Calculation Of Relaxation Times Research Articles

Calculation of vibrational relaxation times in multi-component excitable gases

In the research field of acoustic propagation in excitable gases, one of the most critical parameters is the vibrational relaxation time, which determines the frequency of the acoustic dispersion step or the absorption maximum. In this paper, the vibrational relaxation equations given by Tanczos [J. Chem. Phys. 25, 439 (1956)] have been applied to calculate the vibrational multi-relaxation times in multi-component gases. The eigenvalues of the energy-transition-rate matrix are proven to be the reciprocals of the multi-relaxation times. Comparisons demonstrate that our relaxation frequencies calculated for various gas compositions, including carbon dioxide, methane, chlorine, nitrogen, and oxygen, agree with the experimental data.

단분산성 고분자 용융체의 완화시간분포의 해석적인 근사계산법

Abstract: The relaxation time spectrum is a versatile parameter to calculate various polymer viscoelastic properties,such as the relaxation modulus (G(t)), dynamic modulus (G'(ω)) and loss modulus (G(ω)). However, it cannot be mea-sured experimentally. This study calculated the relaxation time spectrum using a calculation method based on Fusso-Kirkwood’s theoretical research and using the empirical loss modulus formula. The calculated relaxation time spec-trum and Rouse’s model could describe the viscoelastic behavior of monodisperse polystyrene successfully. This ana-lytical approximation of the relaxation time spectrum differed from experimental data in the intermediate regionbetween the reputation and Rouse region. This may have resulted from a limitation of the molecular theory in theRouse region.Keywords: relaxational time spectrum, viscoelastic behavior, relaxation modulus, dynamic modulus, loss modulus 1. 서론 완화시간분포 H(λ)를 알 경우 완화탄성률 G(t), 동적 탄성률 G'(ω) 및 G''(ω) 등의 다양한 선형점탄성 함수들을 쉽게 계산할 수 있다. 게다가 완화시간분포로 부터 물질의 점탄성 완화 메커니즘을 분자론적으로 이해할 수 있게 된다.그러나 다른 선형점탄성 함수들은 실험으로 측정할 수 있지만 완화시간분포는 직접 측정할 수 없는 개념적인 물질함수이다. 따라서 측정된 물질함수인 동적 탄성률로부터완화시간분포를 결정하고자 하는 많은 연구들이 진행되어왔다[1−5]. 이러한 연구들의 대부분은 최소자승법(leastsquare method)에 기반을 둔 수치해석적인 방법들이다.완화시간분포는 연속형과 이산형의 두 가지로 분류할 수있다. 이산형은 연속형의 근사형으로 간주할 수 있으며 연속형과는 달리 유일하게 결정할 수 없는 단점이 있지만 계산상의 편리성을 가지고 있다. 연속형 완화시간분포가 유일하게 결정될 수 있다는 근거는 1941년의 Fousso와Kirkwood의 유전 완화시간분포에 대한 이론적 연구에 있다고 할 수 있다[6]. 이들의 연구결과를 선형점탄성에 대해서 수학적으로 표현하면 다음과 같다[7].(1)여기서 i는 허수단위로 이며 Re와 Im은 각각 복소함수의 실수부와 허수부를 의미한다. 식 (1)은 주파수 ω와완화시간 λ의 자연 로그로의 변환 후에 푸리에 변환(Fouriertransform)을 이용하여 얻은 결과이므로 식 (1)은 유일하게결정되는 관계라고 할 수 있다. 하지만 복소평면에서의 한점에서의 수렴성이 실수축에서도 반드시 반영되지 않기도하므로 동적 탄성률 G'(ω) 및 G''(ω) 등의 함수형태에 따라서 유용한 결과가 얻어지지 않을 수도 있다.이 논문은 손실탄성률 G''(ω)의 간단한 현상학적 모델링을 수행하고 이를 식 (1)에 적용하여 완화시간분포의 함수식을 해석적으로 유도한 결과와 그 유용성에 대한 연구이다. 이 연구결과를 이용하게 되면 섬유형성 고분자 유체의선형점탄성을 매우 넓은 시간범위에 대해서 비교적 간결하면서도 상당한 정밀도로 예측할 수 있게 되고 그 결과를이용하여 비선형점탄성 유동계산을 할 수 있게 해 줄 것으로 예상된다.

Dielectric analysis of the [Bmim][PF6]/TX-100/ethyleneglycol nonaqueous microemulsions: Microstructures and percolation

The ternary system consisting of ethyleneglycol (EG), an ionic liquid (1-butyl-3-methylimidazolium hexafluorophosphate, [Bmim][PF6]) and a nonionic surfactant (p-(1,1,3,3-tetramethylbutyl)phenoxypolyoxyethyleneglycol, TX-100) was studied by dielectric measurements in the frequency range from 40Hz to 110MHz. A remarkable dielectric relaxations caused by interfacial polarization was observed around 10MHz. The dielectric intensity Δɛ and the relaxation time τ could be obtained by fitting the experimental data using the Cole–Cole equation with one dispersion terms. The regions of EG-in-IL (EG/IL), bicontinuous phase (B.C.), IL-in-EG (IL/EG) microemulsions and dilute solution were identified by the dependence of direct current (dc) conductivity on the content of EG, where the dc conductivity was obtained from the total dielectric loss spectra. The scaling relation between conductivity and the content of EG was compared with the predictions of scaling theories. In the IL/EG micro-region, Hanai theory was used to calculate the phase parameters of the constituent phases. The trends of calculated relaxation time τMW and τ as a function of EG content in the IL/EG micro-region were almost the same, inferring that the dielectric relaxation probably arose from the interfacial polarization. In short, this work is helpful to understand the microstructures of different regions and percolation phenomenon in nonaqueous microemulsions.

SAT0189 Muscle T2 Mapping: A Tool in the Diagnostic Imaging of Neuromuscular Disorders

BackgroundAlthough Magnetic Resonance Imaging has been widely used as a diagnostic tool in neuromuscular disorders, the analysis of images has remained essentially qualitative.ObjectivesEven if visual scores of deterioration have been...

Elastically cooperative activated barrier hopping theory of relaxation in viscous fluids. I. General formulation and application to hard sphere fluids.

We generalize the force-level nonlinear Langevin equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage process is dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collective barrier is more strongly dependent on volume fraction, dominates the highly viscous regime, and is well described by a nonsingular law below jamming. The increase of the collective barrier is determined by the amplitude of thermal density fluctuations, dynamic shear modulus or transient localization length, and a growing microscopic jump length. Alpha relaxation time calculations are in good agreement with recent experiments and simulations on dense fluids and suspensions of hard spheres. Comparisons of the theory with elastic models and entropy crisis ideas are explored. The present work provides a foundation for constructing a quasi-universal, fit-parameter-free theory for relaxation in thermal molecular liquids over 14 orders of magnitude in time.

Computational Evaluation of Optoelectronic Properties for Organic/Carbon Materials

CONSPECTUS: Organic optoelectronic materials are used in a variety of devices, including light-emitting diodes, field-effect transistors, photovoltaics, thermoelectrics, spintronics, and chemico- and biosensors. The processes that determine the intrinsic optoelectronic properties occur either in the photoexcited states or within the electron-pumped charged species, and computations that predict these optical and electrical properties would help researchers design new materials. In this Account, we describe recent advances in related density functional theory (DFT) methods and present case studies that examine the efficiency of light emission, carrier mobility, and thermoelectric figures of merit by calculation of the electron-vibration couplings. First we present a unified vibrational correlation function formalism to evaluate the excited-state radiative decay rate constant kr, the nonradiative decay rate constant knr, the intersystem crossing rate constant kISC, and the optical spectra. The molecular parameters that appear in the formalism, such as the electronic excited-state energy, vibrational modes, and vibronic couplings, require extensive DFT calculations. We used experiments for anthracene at both low and ambient temperatures to benchmark the calculated photophysical parameters. In the framework of Fermi's golden rule, we incorporated the non-adiabatic coupling and the spin-orbit coupling to evaluate the phosphorescence efficiency and emission spectrum. Both of these are in good agreement with experimental results for anthracene and iridium compounds. Band electron scattering and relaxation processes within Boltzmann theory can describe charge transport in two-dimensional carbon materials and closely packed organic solids. For simplicity, we considered only the acoustic phonon scattering as modeled by the deformation potential approximation coupled with extensive DFT calculations for band structures. We then related the carrier mobility to the band-edge shift associated with the lattice dilation of longitudinal waves. The calculated relaxation time was in good agreement with experimental data for the graphene sheet, which supports the methodology. We then found that the intrinsic electron mobility for a 6,6,12-graphyne sheet can be even larger than that of graphene. We extended this approach to investigate the thermoelectric transport of electrons in metal phthalocyanines, which showed reasonable Seebeck coefficients when compared with experiments. For the thermal lattice transport, we employed nonequilibrium molecular dynamics simulations. Combining both electron transport and lattice thermal conductivity, we can evaluate the thermoelectric figure of merit.

Effect of Mechanical Stress on Oxygen Potential of Transition Metal Oxides

It is well known that oxygen nonstoichiometry is greatly related to thermomechanical properties and electrochemical properties of the oxide materials such as chemical expansion, Young’s modulus, electrical conductivity and so on. Conversely, it implies that oxygen nonstoichiometry might change due to applied mechanical stress. We have confirmed this phenomenon in our previous study [1]. In other words, it may be possible that material properties could be controlled by mechanical stress. In this study, we aimed to evaluate the relations between mechanical stress and oxygen potential change quantitatively by electromotive force measurement under compressive stress using a YSZ ball.Oxygen concentration cell was equipped with a high-temperature mechanical testing machine to measure electromotive force of the sample under mechanical stress. Oxygen potential of the sample surface could be estimated from measured electromotive force by Nernst equation. A YSZ ball was worked as both an electrolyte and ball indenter. Pt wire was wound around the YSZ ball as a reference electrode. The samples were sintered pellets of La0.6Sr0.4CoO3- δ and La0.6Sr0.4FeO3- δ , which were worked as a working electrode.Fig. 1 shows electromotive force, E, and load, P, of La0.6Sr0.4CoO3- δ as a function of time, t, at 1073 K in air. E changed to negative direction when P was applied (t=60 s). During loading, E gradually increased and went back to the original state. When the P was released (t=150 s), E changed to positive direction. After that, E slowly decreased and went back to the original state. According to Kuhn et al., with increasing p(O2), δ in La0.6Sr0.4CoO3- δ decreased, and correspondingly the lattice constants decreased [2]. That is the partial oxidation of La0.6Sr0.4CoO3- δ induced by the shrinkage of the lattice volume. Therefore, it is expected that δ decreases with mechanical lattice shrinkage. However, it would take a certain time until reaching to equilibrated δ with gas atmosphere because of chemical diffusion process. Thus, at the onset of loading, La0.6Sr0.4CoO3- δ was reduced compared with that of equilibrium with gas phase. Over time, E slowly went back to the original state because of chemical diffusion. On the other hand, when the P was released, oxygen potential changed vice versa. The maximum value of the measured electromotive force change increased with increasing the load. This means that larger stress leaded to larger oxygen potential change. Values of electromotive force changes were similar to those from theoretical calculation using Maxwell relations. The higher the temperature, the shorter the time required for relaxation of E. This corresponds to the relaxation time of chemical diffusion, which becomes shorter at high temperature. The calculated relaxation time of E were also showed same temperature dependence. That is, the relaxation of emf is confirmed to be that of chemical diffusion.These electromotive force behaviors were observed in La0.6Sr0.4CoO3- δ and La0.6Sr0.4FeO3- δ in high p(O2) region. Acknowledgement This work was carried out by Grant-in-Aid for Scientific Research (24656375) and JST-PREST.

Calculation of electron spin relaxation time in germanium using the projection–reduction method

Using the electron spin resonance formula derived by the projection reduction method, the electron spin relaxation times in a system of electrons interacting with phonons through phonon-modulated spin–orbit coupling are calculated. The electron spin relaxation time (T1) in germanium decreases with increasing temperature (T) as at low temperatures and at high temperatures. This means that electrons are scattered mostly by acoustic phonon deformation at low temperatures and optical phonon deformation at high temperatures. The magnetic field (B) dependence of the relaxation time is at 70 K and at 120 K. These results nearly agree with the prediction of Yafet. It is also shown that the acoustic and optical deformation constants do not affect the temperature dependence of the relaxation time.

NMR T1 relaxation time measurements and calculations with translational and rotational components for liquid electrolytes containing LiBF4 and propylene carbonate

Longitudinal relaxation (T1) measurements of (19)F, (7)Li, and (1)H in propylene carbonate/LiBF4 liquid electrolytes are reported. Comparison of T1 values with those for the transverse relaxation time (T2) confirm that the measurements are in the high temperature (low correlation time) limit of the T1 minimum. Using data from pulsed field gradient measurements of self-diffusion coefficients and measurements of solution viscosity measured elsewhere, it is concluded that although in general there are contributions to T1 from both translational and rotational motions. For the lithium ions, this is mainly translational, and for the fluorine ions mainly rotational.

T₁ mapping using variable flip angle SPGR data with flip angle correction.

To improve the calculation of T1 relaxation time from a set of variable flip-angle (FA) spoiled gradient recalled echo images. The proposed method: (a) uses a uniform weighting of all FAs, (b) takes into account global inaccuracies in the generation of the prescribed FAs by estimating the actual FAs, and (c) incorporates data-driven local B1 inhomogeneity corrections. The method was validated and its accuracy tested using simulated data, phantom, and in vivo experiments. Results were compared with existing analysis methods and to inversion recovery (IR). Consistency was assessed by means of repeated scans of two subjects. Reference values were obtained from eight healthy subjects from various brain regions and compared with literature values. The method accurately and consistently estimated T1 values in all cases. The method was more robust, in comparison with the standard method, to the choice of FA set; to inaccuracies in generation of the prescribed FAs (in simulated data, T1 estimation error was 12.1 ms versus 235.5 ms); demonstrated greater consistency (in vivo study showed interscan T1 difference of 80 ms versus 356 ms); and achieved a better agreement with IR on phantom (median absolute difference of 123.8 ms versus 790 ms). Reference T1 values were 883/801 ms for female/male in white matter and 1501/1349 ms in gray matter, within the range previously reported. The proposed method overcomes some inaccuracies in FA production, providing more accurate estimation of T1 values compared with standard methods, and is applicable for currently available data.

A parallel lattice Boltzmann method for large eddy simulation on multiple GPUs

To improve the simulation efficiency of turbulent fluid flows at high Reynolds numbers with large eddy dynamics, a CUDA-based simulation solution of lattice Boltzmann method for large eddy simulation (LES) using multiple graphics processing units (GPUs) is proposed. Our solution adopts the "collision after propagation" lattice evolution way and puts the misaligned propagation phase at global memory read process. The latest GPU platform allows a single CPU thread to control up to four GPUs that run in parallel. In order to make use of multiple GPUs, the whole working set is evenly partitioned into sub-domains. We implement Smagorinsky model and Vreman model respectively to verify our multi-GPU solution. These two LES models have different relaxation time calculation behavior and lead to different CUDA implementation characteristics. The implementation based on Smagorinsky model achieves 190 times speedup over the sequential implementation on CPU, while the implementation based on Vreman model archives more than 90 times speedup. The experimental results show that the parallel performance of our multi-GPU solution scales very well on multiple GPUs. Therefore large-scale (up to 10,240 $$\times $$ × 10,240 lattices) LES---LBM simulation becomes possible at a low cost, even using double-precision floating point calculation.

Relaxation Time of Artificial Periodic Irregularities of the Ionospheric Plasma and Diffusion in the Inhomogeneous Atmosphere

We consider diffusion of the ionospheric-plasma irregularities as applied to the problem of experimental determination of the lower-ionosphere parameters by artificial periodic irregularities of the electron number density. A rigorous solution to the problem of diffusion of one-dimensional plasma irregularities in a weakly ionized medium, whose diffusion coefficient exponentially decreases with the altitude, is obtained. The Green’s function for this problem is found. Three parameters are taken into account in the solution, namely, the size of the region occupied by the irregularities, the size of the irregularities, and a typical spatial scale of the e-fold decrease in the diffusion coefficient. Theoretical relaxation times of the irregularities as functions of these parameters are analyzed. Calculated relaxation times are compared with the times measured in the observation of the artificial periodic irregularities created by the SURA facility. Calculated relaxation times of these irregularities are in good agreement with the observed values.

Bubble-Induced Relaxation in High-Pressure Microfluidic Systems

This work reported an analysis of a noticeable relaxation phenomenon caused by undesirable air bubbles in high-pressure microfluidic systems. A model with compression of air bubble considered was established to address the experimental observed pressure relaxation. The results indicated that the dominative factors were flow rate, flow resistance and initial diameter of the trapped air bubble. Meanwhile, the calculated relaxation times in different cases provided a design guideline for high-pressure microfluidic chip to avoid the long-term pressure relaxation.

Transport behavior of holes in boron delta-doped diamond structures

Boron delta-doped diamond structures have been synthesized using microwave plasma chemical vapor deposition and fabricated into FET and gated Hall bar devices for assessment of the electrical characteristics. A detailed study of variable temperature Hall, conductivity, and field-effect mobility measurements was completed. This was supported by Schrödinger-Poisson and relaxation time calculations based upon application of Fermi's golden rule. A two carrier-type model was developed with an activation energy of ∼0.2 eV between the delta layer lowest subband with mobility ∼1 cm2/Vs and the bulk valence band with high mobility. This new understanding of the transport of holes in such boron delta-doped structures has shown that although Hall mobility as high as 900 cm2/Vs was measured at room temperature, this dramatically overstates the actual useful performance of the device.

NMR characterisation of dynamics in solvates and desolvates of formoterol fumarate

Solid-state NMR is used to characterise dynamics in the ethanol solvate of the pharmaceutical material formoterol fumarate and its associated desolvate. Jump rates and activation barriers for dynamic processes such as phenyl ring rotation and methyl group rotational diffusion are derived from 1D-EXSY and (13)C spin-lattice relaxation times respectively. (2)H and (13)C spin-lattice relaxation times measured under magic-angle spinning conditions are used to show that the fumarate ion in the desolvate is undergoing small-amplitude motion on a frequency scale of 100s of MHz at ambient temperature with an activation parameter of about 32 kJ mol(-1). Exact calculations of relaxation times under MAS provide a simple and robust means to test motional models in cases where relaxation rate maxima are observed, including for systems where the crystal structure of the material is unknown.

Ultrastructure of cellulose crystallites in flax textile fibres

Seven varieties of flax (Linum usitatissimum) fibres were analyzed in order to gain a deeper insight into the morphological features of the crystalline assembly. Different spectroscopic techniques and a chemical bleaching process were used to provide an accurate description of the lateral arrangement of the polysaccharide chains within the fibre cell wall. The flax fibres were analyzed in their natural state and after an extraction treatment of the non-crystalline components such as hemicelluloses, pectins and phenolics. The chemical bleaching process consisted of a Soxhlet extraction in toluene, a sodium chlorite treatment and an alkaline extraction of the residual hemicelluloses. Solid-state 13C nuclear magnetic resonance (NMR) confirmed the sequential removal of the non-cellulosic components from the flax cell wall. Both wide-angle X-ray diffraction (WAXD) and solid-state 13C NMR provided measures of the crystallite thicknesses and overall crystallinities before and after treatment. The existence of non-cellulosic highly ordered paracrystalline domains was also evidenced by proton spin relaxation time calculation. Whereas the overall crystallinity determined by WAXD decreased after treatment, the cellulose crystallinity calculated with the help of the solid-state 13C NMR slightly increased. This is explained by the difference in chemical selectivity between these two techniques and by the paracrystalline state of both hemicelluloses and pectins. Strong adhesion between cellulose crystallites, hemicelluloses and pectins in the fibres was evidenced by low spin–spin relaxation times and by an increase in crystallite thickness after bleaching. A simple model is proposed that describes the rearrangement of the macromolecules during the bleaching process.

Nano-scale temperature dependent visco-elastic properties of polyethylene terephthalate (PET) using atomic force microscope (AFM)

Visco-elastic behaviour at the nano-level of a commonly used polymer (PET) is characterised using atomic force microscopy (AFM) at a range of temperatures. The modulus, indentation creep and relaxation time of the PET film (thickness=100μm) is highly sensitive to temperature over an experimental temperature range of 22–175°C. The analysis showed a 40-fold increase in the amount of indentation creep on raising the temperature from 22°C to 100°C, with the most rapid rise occurring above the glass-to-rubber transition temperature (Tg=77.1°C). At higher temperatures, close to the crystallisation temperature (Tc=134.7°C), the indentation creep reduced to levels similar to those at temperatures below Tg. The calculated relaxation time showed a similar temperature dependence, rising from 0.6s below Tg to 1.2s between Tg and Tc and falling back to 0.6s above Tc. Whereas, the recorded modulus of the thick polymer film decreases above Tg, subsequently increasing near Tc. These visco-elastic parameters are obtained via mechanical modelling of the creep curves and are correlated to the thermal phase changes that occur in PET, as revealed by differential scanning calorimetry (DSC).

Measurement of magnetic nanoparticle relaxation time.

Nanoparticle relaxation time measurements have many applications including characterizing molecular binding, viscosity, heating, and local matrix stiffness. The methods capable of in vivo application are extremely limited. The hypothesis investigated by the authors was that the relaxation time could be measured quantitatively using magnetic spectroscopy of nanoparticle Brownian motion (MSB). The MSB signal (1) reflects the nanoparticle rotational Brownian motion, (2) can be measured from very low nanoparticle concentrations, and (3) is a function of the product of the drive frequency and the relaxation time characterizing Brownian motion. To estimate the relaxation time, the MSB signal was measured at several frequencies. The MSB signal for nanoparticles with altered relaxation time is a scaled version of that for reference nanoparticles with a known relaxation time. The scaling factor linking the altered and reference MSB measurements is the same factor linking the altered and reference relaxation times. The method was tested using glycerol solutions of varying viscosities to obtain continuously variable relaxation times. The measured relaxation time increased with increasing viscosity of the solution in which the nanoparticles resided. The MSB estimated relaxation time matched the calculated relaxation times based on viscosity with 2% average error. MSB can be used to monitor the nanoparticle relaxation time quantitatively through a scale space correlation of the MSB signal as a function of frequency.

A new approach for calculation of relaxation time and magnetic anisotropy of ferrofluids containing superparmagnetic nanoparticles

In this work, a new approach is described for the calculation of the relaxation time and magnetic anisotropy energy of magnetic nanoparticles. Ferrofluids containing monodispersed magnetite nanoparticles were synthesized via hydrothermal method and then heated using the 10 kA/m external AC magnetic fields in three different frequencies: 10, 50 and 100 kHz. By measuring the temperature variations during the application of the magnetic field, the total magnetic time constant including both Brownian and Neel relaxation times can be calculated. By measuring the magnetic core size and hydrodynamic size of particles, the magnetic anisotropy can be calculated too. Synthesized ferrofluids were characterized via TEM, XRD, VSM and PCS techniques and the results were used for the mentioned calculations.

Rotational relaxation characteristics of the monoclinic phase of CCl4

We present a study of crystalline CCl(4) spanning up to 10 orders of magnitude in time at temperatures ranging from 160 K to 190 K using molecular dynamics simulations. The relaxation process is studied using angular self correlation functions. The results show that each of the four nonequivalent molecules of the monoclinic phase have a particular relaxation time. Two of the molecules relax in an exponential way and the two other molecules have a more complex behavior, especially at the lower temperatures. In all cases, the molecular rotations correspond to quick jumps between equivalent tetrahedral equilibrium positions. Most of these rotations are about the C(3) symmetry axes, however at high temperatures, rotations about the C(2) symmetry axes are observed as well. The waiting time between rotations follows a Poisson distribution. The calculated relaxation times show an Arrhenius behavior with different activation energy for different nonequivalent molecules, in line with recently published findings of nuclear quadrupole resonance experiments.