Correlation of second virial coefficients through potential function parameters

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Abstract
An analytical technique based on the method of least squares has been developed to fit experimental second virial coefficients to the functional form derived from the Lennard‐Jones (6–12) potential. Both the functional form and the normal equations of the least squares fit are rigorously derived. Because of the implicit, nonlinear dependence upon one of the adjustable parameters, a computer solution of the normal equations is required. Second virial coefficient data for a large number (60) of materials, including hydrocarbons, halides, alcohols, and cyclic compounds, have been extracted from published sources, carefully evaluated for consistency, and fitted to the Lennard‐Jones potential function.Force constants for these materials as determined from fitting the data in this uniform manner have been found to be related to structural parameters. The final correlation, with the potential well‐depth related to critical temperature and the collision diameter calculated from a set of group contributions with appropriate corrections for polarity and/or association, produces average deviations between computed and experimental second virial coefficients of 10 to 15% or 100 cc./g.‐mole, whichever is greater. In many cases the agreement is much better.

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