New Method to Calculate Thermodynamic and Transport Properties of a Multi-Temperature Plasma: Application to N2 Plasma

Multi-temperature thermal plasmas have often to be considered to account for the nonequilibrium effects. Recently André et al. have developed the calculation of concentrations in a multi-temperature plasma by artificially separating the partition functions into a product by assuming that the excitation energies are those of the lower levels (electronic, vibration, and rotation). However, at equilibrium, differences, increasing with temperature, can be observed between partition functions calculated rigorously and with their method. This paper presents a modified method where it has been assumed that the preponderant rotational energy is that of the vibrational level v=0 of the ground electronic state and the preponderant vibrational energy is that of the ground electronic state. The internal partition function can then be expressed as a product of series expressions. At equilibrium for N ₂ and N ₂ ⁺ partition functions the values calculated with our method differ by less than 0.1% from those calculated rigorously. The calculation has been limited to three temperatures: heavy species T_h , electrons T_e , and vibrational T _v temperatures. The plasma composition has been calculated by minimizing the Gibbs free enthalpy with the steepest descent numerical technique. The nonequilibrium properties have been calculated using the method of Devoto, modified by Bonnefoi and Aubreton. The ratio =T_e/T_h was varied between 1 and 2 as well as the ratio _v =T _v /T _h for a nitrogen plasma. At equilibrium the corresponding equilibrium transport properties of Ar and N ₂ are in good agreement with those of Devoto and Murphy except for T>10,000 K where we used a different interaction potential for N–N ⁺ . The effects of _v and _e on thermodynamic and transport properties of N ₂ are then discussed.     

Kinetics of oxidation of fullerene C60 with dimethyldioxirane

The kinetics of the reaction of dimethyldioxirane with fullerene C₆₀ was studied, and the activation parameters logk = (8.3±0.8) – (14.2±0.9)/, ( = 2.3RT kcal mol^–1) (20—45°C) were determined. The formation of paramagnetic particles was detected.     

A comparison of experimental measurements and theoretical predictions regarding the behavior of a turbulent argon plasma jet discharging into air

Computed results are presented describing the temperature and concentration fields obtained when an argon plasma jet is being discharged into ambient air. A previously published mathematical model for turbulent plasma plumes is used for the calculations. These predictions are compared with recent), published experimental measurements by Brossa and Pfender, performed with an enthalpy probe. The theoretical predictions appear to agree reasonably well with the measurements of both the temperature and concentration profiles, with a maximum deviation in the 10–20% range.Notation A _max maximum temperature or velocity in the torch exit profile - C ₁ C ₂ C _D constants inK- model - h enthalpy - I torch current - K turbulent kinetic energy per unit mass - m mass concentration of plasma p pressure - Q How rate of argon through the torch - r radial coordinate - r _n nozzle radius (inside) - S source term for dependent variable      

Solvent extraction of halogens

Summary The solubility formula previously proposed was applied to the partition of halogens between water and some typical organic solvents, and the character of parameter in the formula was examined. The formula reproduces the experimental data of the solvent extraction of halogens reasonably. The ratio is controlled by the solute independently of the solvent. The ratio is unity for all solutes in the water-hydrocarbon system, and is 3 ^n–1 (n is periodic number) depending on the solute in the water-non-hydrocarbon system.

---

Lösungsmittelextraktion von Halogenen

Zusammenfassung Die früher vorgeschlagene Löslichkeitsformel wurde auf die Verteilung von Halogenen zwischen Wasser und einigen typischen organischen Lösungsmitteln angewendet und der Charakter des Parameters in der Formel untersucht. Die Formel gibt die experimentellen Werte der Halogenextraktion zufriedenstellend wieder. Das Verhältnis der -Werte wird vom Gelösten unabhängig vom Lösungsmittel bestimmt. Dieses Verhältnis ist im Wasser-Kohlenwasserstoff-System in allen Fällen gleich 1. Im System aus Wasser und Nicht-Kohlenwasserstoff hängt es vom Gelösten ab und beträgt 3 ^n–1 (n = Periodenzahl des Halogens).

     

Simple electrostatic models for vibrating unsymmetrical triatomic molecules and triatomic ions

Bond charge, point-dipole models are used to derive simple universal relations,K =0.0435 (K₁₁ K ₂₂)^1/2 –0.0086 (K ₁₁ ⁺ K ₂₂), andK = 0.11 (K ₁₁ K ₂₂)^1/2 –0.0055 (K ₁₁ +K ₂₂), between the bond stretching force constantsK ₁₁ andK ₂₂ and bond bending force constantK for linear and bent unsymmetrical triatomic molecules respectively. The relations are shown to be approximately valid for a number of molecules. An extension of the models to include charged species (ions) in triatomic molecules is also presented and tested, giving good results.Based on part of a thesis submitted by José L. Gázquez in partial fulfillment of the requirements for the degree of Doctor of Philosophy, The Johns Hopkins University, 1976, and aided by research grants to the Johns Hopkins University and University of North Carolina from the National Institutes of Health and the National Science Foundation.     

Activity coefficients for ternary systems: VI. The system HCl + MgCl2 + H2O at different temperatures; application of Pitzer's equations

Electromotive-force measurements have been made on HCl–MgCl₂–H₂O mixtures at 5, 15, 25, 35 and 45°C at eleven different ionic strengths from 0.1–5.0 mol-kg ^–1 . The results are interpreted in terms of the simple Harned's equations, as well as the more complicated Pitzer ion-component treatment of multicomponent electrolyte mixtures. Activity coefficients for HCl in the salt mixtures obey Harned's rule up to and including I=5.0. For the salt in the acid mixtures, Harned's rule holds true up to and including I=0.5. The contribution of higher-order electrostatic terms (E and E') in the Pitzer equations is important for accurate evaluations of unlike cation-cation interactions (_H,Mg), and cation-anion-cation interactions (_H,Mg,Cl). The values of^S_H,Mg and _H,Mg,Cl (determined with E and E'), _H,Mg and _H,Mg,Cl (determined without E and E'), as well as the trace activity coefficients of HCl, _tr ^A , in solutions of MgCl₂ (where ionic strength fraction of the salt,y _B = 1) at all the experimental temperatures and ionic strengths, are reported. Results of this study are compared with those for similar systems. At I=0.1 and 25°C, the results of the Brönsted-Guggenheim specific interaction theory are discussed briefly.     

Enthalpy-entropy compensation in ionic micelle formation

The enthalpy-entropy compensation in ionic surfactant micellization process over a large temperature range is examined. The surfactants SDS and C₁₆TAB are investigated experimentally, and the enthalpy and entropy changes are evaluated based on phase separation or mass action models together with the other three surfactant systems. The relationship between compensation temperature and the reference temperatures is discussed.Notations C _p heat capacity change, J/mol-K - CMC critical micelle concentration,M - CMC₀ critical micelle concentration atT=T ₀,M - G Gibbs free energy change, kJ/mol - H enthalpy chang, kJ/mol - h _c enthalpy change for transfer of a methylene group to water, kJ/mol - R gas constant, 8.314 J/mol-K - S entropy change, J/mol-K - S _c entropy change for transfer of a methylene group to water, J/mol-K - S ^* entropy change atT=T ^*, J/mol-K - T temperature,K - T _c compensation temperature, K - T _H temperature at which H=0, K - T ₀ temperature at the minimum point, K - T ^* 112°C Greek Letters degree of dissociation     

Steric repulsion of polyoxyethylene groups for emulsion stability

Rapid coalescence was studied on liquid paraffin emulsion stabilized with a series of poly(oxyethylene) dodecyl ethers [C₁₂H₂₅ (EO),n=1, 2, 3, 4, 5, 6, 7, 8] and of poly(oxyethylene) nonylphenyl ethers [C₉H₁₉(EO) _n ,n=2, 4, 5, 6, 12]. The turbidity of emulsion was measured as a function of the solution pHs at constant ionic strength of 0.1 mol dm^–3.As a result, it was found that the emulsions (which were formed with C₁₂H₂₅(EO) _n surfactants having less than four oxyethylene groups, or with C₉H₁₉ (EO) _n surfactants having less than six oxyethylene groups) brought about rapid coalescence in the bulk pH between 2.03.5, which corresponded to the zero point of charges for the emulsions of the present systems. According to the Tadros treatment for emulsion flocculation, the total flocculation potennual was estimated as a function of the distance relative to the number of oxyethelene groups in the surfactants. The critical coalescence energy was obtained as –343 ×10^–19 J for the C₁₂H₂₅(EO) _n surfactants and –2.14×10^–19) J for the C₉H₁₉ (EO) _n surfactants. Furthermore, the formation of a hole for coalescence was estimated under the simple assumption that the coalescence was caused only by the energy dissipation.     

Kinetics of Gold Electrodeposition from Cyanide Electrolytes at a Monitored Surface Coverage by Thallium Atoms

A procedure for measuring kinetic parameters of gold electrodeposition in the presence of catalytically active thallium(I) ions while monitoring the coverage of the gold surface by thallium adatoms, , is described. The procedure accounts for the duration of contact between a freshly renewed surface of gold and a thallium-containing solution and assumes that the incorporation rate of thallium adatoms is proportional to and the current density of gold electrodeposition. At = const, kinetic dependences correspond to the Tafel equation. Values of and i ₀ increase with . At = 0.3, 0.6 and i ₀ 3 × 10^–4 A cm^–2, which conforms to values calculated from anodic curves obtained in similar conditions.     

Temperature and velocity fields in a gas stream exiting a plasma torch. A mathematical model and its experimental verification

A mathematical model was developed to predict the velocity and temperature fields in a free plasma jet issuing from a D.C. plasma torch. It was assumed that the temperature and velocity at the torch nozzle were specified and the turbulent Navier-Stokes equations were solved in conjunction with a two-equation model of turbulence and the energy transport equation. The model was formulated in terms of the two-dimensional elliptic equations to facilitate its future extension to nonparabolic problems. The predictions of the model were compared with experimental measurements obtained from laser Doppler and spectroscopic techniques. Good overall agreement was found between the theoretical predictions and the experimental measurements for two sets of initial conditions corresponding to nitrogen/hydrogen and argon/hydrogen plasmas. Radiation was found to have a small effect on the overall heat transfer process, and it is suggested that the assumption of an optically thin radiation loss per unit volume is sufficiently accurate for most engineering applications. The significance of this work lies in the fact that, for the first time, it is possible to test the assumptions of the current model against a reliable set of experimental measurements.Notation C ₁,C ₂,C _D constants inK- turbulence model, Table III - C _P average specific heat of plasma at constant pressure - h ₁ length of integration region - h ₂ width of integration region - K turbulent kinetic energy per unit mass - P pressure - r radial coordinate - R ₀ internal radius of anode - S _K source term forK equation - S _R radiation loss per unit volume - S source term for equation - T ₀ temperature of plasma atz=0 - T temperature of plasma - T _a ambient temperature - u velocity inz direction - u ₀ velocity of plasma atz=0 - v radial velocity of plasma - z axial coordinate - dissipation rate of turbulence energy - , _eff, _t molecular, effective, and turbulent viscosities, respectively - density - _K, _T, Prandtl numbers forK, T, and, respectively     

Interelectronic angle densities of atoms in momentum space

For the 102 atoms from He to Lr in their ground states, the Hartree–Fock interelectronic angle densities,¯A(¯₁₂), in momentum space are reported, where ¯₁₂ is the angle between the momentum vectorsp₁ and p₂ of two electrons. In the first three atoms, He–Be, ¯A(¯₁₂) is found to be uniform independent of ¯₁₂, while in the remaining 99 atoms,¯A(¯₁₂) is larger for a large ¯₁₂ than for a small ¯₁₂. Accordingly, the average interelectronic angles in momentum space are 90° precisely for the three atoms and greater than 90° for the 99 atoms.     

Effect of pore size distribution on the surface diffusivity in activated carbon: Hybrid Dubinin-Langmuir isotherm

The concentration dependence of the observed surface diffusivity for activated carbon due to the pore size distribution is theoretically investigated. The mathematical model is derived based on the assumption of a local hybrid adsorption isotherm (proposed recently by Shethna and Bhatia, 1994) and a local surface diffusive flux for a particular pore of half widthr. Using those local quantities and assuming a Gamma pore size distribution, the observed surface diffusivity is obtained. This observed surface diffusivity was found to increase rapidly with loading if the chemical potential is the driving force for surface flow. Furthermore, this observed surface diffusivity,D/D(0), was found to be the same as the Darken thermodynamic correction factor, using only the macroscopic isotherm information. This indicates that the thermodynamic correction factor contains information on the averaging of the surface heterogeneity.Nomenclature a coefficient for surface diffusivity - A adsorbate molecular area - c affinity parameter of the surface adsorption isotherm - C(P, T) concentration - C _max maximum adsorbed concentration - D _obs observed surface diffusivity - D _s intrinsic surface diffusivity - D _s0 coefficient of intrinsic surface diffusivity - E ₀ characteristic energy of Dubinin isotherm - F(r) pore size distribution - J local flux - J _obs observed flux - k empirical constant of Dubinin isotherm - K Langmuir affinity parameter - K _m Langmuir affinity parameter at maximum micropore half width - m structural parameter defined in Eq. (13) - n Dubinin variable exponent - q structural parameter defined in Eq. (13) - Q function ofr andT defined in Eq. (4) - Q _m function ofn defined in Eq. (8) - P pressure - P ⁰ vapour pressure - P _t threshold pressure defined in Eq. (3) - P ₀,P _L pressure at two end of the slab - P minimum pressure for Dubinin isotherm - P _m threshold pressure at maximum micropore half width - S ₁,S ₂ scaling factors defined in Eq. (15) - r pore half width - r ₀ smallest micropore half width - r _t threshold micropore half width demarcates Dubinin and Langmuir mechanisms - r _m maximum micropore half width - v _M liquid molar volume of adsorbate - V pore volume - R gas constant - T temperature - x axial variable - parameter defined in Eq. (A-7) - affinity factor of Dubinin isotherm - _L constant defined in Eq. (A-7) - small number - pore variance - non dimensional local isotherm - _D non dimensional Dubinin isotherm - _L non dimensional Langmuir isotherm - _S non dimensional surface isotherm - _obs non dimensional overall adsorption isotherm     

Analysis of the Probability of the Mössbauer Effect in Iron(III) β-Diketonates

The probability of the Mössbauer effect f has been evaluated and the Debye temperatures of intermolecular vibrations _M at 295 and 78 K have been determined for ten Fe(III) -diketonates, which are complexes of molecular type. Variation of _M with temperature and molecular mass M has been found; in the latter case, _M decreases as M increases. As a result of this antibatic change in _M and M, the effect of a decreased energy of intermolecular interaction dominates the effect of increased molecular mass, and f decreases in conformity with the prediction provided by the molecular crystal model.     

Solubility of inert gases and liquid hydrocarbons in water

The thermodynamic statistical model based on the distribution of molecular populations among energy levels has been employed for the analysis of the solubility of hydrocarbons and other inert gases or liquids in water at different temperatures. The statistical distribution is described by a convoluted partition function Z_G·_s. The product of a grand canonical partition function Z_G represents the distribution of the species in the reaction while the canonical partition function Z_G represents the properties of the solvent. The first derivative of the logarithm of the partition function with respect to 1/T is the apparent enthalpy which is the result of the contributions of the separate partition functions, {H_aap}_T=H^o+n_wC_p,wT, where {H_app}_T refers to Z_G, n_wC_p,wT=–H_w to _s, and H^o is the change in enthalpy of hydrocarbon-water reaction. The plot {H_app}_T vs/ T results in a straight line with slope n_w at constant C_p,w. The apparent enthalpy is obtained from the coefficients of the polynomial fitting of the solubility data, as a function of 1/T. Alternatively, the apparent enthalpy can be determined calorimetrically. The enthalpy thus obtained is a linear function of the Kelvin temperature. The values of n_w range from 1.6, 1.9, 5.6 to 5.8 for helium, hydorgen, butane and hexane, respectively. For fluorocompounds the range of n_w is 10.1 to 11.1 indicating that n_w is a function of the number of water molecules expelled from the cage of solvent to form a cavity to host the solute molecule. The analysis of several sets of calorimetric or solubility data with the present molecular thermodynamic model yields values of H^o and n_w consistent with the size of the dissolved molecules.List of Symbols p pressure - H _ij average enthalpy - H _i level enthalpy (=H) - H _i enthalpy difference - H _ij intersublevel energy difference - i index of level - j index of sublevel - Z_G grand canonical partition function - _S canonical partition function - Z_G- convoluted partition function - –G ^o/RT standard Gibbs energy normalized toRT - –H ^o/RT standard enthalpy normalized toRT - S ^o/R standard entropy normalized toR - C _p molar heat capacity - T absolute temperature - H _G- enthalpy of the convoluted ensemble - H _G enthalpy of the solute - H enthalpy of the solvent - H _app apparent enthalpy - H _w enthalpy of water - C_yH_z hydrocarbon - W water - K _s solubility equilibrium constant - x ₂ molar fraction of solute - C_yH_zW_(x-nw) hydrocarbon molecule trapped in a cavity - K _H Henry constant - P _s solubility product - [W] concentration of water - reference temperature - a, b, c, d coefficients of the fitting polynomial - {H _app}_T apparent enthalpy at temperatureT - {H }_T standard enthalpy at temperatureT - {H _w}_T water contribution to enthalpy at temperatureT - C _p,w isobaric molar heat capacity of water - L Ostwald coefficient - C _p isobaric heat capacity difference - Bunsen coefficient - C _p,app apparent isobaric heat capacity difference - n _C number of carbon atoms in the chain - h _w interaction enthalpy of one water molecule - H ₀ intercept for the extrapolated enthalpy     

Studies of Nanocrystalline Phase and Residual Amorphous Phase of FeCuNbSib Alloy Using TG(M) Technique

The —T and d/dT—T curves of the FeCuNbSiB amorphous alloy, which are the relationship between the total saturated magnetic moment per unit mass and temperature, are investigated by magnetic thermogravimetry analysis (TG(M)) technique. It is found that the crystallization process of the samples can be divided into five stages. The studies of samples annealed in temperature range of 480–610°C for 1h show that when the annealing temperature (T_a) is less than 540°C, the quantity of nanocrystalline -Fe(Si) phase increases evidently with T_a, and the Curie temperature (T_C) of residual amorphous phase also increases linearly with T_a, i.e. T_C=0.52T_a+91.7°C, with correlation coefficient =0.98. The variation of volume fraction of -Fe(Si) nanocrystalline phase or residual amorphous phase with T_a is measured by TG(M) technique.This revised version was published online in November 2005 with corrections to the Cover Date.     

Effect of Lead Ions on the Kinetics of Gold Deposition from Cyanide Electrolytes

The depolarization of the gold electrodeposition in the presence of lead ions depends on their concentration and the duration of electrode contact with solution preceding a potential scan in an extremum fashion. At constant coverages of the gold surface by lead adatoms , the process rate depends on the overvoltage in accord with the Tafel equation. Effective values of the exchange current i ₀ and transfer coefficient increase with from i ₀ 3 × 10^–5 A cm^–2 and = 0.23 in pure solutions to 3 × 10^–4 A cm^–2 and 0.53 at 0.4. The reaction order by cyanide ions is independent of and equals nearly –0.9. Effects of lead adatoms on the kinetics of cathodic and anodic processes are compared and the obtained data may be brought to conformance given that their mechanisms in pure solutions differ and converge in the presence of lead adatoms.     

151Eu Mössbauer Study of Calcium Aluminate Glass and Glass Ceramics Containing a Small Amount of Europium(III)

¹⁵¹Eu Mössbauer spectrum of IR-transmitting calcium aluminate glass, 60CaO·32Al₂O₃·5Fe₂O₃·3Eu₂O₃, consists of a broad peak due to distorted Eu(III) with and values of 0.91 and –2.02 mm·s^–1, respectively. Debye temperatures (_D) of 360 and 320 K were obtained from the temperature dependence of absorption area (A) and that of , respectively. These _D values indicate that Eu(III) atoms occupy substitutional sites of distorted Al(III)O₄ tetrahedra in calcium aluminate glass. The value of 0.62 mm/s obtained from the heat-treated sample (glass ceramic) indicates that Eu(III)-O bonds became less covalent. A smaller value of –1.20 mm·s^–1 was obtained for Eu(III) in the glass ceramic, indicating less distorted Eu(III)O₄ tetrahedra.     

Origin of the conical intersection between the singlet ionic excited surfaces of twisted ethylene

The potential surfaces of the two valence ionic singlet excited states of twisted ethylene are known to exhibit a conical intersection for a twist angle of the double bond near 82°, and no pyramidalization of the CH₂ groups. The factors responsible for the stabilization of the symmetric excited state near 90° are shown to be ( )² and ( ^*)² double excitations. The analysis is performed in the Quasi Degenerate Perturbation Theory formalism. The analogy with the ¹ A _g ³ B _u ordering problem of the diradical ground and lower triplet states through a double spin polarization of the system is established.     

Geometry and force constant determination from correlated wave functions for polyatomic molecules: Ground states of H2O and CH2

Ab initio calculations including electron correlation are reported for the water and methylene molecules as a function of geometry. A large contracted gaussian basis set is used and the multiconfiguration wave functions, optimized by the iterative natural orbital procedure, include 277 and 617 configurations for H₂O and CH₂ respectively. The method of selecting configurations, yielding first-order wave functions, is discussed in some detail. For H₂O, the SCF geometry is r=0,942 Å, =105,8°, the correlated result is r=0,968 Å, =103,2°, and the experimental r=0,957 Å, =104,5°. The water stretching force constants, in millidynes/Å, are 8,72 (SCF), 8,75 (CI), and 8,4 (experiment). Bending force constants are 0,88 (SCF), 0,83 (CI), and 0,76 (experiment). For methylene the SCF geometry is r=1,072 Å, =129,5°, while the result from first-order wave functions is r=1,088 Å, =134°. The predicted CH₂ force constants are 6,16 (SCF) and 6,13 (CI) for stretching and 0,44 (SCF) and 0,33 (CI) for bending.

---

Zusammenfassung Es wird über ab intito-Rechnungen mit Berücksichtigung der Elektronenkorrelation berichtet, die an Wasser- und Methylenmolekülen als Funktion der Geometrie durchgeführt worden sind. Dazu benutzt man einen großen kontrahierten Gauß-Basissatz. Die Multikonfigurationswellenfunktionen, die unter Benutzung von natürlichen Orbitalen nach der iterativen Prozedur optimiert werden, enthalten für H₂O 277 Konfigurationen und für CH₂ 617. Die Auswahlmethode, die zu Wellenfunktionen 1. Ordnung führt, wird diskutiert. Im Falle des Wassers erhält man die SCF-Geometrie zu r=0,942 Å, =105,8°, das korrelierte Resultat ist: r=0,968 Å, =103,2° und das experimentelle r=0,957 Å, =104,5°. Für Wasser ergeben sich die Valenzkraftkonstanten (in Millidyn Å^–1) 8,72 (SCF), 8,75 (CI) und 8,4 (Experiment). Die Deformationskonstanten sind 0,88 (SCF), 0,83 (CI) und 0,76 (Experiment). Im Falle des Methylens ist die SCF-Geometrie r=1,072 Å, =129,5°, während man mit Wellenfunktionen 1. Ordnung r=1,088 Å und =134° erhält. Die CH₂-Kraftkonstanten werden für die Valenzschwingung zu 6,16 (SCF) und 6,13 (CI) bzw. für die Deformationsschwingung zu 0,44 (SCF) und 0,33 (CI) vorausgesagt.

---

---

Work performed under the auspices of the U.S. Atomic Energy Commision.

---

Supported by the grants from the Research Corporation and the University of California Committee on Research.     

A calorimetric investigation into copper–arginine and copper–alanine solid state interactions

Complexes of formula CuCl₂ · 2arg and CuCl₂ · 4ala (arg = arginine; ala = alanine) were prepared at room temperature by a solid state route. The metal–amino acid solid state interactions were studied by i.r. spectroscopy and solution calorimetry. For both complexes, participation of the carboxylate group as well as nitrogen in coordination are inferred, based on the i.r. data. For the copper–arginine compound, the calculated thermochemical parameters are: _rH_m = –114.9 ± 1.42 and _fH_m = –1608.3 ± 11.6 kJ mol^–1. For copper–alanine compound, a complete set of thermochemical parameters were calculated: _rH_m = –18.0 ± 0.9; _fH_m = –2490.4 ± 4.3; _DH_m = 597.2 ± 17.7; _MH_m = 771.9 ± 18.7; _gH_m = 627.1 ± 22.3 and D (Cu–L) = 156.8 ± 5.7 kJ mol^–1. Based on _rH_m and dissolution enthalpy values, a stronger intermolecular solid state interaction can be inferred for the arginine complex, than for the alanine one complex, probably due to the formation of intermolecular hydrogen bonds in the former.