Relaxation NMR

Conductivity arises from ionic motions in response to the applied electrical field. The associated field fluctuations affect the nuclear spin relaxations of constituent spin bearing nuclei. Therefore, a direct correlation between the two - nuclear spin relaxation (NSR) and the conductivity relaxations - is to be expected. 

Experimentally one generally distinguishes several spin- lattice (longitudinal) relaxation times, Tipd, Tig, Tip etc.. In glasses due to the presence of random potential energy barriers, the relaxation times exhibit a distribution. In general, they can be expressed as  

The phonon assisted tunneling on the other hand has a correlation time i2 given by  

It was also found that the variations of l/Ti required a Davidson-Cole distribution function for best fit. In the mixed alkali glasses the MT plots at high temperatures become symmetrical and broader. The activation energies determined from NMR, Enmr, and the E from conductivity measurements have also been compared. Since Li NMR senses only the lithium ion and not the other alkali, the Enmr in mixed alkali regions Eire observed to be lower than Ea. 

The activation energy determined from the low temperature branch of l/Ti plots in NSR studies are found to be lower than the d.c. activation barrier, E, but comparable with the activation energies for the frequency independent a.c. activation energies. Pradel and Ribes (1991) have deduced / values as EaJ Edc Enmr Edc- They found additionally that P values did not have a clear correlation to 1-5 values, where s is the exponent in of fits to a.c. conductivity. 

---

In this section, I present a few illustrative examples of applications of NMR relaxation studies within different branches of chemistry. The three subsections cover one story each, in order of increasing molecular size and complexity of the questions asked. 

Champmartin D and Rubini P 1996 Determination of the 0-17 quadrupolar coupling constant and of the C-13 chemical shielding tensor anisotropy of the CO groups of pentane-2,4-dione and beta-diketonate complexes in solution. NMR relaxation study/norg. Chem. 35 179-83... 

Maler L, Lang J, Widmalm G and Kowalewski J 1995 Multiple-field carbon-13 NMR relaxation investigation on melezitose Magn. Reson. Chem. 33 541-8... 

Lahajnar, G., Zupancic, L, Rupprecht, A. Proton NMR relaxation and diffusion study of water sorbed in oriented DNA and hyaluronic acid samples. In Biophysics of Water (Franks, F., Mathias, S., eds) Wiley, New York (1982) 231-234... 

Here, the J terms are the spectral densities with the resonance frequencies co of the and nuclei, respectively. It is now necessary to find an appropriate spectral density to describe the reorientational motions properly (cf [6, 7]). The simplest spectral density commonly used for interpretation of NMR relaxation data is the one introduced by Bloembergen, Purcell, and Pound [8]. 

Another way to describe deviations from the simple BPP spectral density is the so-called model-free approach of Lipari and Szabo [10]. This takes account of the reduction of the spectral density usually observed in NMR relaxation experiments. Although the model-free approach was first applied mainly to the interpretation of relaxation data of macromolecules, it is now also used for fast internal dynamics of small and middle-sized molecules. For very fast internal motions the spectral density is given by ... 

Up to now it has been tacitly assumed that each molecular motion can be described by a single correlation time. On the other hand, it is well-known, e.g., from dielectric and mechanical relaxation studies as well as from photon correlation spectroscopy and NMR relaxation times that in polymers one often deals with a distribution of correlation times60 65), in particular in glassy systems. Although the phenomenon as such is well established, little is known about the nature of this distribution. In particular, most techniques employed in this area do not allow a distinction of a heterogeneous distribution, where spatially separed groups move with different time constants and a homogeneous distribution, where each monomer unit shows essentially the same non-exponential relaxation. Even worse, relaxation... 

Gillen K. T., Douglas D. S., Malmberg M. S., Maryott A. A. NMR relaxation study of liquid CCI3F. Reorientational and angular momentum correlation times and rotational diffusion, J. Chem. Phys. 57, 5170-9 (1972). 

Suvernev A. A., Temkin S. I. Spin-rotational NMR-relaxation of spherical molecules in gas phase, Chem. Phys. Lett. 154, 49-55 (1989). 

Since NMR relaxation in proteins is determined by dynamics on the picosecond to nanosecond time scale, experimental NMR relaxation parameters can provide important information concerning picosecond motions. Time correlation func-... 

Urry DW, Trapane TL, McMichens RB et al (1986) N-15 nmr relaxation study of inverse temperature transitions in elastin pol)q)entapeptide and its cross-linked elastomer. Biopolymers 25 5209-5228... 

In addition to giving conformational information, solid state NMR relaxation experiments can be used to probe the thermal motion of polymers in the hydrated cell wall (5). The motion of the polymers can give us clues as to the environment of the polymer. When there are both rigid and mobile polymers within a composite material, NMR spin-diffusion experiments can be used to find out how far apart they are. 

NMR Relaxation Behavior of Perfluorinated Gases 3.5.3.1 Introduction to Gas Phase Relaxation... 

NMR Relaxation of Liquids Versus Cases in Porous Media... 

NMR relaxation of liquids such as water in porous solids has been studied extensively. In the fast exchange regime, the spin-lattice relaxation rate of water in pores is known to increase due to interactions with the solid matrix (so-called surface relaxation ). In this case, T) can be described by Eq. (3.5.6) ... 

In situ NMR measurements can be made in conjunction with down-hole fluid sampling [5, 6]. The NMR relaxation time and diffusivity can be measured under high-temperature, high-pressure reservoir conditions without loss of dissolved gases due to pressure depletion. In cases when the fluids may be contaminated by invasion of the filtrate from oil-based drilling fluids, the NMR analysis can determine when the fluid composition is approaching that of the formation [5, 6]. 

S.-W. Lo, G. J. Hirasaki, W. V. House, R. Kobayashi 2002, Mixing Rules and Correlations of NMR Relaxation with Viscosity, Diffiisivity, and Gas/OU Ratio of Methane/Hydrocarhon Mixtures, presented at SPEJ, March 24-34, 2002. 

C.-C. Huang 1997, (Estimation of rock properties by NMR relaxation methods), MS Thesis, Rice University, 108-113. 

Macroporosity for NMR Relaxation in Sandstones and Grainstones), SPWLA Transactions Annual Logring Symposium, New Orleans, June 26-29. 

We represent the NMR relaxation distribution by the continuous number density function, P( t), of characteristic relaxation time t. Our measurements correspond to a series of CPMG echoes, represented by... 

We have developed a method to spatially resolve permeability distributions. We use MRI to determine spatially resolved velocity distributions, and solve an associated system and parameter identification problem to determine the permeability distribution. Not only is such information essential for investigating complex processes within permeable media, it can provide the means for determining improved correlations for predicting permeability from other measurements, such as porosity and NMR relaxation [17-19]. 

R. M. Kroeker, R. M. Henkelman 1986, (Analysis of biological NMR relaxation data with continuous distributions of relaxation-times),/. Mag. Reson. 69, 218. 

Yuan P, Marshall VP, Petzold GL, Poorman RA, Stockman BJ. Dynamics of stromelysin/inhibitor interactions studied by 15N NMR relaxation measurements Comparison of ligand binding to the SrS3 and S -Sy subsites. J Biomol NMR 1999 15 55-64. 

---