The Boltzmann equation for a polyatomic gas

A formulation of the kinetic theory of dilute, classical polyatomic gases is given which parallels the Waldmann development for structureless molecules. In the first section the Boltzmann equation is written in terms of the specific rates of inelastic collision processes and then the properties of these rates and those of the corresponding collision cross sections are examined. The dependence of the distribution function on the dynamical variables is discussed and the equations of change for the gas are derived. Finally, a study is made of the properties of the linearized Boltzmann collision operation. In the second section the Boltzmann equation is deduced from a rigorous statistical-mechanical point of view and discussed in terms of the basic ideas of Bogoliubov. The computationally important special case of impulsive interactions is then considered.This research was supported in part by a grant from the National Science Foundation and in part by the Ames Laboratory of the U. S. Atomic Energy Commission. Contribution No. 2554.     

Brownian diffusion in a nonuniform gas

An analysis is made of the effects on the diffusion of Brownian particles whose Knudsen number is large compared to unity, of nonuniformities in the host gas. As examples, in one type of nonuniformity of the host gas, the Chapman-Enskog velocity distribution function for the gas molecules is used; in the other, the host gas is a free-molecule Couette flow. In both cases, a new force on the Brownian particles appears. Two techniques are used (extending Kramers' method and utilizing the Chapman-Enskog method) to transform the new Fokker-Planck equation into generalized Smoluchowski and convective diffusion equations. In these equations, the diffusion coefficient appears as a second-order tensor. Thus, it is demonstrated that Brownian diffusion in a nonuniform gas is anisotropic.The work of Slinn was financially supported in part by Battelle Memorial Institute and in part by U.S. Atomic Energy Commission Contract AT(45-1)-1830. The work of Shen was supported in part by U.S. Air Force Office of Scientific Research Contract 49(638)-1346.     

Convergence of branching transport processes to branching brownian motion

Two models are given of branching transport processes that converge to branching Brownian motion starting with one initial particle. The martingale problem method is used.     

Evolution of shock wave surfaces and amplitudes in piezoelectric materials

Summary The general problems of the evolution of wave surfaces and amplitudes associated with mechanical and electrical discontinuities in piezoelectric materials are dealt with in this paper. The results presented are relevant to shock waves propagating in all materials obeying the classical constitutive relations of piezoelectricity, including as a special case linear anisotropic elasticity. A specific example concerning BaTiO₃ single crystal is considered. The example illustrates the intricate quantitative results which may be obtained as a consequence of the analyses.

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Riassunto In questo lavoro si trattano i problemi generali della evoluzione delle ampiezze e superfici d'onda associate a discontinuità meccaniche ed elettriche nei materiali piezoelettrici. I risultati presentati sono importanti per onde d'urto che si propagano in tutti i materiali che obbediscono alle relazioni costitutive classiche della piezoelettricità, incluso come caso speciale l'elasticità anisotropica lineare. Si considera uno specifico esempio che riguarda un singolo cristallo BaTiO₃. L'esempio illustra gli intricati risultati quantitativi che si possono ottenere come conseguenza delle analisi.

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Резюме В этой статье рассматриваются общие проблемы эволюции фронтов и амплитуд ударных волн, связанных с механическими и электрическими разрывами в пьезоэлектрических материалах. Полученные реэультаты относятся к ударным волнам, распространяющимся во всех материалах, которые подчиняются классическим конститутивным соотношениям пьезоэлектричества, включая, как частный случай, линейную анизотропную упрутость. Как пример, рассматривается монокристалл BaTiO₃.

     

Thermal diffusion of dilute aqueous NH4Cl,Me4NCl,Et4NCl,n-Pr4NCl,andn-Bu4NCl solutions at 25°C

The Soret effect (thermal diffusion) of dilute aqueous solutions of NH₄Cl, Me₄NCl, Et₄NCl, n-Pr₄NCl, and n-Bu₄NCl has been investigated potentiometrically using the silver, silver chloride thermocell. The molar entropies (heats) of transport have been derived from the initial and final thermoelectric powers. The concentration dependence of the entropy of transport has been examined and the effect of the ionic size on the heat of transport is discussed. The molar entropy of tetrabutylammonium chloride exhibits a sharp minimum in the neighborhood of 0.002M, the reason of which is as yet unclear.     

SYNTHESIS OF LINEAR POLYSILOXANE WITH PENDANT BENZO－15－C－5 MOIETIES AND ITS TRANPORT PROPERTIES IN BULK LIQUID MEMBRANE SYSTEM

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Plasma chemical vapor deposition of TiN

Experiments indicate that the temperature in chemical vapor deposition (CVD) of TiN can be decreased from about 1000°C in conventional CVD to about 500°C by the application of a D.C. nonequilibrium plasma. The hardness of the TiN film is greater than 2000 kg/mm² (Vickers). The effect of pressure, ratio of gas mixture, and discharge parameters on the film deposition rate, its hardness, and microstructures has been studied.     

Anodic oxide growth on Zr in neutral aqueous solution

Anodization and subsequent cathodic reactions on a thin-film sample of Zr were studied with in-situ neutron reflectometry (NR) and electrochemical impedance spectroscopy (EIS). The NR results during anodization showed the originally 485 Å thick Zr film generally behaved similar to a bulk electrode in neutral solution. The anodization ratio measured at applied potentials increased in steps of 0.5 V was somewhat higher than the value determined by coulometry, while the Pilling Bedworth ratio is in good agreement with published data. Thickening of the oxide layer, accelerated immediately after each potential increase, gradually decreased over several hours, but remained nonzero even after ～12 h. The thickened oxide eventually cracked when its thickness reached ～120 Å, causing loss of passivation. Surprisingly, neither the anodization ratio nor the Pilling Bedworth ratio showed any discontinuity at the time of oxide cracking, and the EIS behaviour remained qualitatively as before. This observation is taken as the evidence that the cracked and intact regions of the electrode behave more or less independently as parallel electrodes. When the potential was eventually switched to cathodic polarity, NR shows, as expected, that the effects of oxide cracking were irreversible. However, the electrode resistance recovered partially suggesting the cracks were rapidly plugged with newly formed oxide.     

Applicability of Raoult's law in nonideal mixed solvents

In general, the vapor-pressure change due to the addition of a solute to a solvent mixture does not follow Raoult's law. We have demonstrated thermodynamically that if one adds to a binary solvent mixture solute and solvents in such a way that the vapor-phase composition remains constant, then the decrease of total pressure follows Raoult's law; a supplementary term which vanishes for very dilute solute concentration is introduced as a consequence of the nonideality of the ternary solution. Precise vapor-pressure measurements of dilute solutions of electrolytes and nonelectrolytes in a 40.000 wt. % water-tetrahydrofuran mixture are used in order to illustrate the applicability of Raoult's law under the above conditions. These may be regarded as a particular case of what has been called endostatic conditions, i.e., addition of a solute under constant solvent activity ratio.