Proton Motions in Complex Hydrogenous Liquids. II. Results Gained from Some Neutron-Scattering Experiments

In an accompanying paper, a cross section for the quasi-elastically scattered neutron spectra from certain types of hydrogenous liquids is given. In the present paper a comparison is made between this theoretical model and some neutron-scattering results obtained on $n$-propyl alcohol and pentane. The quasi-elastically scattered neutron intensity is analyzed in terms of the relaxation times ${\tau }_0$, ${\tau }_1$, ${{\tau }_0}^{\prime }$, and ${{\tau }_1}^{\prime }$, the jump length $l$ of the proton, and the self-diffusion coefficient $D$ of the molecular center of gravity. The nature of the quasi-elastically scattered neutron intensity is generally interpreted as a result of mixed protonic jumps and molecular diffusion. It is shown that the diffusion coefficients derived from neutron-scattering data consist of a combination $D+\frac{l^2}{2{\tau }_0}$, where for very low viscosities $D$ dominates and for higher viscosities the protonic diffusion constant $\frac{l^2}{2{\tau }_0}$ dominates. Protonic jump lengths of 1.5 Å are observed. Definite values of the relaxation times ${\tau }_{00}$, ${{\tau }_0}^{\prime }$, and ${\tau }_0$ are derived from the width of the quasi-elastic line. With the present resolution of the experimental equipment, times ${\tau }_{00}$ in the range ${10}^{-12\mathrm{}}$ to 2×${10}^{-11\mathrm{}}$ sec may be studied. It is shown how in the low-temperature, high-viscosity ranges, ${{\tau }_0}^{\prime }$ is much larger than ${\tau }_0$, the internal mean lifetime for a proton in a fixed-position. ${\tau }_0$ values in a range from ${10}^{-11\mathrm{}}$ to 2.5×${10}^{-12\mathrm{}}$ are derived, whereas derived values of ${{\tau }_0}^{\prime }$ for $n$-propyl alcohol range from 2.5×${10}^{-9\mathrm{}}$ to 2.75×${10}^{-12\mathrm{}}$ sec in a temperature range from 153 to 333°K. It is also shown for the case of pentane that when larger momentum transfers are studied in quasi-elastic scattering, the intensity of the resulting gaslike scattering picture is governed by a Debye-Waller factor. This is due to the fact that even if the center of gravity is moving like a gas particle, the proton jumps within the molecule continue. These results indicate that the quasi-elastic scattering has two components: a diffusive component of width $2\hslash (D+\frac{l^2}{2{\tau }_0}){\kappa }^2$ and a gas component the width of which depends upon the degree of hindrance for the free recoil of a molecule in a collision. Which component dominates depends upon the magnitude of the momentum transfer $\hslash \kappa$ in the scattering process.