Velocity Correlation Time Research Articles

Angular Velocity Correlation Functions and High-Frequency Dielectric Relaxation

The angular velocity correlation function can be studied through measurements of dielectric relaxation and far-infrared absorption. Relations between these quantities are described in this article, and the data of Davies, Pardoe, Chamberlain, and Gebbie are analyzed. Velocity correlation times are obtained for molecules in four simple liquids. Hubbard has obtained a theoretical expression linking the velocity correlation time, the orientation correlation time, and the molecular moment of inertia. This expression is experimentally verified for molecules in nonviscous liquids. Certain paradoxical predictions are found when this expression is applied to viscous liquids and solids. This article considers stochastic models for relaxation, in which the probability of molecular reorientation is modulated by fluctuations in the intermolecular environment. These stochastic models lead to orientation and velocity correlation functions that are consistent with experimental observations.

Nuclear spin relaxation and molecular motion in liquid and solid phosphine

Extensive measurements of the nuclear magnetic resonance relaxation times are reported for the proton, deuteron and phosphorus-31 resonances in a series of solutions of phosphine (PH3) in perdeuterophosphine (PD3) in the liquid and in the solid plastic crystal phase. All these measurements are interpreted in a consistent manner in terms of the molecular motion in spite of the difficulties arising from the proton/deuteron exchange. It is found that both the molecular reorientation and translation are rapid in the liquid. On solidification to the plastic crystal phase the molecular reorientational motion is little affected and is possibly more rapid than in the liquid but the translational motion is much slower. Correlation times are obtained for reorientation, molecular angular velocity and translational motion as well as estimates of the self-diffusion constant in the two states. Independent estimates of the molecular reorientational and angular velocity correlation times have been obtained. Since they ar...

Nuclear magnetic relaxation by spin-rotation interaction.

Spin-rotation interaction constants, c, are calculated from the paramagnetic term of the nuclear magnetic shielding constant, σ p, using a relationship originally due to Ramsey. Calculated values show excellent agreement with experimental determinations from molecular beam measurements. Since σ p can be easily estimated from the chemical shift of the nuclear resonance this provides a general method for estimating spin-rotation interaction constants. Chemical shift anisotropies allow the components c ⊥ and c ‖ of the spin-rotation interaction tensor to be determined. Generally both components have the same sign and are of similar magnitude. The r.m.s. value of the spin-rotation interaction constant, required to calculate nuclear spin-lattice relaxation times, is not expected to differ appreciably from average values obtained from molecular beam measurements or magnetic shielding. Values for the molecular angular velocity correlation time, τ sr, calculated directly from nuclear spin-lattice relaxation times...

19F Spin–Rotational Interactions in 1- and 2-Trifluoromethylnaphthalenes in the Liquid State

The temperature dependences of the 1H and 19F spin–lattice relaxation times in 1- and 2-trifluoromethylnaphthalenes, and also in benzotrifluoride have been measured by the adiabatic fast passage method. The effects of dilution in toluene-d8 on 1H and 19F T1's in the molecules studied have also been investigated. It has been found that the 19F relaxation rates in 2-trifluoromethylnaphthalene and benzotrifluoride are determined by spin–internal-rotation coupling and independent of intermolecular torques within the temperature region studied. An approximate relationship between the angular velocity correlation time and the barrier to internal rotation of the CF3 group has been proposed. The estimated barriers to rotation, 0.2 and 0.4 kcal/mole in benzotrifluoride and 2-trifluoromethylnaphthalene, are in agreement with those calculated by using approximate potential functions. Since there is a steric interaction between the CF3 group and the hydrogen at the 8 position in 1-trifluoromethylnaphthalene, the spin–internal-rotation coupling is quenched to a large extent, and the spin-rotational mechanism is mainly due to the spin–over-all-rotation coupling.

Nuclear spin-lattice relaxation, including the spin-rotation interaction, in liquid benzene and several benzene derivatives up to the critical temperature

Spin-lattice relaxation times have been measured for 1H and 19F nuclei in benzene and several benzene derivatives. In most cases the measurements have been made from the supercooled liquid temperature up to the liquid-vapour critical temperature. The results are analysed in terms of direct dipole-dipole and spin-rotation magnetic interactions. Ring and side group 19F nuclei and methyl side group protons show strong spin-rotation relaxation effects above room temperature. Ring protons in some cases show a possible weak spin-rotation relaxation near the critical temperature. Relaxation time measurements for C6H6 - C6D6 mixtures are used to calculate reliable molecular motion correlation times from the dipole-dipole relaxation for many of the benzene derivatives. A detailed account is given of the physical processes involved in the spin-rotation interaction contribution to nuclear magnetic relaxation in liquids. It is shown that the relaxation due to the spin-rotation interaction is largely independent of the details of the molecular reorientation. In several cases the molecular spin-rotation interaction tensor has been calculated from the relaxation time measurements and the values are found to be in reasonable agreement with values obtained from molecular beam measurements. Quantitative evidence is given for the validity of a simple relation (in an equation) between the spatial and angular momentum correlation times. In these liquids spatial correlation times are of order 10-12 sec, whereas angular velocity correlation times are of order 10-13 sec. The former decreases and the latter increases with temperature and at the critical temperature they are comparable in magnitude.