ESR Studies of Heisenberg Spin Exchange. II. Effects of Radical Charge and Size

Abstract

The Heisenberg spin exchange behavior of several radical–solvent systems has been studied. This work has shown that $k$ , the second‐order rate constant for bimolecular encounters, and ${\mathrm{|\hspace{0.17em}J\hspace{0.17em}|\; \tau }}_1$ (where $\mathrm{|\hspace{0.17em}J\hspace{0.17em}|}$ is twice the exchange integral and ${\tau }_1$ is the lifetime of the collision pair) depend markedly on the ionic strength of the solution and upon the size and charge of the radical. For the peroxylamine disulfonate radical in a ${\text{5\hspace{0.17em}×\hspace{0.17em}10}}^{\text{−2}}M$ solution of 1:2 electrolyte, our simple analysis yields ${\mathrm{|\hspace{0.17em}J\hspace{0.17em}|\; \tau }}_1\text{\hspace{0.17em}∼\hspace{0.17em}0.95}$ and ${\text{k\hspace{0.17em}=\hspace{0.17em}2.0\hspace{0.17em}×\hspace{0.17em}10}}^{\text{+9}}{M}^{\text{−1}}·{\sec }^{\text{−1}}$ at 24°C; increasing the electrolyte concentration to ${\text{6.1\hspace{0.17em}×\hspace{0.17em}10}}^{\text{−1}}M$ gives ${\mathrm{|\hspace{0.17em}J\hspace{0.17em}|\; \tau }}_1\text{\hspace{0.17em}∼\hspace{0.17em}1.3}$ and ${\text{k\hspace{0.17em}=\hspace{0.17em}3.2\hspace{0.17em}×\hspace{0.17em}10}}^9{M}^{\text{−1}}·{\sec }^{\text{−1}}$ . These changes in $k$ and ${\mathrm{|\hspace{0.17em}J\hspace{0.17em}|\; \tau }}_1$ are attributed to screening by the electrolyte of the charge of the dianion radical; this is discussed in terms of the Debye theory. The di‐tertiarybutyl nitroxide (DTBN) radical undergoes apparent strong exchange ${\mathrm{(|\hspace{0.17em}J\hspace{0.17em}|\; \tau }}_1\text{\hspace{0.17em}≫\hspace{0.17em}1)}$ in pure water ${\text{(k\hspace{0.17em}=\hspace{0.17em}2.4\hspace{0.17em}×\hspace{0.17em}10}}^9{M}^{\text{−1}}·{\sec }^{\text{−1}}$ at 24°C). The dependence of the exchange frequency ${\mathrm{(\omega }}_{\mathrm{HE}})$ on added 1:2 electrolyte is of the form ${\omega }_{\mathrm{HE}}{\mathrm{\hspace{0.17em}=\hspace{0.17em}\omega }}_{\mathrm{HE}}\text{(0)}\exp {\mathrm{(-\hspace{0.17em}C}}_E\mathrm{\hspace{0.17em}/\hspace{0.17em}C\prime )}$ , where $C_E$ is the molar electrolyte concentration and ${\omega }_{\mathrm{HE}}\text{(0)}$ the exchange frequency in pure water; for a ${\text{2.4\hspace{0.17em}×\hspace{0.17em}10}}^{\text{−2}}M$ DTBN solution $\text{C′\hspace{0.17em}=\hspace{0.17em}0.23\hspace{0.17em}±\hspace{0.17em}0.02M}$ . This reduction of exchange frequency with electrolyte concentration is attributed to the formation of DTBN aggregates. The durosemiquinone radical undergoes strong exchange in dimethoxyethane ${\text{(k\hspace{0.17em}=\hspace{0.17em}2.9\hspace{0.17em}×\hspace{0.17em}10}}^9{M}^{\text{−1}}·{\sec }^{\text{−1}}\mathrm{at}\text{15°}\mathrm{C})$ . The closeness of $k$ to the diffusion‐controlled limit indicates that ion pairing takes place in solution. The tetraphenyl arsonium peroxylamine disulfonate radical undergoes apparent weak exchange ${\mathrm{(|\hspace{0.17em}J\hspace{0.17em}|\; \tau }}_1\text{\hspace{0.17em}<\hspace{0.17em}1)}$ in dimethyl sulfoxide. However, rapid radical decay made quantitative study of exchange impossible for this radical.