Electron and nuclear spin dynamics in the thermal mixing model of dynamic nuclear polarization

Abstract

A novel mathematical treatment is proposed for computing the time evolution of dynamic nuclear polarization processes in the low temperature thermal mixing regime. Without assuming any a priori analytical form for the electron polarization, our approach provides a quantitative picture of the steady state that agrees with the well known Borghini prediction based on thermodynamic arguments, as long as the electrons-nuclei transition rates are fast compared to the other relevant time scales. Substantially different final polarization levels are achieved instead when the latter assumption is relaxed in the presence of a nuclear leakage term, even though very weak, suggesting a possible explanation for the deviation between the measured steady state polarizations and the Borghini prediction. The proposed methodology also allows to calculate nuclear polarization and relaxation times, once the electrons/nuclei concentration ratio and the typical rates of the microscopic processes involving the two spin species are specified. Numerical results are shown to account for the manifold dynamical behaviours of typical DNP samples.

Relevance of electron spin dissipative processes to dynamic nuclear polarization via thermal mixing

“…While a speed up of the DNP process with the increase in the radical concentration has to be expected, since there are more polarization transfer centers, the significant decrease of the steady state polarization has not been accounted for by any previous theoretical description of TM-DNP. In fact both the Borghini [22] and the finite contact model introduced in [12] and [13] predict no effect of the radical concentration as long as T 1n is negligible whereas, in presence of leakage, a higher number of polarizing centres would push the system towards higher steady state polarizations. Gadolinium doping on the other hand leaves substantially unaffected the nuclear polarization time, while shortening the typical electron spin lattice relaxation time T 1e .…”

“…Guided by these three items we introduced a novel model, based on the same rate equations approach proposed in [12] under the assumption of bad electronnucleus contact and negligible nuclear leakage, but including an additional mechanism accounting for energy exchanges between couples of electron spins (that flip simultaneusly) and the lattice. It is worth to mention that similar flip-flop processes were already introduced by Farrar et al [27] in a high temperature approximation of TM-DNP in presence of inhomogeneusly broadened ESR lines.…”

“…First of all, it has to be realized that the Borghini model and the model introduced in [12,13] rely on the assumption that the energy exchange between the electron system and the lattice occurs only via the Zeeman transitions depicted in FIG. 3, panel C, whereas all transitions involving more than one electron spin are always energy conserving.…”

“…Improvements to the original theoretical picture have been proposed in [11] and [12,13]. In these latter papers, in particular, a novel approach based on rate equations has been introduced, that overcomes several limitations of the traditional approaches and provides the dynamics of the spin polarization of spin ensembles by calculating the evolution induced by any single or multiple spin transitions.…”

The role of the glassy dynamics and thermal mixing in the dynamic nuclear polarization and relaxation mechanisms of pyruvic acid

“…The effect of relevant parameters, including the radical concentration [14][15][16], the concentration of gadolinium complexes [14,17], the nuclear concentration [18,19], the amount of matrix deuteration [20], the effect of microwave saturation and the field strength [15,16,21] on the DNP performances of this molecule have been experimentally studied. Remarkably very recently, the relevance of these physical quantities on DNP kinetics has also been considered in the development of novel models describing TM throughout a rate equation approach [19,22,23]. Nevertheless, the role of the properties of the glassy matrix formed by the polarized molecules and radicals has not been investigated to a deep level.…”