Discrimination of PHIP Signals Through their Evolution in Multipulse Sequences.

The antiphase character of the PHIP associated signals after a hydrogenation reaction is particularly sensitive to line broadening introduced by magnetic field inhomogeneities and interferences by the presence of resonance lines steaming from a large amount of thermally polarized spins. These obstacles impose a limitation in the detection of reaction products as well as in the experimental setups. A simple way to overcome these impediments consists of acquiring the signal with a train of refocusing pulses instead of a single r.f. pulse. We present here a number of examples where this multipulse acquisition, denominated PhD-PHIP, displays its potentiality in improving the information related to hyperpolarized spins performed in a sample, where the former parahydrogen nuclei are part of a complex J-coupling network.

Radiofrequency encoded Only Parahydrogen SpectroscopY.

A new pulse sequence aimed to filter out NMR signals coming from thermally polarized protons in PHIP experiments based on the OPSY pulse sequence (Only Parahydrogen SpectroscopY) is presented. In analogy to OPSY, which removes thermal polarization by using a pair of magnetic field gradient pulses with an intensity ratio 1:2 and equal duration, the same effect can be achieved using inhomogeneous radiofrequency fields. The spatial dependence of the radiofrequency field is used to control the Hamiltonian, which results in an effective suppression of thermal contributions in the NMR signal, while PHIP originated signals remain unmodified. A theoretical model for the radiofrequency encoded only parahydrogen (REOPSY) sequence is presented along with an experimental implementation on a birdcage coil in a 7 T magnetic field. The control level achieved by this strategy allows the inclusion of a long train of refocusing pulses. Therefore, the new sequence can be combined with the parahydrogen discriminated PHIP (PhD-PHIP) pulse sequence as a detection block to improve sensitivity and resolution in a single-scan experiment. Experiments with REOPSY and REOPSY+PhD-PHIP are presented in thermally and hyperpolarized samples.

Diffusion measurements with continuous hydrogenation in PHIP.

DOSY is a powerful spectroscopic NMR technique that resolves components in mixtures through the evaluation of different diffusion coefficients. The application of DOSY to dilute mixtures is hampered by the low signal to noise ratios (SNR), leading to long acquisition times. The use of PHIP may resolve this issue as long as reproducible signals are obtained in order to perform 2D experiments. Here we show that the use of hollow membranes and adequate gas flow produce constant polarization for a time-span that enables the acquisition of 2D experiments. A pressure gradient is evidenced by the presence of convection, which is accounted for by using a DPGSE sequence. The influence of J-coupling evolution during the sequence is studied both numerically and experimentally, to determine the optimum echo-time. The applicability of the method for samples with poor SNR is explored by setting the reaction rate to achieve a low intensity of polarized signals.

Perturbation Independent Decay of the Loschmidt Echo in a Many-Body System.

When a qubit or spin interacts with others under a many-body Hamiltonian, the information it contains progressively scrambles. Here, nuclear spins of an adamantane crystal are used as a quantum simulator to monitor such dynamics through out-of-time-order correlators, while a Loschmidt echo (LE) asses how weak perturbations degrade the information encoded in these increasingly complex states. Both observables involve the implementation of a time-reversal procedure which, in practice, involves inverting the sign of the effective Hamiltonian. Our protocols use periodic radio frequency pulses to modulate the natural dipolar interaction implementing a Hamiltonian that can be scaled down at will. Meanwhile, experimental errors and strength of perturbative terms remain constant and can be quantified through the LE. For each scaling factor, information spreading occurs with a timescale, T_{2}, inversely proportional to the local second moment of the Hamiltonian. We find that, when the reversible interactions dominate over the perturbations, the information scrambled among up to 10^{2} spins can still be recovered. However, we find that the LE decay rate cannot become smaller than a critical value 1/T_{3}≈(0.15±0.02)/T_{2}, which only depends on the interactions themselves, and not on the perturbations. This result shows the emergence of a regime of intrinsic irreversibility in accordance to a central hypothesis of irreversibility, hinted from previous experiments.

Combination of OPSY and PhD-PHIP results in enhanced sensitivity in PHIP.

Despite the large degree of polarization in PHIP experiments compared to the Boltzmann factor, the presence of a large amount of non-reacted molecules with thermal polarization is an important obstacle when dealing with very diluted samples. The feasibility of enhancing both sensitivity and resolution in a single experiment by combining two well established pulse sequences, OPSY and PHD-PHIP is presented. OPSY is used as a block for filtering the signals originated from thermally polarized protons. PhD-PHIP, on the other hand, is used as an acquisition block, increasing the resolution and further improving the sensitivity by preventing signal canceling in the presence of magnetic field inhomogeneities. Experiments in a complex sample with very low hyperpolarization levels are presented showing the excellent performance of the method.

Optimized phases for the acquisition of J-spectra in coupled spin systems for thermally and PHIP polarized molecules.

We demonstrate that the relative phases in the refocusing pulses of multipulse sequences can compensate for pulse errors and off-resonant effects, which are commonly encountered in J-spectroscopy when CPMG is used for acquisition. The use of supercycles has been considered many times in the past, but always from the view point of time-domain NMR, that is, in an effort to lengthen the decay of the magnetization. Here we use simple spin-coupled systems, in which the quantum evolution of the system can be simulated and contrasted to experimental results. In order to explore fine details, we resort to partial J-spectroscopy, that is, to the acquisition of J-spectra of a defined multiplet, which is acquired with a suitable digital filter. We unambiguously show that when finite radiofrequency pulses are considered, the off-resonance effects on nearby multiplets affects the dynamics of the spins within the spectral window under acquisition. Moreover, the most robust phase cycling scheme for our setup consists of a 4-pulse cycle, with phases yyyy‾ or xxxx‾ for an excitation pulse with phase x. We show simulated and experimental results in both thermally polarized and PHIP hyperpolarized systems.

Quantum dynamics of excitations and decoherence in many-spin systems detected with Loschmidt echoes: its relation to their spreading through the Hilbert space.

In this work, we overview time-reversal nuclear magnetic resonance (NMR) experiments in many-spin systems evolving under the dipolar Hamiltonian. The Loschmidt echo (LE) in NMR is the signal of excitations which, after evolving with a forward Hamiltonian, is recovered by means of a backward evolution. The presence of non-diagonal terms in the non-equilibrium density matrix of the many-body state is directly monitored experimentally by encoding the multiple quantum coherences. This enables a spin counting procedure, giving information on the spreading of an excitation through the Hilbert space and the formation of clusters of correlated spins. Two samples representing different spin systems with coupled networks were used in the experiments. Protons in polycrystalline ferrocene correspond to an 'infinite' network. By contrast, the liquid crystal N-(4-methoxybenzylidene)-4-butylaniline in the nematic mesophase represents a finite proton system with a hierarchical set of couplings. A close connection was established between the LE decay and the spin counting measurements, confirming the hypothesis that the complexity of the system is driven by the coherent dynamics.

Parahydrogen discriminated PHIP at low magnetic fields.

Parahydrogen induced polarization (PHIP) is a powerful hyperpolarization technique. However, as the signal created has an anti-phase characteristic, it is subject to signal cancellation when the experiment is carried out in inhomogeneous magnetic fields or in low fields that lack the necessary spectral resolution. The use of benchtop spectrometers and time domain (TD) analyzers has continuously grown in the last years and many applications are found in the food industry, for non-invasive compound detection or as a test bench for new contrast agents among others. In this type of NMR devices the combination of low and inhomogeneous magnetic fields renders the application of PHIP quite challenging. We have recently shown that the acquisition of J-spectra in high magnetic fields not only removes the anti-phase peak cancellation but also produces a separation of thermal from hyperpolarized signals, providing Parahydrogen Discriminated (PhD-PHIP) spectra. In this work we extend the use of PhD-PHIP to low and inhomogeneous fields. In this case the strong coupling found for the protons of the sample renders spin-echo spectra that have a great complexity, however, a central region in the spectrum with only hyperpolarized signal is clearly identified. This experimental approach is ideal for monitoring real time chemical reaction of pure PHIP signals.

Hyperpolarized 1H long lived states originating from parahydrogen accessed by rf irradiation.

Hyperpolarization has found many applications in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI). However, its usage is still limited to the observation of relatively fast processes because of its short lifetimes. This issue can be circumvented by storing the hyperpolarization in a slowly relaxing singlet state. Symmetrical molecules hyperpolarized by Parahydrogen Induced Hyperpolarization (PHIP) provide straightforward access to hyperpolarized singlet states because the initial parahydrogen singlet state is preserved at almost any magnetic field strength. In these systems, which show a remarkably long (1)H singlet state lifetime of several minutes, the conversion of the NMR silent singlet state to observable magnetization is feasible due to the existence of singlet-triplet level anti-crossings. Here, we demonstrate that scaling the chemical shift Hamiltonian by rf irradiation is sufficient to transform the singlet into an observable triplet state. Moreover, because the application of one long rf pulse is only partially converting the singlet state, we developed a multiconversion sequence consisting of a train of long rf pulses resulting in successive singlet to triplet conversions. This sequence is used to measure the singlet state relaxation time in a simple way at two different magnetic fields. We show that this approach is valid for almost any magnetic field strength and can be performed even in the less homogeneous field of an MRI scanner, allowing for new applications of hyperpolarized NMR and MRI.

High resolution para-hydrogen induced polarization in inhomogeneous magnetic fields.

The application of parahydrogen for the generation of hyperpolarization has increased continuously during the last years. When the chemical reaction is carried out at the same field as the NMR experiment (PASADENA protocol) an antiphase signal is obtained, with a separation of the resonance lines of a few Hz. This imposes a stringent limit to the homogeneity of the magnetic field in order to avoid signal cancellation. In this work we detect the signal arising from hyperpolarized Hexene by means of a CPMG pulse train. After Fourier transformation the obtained J-spectra not only presents an enhanced spectral resolution but also avoids partial peak cancellation.

Level anti-crossings in ParaHydrogen Induced Polarization experiments with Cs-symmetric molecules.

Hyperpolarization by means of ParaHydrogen Induced Polarization (PHIP) has found increasing applications since its discovery. However, in the last decade only a few experiments have been reported describing the hydrogenation of symmetric molecules. A general AA'BB' system is studied here. Calculations of the spin dynamics with the density matrix formalism support the experimental findings, providing profound understanding of the experiments in Cs-symmetric molecules. Level anti-crossings between states related to the triplet and the singlet state of one pair of the protons are identified as being responsible for hyperpolarization transfer in a PHIP experiment, when the former p-H(2) protons occupy the sites AA'. The hydrogenation of acetylene dicarboxylic acid dimethylester with parahydrogen is used to illustrate the case. The theoretical treatment applied to this particular reaction explains the signal enhancements in both groups of protons in the spectrum when the sample is placed in the proper magnetic field strength, including the phase inversion of the signal of the methyl group. The treatment described here can be extended to every molecule which can be approximated as an AA'BB' system.

Monitoring mass transport in heterogeneously catalyzed reactions by field-gradient NMR for assessing reaction efficiency in a single pellet.

An important aspect in assessing the performance of a catalytically active reactor is the accessibility of the reactive sites inside the individual pellets, and the mass transfer of reactants and products to and from these sites. Optimal design often requires a suitable combination of micro- and macropores in order to facilitate mass transport inside the pellet. In an exothermic reaction, fluid exchange between the pellet and the surrounding medium is enhanced by convection, and often by the occurrence of gas bubbles. Determining mass flow in the vicinity of a pellet thus represents a parameter for quantifying the reaction efficiency and its dependence on time or external reaction conditions. Field gradient Nuclear Magnetic Resonance (NMR) methods are suggested as a tool for providing parameters sensitive to this mass flow in a contact-free and non-invasive way. For the example of bubble-forming hydrogen peroxide decomposition in an alumina pellet, the dependence of the mean-squared displacement of fluid molecules on spatial direction, observation time and reaction time is presented, and multi-pulse techniques are employed in order to separate molecular displacements from coherent and incoherent motion on the timescale of the experiment. The reaction progress is followed until the complete decomposition of H2O2.

Quasiequilibrium states in thermotropic liquid crystals studied by multiple-quantum NMR.

Previous work showed that by means of the Jeener-Broekaert (JB) experiment, two quasiequilibrium states can be selectively prepared in the proton spin system of thermotropic nematic liquid crystals (LCs) in a strong magnetic field. The similarity of the experimental results obtained in a variety of LC in a broad Larmor frequency range, with crystal hydrates, supports the assumption that also in LC the two spin reservoirs, into which the Zeeman order is transferred, originate in the dipolar energy and that they are associated with a separation in energy scales: A constant of motion related to the stronger dipolar interactions (S), and a second one (W) corresponding to the secular part of the weaker dipolar interactions with regard to the Zeeman and the strong dipolar part. We study the nature of these quasi-invariants in nematic 5CB (4(')-pentyl-4-biphenyl-carbonitrile) and measure their relaxation times by encoding the multiple-quantum coherences of the states following the JB pulse pair on two orthogonal bases, Z and X. The experiments were also performed in powder adamantane at 301 K which is used as a reference compound having only one dipolar quasi-invariant. We show that the evolution of the quantum states during the buildup of the quasiequilibrium state in 5CB prepared under the S condition is similar to the case of powder adamantane and that their quasiequilibrium density operators have the same tensor structure. In contrast, the second constant of motion, whose explicit operator form is not known, involves a richer composition of multiple-quantum coherences of even order on the X basis, in consistency with the truncation inherent in its definition. We exploited the exclusive presence of coherences of +/-4,+/-6,+/-8, besides 0 and +/-2 under the W condition to measure the spin-lattice relaxation time T(W) accurately, so avoiding experimental difficulties that usually impair dipolar order relaxation measurement such as Zeeman contamination at high fields and also superposition of the different quasi-invariants. This procedure opens the possibility of measuring the spin-lattice relaxation of a quasi-invariant independent of the Zeeman and S reservoirs, so incorporating a new relaxation parameter useful for studying the complex molecular dynamics in mesophases. In fact, we report the first measurement of T(W) in a LC at high magnetic fields. Comparison of the obtained value with the one corresponding to a lower field (16 MHz) points out that the relaxation of the W-order strongly depends on the intensity of the external magnetic field, similarly to the case of the S reservoir, indicating that the relaxation of the W-quasi-invariant is also governed by the cooperative molecular motions.