× Updated! Potentials that share interactions are now listed as related models.

1924--Jones-J-E--universal

Citation: J.E. Jones (1924), "On the Determination of Molecular Fields. I. From the Variation of the Viscosity of a Gas with Temperature", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 106(738), 441-462. DOI: 10.1098/rspa.1924.0081.
Abstract: Until our knowledge of the disposition and motion of the electrons in atoms and molecules is more complete, we cannot hope to make a direct calculation of the nature of the forces called into play during an encounter between molecules in a gas. It is true that a step in this direction has recently been made by Debye, who has investigated the nature of the field in the neighbourood of a hydrogen atom, assumed to consist of a negative charge in motion in circular orbit about a positive nucleus, and has shown how the pulsating field gives rise on the whole to a force of repulsion, as well as one of attraction on a unit negative charge. But it is difficult to see how this work can be extended to more complex systems. At present we can only hope to derive information by more indirect methods. One such method is to assume a definite law of force, and then by the methods of the kinetic theory to deduce the appropriate law of dependence of the viscosity of a gas on temperature. Comparison with the actual law, as observed experimentally, serves to support or discredit the assumed law of molecular interaction. Unfortunately, the calculations involved in the application of be kinetic theory are so complicated that progress has been made only in certain simple cases. Thus, the original investigation by Maxwell applied only to molecules repelling as the inverse fifth power law. His work has since be generalised by Chapman and Enskog and formulæ have been obtained: the coefficient of viscosity in the case of (i) molecules, which repel according an inverse nth power law, (ii) molecules which behave on collision like rigid elastic spheres and (iii) molecules which behave as rigid elastic spheres with weak attractive field of force surrounding them. Of these models the latter, generally referred to as Sutherland’s model, is found to give the best agreement between theory and experiment. But the agreement is by no means perfect. As Schmidt, Bestelmeyer, Vogel, and others have pointed out, there is considerable divergence from observed values at low temperatures.
Citation: J.E. Jones (1924), "On the Determination of Molecular Fields. II. From the Equation of State of a Gas", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 106(738), 463-477. DOI: 10.1098/rspa.1924.0082.
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/v2 + D/v4 + E/v6 + F/v8, 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 formulæ for B are easily deduced from the general one given here.
Citation: J.E. Lennard-Jones (1925), "On the Forces between Atoms and Ions", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 109(752), 584-597. DOI: 10.1098/rspa.1925.0147.
Abstract: The ultimate knowledge which we can hope to derive from many of the physical properties of gases and crystals is that which concerns the nature of the forces between the constituent atoms and ions. In terms of these forces many diverse phenomena both of gases and solids should be explicable. In some recent researches the writer has sought to determine the repulsive part of the forces between certain atoms and ions in terms of inverse power laws. This representation is considered superior to the treatment of atoms and ions as rigid spheres with definite diameters, as is generally done, for it permits of the correlation of the physical properties of a gas with those of certain associated crystals. Thus the forces which explain the thermal conductivity of neon have been shown to explain as well the observed spacing constants of crystals like NaF and MgO. These researches had their starting point in an investigation of certain physical properties of the pure gases, and this formed a necessary preliminary step to the later work on crystals. The methods there developed were, however, applicable only to neon and argon, for only in those cases was the necessary experimental information available. Consequently the later extension to include the forces of ions applied only to ions of similar electronic structure to these gases.

Notes: This is a 'universal' parameterization for the Lennard-Jones 6-12 model driver for all species.

See Computed Properties
Notes: Listing found at https://openkim.org.
Link(s):
Date Created: October 5, 2010 | Last updated: June 09, 2022