Nuclear spin relaxation times

By recording My for a number of x values and fitting these data to Eq. (3), both the Tj characterising the system and the value of Mo (which quantifies the number of initially excited spins) are obtained. In a spatially resolved relax-ometry experiment, images are acquired at different values of x, and a fit of Eq. (3) to the intensity as a function of x, for the equivalent pixel, i, in each image allows a complete map of Mq, and Tu to be obtained. Thus, spatial variation in 

On timescales of less than or equal to that of spin-spin relaxation (T2) processes occur. T2 characterises the loss of phase coherence of the individual spin isochromats within the spin ensemble comprising the total magnetisation vector M0. A spin isochromat represents a group of spins that experiences the same homogeneous magnetic field and which, therefore, behaves in the same 

An additional and important relaxation time constant is T, which characterises a faster decay of the magnetisation along y and accounts for, in particular, the additional effects of magnetic field heterogeneities on the loss of phase coherence of the magnetisation. Thus, the simple pulse-acquire sequence (with no re-focusing) shown in Fig. 3, will give a response in which the envelope 

In summary, the reasons that the nuclear spin relaxation times, and in particular Tj and T2, are so important are  

---

On the other hand, NMR spectra appear in general as the average of the spectra of the two spin states [36, 153]. This observation determines an upper limit for the spin-state lifetime shorter than the nuclear spin relaxation time Tl = l/ktH < lO s. In general, therefore, either the superposition or the average of the particular spectroscopic properties of the two spin states is observed, subject to the relative magnitude of lifetime of the excited spectroscopic state and the rate of spin-state conversion. The rate /clh is thus estimated... 

The use of magnetic resonance imaging (MRI) to study flow patterns in reactors as well as to perform spatially resolved spectroscopy is reviewed by Lynn Gladden, Michael Mantle, and Andrew Sederman (University of Cambridge). This method allows even unsteady-state processes to be studied because of the rapid data acquisition pulse sequence methods that can now be used. In addition, MRI can be used to study systems with short nuclear spin relaxation times—e.g., to study coke distribution in catalytic reactors. 

Relaxivity is the term given to a contrast agent s characteristic potency to decrease the nuclear spin relaxation times of water protons. Relaxivity is defined by the following relationship ... 

The majority of the early MRI studies specific to catalysis addressed the heterogeneity in structure and transport within catalyst pellets. In-plane spatial resolution achieved in these investigations was approximately 30 pm, and the pellets themselves were of typical dimension 1-5 mm. In the majority of cases, investigations addressed the pure (usually oxide) support so that the quantitative nature of the data obtained was not lost because of the presence of metal (which introduces an unknown degree of nuclear spin relaxation time contrast into the images). 

Extension of this methodology to porous packing elements (e.g., catalyst support pellets) is not straightforward. The challenge arises because the signal we wish to measure is associated with the liquid (water) in the bed. However, the signal intensity acquired from a specific region of water depends on its local environment, because the nuclear spin relaxation times of water in different physical environments will vary. In this system, the different environments will be (i) free water in the bulk of the inter-pellet space, (ii) water within the intra-pellet pore space, and... 

An important contribution to the nuclear spin relaxation time in paramagnetic nickel(II) complexes comes from the dipole-dipole interaction with the unpaired electron spin. The relaxation rate for this process is proportional to the inverse sixth power of the distance between spins and can be used to provide geometrical data.456... 

There are many experiments which determine only specific frequency components of the power spectra. For example, a measurement of the diffusion coefficient yields the zero frequency component of the power spectrum of the velocity autocorrelation function. Likewise, all other static coefficients are related to autocorrelation functions through the zero frequency component of the corresponding power spectra. On the other hand, measurements or relaxation times of molecular internal degrees of freedom provide information about finite frequency components of power spectra. For example, vibrational and nuclear spin relaxation times yield finite frequency components of power spectra which in the former case is the vibrational resonance frequency,28,29 and in the latter case is the Larmour precessional frequency.8 Experiments which probe a range of frequencies contribute much more to our understanding of the dynamics and structure of the liquid state than those which probe single frequency components. 

The natural line-width of the proton resonances is determined by the nuclear spin relaxation times. Nuclear relaxation in solutions of diamagnetic molecules comes mainly from intramolecular proton-proton dipolar coupling modulated by the rotational tumbling of the molecules, and will be discussed in more detail in section VII. Suffice it here to say that the line-width increases in general with increasing size of the molecule. For a small organic molecule a line-width at half height of the resonances of less than one cps would be expected, whereas the resonances... 

Elastomer-filler interactions were the subject of many intensive investigations. Kaufmann and co-workers [17] investigated carbon-black-filled EPDM by nuclear spin relaxation time measurements and found three distinct regions in the material. These regions are characterised by different mobility of the elastomer chains a mobile region in which the polymer chains have no interaction with the filler particles, loosely bound rubber in an outer shell around the carbon black particles and an inner shell of tightly bound elastomer chain with limited mobility. 

A widespread view is that the feature comes from some crossover in the electronic density of states (DOS). The main result of the present paper is that after a proper re-arrangement of the experimental data no PG feature exists in the 63 Cu nuclear spin relaxation time behaviour. Instead, the data show two independent parallel relaxation mechanisms a temperature independent one that we attribute to stripes caused by the presence of external dopants and an "universal temperature dependent term which turns out to be exactly the same as in the stoichiometric compound YBCO 124. 

Throughout the following treatment, it is appropriate to assume that all nuclear spin relaxation times are long compared to the lifetimes of the transition states for reorganization. This has been called the sudden approximation9. 

In a theoretical treatment, it is necessary to make approximations in the derivation of the spectral densities (Appendix A.2 - equation (A7)), that is, the Fourier transforms of time correlation functions of perturbations used to express the nuclear spin relaxation times. These theories have been tested against experiments and their limitations have been examined under varying conditions. The advantage of MD simulations to evaluate the theoretical models is the realism of the description and that many approximations in the theoretical model can be tested separately. Because of the conceptual differences between theories and the arbitrariness in their parameterization, it is often not possible discriminate between... 

The dynamic characteristics of adsorbed molecules can be determined in terms of temperature dependences of relaxation times [14-16] and by measurements of self-diffusion coefficients applying the pulsed-gradient spin-echo method [ 17-20]. Both methods enable one to estimate the mobility of molecules in adsorbent pores and the rotational mobility of separate molecular groups. The methods are based on the fact that the nuclear spin relaxation time of a molecule depends on the feasibility for adsorbed molecules to move in adsorbent pores. The lower the molecule s mobility, the more effective is the interaction between nuclear magnetic dipoles of adsorbed molecules and the shorter is the nuclear spin relaxation time. The results of measuring relaxation times at various temperatures may form the basis for calculations of activation characteristics of molecular motions of adsorbed molecules in an adsorption layer. These characteristics are of utmost importance for application of adsorbents as catalyst carriers. They determine the diffusion of reagent molecules towards the active sites of a catalyst and the rate of removal of reaction products. Sometimes the data on the temperature dependence of a diffusion coefficient allow one to ascertain subtle mechanisms of filling of micropores in activated carbons [17]. 

Similarities exist between the chemical characteristics of the actinides and those of the lanthanides. The metal ions are generally considered to be relatively hard Lewis acids, susceptible to complexation by hard (i.e., first row donor atom) ligands and to hydrolysis. Both actinide and lanthanide ions are affected by the lanthanide contraction, resulting in a contraction of ionic radius and an increasing reluctance to exhibit higher oxidation states later in the series. Most species are paramagnetic, although the electron spin-nuclear spin relaxation times often permit observation of NMR spectra, and disfavor observation of ESR spectra except at low temperatures. The elements display more than one accessible oxidation state, and one-electron redox chemistry is common. 

---