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Capture Collision Theory

  • Douglas P. Ridge
Part of the NATO ASI Series book series (ASIC, volume 193)

Abstract

A proper treatment of the conductivity of ionized gases lead to Langevin’s discovery of the phenomenon of capture in ion molecule collisions (Langevin, 1905). The background of Langevin’s work was the work of Maxwell (1860a, 1860b) and Boltzmann (1902) on the transport properties of gases. Maxwell first showed that it was possible to proceed from intermolecular force to collision trajectories and cross sections to collision rates to transport coefficients. He considered in particular the case of a repulsive potential which varied as the fifth power of the intermolecular distance. He found that in this case the diffusion collision frequency is independent of the velocity which simplifies the computation of the transport coefficients immensely. Commenting on this work Boltzmann observed:

Even as a musician can recognize his Mozart, Beethoven, or Schubert after hearing the first few bars, so can a mathematician recognize his Cauchy, Gauss, Jacobi, Helmholtz, or Kirchhoff after the first few pages. The French writers reveal themselves by the extreme formal elegance, while the English, especially Maxwell, by their dramatic sense. Who, for example, is not familiar with Maxwell’s memoirs on his dynamical theory of gases?…The variations of the velocities are, at first, developed majestically; then from one side enter the equations of state; and from the other side, the equations of motion in a central field. Ever higher soars the chaos of formulae. Suddenly, we hear, as from kettle drums, the four beats “put n = 5.” The evil spirit V (the relative velocity of the two molecules) vanishes; and, even as in music, a hitherto dominating figure in the bass is suddenly silenced, that which had seemed insuperable has been overcome as if by a stroke of magic…This is not the time to ask why this or that substitution. If you are not swept along with the development, lay aside the paper. Maxwell does not write programme music with explanatory notes…One result after another follows in quick succession till at last, as the unexpected climax, we arrive at the conditions for thermal equilibrium together with the expressions for the transport coefficients. The curtain then falls (Chandrasekhar, 1979) !

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Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1987

Authors and Affiliations

  • Douglas P. Ridge
    • 1
  1. 1.Department of ChemistryUniversity of DelawareNewarkUSA

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