# Second virial coefficients of alkali vapours

About: This article is published in Molecular Physics.The article was published on 1976-03-01. It has received 10 citations till now. The article focuses on the topics: Virial coefficient & Vapours.

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TL;DR: In this paper, a simple potential model for the evaluation of isotropic pairwise interaction energies is proposed and used to predict the lowest triplet state curve of all alkali-alkali interactions.

Abstract: A simple potential model for the evaluation of isotropic pairwise interaction energies is proposed and used here to predict the lowest triplet state curve of all alkali-alkali interactions. The model, which for the alkali dimers contains no adjustable parameters, expresses the interaction potential in terms of the Hartree-Fock interaction energy, V HF(R), and the interatomic correlation energy as approximated semi-empirically from the second order dispersion energy calculated including the effect of charge overlap between the electron clouds of the two interacting species, V inter/disp(R). Lack of repulsive near Hartree-Fock ab initio results for the triplet state of most alkali dimers has been circumvented by proposing a generalized screened Coulomb type repulsion for these systems. The sum of the additional contributions to the interaction energy [V intra(R) + V intra-inter(R)], which arise from intra-atomic correlation effects and intra-inter coupling terms, is also shown to be well approximated by int...

65 citations

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01 Jan 1990TL;DR: In this paper, the second virial coefficients, self-diffusion, viscosity and thermal conductivity of monatomic alkali metal vapours, lithium, sodium, potassium, cesium and rubidium are presented.

Abstract: Theoretical calculations of the second virial coefficients, self-diffusion, viscosity and thermal conductivity of monatomic alkali metal vapours, lithium, sodium, potassium, cesium and rubidium are presented. The calculations have been carried out using reliable analytical two body interaction potential energy functions for the ground singlet 1Σ+g and the excited triplet 3Σ+g molecular states of the alkali dimers. The results are compared with previously calculated values. — The interpretation of experimental data on the thermophysical properties of alkali metal vapours is complicated by the formation of dimers. It follows that theoretical calculations for the monatomic species should thus provide an independent information on the zero density limits for the experimental properties. Full utilization of this principle is tried in Part II of this paper where an assessment of the available experimental data is attempted.

27 citations

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TL;DR: In this article, an improved analytic equation-of-state for the van der Waals model is presented based on a simple but accurate semi-empirical expression for the hard sphere reference fluid and Andrews' development for the attractive perturbation.

Abstract: Molecular Dynamics and Monte Carlo computations for the original van der Waals model potentials, consisting of a hard core and inverse power attractive tails, are reported The results show that the cusp at the minima of these potentials gives rise to anomalous phenomena in the low and intermediate density regions which derive from clustering effects A new improved analytic equation-of-state for the van der Waals model is presented This is based on a simple but accurate semi-empirical expression for the hard sphere reference fluid and Andrews' development for the attractive perturbation A comparison of this first order perturbation equation with the ‘exact’ machine data highlights the limitations arising from clustering effects The pair radial distribution function in the low density regime is not well-represented by using an expansion about the hard sphere distribution function and the attractive potential's second and third virial coefficients, used in Modified Enskog Theory (MET)

27 citations

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TL;DR: In this article, the authors brought the molten alkali metals into the scope of a new statistical mechanical equation of state that is known to satisfy normal fluids over the whole range of temperature.

Abstract: The paper brings the molten alkali metals into the scope of a new statistical mechanical equation of state that is known to satisfy normal fluids over the whole range. As for normal fluids, the latent heat of vaporization and density at freezing temperature are the only inputs (scaling factors). The corresponding-states correlation of normal fluids is used to calculate the second virial coefficient, B{sub 2}(T), of alkali metals, which is scarce experimentally and its calculation is complicated by dimer formation. Calculations of the other two temperature-dependent constants, {alpha}(T) and b (T), follow by scaling. The virial coefficients of alkali metals cannot be expected to obey a law of corresponding states for normal fluids. The fact that two potentials are involved may be the reason for this. Thus, alkali metals have the characteristics of interacting through singlet and triple potentials so that the treatment by a single potential here is fortuitous. The adjustable parameter of the equation of state, {Gamma}, compensates for the uncertainties in B{sub 2}(T). The procedure used to calculate the density of liquids Li through Cs from the freezing line up to several hundred degrees above the boiling temperatures. The results are within 5%.

19 citations

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TL;DR: In this article, the liquid density of binary alloys of Na-K and K-Cs over the whole range of concentrations and that of a ternary molten eutectic of Na−K-Cs from the freezing point up to several hundred degrees above the boiling point are presented.

Abstract: Calculated results of the liquid density of binary molten alloys of Na–K and K–Cs over the whole range of concentrations and that of a ternary molten eutectic of Na–K–Cs from the freezing point up to several hundred degrees above the boiling point are presented. The calculations were performed with the analytical equation of state proposed by Ihm, Song, and Mason, which is based on statistical-mechanical perturbation theory. The second virial coefficients were calculated from the corresponding-states correlation of Mehdipour and Boushehri. Calculation of the other two temperature-dependent parameters was carried out by scaling. The calculated results cover a much wider range of temperatures and are more accurate than those presented in our previous work.

16 citations

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01 Jan 1954

TL;DR: Molecular theory of gases and liquids as mentioned in this paper, molecular theory of gas and liquids, Molecular theory of liquid and gas, molecular theories of gases, and liquid theory of liquids, مرکز

Abstract: Molecular theory of gases and liquids , Molecular theory of gases and liquids , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

11,807 citations

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TL;DR: In this paper, an exact solution for the Schroedinger equation representing the motions of the nuclei in a diatomic molecule, when the potential energy function is assumed to be of a form similar to those required by Heitler and London and others, was obtained.

Abstract: An exact solution is obtained for the Schroedinger equation representing the motions of the nuclei in a diatomic molecule, when the potential energy function is assumed to be of a form similar to those required by Heitler and London and others. The allowed vibrational energy levels are found to be given by the formula $E(n)={E}_{e}+h{\ensuremath{\omega}}_{0}(n+\frac{1}{2})\ensuremath{-}h{\ensuremath{\omega}}_{0}x{(n+\frac{1}{2})}^{2}$, which is known to express the experimental values quite accurately. The empirical law relating the normal molecular separation ${r}_{0}$ and the classical vibration frequency ${\ensuremath{\omega}}_{0}$ is shown to be ${{r}_{0}}^{3}{\ensuremath{\omega}}_{0}=K$ to within a probable error of 4 percent, where $K$ is the same constant for all diatomic molecules and for all electronic levels. By means of this law, and by means of the solution above, the experimental data for many of the electronic levels of various molecules are analyzed and a table of constants is obtained from which the potential energy curves can be plotted. The changes in the above mentioned vibrational levels due to molecular rotation are found to agree with the Kratzer formula to the first approximation.

3,299 citations

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TL;DR: In this paper, it was shown that a molecular model of the same type will also explain available experimental data concerning the equation of state of a gas, and if so, whether the results so obtained, when taken in conjunction with those obtained from viscosity, will definitely fix the molecular field.

Abstract: The investigation of a preceding paper has shown that the temperature variation of viscosity, as determined experimentally, can be satisfactorily explained in many gases on the assumption that the repulsive and attractive parts of the molecular field are each according to an inverse power of the distance. In some cases, in argon, for example, it was further shown that the experimental facts can be explained by more than one molecular model, from which we inferred that viscosity results alone are insufficient to determine precisely the nature of molecular fields. The object of the present paper is to ascertain whether a molecular model of the same type will also explain available experimental data concerning the equation of state of a gas, and if so, whether the results so obtained, when taken in conjunction with those obtained from viscosity, will definitely fix the molecular field. Such an investigation is made possible by the elaborate analysis by Kamerlingh Onnes of the observational material. He has expressed the results in the form of an empirical equation of state of the type pv = A + B/ v + C/ v 2 + D/ v 4 + E/ v 6 + F/ v 8, where the coefficients A ... F, called by him virial coefficients , are determined as functions of the temperature to fit the observations. Now it is possible by various methods to obtain a theoretical expression for B as a function of the temperature and a strict comparison can then be made between theory and experiment. Unfortunately the solution for B, although applicable to any molecular model of spherical symmetry, is purely formal and contains an integral which can be evaluated only in special cases. This has been done up to now for only two simple models, viz., a van der Waals molecule, and a molecule repelling according to an inverse power law (without attraction), but it is shown in this paper that it can also be evaluated in the case of the model, which was successful in explaining viscosity results. As the two other models just mentioned are particular cases of this, the appropriate formulae for B are easily deduced from the general one given here.

2,046 citations