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The relaxation of an I=3/2 spin system in an anisotropic environment characterized by a finite residual quadrupolar splitting ωq is modeled by analytically solving for the density operator from Redfield’s relaxation theory. The resulting equations are cast into the multipole basis in order to describe the tensorial components of the spin density matrix. Included in the relaxation matrix are off-diagonal elements J1 and J2, which account for anisotropic systems with ωq values less than the width of the resonant line. With the Wigner rotation matrices simulating hard pulses, the response to an arbitrary pulse sequence can be determined. An analytical expression for the response to the double quantum filtered (DQF) pulse sequence (π/2)−(τ/2)−π−(τ/2)−θ−δ−θ−AQ for θ=π/2 is presented, showing explicitly the formation of a second rank tensor owing only to the presence of a finite ωq. This second rank tensor displays asymptotic behavior when the (reduced) quadrupole splitting is equal to either of the off-diagonal spectral densities J2 and J1. Line shape simulations for ωq values of less than a linewidth reproduce the general features of some recently reported 23Na DQF line shapes from biological systems. Distinct relaxation dynamics govern each of the tensorial components of the resonant signal revealing the influence of the experimental variables on the line shape.

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Measurements of 19F and 1H nuclear spin−lattice relaxation times from aqueous solutions of PF6 - and (H3C)4N+ containing small concentrations of nitroxide free radicals were made at applied magnetic field strengths ranging from 0.00025 to 7.05 T to directly determine the form of the frequency-dependent spectral densities that modulate relaxation. This magnetic relaxation dispersion (MRD) technique may provide detailed information concerning molecular dynamics over the time scale range from milliseconds to picoseconds. The MRD data compare well to a theory for translational diffusion of hard spheres, one that accounts for the intermolecular electrostatic potential between ionic solutes. Theoretically accessible parameters are extracted, and the treatment of the intermolecular potential as a reduction (increase) in the number of effective translational encounters between ions of like (unlike) charge is discussed. Represented by a mean field, the relatively long range Coulombic interaction does not impose spatial conditions on the diffusion equation through which the short-range magnetic dipole−dipole interactions are correlated. Calculated distances of closest approach are approximately 6.5 Å and are consistent with the dimensions expected for a sterically impeded encounter between the nuclear spin probes and the nitroxide centered paramagnetic spin density. Comparison of the (H3C)4N+ and PF6 - data provides a means of quantifying the Coulombic potential, which has a more dramatic effect on the 19F relaxation of the polarizable PF6 -.

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