Temporal Characteristics of NMR Signals from Spin 3/2 Nuclei of Incompletely Disordered Systems

Anisotropic nuclear quadrupole interactions can produce residual quadrupole splitting in the NMR spectra of rapidly moving quadrupolar nuclei in incompletely disordered aqueous heterogeneous systems. Such systems may include hydrated sodium nuclei in biological tissue and biopolymer gels. To describe the NMR signals from such samples, we use a domain model in which each domain is characterized by a quadrupole frequency and a residence time of the nucleus. We show that the signals from each domain after one pulse, the quadrupole echo sequence, and the various multiple quantum filters (MQFs) can be expressed as a linear combination of five different phase coherences. To simulate the effect of various distributions (Pake powder pattern, Gaussian, etc.) of quadrupole frequencies for different domains on the NMR signal, we have written the computer program CORVUS. CORVUS also includes the effects of exchange between different domains using diffusion and random jump models. The results of computer simulations show that the Gaussian and Pake powder pattern quadrupole frequency distributions produce very different phase coherences and observable NMR signals when the exchange rate (1/taue) between different domains is slow. When 1/taue is similar to the root mean square quadrupole frequency (final sigma), the signals from the two distributions are similar. When 1/taue is an order of magnitude greater than final sigma, there is no apparent evidence of quadrupole splitting in the shape of the signal following one pulse, but the residual effects of the quadrupole splitting make a significant contribution to the fast transverse relaxation rate. Therefore, in this case, it is inappropriate to use the observed biexponential relaxation rates to obtain a single correlation time. The quadrupole echo and the various MQF signals contain an echo from the satellite transitions in the presence of quadrupole splitting. The peak of this echo is very sensitive to 1/taue. The time domain analysis of these signals is more direct and less ambiguous than the frequency domain analysis because the echo does not occur at the beginning of data acquisition. The quadrupole echo pulse sequence is the most sensitive detector of residual quadrupole splitting and exchange of sodium ions between different domains. However, if the sample is compartmentalized so that only a fraction of the nuclei have quadrupole splitting, the double quantum magic angle filter (DQ-MA) is more suitable. This is because the DQ-MA signal contains only the contributions from satellite transitions. Use of simulations to analyze signals from various one-pulse, quadrupole echo, and multiple quantum filter pulse sequences can yield information on substrate order and aid in quantitation of multiple quantum filter signals.