Anisotropic Molecular Rotation in Liquid N,N-Dimethylformamide by Nuclear Magnetic Resonance

The anisotropy in the molecular rotation of N,N‐dimethylformamide (DMF) in the liquid is investigated by considering the NMR relaxation times of the ¹⁴N, ¹⁷O, and formyl deuteron nuclei in DMF, DMF¹⁷O, and DMF‐d₁, respectively. Assuming that the molecular rotation is diffusional and that one principal diffusion axis (the $z$ axis) is perpendicular to the molecular plane, a range of possible orientations for the diffusion axes in the plane and a corresponding range of values for each of the three diffusion constants are calculated. The range of possible orientations of the $x$ diffusion axis, which varies little with temperature, extends over about 26°, from the direction of the $x$ principal inertial axis toward and past the direction of the molecular dipole moment. At 280°K the diffusion constants are $D_x{\text{\hspace{0.17em}=\hspace{0.17em}(2.0\hspace{0.17em}±\hspace{0.17em}0.4)\hspace{0.17em}×\hspace{0.17em}10}}^{11}{\sec }^{\text{−1}}{\mathrm{,\; D}}_y{\text{\hspace{0.17em}=\hspace{0.17em}(6\hspace{0.17em}±\hspace{0.17em}3)\hspace{0.17em}×\hspace{0.17em}10}}^9{\sec }^{\text{−1}},\mathrm{and}{D}_z{\text{\hspace{0.17em}=\hspace{0.17em}(2.9\hspace{0.17em}±\hspace{0.17em}0.7)\hspace{0.17em}×\hspace{0.17em}10}}^{10}{\sec }^{\text{−1}}$ . At 390°K, $D_x{\text{\hspace{0.17em}=\hspace{0.17em}(4.0\hspace{0.17em}±\hspace{0.17em}0.7)\hspace{0.17em}×\hspace{0.17em}10}}^{11}{\sec }^{\text{−1}}{\mathrm{,\; D}}_y{\text{\hspace{0.17em}=\hspace{0.17em}(10\hspace{0.17em}±\hspace{0.17em}8)\hspace{0.17em}×\hspace{0.17em}10}}^9{\sec }^{\text{−1}}$ and $D_z{\text{\hspace{0.17em}=\hspace{0.17em}(2.1\hspace{0.17em}±\hspace{0.17em}0.7)\hspace{0.17em}×\hspace{0.17em}10}}^{11}{}^{\text{sec−1}}$ . The ratio of the rotation rate about the ith axis in the free gas to $D_i$ is a direct measure of the extent to which rotation about the ith axis is hindered in the liquid by intermolecular interactions. Defining this ratio as ${\chi }_i$ (where larger values of ${\chi }_i$ indicate a more hindered rotation), it is found that at low temperatures ${\chi }_y{\mathrm{,\; \chi }}_z{\mathrm{\hspace{0.17em}\gg \hspace{0.17em}\chi }}_x$ and at high temperatures ${\chi }_y{\mathrm{\hspace{0.17em}\gg \hspace{0.17em}\chi }}_z{\mathrm{,\; \chi }}_x$ . Once the rotation of the molecular framework is known, the relaxation times of the methyl deuterons in DMF‐d₇ can be used to calculate the internal rotation rates of the deuterated methyl groups. These rotation rates are shown to be comparable to the rate of the molecular rotation.