Onsager's equation for the effect of an external electric field on the probability of an isolated ion pair escaping neutralization in a dielectric medium has been rearranged for evaluation in a consistent way. The present treatment allows the escape probability to be written as a single series valid for arbitrary field strengths and initial separations. In a given case, procedure is outlined for calculating this probability in the most systematic manner. Although expansion of the escape probability in powers of the external field is not advisable at high field strengths because of the slowness of convergence, the field coefficients are provided for evaluation and comparison at relatively low fields. At high fields possibility of a temperature inversion effect is indicated; that is, the field‐dependent escape probability may actually decrease with temperature.

Effect of an external electric field on the yield of free ions. I. General results from the Onsager theory

A numerical solution of the Smoluchowski equation for diffusion, reaction, and neutralization of ion pairs in a dielectric medium in the presence of a scavenger has been applied for analysis of recent electron scavenging experiments in alkanes. It is shown that these experiments can be quantitatively understood in terms of a simple exponential distribution of initial electron‐positive ion separation distances. The credibility of this distribution is considerably enhanced when it is employed, in conjunction with Onsager's solution for diffusion of an ion pair in the presence of an external field, to calculate ion yields as a function of field strength. The agreement with experiment is once again excellent. The attenuation parameter which characterizes our initial exponential distribution is related to the liquid structure factor and gas phase molecular scattering cross sections through the multiple scattering theory of Lax. The wave nature of electron motion is explicitly considered in a discussion of the physical meaning of ionization in liquids.

The simple exponential distribution for initial electron‐positive ion separation distances as seen in the γ radiolysis of alkanes

Measurements of the photoconductivity of liquid n‐pentane, n‐hexane, cyclopentane, cyclohexane, neopentane, neohexane, and tetramethylsilane induced by far UV radiation (7⩽hν⩽10 eV) have been performed. We have studied the influence of the incident photon energy, of the applied electric field strength, and of the concentration of two electron scavengers (carbon tetrachloride and perfluoromethylcyclohexane). Our results show that in going from the gas phase to the liquid phase, the ionization energy threshold values of these low dielectric constant liquids are lowered by about 1.6 eV. The introduction of an electron scavenger reduces drastically the solvent photocurrent. Our results are consistent with the quenching, by the scavenger, of a solvent expanded excited state, precursor of the geminate ion pair, and not with an epithermal electron scavenging as in high energy photon irradiation.

Photoconductivity studies in some nonpolar liquids

The photoionization of N,N,N′,N′‐tetramethyl‐p‐phenylenediamine (TMPD) dissolved in n‐hexane (HEX), 2,2,4‐trimethylpentane (TMP), and tetramethylsilane (TMS) is studied using measurements of single‐photon photoconductivity. Quantum yields for free carrier production—extrapolated to zero applied field—are reported for the energy range 4.4–7.5 eV. The applied electric field dependence of the quantum yields is measured up to fields approaching 2×107 V/m and interpreted via Onsager’s theory of geminate recombination. The low‐field, slope/intercept predictions of the theory are obeyed quantitatively for HEX and TMP as solvent but fail by 25% for TMS. Various distribution functions for the separations of geminate pairs are used to generate predicted field dependence curves, which are compared with the high‐field data. A broad distribution of thermalization lengths is definitely required to fit the TMP and TMS data, but the TMS result is suspect because of the observed failure of Onsager theory in that solvent. ...

Geminate charge recombination in the photoionization of N,N,N′,N′‐tetramethyl‐p‐phenylenediamine (TMPD) in various solvents

A discrete-ordinate method of solution of the time-dependent Boltzmann-Fokker-Planck equation for electron swarms in rare-gas moderators is employed in the study of the time dependence of the average electron energy, mobility, and transverse diffusion coefficient versus the strength of an externally applied electric field. The solution of the Fokker-Planck equation is based on the expansion of the solution in the eigenfunctions of the Lorentz-Fokker-Planck operator. With the transformation to an equivalent Schroedinger eigenvalue problem, the eigenvalue spectrum is shown to be entirely discrete, thereby validating the eigenfunction-expansion approach. The effects studied include the effect of an electric field on the thermalization times, a comparison of the effects of moderators with and without Ramsauer minima in the momentum-transfer cross sections, and the effect of an external electric field on the transient negative-mobility phenomena predicted in an earlier paper. A comparison with experimental results for Xe shows good agreement with the calculations.

Electric field dependence of transient electron transport properties in rare-gas moderators

The radiation-induced conductivity in liquid neopentane was studied at electric field strengths up to 140 kV/cm. The shape of the ionization current vs. field strength curve is quite different from that of n-hexane. Extrapolation to infinite field strength gives a total ionization yield of G = 4.03 (W = 24.8) which agrees with the gas-phase value.

Werner F. Schmidt

Papers

Radiation-Induced Conductivity and Ion Yields in Neopentane at High Electric Fields