The second virial coefficient for molecules interacting with a spherically symmetric potential is divided into three parts: (1) a contribution Bb, related to the equilibrium constant for the formation of bound double molecules; (2) a contribution Bm, related to the equilibrium constant for the formation of metastably-bound double molecules; and (3) a contribution Bf, due to molecules which interact but are free to separate after the interaction. Equations are given for determining each of the three parts of the second virial coefficient. A detailed treatment of these three contributions together with numerical tables on a reduced temperature basis is given for the square-well, Sutherland, and Lennard-Jones (6–12) potentials.
The mean lifetimes of metastably bound double molecules are discussed, and numerical values are given for the special case of argon. Tables for computing mean lifetimes in other Lennard-Jones gases are given. It is found that most metastably bound double molecules have mean lifetimes considerably longer than the mean time between collisions at ordinary pressures. Finally, an equation is developed for the number of vibrational levels of a double molecule.
The initial pressure dependence of thermal conductivity and viscosity of gases is considered to arise from molecular association and collisional transfer. Since only the initial pressure dependence is investigated, clusters larger than dimers can be neglected. The effect of dimer formation can be calculated from a knowledge of the equilibrium constant for the reaction 2A⇌A2. The effect of collisional transfer is obtained by a semiempirical modification of Enskog's theory. In the case of thermal conductivity, it is found that at low temperatures molecular association is more important than collisional transfer, while at high temperatures collisional transfer predominates. For viscosity, the initial pressure dependence is due primarily to collisional transfer.
Detailed equations for the initial pressure dependence of both thermal conductivity and viscosity are given in terms of dimensionless groupings which include the intermolecular potential parameters. Tables of these dimensionless groupings as functions of a reduced temperature are given for molecules obeying the Lennard-Jones (6–12) potential. Comparisons between theory and experiment are included. It is found that the numerical results are sensitive to the choice of force constants for the interaction of a monomer with a dimer.
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