Isomerization dynamics in viscous liquids: Microscopic investigation of the coupling and decoupling of the rate to and from solvent viscosity and dependence on the intermolecular potential

A detailed investigation of viscosity dependence of the isomerization rate is carried out for continuous potentials by using a fully microscopic, self-consistent mode-coupling theory calculation of both the friction on the reactant and the viscosity of the medium. In this calculation we avoid approximating the short time response by the Enskog limit, which overestimates the friction at high frequencies. The isomerization rate is obtained by using the Grote-Hynes formula. The viscosity dependence of the rate has been investigated for a large number of thermodynamic state points. Since the activated barrier crossing dynamics probes the high-frequency frictional response of the liquid, the barrier crossing rate is found to be sensitive to the nature of the reactant-solvent interaction potential. When the solute-solvent interaction is modeled by a 6-12 Lennard-Jones potential, we find that over a large variation of viscosity (eta), the rate (k) can indeed be fitted very well to a fractional viscosity dependence: (k similar to eta(-alpha)), with the exponent alpha in the range 1 greater than or equal to alpha >0. The calculated values of the exponent appear to be in very good agreement with many experimental results. In particular, the theory, for the first time, explains the experimentally observed high value of alpha even at the barrier frequency, omega(b). similar or equal to 9 X 10(12) s(-1) for the isomerization reaction of 2-(2'-propenyl)anthracene in liquid eta-alkanes. The present study can also explain the reason for the very low value of vb observed in another study for the isomerization reaction of trans-stilbene in liquid n-alkanes. For omega(b) greater than or equal to 2.0 X 10(13) s(-1), we obtain alpha similar or equal to 0, which implies that the barrier crossing rate becomes identical to the transition-state theory predictions. A careful analysis of isomerization reaction dynamics involving large amplitude motion suggests that the barrier crossing dynamics itself may become irrelevant in highly viscous liquids and the rate might again be coupled directly to the viscosity. This crossover is predicted to be strongly temperature dependent and could be studied by changing the solvent viscosity by the application of pressure. (C) 1999 American Institute of Physics. [S0021-9606(9950514-X].

Lithium ion transport in Li2SO4-Li2O-B2O3 glasses

Electrical conductivity and dielectric relaxation studies with a wide range of compositions of lithium ion conducting glasses belonging to the ternary glass system Li2SO4-Li2O-B2-O3- have been carried out over the temperature range 150-450 K and between 10 - 10(7) Hz. DC conductivities exhibit two different activation regions. This seems to suggest the presence of a cluster tissue texture in these glasses with weakly ordered clusters of Li2SO4 and lithium berates being held together by a truly amorphous tissue of the same average composition as clusters. AC conductivity behaviour of these glasses has been analysed using both power law and stretched exponential relaxation functions. The variation of the power law exponent s and the stretched exponent beta with temperature seems to be consistent with the presence of a cluster tissue texture in these glasses.

Hidden order in serrated flow of metallic glasses

We report results of statistical and dynamic analysis of the serrated stress-time curves obtained from compressive constant strain-rate tests on two metallic glass samples with different ductility levels in an effort to extract hidden information in the seemingly irregular serrations. Two distinct types of dynamics are detected in these two alloy samples. The stress-strain curve corresponding to the less ductile Zr65Cu15Ni10Al10 alloy is shown to exhibit a finite correlation dimension and a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. In contrast, for the more ductile Cu47.5Zr47.5Al5 alloy, the distributions of stress drop magnitudes and their time durations obey a power-law scaling reminiscent of a self-organized critical state. The exponents also satisfy the scaling relation compatible with self-organized criticality. Possible physical mechanisms contributing to the two distinct dynamic regimes are discussed by drawing on the analogy with the serrated yielding of crystalline samples. The analysis, together with some physical reasoning, suggests that plasticity in the less ductile sample can be attributed to stick-slip of a single shear band, while that of the more ductile sample could be attributed to the simultaneous nucleation of a large number of shear bands and their mutual interactions. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Residence time distribution for a class of Gaussian Markov processes

We study the distribution of residence time or equivalently that of "mean magnetization" for a family of Gaussian Markov processes indexed by a positive parameter alpha. The persistence exponent for these processes is simply given by theta=alpha but the residence time distribution is nontrivial. The shape of this distribution undergoes a qualitative change as theta increases, indicating a sharp change in the ergodic properties of the process. We develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary alpha. For some special values of alpha, we obtain closed form expressions of the distribution function. [S1063-651X(99)03306-1].

Dielectric Relaxation in CaO-Bi2O3-B2O3 Glasses

Glasses in the system CaO-Bi2O3-B2O3 (in molar ratio) have been prepared using melt-quenching route. Ion transport characteristics were investigated for this glass using electric modulus, ac conductivity and impedance measurements. The ac conductivity was rationalized using Almond-West power law. Dielectric relaxation has been analyzed based on the behavior of electric modulus behavior. The activation energy associated with the electrical relaxation determined from the electric modulus spectra was found to be 1.76 eV, close to that the activation energy for dc conductivity (1.71 eV) indicating that the same species took part in both the processes. The stretched exponent beta (0.5-0.6) is invariant with temperature for the present glasses.

Chaotic and power law states in the Portevin-Le Chatelier effect

Recent studies on the Portevin-Le Chatelier effect report an intriguing crossover phenomenon from low-dimensional chaotic to an infinite-dimensional scale-invariant power law regime in experiments on CuAl single crystals and AlMg polycrystals, as function of strain rate. We devise fully dynamical model which reproduces these results. At low and medium strain rates, the model is chaotic with the structure of the attractor resembling the reconstructed experimental attractor. At high strain rates, power law statistics for the magnitudes and durations of the stress drops emerge as in experiments and concomitantly, the largest Lyapunov exponent is zero.

Dynamics of crystal size distributions with size-dependent rates

The growth and dissolution dynamics of nonequilibrium crystal size distributions (CSDs) can be determined by solving the governing population balance equations (PBEs) representing reversible addition or dissociation. New PBEs are considered that intrinsically incorporate growth dispersion and yield complete CSDs. We present two approaches to solving the PBEs, a moment method and a numerical scheme. The results of the numerical scheme agree with the moment technique, which can be solved exactly when powers on mass-dependent growth and dissolution rate coefficients are either zero or one. The numerical scheme is more general and can be applied when the powers of the rate coefficients are non-integers or greater than unity. The influence of the size dependent rates on the time variation of the CSDs indicates that as equilibrium is approached, the CSDs become narrow when the exponent on the growth rate is less than the exponent on the dissolution rate. If the exponent on the growth rate is greater than the exponent on the dissolution rate, then the polydispersity continues to broaden. The computation method applies for crystals large enough that interfacial stability issues, such as ripening, can be neglected. (C) 2002 Elsevier Science B.V. All rights reserved.

Magnetically tunable nonlinear current-voltage characteristics in oxygen deficient manganite perovskites

(La0.667Ca0.333Mn1-xMO3-delta)-O-x (M = Mg, Li or Re) exhibit insulating behaviour and nonlinear current-voltage (J-E) relationship with voltage-limiting characteristics at temperatures below the ferromagnetic transition (T-c). The high current region is set in at field strengths <60 V/cm. Nonlinearity exponent, alpha in the relation J = kE(alpha) increases inversely with temperature. In presence of an external magnetic field, the J-E curves show higher current density at lower field strengths. Microstructural studies indicate that there is no segregation of secondary phases in the grain boundary regions. There is remarkable changes in p(T) as well as J-E curves with the grain size. Annealing studies in lower p(O2) atmospheres indicate that there is significant out-diffusion of oxygen ions through the grain boundary layer (GBL) regions creating oxygen vacancies in the GBL regions. The concentration of Mn4+ ions is lowered at the GBL due to oxygen vacancies, reducing the probability of hopping and resulting in insulating behaviour. Therefore an insulating barrier is introduced between two conducting grains and the carrier motion between the grains is inhibited. Thus below T-c, where sufficient increase in resistivity is observed the conduction may be arising as a result of spin dependent tunneling across the barrier. External electric field lowers the barrier height and establishes carrier transport across the barrier. Above certain field strength, barrier height diminishes significantly and thereby allowing large number of carriers for conduction, giving rise to highly nonlinear conductivity. (C) 2002 Elsevier Science B.V. All rights reserved.

Major depression with ischemic heart disease: Effects of paroxetine and nortriptyline on measures of nonlinearity and chaos of heart rate

Depression is associated with increased cardiovascular mortality in patients with preexisting cardiac illness. A decrease in cardiac vagal function as suggested by a decrease in heart rate variability (HRV) or heart period variability has been linked to sudden death in patients with cardiac disease as well as in normal controls. Recent studies have shown decreased vagal function in cardiac patients with depression as well as in depressed patients without cardiac illness. In this study, we compared 20 h awake and sleep heart period nonlinear measures using quantification of nonlinearity and chaos in two groups of patients with major depression and ischemic heart disease (mean age 59-60 years) before and after 6 weeks of treatment with paroxetine or nortriptyline. Patients received paroxetine, 20-30 mg/day or nortriptyline targeted to 190-570 nmol/l for 6 weeks. For HRV analysis, 24 patients were included in the paroxetine treatment study and 20 patients in the nortriptyline study who had at least 20,000 s of awake data. The ages of these groups were 60.4 +/- 10.5 years for paroxetine and 60.8 +/- 13.4 years for nortriptyline. There was a significant decrease in the largest Lyapunov exponent (LLE) after treatment with nortriptyline but not paroxetine. There were also significant decreases in nonlinearity scores on S-netPR and S-netGS after nortriptyline, which may be due to a decrease in cardiac vagal modulation of HRV. S-netGS and awake LLE were the most significant variables that contributed to the discrimination of postparoxetine and postnortriptyline groups even with the inclusion of time and frequency domain measures. These findings suggest that nortriptyline decreases the measures of chaos probably through its stronger vagolytic effects on cardiac autonomic function compared with paroxetine, which is in agreement with previous clinical and preclinical reports. Nortriptyline was also associated with a significant decrease in nonlinearity scores, which may be due to anticholinergic and/or sympatholytic effects. As depression is associated with a strong risk factor for cardiovascular mortality, one should be careful about using any drug that adversely affects cardiac vagal function. Copyright (C) 2002 S. Karger AG, Basel.

Nonlinear measures of respiration: Respiratory irregularity and increased chaos of respiration in patients with panic disorder

Background. Respiratory irregularity has been previously reported in patients with panic disorder using time domain measures. However, the respiratory signal is not entirely linear and a few previous studies used approximate entropy (APEN), a measure of regularity of time series. We have been studying APEN and other nonlinear measures including a measure of chaos, the largest Lyapunov exponent (LLE) of heart rate time series, in some detail. In this study, we used these measures of respiration to compare normal controls (n = 18) and patients with panic disorder (n = 22) in addition to the traditional time domain measures of respiratory rate and tidal volume. Methods: Respiratory signal was obtained by the Respitrace system using a thoracic and an abdominal belt, which was digitized at 500 Hz. Later, the time series were constructed at 4 Hz, as the highest frequency in this signal is limited to 0.5 Hz. We used 256 s of data (1,024 points) during supine and standing postures under normal breathing and controlled breathing at 12 breaths/min. Results: APEN was significantly higher in patients in standing posture during normal as well as controlled breathing (p = 0.002 and 0.02, respectively). LLE was also significantly higher in standing posture during normal breathing (p = 0.009). Similarly, the time domain measures of standard deviations and the coefficient of variation (COV) of tidal volume (TV) were significantly higher in the patient group (p = 0.02 and 0.004, respectively). The frequency of sighs was also higher in the patient group in standing posture (p = 0.02). In standing posture, LLE (p < 0.05) as well as APEN (p < 0.01) contributed significantly toward the separation of the two groups over and beyond the linear measure, i.e. the COV of TV. Conclusion: These findings support the previously described respiratory irregularity in patients with panic disorder and also illustrate the utility of nonlinear measures such as APEN and LLE as additional measures toward a better understanding of the abnormalities of respiratory physiology in similar patient populations as the correlation between LLE, APEN and some of the time domain measures only explained up to 50-60% of the variation. Copyright (C) 2002 S. Karger AG, Basel.

Analysis of deformation mechanisms in superplastic yttria-stabilized tetragonal zirconia

There have been extensive experimental observations of changes in the apparent rate controlling creep parameters in studies on superplastic materials. The three most common explanations associated with these changes in the stress exponent, n, the activation energy Q and the inverse grain size exponent, p involve the effect of concurrent grain growth, the operation of a threshold stress or transitions in creep mechanisms. Each of these factors may influence experimental creep data in a similar manner. Therefore, a careful analysis of the consequences of all three factors must involve the development of a consistent set of experimental observations in order to adequately distinguish the effects of each. This paper discusses the role of concurrent grain growth, a threshold stress and transitions in creep mechanisms in superplastic materials. Specific attention is given to the analysis of data on superplastic yttria-stabilized zirconia ceramics for which an increase in n has been observed at low applied stresses. It is demonstrated that neither concurrent grain growth nor a threshold stress can account for all the relevant experimental observations in this material. It is concluded that the changes in rate controlling creep parameters are associated with the operation of two distinct sequential mechanisms as part of a grain boundary sliding process.

Influence of temperature and strain rate on the flow stress of an FeAl alloy

The deformation behavior of an FeAl alloy processed by hot extrusion of water atomized powder has been investigated. Compression tests are performed in the temperature range 1073–1423 K and in the strain rate range 0.001–100 s−1 up to a true plastic strain of 0.5. The flow stress has been found to be strongly dependent on temperature as well as strain rate. The stress exponent in the power law rate equation is estimated to be in the range 7.0–4.0, decreasing with temperature. The activation energy for plastic flow in the range 1073–1373 K varies from 430 kJ mol−1 at low stresses to 340 kJ mol−1 at high stresses. However, it is fairly independent of strain rate and strain. The activation area has similarly shown a stress dependence and lies in the range 160–45b2. At 1423 K and at strain rates lower than 0.1 s−1 a strain rate sensitivity of 0.3 is observed with an associated activation energy of 375 kJ mol−1. The plastic flow in the entire range of temperature and strain rate investigated appears to be controlled by a diffusion mechanism. The results have revealed that it is possible to process the alloy by superplastic forming in the range 1373–1423 K at strain rates lower than 0.1 s−1.

Effect of strain rate on tensile and compression behaviour of Al-Si/graphite composite

Effects of strain rate (10(-4)-10(-2) s(-1)) on tensile and compressive strength of the Al-Si alloy and Al-Si/graphite composite are investigated. The strain hardening exponent value of the composite was more than that of the alloy for all strain rates during tensile and compressive loading. The yield stress of the composite was more than that of the ultimate tensile strength of the alloy for all strain rates. Tensile and compressive properties of the alloy and composite are dependent on strain rates. The negative strain rate sensitivity was observed for the composite and alloy at lower strain rates during the compression and tension loading respectively. (C) 2011 Elsevier B.V. All rights reserved.

Critical properties of the double-exchange ferromagnet Nd(0.6)Pb(0.4)MnO(3)

Results of a study of dc magnetization M(T,H), performed on a Nd(0.6)Pb(0.4)MnO(3) single crystal in the temperature range around T(C) (Curie temperature) which embraces the supposed critical region \epsilon\=\T-T(C)\/T(C)less than or equal to0.05 are reported. The magnetic data analyzed in the critical region using the Kouvel-Fisher method give the values for the T(C)=156.47+/-0.06 K and the critical exponents beta=0.374+/-0.006 (from the temperature dependence of magnetization) and gamma=1.329+/-0.003 (from the temperature dependence of initial susceptibility). The critical isotherm M(T(C),H) gives delta=4.54+/-0.10. Thus the scaling law gamma+beta=deltabeta is fulfilled. The critical exponents obey the single scaling equation of state M(H,epsilon)=epsilon(beta)f(+/-)(H/epsilon(beta+gamma)), where f(+) for T>T(C) and f(-) for Texponent values are very close to those expected for the universality class of three-dimensional Heisenberg ferromagnets with short-range interactions.

Effect of nortriptyline and paroxetine on measures of chaos of heart rate time series in patients with panic disorder

Tricyclic antidepressants have notable cardiac side effects, and this issue has become important due to the recent reports of increased cardiovascular mortality in patients with depression and anxiety. Several previous studies indicate that serotonin reuptake inhibitors (SRIs) do not appear to have such adverse effects. Apart from the effects of these drugs on routine 12-lead ECG, the effects on beat-to-beat heart rate (HR) and QT interval time series provide more information on the side effects related to cardiac autonomic function. In this study, we evaluated the effects of two antidepressants, nortriptyline (n = 13), a tricyclic, and paroxetine (n = 16), an SRI inhibitor, on HR variability in patients with panic disorder, using a measure of chaos, the largest Lyapunov exponent (LLE) using pre- and posttreatment HR time series. Our results show that nortriptyline is associated with a decrease in LLE of high frequency (HF: 0.15-0.5 Hz) filtered series, which is most likely due to its anticholinergic effect, while paroxetine had no such effect. Paroxetine significantly decreased sympathovagal ratios as measured by a decrease in LLE of LF/HF. These results suggest that paroxetine appears to be safer in regards to cardiovascular effects compared to nortriptyline in this group of patients. (C) 2003 Elsevier Inc. All rights reserved.