Model – free approach to quadrupole spin relaxation in solid ²⁰⁹Bi-aryl compounds

Abstract

Nuclear Quadrupole Resonance (NQR) experiments were performed for deuterated and non-deuterated triphenylbismuth (BiPh3) to inquire into 209Bi relaxation mechanisms. The studies are motivated by the idea of exploiting Quadrupole Relaxation Enhancement (QRE) as a novel contrast mechanism for Magnetic Resonance Imaging. From this perspective relaxation features of nuclei possessing quadrupole moment (quadrupole nuclei) are of primary importance for the contrast effect. Spin-spin relaxation rates associated with the NQR lines were described in terms of the Redfield relaxation theory assuming that the relaxation is caused by fluctuations of the electric field gradient tensor at the position of the quadrupole nucleus that are described by an exponential correlation function. The description referred to as a model-free approach is an analogy of the description used for paramagnetic contrast agents. It was demonstrated that for the deuterated compound this approach captures the essential features of 209Bi relaxation, but it should not be applied for non-deuterated compounds as dipolar interactions between neighbouring protons and the quadrupole nucleus considerably contribute to the relaxation of the last one. Thus, the relaxation scenario for species containing quadrupole nuclei is fundamentally different than for paramagnetic contrast agents and this fact has to be taken into account when predicting contrast effects based on QRE.

Tris(2-Methoxyphenyl)Bismuthine Polymorphism Characterized by Nuclear Quadrupole Resonance Spectroscopy

“…The results clearly show the impact of an altered environment on the dynamics of spin relaxation in case for T 2 ( Table 5). We will not attempt to analyse the relaxation times further here, as this requires proper application of relaxation theory [38] which is out of scope of this work.…”

Spin–spin relaxation of nuclear quadrupole resonance coherences and the important role of degenerate energy levels

“…amplitude and has been applied for example in [26] for proton relaxation in metal aquo complexes due to zero field splitting as well as to describe EFG fluctuations in solids [24]. The second derivation (concept (2)), on the contrary, assumes a time-dependent amplitude of the EFG fluctuations along certain directions with respect to the main EFG.…”

“…2,sim (τ c ) are just the diagonal elements of the relaxation matrix of the associated transition according to Equation (A10), without using the lineshape approach (as in [24]). The relaxation rate for t1 is much larger in panel (a) than in panel (b) due to the incorporation of off-diagonal elements in the Redfield matrix, which is indicated by the inserts.…”

“…In this work, we present an extension of an earlier article [24] where spin-spin relaxation rates of quadrupole transitions at zero field were calculated for I = 9/2 nuclei using Redfield theory [11,25]. In [24], fluctuations of the electric field gradient according to the simple two parameter pseudo rotational (PR) model are assumed, which is originally used for modelling fluctuations of the zero field splitting interaction in electron spin relaxation [26].…”

“…As we do not intend to discuss in detail all possible motions in a molecular crystal, we formulate, in a heuristic manner, an as simple as possible model for the EFG fluctuations to keep the number of parameters low while maintaining physical reasoning. Instead of the PR model used in [24], we introduce a so-called flickering amplitude (FA) model [29], using a monoexponential correlation function for the EFG amplitude which is extended in a second step with a vibrational mode to form the flickering vibrational amplitude (FVA) model. For the assumption of an isotropic distribution of fluctuation directions, the FA model becomes equivalent with the PR model.…”