Thermophoretic Force on a Small Particle Suspended in a Plasma with a Combined Specular and Diffuse Reflection at the Particle Surface

Additional kinetic-theory analytical results are presented concerning the thermophoretic force acting on a spherical nonmetallic or metallic, nonevaporating or evaporating particle suspended in a plasma for the extreme case of free-molecule regime and thin plasma sheath. A combined specular and diffuse reflection of the atoms incident on or formed in the ion–electron recombination process at the particle surface has been taken into account in this analysis as an extension of the previous paper (Xi Chen, J. Phys. D: Appl. Phys. 30, 826–841, 1997). It has been shown that the specular reflection fraction of gas particles at the surface does not affect the thermophoretic force acting on a nonevaporating, metallic or nonmetallic, spherical particle, but they affect significantly the evaporation-added thermophoretic force. The evaporation-added thermophoretic force decreases linearly with the increase of the specular reflection fraction, and the decreasing rate for a nonmetallic evaporating particle is much greater than that for a metallic one at high plasma temperatures.     

Heat transfer from a rarefied plasma flow to a metallic or nonmetallic particle

Heat transfer from a plasma flow to a metallic or nonmetallic spherical particle is studied in this paper for the extreme case of free-molecule flow regime. Analytical expressions are derived for the heat flux due to, respectively, atoms, ions, and electrons and for the floating potential on the sphere exposed to a two-temperature plasma flow. It has been shown that the local or average heat flux density over the whole sphere is independent of the sphere radius and approximately in direct proportion to the gas pressure. The presence of a macroscopic relative velocity between the plasma and the sphere causes substantially nonuniform distributions of the local heat flux and enhances the total heat flux to the sphere. The heat flux is also enhanced by the gas ionization. Appreciable difference between metallic and nonmetallic spheres is found in the distributions along the oncoming flow direction of the floating potential and of the local heat flux densities due to ions and electrons. The total heat flux to the whole sphere is, however, almost the same for these different spheres. For a fixed value of the electron temperature, the heat flux decreases with increasing temperature ratio T_e/T_h.     

Drag on a metallic or nonmetallic particle exposed to a rarefied plasma flow

Drag force on a metallic or nonmetallic spherical particle exposed to a plasma flow is studied for the extreme case of a free-molecule regime. Analytical expressions are derived for the drag components due to, respectively, atoms, ions, and electrons and for the total drag on the whole sphere due to all the gas species. It has been shown that the drag is proportional to the square of the particle radius or the drag coefficient is independent of the particle radius. At low gas temperatures with a negligible degree of ionization, the drag is caused mainly by atoms and could be predicted by using the well-known drag expression given in ordinary-temperature rarefied gas dynamics. On the other hand, the drag is caused mainly by ions at high plasma temperatures with a great degree of ionization. The contribution of electrons to the total drag is always negligible. Ignoring gas ionization at high plasma temperatures would overestimate the particle drag. There is a little difference between metallic and nonmetallic spheres in their total drag forces, with a slightly higher value for a metallic sphere at high plasma temperatures, but usually such a small difference could be neglected in engineering calculations. The drag increases rapidly with increasing gas pressure or oncoming speed ratio. For a two-temperature plasma, the drag increases at low electron temperatures but decreases at high electron temperatures with the increase in the electron/heavy-particle temperature ratio.Nomenclature C _d Drag coefficient - e Elementary charge - f _D,F _D Local and total drag (N/m ² andN) - f ^– Velocity distribution function for incident gas particles - f ⁺ Velocity distribution function for reflected gas particles - k Boltzmann's constant - m Gas particle mass (kg) - n Number density of gas species (m ^–3) - P ^–,P ⁺ Surface pressure due to incident and reflected gas particles - R ₀ Sphere radius (m) - S Speed ratio,S _j=U/(2kT _j/m_j)^1/2 - T _e,T _h Electron and heavy-particle (atom, ion) temperature - T _w Wall temperature - U Oncoming plasma flow velocity - v _x, v_y, v_z Velocity components of gas particles in thex, y, andz directions (m/sec) - v Thermal motion speed of gas particles,v _j =(8kT _j /m _j )^1/2 - v _ze Smallestv _z of electrons which could reach the sphere surface,v _ze=(2e/m _e)^1/2 (m/sec) - v _zw Value ofv _z of ions or electrons as arriving at the sphere surface (m/sec) - Center angle - Gas density (kg/m³) - Shear stress (N/m²) - Absolute value of the floating potential (V) - , Local and total particle fluxes incident to the surface - a Atoms - e Electrons - h Heavy particles - i Ions - j jth gas species - m Metallic sphere - mn Nonmetallic sphere A preliminary version of this paper was presented at the Eighth International Symposium on Plasma Chemistry held in Tokyo, September 1987.     

Plasma-particle momentum transfer under conditions of great knudsen numbers and thin plasma sheath

Particle drag force and thermophoresis results previous obtained are revised by including modified expressions for ion and electron components of the surface pressure. The present analysis shows that there is almost no difference between non-evaporating metallic and nonmetallic particles in their drags and there is only a little difference between those particles in their thermophoretic forces. The effect of evaporation on thermophoretic and drag forces is still marked, but the drag or thermophoretic force ratio with to without accounting for evaporation assumes somewhat different values from those obtained previously and depends notably on whether the particle is metallic or nonmetallic at high plasma temperatures.     

Thermophoretic force acting on an evaporating particle suspended in a rarefied plasma

Analytical results of the thermophoretic force on an evaporating spherical particle immersed in a rarefied plasma with a large temperature gradient are presented for the extreme case of free-molecule regime and thin plasma sheath. It has been shown that the existence of a temperature gradient in the plasma causes a nonuniform distribution of the local heat flux density on the sphere surface with its maximum value at the fore-stagnation point of the sphere, although the total heal flux to the whole particle is independent of the temperature gradient existing in the plasma. This nonuniform-distribution of the local heat flux density causes a nonuniform distribution of the. local evaporated-mass flux and related reaction force around the surface of an evaporating particle, and thus causes an additional force on the particle. Calculated results show that the thermophoretic force on an evaporating particle may substantially exceed that on a nonevaporating one, especially for the case of a metallic particle (with infinite electric conductivity). The effect of evaporation on the thermophoretic force is more pronounced as the evaporation latent heat of the particle material is comparatively low and as high plasma temperatures are involved.     

Drag force acting on an evaporating particle immersed in a rarefied plasma flow

Analytical expressions are presented for the drag force acting on an evaporating or nonevaporating particle immersed in a plasma flow for the extreme case of free-molecule flow regime and thin plasma .sheath. It is shown that the drag force on a spherical particle is proportional to the square of the particle radius and to the relative velocity between the particle and the bulk plasma at low speed ratios. The existence of a relative velocity between the particle and the plasma results in a nonuniform heat flux distribution with its rnaximum value at the frontal stagnation point of tire sphere. This nonuniform distribution of the local heat fux density causes a nonuniforrn distribution of the local evaporated-mass flux and vapor reaction force around the surface of an evaporating particle, and thus induces an additional force on the particle. Consequently, the drag force acting on art evaporating particle is always greater than that on a nonevaporating one. This additional drag force due to particle evaporation is more significant for nonmetallic particles and for particle materials with lower latent heat of evaporation and lower vapor molecular mass. It increases with increasing plasma temperature and with decreasing gas pressure at the high plasma temperatures associated with appreciable gas ionization. The drag ratio increases with increasing electron/heavy-particle temperature ratio at high electron temperatures for a two-temperature plasma.     

Two-Temperature Transport Coefficients in Argon–Hydrogen Plasmas—II: Inelastic Processes and Influence of Composition

Recently, a two-temperature transport properties theory has been proposed that retains the coupling between electrons and heavy species in thermal plasmas where the kinetic temperature of electrons Te can be different from that of heavy species Th. This paper is devoted to the application of this approach to an argon–hydrogen mixture at atmospheric pressure, taking into account inelastic processes and considering chemical equilibrium. In this second part are studied: the development of a new method to calculate the reaction thermal conductivity (inelastic collisions) in a non-equilibrium (two-temperature) plasma taking into account the coupling between electrons and heavy species; the influence of the composition calculation methods comparing the modified equilibrium constant method used in part 1 to the stationary kinetic calculation one; the influence on the transport properties (, , ) of the composition calculation method and non-equilibrium parameter =T_e/T_h.The different plasma compositions obtained either through an equilibrium constant or a stationary kinetic method are first compared and, for example, for =1.6, a discontinuity at T_e=11,000 K and an ionization delay are observed in stationary kinetic calculation, relative to the equilibrium constant method. Electrical conductivity, viscosity as well as thermal conductivity, including the translational, internal and reactional contributions, are calculated up to 25,000 K. It is shown that the plasma composition has a strong influence on transport coefficients, inducing shifts or discontinuities in the curves of transport coefficients, depending on the chosen method of calculation.     

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.

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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.

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

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

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.     

Some Anomalies in Coadsorption of Two Organic Substances Due to Differences in Molecular Interaction of Species Undergoing Coadsorption

Effect of molecular interaction between species undergoing coadsorption on the potential dependences of coverages ₁and ₂, surface tension, and equilibrium and nonequilibrium differential capacitances is analyzed on the basis of a set of isotherms for coadsorption of components 1 and 2 within a common monolayer when the EDL inner part obeys a model of three parallel capacitors. It is shown that, in a certain potential interval, at a certain ratio between adsorption parameters, the set of isotherms may have solutions that correspond to a minimum in a free energy surface, which is a function of ₁and ₂.     

Effects of adsorbed bismuth on Si(001) surface electronic states

It is shown that depositing Bi on an Si(001) surface fills the free broken-bond surface states, whose concentration decreases linearly as the bismuth coating 8 increases up to _st, = 0.6 monolayer. The bismuth desorption activation energy is constant < _st, (E_d = 2.77 ± 0.1 eV) and decreases for > _st.Taras Shevachenko Kiev National University, ul. Vladimirskaya 64, 252601 Kiev-17, Ukraine. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 32, No. 3, pp. 168–171, May–June, 1996. Original article submitted September 19, 1995.     

Heat transfer to nonspherical particles in a rarefied plasma flow

The interaction of a nonspherical metallic or nonmetallic particle with a rarefied thermal plasma flow is considered. Heat transfer to a particle of arbitrary shape with an extremely thin plasma sheath due to, respectively, gas molecules, electrons, and ions is described. Analytical expressions are derived for charge and heat fluxes in the particular case of a spheroidal metallic or nonmetallic particle in a subsonic plasma flow. It has been shown that the intensity of heat exchange is greatly influenced by gas ionization, charge transfer processes, and particle shape, velocity, and orientation in the plasma flow.     

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.     

Preparation of Highly Oriented LaNiO3 Thin Films by Spin-Coating Technique

LaNiO3 thin films were deposited by spin-coating technique on various substrates using metal naphthenates as starting materials. Highly oriented LaNiO3 films with smooth and crack-free surfaces grown on SrTiO3 (100) and LaAlO3 (012) substrates were observed by XRD -2 scans, while film on sapphire (0001) substrate showed polycrystalline structure. The resistivity vs. temperature curves of the textured LaNiO3 films showed that the film possessed good metallic character.     

Investigation of supported WO3 catalysts for propene metathesis by diffuse reflectance spectroscopy

Diffuse reflectance spectra have been recorded for WO₃/SiO₂ and WO₃/-Al₂O₃ catalysts after various steps of treatment of these samples, in particular, after treatment of WO₃/SiO₂ by HCl. It is shown that for WO₃/-Al₂O₃ the temperatures of the onset of reaction and WO₃ reduction coincide.

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WO₃/SiO₂ WO₃/-Al₂O₃ , , WO₃/SiO₂ HCl. , WO₃/-Al₂O₃ .

     

Two-Temperature Transport Coefficients in Argon–Hydrogen Plasmas—I: Elastic Processes and Collision Integrals

The calculation of two-temperature transport coefficients in an argon–hydrogen plasma at atmospheric pressure is performed using a new theory of two-temperature transport properties recently presented. The latter takes into account the coupling between electrons and heavy species, coupling neglected in the already existing theories of Devoto and Bonnefoi. Transport coefficients are calculated at two-temperatures, the kinetic temperature of electrons T_e being different from that of heavy species T_h. This paper is divided into two parts. The first one is related to elastic processes and its aim is to compare the results obtained with this new theory for viscosity , translational thermal conductivities ^tr _e and ^tr _h and electrical conductivity with the previous results of Bonnefoi. The composition is calculated with the modified equilibrium constant of van de Sanden et al. and the most recent interaction potential are discussed. As it could be expected the electron translational thermal conductivity and the electrical conductivity calculated when taking into account or not the coupling between electrons and heavy species show non-negligible discrepancies. Besides this comparison, the results also show the drastic influence of the non-equilibrium parameter =T_e/T_h on the values of , , ^tr _e, and ^tr _h.     

Lower critical solution temperature (LCST) and theta temperature of aqueous solutions of nonionic surface active agents of various polyoxyethylene chain lengths

Cloud points of aqueous solutions of homogeneous poly(oxyethylene)dodecyl ether derivatives (C₁₂(OE)_n: n=2–8) and the apparent theta temperatureT ^ap were determined from the abrupt changes in optical transmittance and the temperature dependence of the second virial coefficient obtained by light scattering measurements. It was found that the lower critical solution temperature (LCST) shifts to a lower temperature and lower concentration as the number of oxyethylene units in a molecule decreases. Because of this behavior of LCST, the modified Flory-Schultz plot of phase separation was applied to the present nonionic surfactant-water system, and its theta temperature obtained. The dependence ofT ^ap on the number of oxyethylene units suggests that the polyoxyethylene chain has different effects on the solubility of C₁₂(OE)_n in water forn less than or equal to 3 from those forn greater than or equal to 4.     

Mechanism of ring expansion in 1-ethylindane under dehydrogenation conditions

Studies of 1-ethyl-(-¹⁴C)-indane dehydroisomerization over a Pt/Al₂O₃ catalyst (AP-64) have revealed that 34.5% or 16.5% of the initial tracer label migrates into the -position of the expanded methylnaphthalene ring when the catalyst is pretreated at 763 K in Ar or H₂, respectively. The reaction mechanism is discussed.

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1--(¹⁴C)- -64. , 763 - 34,5% , —16,5%. .

     

Ferromagnetism of Two-Bridge Clusters

A generalized model of angular overlapping was used to analyze the magnetic properties of polynuclear complexes. The structural elements of these complexes contain planar binuclear fragments of the M(LR)₂M type. The maximum ferromagnetism for the monoatomic bridges corresponds to = MLM, which is about 100°. Weak planar interactions between L and R displace the ferromagnetism maximum towards lower , while interactions shift it towards higher . In almost all cases, strong planar interactions (LLR 180°) are responsible for strong antiferromagnetism.