Relaxivity unpaired spin dependence

Relaxation measurements provide a wealth of information both on the extent of the interaction between the resonating nuclei and the unpaired electrons, and on the time dependence of the parameters associated with the interaction. Whereas the dipolar coupling depends on the electron-nucleus distance, and therefore contains structural information, the contact contribution is related to the unpaired spin density on the various resonating nuclei and therefore to the topology (through chemical bonds) and the overall electronic structure of the molecule. The time-dependent phenomena associated with electron-nucleus interactions are related to the molecular system, and to the lifetimes of different chemical situations, for the resonating nucleus. Obtaining either structural or dynamic information, however, is only possible if an in-depth analysis of a series of experimental results provides sufficient data to characterize the system within the theoretical framework discussed in this chapter. 

It has been known since the earliest days of magnetic resonance spectroscopy that paramagnetic compounds, containing one or more unpaired spins, enhance the relaxation rates for the water protons in which they are dissolved." The extent of this enhancement, termed relaxivity, is highly dependent on the magnitude of the dipole-dipole interactions between the electron spin on the paramagnetic metal complex and the proton spin on the water molecule in question. These interactions are often quite complex. They can be treated on a formal (theoretical) level by the Solomon-Bloembergen equations." On a strictly practical level, however, the devel-... 

By the same experimental technique, the temperature dependence of the nuclear spin relaxation rates was investigated for the radical cations of dimethoxy- and trimethoxybenzenes [89], The rates of these processes do not appear to be accessible by other methods. As was shown, l/Tfd of an aromatic proton in these radicals is proportional to the square of its hyperfine coupling constant. This result could be explained qualitatively by a simple MO model. Relaxation predominantly occurs by the dipolar interaction between the proton and the unpaired spin density in the pz orbital of the carbon atom the proton is attached to. Calculations on the basis of this model were performed with the density matrix formalism of MO theory and gave an agreement of experimental and predicted relaxation rates within a factor of 2. 

Saturation of the upper energy level of the unpaired spins can occur at high micrqwave powers, the actual power depending on the relaxation time and hence on the nature of the radical. Therefore for quantitative measurements of radical concentrations the power dependence of the spectrum must be examined. Deviation from linearity in a plot of spectrum area versus the square root of the microwave power indicates the onset of microwave power saturation and the upper limit for quantitative measurements of radical concentrations. Microwave power saturation measurements for methacrylate propagation radicals during polymerization is shown in Figure 10.2. 

Nuclear magnetic dipole relaxation interactions may occur with other nuclei, or with unpaired electrons. These processes usually dominate the relaxation of spin - nuclei. Both intra- and intermolecular interactions may contribute to dipole-dipole nuclear relaxation times. The value of due to the intramolecular dipole-dipole process is proportional to the sixth power of the internuclear separation. Consequently, this process becomes rather inefficient in the absence of directly bonded magnetic nuclei. However, it follows that a measurement of can be provide an estimate of internuclear separation that can be of chemical interest. The nuclear Overhauser effect (NOE) depends upon the occurrence of dipole-dipole relaxation processes and can similarly provide an estimate of internuclear separation. 

ESR can detect unpaired electrons. Therefore, the measurement has been often used for the studies of radicals. It is also useful to study metallic or semiconducting materials since unpaired electrons play an important role in electric conduction. The information from ESR measurements is the spin susceptibility, the spin relaxation time and other electronic states of a sample. It has been well known that the spin susceptibility of the conduction electrons in metallic or semimetallic samples does not depend on temperature (so called Pauli susceptibility), while that of the localised electrons is dependent on temperature as described by Curie law. 

In the absence of an endogenous centre, the specificity of relaxation data can be improved by introducing in known positions paramagnetic probes. The unpaired electron spin enhances the relaxation rate of the surrounding nuclei in a distance-dependent fashion. In this way, it is possible to evaluate specific interaction sites between a marked polymer and the small molecules. 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

Unpaired electronic density can be delocalized onto the various nuclei of the complex via through-bond scalar hyperfine interactions involving occupied orbitals containing s-character (direct interaction or polarization according to the Fermi mechanism, Wertz and Bolton (1986)). Random electron relaxation thus produces a flip-flop mechanism which affects the nuclear spin and increases nuclear relaxation processes (Bertini and Luchinat, 1996). Since these interactions are isotropic, they do not depend on molecular tumbling and re is the only relevant correlation time for non-exchanging semi-rigid complexes. Moreover, only electronic spin can be delocalized via hyperfine interactions (no orbital contribution) and the contact re-... 

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