Intermolecular Potentials from NMR Data: II. CH₄, CF₄, and SiF₄

Abstract

Proton and fluorine spin–lattice relaxation times per unit density, T1/ρ, in pure gases CH4, CF4, and SiF4 are experimentally found to be proportional to T−1.5 where T is the temperature. Using either a hard sphere or a 12–6 Lennard–Jones potential for the isotropic part of the intramolecular potential, it is shown here that these data can be analyzed to obtain information on the anisotropic part of the potential in these systems. The analysis is made within the framework of the Bloom–Oppenheim theory, assuming that the correlation time of the spin–rotation interaction can be approximated by the average lifetime of a molecule in the given J state. From the strength of the attractive term in the anisotropic potential, the octopole moments of all the three molecules are obtained. These values are comparable with the values reported earlier based on other techniques for CH4 and CF4 in case of the Lennard–Jones model. The octopole moments of CH4 and CF4 obtained from the hard sphere model are smaller by 25% than those from the Lennard–Jones model. For SiF4, we obtain values of 4.14 × 10−34 e.s.u. cm3 and 5.3 × 10−34 e.s.u. cm3, as the octopole moments from the Lennard–Jones and the hard sphere models respectively and no other value exists in the literature.

Relaxation and diffusion of perfluorocarbon gas mixtures with oxygen for lung MRI

“…The 19 F-19 F dipolar interactions are weak by comparison, which may be inferred by comparing the relaxation times of (say) CH 4 and CF 4 : despite the dipolar interactions between 19 F spins being slightly smaller than those in the smaller molecule CH 4 , the relaxation time T 1 at a given density is much smaller for CF 4 [33,34].…”

Inert fluorinated gas T1 calculator

“…There have been measurements of coupling constants and collision cross sections [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] that clearly lay out the physical framework, but to calculate a given T 1 often requires determining whether the desired range of physical parameters has been explored, sifting through different parameterizations of relaxation equations, and interpolating between tabulated parameters, after which it can be difficult to calculate the accuracy of the result. We present a unified calculation for common laboratory conditions so that a computer program will generate T 1 within a known accuracy if given pressure, temperature, and mixture composition.…”

“…Some studies have used more realistic molecular potential models for collision dynamics as tools for measuring physical constants and deeper understanding of the physics (e.g. [14], see [1]). We use the Lennard-Jones model to take care of some of the temperature dependence in the hope that the remaining dependence is easy to match with a small number of curve-fitting parameters.…”

Fluid-Rock Characterization and Interactions in NMR Well Logging

“…The mixing rule is tested for five CH 4 gas mixtures, including CH 4 -CO 2 , CH 4 -N 2 , CH 4 -He, CH 4 -Ne and CH 4 -Ar gas mixtures [30][31][32] . In these gas mixtures, only methane contributes to proton relaxation times of the mixtures.…”

“…In order to calculate T 1 of CH 4 mixtures using Equation (49) and Equation 51, we need the knowledge of cross sections for angular momentum transfer for CH 4 molecules with various collision partners. In general, the collision cross section for angular momentum transfer can be reasonably represented by a function of the form [30][31][32][33]…”