Solvent Relaxation by Uniformly Magnetized Solute Spheres: The Classical-Quantal Connection

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Large magnetic entities, with diameters in the range of 4 nm to 4 μm, are becoming of increasing interest for magnetic resonance imaging (MRI). The smaller are iron oxide nanoparticles, used for the RE system, and the larger are deoxygenated blood cells, for functional MRI. It can be useful to model such systems as magnetized solute spheres in water. Classical computations of 1/T2 have been reported for the larger particles, in the micron range, where the computational complexities are simplified by Monte Carlo methods. For smaller particles, the quantum mechanical (quantal) expressions for outer sphere relaxation, for both 1/T1 and 1/T2, have been available for some time, and are particularly simple to apply at MRI fields. The questions that arise, and which the author addresses, are how to interrelate the classical and quantal approaches and when to use which.


The author compares published results of Monte Carlo calculations of 1/T2 for diamagnetic polystyrene solute spheres of various sizes in water, made paramagnetic by addition of dysprosium-(DTPA)2−, with quantum mechanical outer sphere theory applied to the same system. The latter includes the usual assumption of motional narrowing and yields both 1/T1 and 1/T2.


For particles with diameters less than about 1 μm, both approaches give identical results for 1/T2. For larger particles, the conditions for motional narrowing breakdown, and quantal theory overestimates 1/T2. In addition, in the particular system studied, relaxation becomes so effective near solute that there is insufficient time for all water molecules to experience their maximal effect. Classical theory handles this well whereas quantal theory does not.


In comparing the classical and quantal approaches, one balances computational complexity but broader applicability with more limited but far simpler mathematics. In addition, because the quantal approach shows that 1/T1 and 1/T2 are intimately related, the author suggests, by analogy, how to extend classical methods to computation of 1/T1.

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