Interpretation of Rate Constants Measured in Drift Tubes in Terms of Cross Sections

Abstract

The basic equation of the rate constant of a two‐body reaction, $$\mathrm{\kappa =}{\displaystyle {\int }_{{\mathrm{v}}_g}}{\displaystyle {\int }_{v_i}}{f}_{\mathrm{gas}}(v_g{\mathrm{)f}}_{\mathrm{ion}}(v_i{\mathrm{)v}}_r{\mathrm{\sigma (v}}_r\mathrm{)d}{v}_{i}d{v}_g,$$ is used to infer the cross section from the rate constant of ion—molecule reactions measured in drift tubes as a function of E/p₀, κ, v_r, and σ are the rate constant, relative speed, and cross section, respectively. The Maxwellian distribution at gas temperature is used for f_gas. A displaced Maxwellian, having a temperature parameter defined by the diffusion coefficients, and a displacement defined by ${\mathrm{〈\; v}}_z{\mathrm{〉=v}}_d$ , is used for f_ion. v_d is the drift velocity. Justifications are given. The advantage of this approach is in the interpretation of rate constants of endothermic reactions. Qualitative and quantitative examples are considered. Very good agreements with experimental results are obtained. A way for calculating the rate constant of ion—molecule reactions under thermal equilibrium conditions is proposed. Its limitations are discussed. The importance of endothermic reactions to ionospheric model calculations is emphasized.