Distribution Of Relaxation Rates Research Articles

Magnetic skin effect in Pb(Fe _{1/2}$ Nb _{1/2}$ )O3

Relaxor-ferroelectrics display exceptional dielectric properties resulting from the underlying random dipolar fields induced by strong chemical inhomogeneity. An unusual structural aspect of relaxors is a skin-effect where the near-surface region in single crystals exhibit structures and critical phenomena that differ from the bulk. Relaxors are unique in that this skin effect extends over a macroscopic lengthscale of ∼100 μm whereas usual surface layers only extend over a few unit cells (or ∼nm). We present a muon spectroscopy study of Pb(Fe _{1/2} Nb _{1/2} )O3 (PFN) which displays ferroelectric order, including many relaxor-like dielectric properties such as a frequency broadened dielectric response, and antiferromagnetism with spatially short-range polar correlations and hence can be termed a multiferroic. In terms of the magnetic behavior determined by the Fe3+ ( S=5/2 , L ≈ 0) ions, PFN has been characterized as a unique example of a ‘cluster spin-glass’. We use variable momentum muon spectroscopy to study the depth dependence of the slow magnetic relaxations in a large 1 cm3 crystal of PFN. Zero-field positive muon spin relaxation is parameterized using a stretched exponential, indicative of a distribution of relaxation rates of the Fe3+ spins. This bandwidth of frequencies changes as a function of muon momentum, indicative of a change in the Fe3+ relaxation rates as a function of muon implantation depth in our single crystal. Using negative muon elemental analysis, we find small-to-no measurable change in the Fe3+/Nb5+ concentration with depth implying that chemical concentration alone cannot account for the change in the relaxational dynamics. PFN displays an analogous magnetic skin effect reported to exist in the structural properties of relaxor-ferroelectrics.

Multivariate Machine Learning Models of Nanoscale Porosity from Ultrafast NMR Relaxometry.

Nanoporous materials are of great interest in many applications, such as catalysis, separation, and energy storage. The performance of these materials is closely related to their pore sizes, which are inefficient to determine through the conventional measurement of gas adsorption isotherms. Nuclear magnetic resonance (NMR) relaxometry has emerged as a technique highly sensitive to porosity in such materials. Nonetheless, streamlined methods to estimate pore size from NMR relaxometry remain elusive. Previous attempts have been hindered by inverting a time domain signal to relaxation rate distribution, and dealing with resulting parameters that vary in number, location, and magnitude. Here we invoke well-established machine learning techniques to directly correlate time domain signals to BET surface areas for a set of metal-organic frameworks (MOFs) imbibed with solvent at varied concentrations. We employ this series of MOFs to establish a correlation between NMR signal and surface area via partial least squares (PLS), following screening with principal component analysis, and apply the PLS model to predict surface area of various nanoporous materials. This approach offers a high-throughput, non-destructive way to assess porosity in c.a. one minute. We anticipate this work will contribute to the development of new materials with optimized pore sizes for various applications.

Multivariate Machine Learning Models of Nanoscale Porosity from Ultrafast NMR Relaxometry

AbstractNanoporous materials are of great interest in many applications, such as catalysis, separation, and energy storage. The performance of these materials is closely related to their pore sizes, which are inefficient to determine through the conventional measurement of gas adsorption isotherms. Nuclear magnetic resonance (NMR) relaxometry has emerged as a technique highly sensitive to porosity in such materials. Nonetheless, streamlined methods to estimate pore size from NMR relaxometry remain elusive. Previous attempts have been hindered by inverting a time domain signal to relaxation rate distribution, and dealing with resulting parameters that vary in number, location, and magnitude. Here we invoke well‐established machine learning techniques to directly correlate time domain signals to BET surface areas for a set of metal‐organic frameworks (MOFs) imbibed with solvent at varied concentrations. We employ this series of MOFs to establish a correlation between NMR signal and surface area via partial least squares (PLS), following screening with principal component analysis, and apply the PLS model to predict surface area of various nanoporous materials. This approach offers a high‐throughput, non‐destructive way to assess porosity in c.a. one minute. We anticipate this work will contribute to the development of new materials with optimized pore sizes for various applications.

Origin of dynamical heterogeneities in borosilicate glass-forming systems

Dynamical heterogeneities give rise to spatiotemporal fluctuations yielding a broad distribution of relaxation rates in glass-forming systems. In alkali-(alumino)borosilicate glass, a highly complex glass system with a wide variety of structural components involving mixed network former and mixed network modifier effects, the factors governing dynamical heterogeneities in short-range order remain unknown. This paper reports an investigation of the dominant factors governing dynamical heterogeneities in borosilicate glass. The dynamical heterogeneities of two alkali-(alumino)borosilicate glasses are investigated using the isoconfigurational ensemble method via molecular dynamics simulations. We find that alkali ions drive high dynamical propensities in local spatial regions. The average number of bridging oxygens for both boron and silicon does not monotonically correlate with the corresponding calibrated dynamical propensity. The local alkali agglomeration affects the dynamical propensity of the alkali ion. The agglomeration of lighter-weighted alkali ions surrounding an alkali ion favors its high dynamical propensity, while the agglomeration of equal-weighted or heavier-weighted alkali ions favors its low dynamical propensity. The separation distance between the alkali ion and the alkali-modified boron or silicon atom affects the dynamical propensity of the alkali ion. Mixed-alkali environments perturb the relationship between the calibrated dynamical propensity of an alkali ion and its separation distance from its modified boron or its modified silicon atom.

Quantitative MRI maps of human neocortex explored using cell type-specific gene expression analysis.

Quantitative magnetic resonance imaging (qMRI) allows extraction of reproducible and robust parameter maps. However, the connection to underlying biological substrates remains murky, especially in the complex, densely packed cortex. We investigated associations in human neocortex between qMRI parameters and neocortical cell types by comparing the spatial distribution of the qMRI parameters longitudinal relaxation rate (${R_{1}}$), effective transverse relaxation rate (${R_{2}}^{\ast }$), and magnetization transfer saturation (MTsat) to gene expression from the Allen Human Brain Atlas, then combining this with lists of genes enriched in specific cell types found in the human brain. As qMRI parameters are magnetic field strength-dependent, the analysis was performed on MRI data at 3T and 7T. All qMRI parameters significantly covaried with genes enriched in GABA- and glutamatergic neurons, i.e. they were associated with cytoarchitecture. The qMRI parameters also significantly covaried with the distribution of genes enriched in astrocytes (${R_{2}}^{\ast }$ at 3T, ${R_{1}}$ at 7T), endothelial cells (${R_{1}}$ and MTsat at 3T), microglia (${R_{1}}$ and MTsat at 3T, ${R_{1}}$ at 7T), and oligodendrocytes and oligodendrocyte precursor cells (${R_{1}}$ at 7T). These results advance the potential use of qMRI parameters as biomarkers for specific cell types.

High-resolution vibronic spectroscopy of a single molecule embedded in a crystal.

Vibrational levels of the electronic ground states in dye molecules have not been previously explored at a high resolution in solid matrices. We present new spectroscopic measurements on single polycyclic aromatic molecules of dibenzoterrylene embedded in an organic crystal made of para-dichlorobenzene. To do this, we use narrow-band continuous-wave lasers and combine spectroscopy methods based on fluorescence excitation and stimulated emission depletion to assess individual vibrational linewidths in the electronic ground state at a resolution of ∼30MHz dictated by the linewidth of the electronic excited state. In this fashion, we identify several exceptionally narrow vibronic levels with linewidths down to values around 2GHz. Additionally, we sample the distribution of vibronic wavenumbers, relaxation rates, and Franck-Condon factors, in both the electronic ground and excited states for a handful of individual molecules. We discuss various noteworthy experimental findings and compare them with the outcome of density functional theory calculations. The highly detailed vibronic spectra obtained in our work pave the way for studying the nanoscopic local environment of single molecules. The approach also provides an improved understanding of the vibrational relaxation mechanisms in the electronic ground state, which may help create long-lived vibrational states for applications in quantum technology.

Spatially Resolved Spin–Lattice Relaxation Times and Line Widths in Manganese-Grafted Detonation Nanodiamonds

We report on a novel approach that allows determining the spatially resolved nuclear spin–lattice relaxation times and NMR line widths in nanomaterials. The approach was applied to a newly synthesized nanomaterial─detonation nanodiamonds with manganese ions directly grafted to the surface of the nanodiamond particles. The interaction of the carbon nuclear spins with paramagnetic Mn2+ ions results in acceleration of nuclear spin–lattice relaxation and broadening of the 13C resonance line. Using spin dephasing experiments, we were able to determine the layer-by-layer contributions of the paramagnetic Mn2+ions to the spin–lattice relaxation time and line width of the carbon spins positioned at different depths from the diamond surface. Developed for nanodiamonds, this approach is more general and can be successfully applied to study the distribution of nuclear relaxation rates and line broadening and for mapping magnetic interactions inside various nanoparticles, being of practical use in various nanotechnologies.

Inverse Laplace transformation analysis of stretched exponential relaxation

We investigate the effectiveness of the Inverse Laplace Transform (ILT) analysis method to extract the distribution of relaxation rates from nuclear magnetic resonance data with stretched exponential relaxation. Stretched-relaxation is a hallmark of a distribution of relaxation rates, and an analytical expression exists for this distribution for the case of a spin-1/2 nucleus. We compare this theoretical distribution with those extracted via the ILT method for several values of the stretching exponent and at different levels of experimental noise. The ILT accurately captures the distributions for β≲0.7, and for signal to noise ratios greater than ∼40; however the ILT distributions tend to introduce artificial oscillatory components. We further use the ILT approach to analyze stretched relaxation for spin I>1/2 and find that the distributions are accurately captured by the theoretical expression for I=1/2. Our results provide a solid foundation to interpret distributions of relaxation rates for general spin I in terms of stretched exponential fits.

Accelerating quantitative susceptibility and R2* mapping using incoherent undersampling and deep neural network reconstruction

Quantitative susceptibility mapping (QSM) and R2* mapping are MRI post-processing methods that quantify tissue magnetic susceptibility and transverse relaxation rate distributions. However, QSM and R2* acquisitions are relatively slow, even with parallel imaging. Incoherent undersampling and compressed sensing reconstruction techniques have been used to accelerate traditional magnitude-based MRI acquisitions; however, most do not recover the full phase signal, as required by QSM, due to its non-convex nature. In this study, a learning-based Deep Complex Residual Network (DCRNet) is proposed to recover both the magnitude and phase images from incoherently undersampled data, enabling high acceleration of QSM and R2* acquisition. Magnitude, phase, R2*, and QSM results from DCRNet were compared with two iterative and one deep learning methods on retrospectively undersampled acquisitions from six healthy volunteers, one intracranial hemorrhage and one multiple sclerosis patients, as well as one prospectively undersampled healthy subject using a 7T scanner. Peak signal to noise ratio (PSNR), structural similarity (SSIM), root-mean-squared error (RMSE), and region-of-interest susceptibility and R2* measurements are reported for numerical comparisons. The proposed DCRNet method substantially reduced artifacts and blurring compared to the other methods and resulted in the highest PSNR, SSIM, and RMSE on the magnitude, R2*, local field, and susceptibility maps. Compared to two iterative and one deep learning methods, the DCRNet method demonstrated a 3.2% to 9.1% accuracy improvement in deep grey matter susceptibility when accelerated by a factor of four. The DCRNet also dramatically shortened the reconstruction time of single 2D brain images from 36-140 seconds using conventional approaches to only 15-70 milliseconds.

Theory of structural relaxation in glass from the thermodynamics of irreversible processes

This work proposes a fundamental thermodynamic description of structural relaxation in glasses by establishing a link between the Prony series solution to volume relaxation derived from the principles of irreversible thermodynamics and asymmetric Lévy stable distribution of relaxation rates. Additionally, it is shown that the bulk viscosity of glass, and not the shear viscosity, is the transport coefficient governing structural relaxation. We also report the distribution of relaxation times and energy barrier heights underpinning stretched exponential relaxation. It is proposed that this framework may be used for qualitative and quantitative descriptions of the relaxation kinetics in glass.

Shortening of NMR 1/T1 and 1/T2 Relaxation Rate Distribution Intervals in D2O Containing Jaw Cysts or Abscesses: Separation of Cysts from Abscesses

It is well known that the relaxation rates (1/T1 and 1/T2) in H2O/D2O mixtures are smaller than those in H2O alone. The results of this have not been examined in the presence of a low rate of cysts or abscess contents in D2O. One purpose of this study was to determine the shortening of the relaxation rate distribution interval (SRDI) for D2O containing cysts or abscess contents. Another goal is to investigate the differentiation of cysts from abscesses with T1 and T2 measurements. The ultimate objective is the possibility of a new MRI contrast mechanism for dental lesions. Nineteen odontogenic jaw cysts and 12 jaw abscesses were collected from patients. A mixture was prepared by adding 0.06 mL cyst or abscess content to 0.94 mL D2O. The experiments were carried out with a nuclear magnetic resonance spectrometer operating at 400 MHz. The mean 1/T2 of the abscesses was significantly different from that of the cysts (P < 0.005), but the mean 1/T1 of the non-haemorrhagic cysts was not different from that of the abscesses (P = 0.626). The interval shortening ratios (SRDIs) of 1/T1 and 1/T2 for the cystic mixture were 16.36 and 4.22, respectively. The ratios were 8.39 and 2.68, respectively, for the mixture containing abscess contents. In conclusion, the relaxation rate reduction of the mixture results in a shortening of the distribution intervals, which leads to the separation of cysts from abscesses. In addition, the high interval shortening ratios indicate that the results of this study can provide a basis for studies on a new MR contrast mechanism for jaw lesions.

Investigation of Transverse Relaxation Rate Distribution via Magnetic Resonance Imaging: Impact of Electrode Formation

The impact of electrode formation is studied by the spatially and time‐resolved distribution of transverse relaxation. In situ 7Li nuclear magnetic resonance experiments are performed on an experimental lithium‐ion battery cell to study the impact of electrode passivation via imaging and transverse relaxation in the interelectrode volume. The electrolyte in the battery, using technically relevant electrode material, i.e., graphite and lithium–nickel–cobalt–manganese–oxide, is studied by 2D magnetic resonance imaging. The electrolyte is 1 mol L−1 lithium hexafluorophosphate dissolved in a binary mixture of ethylene carbonate and dimethyl carbonate. 1D profiles are acquired and related to 7Li concentration during passivation and during a constant current/constant voltage cycle. The transverse relaxation rate R2(z,t) measured by multiecho profiles revealed changes within the electrolyte volume. The ongoing process changes the relaxation distribution. Indications for a defective electrode passivation are deduced from the data. During one charging cycle with constant current/constant voltage, the lithium concentration is measured spatially resolved, and the data are modeled by the Nernst–Planck equation.

Structural insights for vanadium catecholates and iron‑sulfur clusters obtained from multiple data analysis methods applied to electron spin relaxation data

Electron paramagnetic resonance (EPR) inversion recovery curves for vanadium catecholates and iron‑sulfur clusters were analyzed with three models: the sum of two exponentials, a stretched exponential, and a model-free distribution of exponentials (UPEN). For all data sets studied fits with a stretched exponential were statistically indistinguishable from the sum of two exponentials, and were significantly better than for single exponentials. UPEN provides insights into the structures of the distributions. For a vanadium(IV) tris catecholate the distribution of relaxation rates calculated with UPEN shows the contribution from spectral diffusion at low temperatures. The energy of the local mode for this complex, found from the temperature dependence of the spin lattice relaxation, is consistent with values expected for a metal-ligand vibration. For the [2Fe-2S]+ cluster in pyruvate formate lyase activating enzyme (PFL-AE) the small stretched exponential β values (0.3) at low temperature and the distributions calculated with UPEN reflect the contribution from a second rapidly relaxing species that could be difficult to detect by continuous wave EPR. The distributions in 1/T1 for the [4Fe-4S]+ clusters in Mycofactocin maturase were about a factor of four wider than for the three other systems studied. The very broad distribution of relaxation rates may be due to protein mobility and distributions in electronic energies and local environments for the clusters. UPEN provides insight into several situations that can result in low values of stretch parameter β including contributions from spectral diffusion, overlapping signals from distinguishable clusters, or very wide distributions.

An application of the spectral Radon–Nikodym approach to fluorescence dynamics study of cold atomic cloud ensemble

A fluorescence dynamics of a cold atomic cloud, laser–cooled to a very low temperature, optically excited by a short laser impulse is calculated by applying non–stationary Schrödinger equation to the system of atoms and electromagnetic field. The solution gives fluorescence time–relaxation dependence, with relaxation time distribution depending on the system itself and external electromagnetic field applied. The distribution of the relaxation rates changes, when an external electric field affecting the atomic ensemble is applied. To analyze the relaxation process a novel Radon–Nikodym approach is applied: the relaxation curve is not piece–wise interpolated, but instead is converted to a matrix, the eigenvalues of which provide relaxation rate distribution. In contrasts to the random matrix theory, where the weights, corresponding to an eigenvalue, are considered equal, in this work the weight, corresponding to an individual eigenvalue, is determined by the Lebesgue integral quadrature weights.

Numerical study of the temperature dependence of the NMR relaxation rate across the superfluid–Bose glass transition in one dimension

We study the nuclear magnetic resonance (NMR) spin-lattice relaxation rate $1/T_1$ in random one-dimensional spin chains as function of the temperature and disorder strength. In the zero temperature limit, the system displays a disorder-induced quantum phase transition between a critical Tomonaga-Luttinger liquid (TLL) phase and a localized Bose glass phase. The $1/T_1$ is investigated across this transition using large-scale simulations based on matrix product state techniques. We find that this quantity can detect the transition and probe the value of the dimensionless TLL parameter $K$. We also compute the NMR relaxation rate distributions for each temperature and disorder strength considered. In particular we discuss the applicability of the stretched exponential fit to the return-to-equilibrium function in order to extract the $1/T_1$ experimentally. The results presented here should provide valuable insights in regards of future NMR experiments in realistic disordered spin compounds.

Dynamical landscape in DODAB membrane system: MD simulation & neutron scattering studies

The nature of diffusion of lipids in a bilayer membrane plays a key role in various biological processes like cell signaling, cellular transport etc. Dioctadecyldimethylammonium bromide (DODAB) is a synthetic lipid that self-assembles to form bilayer. Here we describe the dynamical landscape of the DODAB bilayer in fluid phase using molecular dynamics (MD) simulation and quasielastic neutron scattering (QENS) techniques. MSD of lateral motion of the lipids calculated from MD simulations show subdiffusive behaviour. A model free approach is employed to describe the dynamics of lipids in the bilayer where the relaxation rates are distributed over a wide range. A stretched exponential relaxation function used to describe the incoherent intermediate scattering function of the lipids obtained from MD simulation and QENS experiments. The distribution of relaxation rates covers over three decades. The results of the MD simulation and QENS experiments agree well.

Impact of Molecular Architecture on Dynamics of Miktoarm Star Copolymers

Broadband dielectric spectroscopy (BDS) is used to probe the chain and segmental dynamics of A2B2 and AB2 miktoarm star copolymers based on polystyrene (PS, A block) and polyisoprene (PI, B block) that display lamellar morphologies as determined using small-angle X-ray scattering (SAXS). While no changes in the distribution of PI segmental relaxation times are observed with variation of the molecular architecture, an unexpected increase in the normalized PI chain relaxation intensity is realized for AB2 miktoarm star copolymers as well as a change in the distribution of chain relaxation rates as compared to A2B2 and AB diblock copolymer systems. This result is attributed to asymmetry in the molecular architecture near the junction point, which affects the osmotic constraint of the tethered PI chains within the interfacial region of the lamellae. The results highlight the importance of macromolecular design on fundamental chain dynamics in phase-separated thermoplastic elastomers.

1/f electrophysiological spectra in resting and drug-induced states can be explained by the dynamics of multiple oscillatory relaxation processes

Neurophysiological recordings are dominated by arhythmical activity whose spectra can be characterised by power-law functions, and on this basis are often referred to as reflecting scale-free brain dynamics (1/fβ). Relatively little is known regarding the neural generators and temporal dynamics of this arhythmical behaviour compared to rhythmical behaviour. Here we used Irregularly Resampled AutoSpectral Analysis (IRASA) to quantify β, in both the high (5–100 Hz, βhf) and low frequency bands (0.1–2.5 Hz, βlf) in MEG/EEG/ECoG recordings and to separate arhythmical from rhythmical modes of activity, such as, alpha rhythms. In MEG/EEG/ECoG data, we demonstrate that oscillatory alpha power dynamically correlates over time with βhf and similarly, participants with higher rhythmical alpha power have higher βhf. In a series of pharmaco-MEG investigations using the GABA reuptake inhibitor tiagabine, the glutamatergic AMPA receptor antagonist perampanel, the NMDA receptor antagonist ketamine and the mixed partial serotonergic agonist LSD, a variety of effects on both βhf and βlf were observed. Additionally, strong modulations of βhf were seen in monkey ECoG data during general anaesthesia using propofol and ketamine. We develop and test a unifying model which can explain, the 1/f nature of electrophysiological spectra, their dynamic interaction with oscillatory rhythms as well as the sensitivity of 1/f activity to drug interventions by considering electrophysiological spectra as being generated by a collection of stochastically perturbed damped oscillators having a distribution of relaxation rates.

Generalized Radon--Nikodym Spectral Approach. Application to Relaxation Dynamics Study.

Radon--Nikodym approach to relaxation dynamics, where probability density is built first and then used to calculate observable dynamic characteristic is developed and applied to relaxation type signals study. In contrast with L² norm approaches, such as Fourier or least squares, this new approach does not use a norm, the problem is reduced to finding the spectrum of an operator (virtual Hamiltonian), which is built in a way that eigenvalues represent the dynamic characteristic of interest and eigenvectors represent probability density. The problems of interpolation (numerical estimation of Radon--Nikodym derivatives is developed) and obtaining the distribution of relaxation rates from sampled timeserie are considered. Application of the theory is demonstrated on a number of model and experimentally measured timeserie signals of degradation and relaxation processes. Software product, implementing the theory is developed.

Preparation and characterization of dispersions based on chitosan and poly(styrene sulfonate)

Interpolyelectrolyte complexes (IPECs) were obtained by the mixture of solutions of chitosan and poly(sodium 4-styrene-sulfonate). The resultant dispersions were characterized using small-angle X-ray scattering (SAXS) and dynamic light scattering (DLS). Gyration radius from SAXS increased as sulfonate to aminium molar ratio, r SA , increased, while pair distance distributions, P(r), shifted to higher values of r, describing the process of particle formation as resultant from collapse of solubilized IPEC clusters in the form of solid particles, followed by nucleation of larger ones. Intensity correlation curves from DLS were used to obtain parameters related to Brownian motion of (or within) IPEC clusters. IPEC cluster dimension growth was related to characteristic relaxation rate and relaxation rate distribution width. Association of DLS-derived results to SAXS-resultant data yielded a description of nanoparticles made of solid IPEC clusters stabilized by solubilized IPEC species.