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Reactions of Gaseous Molecule Ions with Gaseous Molecules. V. Theory
1.D. P. Stevenson and D. O. Schissler, J. Chem. Phys. 23, 1353 (1955).
2.Eyring, Hirschfelder, and Taylor, J. Chem. Phys. 4, 479 (1936).
3.Field, Franklin, and Lampe, J. Am. Chem. Soc. 79, 2419 (1957).
4.D. P. Stevenson and D. O. Schissler, J. Chem. Phys. 29, 282 (1958).
5.Hirschfelder, Curtiss, and Bird, Molecular Theory of Gases and Liquids (John Wiley and Sons, Inc., New York, 1949), p. 502.
6.P. Langevin, Ann. Chim. Phys. 5, 245 (1905).
7.Field et al. (see reference 3) use the distance of closest approach in place of the impact parameter in calculating the cross section, with result that their value is incorrect by a factor of two.
8.It should be recognized that the inverse square root dependence on energy of the cross section is not universal, but rather depends on the particular form of the potential chosen. For an inverse nth power potential, (with ), the cross section varies as
9.Except for an obvious misprint, Eq. (8c) of reference 2 is the same as Eq. (19). It appears surprising that a classical and quantum mechanical argument should agree exactly, but the Eyring treatment uses a classical approximation at a late stage, so both are really classical.
10.Hirschfelder et al., reference 5, p. 950.
11.In general, one would expect the reaction cross sections for molecules with permanent electric dipole moments, to be greater than those given above, because the net effect would be an attractive force. However, the potential depends on the orientation of the molecule, so that some suitable average potential must be found. If a Boltzmann factor is used, the resulting potential has an inverse fourth power dependence on distance, and so could be included within the model we have assumed. However, the potential as so derived assumes thermal equilibrium, while here, as noted already, we are far from thermal equilibrium. The matter is speculative, and must be considered further.
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