Estimated Distribution Functions of Electronic Redox Levels and the Rate of Chemical Reactions of Excess Electrons in Dielectric Liquids

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Abstract
A crude estimate of the distributions of occupied and unoccupied electronic redox levels of the system s/es− and of various acceptor systems As/As− in n‐hexane was made (es−: solvated electron; s: unoccupied solvent trap). Expressions for the rate constants of reactions of solvated and mobile electrons em− in dielectric liquids are also given. These expressions are based on the assumption that electron reactions in solution are vertical attachment processes as in the gas phase.The following conclusions can be drawn using these expressions and the estimated distribution functions of electronic redox levels: The rate constant of reaction of excess electrons with an acceptor A should initially increase proportionally to the electron mobility μ (in various solvents with different mobilities) and at high μ values level‐off if the system As/As− has a broad distribution of unoccupied levels. k may pass through a maximum with changing μ if the distribution of unoccupied levels of As/As− is concentrated at relatively high energies (acceptors that strongly change their atomic configuration upon electron attachment). The temperature dependence of k should roughly correspond to the activation energy of the electron mobility in solvents of low mobility. In solvents of high electron mobility, a negative activation energy or a maximum of the rate constant at a certain temperature may occur if the acceptor system has a low density of states at the energy level of the mobile electron. All these effects have recently been observed by Beck and Thomas and Allen, Gangwer and Holroyd. In the case of acceptors such as oxygen, whose redox potential is significantly more positive than that of s/es−, a relatively slow rate of reaction with excess electrons may be expected provided that the electron cannot be captured into a higher orbital of the product‐anion. An upper limit of 0.45 eV of the difference in the redox potentials of the system s/es− and C12H/C12H− in tetramethylsilane was obtained. It is in agreement with the dissociation constant of the biphenyl anion (s + C6H → C6H + es−) which has recently been measured by Warman et al.

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