2882
James K. Baird
Continuum Dielectric Model for an Electron in a Nonpolar Fluid James K. Baird Health Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830 (Received August 13, 1975) Publication costs assisted by the Oak Ridge National Laboratory
A function expressing the electrostatic polarization energy experienced by an electron immersed in a nonpolar fluid is derived on the basis of classical electrostatics. A continuum dielectric model is used to represent the collective effect of the fluid molecules, which are assumed individually to possess spherical symmetry. The local electric field in the fluid is calculated from the sum of a cavity field and a dielectric reaction field. The model is parametrized by constants (the molecular electric dipole and quadrupole polarizabilities and the effective cavity radius presented by a molecule in the fluid), which for the example of argon can be determined from published literature data. The results obtained from the continuum model are compared with a recent theory dealing with the same question, but based on a model in which the molecules in the fluid are regarded as being discrete, and the local electric field is taken to be the traditional one due to Lorentz.
Introduction The properties of excess electrons introduced into dielectric fluids by ionizing radiation or by field emission tips have been actively studied in recent years.’ Part of the effort has centered about attempts to describe the microscopic interactions of the electrons with the molecules of the fluid and to formulate a theory of electron transport.2-10 Pursuing the problem of microscopic description, we calculate herein the electrostatic polarization energy for an electron immersed in a nonpolar fluid consisting of molecules having spherical symmetry. The electron is taken to be a point charge, while a molecule in the fluid is assumed to consist of point polarizable electric multipoles at the center of a spherical cavity in an otherwise continuous dielectric. This molecular model is a generalization of that introduced by Bellll and used by Onsager12 to calculate the density dependence of the dielectric constant of a polar fluid. The contributions of Bell and Onsager, taken together, differed from previous inve~tigationsl~ in three fundamental ways: (1)the electric lines of force produced by an external field were allowed to bend in the vicinity of the cavity; (2) the cavity was taken to be of approximately molecular size; and (3) the elementary charges making up a molecule were replaced by a point electric dipole at the center of the cavity, and the interaction of the molecule with its neighbors was represented by a dipolar reaction field. Although Onsager was concerned with polar substances, Bottcherl4 has since demonstrated the applicability of his concepts to explain the density dependence of the dielectric constant of nonpolar fluids. In what follows, the model developed by Bell, Onsager, and Bottcher will be used to represent the many body nature of the interaction of the electron with the fluid. Mathematical Development Cavity Field. Consider, as shown in Figure la, a point charge of magnitude q located a distance b from the center of a spherical cavity of radius a in a uniform dielectric of dielectric constant e. Using standard methods of analysis,24 we may solve the equation The Journal of Physical Chemistry, Vol. 79. No. 26, 1975
V 2 V ( r , %= ) 0
r#b
(1)
for the electrostatic potential V(r,O)subject to the boundary conditions
V ( r , 8 )- (q/c)lr - b q - l = continuous
