Characteristic Relaxation Time Research Articles

Анализ кривой восстановления давления с учетом неравновесного растворения газа

The article discusses practical issues of modeling the reverse dissolution of gas released from oil, taking into account the nonequilibrium phase transition. An approximate method has been developed for taking into account the nonequilibrium gas dissolution process based on standard reservoir flow simulators without the corresponding option. The developed methodology was tested on the example of pressure build up (PBU) taken on a real field. The possibility of determining the characteristic relaxation time from the PBU is demonstrated in the framework of relaxation models for nonequilibrium phase transitions. The effect of nonequilibrium phase transitions on the dynamics of pressure recovery is determined. Well testing design is proposed that makes it possible to detect nonequilibrium gas dissolution and determine the necessary parameters for its consideration in flow simulations.

A Numerical Investigation of Different Behavioral Regimes of the Free-Falling Solid Objects in Laponite Suspension

In this paper, we have numerically examined models that are capable of describing free falling regimes of a rigid sphere in a thixotropic fluid as Laponite. By simultaneously solving the dynamical equations governing both sphere and fluid systems, different regimes referred to in the experimental methods, are obtained. Three common behavioral regimes are: i) quickly stopping object, ii) fall with decreasing velocity, and iii) falling with a constant velocity in a steady-state mode. The initial state of the fluids (which is a function of the aging time), the characteristic relaxation time of microstructure's building up under shear, the characteristic thickness of the yielded zone around the sphere, and critical yield stress value besides the diameter and density of the sphere are effective parameters that change the regime.

Anticorrelation between the Intensity of Stimulated Picosecond Emission in GaAs and the Characteristic Time of Charge-Carrier Cooling

During the powerful picosecond optical pumping, intense stimulated picosecond emission arises in a thin GaAs layer. It is found that, first, the maximum emission intensity decreases as the diameter of the pump beam increases (while the pump energy density is fixed). Second, this dependence anticorrelates with the dependence of the characteristic relaxation time of the emission on the beam diameter. This time is related to the characteristic cooling time of charge carriers, which is slowed due to carrier heating by emission. This leads to the anticorrelation given in the title.

Оптические и транспортные свойства эпитаксиальных пленок Pb-=SUB=-0.74-=/SUB=-Sn-=SUB=-0.26-=/SUB=-Te(In) с модифицируемой поверхностью

Abstract The results of studies of the optical and transport properties of epitaxial Pb_0.74Sn_0.26Te(In) films with a differently treated surface are presented. A comparative analysis of the results makes it possible to establish that the characteristic features of the photoconductivity spectra are defined by processes in the bulk while the surface states have practically no effect on the spectra. At the same time, the photoresponse kinetics and the rate of relaxation processes are heavily dependent on the state of the surface. The characteristic relaxation times of nonequilibrium charge carriers (about several milliseconds) are such that it is possible to use the methods of standard Fourier-transform spectroscopy to characterize optical transitions in the bulk.

Антикорреляция интенсивности стимулированного пикосекундного излучения GaAs и характерного времени остывания носителей заряда

During the powerful picosecond optical pumping, intense stimulated picosecond emission arises in a thin GaAs layer. It was found that, firstly, the maximum emission intensity decreases with increasing diameter of the pump beam (the pump energy density is fixed). Secondly, this dependence is anticorrelated with the dependence on the diameter of the characteristic relaxation time of the emission. And this time, in turn, is associated with the characteristic cooling time of charge carriers, which is slowed down due to heating of the carriers by emission. As a result, the autocorrelation indicated in the title is revealed.

Low-temperature quantum magnetotransport of graphene on SiC (0 0 0 1) in pulsed magnetic fields up to 30 T

Resistivity, ρ(T), and magnetoresistance (MR) are investigated in graphene grown on SiC (0 0 0 1), at temperatures between T ~ 4–85 K in pulsed magnetic fields of B up to 30 T. According to the Raman spectroscopy and Kelvin-probe microscopy data, the material is a single-layer graphene containing ~20% double-layer islands with a submicron scale and relatively high amount of intrinsic defects. The dependence of ρ(T) exhibits a minimum at temperature Tm ~ 30 K. The low-field Hall data have yielded a high electron concentration, nR ≈ 1.4 × 1013 cm−2 connected to intrinsic defects, and a mobility value of µH ~ 300 cm2 (Vs)−1 weakly depending on T. Analysis of the Shubnikov–de Haas oscillations of MR, observed between B ~ 10–30 T, permitted to establish existence of the Berry phase β ≈ 0.55 and the cyclotron mass, mc ≈ 0.07 (in units of the free electron mass) close to expected values for the single-layer graphene, respectively. MR at 4.2 K is negative up to B ~ 9 T, exhibiting a minimum near 3 T. Analysis of MR within the whole range of B = 0–10 T below the onset of the SdH effect has revealed three contributions, connected to (i) the classical MR effect, (ii) the weak localization, and (iii) the electron–electron interaction. Analysis of the ρ(T) dependence has confirmed the presence of the contributions (ii) and (iii), revealing a high importance of the electron–electron scattering. As a result, characteristic relaxation times were obtained; an important role of the spin–orbit interaction in the material has been demonstrated, too.

Internal resonances and relaxation memory kernels incomposites.

In heterogeneous composite materials, the behaviour of the medium on larger scales is determined by the microgeometry and properties of the constituents on finer scales. To model the influence of the microlevel processes in composite materials, they are described as materials with memory in which the constitutive relations between stress and strain are given as time-domain convolutions with some relaxation kernel. The paper reveals the relationship between the viscoelastic relaxation kernel and the spectral measure in the Stieltjes integral representation of the effective properties of composites. This spectral measure contains all information about the microgeometry of the material, thus providing a link between the relaxation kernel and the microstructure of the composite. We show that the internal resonances of the microstructure determine the characteristic relaxation times of the fading memory kernel and can be used to introduce a set of internal variables that captures dissipation at the microscale. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.

Conformational Entropy as a Means to Control the Behavior of Poly(diketoenamine) Vitrimers In and Out of Equilibrium

AbstractControl of equilibrium and non‐equilibrium thermomechanical behavior of poly(diketoenamine) vitrimers is shown by incorporating linear polymer segments varying in molecular weight (MW) and conformational degrees of freedom into the dynamic covalent network. While increasing MW of linear segments yields a lower storage modulus at the rubbery plateau after softening above the glass transition (Tg), both Tg and the characteristic time of stress relaxation are independently governed by the conformational entropy of the embodied linear segments. Activation energies for bond exchange in the solid state are lower for networks incorporating flexible chains; the network topology freezing temperature decreases with increasing MW of flexible linear segments but increases with increasing MW of stiff segments. Vitrimer reconfigurability is therefore influenced not only by the energetics of bond exchange for a given network density, but also the entropy of polymer chains within the network.

Conformational Entropy as a Means to Control the Behavior of Poly(diketoenamine) Vitrimers In and Out of Equilibrium.

Control of equilibrium and non-equilibrium thermomechanical behavior of poly(diketoenamine) vitrimers is shown by incorporating linear polymer segments varying in molecular weight (MW) and conformational degrees of freedom into the dynamic covalent network. While increasing MW of linear segments yields a lower storage modulus at the rubbery plateau after softening above the glass transition (Tg ), both Tg and the characteristic time of stress relaxation are independently governed by the conformational entropy of the embodied linear segments. Activation energies for bond exchange in the solid state are lower for networks incorporating flexible chains; the network topology freezing temperature decreases with increasing MW of flexible linear segments but increases with increasing MW of stiff segments. Vitrimer reconfigurability is therefore influenced not only by the energetics of bond exchange for a given network density, but also the entropy of polymer chains within the network.

Delayed Weakening and Reactivation of Rate‐and‐State Faults Driven by Pressure Changes Due to Fluid Injection

AbstractFault reactivation induced by pore pressure changes involves complex frictional phenomena because effective normal stresses vary in space and time due to fluid flow and rock deformation. The impact of time‐varying normal stresses on fault friction has been characterized in stress‐step laboratory experiments and modeled through extended rate‐and‐state laws that incorporate a stressing‐rate dependence of the state variable. Building on these rate‐and‐state models, we use 2‐D poroelastic simulations to understand how the evolution of pore pressures due to fluid injection affects fault strength and reactivation. A sharp increase in pore pressure, associated with fluid injection, leads to an increase in friction coefficient and to a delayed weakening of the fault. Conversely, a sharp pressure decrease during extraction leads to a delayed strengthening. Stressing‐rate effects emerge as a purely frictional mechanism that delays or accelerates the onset of fault slip, suggesting that reactivation under fluid injection may occur long after flow rates have decreased and pore pressures have stabilized at the fault. Hence, earthquakes induced by injection may ensue as a deferred process triggered several days later than predicted by simple estimates based on constant friction. The duration of the delay depends on the type of rate‐and‐state law used in calculations and on a characteristic relaxation time: The memory time over which the state variable evolves under stationary contact. Our results help understand the connection between injection protocols and frictional weakening mechanisms, suggesting that injection processes can be engineered to minimize the risk of induced seismicity for a given injected volume.

Comparison of the Radon–Nikodym Method with a Multistage Relaxation Model in the Analysis of the Fluorescence Dynamics of a Cold Atomic Ensemble

The fluorescence of cold atoms, cooled to ultra-low temperatures and excited by pulsed laser radiation, is calculated. The fluorescence of cold atoms is calculated based on the solution of the non-steady-state Schrodinger equation for a combined system of atoms and an electromagnetic field. A universal function is proposed in the work showing the deviation of the fluorescence decay at the end of the pulse from the single-exponential model. To analyze the dynamics of fluorescence, a Radon–Nikodym method has been used based on the studies on the eigenvalues of a matrix constructed on the basis of the fluorescence signal. It is shown that a correlation exists between the parameter of distribution asymmetry inherent in signal matrix eigenvalues, and the temporal law of fluorescence decay. As an alternative method of fluorescence analysis, a multistage relaxation model is used, caused by collective multiatomic effects. The values of characteristic amplitude and relaxation time both at short times (“superradiance”) and at long times (“subradiance”) have been found.

Deciphering How the Viscoelastic Properties of Mussel-Inspired Metal-Coordinate Transiently Cross-Linked Gels Dictate Their Tack Behavior.

In recent years, researchers have incorporated mussel-inspired metal-coordinate cross-links into various types of gels to improve their mechanical properties, particularly toughness and self-healing. However, not much is understood about how the linear mechanical properties of these gels dictate their tack properties. In this study, we use shear rheology and tack tests to explore correlations between linear viscoelastic properties (i.e., plateau modulus, Gp, and characteristic relaxation time, τc) and tack behavior (i.e., peak stress, σmax, and energy dissipation per volume, EDV) of transiently cross-linked hydrogels comprised of histidine-functionalized 4-arm PEG coordinated with Ni2+. By using the Ni2+-histidine ratio and polymer wt % of the transient networks to control their viscoelastic properties, we demonstrate a strong dependence of σmax on Gp and τc. The observed correlation between network dynamics and mechanics under tensile load is in good quantitative agreement with a theoretical framework for σmax, which includes the linear viscoelastic properties as parameters. EDV is also influenced by Gp and τc, and the EDV after reaching σmax is additionally dependent on the polymer wt %. These findings are consistent with previously proposed molecular mechanics of reversible HisxNi2+ cross-links and provide us with new insights into the correlations between bulk mechanics and adhesive dynamics of gels with transient metal-coordinate cross-links.

Phonon-mediated intervalley relaxation of positive trions in monolayer WSe2

The valley relaxation mechanism of the bright state of positively charged excitons (bright positive trions) in monolayer (1L-) ${\mathrm{WSe}}_{2}$ is studied through polarization- and time-resolved photoluminescence and transient reflection measurements. A long valley relaxation time, exceeding 100 ps, is observed for positive trions at low temperature, which is notably prolonged when compared with the characteristic excitonic valley relaxation time of 10 ps. With increasing temperature, the relaxation time decreases to a few ps. This finding implies that phonon-mediated intervalley scattering is important for the relaxation process of the valley-polarized bright state of positive trions.

Interfacial Irreversibly and Loosely Adsorbed Layers Abide by Different Evolution Dynamics.

Within the interfacial region of the substrate, polymer chains can form the inner irreversibly adsorbed and outer loosely adsorbed layers upon annealing. Owing to their different constrained environments, the evolution dynamics of the two layers are supposedly different. To trace such evolution dynamics, we thus resorted to sum frequency generation (SFG) vibrational spectroscopy, using polystyrene (PS) with a series of molar masses on sapphire substrates. By plotting the integrated SFG intensity as a function of the annealing time, we found that the inner irreversibly adsorbed layer had two segmental evolution processes (replacement and local structural relaxation), and the outer loosely adsorbed layer had the monotonical evolution dynamics (structural relaxation), with both evolving toward the dissipation of the interfacial molecular order of the backbones. A critical evolution time was defined for the inner irreversibly adsorbed layer, and a characteristic relaxation time was defined for the outer loosely adsorbed layer. With respect to the molar mass, phenomenologically, both the critical evolution time and the characteristic relaxation time show an asymptotic increase. In summary, this SFG investigation provides the first-hand experimental data on understanding the structural evolution dynamics of the interfacial adsorbed polymer chains, which would gradually split up into the irreversibly adsorbed layer and loosely adsorbed layer upon annealing.

Impact of nanoparticles and radiative heat flux in von Kármán swirling flow of Maxwell fluid

In this paper, the classical von Kármán swirling flow problem due to a rotating disk is modeled and studied for the rate type Maxwell nanofluid together with heat and mass transfer mechanisms. The model under consideration predicts the relaxation time characteristics. The novel aspects of thermophoresis and Brownian motion features due to nanoparticles are investigated by employing an innovative Buongiorno’s model. The analysis further explores the impact of linear Rosseland radiation on heat transfer characteristics. The concept of boundary layer approximations is utilized to formulate the basic governing equations of Maxwell fluid. The dimensionless form of a system of ordinary differential equations is obtained through similarity approach adopted by von Kármán. The system of equations is integrated numerically in domain [0,∞) by using bvp midrich scheme in Maple software. The obtained results intimate that higher rotation raises the radial and angular velocity components. The nano-particles concentration enhances with Brownian motion parameter. Further, the heat transfer rate at the disk surface diminishes with thermophoresis parameter. The achieved numerical computations of velocity profiles, friction coefficient and Nusselt number are matched in limiting cases with previously published literature and an outstanding agreement is observed.

Effect of Conductivity Type and Doping Level of Silicon Crystals on the Size of Formed Pore Channels during Anodic Etching in Hydrofluoric Acid Solutions

In this paper, we discuss causes of the multidirectional effect of changes in the concentrations of free charge carriers in silicon crystals of p- and n-type conductivity on the transverse dimensions of pores formed as a result of anodic etching in hydrofluoric acid solutions, as well as the effect of anodic current density on pore size. The observed dependences are explained based on the concepts of electrochemical pore formation in semiconductor crystals as self-organizing cooperative processes accompanied by the injection of electrons from the chemical reaction region at the pore advancement front. Differences in the size of pores forming at the same current density in crystals differing in type and concentration of free charge carriers are associated with the effective temperature of the front of the cooperative chemical reaction at the bottom of germinating pores. This temperature, in turn, correlates with the power density of thermal energy released in the near-surface region of the etching crystal, either due to recombination processes for a p-type semiconductor or direct or indirect energy transfer from hot electrons to lattice vibrations in the case of a n-type semiconductor. The characteristic relaxation times of injected nonequilibrium electrons were calculated depending on the concentrations of the majority charge carriers in silicon crystals of both types of conductivity and the corresponding thicknesses of the regions of relaxation energy release. The revealed patterns of concentration changes in the power density of heat release in the near-frontal region of etching silicon crystals of p- and n-type conductivity are in good agreement with observed changes in the size of germinating pores.

Optimal motion of triangular magnetocapillary swimmers.

A system of ferromagnetic particles trapped at a liquid-liquid interface and subjected to a set of magnetic fields (magnetocapillary swimmers) is studied numerically using a hybrid method combining the pseudopotential lattice Boltzmann method and the discrete element method. After investigating the equilibrium properties of a single, two, and three particles at the interface, we demonstrate a controlled motion of the swimmer formed by three particles. It shows a sharp dependence of the average center-of-mass speed on the frequency of the time-dependent external magnetic field. Inspired by experiments on magnetocapillary microswimmers, we interpret the obtained maxima of the swimmer speed by the optimal frequency centered around the characteristic relaxation time of a spherical particle. It is also shown that the frequency corresponding to the maximum speed grows and the maximum average speed decreases with increasing interparticle distances at moderate swimmer sizes. The findings of our lattice Boltzmann simulations are supported by bead-spring model calculations.

Effect of Conductive Carbon Black on Mechanical Properties of Aqueous Polymer Binders for Secondary Battery Electrode.

To predict the cyclic stability of secondary battery electrodes, the mechanical behaviors of polymer binders and conductive composites (BCC) is of great significance. In terms of uniaxial tension, tensile stress relaxation, and bonding strength tests, the present study encompasses a systematic investigation of the mechanical properties of two typical aqueous binders with different contents of Super-S carbon black (SS) under a liquid electrolyte. Meanwhile, the microstructure of cured film and the surface morphology of the bonding interface are investigated in detail. When the weight ratio of SS increases from 0% to 50%, the cured BCC films manifest a higher ratio of tensile strength to modulus and a shorter characteristic relaxation time. Moreover, suitable loadings of SS can improve the tensile shear strength and remarkably reduce the percentage of interface failure of aqueous polymer-bonded Cu current collector. Nevertheless, an excess of carbon black amount cannot maintain its enhancing effect and can even impair the adhesive layer. Finally, a sodium alginate-based polymer composite holds much more superior mechanical properties than the mixture of sodium carboxymethyl cellulose and styrene-butadiene rubber at the same content of carbon black. Noticeably, the two kinds of aqueous polymer doped by 50 wt % of SS exhibit the best adhesive properties.

Trap-controlled fractal diffusion model of the Havriliak-Negami dielectric relaxation

A new model of non-Debye dielectric relaxation, which leads to the popular in broadband dielectric spectroscopy Havriliak-Negami expression for two-power-law dielectric response, is proposed. The new model is based on the multiple trapping model and the fractal diffusion model. Explicit analytical expressions for experimentally measured values such as dielectric strength, characteristic relaxation time, and power-law exponents, which include the microscopic parameters of the medium, are obtain. The comparison of the expression for the relaxation time with the experiment is demonstrated. A clear physical interpretation of the power-law exponents of the Havriliak-Negami relaxation function is found, one makes it possible to extend the area application of this function and to use it for the fitting of dielectric data, which exhibit atypical relaxation behavior.

Electronic Nature of Neutral and Charged Two-Photon Absorbing Squaraines for Fluorescence Bioimaging Application

The electronic properties of neutral 2,4-bis(4-bis(2-hydroxyethyl) amino-2-hydroxy-6-(2-(2-(2-methoxyethoxy)ethoxy)ethoxy)phenyl)squaraine (1) and charged 2-((3-octadecylbenzothiazol-2(3H)-ylidene)methyl)-3-oxo-4-((3-(4-(pyridinium-1-yl)butyl)benzo-thiazol-3-ium-2-yl)methylene)cyclobut-1-enolate iodide (2) squaraine derivatives were analyzed based on comprehensive linear photophysical, photochemical, nonlinear optical studies (including two-photon absorption (2PA) and femtosecond transient absorption spectroscopy measurements), and quantum chemical calculations. The steady-state absorption, fluorescence, and excitation anisotropy spectra of these new squaraines revealed the values and mutual orientations of the main transition dipoles of 1 and 2 in solvents of different polarity, while their role in specific nonlinear optical properties was shown. The degenerate 2PA spectra of 1 and 2 exhibited similar shapes, with maximum cross sections of ∼300–400 GM, which were determined by the open aperture Z-scan method over a broad spectral range. The nature of the time-resolved excited-state absorption spectra of 1 and 2 was analyzed using a femtosecond transient absorption pump–probe technique and the characteristic relaxation times of 4–5 ps were revealed. Quantum chemical analyses of the electronic properties of 1 and 2 were performed using the ZINDO/S//DFT theory level, affording good agreement with experimental data. To demonstrate the potential of squaraines 1 and 2 as fluorescent probes for bioimaging, laser scanning fluorescence microscopy images of HeLa cells incubated with new squaraines were obtained.