Waiting Time Dependence Research Articles

Waiting time dependence of aging

Aging phenomena have been observed in many non-equilibrium systems such as polymers and glasses, where physical properties depend on the waiting time between the starting time of observation and the time when the temperature is changed. The aging is classified into two types on the basis of the waiting time dependence of an instantaneous relaxation time: When the relaxation time is always an increasing function of the waiting time, the aging is called Type I and when it depends on the protocol of the temperature change, the aging is called Type II. Aging of a random walk in three dimensions is investigated when the free energy landscape controlling the jump rate responds to temperature change with a delay. It is shown that the intermediate scattering function of the random walk model exhibits Type II aging. It is also shown that the relaxation time of the free energy landscape can be deduced from the waiting time dependence of the instantaneous relaxation time.

Two-dimensional spectroscopy of two-dimensional materials: A Mahan-Nozières-De Dominicis model of electron-exciton scattering

In this paper, we provide a systematically convergable and efficient numerical approach to simulate multitime correlation functions in the Mahan-Nozi\`eres-De Dominicis model, which crudely mimics the spectral properties of doped two-dimensional (2D) semiconductors such as monolayer transition metal dichalcogenides. We apply this approach to study the coherent 2D electronic spectra of the model. We show that several experimentally observed phenomena, such as peak asymmetry and coherent oscillations in the waiting-time dependence of the trion-exciton cross peaks of the 2D rephasing spectrum, emerge naturally in our approach. Additional features are also present which find no correspondence with experimentally expected behavior. We trace these features to the infinite hole mass property of the model. We use this understanding to construct an efficient approach which filters out configurations associated with the lack of exciton recoil, enabling the connection to previous work and providing a route to the construction of realistic 2D spectra over a broad doping range in 2D semiconductors.

How Intramolecular Vibrational Energy Transport Changes with Rigidity and Polarity of the Environment?

Vibrational energy transport through oligomeric polyethylene glycol (PEG) chains can occur ballistically via optical vibrational chain bands, showing fast and constant transport speed and high efficiency of the transport, thus offering means to transfer significant quanta of energy, exceeding 1000 cm–1, to large distances exceeding 60 A. We report how the intramolecular energy transport time, through-chain transport speed, and end-group cooling rate depend on the rigidity and polarity of the environment. The experiments were performed with end-group labeled PEG oligomers using two-dimensional infrared (2DIR) spectroscopy. The ballistic energy transport was initiated at one end of the chain by exciting an azido moiety at ca. 2100 cm–1 and recorded at another end of the chain by probing the carbonyl stretching mode of succinimide ester. We found that the rigidity of the environment, polystyrene (PS) matrix vs. a solution of similar polarity, did not change the energy transport times much, nor the through-chain transport speed. These results suggest that in mildly polar media, dynamic fluctuations, occurring in solution but largely frozen in a solid matrix, are not the dominant cause of the dephasing of the chain states, despite the presence of fast relaxation components in the solution. The similarity of the transport times in different media suggests that the secondary chain structure does not affect much the transport in PEG chains. The solvent polarity affected the intramolecular transport significantly: the transport efficiency in polar DMSO is ca. 1.6 fold smaller than that in nonpolar CCl4 or PS. The cooling time of the succinimide ester end group is reduced in more polar solvents affecting the waiting time dependence shape and thus the energy arrival time to the reporter. The analysis of different ways of extracting the energy arrival time from the data is presented. The observed dependences of the through-chain transport time on the solvent polarity suggests the presence of multiple wavepackets propagating in the PEG chain with different group velocities.

γ-Fe2WO6 – A magnetodielectric with disordered magnetic and electronic ground states

The magnetic, thermodynamic and dielectric properties of the γ-Fe2WO6 system is reported. Crystallizing in the centrosymmetric Pbcn space group, this particular polymorph exhibits a number of different magnetic transitions, all of which are seen to exhibit a finite magneto-dielectric coupling. At the lowest measured temperatures, the magnetic ground state appears to be glass-like, as evidenced by the waiting time dependence of the magnetic relaxation. Also reflected in the frequency dependent dielectric measurements, these signatures possibly arise as a consequence of the oxygen non-stoichiometry, which promotes a disordered magnetic and electronic ground state.

Couplings between hierarchical conformational dynamics from multi-time correlation functions and two-dimensional lifetime spectra: Application to adenylate kinase.

An analytical method based on a three-time correlation function and the corresponding two-dimensional (2D) lifetime spectrum is developed to elucidate the time-dependent couplings between the multi-timescale (i.e., hierarchical) conformational dynamics in heterogeneous systems such as proteins. In analogy with 2D NMR, IR, electronic, and fluorescence spectroscopies, the waiting-time dependence of the off-diagonal peaks in the 2D lifetime spectra can provide a quantitative description of the dynamical correlations between the conformational motions with different lifetimes. The present method is applied to intrinsic conformational changes of substrate-free adenylate kinase (AKE) using long-time coarse-grained molecular dynamics simulations. It is found that the hierarchical conformational dynamics arise from the intra-domain structural transitions among conformational substates of AKE by analyzing the one-time correlation functions and one-dimensional lifetime spectra for the donor-acceptor distances corresponding to single-molecule Förster resonance energy transfer experiments with the use of the principal component analysis. In addition, the complicated waiting-time dependence of the off-diagonal peaks in the 2D lifetime spectra for the donor-acceptor distances is attributed to the fact that the time evolution of the couplings between the conformational dynamics depends upon both the spatial and temporal characters of the system. The present method is expected to shed light on the biological relationship among the structure, dynamics, and function.

Probing chirality fluctuations in molecules by nonlinear optical spectroscopy.

Symmetry breaking caused by geometric fluctuations can enable processes that are otherwise forbidden. An example is a perylene bisimide dyad whose dipole moments are perpendicular to each other. Förster-type energy transfer is thus forbidden at the equilibrium geometry since the dipolar coupling vanishes. Yet, fluctuations of the geometric arrangement have been shown to induce finite energy transfer that depends on the dipole variance, rather than the mean. We demonstrate an analogous effect associated with chirality symmetry breaking. In its equilibrium geometry, this dimer is non-chiral. The linear chiral response which depends on the average geometry thus vanishes. However, we show that certain 2D chiral optical signals are finite due to geometric fluctuations. Furthermore, the correlation time of these fluctuations can be experimentally revealed by the waiting time dependence of the 2D signal.

Experimental study on transverse relaxation rate of protons in aqueous suspensions of magnetite nanocrystal clusters with a SiO2 shell

The transverse relaxation rate (1/T2) of aqueous suspensions of magnetite nanocrystal clusters with a SiO2 shell of different thicknesses has been studied experimentally. With the increase of the shell thickness, 1/T2 decreases slightly due to the aggregation of clusters during coating process. In T2 measurement, the waiting time dependence decreases when the shell gets thicker, because of the decreased magnetic attractive energy, particle number concentration and diffusion coefficient of magnetite nanocrystal clusters with a thicker SiO2 shell. These experimental results, supporting the relaxation theory and computer simulations, may promote future development of magnetic contrast agents.

Memory Effects and Relaxation Dynamics of ${\rm MnCo}_{2}{\rm O}_{4}$ Nanocrystallites

We present a detailed analysis of the time decay of magnetization (M) and ac-magnetic susceptibility (χac)of hexagonal-shaped MnCo2O4 nanocrystals of average size 28 nm. The temperature (T) and magnetic field (H) dependence of the magnetization measurements reveal that even in the ferromagnetic state these nanocrystals do not exhibit conventional long-range ordering. The Curie temperature TC=176.4 K and the Hopkinson peak TH=146 K are found to be lower than those of the bulk values 184 and 175 K, respectively. Such a major decrease in TC and TH accounted for by the effect of finite-size scaling that has been thought to change the critical ordering temperatures. The dynamical properties studied by χac (T ) measurements suggest the existence of a spin-glass phase for T ≤ TF(=165 K) associated with the magnetic frustration of spins in the nanocrystals. The presence of glassy magnetic state is supported by the frequency (f) dependent studies of χac(T) and H2/3 dependence of TF in the intermediate-field region (50 Oe ≤ H ≤ 1000 Oe). Various measurement protocols including temperature quenching, step-field and wait-time dependence have been used to investigate the relaxation dynamics both in MZFC and in MFC for T ≤ TF, which show prominent memory and aging effects and supports the spin-glass state that established below TF. The magnetic viscosity (S) and microscopic spin-flip time (τ) were deduced from the time (t) dependence of MZFC using the expression M(t,T)=M(0,T)+S ln(1+t/t0) in which the magnitude of M(t) strongly depends on the wait-time spend at temperatures below TF.

Picosecond Rotational Interconversion Adjacent to a C═O Bond Studied by Two-Dimensional Infrared Spectroscopy

Molecular conformations around the C═O group of carbonyl compounds like ketones and aldehydes play an important role in determining their reaction properties in solutions, including reaction rate, mechanism, steric structure, and chirality of products. Investigating different rotational conformers and their rapid exchange at room temperature will provide information on the rotational barrier and insights into how different rotamers may contribute to fundamental reactions in chemistry. We applied two-dimensional infrared (2D IR) spectroscopy and polarization-dependent IR transient grating technique to the study of 4,4-dimethyl-2-pentanone in CCl(4). Spectroscopic evidence showed that the internal rotation around the single carbon-carbon bond adjacent to the C═O group takes place on a picosecond time scale. DFT calculations suggested the presence of three different rotational conformations, one eclipsed and two staggered forms. Spectral simulation utilized the stochastic Liouville equation with a three-state jump model and incorporated the polarization factors that take into account the different direction of transition dipole moment in the three rotamers. The effects of the intramolecular vibrational energy redistribution process on the waiting time dependence of the 2D absorptive spectra were also included. Through comprehensive simulation of the observed spectral features, the exchange time constants between the three rotamers were determined: 5.4 ps from the eclipsed to staggered forms and 1.7 ps for the reverse direction.

On-the-fly coarse-graining methodology for the simulation of chain formation of superparamagnetic colloids in strong magnetic fields

The aim of this work is the description of the chain formation phenomena observed in colloidal suspensions of superparamagnetic nanoparticles under high magnetic fields. We introduce a methodology based on an on-the-fly coarse-grain (CG) model. Within this approach, the coarse-grain objects of the simulation and their dynamic behavior are not fixed a priori at the beginning of the simulation but rather redefined on the fly. The motion of the CG objects (single particles or aggregates) is described by an anisotropic diffusion model and the magnetic dipole-dipole interaction is replaced by an effective short-range interaction between CG objects. The methodology correctly reproduces previous results from detailed Langevin dynamics simulations of dispersions of superparamagnetic colloids under strong fields while requiring an amount of CPU time orders of magnitude smaller. This substantial improvement in the computational requirements allows the simulation of problems in which the relevant phenomena extend to time scales inaccessible with previous simulation techniques. A relevant example is the waiting time dependence of the relaxation time T(2) of water protons observed in magnetic resonance experiments containing dispersions of superparamagnetic colloids, which is correctly predicted by our simulations. Future applications may include other popular real-world applications of superparamagnetic colloids such as the magnetophoretic separation processes.

Waiting time dependence of T2 of protons in water suspensions of iron-oxide nanoparticles: Measurements and simulations

The transverse relaxation time T2 of protons in water suspensions of iron-oxide particles increases with the waiting time tw after the sample is inserted in the gap of the spectrometer magnet. Such a T2 increase becomes significant if the particles are aggregated into large clusters, for which field-induced formation of cluster-chains will occur and T2 should increase with increasing the length of chains. T2 increases with tw even for small particles, for which no chain formation may be induced, and for large clusters when tw is too small to form long enough chains. The T2 increase is accompanied by a significant echo-time dependence. All this is experimentally and theoretically studied.

Non-equilibrium effects in the magnetic behavior of Co 3O 4 nanoparticles

We report detailed studies of the non-equilibrium magnetic behavior of antiferromagnetic Co 3O 4 nanoparticles. The temperature and field dependence of magnetization, wait time dependence of magnetic relaxation (aging), memory effects, and temperature dependence of specific heat have been investigated to understand the magnetic behavior of these particles. We find that the system shows some features that are characteristic of nanoparticle magnetism such as bifurcation of field-cooled (FC) and zero-field-cooled (ZFC) susceptibilities and a slow relaxation of magnetization. However, strangely, the temperature at which the ZFC magnetization peaks coincides with the bifurcation temperature and does not shift on application of magnetic fields up to 1 kOe, unlike most other nanoparticle systems. Aging effects in these particles are negligible in both FC and ZFC protocols, and memory effects are present only in the FC protocol. We show that Co 3O 4 nanoparticles constitute a unique antiferromagnetic system which enters into a blocked state above the average Néel temperature.

Dispersive kinetics in discotic liquid crystals

The dynamics of the discotic liquid-crystalline system, hexakis (n-hexyloxy) triphenylene (HAT6), is considered in the frame of the phenomenological model for rate processes proposed by Berlin. It describes the evolution of the system in the presence of the long-time scale correlations in the system, and we compare this with experimental quasielastic neutron scattering of the molecular assembly of HAT6 in the columnar phase. We interpret the parameters of this model in terms of nonextensive thermodynamics in which rare events in the local fast dynamics of some parts of the system control the slower dynamics of the larger molecular entity and lead to a fractional diffusion equation. The importance of these rare local events to the overall dynamics of the system is linked to the entropic index, this being obtained from the data within the model approach. Analysis of the waiting-time dependence from momentum transfer reveals a Lévy distribution of jump lengths, which allows us to construct the van Hove correlation function for discotic liquid-crystalline system.

Static friction as a function of waiting time probed by the dynamics of driven vortices inLa2 − xSrxCuO4 thin films

We systematically investigated the waiting-time dependence of the maximum static friction force,Fs(tw), using the dynamics of driven vortices in a high-Tc superconductor asa model system. Fs(tw) was measured in La2 − xSrxCuO4 thin films with different structures, sample sizes and pinning force. We found thatFs(tw) by thermal fluctuation is strongly affected by the pinning strength, the vortex bundlesize and the system size. Based on these results, we found crucial conditions todetermine the validity of the Amontons–Coulomb’s law, and proposed a criterion.

From equilibrium to steady-state dynamics after switch-on of shear

A relation between equilibrium, steady state, and waiting-time-dependent dynamical two-time correlation functions in dense glass-forming liquids subject to homogeneous steady shear flow is discussed. The systems under study show pronounced shear thinning, i.e., a significant speedup in their steady-state slow relaxation as compared to equilibrium. An approximate relation that recovers the exact limit for small waiting times is derived following the integration through transients (ITT) approach for the nonequilibrium Smoluchowski dynamics, and is exemplified within a schematic model in the framework of the mode-coupling theory of the glass transition (MCT). Computer simulation results for the tagged-particle density correlation functions corresponding to wave vectors in the shear-gradient directions from both event-driven stochastic dynamics of a two-dimensional hard-disk system and from previously published Newtonian-dynamics simulations of a three-dimensional soft-sphere mixture are analyzed and compared with the predictions of the ITT-based approximation. Good qualitative and semiquantitative agreement is found. Furthermore, for short waiting times, the theoretical description of the waiting time dependence shows excellent quantitative agreement to the simulations. This confirms the accuracy of the central approximation used earlier to derive fluctuation dissipation ratios [M. Krüger and M. Fuchs, Phys. Rev. Lett. 102, 135701 (2009)]. For intermediate waiting times, the correlation functions decay faster at long times than the stationary ones. This behavior is predicted by our theory and observed in simulations.

Water-Induced Relaxation of a Degenerate Vibration of Guanidinium Using 2D IR Echo Spectroscopy

The nearly degenerate asymmetric stretch vibrations near 1600 cm(-1) of the guanidinium cation in D-glycerol/D(2)O mixtures having different viscosity were studied by 2D IR photon echo spectroscopy. The polarization-dependent photon echo signal shows two separate frequency distributions in the 2D spectrum in D(2)O, even though only one band is evident from inspection of the linear FTIR spectrum. The split components are more clearly seen at higher viscosity where the distortion of the molecule from 3-fold symmetry is even more evident. The interactions with solvent induce energy transfer between the degenerate component modes on the time scale of 0.5 ps. The energy transfer between modes is directly observed in 2D IR and distinguished by the waiting time dependence of the cross peaks from the transfers between configurations of the distorted ion and solvent. The 2D IR analysis carried out for various polarization conditions gave frequency-frequency auto- and cross-correlation functions for the degenerate components which derive from the solvent induced wagging of the -ND(2) groups of the guanidinium ion.

Ultrafast Interconversion between Protein Conformational Substates: Directly Observed by 2D IR Vibrational Echo Spectroscopy

Conformational dynamics of flexible biomolecules play an important role in the function and stability of proteins. Folded proteins can exist in multiple conformational substates, where each substate has a distinct structure and corresponds to a local minimum on the free energy landscape. Transitions from one minimum to another correspond to dynamical changes in the structure of the protein. By using 2D IR spectroscopy, conformational interconversion between these well defined substates of a myoglobin double mutant is observed on picoseconds timescale. The conformational dynamics are directly measured through the evolution of cross peaks in the 2D IR spectra of CO bound to the heme active site. The conformational switching changes the CO frequency, as detected by the waiting time dependence of the 2D IR vibrational echo spectrum. This result is an example where conformational switching between protein substates occurs on very fast time scales. Moreover, this myoglobin mutant shows enzymatic activity upon substrate binding, which makes it an excellent system to study the influence of substrate binding on structural dynamics.

Memory and aging effects in NiO nanoparticles

We report studies on magnetization dynamics in NiO nanoparticles of average size 5 nm.Temperature and time dependence of dc magnetization, wait time dependence of magneticrelaxation (aging) and memory phenomena in dc magnetization are studied with varioustemperature and field protocols. We observe that the system shows memory and aging infield-cooled and zero-field-cooled magnetization measurements. These experiments showthat the magnetic behavior of NiO nanoparticles is similar to spin glasses. We argue thatthe spin glass behavior originates from the freezing of spins at the surface of the individualparticles.

Growing correlations and aging of an elastic line in a random potential

We study the thermally assisted relaxation of a directed elastic line in a two-dimensional quenched random potential by solving numerically the Edwards-Wilkinson equation and the Monte Carlo dynamics of a solid-on-solid lattice model. We show that the aging dynamics is governed by a growing correlation length displaying two regimes: an initial thermally dominated power-law growth which crosses over, at a static temperature-dependent correlation length ${L}_{T}\ensuremath{\sim}{T}^{3}$, to a logarithmic growth consistent with an algebraic growth of barriers. We present scaling arguments to deal with the crossover-induced geometrical and dynamical effects. This analysis allows us to explain why the results of most numerical studies so far have been described with effective power laws and also permits us to determine the observed anomalous temperature dependence of the characteristic growth exponents. We argue that a similar mechanism should be at work in other disordered systems. We generalize the Family-Vicsek stationary scaling law to describe the roughness by incorporating the waiting-time dependence or age of the initial configuration. The analysis of the two-time linear response and correlation functions shows that a well-defined effective temperature exists in the power-law regime. Finally, we discuss the relevance of our results for the slow dynamics of vortex glasses in high-${T}_{c}$ superconductors.

Dissecting Enthalpic and Entropic Barriers to Ultrafast Equilibrium Isomerization of a Flexible Molecule Using 2DIR Chemical Exchange Spectroscopy

Ultrafast 2DIR chemical exchange spectroscopy was used to study the dynamic equilibrium between different isomers of dicobalt octacarbonyl. Exchange of population between bridged and unbridged isomers takes place on the time scale of a few picoseconds, corresponding to activation barriers of several kcal/mol. Despite overlapping spectral features in the 2DIR spectrum, the exchange component of the waiting time dependence was isolated by exploiting the well-characterized coherent modulation of nonexchange crosspeaks. The temperature dependence of the forward and reverse rate constants enabled extraction of isomerization energy barriers, where analysis using the Eyring equation indicated a substantial entropic contribution to the free energy barrier (DeltaS(double dagger)(exp) > 0). Comparison to quantum chemical calculations showed reasonable enthalpy agreement, but qualitative disagreement for the entropy of the transition state relative to the isomers (DeltaS(double dagger)(comp) < 0).