The Influence of Organo-Clay Ratio in the HIPS-OMMT Nanocomposites Analyzed by Proton Spin-Lattice and Spin-Spin Relaxation Times

Spin-lattice and spin-spin relaxation times are one of the most attractive tools in the solid-state nuclear magnetic resonance spectroscopy to evaluate the level of clay dispersion in the nanocomposite matrices. The efficiency of the relaxation processes can be used to evaluate the nanoparticles intermolecular interactions and, consequently, the dispersion of them in the polymer matrix, the molecular dynamic of the hybrid compounds, as well as the molecular domains formation in an organic material. The determination of relaxation parameters was carried out to evaluate the organoclay exfoliation and intercalation process in the polymeric matrix, in addition to their dispersion and distribution in the matrix. The proton NMR relaxation data showed that the polymeric nanomaterials investigated presented good intermolecular interaction that promoted good nanoparticles dispersion and distribution in the hybrid materials. The proportion of 2% clay promoted a greater heterogeneity in the matrix compared to other ratios;1% clay influenced only to the higher molecular rigidity phase;and 3% clay had a decrease in heterogeneity compared to 2% though still influenced the matrix as a whole. These results prove the efficiency of NMR technique in the evaluation of nanofillers interaction with polymer matrices, as well as their dispersion and distribution.

Dynamic Properties of Polyampholyte Hydrogel Elucidated by Proton NMR Spin-spin Relaxation Time

1H spin-spin relaxation time（T2） measurement of polyampholyte hydrogel poly（methylacrylic acidacryloyloxyethyl trimethylammonium chloride）[P（MA-DAC）] in different pH, ionic strength and temperature was carried out to reveal the molecular mobility. Spontaneous volume transition of the polyampholyte hydrogel was also investigated by spin-spin relaxation time measurement. Meanwhile T2 and the proton component fraction were acquired to study the swelling behaviour of the hydrogel. Moreover the changes of T2 characterized the molecular mo- bility of polyampholyte hydrogel in various swelling states. And the results suggest that the mobility of the main chains and a few free side chains（the long T2） of P（MA-DAC） was dominated by the mesh size in the hydrogel net- work, depending on the swelling ratio（Q） and the mobility of the side chains（the short T2） was influenced by electrostatic interaction between different charges in polymer side chains. Finally the T2 measurements of P（MA-DAC） hydrogel in the spontaneous swelling-deswelling process demonstrated the electrostatic interaction of the charged side chains caused deswelling behavior. At the same time, the mobility state transition temperature of the charged side chains was also studied by the lH spin-spin relaxation time measurements, and the transition activation energy of the side chains is 2.72 kJ.

Prediction of impedance responses of protonic ceramic cells using artificial neural network tuned with the distribution of relaxation times

A deep-learning-based framework is proposed to predict the impedance response and underlying electrochemical behavior of the reversible protonic ceramic cell(PCC) across a wide variety of different operating conditions.Electrochemical impedance spectra(EIS) of PCCs were first acquired under a variety of opera ting conditions to provide a dataset containing 36 sets of EIS spectra for the model.An artificial neural network(ANN) was then trained to model the relationship between the cell operating condition and EIS response.Finally,ANN model-predicted EIS spectra were analyzed by the distribution of relaxation times(DRT) and compared to DRT spectra obtained from the experimental EIS data,enabling an assessment of the accumulative errors from the predicted EIS data vs the predicted DRT.We show that in certain cases,although the R^(2)of the predicted EIS curve may be> 0.98,the R^(2)of the predicted DRT may be as low as~0.3.This can lead to an inaccurate ANN prediction of the underlying time-resolved electrochemical response,although the apparent accuracy as evaluated from the EIS prediction may seem acceptable.After adjustment of the parameters of the ANN framework,the average R^(2)of the DRTs derived from the predicted EIS can be improved to 0.9667.Thus,we demonstrate that a properly tuned ANN model can be used as an effective tool to predict not only the EIS,but also the DRT of complex electrochemical systems.

RELAXATION TIME LIMITS PROBLEM FOR HYDRODYNAMIC MODELS IN SEMICONDUCTOR SCIENCE

In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler-Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales.

A time domain induced polarization relaxation time spectrum inversion method based on a damping factor and residual correction

Relaxation time spectra （RTS） derived from time domain induced polarization data （TDIP） are helpful to assess oil reservoir pore structures. However, due to the sensitivity to the signal-to-noise ratio （SNR）, the inversion accuracy of the traditional singular value decomposition （SVD） inversion method reduces with a decrease of SNR. In order to enhance the inversion accuracy and improve robustness of the inversion method to the SNR, an improved inversion method, based on damping factor and spectrum component residual correction, is proposed in this study. The numerical inversion results show that the oscillation of the RTS derived from the SVD method increased with a decrease of SNR, which makes it impossible to get accurate inversion components. However, the SNR has little influence on inversion components of the improved method, and the RTS has high inversion accuracy and robustness. Moreover, RTS derived from core sample data is basically in accord with the pore-size distribution curve, and the RTS derived from the actual induced polarization logging data is smooth and continuous, which indicates that the improved method is practicable.

Multi-relaxation time lattice Boltzmann simulation of inertial secondary flow in a curved microchannel

The inertial secondary flow is particularly important tbr hydrodynamic lbcusing and particle manipulation m biomed- ical research. In this paper, the development of the inertial secondary flow structure in a curved microchannel was investi- gated by the multi relaxation time lattice Boltzmann equation model with a force term. The numerical results indicate that the viscous and inertial competition dominates the development of secondary flow structure development. The Reynolds number, Dean number, and the cross section aspect ratio influence significantly on the development of the secondary vor- texes. Both the intensity of secondary flow and the distance between the normalized vortex centers are functions of Dean numbers but independent of channel curvature radius. In addition, the competition mechanism between the viscous and inertial effects were discussed by performing the particle focusing experiments. The present investigation provides an improved understanding of the development of inertial secondary flows in curved microchannels.

Concise review of relaxations and approximation algorithms for nonidentical parallel-machine scheduling to minimize total weighted completion times

A class of nonidentical parallel machine scheduling problems are considered in which the goal is to minimize the total weighted completion time. Models and relaxations are collected. Most of these problems are NP-hard, in the strong sense, or open problems, therefore approximation algorithms are studied. The review reveals that there exist some potential areas worthy of further research.

Effect of optical pumping on the momentum relaxation time of graphene in the terahertz range

The momentum relaxation time of a photoexcited graphene in the THz frequency range has been studied by using terabertz time domain spectroscopy under optical pumping at room temperature. It is found that the momentum relaxation time of the graphene as a function of the optical pumping intensity exhibits a threshold behavior. The features of the momentum relaxation time as a function of the optical pumping intensity are also investigated. The results are useful for understanding the basic underlying physics of graphene scattering as well as finding the possible applications in carbon- based electronics.

Effective relaxation time and viscosity of the earth inferred from the postseismic vertical deformations of the 1990 MS=7.0 Gonghe earthquake

The postseismic vertical deformation rates of the 1990 Gonghe M S=7.0 earthquake appears to have decreased exponentially. Based on Okada′s coseismic surface displacement solution caused by a uniform fault slip in an elastic homogeneous half space, we derived its postseismic surface displacement by using a single layer standard linear solid model, and further derived a simplified formula for determining the effective relaxation time and viscosity of the earth, which is independent of the dislocation parameters of the causative fault. From the postseismic vertical deformation of the 1990 Gonghe earthquake, we inferred that the effective relaxation time defined by τ = η/μ is 2.6 years, and the effective viscosity η is about 10 18 Pa·s.

Combined immersed boundary method and multiple-relaxation-time lattice Boltzmann flux solver for numerical simulations of incompressible flows

A method combining the immersed boundary technique and a multi- relaxation-time （MRT） lattice Boltzmann flux solver （LBFS） is presented for numerical simulation of incompressible flows over circular and elliptic cylinders and NACA 0012 Airfoil. The method uses a simple Cartesian mesh to simulate flows past immersed complicated bodies. With the Chapman-Enskog expansion analysis, a transform is performed between the Navier-Stokes and lattice Boltzmann equations （LBEs）. The LBFS is used to discretize the macroscopic differential equations with a finite volume method and evaluate the interface fluxes through local reconstruction of the lattice Boltzmann solution. The immersed boundary technique is used to correct the intermediate velocity around the solid boundary to satisfy the no-slip boundary condition. Agreement of simulation results with the data found in the literature shows reliability of the proposed method in simulating laminar flows on a Cartesian mesh.

Effect of relaxation time on the squeezed correlations of bosons for evolving sources in relativistic heavy-ion collisions

The squeezed back-to-back correlation(SBBC)of a boson-antiboson pair is sensitive to the time distribution of the particle-emitting source,and the SBBC function for an evolving source is expected to be affected by the relaxation time of the system.In this study,we investigated the effect of relaxation time on the SBBC function.We propose a method for calculating the SBBC function with relaxation-time approximation for evolving sources.SBBC functions of D^(0)D^(-0)in relativistic heavy-ion collisions were investigated using a hydrodynamic model.We found that the relaxation time reduces the amplitudes of the SBBC functions.This becomes apparent for long relaxation times and large initial relative deviations of the chaotic and squeezed amplitudes from their equilibrium values in the temporal steps.

Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method

By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number （Re） flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50 000 in the literature; however, this paper can readily extend the maximum to 1000 000 with the above combination.

A multiple-relaxation-time lattice Boltzmann method for high-speed compressible flows

This paper presents a coupling compressible model of the lattice Boltzmann method. In this model, the multiplerelaxation-time lattice Boltzmann scheme is used for the evolution of density distribution functions, whereas the modified single-relaxation-time （SRT） lattice Boltzmann scheme is applied for the evolution of potential energy distribution functions. The governing equations are discretized with the third-order Monotone Upwind Schemes for scalar conservation laws finite volume scheme. The choice of relaxation coefficients is discussed simply. Through the numerical simulations, it is found that compressible flows with strong shocks can be well simulated by present model. The numerical results agree well with the reference results and are better than that of the SRT version.

TRANSVERSAL INERTIAL EFFECT ON RELAXATION/RETARDATION TIME OF CEMENT MORTAR UNDER HARMONIC WAVE

Under dynamic loading, the constitutive relation of the cement mortar will be significantly affected by the transversal inertial effect of specimens with large diameters. In this paper, one-dimensional theoretical analysis is carried out to determine the transversal inertial effect on the relaxation/retardation time of the cement mortar under the harmonic wave. Relaxation time or retardation time is obtained by means of the wave velocity, attenuation coefficient and the frequency of the harmonic wave. Thus, the transversal inertial effect on the relaxation time from Maxwell model, as well as on retardation time from Voigt model is analyzed. The results show that the transversal inertial effect may lead to the increase of the relaxation time, but induce the decrease of the retardation time. Those should be taken into account when eliminating the transversal inertial effect in applications.

Solid State NMR Study of Polystyrene Nanolatex Particles(I) ^(13)C Spin-Lattice Relaxation Time

C spin-lattice relaxtion times for polystyrene nanolatex particles have been investigated. It was found that the dramatic increase at 80℃ annealing temperature is well below the Tg temperature of bulk polystyrene, the increase of relaxation time of aromatic carbons is larger than that of for aliphatic carbons at transition annealing temperature.

MECHANICAL RELAXATION TIME OF A TWO-COMPONENT EPOXY NETWORKLiClO_4 POLYMER ELECTROLYTE

The mechanical relaxation time of a two-component epoxy network-LiClO_4 system as a polymer electrolyte was investigated. The network is composed of diglycidyl ether of polyethylene glycol (DGEPEG) and triglycidyl ether of glycerol (TGEG), wherein LiCIO_4 was incorporated and acts as both the ionic carrier and the curing catalyst. As the relaxation time is informative to the segmental mobility, which is known to be essential for ionic conductivity, the average relaxation times of the specimens were determined through master curve construction. Experimental results showed that the salt concentration, molecular weight of PEG in DGEPEG and DGEPEG/TGEG ratio have profound effect on the relaxation time of the specimen. Among these factors , the former reinforces the network chains, leading to lengthen the relaxation time, whereas the latter two are in favour of the chain flexibility and show an opposite effect. The findings was rationalized in terms of the free volume concept.

The Mathematical Modelling for Studying the Influence of the Initial Stresses and Relaxation Times on Reflection and Refraction Waves in Piezothermoelastic Half-Space

The present paper concentrates on the study of reflection and refraction phenomena of waves in pyroelectric and piezo-electric media under initial stresses and two relaxation times influence by apply suitable conditions. The generalized theories of linear piezo-thermoelasticity have been employed to investigate the problem. In two-dimensional model of transversely isotropic piezothermoelastic medium, there are four types of plane waves quasi-longitudinal (qP), quasi-transverse (qSV), thermal wave (T-mode), and potential electric waves (φ-mode) The amplitude ratios of reflection and refraction waves have been obtained. Finally, the results in each case are presented graphically.

Mesoscopic relaxation time of dynamic image correlation spectroscopy

Dynamical images contain useful information of how the objects behave in time and space. When the system is in biological fluids, the motion of the object is much over-damped;the relaxation time is the characteristics in a diffusive time scale. We have found dynamical states of melting and forming of small nematic domains (10—30 μm) that are exhibited in the suspensions of fd-viruses under applied AC electric field amplitude at low frequency. Dynamic image correlation function is used for extracting the mes- oscopic relaxation times of the dynamical states, which can be employed as an application to other dynamic imaging process of biologically relevant soft condensed matter and biomedical systems.

The Study of Relaxation Time in Test of 940 nm Semiconductor Laser

Conventional test of the peak wavelength of a laser used to be applied immediately after a device is injected current. However, the results can not be considered as an accurate description to temperature characteristic. This passage puts forward a concept of relaxation time in wavelength texts, mainly based on the experiment of 940 nm strain quantum well laser, confirming that under constant current, wavelength will get through a process of rising, and then, reach the limit. This process brings the effect on spectral characteristics of a device which cannot be ignored and the accumulated heat in relaxation time will gradually impact the emission wavelength of the laser, even crest split to form bimodal phenomenon.

Effects of relaxation time on start-up time for starting flow of Maxwell fluid in a pipe

Although the analytical solution of the starting flow of Maxwell fluid in a pipe has been derived for a long time, the effect of relaxation time λ on start-up time ts of this flow is still not well understood. Especially, there exist a series of jumps on the ts-λ. curve. In this paper we introduce a normalized mechanical energy by mode decomposition and mathematical analogy to describe the start-up process. An improved definition of start-up time is presented based on the normalized mechanical energy. It is proved that the ts-λ. curve contains a series of jumps if λ is larger than a critical value. The exact positions of the jumps are determined and the physical reason of the jumps is discussed.