercritical state.     

Relative intensities in X-ray photoelectron spectra. Part IX. Estimates for photoelectron mean free paths taking into account elastic collisions in a solid

By means of the Monte Carlo method the angular dependences of photoelectron peak intensities have been calculated for substrates covered with films of various thicknesses D. The calculations have been carried out for several sets of parameters of the elastic and inelastic interactions of electrons with solids and for various experimental geometries. On the basis of numerical theoretical results, analytical expressions are derived for estimating the difference between the effective mean free path of photoelectrons (λ_eff) and the inelastic mean free path (λ_n) in solids. These expressions are used to analyse experimental data for the determination of thin-film thicknesses by means of ESCA. It is concluded that the values determined experimentally are apparently D/λ_eff ratios — not D/λ_n, as is usually assumed. The importance of the results obtained is discussed with reference to the determination of photoelectron mean free paths in solids and of thin-film thicknesses by means of ESCA.     

Shock compression of simple molecules

A simple approach is developed to calculate shock compression of simple molecules. This approach is based upon an accurate analytic representation of the Lennard-Jones fluids in conjunction with the Enskog theory, which is used to calculate the molecular diameter as a function of temperature along the Hugoniot. The model permits rapid, yet reliable calculations. It is applied to N₂, O₂, H₂, D₂, CH₄, CO, and CO₂. The results are tested by the comparison with experimental data and with other calculations. The computed Hugoniots agree reasonably with experimental results for many (but not all) simple molecules and are comparable to those of more complicated models.     

Thermal conductivity of La0.67(CaxSr1−x)0.33MnO3 (x=0, 0.5, 1) and La0.6Y0.07Ca0.33MnO3 pellets between 10 and 300 K

Thermal conductivity (λ) of nanocrystalline La_0.67(Ca_xSr_1−x)_0.33MnO₃ (x=0, 0.5, 1) and La_0.6Y_0.07Ca_0.33MnO₃ pellets prepared by a novel ‘pyrophoric’ method have been studied between the temperature range 10 and 300 K. Our data show that the magnitude of thermal conductivity is strongly influenced by the ion substitutions at La-site. The analysis of the thermal conductivity data indicates that the thermal transport is governed largely by phonons scattering in these systems and the electronic contribution is as small as 0.2-1% of total thermal conductivity (λ_total). At low temperatures (<90 K) 2D like lattice defects contribute to the phonon scattering dominantly and its strength increases with increasing Sr content and also with partial substitution of La by Y. Depending upon the composition of the samples, the magnon thermal conductivity contributes 2-15% of λ_total close to T_C. In the paramagnetic regime the unusual increase in λ_total keeps signature of large dynamic lattice distortion.     

Evaluation of XPS-data of oxide layers

XPS with variable take-off angle has been applied to the determination of the thickness of thin oxide layers (SiO₂ on Si). The information about D/λ_ox gained by such measurements is strongly influenced by surface roughness. This influence can be demonstrated when the parameters R and D/λ_ox are calculated from sets of the experimental results and for each set the corresponding pair of R and D/λ_ox is plotted in a diagram D/λ_ox = f(R). Having the true value of R it is possible to determine D/λ_ox. With the XPS-results of at least three different oxide layers and their ellipsometric thicknesses D_e one is able to calculate λ_Si, λ_ox/λ_Si and the difference ΔD between D_e and the XPS-thickness D.     

Effects of anisotropy,order parameter,and viscosity on translational self-diffusion in nematic liquid crystals

A theory developed for the translational diffusion in nematic liquids crystals shows a dependence on the viscosities, order parameter, and molecular structure. Theoretical results for self-diffusion in p-azoxyanisole at 125°C are D^{∥ = 4.3 × 10?6, D⊥ = 3.1 × 10?6 c2/s}, andD^∥/D^⊥ = 1.4.     

Photochemical preparation of nitrosomethanol: Vibrational frequencies,force field,and normal coordinate analysis of the cis and trans isomers

The previously unknown molecule C-nitrosomethanol [H₂C(OH)(NO)] and seven of its isotopic modification [¹³C, ¹⁸OH, ¹⁵N, D₃, D₃-¹⁵N, H₂C(OD)(NO), and HDC(OH)(NO)] have been photolytically prepared from the corresponding methylnitrite isotopes in a low-temperature argon matrix. By irradiating methylnitrite into its $\text{S}{}_1\text{(nπ}{}^1\text{← S}{}_0$ transition at 365 nm, the molecule is transformed into a hydrogen-bonded 1:1 complex between formaldehyde and nitroxyl. Photolysis of this complex produces either the trans (λ_exc = 345 nm) or the cis (λ_exc ≥ 645 nm) isomer of nitrosomethanol. Selective photoisomerization processes permit interconversion of the conformers (cis → trans with λ_exc = 510 nm and trans → cis with λ_exc ≥ 645 nm). The ir spectra (40–170 cm^?1) of cis- and trans-nitrosomethanol were measured and analyzed in conjunction with a normal coordinate analysis based on a constrained valence force field (transferable valence force field approach). The frequencies of cis- and trans-nitrosomethanol were assigned and their force fields determined.     

Temperature dependence of effective thermal conductivity and effective thermal diffusivity of Se90In10 bulk chalcogenide glass

Measurement of effective thermal conductivity (λ_e) and effective thermal diffusivity (χ_e) of twin pellets of Se₉₀In₁₀ bulk chalcogenide glass has been carried out in the temperature range from 303 to 323 K and cooling from 323 to 303 K using transient plane source (TPS) technique. In the heating process variation of effective thermal conductivity (λ_e) and effective thermal diffusivity (χ_e) is observed. Both quantities are found to be maximum at 313 K, which lies in the vicinity of glass transition temperature (T_g). During the cooling process λ_e and χ_e remain same at all temperatures. Such type of behavior shows thermal hysteresis in this sample, which can be explained on the basis of structural change of the Se₉₀In₁₀ bulk chalcogenide glass.     

The effective thermal conductivity of porous media based on statistical self-similarity

A fractal model is presented based on the thermal-electrical analogy technique and statistical self-similarity of fractal saturated porous media. A dimensionless effective thermal conductivity of saturated fractal porous media is studied by the relationship between the dimensionless effective thermal conductivity and the geometrical parameters of porous media with no empirical constant. Through this study, it is shown that the dimensionless effective thermal conductivity decreases with the increase of porosity (?) and pore area fractal dimension (Df) when ks/kg>1. The opposite trends is observed when ks/kg<1. In addition, the dimensionless effective thermal conductivity decreases with increasing tortuous fractal dimension (Dt). The model predictions are compared with existing experimental data and the results show that they are in good agreement with existing experimental data.     

Influence of isotopic substitution on the diffusion and thermal diffusion coefficient of binary liquids

The mutual mass diffusion coefficient (D) and the thermal diffusion coefficient ( D _T) of the liquids acetone, benzene, benzene-d ₁, benzene-d ₃, benzene-d ₅, benzene-d ₆, benzene- ¹³C₆, n-hexane, toluene, 1, 2, 3, 4-tetrahydronaphtalene, isobutylbenzene, and 1, 6-dibromohexane in protonated and perdeuterated cyclohexane have been measured with a transient holographic grating technique at a temperature of 25 ^°C. The mass diffusion coefficient shows a pronounced concentration dependence. Perdeuteration of cyclohexane only leads to marginal changes of the mass diffusion coefficient. The Stokes-Einstein equation describes the limiting tracer diffusion coefficients well if the solute molecule is smaller than the solvent. It is not capable to describe the small isotope effect of a few percent. On the other hand, the isotope effect, which is independent of concentration, is in agreement with the Enskog theory, that does not provide the absolute value of the mass diffusion coefficient of the liquid mixtures. The thermal diffusion coefficient of all the binary mixtures shows a moderate and almost linear concentration dependence. Its isotope effect, which is the change of D _T upon deuteration of cyclohexane, varies with mole fraction. The thermophoretic force acting on any tracer molecule in cyclohexane changes by the same amount when cyclohexane is perdeuterated, irrespective of the magnitude of the thermophoretic force before deuteration. This change of the thermophoretic force is equal but of opposite sign to the difference between the thermophoretic forces acting on cyclohexane and perdeuterated cyclohexane as tracers in any of the above liquids.     

The localization of local and gap modes by the sign count method

In the theory of local states it is usual to bring the linear problem ¦glI _N ?D¦=0 into a non-linear one ¦R(λ)¦=0, where the ordern of the condensed stiffness matrixR(λ) is much smaller than the orderN of the matrixD. Powerful methods exist for determining the number of the eigenvalues ofD in some interval without solving the equation ¦glI _N ?D¦=0 explicitly. It is shown, that analogous methods can be applied to the condensed matrix R(λ), when computing the eigen-valuesλ outside the frequency spectrum of the ideal lattice.     

Spatial-temporal dispersion of the kinetic coefficients near the Anderson transition

A generalization of the Vollhardt-Wölfle localization theory is proposed to make it possible to study the spatial-temporal dispersion of the kinetic coefficients of a d-dimensional disordered system in the low-frequency, long-wavelength range (ω?_F and q?k _F ). It is shown that the critical behavior of the generalized diffusion coefficient D(q,ω) near the Anderson transition agrees with the general Berezinskii-Gor’kov localization criterion. More precisely, on the metallic side of the transition the static diffusion coefficient D(q,0) vanishes at a mobility threshold λ _c common for all q: D(q, 0)∝t=(λ _c ?λ)/λ _c →0, where λ=1/(2π?_F τ) is a dimensionless coupling constant. On the insulator side, q≠0 D(q,ω)∝?iω as ω→0 for all finite q. Within these limits, the scale of the spatial dispersion of D(q,ω) decreases in proportion to t in the metallic phase and in proportion to ωξ ², where ξ is the localization length, in the insulator phase until it reaches its lower limit ～λ _F. The suppression of the spatial dispersion of D(q,ω) near the Anderson transition up to the atomic scale confirms the asymptotic validity of the Vollhardt-Wölfle approximation: D(q,ω)?D(ω) as |t|→0 and ω→0. By contrast, the scale of the spatial dispersion of the electrical conductivity in the insulator phase is of order of the localization length and diverges in proportion to |t|^?v as |t|→0.     

Autodiffusion en volume dans la phase plastique de l'acide pivalique (acide 2.2 dimethyl propanoique)—II: Etude des mecanismes de diffusion

Dislocations and impurities had no influence on the self-diffusion coefficient measurements described in the previous paper (part I). Therefore, the activation enthalpy, ΔH_D, and the mass factor fΔK are characteristic of lattice self-diffusion. The diffusion mechanism is discussed. The correlation factor has been calculated assuming that the life time of the dimers (two molecules of pivalic acid linked by two hydrogen-bonds) is long compared to the mean molecular jump time. From the values of ΔH_D and fΔK the migration of highly relaxed monovacancies in a solid of dimers seems the most probable diffusion mechanism.     

Limits of the validity of the mass ratio independence of the Stokes—Einstein relation: molecular dynamics calculations and comparison with the Enskog theory

Detailed molecular dynamics simulations have been carried out to investigate the mass ratio dependence of the tracer self-diffusion coefficient D ₂ in binary, atomic Lennard-Jones mixtures as a function of density n and length diameter ratio σ₂₂/σ₁₁. For a compact representation of our results an exponential approach is employed. The results are compared with the Stokes-Einstein relation, which predicts no mass ratio dependence, and the Enskog theory. The validity ranges regarding the mass ratio dependence for Enskog and Stokes-Einstein like behaviour are given as well as the mass ratio dependence in the crossover regions between these two cases. For length parameter ratios σ₂₂/₁₁ <1, the Stokes-Einstein prediction is not valid for mass ratios 1/16≤m₂/m₁ ≤50. For length parameter ratios σ₂₂/σ₁₁>2 and for mass ratios m₂/m₁ < 1, the Stokes-Einstein regime (regarding the mass ratio dependence) is reached for smaller densities than for the same system but m₂/m₁ >1.     

Composition dependence of effective thermal conductivity and effective thermal diffusivity of Se100−xInx (x=0, 5, 10, 15 and 20) chalcogenide glasses

Simultaneous measurement of effective thermal conductivity (λ_e) and effective thermal diffusivity (χ_e) of twin pallets of Se_100−xIn_x (x=0,5, 10, 15, and 20) glasses, prepared under a load of 5 tons, have been made at room temperature using the Transient Plane Source (TPS) technique. The values of λ_e and χ_e were found to increase initially with the increase of concentration of In in Se-In alloy and had their maximum at 10 at.wt% of indium. For indium concentration beyond 10 at.wt% of the values of effective thermal conductivity and effective thermal diffusivity decrease linearly. This is suggestive of fact that 10 at.wt% of indium can be considered as a critical composition at which the alloy becomes, chemically ordered and maximum thermally stable than other composition. Further addition of indium in selenium decreases the values of λ_e and χ_e. The behaviour is explained on the basis of decrease of localized states and increase in disorderness for higher composition indium.     

Surface self-diffusion studied by microscopic measurements of crystallite profile evolutions

Dendritic gold crystallites on graphite are heated in ultra high vacuum up to less than 0.5 of the melting point (T_m). Electron microscopy shows that the gold crystallites change their shapes by surface self-diffusion. The dendritic contours round off while the crystallite remains very flat (20 to 40 Å). The increase with time of the radii of dendrite tips is measured statistically. Such an evolution can be described by analogy to the blunting of either metal tips (Nichols and Mullins) or monoatomic cleavage tips (Höche and Bethge). Using this result, a new technique to measure surface self-diffusion coefficients (D) is proposed. Test measurements have shown that this is an interesting, very sensitive method to measure D (down to 10^?13 cm^?2 s^?1) which enables measurements to be made in an unusual low temperature range (0.25 T_m < T < 0.5T_m). In special cases the dendrites are split by the surface self-diffusion which is qualitatively in agreement wih the theory.