Dipolar NMR Strategies for Multispin Systems Involving Quadrupolar Nuclei:  31P{23Na} Rotational Echo Double Resonance (REDOR) of Crystalline Sodium Phosphates and Phosphate Glasses

A new procedure for the site-selective measurement of heteronuclear magnetic dipole−dipole interactions involving quadrupolar nuclei has been developed. Particular attention is given to the case of S{I} rotational echo double resonance (REDOR) with S = 1/2 and I = 3/2, where the nuclear electric quadrupole splitting affects the efficiency of the π(I) pulses in recoupling the S−I dipolar interactions. Detailed two- and three-spin simulations using the SIMPSON code indicate that the REDOR response is sensitively affected by the quotient of the nutation frequency and the nuclear electric quadrupole frequency (ν1/νq). Multispin systems can be conveniently analyzed using a curvature determination of REDOR data in the limit of short dipolar evolution times (ΔS/S 0 < 0.2), to yield dipolar second moment (M 2) values. The apparent M 2 values measured in this fashion include a scaling factor f 1, the magnitude of which can be predicted if ν1/νq is known. Based on this finding, a robust method has been developed to analyze experimental REDOR data in multispin systems, in terms of average dipolar M 2 values, which are shown to be affected by distributions of magnetic dipolar and nuclear electric quadrupolar coupling constants only to a minor extent. Validation experiments on suitable model compounds indicate that dipolar M 2 values can be measured within 10% accuracy in this fashion for crystalline compounds. For glasses, the error may be higher, because of possible cumulative errors that may occur from unknown geometries and distribution effects. Experiments conducted on glassy sodium phosphates indicate that the 31P−23Na dipolar interaction strengths in these systems are differentiable for the various Q ( n ) sites and increase as the charge of the phosphate moiety increases.