Slow-motion Regime Research Articles

1,1'-Biolympicenyl: A Stable Non-Kekulé Diradical with a Small Singlet and Triplet Energy Gap.

Dimerization of delocalized polycyclic hydrocarbon radicals is a simple and versatile method to create diradicals with tailored electronic structures and accessible high-spin states. However, the synthesis is challenging, and the stability issue of the diradicals remains a concern. In this study, we present the synthesis of a stable non-Kekulé 1,1'-biolympicenyl diradical 1 using a protection-oxidation-protection strategy. Diradical 1 demonstrated exceptional stability, with a solution half-life time exceeding 3.5 years and a solid state thermal decomposition temperature above 300 °C. X-ray crystallographic analysis revealed its intersected molecular structure and tightly bound dimer configuration. A singlet ground state with a small singlet-triplet energy gap is consistently identified using electron paramagnetic resonance (EPR) and a superconducting quantum interference device (SQUID) in a rigid matrix, and the triplet state is thermally accessible at room temperature. The solution phase properties were systematically examined through EPR, absorption spectroscopy, and cyclic voltammetry, revealing a rotational motion in the slow-motion regime and multistage redox characteristics. This study presents an efficient synthetic and stabilization strategy for organic diradicals, enabling the development of various high-spin functional materials.

Mobility of sodium ions in agarose gels probed through combined single- and triple-quantum NMR

Metal ions, including biologically prevalent sodium ions, can modulate electrostatic interactions frequently involved in the stability of condensed compartments in cells. Quantitative characterization of heterogeneous ion dynamics inside biomolecular condensates demands new experimental approaches. Here we develop a 23Na NMR relaxation-based integrative approach to probe dynamics of sodium ions inside agarose gels as a model system. We exploit the electric quadrupole moment of spin-3/2 23Na nuclei and, through combination of single-quantum and triple-quantum-filtered 23Na NMR relaxation methods, disentangle the relaxation contribution of different populations of sodium ions inside gels. Three populations of sodium ions are identified: a population with bi-exponential relaxation representing ions within the slow motion regime and two populations with mono-exponential relaxation but at different rates. Our study demonstrates the dynamical heterogeneity of sodium ions inside agarose gels and presents a new experimental approach for monitoring dynamics of sodium and other spin-3/2 ions (e.g. chloride) in condensed environments.

Novel tests of gravity using nano-Hertz stochastic gravitational-wave background signals

Gravity theories that modify General Relativity in the slow-motion regime can introduce nonperturbative corrections to the stochastic gravitational-wave background (SGWB) from supermassive black-hole binaries in the nano-Hertz band, while not affecting the quadrupolar nature of the gravitational-wave radiation and remaining perturbative in the highly-relativistic regime, as to satisfy current post-Newtonian (PN) constraints. We present a model-agnostic formalism to map such theories into a modified tilt for the SGWB spectrum, showing that negative PN corrections (in particular -2PN) can alleviate the tension in the recent pulsar-timing-array data if the detected SGWB is interpreted as arising from supermassive binaries. Despite being preliminary, current data have already strong constraining power, for example they set a novel (conservative) upper bound on theories with time-varying Newton's constant (a -4PN correction) at least at the level of Ġ/G ≲ 10^-5 yr^-1 for redshift z=[0.1÷1]. We also show that NANOGrav data are best fitted by a broken power-law interpolating between a dominant -2PN or -3PN modification at low frequency, and the standard general-relativity scaling at high frequency. Nonetheless, a modified gravity explanation should be confronted with binary eccentricity, environmental effects, nonastrophysical origins of the signal, and scrutinized against statistical uncertainties. These novel tests of gravity will soon become more stringent when combining all pulsar-timing-array facilities and when collecting more data.

Weak-field regime of the generalized hybrid metric-Palatini gravity

In this work we explore the dynamics of the generalized hybrid metric-Palatini theory of gravity in the weak-field, slow-motion regime. We start by introducing the equivalent scalar-tensor representation of the theory, which contains two scalar degrees of freedom, and perform a conformal transformation to the Einstein frame. Linear perturbations of the metric in a Minkowskian background are then studied for the metric and both scalar fields. The effective Newton constant and the PPN parameter $\ensuremath{\gamma}$ of the theory are extracted after transforming back to the (original) Jordan frame. Two particular cases where the general method ceases to be applicable are approached separately. A comparison of these results with observational constraints is then used to impose bounds on the masses and coupling constants of the scalar fields.

Trajectory-Based Approach for the Analysis of CODEX Solid-State Exchange Experiments in the Slow and Intermediate Motion Regime: Comparison of Experiment, Simulation, and Analytical Treatment

We present an efficient approach to analyze CODEX-MAS exchange NMR data by comparing the experimental results with simulated data that are calculated from separately simulated motional trajectories...

Tailored flavoproteins acting as light-driven spin machines pump nuclear hyperpolarization

The solid-state photo-chemically induced dynamic nuclear polarization (photo-CIDNP) effect generates non-Boltzmann nuclear spin magnetization, referred to as hyperpolarization, allowing for high gain of sensitivity in nuclear magnetic resonance (NMR). Well known to occur in photosynthetic reaction centers, the effect was also observed in a light-oxygen-voltage (LOV) domain of the blue-light receptor phototropin, in which the functional cysteine was removed to prevent photo-chemical reactions with the cofactor, a flavin mononucleotide (FMN). Upon illumination, the FMN abstracts an electron from a tryptophan to form a transient spin-correlated radical pair (SCRP) generating the photo-CIDNP effect. Here, we report on designed molecular spin-machines producing nuclear hyperpolarization upon illumination: a LOV domain of aureochrome1a from Phaeodactylum tricornutum, and a LOV domain named 4511 from Methylobacterium radiotolerans (Mr4511) which lacks an otherwise conserved tryptophan in its wild-type form. Insertion of the tryptophan at canonical and novel positions in Mr4511 yields photo-CIDNP effects observed by 15N and 1H liquid-state high-resolution NMR with a characteristic magnetic-field dependence indicating an involvement of anisotropic magnetic interactions and a slow-motion regime in the transient paramagnetic state. The heuristic biomimetic design opens new categories of experiments to analyze and apply the photo-CIDNP effect.

A Global Minimization Toolkit for Batch-Fitting and χ2 Cluster Analysis of CW-EPR Spectra

Electron paramagnetic resonance spectroscopy (EPR) is a uniquely powerful technique for characterizing conformational dynamics at specific sites within a broad range of molecular species in water. Computational tools for fitting EPR spectra have enabled dynamics parameters to be determined quantitatively. These tools have dramatically broadened the capabilities of EPR dynamics analysis, however, their implementation can easily lead to overfitting or problems with self-consistency. As a result, dynamics parameters and associated properties become difficult to reliably determine, particularly in the slow-motion regime. Here, we present an EPR analysis strategy and the corresponding computational tool for batch-fitting EPR spectra and cluster analysis of the χ2 landscape in Linux. We call this tool CSCA (Chi-Squared Cluster Analysis). The CSCA tool allows us to determine self-consistent rotational diffusion rates and enables calculations of activation energies of diffusion from Arrhenius plots. We demonstrate CSCA using a model system designed for EPR analysis: a self-assembled nanoribbon with radical electron spin labels positioned at known distances off the surface. We anticipate that the CSCA tool will increase the reproducibility of EPR fitting for the characterization of dynamics in biomolecules and soft matter.

Gravity Tests with Radio Pulsars

The discovery of the first binary pulsar in 1974 has opened up a completely new field of experimental gravity. In numerous important ways, pulsars have taken precision gravity tests quantitatively and qualitatively beyond the weak-field slow-motion regime of the Solar System. Apart from the first verification of the existence of gravitational waves, binary pulsars for the first time gave us the possibility to study the dynamics of strongly self-gravitating bodies with high precision. To date there are several radio pulsars known which can be utilized for precision tests of gravity. Depending on their orbital properties and the nature of their companion, these pulsars probe various different predictions of general relativity and its alternatives in the mildly relativistic strong-field regime. In many aspects, pulsar tests are complementary to other present and upcoming gravity experiments, like gravitational-wave observatories or the Event Horizon Telescope. This review gives an introduction to gravity tests with radio pulsars and its theoretical foundations, highlights some of the most important results, and gives a brief outlook into the future of this important field of experimental gravity.

Rotating frame MRI relaxations as markers of diffuse white matter abnormalities in multiple sclerosis

Even though MRI visualization of white matter lesions is pivotal for the diagnosis and management of multiple sclerosis (MS), the issue of detecting diffuse brain tissue damage beyond the apparent T2-hyperintense lesions continues to spark considerable interest. Motivated by the notion that rotating frame MRI methods are sensitive to slow motional regimes critical for tissue characterization, here we utilized novel imaging protocols of rotating frame MRI on a clinical 3 Tesla platform, including adiabatic longitudinal, T1ρ, and transverse, T2ρ, relaxation methods, and Relaxation Along a Fictitious Field (RAFF) in the rotating frame of rank 4 (RAFF4), in 10 relapsing-remitting multiple sclerosis patients and 10 sex- and age-matched healthy controls. T1ρ, T2ρ and RAFF4 relaxograms extracted from the whole white matter exhibited a significant shift towards longer relaxation time constants in MS patients as compared to controls. T1ρ and RAFF4 detected alterations even when considering only regions of normally appearing white matter (NAWM), while other MRI metrics such as T1w/T2w ratio and diffusion tensor imaging measures failed to find group differences. In addition, RAFF4, T2ρ and, to a lesser extent, T1ρ showed differences in subcortical grey matter structures, mainly hippocampus, whereas no functional changes in this region were detected in resting-state functional MRI metrics. We conclude that rotating frame MRI techniques are exceptionally sensitive methods for the detection of subtle abnormalities not only in NAWM, but also in deep grey matter in MS, where they surpass even highly sensitive measures of functional changes, which are often suggested to precede detectable structural alterations. Such abnormalities are consistent with a wide spectrum of different, but interconnected pathological features of MS, including the loss of neuronal cells and their axons, decreased levels of myelin even in NAWM, and altered iron content.

Regarding the measurement of microviscosity in lipid bilayers by EPR

Simulations of electron paramagnetic resonance spectra of stearic acid spin labels in lipid bilayers are used to illustrate the fact that the apparent order parameter Sapp calculated from the spectral shape does not coincide with the true order parameter S in the case of slow motions. While S reflects a static property as the degree of order of the lipid chains, Sapp depends on both order and dynamics. Thus, calibration procedures intended to obtain bilayer microviscosity values from Sapp in the slow motion regime are not reliable. However, Sapp is a useful tool to describe trends in membrane fluidity.

Controlling the transverse proton relaxivity of magnetic graphene oxide

The engineering of materials with controlled magnetic properties by means other than a magnetic field is of great interest in nanotechnology. In this study, we report engineered magnetic graphene oxide (MGO) in the nanocomposite form of iron oxide nanoparticles (IO)-graphene oxide (GO) with tunable core magnetism and magnetic resonance transverse relaxivity (r2). These tunable properties are obtained by varying the IO content on GO. The MGO series exhibits r2 values analogous to those observed in conventional single core and cluster forms of IO in different size regimes—motional averaging regime (MAR), static dephasing regime (SDR), and echo-limiting regime (ELR) or slow motion regime (SMR). The maximum r2 of 162 ± 5.703 mM−1s−1 is attained for MGO with 28 weight percent (wt%) content of IO on GO and hydrodynamic diameter of 414 nm, which is associated with the SDR. These findings demonstrate the clear potential of magnetic graphene oxide for magnetic resonance imaging (MRI) applications.

A Quadrupole-Central-Transition 59 Co NMR Study of Cobalamins in Solution.

We report the first observation of quadrupole-central-transition (QCT) 59 Co (I=7/2) NMR signals from three cobalamin (Cbl) compounds (CNCbl, MeCbl, and AdoCbl) dissolved in glycerol/water. Measurements were performed at four magnetic fields ranging from 11.7 to 21.1 T. We found that the 59 Co QCT signals observed for cobalamin compounds in the slow motion regime (ω0 τC ≫1) are significantly narrower than those observed from their aqueous solutions where the molecular tumbling is near the condition of ω0 τC ≈1. We demonstrated that an analysis of 59 Co QCT signals recorded over different temperatures and at multiple magnetic fields allowed determination of both the 59 Co quadrupole coupling constant and chemical shift anisotropy for each of the three cobalamins. We successfully applied the 59 Co QCT NMR approach to monitor in situ the transformation of CNCbl to its "base off" form in the presence of KCN. We further discovered that, to obtain the maximum QCT signal intensity with the Hahn-echo sequence, a strong B1 field should be used for the first 90° pulse, but a weak B1 field for the second 180° pulse. The reported 59 Co QCT NMR methodology opens up a new direction for studying structure and function of cobalamin compounds and their roles in biological processes.

Dynamic investigations of liquid crystalline elastomers and their constituents by 2H NMR spectroscopy

ABSTRACTSeveral side-chain liquid single crystalline elastomers (LSCEs) were investigated by means of 2H NMR spectroscopy focusing on the temperature dependence of the spectral line width and spectral shape, as well as the T-dependence of spin–lattice and spin–spin relaxation times (T1 and T2). All measurements were performed at the Larmor frequency of 76.753 MHz for 2H. The LSCEs were prepared in the form of monodomain films by using either 2H-labelled monomers (or co-monomers), 2H-labelled cross-linkers or 2H-labelled molecular probes free to diffuse in the LSCE matrix. In all cases, deuterons are on the phenyl moiety. The main features of the measured 2H NMR properties (static and dynamic ones) in these different cases were discussed and compared with those of low-molecular-weight mesogens (i.e. the same molecules used as monomers or co-monomers in the side-chain LSCEs) in the nematic and smectic A phases. Among all investigated LSCE samples, those 2H-labelled on the cross-linker sites present distinct properties either on the 2H NMR spectral line width and spectral shape in the paranematic and in the nematic phases, which can be interpreted in terms of director reorientational dynamics in the intermediate–slow motional regime, taking into account the inherent local director misalignment of LSCEs.

Self-force on a scalar charge in a circular orbit about a Reissner-Nordström black hole

Motivated by applications to the study of self-force effects in scalar-tensor theories of gravity, we calculate the self-force exerted on a scalar charge in a circular orbit about a Reissner-Nordstr\"{o}m black hole. We obtain the self-force via a mode-sum calculation, and find that our results differ from recent post-Newtonian calculations even in the slow-motion regime. We compute the radiative fluxes towards infinity and down the black hole, and verify that they are balanced by energy dissipated through the local self-force - in contrast to the reported post-Newtonian results. The self-force and radiative fluxes depend solely on the black hole's charge-to-mass ratio, the controlling parameter of the Reissner-Nordstr\"{o}m geometry. They both monotonically decrease as the black hole reaches extremality. With respect to an extremality parameter $\epsilon$, the energy flux through the event horizon is found to scale as $\sim \epsilon^{5/4}$ as $\epsilon \rightarrow 0$.

Interpretation of NMR Relaxation in Bitumen and Organic Shale Using Polymer–Heptane Mixes

One of the much debated mysteries in 1H NMR relaxation measurements of bitumen and heavy crude oils is the departure from expected theoretical trends at high viscosities, where traditional theories of 1H–1H dipole–dipole interactions predict an increase in T1 with increasing viscosity. However, previous experiments on bitumen and heavy crude oils clearly show that T1LM (i.e., log-mean of the T1 distribution) becomes independent of viscosity at high viscosities; in other words, T1LM versus viscosity approaches a plateau. We report 1H NMR data at ambient conditions on a set of pure polymers and polymer–heptane mixes spanning a wide range of viscosities (η = 0.39 cP ↔ 334 000 cP) and NMR frequencies (ω0/2π = f0 = 2.3 MHz ↔ 400 MHz) and find that at high viscosities (i.e., in the slow-motion regime) T1LM plateaus to a value T1LM> ∝ ω0 independent of viscosity, similar to bitumen. More specifically, on a frequency-normalized scale, we find that T1LM> × 2.3/f0 ≃ 3 ms (i.e., normalized relative to 2.3 MHz), in g...

Spin-label Order Parameter Calibrations for Slow Motion

Calibrations are given to extract orientation order parameters from pseudo-powder electron paramagnetic resonance line shapes of 14N-nitroxide spin labels undergoing slow rotational diffusion. The nitroxide z-axis is assumed parallel to the long molecular axis. Stochastic-Liouville simulations of slow-motion 9.4-GHz spectra for molecular ordering with a Maier–Saupe orientation potential reveal a linear dependence of the splittings, 2A_{hbox{max} } and 2A_{hbox{min} }, of the outer and inner peaks on order parameter S_{zz} that depends on the diffusion coefficient D_{{{text{R}} bot }} which characterizes fluctuations of the long molecular axis. This results in empirical expressions for order parameter and isotropic hyperfine coupling: S_{zz} = s_{1} times left( {A_{hbox{max} } - A_{hbox{min} } } right) - s_{o} and a_{o}^{{}} = tfrac{1}{3}left( {f_{hbox{max} } A_{hbox{max} } + f_{hbox{min} } A_{hbox{min} } } right) + delta a_{o}, respectively. Values of the calibration constants s_{1}, s_{text{o}}, f_{hbox{max} }, f_{hbox{min} } and delta a_{o} are given for different values of D_{{{text{R}} bot }} in fast and slow motional regimes. The calibrations are relatively insensitive to anisotropy of rotational diffusion (D_{{{text{R}}//}} ge D_{{{text{R}} bot }} ), and corrections are less significant for the isotropic hyperfine coupling than for the order parameter.

Simulating Electron Paramagnetic Resonance Spectra of Slow-Motion Systems in the Time Domain

Electron paramagnetic resonance (EPR) spectroscopy has proven to be an excellent tool for probing local structure and dynamics in biological systems. However, the corresponding spectra can be complex and difficult to interpret. In order to accurately interpret experimental data, there has been a corresponding active development of computational tools and user-friendly programs to simulate continuous-wave (CW) EPR spectra, especially those in the slow-motion regime (dynamical time scales of ≈10-100 ns for nitroxides at 9-10 GHz). Though the standard method has been to numerically solve the stochastic Liouville equation in the frequency domain, more recently, simulating CW EPR spectra in the time domain has become increasingly popular. Existing works have applied this method by simulating spin relaxation due to rotational diffusion, either by generating stochastic or molecular dynamics trajectories. Other significant spin relaxation mechanisms that affect CW EPR spectral lineshapes have been treated in a phenomenological manner. In order to bridge this gap in computational complexity and more accurately simulate EPR spectra obtained in experiments, we extend previous treatments by explicitly including other spin relaxation mechanisms and explore additional motional models. In addition, our programs are implemented in the widely used Matlab software environment.

On the mutual relationships between spin probe mobility, free volume and relaxation dynamics in organic glass-formers: Glycerol

The rotation dynamics of the spin probe TEMPO in glycerol from ESR is compared with the ortho-positronium (o-Ps) annihilation from PALS and interpreted using the relaxation dynamics from BDS. Rotation time scale within the slow motion regime exhibits two Arrhenius regions with the characteristic ESR temperature, TX1τ, close to the characteristic PALS temperature, Tb1L, which is related to the secondary β process above Tg. Next, a slow to fast motion regime transition at the characteristic ESR temperature, Tcτ, close to the characteristic PALS temperature, Tb2L, followed by non-Arrhenius fast motion regime region is fully coupled with the primary α process.

Low-power suppression of fast-motion spin 3/2 signals

Triple Quantum Filters (TQFs) are frequently used for the selection of bi-exponentially relaxing spin 3/2 nuclei (in particular 23Na) in ordered environments, such as biological tissues. These methods provide an excellent selection of slow-motion spins, but their sensitivity is generally low, and coherence selection requirements may lead to long experiments when applied in vivo. Alternative methods, such as 2P DIM, have demonstrated that the sensitivities of the signals from bi-exponentially relaxing sodium can be significantly increased using strategies other than TQFs. A shortcoming of the 2P DIM method is its strong dependence on B0 inhomogeneities. We describe here a method, which is sensitive to the slow-motion regime, while the signal from spins in the fast-motion regime is suppressed. This method is shown to be more effective than TQFs, requires minimal phase cycling for the suppression of the influence of rf inhomogeneity, and has less dependence on resonance offsets and B0-inhomogeneity than 2P DIM.

Mechanisms of water interaction with pore systems of hydrochar and pyrochar from poplar forestry waste.

The aim of this study was to understand the water-surface interactions of two chars obtained by gasification (pyrochar) and hydrothermal carbonization (hydrochar) of a poplar biomass. The two samples revealed different chemical compositions as evidenced by solid state (13)C NMR spectroscopy. In fact, hydrochar resulted in a lignin-like material still containing oxygenated functionalities. Pyrochar was a polyaromatic system in which no heteronuclei were detected. After saturation with water, hydrochar and pyrochar were analyzed by fast field cycling (FFC) NMR relaxometry. Results showed that water movement in hydrochar was mainly confined in very small pores. Conversely, water movement in pyrochar led to the conclusion that a larger number of transitional and very large pores were present. These results were confirmed by porosity evaluation derived from gas adsorption. Variable-temperature FFC NMR experiments confirmed a slow-motion regime due to a preferential diffusion of water on the solid surface. Conversely, the higher number of large pores in pyrochar allowed slow movement only up to 50 °C. As the temperature was raised to 80 °C, water interactions with the pore surface became weaker, thereby allowing a three-dimensional water exchange with the bulk liquid. This paper has shown that pore size distribution was more important than chemical composition in affecting water movement in two chemically different charred systems.