Abstract
The population imbalance between nuclear singlet states and triplet states of strongly coupled spin-1/2 pairs, also known as nuclear singlet order, is well protected against several common relaxation mechanisms. We study the nuclear singlet relaxation of 13C pairs in aqueous solutions of 1,2-13C2 squarate over a range of pH values. The 13C singlet order is accessed by introducing 18O nuclei in order to break the chemical equivalence. The squarate dianion is in chemical equilibrium with hydrogen-squarate (SqH-) and squaric acid (SqH2) characterized by the dissociation constants pK1 = 1.5 and pK2 = 3.4. Surprisingly, we observe a striking increase in the singlet decay time constants TS when the pH of the solution exceeds ∼10, which is far above the acid-base equilibrium points. We derive general rate expressions for chemical-exchange-induced nuclear singlet relaxation and provide a qualitative explanation of the TS behavior of the squarate dianion. We identify a kinetic contribution to the singlet relaxation rate constant, which explicitly depends on kinetic rate constants. Qualitative agreement is achieved between the theory and the experimental data. This study shows that infrequent chemical events may have a strong effect on the relaxation of nuclear singlet order.
Highlights
Optimized M2S parameters for 18Oenriched 1,2-13C2 squaric acid are given as a function of pH in Table I. (b) After singlet order excitation, an optional field cycling step is introduced to transport the sample to a desirable magnetic field strength. (c) Singlet order is allowed to freely evolve for a variable duration τevol. (d) For the case of field cycling experiments, the sample is shuttled back into the active region of the magnet. (e) Application of a gradient-based singlet order filter [see Fig. 6(b)] isolates nuclear magnetic resonance (NMR) signals passing through singlet order.[81]
This effect has not been analyzed in detail but is provisionally attributed to small changes in the equilibrium fractions of the different protonated species upon 18O substitution. 18O substitution changes the zero-point vibrational energy of –OH bonds and influences the equilibrium fractions of the various protonated species, which leads, in turn, to a perturbation of the 13C chemical shifts when averaged over all exchanging species
The study of 13C nuclear singlet relaxation in 18O-enriched 1,213C2 squarate reveals a surprising dependence of the singlet relaxation time constant TS on the pH of the solution
Summary
Long-lived nuclear spin states (LLS) are configurations of nuclear spins, which are protected against common relaxation or dissipation mechanisms and which display extended decay time constants.[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] A seminal example is the singlet order of a spin-1/2 pair ensemble, corresponding to a population imbalance between the singlet and triplet states of the spin-1/2 pairs.[10,16] The decay time constants of such states are often many times the spin–lattice relaxation time constant T1, with lifetimes exceeding 1 hour being observed in favorable cases.[12,19] Long-lived states have been applied to the study of slow chemical and transport processes,[20,21,22,23,24,25,26,27,28,29] to the characterization of biomolecular ligand binding,[30,31,32,33,34] and to the transport and storage of nuclear hyperpolarization.[5,7,35–43] Longlived nuclear singlet order plays a central role in the generation of nuclear hyperpolarization from hydrogen gas enriched in the para spin isomer.[44–59]. In aqueous solution and neutral pH, we observed a singlet decay time constant of around TS ∼ 30 s in a field of 9.4 T, which is slightly shorter than the value of T1 under the same conditions Conventional mechanisms such as CSA-induced relaxation are insufficient to explain this low value of TS. The first two terms are the population-weighted averages of the TS−1 values for the participating species These terms correspond closely to the theory developed for ligand binding applications of singlet nuclear magnetic resonance (NMR).[30,31,32,33,34] Since these terms depend on equilibrium populations, they do not depend on the individual values of the kinetic rate constants but only on their ratio. We verified by conventional acid–base titration, using the same solvent composition as for the NMR experiments, that the pKa values of squaric acid are 1.3 and 3.4, in good agreement with the literature,[78] indicating that any isotope effects on the acid–base equilibria are minor
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