Relaxation Dynamics Research Articles

Magnetic relaxation between ferromagnetic and helix spin configurations in holmium films

Multiple noncollinear spin structures and transitions between them initiated by field and temperature have attracted attention due to the extraordinary coexistence of complicated spin phases in Ho. We explore the magnetic relaxation dynamics within thin films undergoing transitions between ferromagnetic (FM) and helix states. When measuring susceptibility in a relatively high frequency range (∼100–1500 Hz) and magnetic viscosity at lower frequency (∼0.01 Hz), we focus on 400 nm thick Ho film. Notably, sharp variations in the real and imaginary components of magnetic susceptibility are discerned during the FM – Helix transition, occurring at temperatures between 15 and 30 K. Hysteresis effects in the magnetic susceptibility components are identified during cyclic variations in the external field, indicating a relatively rapid process with a timescale of approximately 10 ms accompanying the FM – Helix transition. The slow relaxation process is also found to exhibit sensitivity to this transition. Furthermore, the field dependence of magnetic viscosity displays a marked decline at the FM – Helix transition. The research methodologies proposed for the investigation of relaxation processes in materials with multiphase spin structures are deemed universally applicable and offer insights into transitions between spin states in materials manifesting non collinear spin structures.

Collective dynamics of liquid sulphur across the polymerisation transition temperature probed by inelastic x-ray scattering

Inelastic x-ray scattering (IXS) experiments on liquid sulphur were carried out below (140 ∘C) and above (180 ∘C) the polymerisation temperature T λ of about 159 ∘C to investigate changes in the collective dynamics of this unique liquid, that exhibits a liquid–liquid transition. As reported earlier, broad longitudinal acoustic excitation signals were observed at both temperatures, and only the width of the quasielastic peaks slightly decreased when the temperature crossed the transition temperature. A model analysis was performed using a generalised Langevin formalism with a memory function having one thermal and two viscoelastic decay channels with the help of simple sparse modelling, and large positive deviations from the hydrodynamic sound velocity by 51%–54% were observed. The fast viscoelastic relaxation time τ µ is close to the correlation times of intermolecular stretching and bending motions of local sulphur connections in both ring and chain structures, and is similar to those of other molecular liquids. The small contrasts in the IXS spectra across the λ transition result in large changes in only the slow viscoelastic decay time τ α of the memory function. The τ α value at 140 ∘C matches the mixed internal/external torsional modes of S8 molecules well, whereas that at 180 ∘C has no corresponding molecular motion mode. The kinematic viscosity values at the Q→0 limit are much smaller than the minimum values of macroscopic shear viscosity, indicating that large changes in relaxation dynamics are expected with Q in the GHz and MHz excitation regimes.

Polysquaramides.

Thermoplastics, while advantageous for their processability and recyclability, often compromise thermochemical stability and mechanical strength compared to thermosets. Addressing this limitation, we introduce an innovative approach employing reversibly cross-linked polymers, utilizing squaramide moieties to reconcile recyclability and robustness. Herein, we detail the synthesis of supramolecularly cross-linked polysquaramides through the condensation polymerization of diethyl squarate with primary and secondary diamines. This methodology embeds hydrogen-bonding squaramide motifs into the polymer chains, yielding materials with significantly enhanced storage moduli, reaching up to 1.2 GPa. Material characterization via dynamic mechanical analysis, creep-recovery, and stress relaxation experiments delineate a distinctive rubbery plateau across a broad temperature range, excellent creep resistance, and multimodal viscoelastic flow, respectively, attributable to the dynamic nature of the supramolecular cross-links. Additionally, the study showcases the modulation of glass transition temperature (Tg) by altering the monomer composition and stoichiometry, demonstrating the tunability of polymer viscoelastic properties through precise control over hydrogen bonding interactions. Overall, the incorporation of squaramide motifs not only provides the structural integrity and mechanical performance of these thermoplastics but also leads to engineering materials with tailored viscoelastic characteristics.

Slow vibrational relaxation drives ultrafast formation of photoexcited polaron pair states in glycolated conjugated polymers

Glycol sidechains are often used to enhance the performance of organic photoconversion and electrochemical devices. Herein, we study their effects on electronic states and electronic properties. We find that polymer glycolation not only induces more disordered packing, but also results in a higher reorganisation energy due to more localised π-electron density. Transient absorption spectroscopy and femtosecond stimulated Raman spectroscopy are utilised to monitor the structural relaxation dynamics coupled to the excited state formation upon photoexcitation. Singlet excitons are initially formed, followed by polaron pair formation. The associated structural relaxation slows down in glycolated polymers (5 ps vs. 1.25 ps for alkylated), consistent with larger reorganisation energy. This slower vibrational relaxation is found to drive ultrafast formation of the polaron pair state (5 ps vs. 10 ps for alkylated). These results provide key experimental evidence demonstrating the impact of molecular structure on electronic state formation driven by strong vibrational coupling.

A modified dynamic relaxation form-finding method for symmetrical tensegrity structures with group theory and fuzzy clustering

For tensegrity structures, there are many groups of cables and bars with symmetrical structures or similar internal forces. In this paper, an application of a fuzzy clustering algorithm in the context of form-finding processes for symmetric tensegrity structures is proposed. This algorithm aims to automate grouping, optimize form-finding strategies, and expedite convergence. Point sets are generated through the segmentation of structural components, and Hausdorff distance is used to extract spatial features. Following this, fuzzy clustering automatically groups components with geometric symmetry. The resultant clustering matrix facilitates the refinement of form-finding processes, thus reducing the computational load associated with solving the equilibrium matrix for internal forces within tensegrity structures. By clustering components with analogous internal forces, computational efficiency is enhanced. Additionally, this methodology refines numerical form-finding outcomes based on symmetrical attributes, improving form-finding precision.

Relaxation dynamics in the alternating XY chain following a quantum quench

We investigate the relaxation dynamics of the fermion two-point correlation function Cmn(t)=〈ψ(t)∣cm†cn∣ψ(t)〉 in the XY chain with alternating nearest-neighbor hopping interaction after a quench. We find that the deviation δ C mn (t) = C mn (t) − C mn (∞) decays with time following the power law behavior t −μ , where the exponent μ depends on whether the quench is to the commensurate phase (μ = 1) or incommensurate phase ( μ=12 ). This decay of δ C mn (t) arises from the transient behavior of the double-excited quasiparticle occupations and the transitions between different excitation spectra. Furthermore, we find that the steady value C mn (∞) only involves the average fermion occupation numbers (i.e. the average excited single particle) over the time-evolved state, which are different from the ground state expectation values. We also observe nonanalytic singularities in the steady value C mn (∞) for the quench to the critical points of the quantum phase transitions (QPTs), suggesting its potential use as a signature of QPTs.

Relaxation dynamics of higher excited states of perylene-substituted perylene bisimide derivatives.

Stepwise two-photon absorption processes have received considerable attention, especially in photocatalysis, due to their relatively lower power threshold, characteristic spatial selectivity, amplification of chemical reactions, and so on. Meanwhile, studies on the relaxation dynamics of higher excited states in condensed systems have been limited for several molecular systems due to the short-lived nature of these states. In this study, we synthesized perylene-substituted perylene bisimide (PBI) and its derivate as model compounds and investigated their excited-state dynamics, including higher excited states, using pump-repump-probe spectroscopy. We revealed that these molecules form charge-transfer (CT) states instantaneously after the excitation, regardless of whether it is the perylene moiety or the PBI moiety that is excited. The lifetime of the CT state was shorter when the distance between the donor (perylene) and the acceptor (PBI) was shorter. Moreover, we also revealed that a higher-lying CT state generated by the stepwise excitation of the CT state using a 740-nm pulse induced Stark effect to the neighboring perylene moiety. The Stark effect not only gives more detailed information about the CT state, but also presents the possibility of new photofunctions, such as instantaneous modulation of the electronic state to achieve optimal electronic properties. These insights contribute to understanding advanced photochemical reactions and would be important for exploring photocatalytic reactions involving higher excited states.

AI-NERD: Elucidation of relaxation dynamics beyond equilibrium through AI-informed X-ray photon correlation spectroscopy

Understanding and interpreting dynamics of functional materials in situ is a grand challenge in physics and materials science due to the difficulty of experimentally probing materials at varied length and time scales. X-ray photon correlation spectroscopy (XPCS) is uniquely well-suited for characterizing materials dynamics over wide-ranging time scales. However, spatial and temporal heterogeneity in material behavior can make interpretation of experimental XPCS data difficult. In this work, we have developed an unsupervised deep learning (DL) framework for automated classification of relaxation dynamics from experimental data without requiring any prior physical knowledge of the system. We demonstrate how this method can be used to accelerate exploration of large datasets to identify samples of interest, and we apply this approach to directly correlate microscopic dynamics with macroscopic properties of a model system. Importantly, this DL framework is material and process agnostic, marking a concrete step towards autonomous materials discovery.

Measurement of the depth-dependent local dynamics in thin polymer films through rejuvenation of ultrastable glasses

The depth dependence of structural relaxation dynamics is a key part of understanding thin glassy films. Despite this importance and decades of research, a method to provide this information has proved elusive. We measure the isothermal rejuvenation of stable glass films of poly(styrene), and demonstrate that the propagation of the front responsible for the transformation to a supercooled-liquid state serves as a highly localized probe of the local dynamics of the supercooled liquid. We use this connection to probe the depth-dependent relaxation rate with nanometric precision for a series of polystyrene films over a range of temperatures near the bulk glass transition temperature. The analysis shows the spatial extent of enhanced surface mobility and reveals the existence of an unexpected large dynamical length scale in the system. The results are compared with the cooperative-string model for glassy dynamics. The data reveals that the film-thickness dependence of whole film properties arises mainly from the volume fraction of the near-surface region. While the dynamics farthest from the free surface shows the expected bulk-like temperature dependence, the dynamics in the near-surface region shows very little dependence on temperature. This technique can be used in a broad range of thin film materials to gain previously unattainable information about localized structural relaxation.

60 Years of Betaine 30─From Solvatochromic Discovery to Future Frontiers.

Betaine-30 (B30) was reported by Karl Dimroth and Christian Reichardt et al. in 1963 as a solvatochromic probe that can be easily synthesized, shows good solubility, and remains stable in various organic solvents and solutions. Its strongly negatively solvatochromic behavior arises from differential solvation between its electronic ground and excited states, making it a valuable tool for assessing solvent polarity using the ET(30) polarity scale, also devised by Dimroth and Reichardt. In addition, advancements in femtosecond laser spectroscopy in the 1990s greatly improved the understanding of B30's relaxation dynamics following photoexcitation. In solvents capable of hydrogen bonding, such as alcohols, intermolecular hydrogen-bond rearrangement contributes to the multiple relaxation components observed. Since the 1990s, the applications of B30 have expanded beyond simple organic solvents to include complex solvent mixtures, such as electrolyte solutions for battery technologies and eutectic solvent mixtures. Given the growing importance of these complex solvent mixtures, B30 is becoming an increasingly valuable tool for studying previously unexplored solvation properties.

Spin-lattice relaxation with non-linear couplings: Comparison between Fermi's golden rule and extended dissipaton equation of motion.

Fermi's golden rule (FGR) offers an empirical framework for understanding the dynamics of spin-lattice relaxation in magnetic molecules, encompassing mechanisms like direct (one-phonon) and Raman (two-phonon) processes. These principles effectively model experimental longitudinal relaxation rates, denoted as T1-1. However, under scenarios of increased coupling strength and nonlinear spin-lattice interactions, FGR's applicability may diminish. This paper numerically evaluates the exact spin-lattice relaxation rate kernels, employing the extended dissipaton equation of motion formalism. Our calculations reveal that when quadratic spin-lattice coupling is considered, the rate kernels exhibit a free induction decay-like feature, and the damping rates depend on the interaction strength. We observe that the temperature dependence predicted by FGR significantly deviates from the exact results since FGR ignores the higher order effects and the non-Markovian nature of spin-lattice relaxation. Our methods can be easily extended to study other systems with nonlinear spin-lattice interactions and provide valuable insights into the temperature dependence of T1 in molecular qubits when the coupling is strong.

Dynamic Compressive Stress Relaxation Model of Tomato Fruit Based on Long Short-Term Memory Model.

Tomatoes are prone to mechanical damage due to improper gripping forces during automated harvest and postharvest processes. To reduce this damage, a dynamic viscoelastic model based on long short-term memory (LSTM) is proposed to fit the dynamic compression stress relaxation characteristics of the individual fruit. Furthermore, the classical stress relaxation models involved, the triple-element Maxwell and Caputo fractional derivative models, are compared with the LSTM model to validate its performance. Meanwhile, the LSTM and classical stress relaxation models are used to predict the stress relaxation characteristics of tomato fruit with different fruit sizes and compression positions. The results for the whole test dataset show that the LSTM model achieves a RMSE of 2.829×10-5 Mpa and a MAPE of 0.228%. It significantly outperforms the Caputo fractional derivative model by demonstrating a substantial enhancement with a 37% decrease in RMSE and a 36% reduction in MAPE. Further analysis of individual tomato fruit reveals the LSTM model's performance, with the minimum RMSE recorded at the septum position being 3.438×10-5 Mpa, 31% higher than the maximum RMSE at the locule position. Similarly, the lowest MAPE at the septum stands at 0.375%, outperforming the highest MAPE at the locule position by a significant margin of 90%. Moreover, the LSTM model consistently reports the smallest discrepancies between the predicted and observed values compared to classical stress relaxation models. This accuracy suggests that the LSTM model could effectively supplant classical stress relaxation models for predicting stress relaxation changes in individual tomato fruit.

Understanding the Vibrational Structure and Ultrafast Dynamics of the Metal Carbonyl Precatalyst [Mn(ppy)(CO)4

The solution phase structure, vibrational spectroscopy, and ultrafast relaxation dynamics of the precatalyst species [Mn(ppy)(CO)4] (1) in solution have been investigated using ultrafast two-dimensional infrared (2D-IR) spectroscopy. By comparing 2D-IR data with the results of anharmonic density functional theory (DFT) calculations, we establish an excellent agreement between measured and predicted inter-mode couplings of the carbonyl stretching vibrational modes of 1 that relates to the atomic displacements of axial and equatorial ligands in the modes and the nature of the molecular orbitals involved in M-CO bonding. Measurements of IR pump-probe spectra and 2D-IR spectra as a function of waiting time reveal the presence of ultrafast (few ps) intramolecular vibrational energy redistribution between carbonyl stretching modes prior to vibrational relaxation. The vibrational relaxation times of the CO-stretching modes of 1 are found to be relatively solvent-insensitive, suggestive of limited solvent-solute interactions in the ground electronic state. Overall, these data provide a detailed picture of the complex potential energy surface, bonding and vibrational dynamics of 1, establishing a fundamental basis for the next steps in understanding and modulating precatalyst behavior.

Non-adiabatic electronic relaxation of tetracene from its brightest singlet excited state.

The ultrafast relaxation dynamics of tetracene following UV excitation to the bright singlet state S6 has been studied with time-resolved photoelectron spectroscopy. With the help of high-level abinitio multireference perturbation theory calculations, we assign photoelectron signals to intermediate dark electronic states S3, S4, and S5 as well as to a low-lying electronic state S2. The energetic structure of these dark states has not been determined experimentally previously. The time-dependent photoelectron yields assigned to the states S6, S5, and S4 have been analyzed and reveal the depopulation of S6 within 60fs, while S5 and S4 are populated with delays of about 50 and 80fs. The dynamics of the lower-lying states S3 and S2 seem to agree with a delayed population coinciding with the depopulation of the higher-lying states S4-S6 but could not be elucidated in full detail due to the low signal levels of the corresponding two-photon ionization probe processes.

Spin Coherence and Relaxation Dynamics of Localized Electrons and Holes in FAPbI3 Films

Spin Coherence and Relaxation Dynamics of Localized Electrons and Holes in FAPbI₃ Films

Epoxy/clay nanodielectrics: from relaxation dynamics to capacitive energy storage

Epoxy/clay nanodielectrics: from relaxation dynamics to capacitive energy storage

Optimization and validation of multi-echo, multi-contrast SAGE acquisition in fMRI.

The purpose of this study was to optimize and validate a multi-contrast, multi-echo fMRI method using a combined spin- and gradient-echo (SAGE) acquisition. It was hypothesized that SAGE-based blood oxygen level-dependent (BOLD) functional MRI (fMRI) will improve sensitivity and spatial specificity while reducing signal dropout. SAGE-fMRI data were acquired with five echoes (2 gradient-echoes, 2 asymmetric spin-echoes, and 1 spin-echo) across 12 protocols with varying acceleration factors, and temporal SNR (tSNR) was assessed. The optimized protocol was then implemented in working memory and vision tasks in 15 healthy subjects. Task-based analysis was performed using individual echoes, quantitative dynamic relaxation times T2 * and T2, and echo time-dependent weighted combinations of dynamic signals. These methods were compared to determine the optimal analysis method for SAGE-fMRI. Implementation of a multiband factor of 2 and sensitivity encoding (SENSE) factor of 2.5 yielded adequate spatiotemporal resolution while minimizing artifacts and loss in tSNR. Higher BOLD contrast-to-noise ratio (CNR) and tSNR were observed for SAGE-fMRI relative to single-echo fMRI, especially in regions with large susceptibility effects and for T2-dominant analyses. Using a working memory task, the extent of activation was highest with T2 *-weighting, while smaller clusters were observed with quantitative T2 * and T2. SAGE-fMRI couples the high BOLD sensitivity from multi-gradient-echo acquisitions with improved spatial localization from spin-echo acquisitions, providing two contrasts for analysis. SAGE-fMRI provides substantial advantages, including improving CNR and tSNR for more accurate analysis.

Modulation of Triton X-100 Aqueous Micelle Interface by Ionic Liquid: A Molecular Level Interaction Studied by Time-resolved Fluorescence Spectroscopy

Background: Self-assembly structure is an important area of research for understanding biological systems, owing to its resemblance to the membrane structure of the phospholipid bilayer. In a self-assembly medium, chemical reactions and chemical or physical processes are dramatically different than the bulk phase. Understanding this process in synthesizing self-assembly structures may allow us to explore various biological processes occurring in cell membranes. Objective: The study aimed to understand water dynamics in the TX-100 micellar interface via steady state and a time-resolved fluorescence spectroscopy study. The objective was also to determine the two different ionic liquids (ILs), namely 1-butyl-3-methyl imidazolium tetrafluoroborate ([bmim][BF4]) and 1-decyl-3-methyl imidazolium tetrafluoroborate ([dmim][BF4]), inducing surfactant aggregation changes at the molecular level. Also, the focus was on determining the hydration and its dynamics at the palisade layer of TX-100 micelle in the presence of two different ionic liquids. Methods: Steady state and time-resolved fluorescence spectroscopy have been used to study TX-100 micellar systems. Employing time-resolved spectroscopy, two chemical dynamic processes, solvation dynamics and rotational relaxation dynamics, have been studied to investigate structural changes in TX100 by adding ILs. Solvation dynamics was studied by measuring the time-dependent Stokes shift of the fluorescent probe. From the Stokes shift, time-resolved emission spectra were constructed to quantify the solvation dynamics. Also, using the polarization properties of light, time-resolved anisotropy was constructed to explore the rotation relaxation of the probe molecule. Results: The absorption and emission spectra of C-153 in TX-100 were red-shifted in the presence of both the ILs. Also, the C-153 experienced faster solvation dynamics and rotational relaxation with the addition of both ILs. In our previous study, we observed a significantly increased rate of solvation dynamics with the addition of [bmim][BF4] (J. Phys. Chem. B, 115, 6957-6963) [38]. However, with the addition of the same amount of [dmim][BF4], the IL rate of solvation enhancement was more pronounced than with [bmim][BF4]. The faster solvation and rotational relaxation have been found to be associated with the penetration of more free water at the TX100 micellar stern layer, leading to increased fluidity of the micellar interface. Conclusion: Upon incorporating ILs in TX100 micelle, substantially faster solvation dynamics of water as well as rotational relaxation dynamics of C-153 have been observed. By decreasing surfactant aggregations, [bmim][BF4] ILs facilitated more water molecules approaching the TX-100 micellar phase. On the other hand, [dmim][BF4] ILs comprising mixed micelles induced even more free water molecules at the palisade layer, yielding faster solvation dynamics in comparison to pure TX-100 micelle or TX100 micelle + [bmim][BF4] ILs systems. Time-resolved anisotropy study has also supported the finding and strengthened the solvation dynamics observation.

Unraveling the complexity of Fe-based bulk metallic glasses: Insights into dynamic mechanical relaxation in atomic-scale

This research conducts a thorough investigation into the structural and mechanical evolution of Fe74B20Nb2Hf2Si2 bulk metallic glass (BMG) subjected to thermal aging. Utilizing X-ray diffraction (XRD) and selected area electron diffraction (SAED), the study verifies the amorphous structure of the as-cast BMG, highlighting evidence of short-range ordering (SRO). Thermal aging conducted between 342 and 570 K induces substantial changes, notably the formation of Fe23B6 and α-Fe phases and reduced defect concentrations. During dynamic mechanical analysis, a significant shift was observed, which is characterized by a decrease in the intensity of β-relaxation and an increase in β-activation energy from 333.3±2.1 kJ/mol (for the sample aged at 342 K) to 384.6±5.6 kJ/mol (for the sample aged at 570 K). Nanoindentation evaluations reveal an increase in hardness from 11.85±0.22 GPa (for the as-cast BMG) to 14.65±0.41 GPa (for the sample aged at 570 K), accompanied by an increase in Young’s modulus from 211.61±3.00–244.24±2.00 GPa. These changes imply tighter atomic packing and diminished free volume due to aging, suggesting an advanced stage of structural relaxation. Additionally, the material demonstrates a decrease in plastic strain from 0.0052 in its as-cast state to 0.0026 at 342 K, progressing to brittle behavior with further aging. This study shows the pivotal role of precise aging temperature control in optimizing BMGs for diverse applications, illustrating the intricate interplay between thermodynamics and kinetics in material science.

Modulation of mechanical properties of low molecular weight supramolecular hydrogels of calcium cholate by drugs of varying hydrophobicity: Effect on drug release, antioxidant, and antibacterial properties

Bile salt based low-molecular-weight supramolecular hydrogels (LMWSH) serve as an appealing framework for drug delivery applications, owing to their natural origin, biocompatibility, and the peculiar distribution of hydrophobic and hydrophilic domains. In this work, LMWSH based on an ionotropic gel of sodium cholate assisted by Ca2+ ions (CaC) was developed as a drug delivery system for both hydrophilic and hydrophobic drugs. Diosgenin, Quercetin, Rutin, and Amygdalin were chosen as model drugs, having varying hydrophobicity. The mechanical strength of the CaC hydrogel is enhanced by increasing the hydrophobicity of the loaded drug. The close-knit mesh design of CaC hydrogels loaded with hydrophobic drugs resulted in controlled drug release compared to the hydrophilic drugs. Drug-loaded CaC hydrogels exhibited good swelling and thixotropy, making them suitable for injectable formulations. In kinetic drug release, both relaxation and diffusion mechanisms play a pivotal role. The antioxidant and antibacterial activity of the loaded drugs increased synergistically in the hydrogels. Thus, due to these properties, the hydrogels can be safely used as topical gels against wound healing. This study shows that bile salts exhibit potential to enhance the delivery of both hydrophobic and hydrophilic drugs, making them promising candidates for biomedical applications.