Microwave-free $J$-driven dynamic nuclear polarization: A proposal for enhancing the sensitivity of solution-state NMR

$J$-driven dynamic nuclear polarization (JDNP) was recently proposed for enhancing the sensitivity of solution-state nuclear magnetic resonance (NMR), while bypassing the limitations faced by conventional (Overhauser) DNP at magnetic fields of interest in analytical applications. Like Overhauser DNP, JDNP also requires saturating the electronic polarization using high-frequency microwaves known to have poor penetration and associated heating effects in most liquids. The present microwave-free JDNP (MF-JDNP) proposal seeks to enhance solution NMR's sensitivity by shuttling the sample between higher and lower magnetic fields, with one of these fields providing an electron Larmor frequency that matches the interelectron exchange coupling $J_{\mathrm{ex}}$. If spins cross this so-called JDNP condition sufficiently fast, we predict that a sizable nuclear polarization will be created without microwave irradiation. This MF-JDNP proposal requires radicals whose singlet–triplet self-relaxation rates are dominated by dipolar hyperfine relaxation, and shuttling times that can compete with these electron relaxation processes. This paper discusses the theory behind the MF-JDNP, as well as proposals for radicals and conditions that could enable this new approach to NMR sensitivity enhancement.

Figure 1

Example of random walks undertaken by a nuclear “solvent” spin with in a 3D box with a size equal to $30\times 30\times 30{\AA }^3$, with a diffusion constant of $1\mu {\mathrm{m}}^2/\mathrm{ms}$, corresponding to a random walk of 10000 steps of $1\AA$ in $1\mathrm{ms}$. Periodic boundary conditions were set to represent an infinite system in which the nuclear spin can get out from a side of the box and get in from the other. Inset: Polarization region accessible by the solvent (violet region) surrounding the biradical (gray circles connected by a linker). A and B represent proton configurations inside and outside of the polarization region, respectively; C represents an intra-radical proton. Representative particles’ coordinates are as given in Table 1. The code used to perform this random walk is provided in the Supplemental Material [47].

Figure 1

Example of random walks undertaken by a nuclear “solvent” spin with in a 3D box with a size equal to $30\times 30\times 30{\AA }^3$, with a diffusion constant of $1\mu {\mathrm{m}}^2/\mathrm{ms}$, corresponding to a random walk of 10000 steps of $1\AA$ in $1\mathrm{ms}$. Periodic boundary conditions were set to represent an infinite system in which the nuclear spin can get out from a side of the box and get in from the other. Inset: Polarization region accessible by the solvent (violet region) surrounding the biradical (gray circles connected by a linker). A and B represent proton configurations inside and outside of the polarization region, respectively; C represents an intra-radical proton. Representative particles’ coordinates are as given in Table 1. The code used to perform this random walk is provided in the Supplemental Material [47].

Figure 2

Schematic description of the high→low→high $B_0$-cycling in MF-JDNP, in which the sample is shuttled $n$ times at constant 0.25 T/ms rates from a starting magnetic field to a lower field corresponding to the JDNP condition, and then back to the NMR field in which the measurement is performed.

Figure 2

Schematic description of the high→low→high $B_0$-cycling in MF-JDNP, in which the sample is shuttled $n$ times at constant 0.25 T/ms rates from a starting magnetic field to a lower field corresponding to the JDNP condition, and then back to the NMR field in which the measurement is performed.

Figure 3

MF-JDNP performed according to the scheme in Fig. 2, with $n=7$ loops between an NMR field of 14.1 T, and a 9.1 T polarizing field fulfilling the JDNP condition. (a) Simulations assuming a three-spin system where the solvent proton exchanges between configurations A and B (Fig. 1). (b) Simulations assuming that the solvent proton was fixed in configuration A. In neither case were intra-radical protons considered. Left-hand column: Time (magnetic-field) evolution of the nuclear enhancement, scaled over the instantaneous thermal equilibrium magnetization value at each magnetic field. Black arrows indicate the JDNP condition; asterisks indicate NMR observation points. Center column: Time (magnetic-field) evolution of the ${\widehat{S}}_0{\widehat{N}}_Z, {\widehat{T}}_0{\widehat{N}}_Z$ and ${\widehat{T}}_{\pm 1}{\widehat{N}}_Z$ states arising from the population imbalance between the α and β nuclear components of the singlet and triplet states; the sum of all these states corresponds to nuclear polarization scaled over the thermal equilibrium value at each magnetic field shown in the left-hand column. Right-hand column: Time (magnetic-field) evolution of the ${\widehat{S}}_{0,\alpha /\beta }, {\widehat{T}}_{0,\alpha /\beta }$, and ${\widehat{T}}_{\pm 1,\alpha /\beta }$ states (straight and dashed lines, respectively) compared to their thermal equilibrium values (dotted lines; the α and β nuclear components overlap).

Figure 4

Expectations of MF-JDNP experiments performed according to the scheme in Fig. 2, with three high-low-high $B_0$ shuttling repetitions. All plots show time (magnetic-field) evolution of the nuclear enhancement over the thermal equilibrium value. Black arrows indicate the JDNP condition; asterisks indicate potential NMR observation points. (a) Predictions for a four-spin system including a fixed intraradical proton (the electron-proton scalar coupling was set to 1 MHz) and a diffusion solvent. (b) The same as (a), but after replacing the intraradical proton by a deuterium (blue line) but including an ad hoc term in the Redfield relaxation superoperator, applied only to the electron longitudinal states, representing a $6\times {10}^4\mathrm{Hz}$ local vibrations-driven contribution to the relaxation modes (violet line).