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Nuclear magnetic resonance study of ethane near the critical point Noble, John Dale

Abstract

A nuclear magnetic resonance study of the critical region has been made in ethane which was chosen as the working substance for its convenient critical temperature and pressure. Standard radio frequency pulse techniques were used to measure the spin-lattice relaxation time T₁ and the self diffusion constant D by the method of spin echoes. A spectrometer having good stability and very flexible timing circuits was designed and constructed. An automatic temperature control system capable of holding the sample temperature constant to better than 0.01° C for long periods of time was also designed and constructed. The spin-lattice relaxation time in ethane has been measured along the vapor pressure curve over the entire liquid temperature range as well as in the equilibrium vapor from 0° C to the critical temperature (Tc =32.32° C) and in the dense gas from Tc to 60°C. In the liquid T₁ rises rapidly with increasing temperature and goes through a maximum at about 0°C after which it begins to fall. In the vapor T₁ is always less than in the liquid and increases with increasing temperature. In the dense gas above Tc the relaxation time decreases slowly with increasing temperature. These results are compared with the conventional theory for relaxation in liquids and dense gases. The theory gives the relaxation rate 1/T₁ in terms of three relaxation mechanisms: the dipole-dipole intermolecular interaction the dipole-dipole intramolecular interaction and the spin-rotational interaction. In view of the gross approximations made in the theory a very reasonable fit to the experimental data is obtained. For the low temperature liquid the dipole-dipole interactions are sufficient to account for the relaxation. At high temperatures the spin-rotational interaction seems to contribute significantly to the relaxation and near the critical point it is the dominant relaxation mechanism. No anomalous behaviour was observed in the relaxation near the critical point and to within the error of measurement it is adequately described in terms of changes in density and self diffusion constant. T₁ was also measured in dilute ethane gas over a temperature range of 180°K to 300°K. It was observed that T₁ is proportional to density ρ and the temperature dependence of T/ρ is about T⁻¹˙³⁷. Measurements of the diffusion constant reveal that for low temperatures the product Dρ for liquid ethane varies approximately as T³. As the temperature approaches the critical temperature there appears to be anomalous behaviour in D. For both the liquid and vapor the product Dρ begins to decrease and goes through a minimum and then increases rapidly as the critical point is reached. Oxygen has been added to these samples to decrease their relaxation time and this may well be an impurity effect. Particular attention was devoted to the question of the equilibrium state in the critical region and measurements were made on the time taken to achieve equilibrium. The approach of the ratio of liquid to vapor density to its equilibrium value was found to vary in a roughly exponential manner with a time constant of the order of several hours. Sufficient time was allowed after changing the sample temperature for equilibrium to be established and all measurements of diffusion constant and spin-lattice relaxation time reported here are thought to be equilibrium values.

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