A nuclear magnetic resonance investigation of solid cyclo hexane

Abstract

The nuclear magnetic resonance absorption spectrum and the spin-lattice relaxation time have been measured for the protons in polycrystalline cyclo hexane between 100° K and its freezing-point (279·6° 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° K, is consistent with a molecular structure having D 3d symmetry, tetrahedral bond angles, C—C bond lengths of 1.54 Å and C—H bond lengths of 1.10 A. If the HCH angle is treated as a parameter to be determined, it is found to be 1071/2 ± 3°. On warming from 155 to 180° 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 ± 1 kcal/mole. Just below 186° 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° K the mean reorientation frequency exceeds 3 x 10 7 c/s. A final narrowing of the line between 220 and 240° 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.