Distribution functions, Fn(z, {n}), for multicomponent systems are defined proportional to the probability density that n molecules in an infinite isothermal system of fugacity set z will occupy the configurational coordinates symbolized by {n}. All thermodynamic functions may be obtained as certain sums of integrals of these distribution functions. These sums are always convergent, but impractically slow in convergence for numerical use without further transformation. In particular, the grand-partition function, exp [VP(z)/kT], may be expanded in a power series in the fugacities z with coefficients given by integrals of the distribution functions Fn(0, {n}) at the fugacity set 0. As has been previously demonstrated for one component systems, this is shown to be a special case of a more general relation permitting the calculation of the distribution functions (and therefore the thermodynamic functions) for one fugacity set from those at another set. The function —kT ln Fn(z, {n}) is the potential of average force, Wn(z, {n}), of n molecules at the fugacity set z; at zero fugacities, the potential of average force is simply the potential energy. When only short range forces are present, by employing the procedure previously used for the imperfect gas, the integrals of the distribution functions may be simplified to integrals of lower order which become the coefficients in such expressions as the power-series expansion of the pressure increment in terms of the fugacity increments. These series have the advantage of a much higher rate of convergence than those involving integrals of the distribution functions, themselves; however, they do not converge when the initial and final fugacity sets bridge a phase transition. The general equations are applied to the imperfect multicomponent gas, to isotopic gas mixtures, and to condensed systems with the variables converted to the usual activities and activity coefficients. A change of independent variable with a corresponding change in coefficients then permits the evaluation of the pressure increment in terms of the solute concentrations. The equations for osmotic pressure are developed and found to be entirely analogous to those for the pressure of an imperfect gas. Finally, the osmotic pressure in a binary system and its behavior near phase transitions are discussed with emphasis on the critical mixing phenomenon, for which the existence of a region of anomalous first-order transition is shown to be probable.
Two portable aerosol time-of-flight mass spectrometers (ATOFMS) of identical design are described. These instruments are powerful new tools for providing temporal and spatial information on the origin, reactivity, and fate of atmospheric aerosols. Each is capable of analyzing the size and composition of individual particles from a polydisperse aerosol in real-time. Particles are introduced into the instrument through a particle beam interface, sized by measuring the delay time between two scattering lasers, and compositionally analyzed using a dual-polarity laser desorption/ionization time-of-flight mass spectrometer. These are the first dual-ion TOFMS instruments to utilize a dual reflectron design. The instruments measure 72 in. long × 28 in. wide × 60 in. high and weigh ∼500 lb. Pneumatic tires allow them to be transported through standard doorways, elevators, and handicap ramps, granting access to virtually any location. Furthermore, because of rugged construction they will be able to operate during transport by automobile, boat, or aircraft.
Die Gittertheorie der Ienenkristalle wird durch drei _~mderungen des Energieansatzes verseh~ixft : ])as Abstol3ungspotential wird nieht als Pote nz des Gitterabstandes, sondern als Exponentialfunktion angenommen. Dabei wird das Gesetz der Adclitivit~t der Ionenradien beriieksiehtigt. End]ich werden die van der Waalssehen Kohfisionskr~ifte mit in Reehnung gesetzt. Es wird gezeigt, dal~ hierdurch die versehiedene Stabi]it~ der Gittertypen NaC1 und CsC1 verst~indlich gemacht werden kann. Einleitung. Der zweigliedrige Ansa~z ffir die ~i~terenergie eines Ionenkristallsl), der ~uBer der elektrostatischen C oulombsehen Energie noch eine Abstol~ungskraf~ der Form b/r ~ (mi~ zwei Konstanten) einffihrt, gibt zweifellos branehbare N~herungswerte; allerdings liegt erst eine einzige Messung 2) vor, die als einwandfreie direkte Prfifung angesprochen werden kann, doeh ffihren eine Menge Folgerungen fiber die Elek~rbnenaffinit~ten der Halogene, die LSsungsw~rmen tier Salze3), die Dissoziationsw~rmen der Salzd~mpfe 4) u.a. zur indirekten Best~tigung. In neuerer Zeit ist aber das experimentelle Material so vervoIlkommnet worden, dab sich deutiiche Abweichungen der Theorie yon den Experimenten zeigen. So hebt Fajans 5) hervor, dal~ man aus den LSsungsw~irmen der Salze auf Fehler der theoretisehen Gitterenergie schliel3en mul~, die bei den vier Salzen LiF, RbF, Li I, Rb Ibis zu 15 kcM, d.h. 10% betragen kSnnen. Ein ebenso gewiehtiger Einwand gegen die Theorie beruht auf einer rein qualitativen Tatsaehe. In der Natur kommen unter den AlkalihMogeniden zwei Gittertypen, S~einsalz-und C~siumeMoridtypus vor, trod die Theorie ist nieh~ imstande, yon dieser Tatsaehe Reehensehaft zu geben; die in dem urspriingliehen Ansatz auftre~enden Konstanten sind ja dutch mel~bare Eigenselmften des Kristalls (Gitterabstand, Kompressibflit~t) festgelegt 1) Siehe ~. B. M. Born, Atomtheorie des festen ~ustandes. Leipzig,
The virial development for the osmotic pressure of a solution may be used, if the potentials of average force of the solute molecules at infinite dilution are known, to compute the deviations from perfect solution behavior. The expression for the logarithm of the activity coefficient can thus be obtained as a sum of coefficients multiplied by powers of the concentration. For an ionic solution, with 1/R2 forces, the series is only conditionally convergent. By summing certain additive terms occurring in the coefficients over all powers of concentration convergence can be attained. The integrations necessary to obtain terms correct up to and including c32 are performed. The results are given in terms of certain functions which can readily be computed.
Vertical and horizontal profiles of atmospheric aerosols are necessary for understanding the impact of air pollution on regional and global climate. To gain further insight into the size-resolved chemistry of individual atmospheric particles, a smaller aerosol time-of-flight mass spectrometer (ATOFMS) with increased data acquisition capabilities was developed for aircraft-based studies. Compared to previous ATOFMS systems, the new instrument has a faster data acquisition rate with improved ion transmission and mass resolution, as well as reduced physical size and power consumption, all required advances for use in aircraft studies. In addition, real-time source apportionment software allows the immediate identification and classification of individual particles to guide sampling decisions while in the field. The aircraft (A)-ATOFMS was field-tested on the ground during the Study of Organic Aerosols in Riverside, CA (SOAR) and aboard an aircraft during the Ice in Clouds Experiment-Layer Clouds (ICE-L). Initial results from ICE-L represent the first reported aircraft-based single-particle dual-polarity mass spectrometry measurements and provide an increased understanding of particle mixing state as a function of altitude. Improved ion transmission allows for the first single-particle detection of species out to approximately m/z 2000, an important mass range for the detection of biological aerosols and oligomeric species. In addition, high time resolution measurements of single-particle mixing state are demonstrated and shown to be important for airborne studies where particle concentrations and chemistry vary rapidly.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.