paper with the statement: “High-temperature transport properties computed with a Lennard-Jones potential based upon low-temperature gas properties and lacking other corroboration must therefore be viewed with extreme skepticism.” \Ve are a t a loss to see how Holsen and Strunk, having read the paper of Walker and Westenberg, could make the statement: ”Likewise, experimental diffusivities obtained a t elevated temperatures appear to correlate well with theoretical predictions, yielding intermolecular parameters which correspond to similar parameters obtained from viscosity data.” Apparently on the basis (of this statement, which is simply not correct, Holsen and Strunk assumed a n asymmetry parameter with reciprocal temperature dependence. The use of such a n asymmetry parameter is inconsistent with empirical evidence and probably with theoretical evidence ( 7 ) ; such use undoubtedly gives misleading results.
SIR: Although sratistical or numerical search procedures can produce most probable values for the pair of Lennard-Jones potential parameters, the results are hardly satisfying when parameters determined from diffusion data for polyatomic molecules are compared with the corresponding parameters from viscosity data. This is evident from Pakurar and Ferron’s (5) Table I, where a series of parameters is tabulated for the COZ-Ar system. Yet relatively close agreement is found in the corresponding pairs of parameters from P-V- T and viscosity data. as noted by Hirschfelder. Curtiss, and Bird ( 3 ) . I n attempting to correlate iheir room temperature diffusion coefficients with Lennard-Jones parameters, the writers found that the temperature dependence of the data was inconsistent 1% ith the diffusion coefficimt equation when used with LennardJones parameters. Thus they were led to seek a n explanation which mas temperature dependent. T h e asymmetry parameter defined by Holsen and Strunk ( 4 ) was empirical, and was so noted. T h e form cited was suggested in part by a theoretical derivation of De Boer (7) which considered the effects of asymmetric polarizabilities on the field between two hydrogen molecules. For the effrctive attractive field de Boer obtained a n expression of the form
Literature Cited
(1) Ember, G., Ferron, J. R., Wohl, K., J . Chem. Phys. 37, 891-7 (1962).
(4) Saxena, S. C., Mason, E. .4., Mol. Phys. 2, 379 (1959). (5) Walker, R. E., IVestenberg, A. A., J . Chem. Phys. 31, 519 (1959). Thomas A . Pakurar’ John R. Ferron University of Delaware :Yewark, Del. 1
Present address, E. I. du Pont de Nemours & Co., Richmond,
Va.
T h e effective repulsive field was characterized by a negative inverse temperature dependence related to the fact that “at low temperatures the molecules prefer orientations of small potential energy, which contribute only little to the repulsive field.” A reciprocal temperature dependence also appears in analyses of the effects of strong electric fields on the polarizability. T h e reciprocal temperature dependence of the anisotropic polarizability parameter was suggested by the above arguments and not by reference to other high temperature diffusion data. T h e remarks made should have been limited to the data cited in the paper and not extended to the interpretation of diffusion data a t higher temperatures. T h e correlation of experimental data presented in Figure 3 of (4) shows a consistent deviation from the temperature dependence found with Lennard- Jones viscosity parameters which would be evident regardless of the specific function of temperature selected. T h e fact that these deviations may differ in nature from the high temperature deviations noted by Ember, Ferron, and Ll’ohl (2) may indicate that the nonspherical effects in the two regions differ in nature.
literature Cited
T h e nature of C is discussed by De Boer (7). mean polarizability defined by
Here 5 is the
where Q and aI. denote polarizabilities along axes parallel and perpendicular, respectively, to the bond, and
(1) De Boer, J., Physica 9, 363 (1942). (2) ..Ember, G., Ferron, J. R., Wohl, K., J . Chem. Phys. 37, 891 (1962).
(3) Hirschfelder, J. O., Curtiss, C. F., Bird, R. B., “Molecular Theory of Gases and Liquids,” Wiley, Xew York, 1954. (4) Holsen, J. N., Strunk, M. R., IND.ENG.CHEM.FUNDAMEKTALS 3, 143 (1964). (5) Pakurar, T. A , , Ferron, J. R., Ibid., 5 , 144 (1966). James X. Holsen Tt’ashington University, St. Louis, M o . Mailand R. Strunk University of Missouri, Rolla, Mo.
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NO. 1
FEBRUARY 1966
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