The indeterminacy of the values of potential parameters as derived from transport and virial coefficients

Abstract

The present work originated in a re-examination of the application of the Lennard-Jones ( 12:6) potential function to the viscosity-temperature relations of gases and vapors at low pressures. In particular, attention was focused on a phenomenon mentioned by Mueller and Lewis (1957) and described in more detail by Reid and Sherwood (1966) and Reid (1968) whereby disparate sets of values of u and d k (the Lennard-Jones potential parameters) represent experimental data equally well. Several examples of this behavior are quoted in the paper by Reid (1968), but only one example will be considered here. Flynn and Thodos (1962) Reid and Sherwood point out that the respective authors used somewhat different numerical methods to evaluate the parameters. However, such differences in the methods do not in themselves explain either the enormous differences in the values obtained or the remarkably good fit which each set gives to the experimental viscosity values.An explanation for these facts was given by Kim and Ross (1967) in a brief but important note which appears to have been overlooked by later authors. When the work reported here was begun, the author, too, was unaware of Kim and Ross's note and analyzed the problem independently. The solution obtained in the present study is virtually identical with that obtained by these authors, but since the scope of the present work is wider, some degree of restatement is necessary.A number of physical properties of gases are affected by the mutual interaction of molecules at close distances. In relation to the properties of gases at relatively low pressures, only binary interactions are significant. Numerical values for a number of properties of gases can then be predicted from the kinetic theory of gases, provided one assumes a particular pairwise interaction potential function, expressing the energy of interaction of two molecules as a function of their distance apart and (where relevant) relative orientation. This note is concerned only with cases where orientation is not significant. In these circumstances, the theoretical expressions often take the formwhere y is the predicted numerical value of the physical property (for example, viscosity, or second virial coefficient) and A is a constant (at least for a particular substance) not depending in any way on the parameters of the interaction potential function. The collision diameter u is one of the parameters of the interaction potential function and may be defined as the distance (other than infinity) between the centers of the two molecules when the net potential energy is zero. T is the absolute temperature, i and i are absolute constants, and D* is a dimensionless quantity dependent on the form of the particular interaction potential function. If a particular potential function is assumed, values of D o may be calculated from theoretical considerations, classical or quantum-mechanical; D" can then be expressed as a function of dimensionless variables, one of which is always T' = k T / c k is here the Boltzmann constant, ...

Critical properties, potential force constants, and structure of organic molecules

“…The observed linearity of T,Vzf3 and P,V,5f3 with the number of C, N, and 0 atoms in the organic molecule further confirms that pair potential force constants are coupled in a very specific way. The general interdependence of c, and a, has been commented upon before (Kim and Ross, 1967;Reichenberg, 1973), but the present correlation and that of Sanchez 1983) are the strongest statements made about this interdependence. However, there is one caveat worth mentioning: As illustrated in Table 1, T,VZf3 and PcV,5f3 do not vary exactly in the same way with structure, i.e., ai is not strictly proportional to 4.…”

A critical evaluation of Lennard–Jones and Stockmayer potential parameters and of some correlation methods

“…Such indetermii~acy is not really serious when viscosities are recalculated; any combination o, &/k such that the product P(n) is equal to the experimental value will reproduce viscosities to good precision. In the above stated T* range the parameters in [3] and [5] are thus related as follows: [6], therefore, the large compilation by Franck (9) of om and C parameters can be converted to o and ~/ k parameters; the latter being just as much subject to indeterminacy, however, as when obtained directly through [3].…”

New methods for the estimation of the viscosity coefficients of pure gases at moderate pressures (with particular reference to organic vapors)

“…Thin Liquid Films," ibid., 21, 178 (1975 In an earlier communication (Reichenberg, 1973) it was shown that the frequently observed numerical indeterminacy of the potential parameters u and d k is due to the fact that, under certain circumstances, these two parameters "collapse" together. When this occurs with a potential function involving only these two parameters, the predicted values of the physical property in question are effectively determined by a single parameter characteristic of the substance.…”

“…For the nonpolar compounds, 48 data points gave a mean deviation of 1.9% and for the polar compounds, 45 data points gave a mean deviation of 2.0%. dimensionless quantity defined by Equation (3) depth of the potential well [defined more fully in Reichenberg ( 1973) ] gas viscosity at temperature T and moderate pressures gas viscosity at the critical temperature and moderate pressures (not at the critical point! ) value of 7) calculated from Equation ( 6 ) value of 9 determined experimentally collision diameter [defined more fully in Reichenberg (1973) ]…”