A nuclear magnetic resonance investigation of solid cyclo hexane

The nuclear magnetic resonance absorption spectrum and the spin-lattice relaxation time have been measured for the protons in polycrystalline cyclohexane between 100 degrees K and its freezing-point (279$\cdot $6 degrees K). It has been found that the second moment (mean square width) of the measured spectrum for temperatures at which the lattice is effectively rigid, namely, below 150 degrees K, is consistent with a molecular structure having D$_{3d}$ symmetry, tetrahedral bond angles, C$\chembond{1,0} $C bond lengths of 1$\cdot $54 angstrom and C$\chembond{1,0} $H bond lengths of 1$\cdot $10 angstrom. If the HCH angle is treated as a parameter to be determined, it is found to be 107$\frac{1}{2}\pm $ 3 degrees. On warming from 155 to 180 degrees K the second moment decreases to a value which indicates the reorientation of the molecules about their triad axes. Analysis of the spin-lattice relaxation time, which falls rapidly in this temperature range, shows that the height of the barrier hindering this reorientation is 11 $\pm $ 1 kcal/mole. Just below 186 degrees K, the temperature at which there is a polymorphic change, the reorientation frequency is of the order 10$^{6}$ c/s. The polymorphic transformation is accompanied by discontinuous changes in the second moment and the relaxation time. It is concluded that in the higher temperature modification the molecules have a considerable freedom of reorientation, such that the intramolecular contribution to the second moment becomes negligibly small. Just above 186 degrees K the mean reorientation frequency exceeds 3 $\times $ 10$^{7}$ c/s. A final narrowing of the line between 220 and 240 degrees K is thought to be due to vacancy diffusion of the molecules within the lattice, causing the intermolecular contribution to the second moment to vanish also. Details are given of the gas-flow cryostat used in this work. The theoretical formulation of the second moment has been extended to include the modification of the intermolecular contribution during reorientation.