Viscosity of biniary mixtures. III. Tri-n-butylamine with alkanes and monoalkylamines at 303.15 and 313.15 K

Viscosities of seven binary systems of n-propylamine, n-butylamine, n-hexylamine, n-octylamine, n-hexane, n-octane, and isoctane (2,2,4-trimethylpentane) with tributylamine have been measured at 303.15 and 313.15 K with an Ubbelohde suspended-level viscometer. Based on Eyring's theory, values of excess Gibbs energy of activation G ^*E of viscous flow have been calculated. Deviations of viscosities from linear dependence on the mole fraction and values of G ^*E are attributed to the H-bonding and to the size of alkylamine and alkane molecules. The free volume theory of Prigogine-Flory-Patterson in combination with work by Bloomfield-Dewan has been used to estimate the excess viscosity ln and the terms corresponding to enthalpy, entropy, and free volume contributions for the present binary mixtures.     

Correlation and prediction of dense fluid transport coefficients. I. n-alkanes

Recent accurate measurements of the self-diffusion coefficient for n-hexadecane and n-octane and of the viscosity coefficient for n-heptane, n-nonane, and n-undecane over wide pressure ranges have been used to provide a critical test of a previously described method, based on consideration of hard-sphere theory, for the correlation of transport coefficient data. It is found that changes are required to the universal curve for the reduced viscosity coefficient as a function of reduced volume and, also, to the parameters R _D, R , and R which were introduced to account for effects of nonspherical molecular shape. The scheme now accounts most satisfactorily for the self-diffusion, viscosity, and thermal conductivity coefficient data for all n-alkanes from methane to hexadecane at densities greater than the critical density.     

The Viscosity of Gaseous n-Butane and Its Initial Density Dependence

New relative high-precision measurements of the viscosity of gaseous n-butane were carried out in an oscillating-disk viscometer. Seven series of measurements were performed between 298 and 627 K. in the density range from 0.01 to 0.05 mol·L^–1. Isotherms recalculated from the original experimental data were analyzed with a first-order expansion, in terms of density, for the viscosity. Reduced values of the second viscosity virial coefficient deduced from the zero-density and initial-density viscosity coefficients for n-butane are in good agreement with the representation of the Rainwater–Friend theory. The new experimental data and some data sets from the literature were used to develop a representation for the viscosity of n-butane in the limit of zero density on the basis of the extended principle of corresponding states. It has been shown that an individual correlation is needed to represent the experimental data between 293 and 627 K with an uncertainty of ±0.4%.     

Correlation of high-pressure diffusion and viscosity coefficients for n-alkanes

Self-diffusion coefficient and viscosity coefficient data for liquid n-alkanes over the whole pressure range at different temperatures are satisfactorily correlated simultaneously by a method which is just an extension of that previously used to apply the smooth hard-sphere theory of transport properties to individual transport coefficients. Universal curves are developed for reduced quantities D ^* and ^* as a function of reduced volume. A consistent set of values is derived for the characteristic volume V ₀ and for parameters R _D and R , introduced to account for effects of nonspherical molecular shape and molecular roughness. On this basis, accurate calculation can be made of self-diffusion and viscosity coefficients for other members of the n-alkane series, for which data are at present limited.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Correlation of high-pressure thermal conductivity,viscosity, and diffusion coefficients for n-alkanes

Thermal conductivity, viscosity, and self-diffusion coefficient data for liquid n-alkanes are satisfactorily correlated simultaneously by a method based on the hard-sphere theory of transport properties. Universal curves are developed for the reduced transport properties ^*, ^*, and D ^* as a function of the reduced volume. A consistent set of equations is derived for the characteristic volume and for the parameters R , R , and R _D, introduced to account for the nonsphericity and roughness of the molecules. The temperature range of the above scheme extends from 110 to 370 K, and the pressure range up to 650 MPa.     

Thermodynamics of hydrogen-bonding mixtures 2.G E,H E,andS E of 1-propanol +n-heptane

A metal ebulliometcr was used to measure total vapor-pressure (PTx) data on 18 mixtures of 1-propanol +n-heptane (and the pure components) between 380 and 445 K. Bubble-point data were measured at seven pressures between 200 kPa and I MPa. These data cover an intermediate region between previous data reported near atmospheric pressure and below and high-temperature data extending to the critical region. A Redlich--Kister G' model fit isotherms between 373.15 and 463.15 K via Barker's method with an average standard error of 0.2 to 0.5% in pressure. The system exhibits large positive deviations from ideality (derived =2.7–10.5) which decrease with temperature. EquimolarG ^E/T values thus derived also decrease with increasing temperature, which predicts a positiveH ^E An azeotrope exists under all conditions studied: the azeotropic composition increases in alcohol content with increasing temperature. These mixture thermodynamic data show that, above 345 K, the system 1-propanol +n-heptane belongs to the class of mixtures whereG ^E > 0,H ^E >0. andTS ^E > 0. This probably occurs because the 1-I orientational effect (in this case, hydrogen-bonding of the alcohol molecules) is more readily disrupted in the inert solvent than it would be a( lower temperatures, where the effect of hydrogen-bonding is stronger.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Densities, Sound Speeds, Excess Volumes, and Excess Isentropic Compressibilities of Methyl Acrylate + 1-Propanol (or 1-Butanol) + Hydrocarbons(n-Hexane, n-Heptane, Cyclohexane, Benzene, and Toluene) at 308.15 K

Densities and sound speeds of ten ternary mixtures of methyl acrylate (1)+1-propanol (2) or 1-butanol (2)+n-hexane (3), +n-heptane (3), +cyclohexane (3), +benzene (3), and +toluene (3) have been measured at 308.15 K. The excess volumes, V ^E , and excess isentropic compressibilities, ^E _s , have been estimated. These two experimentally derived excess functions were also compared with those predicted by empirical equations of Redlich–Kister, Kohler, and Tsao–Smith. A qualitative analysis of V ^E and ^E _s data of ternary mixtures reveals that in MA (1)+1-alcohols (2)+n-hexane (3), +n-heptane (3), and +cyclohexane (3), structure disruptions are more predominant while in MA (1)+1-alcohols (2)+benzene (3) or +toluene (3) mixtures, the weak but specific structure making interactions dominate. A perusal of deviations between the experimental and calculated V ^E and ^E _s results shows that the predictive expressions give only a rough estimate of the functions for the ten studied mixtures.     

SrCuO2 and related high-pressure phases

Treatment at high pressures and temperatures of 6 GPa and 1120 K, typically, have proved to be useful to find new layered complex cupric oxides. Among these, SrCuO₂ crystallizing in the infinite-layer structure may be considered to be the key material not only because of its simple composition and structure but also because of the fact that interesting homologous series of high-pressure phases like Sr _n+1Cu _n O_2n+1+ and Sr _n–1Cu _n+1O _2n converge to SrCuO₂ asn increases.     

Viscosities of nonelectrolyte liquid mixtures. II. Binary mixtures ofn-hexane with alkanoates and bromoalkanoates

Viscosity measurements are reported for mixtures of ethyl ethanoate, ethyl propionate, ethyl butyrate, ethyl-2-bromopropionate, ethyl-3-bromopropionate, ethyl-2-bromobutyrate, and ethyl-4-bromobutyrate withn-hexane at 303.15 K. The viscosity data have been correlated with equations of Grunberg and Nissan, of McAllister, and of Auslaender. Furthermore, excess Gibbs energies of activationG ^*E of viscous flow have been calculated with Eyring's theory of absolute reaction rates and values ofG ^*E for the present binary mixtures have been explained in terms of the dipole-dipole interaction in alkanoates and the intramolecular Br...O interaction in bromoalkanoates.     

Theory of superconductivity. 3. 2D conduction bands for high Tc. Bose-Einstein condensation transition of the third order

A general theory of superconductivity is developed, starting with a BCS Hamiltonian in which the interaction strengths (V ₁₁,V ₂₂,V ₁₂) among and between electron (1) and hole (2) Cooper pairs are differentiated, and identifying electrons (holes) with positive (negative) masses as those Bloch electrons moving on the empty (filled) side of the Fermi surface. The supercondensate is shown to be composed of equal numbers of electron and hole ground (zero-momentum) Cooper pairs with charges ±2e and different masses. This picture of a neutral supercondensate naturally explains the London rigidity and the meta-stability of the supercurrent ring. It is proposed that for a compound conductor the supercondensate is formed between electron and hole Fermi energy sheets with the aid of optical phonons having momenta greater than the minimum distance (momentum) between the two sheets. The proposed model can account for the relatively short coherence lengths observed for the compound superconductors including intermetallic compound, organic, and cuprous superconductors. In particular, the model can explain why these compounds are type II superconductors in contrast with type I elemental superconductors whose condensate is mediated by acoustic phonons. A cuprous superconductor has 2D conduction bands due to its layered perovskite lattice structure. Excited (nonzero momentum) Cooper pairs (bound by the exchange of optical phonons) aboveT _c are shown to move like free bosons with the energy-momentum relation=1/2v_Fq. They undergo a Bose-Einstein condensation atT _c = 0.977v _F k _b ^–1 n ^1/2, wheren is the number density of the Cooper pairs. The relatively high value ofT _c (100 K) arises from the fact that the densityn is high:n ^1/2–1 10⁷ cm^–1. The phase transition is of the third order, and the heat capacity has a reversed lambda ()-like peak atT _c .     

Excess thermodynamic properties of mixtures of alkyl benzoates withn-heptane

The paper reportsh ^E values at 298.15 K andv ^E and values at various temperatures for binary mixtures of propyl or butyl benzoate andn-heptane. The excess Gibbs energy of viscous flow,g ^*E, and the thermodynamic activation properties were calculated from these values. The results are compared with those for similar mixtures and interpreted on the basis of the characteristic dipole-dipole interactions of alkyl esters.Nomenclature A _i Parameters in Eq. (2) - dg ^*E Gibbs free energy of viscous flow (J · mol^–l) - dg Activation free energy (kJ · mol^–1) - K Parameter in Eq. (2) - h Planck constant - h ^E Excess enthalpy (J · mol^–1) - h Activation enthalpy (kJ · mol^–1) - N Avogadro number - R Universal gas constant (J · K^–1 · mol^–1) - s Standard deviation - s Activation entropy (J · K^–1 · mol^–1) - T Temperature (K) - v Molar volume of pure component (m³ · mol^–1) - v ^E Excess volume (m³ · mol^–1) - x _i Mole fraction of componenti Greek Letters Expansion coefficient (K^–1) - Density (kg · m^–1 ) - Viscosity (mPa · s ) - Apparent excess viscosity (mPa · s)     

Viscosities of nonelectrolyte liquid mixtures. I. binary mixtures containing p-dioxane

Viscosity measurements are reported for p-dioxans with cyclohexane, n-hexane, benzene, toluene, carbon tetrachloride, tetrachloroethane, chloroform, pentachloroethane, and ethyl acetate at 303.15 K. Excess Gibbs energies of activation G ^*E of viscous flow have been calculated with Eyring's theory of absolute reaction rates. The deviations of the viscosities from a linear dependence on the mole fraction and values of G ^*E for binary mixtures have been explained in terms of molecular interactions between unlike pairs. The Prigogine-Flory-Patterson theory has been used to estimate the excess viscosity, ln , and corresponding enthalpy ln _H, entropy ln _S, and free volume ln _v terms for binary mixtures of p-dioxane with cyclohexane, n-hexane, benzene, toluene, carbon tetrachloride, and chloroform. Estimates of excess viscosities from this theory for p-dioxane with benzene, toluene, and carbon tetrachloride are good, while for the other three mixtures they are poor. The local-composition thermodynamic model of Wei and Rowley estimates the excess viscosity quite well even for p-dioxane mixtures with cyclohexane and n-hexane.     

Volumetric and Acoustic Properties for Binary Mixtures of Dipropylene Glycol Monopropyl Ether with Alkylamines at Temperatures Between 288.15 K and 308.15 K

The densities, ρ, and speeds of sound, u, have been measured as a function of composition for binary liquid mixtures of dipropylene glycol monopropyl ether (DPGMPE) with n-butylamine (BA), dibutylamine (DBA), and tributylamine (TBA) at (288.15, 293.15, 298.15, 303.15, and 308.15) K and atmospheric pressure using an Anton Paar DSA-5000 instrument. The ρ and u values were used to calculate excess molar volumes, V ^E, deviations from the ideal behavior of the thermal expansion coefficient, α ^E, and the isentropic compressibilities, Δκ _S . Moreover, the apparent molar volume , and apparent molar compressibility , of the components have been calculated at infinite dilution. The Jouyban–Acree model is used to correlate the experimental values of density and ultrasonic speed at different temperatures.     

Thermal conductivity of liquid n-alkanes

The thermal conductivity of liquids has been shown in the past to be difficult to predict with a reasonable accuracy, due to the lack of accurate experimental data and reliable prediction schemes. However, data of a high accuracy, and covering wide density ranges, obtained recently in laboratories in Boulder, Lisbon, and London with the transient hot-wire technique, can be used to revise an existing correlation scheme and to develop a new universal predictive technique for the thermal conductivity of liquid normal alkanes. The proposed correlation scheme is constructed on a theoretically based treatment of the van der Waals model of a liquid, which permits the prediction of the density dependence and the thermal conductivity of liquid n-alkanes, methane to tridecane, for temperatures between 110 and 370 K and pressures up to 0.6 MPa, i.e., for 0.3T/T _c0.7 and 2.4P/P _c3.7, with an accuracy of ±1%, given a known value of the thermal conductivity of the fluid at the desired temperature. A generalization of the hard-core volumes obtained, as a function of the number of carbon atoms, showed that it was possible to predict the thermal conductivity of pentane to tetradecane±2%, without the necessity of available experimental measurements.     

A new family of superconductors containing carbonate group

Three new oxycarbonate superconductors recently obtained in our laboratory are described. (1) Sr₂CuO₂(CO₃)_1–x (BO₃) _x (T _c = 35 K) was synthesized under ambient pressure, providing a new method for carrier doping on the layered copper oxycarbonate system. (2) Ca _n (Ca, Sr)₂Cu _n+1(CO₃)O _y (n = 1, 2, 3) was synthesized under high pressure. Superconductivity was achieved by substituting (BO₃)^3– for a part of (CO₃)^2–. (3) A new Hg system HgBa₂Sr₂Cu₂(CO₃)O₆₊ was synthesized.T _c obtained from the magnetic susceptibility is about 66 K.     

Nonequilibrium Molecular Dynamics Simulations of Shear Viscosity: Isoamyl Alcohol, n-Butyl Acetate, and Their Mixtures

Nonequilibrium, NVT, molecular dynamics (NEMD) simulations were used to obtain the shear viscosity, , of isoamyl alcohol, n-butyl acetate, and their binary mixtures at 35°C and 0.1 MPa. The fluids were modeled using rigid bonds, rigid bond angles, appropriate torsional potentials, pairwise-additive Lennard–Jones dispersion interactions between united-atom sites, and partial point charges located at atomic centers. Simulations were performed at different shear rates, , and values obtained at =0 are compared to experimental values. Two methods are commonly used to extrapolate pure-fluid simulated data to zero shear, (0). The applicability of these two methods to mixtures of polar fluids was examined in this study. It was found that linear extrapolation with respect to ^1/2 can lead to ambiguous (0) results for some mixtures because of a curvature in the data that shows no observably distinct change in rheology. On the other hand, a log–log plot of () versus is consistently very linear with a distinct change from shear-thinning to Newtonian rheology at lower shear rates. The latter method is recommended for consistency sake, even though agreement between experiment and (0) values was better with the former method. This agreement was 12 and 21% for the two methods, respectively. A negative bias in the simulated values is attributable to the united-atom model.     

Collinearity between the Shapley value and the egalitarian division rules for cooperative games

For each cooperativen-person gamev and eachh{1, 2, ,n}, letv _h be the average worth of coalitions of sizeh andv _h ⁱ the average worth of coalitions of sizeh which do not contain playeriN. The paper introduces the notion of a proportional average worth game (or PAW-game), i.e., the zero-normalized gamev for which there exist numbersc _h such thatv _h –v _h ⁱ =c _h (v _n–1–v _n ^–1/i ) for allh{2, 3, ,n–1}, andiN. The notion of average worth is used to prove a formula for the Shapley value of a PAW-game. It is shown that the Shapley value, the value representing the center of the imputation set, the egalitarian non-separable contribution value and the egalitarian non-average contribution value of a PAW-game are collinear. The class of PAW-games contains strictly the class ofk-coalitional games possessing the collinearity property discussed by Driessen and Funaki (1991). Finally, it is illustrated that the unanimity games and the landlord games are PAW-games.     

New bounds on the reliability of the consecutive k-out-of-r-from-n:F system

The main goal of this article is to show that the lower and upper bounds on the failing probability resp. reliability of consecutive k-out-of-r-from-n:F reliability systems developed by Sfakianakis, Kounias and Hillaris [M. Sfakianakis, S. Kounias, A. Hillaris, IEEE Trans. Reliability 1992;R-41:442–447] can be improved by applying fourth order Boole–Bonferroni bounds. Further we propose the application of the Hunter–Worsley bound in the framework of reliability system analysis, too. Numerical results of the formerly published test examples and harder problems are given. The computer code was written in and is available on request from the authors.     

Measurements of the viscosity of n-heptane,n-nonane,and n-undecane at pressures up to 70 MPa

New absolute measurements of the viscosity of n-heptane, n-nonane, and n-undecane are presented. The measurements were performed with a vibrating-wire instrument at temperatures of 303.15 and 323.15 K and pressures up to 70 MPa. The overall uncertainty in the reported viscosity data is estimated to be ±0.5%. A recently developed semiempirical scheme for the correlation and prediction of the thermal conductivity, viscosity, and self-diffusion coefficients of n-alkanes is applied to the prediction of the viscosity of n-heptane, n-nonane, and n-undecane. The comparison of these predicted values with the present high-pressure measurements demonstrates the predictive power of this scheme.     

A generalized scaled equation of state for n-alkanes (methane to n-nonane) in the critical region

A generalized scaled equation of state has been developed to calculate thermodynamic properties of n-alkanes from methane (CH₄) to n-nonane (C₉H₂₀) in the critical region. The equation is valid in the reduced density range 0.7 _c1.3 at T=T _c and up to 1.2T _c at = _c.