Showing papers on "Rate equation published in 1997"

Atomic and Macroscopic Reaction Rates of a Surface-Catalyzed Reaction

Abstract: The catalytic oxidation of carbon monoxide (CO) on a platinum (111) surface was studied by scanning tunneling microscopy The adsorbed oxygen atoms and CO molecules were imaged with atomic resolution, and their reactions to carbon dioxide (CO 2 ) were monitored as functions of time The results allowed the formulation of a rate law that takes the distribution of the reactants in separate domains into account From temperature-dependent measurements, the kinetic parameters were obtained Their values agree well with data from macroscopic measurements In this way, a kinetic description of a chemical reaction was achieved that is based solely on the statistics of the underlying atomic processes

Extraction of DFB laser rate equation parameters for system simulation purposes

Abstract: Values for the parameters in a rate equation description of a distributed feedback (DFB) laser must be chosen appropriately in order to obtain agreement between calculated and measured results for system performance. A technique is described for readily extracting values of the rate equation parameters using measurements of the threshold current and the optical power, resonance frequency and damping factor for a bias current well above the threshold current. When used to estimate system performance, it is shown that different sets of physically reasonable parameter values which reproduce the measurements yield the same dependence of the receiver sensitivity on fiber length. Calculated and measured results for the receiver sensitivity and time resolved chirp exhibit good agreement when the extracted parameter values are used.

Energy rate equations for mode-locked lasers

Abstract: A rate equation for pulse energy is obtained from the master equation of mode locking. This rate equation is used to investigate self-starting, steady-state pulse energy, stability, pulse quantization, simultaneous cw and pulse operation, hysteresis in mode locking, multiple-pulse operation, relaxation oscillations, and noise behavior. The theory also provides criteria for low-noise as well as high-power operation. The formulation is applied to both soliton lasers and stretched-pulse lasers, and their operations are compared.

Kinetics of hydroformylation of l-dodecene using homogeneous HRh(CO) (PPh3)3 catalyst

Abstract: The kinetics of the HRh(CO(PPh 3 ) 3 catalyzed hydroformylation of l-dodecene has been investigated in a temperature range of 323–343, K. The effect of l-dodecene and catalyst concentration, P H and P CO , on the rate of reaction has been studied. The rate was found to be first order with respect to catalyst concentration and partial pressure of hydrogen. The rate vs. P CO shows a typical case of substrate inhibited kinetics. The rate was found to be first order with respect to l-dodecene in the lower concentration range while at higher concentrations a zero order dependence was observed. A rate equation has been proposed and kinetic parameters evaluated. The activation energy was found to be 57.12 kJ/mol. A batch reactor model has been a used to predict the concentration-time profiles which were found to agree well with the experimental data at different temperatures. This indicates the applicability of the rate model over a wide range of conditions.

Reaction kinetics of the CO2 reforming of methane

Abstract: The kinetics of the CO 2 reforming of methane was investigated in the temperature range 700-850°C at normal pressure with a 1:1 mixture of CH 4 and CO 2 on Ir/Al 2 O 3 catalysts. The feed composition was kept constant to avoid a change in mechanism associated with composition changes. Various rate models were fitted to the experimental data by numerically integrating the rate equations. All rate models included the reverse water gas shift reaction as the most important side reaction at these reaction conditions. The best agreement was obtained with a rate model based on the stepwise mechanism, where in the rate-determining step methane is decomposed to hydrogen and active carbon followed by the direct and fast conversion of this active carbon with CO 2 to 2CO. This model is also the first and only one containing a complete subset of reactions necessary to describe the network of reactions known to occur at these reaction conditions. Comparable fit quality was obtained with a simple first order model and with a model based on a Langmuir-Hinshel-wood rate expression, where the latter provided physically meaningless parameters. Values of the reaction parameters are given for the 5 best rate models studied.

Development of a Predictive Model for Activation-Controlled Corrosion of Steel in Solutions Containing Carbon Dioxide

Abstract: Corrosion of steel in carbon dioxide (CO2)-containing solutions is considered a chemical reaction-controlled process. A corrosion rate equation was derived on the basis of fundamental reaction rate theory and compared to empirically determined relationships reported in the literature. The predictive equation was developed as a function of pH, partial pressure of CO2 (PCO2), and temperature. The equation allows the inclusion of other variables, such as flow, impurities, inhibitors, and steel microstructure, through the reaction constant. The application limit for this equation extends to the point where corrosion becomes diffusion-controlled as a result of the formation of stable corrosion products on the steel surface.

High-carrier-density electron dynamics in low-temperature-grown GaAs

Abstract: Pump-probe differential transmission measurements examine high-carrier-density phenomena in as-grown and annealed GaAs samples grown at temperatures from 210 to 270 °C. We observe trap saturation and Auger recombination, and accurately model the measurements on annealed samples with a simple two level rate equation, allowing us to extract the trapped-electron lifetimes.

Novel kinetic model in amorphous polymers. Spiropyran-merocyanine system revisited

Abstract: A kinetic model for the description of non-monoexponential decay of unimolecular reactions in amorphous polymers is developed. The thermal decay of the merocyanine (MC) form of 1,3‘,3‘-trimethyl-6-nitrospiro-[2H-1-benzopyran-2,2‘-indoline] (spiropyran, SP) in poly(alkyl methacrylates) is taken as an example. The model assumes that the time dependent first-order rate constant describing the decay relaxes from an initial value k0 to a completely relaxed value k∞ with a relaxation time τm that depends on the matrix. A rate equation similar to the one provided by this model is found in fluorescence quenching either in micelles or in the picosecond range in solution. The fit of the temperature dependent decays of MC to SP with this model is as good as or better than the one obtained by other models such as the sum of exponential terms or the stretched exponential equation. The simple relaxation picture is unable to account for the decay at temperatures far below the glass transition temperature of the polymer....

Femtosecond investigation of charge carrier dynamics in CdSe nanocluster films

Abstract: The charge carrier dynamics in the novel CdSe nanocluster films fabricated by a chemical deposition method was studied by the femtosecond pump–probe measurements. The intensity dependent signals can be well described by a rate equation model. The overall kinetic process is listed as follows: a rapid electron trapping (<1 ps), the Auger recombination, the recombination of electrons in the surface states (∼46 ps) and the long-lived trapped electron–hole recombination. When the cluster radius is as large as 27 nm, an induced transient absorption can be observed. We attribute the induced transient absorption to the formation of the biexcitons or the trapped-carrier-induced Stark effect.

A quantitative comparison of the classical rate-equation model with the carrier heating model on dynamics of the quantum-well laser: the role of carrier energy relaxation, electron-hole interaction, and Auger effect

Abstract: In this paper, a quantitative theoretical comparison of the classical rate-equation model with the carrier heating model for large signal dynamic response of 1.5-/spl mu/m InGaAs-InGaAsP single-mode quantum-well (QW) lasers Is performed. The contributions of carrier energy relaxation, electron-hole interaction, and Auger effect to the nonlinear gain are inspected in detail by a numerical comparison of the two models at room temperature (293 K) and low temperature (50 K). It can be shown that contribution of the carrier heating to the nonlinear gain coefficient is proportional to an effective carrier energy relaxation time, and the contribution of the electron-hole energy exchange time shows a nonlinear relation. Furthermore, the influence of Auger heating on the modulation dynamics is also considered and is found to be indescribable by a single phenomenological nonlinear gain coefficient. The dependence of the nonlinear gain coefficient on the laser emission wavelength of distributed feedback lasers is also demonstrated quantitatively for the first time.

High speed characteristics of VCSELs

Abstract: The high speed characteristics of Vertical Cavity Surface Emitting Lasers (VCSELs) for use in modern high bandwidth fiber optical networks is presented. An equivalent circuit model based on microwave network analyzer S11 measurements is developed. The dynamic operation of multi- transverse mode VCSELs is also investigated. Experimentally, a laser with two orthogonally polarized modes is examined. We show that each of the transverse laser modes may have significantly different rise and fall times. A multimode rate equation model is used to predict the exact pulseshape for each mode. The laser gain is saturated by the total optical intensity, and the sum of the modal powers is shown to have a constant rise and fall time. The system performance in terms of the bit error rate is also investigated. We demonstrate that selective attenuation of the optical modes can lead to an increase in the bit error rate due to polarization partitioning noise.

Stability analysis of semiconductor laser with phase-conjugate feedback

Abstract: The stability of the output power of a semiconductor laser with phase-conjugate feedback (PCF) is studied by numerical simulations based on the rate equations. We investigated the critical reflectivity at which the stable fixed output power evolves into periodic oscillation. As a result, we found that the critical reflectivity shows a periodic structure against the external cavity length and the stability is much enhanced at the periodic peak positions. The stability and dynamic behavior of a semiconductor laser with PCF are compared with those for conventional optical feedback. It is also found that the periods of the nearby peaks correspond to the frequency of the laser relaxation oscillation frequency and the stable peaks for the PCF are located at external lengths completely out of phase from those for the conventional feedback. Linear stability analysis using the rate equations is performed and the theoretical background for the stability is also given.

Master equation analysis of intermolecular energy transfer in multiple-well, multiple-channel unimolecular reactions. I. Basic theory

Abstract: We present a full theoretical analysis of the master-equation formulation of the problem of intermolecular energy transfer in multiple-well, multiple-channel systems. It is shown that the master equation for chemical or thermal activation possesses a unique steady state, that corresponding to the trivial solution. Rate equations local in time and therefore time-independent rate coefficients for the dissociating processes may be obtained only if a state of secular equilibrium exists. For chemically-activated systems, a general state of secular equilibrium may exist which may contain within it a regime wherein there is a well-separated, nontrivial, least negative eigenvalue of the master equation kernel. The dynamics of thermally activated systems are similarly deduced by treating them as chemically activated systems with appropriate modifications to the inhomogeneous source term of the master equation. A degenerate and nondegenerate perturbation theory analysis of the case of rapid thermalization in the vi...

Modulation bandwidth optimisation for unipolar intersubband semiconductor lasers

Abstract: A rate equation analysis of the direct-current modulation response of intersubband semiconductor lasers is reported using a rate equation model for a triple quantum well structure. It is demonstrated that terahertz modulation bandwidths may be achievable due to the picosecond carrier lifetimes which are characteristic of such structures. A novel feature of the modulation response of intersubband semiconductor lasers is the existence of an optimum output power for achieving maximum modulation bandwidth in a given structure. Further optimisation of the modulation performance is achievable via appropriate design of the coupled quantum well structure.

Quantum noise and polarization fluctuations in vertical-cavity surface-emitting lasers

Abstract: We investigate the polarization fluctuations caused by quantum noise in quantum-well vertical-cavity surface-emitting lasers (VCSELs). Langevin equations are derived on the basis of a generalized rate equation model in which the influence of competing gain-loss and frequency anisotropies is included. This reveals how the anisotropies and the quantum-well confinement effects shape the correlations and the magnitude of fluctuations in ellipticity and in the polarization direction. According to our results, all parameters used in the rate equations may be obtained experimentally from precise time-resolved measurements of the intensity and polarization fluctuations in the emitted laser light. To clarify the effects of anisotropies and of quantum-well confinement on the laser process in VCSELs we therefore propose time-resolved measurements of the polarization fluctuations in the laser light. In particular, such measurements allow us to distinguish the effects of frequency anisotropy and of gain-loss anisotropy and would provide data on the spin relaxation rate in the quantum-well structure during cw operation as well as representing a different way of experimentally determining the linewidth enhancement factor $\ensuremath{\alpha}$.

Kinetics of growth of AlAs oxide in selectively oxidized vertical cavity surface emitting lasers

Abstract: The wet oxidation kinetics of AlAs layers of interest in vertical cavity surface emitting laser (VCSEL) fabrication are investigated in detail. The process is modeled as a diffusion-reaction process. For oxidation over a long time interval, variation of the oxidation rate with the variation of the radius of the etched mesa of the VCSEL is observed. A theory has been developed to obtain the rate equation of the oxidation process and the dependence of the oxidation rate on the size of the VCSEL is explained.

Radiation chemistry of aqueous solutions of hydrazine at elevated temperatures . part 2. solutions containing oxygen

Abstract: The rate of reaction for has been measured by pulse radiolysis up to 110°C in aqueous solutions of hydrazine having a pH of 10.3 at room temperature. The values of the kinetic parameters are k 1 =(3.8±0.1)×10 8 dm3 mol -1 s -1 at 20°C and E act =5.6±2.1 kJ mol -1 . This small activation energy is interpreted in terms of the formation of an intermediate adduct N 2 H 3 O 2 which is in a pre-equilibrium with the reactants and whose stability with respect to dissociation back to the reactants decreases with increasing temperature. The rate of the thermal reaction has also been determined up to 110°C by measuring the decrease in k 1 with increasing age of the oxygenated hydrazine solution in order to monitor the depletion of [O 2 ]. The kinetic parameters are k 12 =(1.2±0.8)×10 -3 dm3 mol -1 s -1 at 20°C and E act =70±5 kJ mol -1 . γ-Radiolysis studies show that N 2 H 4 is destroyed in a short chain reaction in oxygenated hydrazine solutions with G(-N 2 H 4 )∝(dose rate) -0.5 , indicating chain termination by radical–radical reactions. Added EDTA shortens the chain but does not alter the form of the rate law, indicating that metal ions present as impurities accelerate the chain-propagating reactions more than the termination steps. In each case the chain length increases as ca. [N 2 H 4 ] 0.5 .

Numerical and theoretical study of the crosstalk in gain clamped semiconductor optical amplifiers

Abstract: A rate equation model of a gain clamped semiconductor optical amplifier (GCSOA) is presented. Both a time-domain and a small-signal analysis of those rate equations are used to investigate the crosstalk between different signal channels. It is shown that the crosstalk of GCSOA's strongly depends on the bit rate of the amplified signals and is lower at both very high bit rates and low bit rates. This crosstalk is proportional with the input power and, approximately, with the amplification.

A capacitance study of the silver(I)/copper displacement reaction

Abstract: Metal displacement (cementation) reactions are usually diffusion controlled and conform to first order kinetics. When a displacement reaction is carried out in a batch reactor, positive deviations from a first order rate plot are commonly observed once the deposit becomes sufficiently thick. It has been suggested that these rate enhancements are the result of changes in deposit structure resulting in increases in surface area. Another theory argues that the rate enhancements are due to turbulence associated with increasing roughness of the deposit. In this paper, an attempt is made to discriminate between these two possibilities by measuring the capacitance of a copper electrode immersed in a silver(I) solution. It was found that no anomalous capacitance changes were observed corresponding to the region in which rate increases were observed. This suggests that turbulence effects, rather than area effects, are responsible for the increased reaction rate. Capacitance measurements were also conducted for the reaction between silver(I) and copper in the presence of cyanide which caused the silver to deposit in a thin uniform layer on the copper surface, thus blocking the displacement reaction. It was found that the capacitance changed very little with time under these circumstances.

Asymptotic behaviour of initially separated a + b(static) 0 reaction-diffusion systems

Abstract: We examine the long-time behaviour of A + B(static) → 0 reaction-diffusion systems with initially separated species A and B. All of our analysis is carried out for arbitrary (positive) values of the diffusion constant D A of particles A and initial concentrations a 0 and b 0 of A's and B's. We derive general formulae for the location of the reaction zone centre, the total reaction rate, and the concentration profile of species A outside the reaction zone. The general properties of the reaction zone are studied with a help of the scaling ansatz. Using the mean-field approximation we find the functional forms of ‘tails’ of the reaction rate R and the dependence of the width of the reaction zone on the external parameters of the system. We also study the change in the kinetics of the system with D B > 0 in the limit D B → 0. Our results are supported by numerical solutions of the mean-field reaction-diffusion equation.

Laser dynamics with excited-state absorption

Abstract: The dynamics of a laser with excited-state absorption at the lasing wavelength is theoretically studied. The model is based on the rate equations for a four-level system. The stationary state is analytically calculated, permitting both the investigation of the laser characteristics and linear stability analysis. The latter shows that, in some conditions, the steady state is not stable in a particular range of pumping rates. However, a stable solution is restored for sufficiently high pumping rates. Stable self-pulsing solutions are obtained by numerical integration of the coupled equations. Also, the transient regimes are numerically analyzed.

Investigation of threshold transition in semiconductor lasers

Abstract: Semiconductor laser threshold transition is investigated by high precision power and linewidth measurements giving specific behavior of linewidth at threshold depending on linewidth enhancement /spl alpha/ factor. An analytical model based on Fokker-Planck equation resolution is proposed for extraction of major laser parameters by fitting simultaneously below and above threshold behaviors. Parameters are extracted for two single-mode semiconductor lasers with different detunings. Comparison with a threshold adapted rate equation model shows identical asymptotic behavior (Schawlow-Townes) for both models but simpler calculations and higher precision at threshold are obtained with the Fokker-Planck method. Detailed investigation of laser phase transition can profit microcavity and surface-emitting laser development by giving unique insight on spontaneous emission evolution and precise noise models.