PHYSICAL CHEMISTRY

N. Ya. BUBEN, Yu. N. MOLIN, A. I. PRISTUPA, V. N. SHAMSHEV

THE E.P.R. SPECTRUM OF THE CYCLOHEXYL RADICAL UPON RADIOLYSIS OF CYCLOHEXANE IN THE GAS–CRYSTALLINE STATE

(Presented by Academician N. N. Semenov, 26 IV 1963)

The spectrum of electron paramagnetic resonance (e.p.r.) of radicals formed under the action of $\gamma$-rays in frozen cyclohexane has been published in a number of works ($^{1-3}$). At $77^\circ$ K, six poorly resolved components of the hyperfine structure (h.f.s.) are observed, with an intensity ratio close to $1:1:2:2:1:1$. According to ($^2$), the magnitudes of the splittings and the intensities of the hyperfine-structure components can be explained if one assumes that the spectrum is a triplet with $\Delta H_\beta = 37$ oersted and an intensity ratio of $1:1:1$, each component of which is additionally split into two, $\Delta H_\alpha = 20$ oersted. Such a spectrum was assigned to the radical $\mathrm{C_6H_{11}}$ on the assumption that the hyperfine splitting is caused by one hydrogen atom in the $\alpha$-position and by two hydrogen atoms in the $\beta$-position relative to the free valence, while the other two $\beta$-hydrogens are oriented in such a way that their interaction with the unpaired electron is small. In work ($^3$), somewhat larger splitting values were obtained ($\Delta H_\beta = 44$ oersted, $\Delta H_\alpha = 26$ oersted), and it was shown that, with increasing temperature, the resolution of the spectrum improves. However, beginning at a temperature of $160^\circ$ K, recombination of radicals proceeds at a noticeable rate ($^{3,4}$), and at the polymorphic transition point, $T_{\mathrm{p}} = 186^\circ$ K ($^5$), the radicals rapidly disappear completely ($^{4,6}$). By observing radicals formed in cyclohexane directly during irradiation with fast electrons ($^7$), it proved possible to study their e.p.r. spectrum at higher temperatures, when the lifetime of the radicals is of the order of 1 second. This was the subject of the present work.

Cyclohexane of “chemically pure” grade was used; it was additionally purified from traces of benzene and cyclohexene and distilled. About 70 mg of cyclohexane in a thin-walled ampoule made of “Luch” glass was placed in the resonator of the spectrometer in a stream of cold nitrogen. The temperature was measured with a thin copper–constantan thermocouple located in the ampoule. The e.p.r. spectrum was recorded during irradiation of the sample with electrons of energy 1.6 MeV. The measurements were carried out on an EPR-2 spectrometer with a cylindrical resonator of the $H_{011}$ type.

Passage through the temperature of the polymorphic transition $T_{\mathrm{p}}$ is accompanied by a change in the form of the e.p.r. spectrum of irradiated cyclohexane. At a temperature of $183^\circ$ K, i.e., only $3^\circ$ below $T_{\mathrm{p}}$, accumulation of radicals is observed under the electron beam; their spectrum is shown in Fig. 1a. It consists of 6 lines with a total splitting of 98 oersted and splittings between the lines of 20.5; 18.0; 20.5; 18.0; 20.5. However, already at $T = 188^\circ$ K, as is seen from Fig. 1b, a sharp change in the form of the spectrum occurs: the lines become greatly narrowed (from about 10 gauss to about 3 gauss), and an additional splitting of each of them into three is observed. The magnitude of this additional splitting is about 5 gauss. With increasing temperature, further changes in the spectrum occur. At $T > 215^\circ$ K, only 6 components of about 3 gauss width again remain in the spectrum, but the splittings between them change and are 20; 24; 20; 24; 20. Figure 2b shows a spectrum recorded at $223^\circ$ K. With further increase in temperature, the form of the spectrum does not change up to $T = 270^\circ$ K, but its intensity decreases at constant pow—

dose rate. In the temperature range 215–270° K the ratio of the intensities of the hfs components is approximately \(1 : 1 : 4.3 : 4.5 : 1 : 1\).

The change in the magnitudes of the splitting between the components is connected with the fact that, as the temperature is raised, different components of triplets with small splitting disappear. In the central triplets (\(v\) and \(g\) in Fig. 2) the middle components remain, whereas in the others (Fig. 2 \(a, b, d, e\)) only the outer components, relative to the center of the spectrum, are retained. In Fig. 1b the components retained at higher temperatures are marked with a cross (+). When the temperature is changed from 186° K to 215° K, a gradual change in the intensities of the components in each triplet can be clearly seen; Fig. 2a shows the spectrum at 206° K.

The appearance of the spectrum does not depend on the direction in which the temperature is changed, i.e., it is uniquely determined by the temperature of the sample.

Fig. 1. EPR spectra of the cyclohexyl radical:
\(a\)—at 183° K, \(b\)—at 188° K

Discussion of results. The spectrum of the cyclohexyl radical at \(T = 183^\circ\) K gives average splitting values \(\Delta H_\alpha \simeq 20\) oersted and \(\Delta H_\beta \simeq 38\) oersted, which agrees well with the data of work \((^{2})\). At \(T > T_{\mathrm{p}}\), when cyclohexane passes into the gas-crystalline state \((^{8})\) and intense rotation of the molecules in the lattice is unfrozen \((^{9})\), a considerable narrowing of the lines occurs, apparently due to averaging of the anisotropy of the hyperfine interaction. As a result, an additional splitting of each line into a triplet with \(\Delta H \simeq 5\) oersted between the components becomes noticeable. It is natural to assume that it is connected with a weak interaction of the unpaired electron with the second pair of \(\beta\)-hydrogens in the cyclohexyl radical.

Fig. 2. EPR spectra of the cyclohexyl radical: \(a\)—at 206° K, \(b\)—at 223° K

Treatment of a large number of spectra leads to the following values of the hyperfine-interaction constants in the cyclo-\(\mathrm{C_6H_{11}}\) radical:
\(a_\alpha = 20.5 \pm 0.5\) oersted; \(a_{\beta_1} = 38.7 \pm 0.5\) oersted; \(a_{\beta_2} = 5.0 \pm 0.5\) oersted. The theoretical distribution of intensities in the spectrum of such a radical is shown in the lower part of Fig. 2 and corresponds to the ratio
\((1 : 2 : 1) : (1 : 2 : 1) : (2 : 4 : 2) : (2 : 4 : 2) : (1 : 2 : 1) : (1 : 2 : 1)\). In experiment, at \(T = 188^\circ\), the ratio of intensities, measured from the heights of the first derivatives, deviates appreciably from this theoretical distribution. Devi-

are especially noticeable on the central components of the main triplet (1 : 3.5 : 1 instead of 1 : 2 : 1; see Fig. 2).

This fact, as well as the changes in the spectrum observed with increasing temperature, can in our opinion be explained by inversion of cyclohexyl radicals, the frequency of which at \(T > T_{\mathrm{m}}\) is sufficiently high. According to NMR data, in a solution of cyclohexane in carbon disulfide, inversion of \(C_6H_{12}\) molecules of the “chair”–“chair” type occurs at an appreciable rate

Fig. 3. Schematic spectrum of the cyclohexyl radical: \(a\)—in the absence of inversion, \(b\)—with rapid inversion

up to a temperature of \(-70^\circ\mathrm{C}\) \((^{10})\). In the cited work, from the temperature dependence of the magnitude of the shift between the absorption lines of axial and equatorial protons, the height of the energy barrier for such inversion was estimated to be 9.7 kcal/mole. The rate constant for inversion of the molecules at \(-66.5^\circ\mathrm{C}\) was \(120\ \mathrm{s}^{-1}\).

Rapid inversion of an analogous type in the case of cyclohexyl radicals should lead to the axial protons frequently becoming equatorial, and vice versa. As a result, those hfs components corresponding to transitions for which the magnetic quantum numbers of the \(\beta_1\)- and \(\beta_2\)-protons are different will broaden, since inversion produces an instantaneous change in the position of the absorption line. Such broadening is in principle no different from the broadening observed in an NMR spectrum during exchange of nonequivalent protons. In Fig. 3a, the horizontal arrows connect the lines that transform into one another upon inversion. In contrast to these lines, the component with \(m_{\beta_1} = m_{\beta_2}\) is not displaced upon inversion and, consequently, will not broaden. As can be seen, the lines marked with crosses in Fig. 2 correspond to equal values of \(m_{\beta_1}\) and \(m_{\beta_2}\). With increasing temperature, not only these spectral lines fail to broaden. The possibility of observing such an effect by the EPR method suggests that the inversion frequency is considerably greater than in the case of molecules. Indeed, the sharp change in the appearance of the spectrum in the temperature intervals 186–215 K indicates that, in this interval, the additional broadening of components with \(m_{\beta_1} \ne m_{\beta_2}\) is of the order of the initial linewidth \((\Delta H = 3\ \mathrm{Oe}\), or \(\Delta \nu \cong 10^7\ \mathrm{s}^{-1})\). Consequently, the inversion frequency of the radical at these temperatures is about \(10^7\ \mathrm{s}^{-1}\), i.e., approximately \(10^4\)–\(10^5\) times greater than in the case of the molecule. Such an increase in frequency is equivalent to a lowering of the inversion barrier to 5–6 kcal/mole.

It may be assumed that the facilitation of inversion of the “chair”–“chair” type for the cyclohexyl radical may be connected with the presence of additional strains arising in the radical as a result of a change in the hybridization of the bonds at the carbon atom bearing the free valence.

As noted above, up to temperatures close to the melting point of cyclohexane, no new lines are observed in the EPR spectrum, whose appearance might be expected at high frequencies of site exchange-

of the \(\beta_1\) and \(\beta_2\) protons. Thus, up to the melting point, the inversion frequency is considerably lower than the frequency at which observation of these lines becomes possible (according to our estimates, \(\nu \sim 10^{10}\ \mathrm{s}^{-1}\)). This result is consistent with the high barrier for inversion of the radicals given above.

At higher temperatures (in liquid cyclohexane) the exchange frequency may become sufficiently large. The EPR spectrum of the cyclohexyl radical in this limiting case should have the form shown in Fig. 3b, where the dashed lines mark the lines corresponding to a high exchange frequency.

Institute of Chemical Physics,
Academy of Sciences of the USSR

Institute of Chemical Kinetics and Combustion,
Siberian Branch, Academy of Sciences of the USSR

Received
25 IV 1963

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