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

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.