Complex Relaxation Research Articles

Sodium Dynamics in the Cellular Environment.

Sodium ions are essential for the functions of biological cells, and they are maintained at the balance between intra- and extracellular environments. The quantitative assessment of intra- and extracellular sodium as well as its dynamics can provide crucial physiological information on a living system. 23Na nuclear magnetic resonance (NMR) is a powerful and noninvasive technique to probe the local environment and dynamics of sodium ions. However, due to the complex relaxation behavior of the quadrupolar nucleus in the intermediate-motion regime and because of the heterogeneous compartments and diverse molecular interactions in the cellular environment, the understanding of the 23Na NMR signal in biological systems is still at the early stage. In this work, we characterize the relaxation and diffusion of sodium ions in the solutions of proteins and polysaccharides, as well as in the in vitro samples of living cells. The multi-exponential behavior of 23Na transverse relaxation has been analyzed according to the relaxation theory to derive the crucial information related to the ionic dynamics and molecular binding in the solutions. The bi-compartment model of transverse relaxation and diffusion measurements can corroborate each other to quantify the fractions of intra- and extracellular sodium. We show that 23Na relaxation and diffusion can be used to monitor the viability of human cells, which offers versatile NMR metrics for in vivo studies.

Open-circuit photopotential characterization of photoelectrochemical activities of Au-modified TiO2 nanorods

The open circuit potential (OCP) of a semiconductor electrode can be used to quantify the transient photopotential (Ep), which represents wavelength-dependent charge accumulation and relaxation kinetics of a photoelectrode. Here OCP responses of a plasmonic Au@TiO2 nanorods (NRs) photoelectrode can be quantified without causing electrochemical corrosion of Au. The photogenerated charge accumulation kinetics data based on the wavelength-dependent growth rates of |Ep| can resolve the plasmonic effects on photoelectrochemistry (PEC) of Au@TiO2 NRs. Data fitting with Kohlrausch-Williams-Watts (KWW) stretched exponential kinetics model illustrates the complex charge relaxations at the Au/TiO2 Schottky contact, from which long relaxation lifetimes with broad lifetime distributions can be obtained. This is attributed to the abundant deep defects in the nanostructure TiO2, which has been strongly confirmed by reducing the oxygen vacancies using a post-thermal annealing treatment. Single-particle dark-field scattering (DFS) spectrum is measured with a tunable wavelength light source to support visible light activities of PEC characteristics of Au@TiO2 NRs. Light scattering spectra of >200 single Au@TiO2 NRs particles are collected to compare directly with PEC responses of OCP of the ensemble Au@TiO2 NRs.

Critical evaluation of unit response function interconversions for asphalt concrete linear viscoelastic modeling using discrete spectrum

It is well-known that asphalt concrete has three unit response functions (URFs): complex modulus, relaxation modulus, and creep compliance. The interconversions among these three URFs are generally done through discrete relaxation/retardation spectrum. Since different methods of determining discrete spectrum have been developed in the past, this study focused on systematically comparing and evaluating three classical methods: collocation, multidata, and windowing methods, with four relaxation/retardation time selections. Additionally, considering theoretical requirement and practical preference, both wide and narrow relaxation/retardation time ranges are evaluated to quantify their influences on the result qualities. After multiple sets of result comparisons, it has been found that all three methods can lead to reasonable results as long as wide and appropriate relaxation/retardation time range is given. However, since in practice shorter time range may be used more often, in this scenario attention needs to be paid to the solution quality including the spectrum values and shape, and the characterized function accuracy. Overall, the windowing method causes fewer solving issues than the other two methods due to its optimization nature, which prohibits the negative relaxation/retardation strength values. Despite that, the collocation and multidata methods occasionally lead to more reasonable results when narrower relaxation/retardation time range is used. From these observations, a hybrid procedure, which takes advantage of each interconversion method, is proposed in this study to optimize the discrete spectrum determination for asphalt concrete.

Viscoelastic Effects on Molecular Dynamics of Dielectric Probes in Polymer Matrices

Viscoelastic effects of the matrix polymer on molecular dynamics of dielectric probes were examined using the generalized Langevin equation, which was derived to include the retardation effect of viscous force. By solving the equation, we successfully obtained the universal relationship between the complex relaxation modulus and the dielectric spectrum of the probe. When the viscoelastic properties of the matrix are assumed to be viscous, the obtained dielectric relaxation spectrum is described with the Debye function. On the other hand, if they are supposed to be a power-law type relaxation spectrum, the dielectric relaxation spectrum is found to be the Cole-Cole function. The proposed method was applied to a previous study on a low-mass probe in a polystyrene matrix. The estimated effective modulus of the polystyrene was found to be close to a power-law-type relaxation. The present study provides a new microrheological method to estimate the viscoelastic properties in nanometer size.

Research Progress on the Point-defect Relaxation in β-Ti Alloys

The anelastic relaxation is measured at a low and high frequency from low to high temperature in some Ti alloys, most of which are usually recorded in the internal friction-temperature spectra. In this paper, the point-defect relaxation in β-Ti alloys is described and discussed. The point defects are the interstitial impurity atoms, substitution atoms and vacancies in β-Ti alloys. The reorientation of interstitial impurity O atoms around matrix Ti and substitute atoms produces Snoek-type peaks. The various interactions between the interstitial impurity atoms (O,N,et al.) and matrix atoms/substitute atoms (Ti, Nb,Mo,V,et al. ) can also produce a complex relaxation spectra consisting of several Snoek-type peaks. The concentrations of interstitial impurity atoms and the substitute atoms have important roles on the height and width of the Snoek-type peaks. The reorientation of defect pairs consisting of the interstitial impurity atoms and vacancies is also involved in the relaxation processes. At high temperatures, the Mo-Mo atom-pairs can be reoriented under the inducing of cycle stress and produce similar Zener relaxation peak.

Magnetism and hyperfine interactions in the hexagonal polymorph of delafossite CuFeO[formula omitted

The magnetic susceptibility of and hyperfine interactions in the hexagonal 2H polymorph of delafossite CuFeO2 were investigated by SQUID magnetometry and Mössbauer spectroscopy, respectively, at low temperatures. The hydrothermally synthesized 2H-CuFeO2 sample contained a 10 vol-% α-Fe2O3 impurity detected by X-ray diffraction, whose contribution to the susceptibility and hyperfine interactions were easily distinguishable from the major 2H-CuFeO2 one. Morphology and indirect optical band gap investigated by scanning electron microscopy and diffuse reflectance measurements showed well expected results for a hydrothermally synthesized delafossite sample. The magnetic susceptibility of 2H-CuFeO2 revealed a first antiferromagnetic like transitions at 16 K and a second transition at 13.5 K or 10 K depending on measurement protocol, which points towards modified exchange interactions as compared to the 3R polymorph. Complementary Mössbauer measurements revealed complicated spectral shapes at low temperatures indicating rather complex magnetic structures and magnetic relaxations above 20 K.

Slow magnetic relaxation in a ferromagnetic CuII chain complex, induced by a phonon bottleneck effect.

The first slow magnetic relaxation in a ferromagnetic Cu(II) chain compound, Cu(dipic)(OH2)2 (dipicH2 = pyridine-2,6-dicarboxylic acid), induced by a phonon bottleneck effect under a magnetic field of 0.6 T, with a relaxation time of 2.2 s at 2.8 K, was observed.

Non-homogeneous plastic deformation of amorphous metallic alloys under the action of a quasi-static mechanical load

A hypothesis is formulated and substantiated that quasi-static deformation in an amorphous metal alloy is a complex relaxation multi-stage process, which is a hierarchical sequence of interrelated structural transitions of the first order ordered in time. These nonequilibrium processes sequentially proceed at different scale space-time levels, starting from the lowest level --- a cluster of atoms of the first coordination sphere with a relaxation time taueta, then the middle level - a nanocluster of atoms of the fifth coordination sphere with a relaxation time tauφ, spatial scale of 10 nm and relaxation time tau, and tau>>tauφ>>taueta. They are accompanied by transformations of various types of potential energy of atoms (elastic, inelastic, plastic deformation, ZST) into each other. A mechanism and a model of a nonequilibrium transition from an elastic mechanical state to a state with shear transformation zones, a mechanism and a model of localized plastic deformation in an amorphous metal alloy are constructed. In the interval of non-uniqueness, in response to a locally introduced perturbation, a traveling autowave arises, which transfers the slip band from the inelastic deformation regime to the plastic deformation regime. Model parameters are estimated and important physical properties of plastic deformation are calculated. Keywords: Amorphous metal alloys, mechanical load, plastic deformation, nonequilibrium structural transition, synergetic model, kinetic equations, autowave.

Dynamics of core-excited ammonia: disentangling fragmentation pathways by complementary spectroscopic methods.

Fragmentation dynamics of core-excited isolated ammonia molecules is studied by two different and complementary experimental methods, high-resolution resonant Auger spectroscopy and electron energy-selected Auger electron-photoion coincidence spectroscopy (AEPICO). The combined use of these two techniques allows obtaining information on different dissociation patterns, in particular fragmentation before relaxation, often called ultrafast dissociation (UFD), and fragmentation after relaxation. The resonant Auger spectra contain the spectral signature of both molecular and fragment final states, and therefore can provide information on all events occurring during the core-hole lifetime, in particular fragmentation before relaxation. Coincidence measurements allow correlating Auger electrons with ionic fragments from the same molecule, and relating the ionic fragments to specific Auger final electronic states, and yield additional information on which final states are dissociative, and which ionic fragments can be produced in timescales either corresponding to the core-hole lifetime or longer. Furthermore, we show that by the combined use of two complementary experimental techniques we are able to identify more electronic states of the NH2+ fragment with respect to the single one already reported in the literature.

The impact of the chalcogen-substitution element and initial spectroscopic state on excited-state relaxation pathways in nucleobase photosensitizers: a combination of static and dynamic studies.

The substitution of oxygen with chalcogen in carbonyl group(s) of canonical nucleobases gives an impressive triplet generation, enabling their promising applications in medicine and other emerging techniques. The excited-state relaxation S2(ππ*) → S1(nπ*) → T1(ππ*) has been considered the preferred path for triplet generation in these nucleobase derivatives. Here, we demonstrate enhanced quantum efficiency of direct intersystem crossing from S2 to triplet manifold upon substitution with heavier chalcogen elements. The excited-state relaxation dynamics of sulfur/selenium substituted guanines in a vacuum is investigated using a combination of static quantum chemical calculations and on-the-fly excited-state molecular dynamics simulations. We find that in sulfur-substitution the S2 state predominantly decays to the S1 state, while upon selenium-substitution the S2 state deactivation leads to simultaneous population of the S1 and T2,3 states in the same time scale and multi-state quasi-degeneracy region S2/S1/T2,3. Interestingly, the ultrafast deactivation of the spectroscopic S3 state of both studied molecules to the S1 state occurs through a successive S3 → S2 → S1 path involving a multi-state quasi-degeneracy S3/S2/S1. The populated S1 and T2 states will cross the lowest triplet state, and the S1 → T intersystem crossing happens in a multi-state quasi-degeneracy region S1/T2,3/T1 and is accelerated by selenium-substitution. The present study reveals the influence of both the chalcogen substitution element and initial spectroscopic state on the excited-state relaxation mechanism of nucleobase photosensitizers and also highlights the important role of multi-state quasi-degeneracy in mediating the complex relaxation process. These theoretical results provide additional insights into the intrinsic photophysics of nucleobase-based photosensitizers and are helpful for designing novel photo-sensitizers for real applications.

Non-Maxwellian viscoelastic stress relaxations in soft matter.

Viscoelastic stress relaxation is a basic characteristic of soft matter systems such as colloids, gels, and biological networks. Although the Maxwell model of linear viscoelasticity provides a classical description of stress relaxation, it is often not sufficient for capturing the complex relaxation dynamics of soft matter. In this Tutorial, we introduce and discuss the physics of non-Maxwellian linear stress relaxation as observed in soft materials, the ascribed origins of this effect in different systems, and appropriate models that can be used to capture this relaxation behavior. We provide a basic toolkit that can assist the understanding and modeling of the mechanical relaxation of soft materials for diverse applications.

The First Tetranuclear Iron(II)‐Gadolinium(III) Carboxylate Complex [Fe2Gd2(piv)10(bpy)2]: Synthesis, Structure Elucidation and Magnetic Properties

AbstractThe interaction of in situ generated iron(II) complex {Fe(piv)2(bpy)} and gadolinium(III) pivalate [Gd(piv)3]n in the ratio Fe : Gd=1 : 1 leads to new tetranuclear heterometallic complex [Fe2Gd2(piv)10(bpy)2] (1) of the rare {FeII2GdIII2} type (piv is pivalate anion, bpy is 2,2′‐bipyridine). According to X‐ray analysis, a tetranuclear zig‐zag {FeGdGdFe} heterometallic core is formed from two {FeGd} fragments connected by two bridging piv‐anions. The coordination environments of two iron(II) (FeO4N2) can be described as strongly distorted octahedrons, while the environment of the gadolinium(III) (GdO7) – as capped trigonal prisms. The coordination environment of each iron(II) is supported by terminal bpy ligands. The measurements of the temperature dependence of magnetic susceptibility of 1 show avery weak antiferromagnetic exchange between high‐spin Gd3+ (SGd=7/2) and Fe2+ (SFe=2) paramagnetic centers. The alternating current magnetic susceptibility measurements did not reveal any sign of magnetization slow relaxation in complex 1.

Transition state search and geometry relaxation throughout chemical compound space with quantum machine learning.

We use energies and forces predicted within response operator based quantum machine learning (OQML) to perform geometry optimization and transition state search calculations with legacy optimizers but without the need for subsequent re-optimization with quantum chemistry methods. For randomly sampled initial coordinates of small organic query molecules, we report systematic improvement of equilibrium and transition state geometry output as training set sizes increase. Out-of-sample SN2 reactant complexes and transition state geometries have been predicted using the LBFGS and the QST2 algorithms with an root-mean-square deviation (RMSD) of 0.16 and 0.4 Å-after training on up to 200 reactant complex relaxations and transition state search trajectories from the QMrxn20 dataset, respectively. For geometry optimizations, we have also considered relaxation paths up to 5'595 constitutional isomers with sum formula C7H10O2 from the QM9-database. Using the resulting OQML models with an LBFGS optimizer reproduces the minimum geometry with an RMSD of 0.14 Å, only using ∼6000 training points obtained from normal mode sampling along the optimization paths of the training compounds without the need for active learning. For converged equilibrium and transition state geometries, subsequent vibrational normal mode frequency analysis indicates deviation from MP2 reference results by on average 14 and 26 cm-1, respectively. While the numerical cost for OQML predictions is negligible in comparison to density functional theory or MP2, the number of steps until convergence is typically larger in either case. The success rate for reaching convergence, however, improves systematically with training set size, underscoring OQML's potential for universal applicability.

A dynamic hysteresis model for customized glass transition in amorphous polymer towards multiple shape memory effects

Coexistence of multiple and discrete segments as well as their distinctive hysteresis relaxations enables amorphous shape memory polymers (SMPs) exhibiting complex disordered dynamics, which is critical for the glass transition behavior to determine the shape memory effect (SME), but remained largely unexplored. In this study, a dynamic hysteresis model is proposed to explore the working principle and collective dynamics in discrete segments of amorphous SMPs, towards a dynamic connection between complex relaxation hysteresis and glass transition behavior, which can be applied for design and realization of multiple SMEs in the amorphous SMPs. In combination of free volume theory and Adam-Gibbs domain size model, a phase transition model is formulated to identify the working principle of dynamic relaxation hysteresis in the glass transition of amorphous SMP. Furthermore, constitutive relationships among relaxation time, strain, storage modulus, loss angle and temperature have been established to describe the dynamic connection between complex relaxation hysteresis and customized glass transition, which is then utilized to achieve multiple SMEs based on the extended Maxwell model. Finally, effectiveness of the proposed models is verified using experimental results of SMPs with multiple SMEs reported in literature.

Pressure weakening unusual-caged dynamics of La80Al20 metallic glass-forming liquid

Caged dynamics is the precursor of β-relaxation and is part of the complex relaxation dynamics of metallic glasses. However, limited by the lack of suitable experimental techniques, the pressure dependence of the caged dynamics of glass-forming metallic liquids and its underlying mechanism are still an open question to date. An unusual caged dynamics manifests a sudden drop near 0.1 ps in the partial non-Gaussian parameter of Al atoms in metallic alloy La80Al20 liquid was recently found by molecular dynamics simulations. The present work investigates the caged dynamics of the La80Al20 liquid with strong atomic interactions under different pressures again by molecular dynamics simulations. It is found that the dominant polyhedra are transformed from the stable icosahedral-like polyhedra to the unstable ones that are compatible with crystal symmetry, resulting in the promotion of the rearrangement of atoms. These changes in turn cause the central Al atoms to be less hindered by the surrounding atoms, enhancing the cage-breaking motion and weakening the unusual caged dynamics. In addition, the applied pressure not only increases the diversity of vibrational frequencies but also weakens the difference in atomic vibrational amplitudes, leading to the weakening of the unusual caged dynamics. These findings provide new insights into the caged dynamics under pressure from the perspective of microstructure and vibrational properties.

Flexible Composites with Variable Conductivity and Memory of Deformation Obtained by Polymerization of Polyaniline in PVA Hydrogel

Flexible materials that provide an electric, magnetic, or optic response upon deformation or tactile pressure could be important for the development of smart monitors, intelligent textiles, or in the development of robotic skins. In this work we demonstrate the capabilities of a flexible and electrically conductive polymer material that produces an electrical response with any deformation, namely the electrical resistance of the material changes proportionally with the deformation pressure. Furthermore, the material exhibits a memory effect. When compressed beyond the elastic regime, it retains the memory of the plastic deformation by increasing its resistance. The material was obtained by in situ polymerization of semiconducting polyaniline (PANi) in a polyvinyl alcohol/glycerol (PVA/Gly) hydrogel matrix at -17 °C. Upon drying of the hydrogel, an elastomer composite is obtained, with rubber-like characteristics. When compressed/decompressed, the electrical resistance of the material exhibits an unusually long equilibration/relaxation time, proportional with the load applied. These phenomena indicate a complex relaxation and reconfiguration process of the PANi/PVA elastomer matrix, with the shape change of the material due to mechanical stress.

Correlation analysis between the complex electrical permittivity and relaxation time of tissue mimicking phantoms in 7 T MRI

Dielectric relaxation theory describes the complex permittivity of a material in an alternating field; in particular, Debye theory relates the time it takes for an applied field to achieve the maximum polarization and the electrical properties of the material. Although, Debye’s equations were proposed for electrical polarization, in this study, we investigate the correlation between the magnetic longitudinal relaxation time T1 and the complex electrical permittivity of tissue-mimicking phantoms using a 7 T magnetic resonance scanner. We created phantoms that mimicked several human tissues with specific electrical properties. The electrical properties of the phantoms were measured using bench-test equipment. T1 values were acquired from phantoms using MRI. The measured values were fitted with functions based on dielectric estimations, using relaxation times of electrical polarization, and the mixture theory for dielectrics. The results show that, T1 and the real permittivity are correlated; therefore, the correlation can be approximated with a rational function in the case of water-based phantoms. The correlation between index loss and T1 was determined using a fitting function based on the Debye equation and mixture theory equation, in which the fraction of the materials was taken into account. This phantom study and analysis provide an insight into the application relaxation times used for estimating dielectric properties. Currently, the measurement of electrical properties based on dielectric relaxation theory is based on an antenna, sometimes invasive, that irradiates an electric field into a small sample; thus, it is not possible to create a map of electrical properties for a complex structure such as the human body. This study could be further used to compute the electrical properties maps of tissues by scanning images and measuring T1 maps.

Modified Block Coordinate Descent Method for Intelligent Reflecting Surface-Aided Space-Time Line Coded Systems

The intelligent reflecting surface (IRS) technology can be combined with the space-time line code (STLC) to reduce the channel estimation overhead for adjusting the IRS phase shifts. However, the computational complexity to design the phase shift values of IRS elements can increase prohibitively with the increment of IRS elements. To reduce the design complexity for the IRS-aided STLC system, we propose a modified block coordinate descent (MBCD) algorithm that can simply design the phase shift values of the IRS. The proposed MBCD algorithm can dramatically reduce the computational complexity with no compromise of performance compared to the various existing methods, such as a semidefinite relaxation method, an alternating direction method of multipliers, an analytic constant modulus algorithm, and a complex unit-modulus constraint relaxation method.

Engineering Photoresponse in Epitaxial BiFe0.5Cr0.5O3 Thin Films through Structural Distortion

Multiferroic BiFe0.5Cr0.5O3 (BFCO) thin films are promising candidates for emerging optoelectronics and all-oxide solar absorbers. Yet, a thorough understanding of the structural evolution and associated changes in the functional properties of BFCO is lacking. Here, we explore thickness-dependent structural phase transitions in the epitaxial BFCO films and ascertain the impact of the accompanying crystallographic distortions on their photoresponse. The results show that the strain imposed by the substrate changes the crystal symmetry, inducing a transition from a tetragonal-like phase to a rhombohedral-like phase through a rather complex strain relaxation mechanism upon increasing film thickness. This change in crystallographic distortion also induces a shift of ∼150 meV in the bandgap. Moreover, wavelength-resolved photocurrent measurements reveal that the absorption onset is red-shifted for the tetragonal-like structure, implying light absorption up to wavelengths of 800 nm. First-principles calculations shed further light on the symmetry-induced changes in the electronic structure of the BFCO films. The crystallographic symmetry is shown to be a decisive factor in modifying the valence band maximum and conduction band minimum characteristics in the perovskite oxides, revealing an emerging type of Mott multiferroic in the BFCO system. This work provides a practical strategy to further engineer the optoelectronic properties of the multiferroic oxide films through thickness-induced phase transitions.

A series of tetranuclear rare-earth complexes and two-step slow magnetic relaxation in Dy4 complex

A series of new tetranuclear lanthanide metal complexes of [Ln4(μ4-O2−)(HL)2(L)2]·0.5(H2NCH2CHOHCH2NH2)·(CH3CN)·1.25(H2O) (Ln = Tb(1)), [Ln4(μ4-O2−)(HL)2(L)2]·0.5(H2NCH2CHOHCH2NH2)·0.5(CH3CN)·0.25(H2O) (Ln = Dy(2) or Ho(3)), were elaborately synthesized using a Schiff base ligand, 1,3-bis(5-bromosalicylideneamino)-2-propanol) (H3L). They were structurally and magnetically characterized. The crystallographic data reveal the tetranuclear lanthanide core of complexes 1–3 bridged by one μ4-O2− ion. Complexes 1–3 contained one unusual Ln4 boat-shaped unit, forming a novel Ln4 cluster. Detailed static and dynamic magnetic analysis of complexes 1–3 revealed single-molecule magnet (SMM) behavior with anisotropy barrier of Ueff = 20.98 K and Ueff = 43.47 K and two pre-exponential factors τ0 = 7.66 × 10−7 s and τ0 = 9.75 × 10−7 s for complex 2.