Showing papers on "Rate equation published in 2009"

Insights into the Kinetics of Semiconductor Nanocrystal Nucleation and Growth

Abstract: A model is presented for the colloidal synthesis of semiconductor nanocrystals capturing the reactions underlying nucleation and growth processes. The model combines an activation mechanism for precursor conversion to monomers, discrete rate equations for formation of small-sized clusters, and continuous Fokker-Planck equation for growth of large-sized clusters. The model allows us to track the temporal evolution of the entire cluster size distribution and compute several experimental observables including mean size and size distribution. The model predicts five distinct regions: generation of monomers, small cluster formation, size distribution focusing due to precursor depletion, pseudo steady state region, and size distribution broadening, with the latter three explicitly reproducing available experimental data at larger cluster sizes. Furthermore, we identify two nondimensional parameter combinations and discuss how these can be used to guide experiments to yield a more rational approach to synthesis modification. Contrary to the common hypothesis that diffusion is essential for size distribution focusing, the model shows that focusing can be achieved under pure reaction control. In addition, the model yields new insights into the synthesis of small nanocrystals with narrow size distributions either by modulation of temperature over the duration of nanocrystal synthesis or by introduction of small quantities of additives that enhance the rate of precursor conversion to monomers. We show that for a given set of reaction parameters, there is an optimum in the duration of high temperature and additive concentration minimizing polydispersity.

Rate equation analysis of efficiency droop in InGaN light-emitting diodes

Abstract: Efficiency droop in InGaN light-emitting diodes (LEDs) is analyzed based on the rate equation model. By using the peak point of the efficiency versus current-density relation as the parameters of the rate equation analysis, internal quantum efficiency and each recombination current at arbitrary current density can be unambiguously determined without any knowledge of A, B, and C coefficients. The theoretical analysis is compared with measured efficiency of a LED sample and good agreement between the model and experiment is found. The investigation of recombination coefficients shows that Auger recombination alone is not sufficient to explain the efficiency droop of InGaN LEDs.

A unified monte carlo treatment of gas-grain chemistry for large reaction networks. i. testing validity of rate equations in molecular clouds

Abstract: In this study, we demonstrate for the first time that the unified Monte Carlo (MC) approach can be applied to model gas-grain chemistry in large reaction networks. Specifically, we build a time-dependent gas-grain chemical model of the interstellar medium, involving about 6000 gas-phase and 200 grain-surface reactions. This model is used to test the validity of the standard and modified rate equation methods in models of dense and translucent molecular clouds and to specify under which conditions the use of the stochastic approach is desirable. Two cases are considered: (1) the surface mobility of all species is due to thermal hopping; (2) in addition to thermal hopping, a temperature-independent quantum tunneling for H and H2 is allowed. The physical conditions characteristic for the core and the outer region of the TMC1 cloud are adopted. The gas-phase rate file RATE 06 together with an extended set of gas-grain and surface reactions is utilized. We found that at temperatures of 25-30 K gas-phase abundances of H2O, NH3, CO, and many other gas-phase and surface species in the stochastic model differ from those in the deterministic models by more than an order of magnitude, at least when tunneling is accounted for and/or diffusion energies are three times lower than the binding energies. In this case, surface reactions, involving light species, proceed faster than accretion of the same species. In contrast, in the model without tunneling and with high binding energies, when the typical timescale of a surface recombination is greater than the timescale of accretion onto the grain, we obtain almost perfect agreement between results of MC and deterministic calculations in the same temperature range. At lower temperatures (~10 K), gaseous and, in particular, surface abundances of most important molecules are not much affected by stochastic processes.

Noise-induced breakdown of the Michaelis-Menten equation in steady-state conditions.

Abstract: The Michaelis-Menten (MM) equation is the basic equation of enzyme kinetics; it is also a basic building block of many models of biological systems. We build a stochastic and microscopic model of enzyme kinetics inside a small subcellular compartment. Using both theory and simulations, we show that intrinsic noise induces a breakdown of the MM equation even if steady-state metabolic conditions are enforced. In particular, we show that (i) given a reaction velocity, deterministic rate equations can severely underestimate steady-state intracellular substrate concentrations and (ii) different reaction schemes which on a macroscopic level are indistinguishable because they are described by the same MM equation obey distinctly different equations in subcellular compartments.

Computed rate coefficients and product yields for c-C5H5 + CH3 --> products.

Abstract: Using quantum chemical methods, we have explored the region of the C6H8 potential energy surface that is relevant in predicting the rate coefficients of various wells and major product channels following the reaction between cyclopentadienyl radical and methyl radical, c-C5H5 + CH3. Variational transition state theory is used to calculate the high-pressure-limit rate coefficient for all of the barrierless reactions. RRKM theory and the master equation are used to calculate the pressure dependent rate coefficients for 12 reactions. The calculated results are compared with the limited experimental data available in the literature and the agreement between the two is quite good. All of the rate coefficients calculated in this work are tabulated and can be used in building detailed chemical kinetic models.

Rate-equation model for the loading-rate-dependent mechanoluminescence of SrAl2O4:Eu2+,Dy3+.

Abstract: The mechanoluminescence (ML) of SrAl2O4:Eu2+,Dy3+ (SAO) phosphors was monitored as a function of its instantaneous loading rate, on which it was found to be strongly dependent The effect of the loading rate on the ML of SAO was investigated in a systematic manner using rate equations involving the loading rate term The rate equations and the experimental data matched well We confirmed that the ML of SAO was created by the change in load rather than by the static load, and that the loading rate determined the shape of the ML versus the time curve in the transient regime

Detailed balance in multiple-well chemical reactions

Abstract: Chemical reactions that involve multiple, interconnected potential wells are of paramount importance in applications of chemical kinetics, particularly combustion and atmospheric chemistry. The only accurate way of determining phenomenological rate constants theoretically for this type of reaction is from the solution of a time-dependent, multiple-well master equation. In this Perspective we address the issue of whether or not (and to what extent) detailed balance is satisfied by rate constants obtained from such solutions. In addressing this issue we discuss a number of related topics, including necessary and sufficient conditions for a system of first-order rate equations to evolve to chemical equilibrium and the relationship between detailed balance and Wegscheider conditions. The assumption of a “near-Boltzmann” distribution in the wells sheds considerable light on the issue at hand. We discuss this approximation in some detail and suggest a quantitative measure of “near-Boltzmann”. It is extremely unlikely that the rate constants of interest satisfy detailed balance exactly (there is no reason to believe that they do). However, the discrepancies are expected to be vanishingly small, as observed in practice.

Quantum rate dynamics for proton transfer reactions in condensed phase: The exact hierarchical equations of motion approach

Abstract: We apply the recently developed Liouville space hierarchical equations of motion (HEOM) method to calculate the quantum rate dynamics for a model system of proton transfer reaction in condensed phase, which consist of a double well coupled to a harmonic bath with the Debye spectral density. The HEOM method provides a new way to directly calculate nonequilibrium reduced system dynamics, and the calculated reaction rate constants compare well with previous numerical exact results. The HEOM method also allows us to perform long time simulations, which enables systematic studies of the reaction dynamics at low frictions. The applicability of perturbative quantum master equations at various orders is also investigated by comparing with numerical exact HEOM results.

Suppression of the stellar enhancement factor and the reaction 85Rb(p,n)85Sr

Abstract: Astrophysical reaction rates are central to tracing changes in the abundances of nuclei by nuclear reactions. They provide the temperature- and density-dependent coefficients entering reaction networks, the large sets of coupled differential equations required to study nucleosynthesis and energy generation in astrophysical environments. The reaction rates are computed from reaction cross sections which, in turn, may be predicted in theoretical models or extracted from experiments. In addition to the difficulties arising in the determination of the cross sections, the conversion to reaction rates is further complicated by modifications of the rates in a hot plasma and the fact that the rates of forward and reverse rate for the same reaction have to be consistent to ensure numerical stability and proper equilibrium abundances at high temperature. Both issues can be addressed at once by accounting for the thermal population of target states which leads to stellar rates obeying a reciprocity relation between forward and reverse rate. Using this reciprocity, knowledge of the rate in only one direction is needed because the other reaction direction can be directly computed from that rate, thus ensuring consistency. For numerical reasons, further elaborated in Sec. IIB, it is usually preferable to start from the rate of a reaction with positive reaction Q value when computing the rate for its inverse reaction. Even more importantly, experimentalists want to determine rates as close as possible to the actual stellar rates, i.e. rates with minimal thermal population effects of the target. Again, it can be argued that this is the case for exothermic reactions. This led to the commonly applied rule that measurements of exothermic reactions are more important than those of endothermic ones. In this paper we show that there is a

Effects of soil properties on the kinetics of desorption of phosphate from Alfisols by anion-exchange resins

Abstract: Phosphorus-desorption rates by anion-exchange resins were best described by three empirical kinetic models: Elovich equation, the parabolic diffusion equation, and the fractional power equation in that order The objective of this study was to determine the relationship between kinetic rate constants from Elovich, fractional power, and parabolic rate equations and soil physical and chemical properties from soils of different lithogenic origins from the Nigerian savanna Phosphorus-desorption patterns included an initial fast reaction, followed by a slow release that continued up to 20 h Particle diffusion was observed to be the rate-limiting step in the kinetic desorption of native P in the soils studied as opposed to ligand exchange or surface reaction The influence of parent material is not prominent due to long history of pedogenesis over the soils The rate coefficients from the Elovich equation, parabolic diffusion equation, and the fractional power model were best predicted from clay, pH, and extractable Al and Fe oxides and therefore exert a profound influence on the rate of P release from the soils These soil properties together explained between 93% and 99% of the variance in the rate coefficients of P desorption from the soils

Lattice model of diffusion-limited bimolecular chemical reactions in confined environments.

Abstract: We study the effect of confinement on diffusion-limited bimolecular reactions within a lattice model where a small number of reactants diffuse among a much larger number of inert particles. When the number of inert particles is held constant, the rate of the reaction is slow for small reaction volumes due to limited mobility from crowding and for large reaction volumes due to the reduced concentration of the reactants. The reaction rate proceeds fastest at an intermediate confinement corresponding to a volume fraction near 50%. We generalize the model to off-lattice systems with hydrodynamic coupling and predict that the optimal reaction rate for monodisperse colloidal systems occurs when the volume fraction is approximately 19%. Finally, we discuss the implications of our model for bimolecular reactions inside cells and the dynamics of confined polymers.

Matrix rheology effects on reaction rim growth II: coupled diffusion and creep model

Abstract: Chemical reactions and phase changes generally involve volume changes. In confined settings this will cause a mechanical deformation of the matrix that surrounds the reaction sites where the volume change takes place. Consequently, mineral reactions and the mechanical response of the rock matrix are coupled. A companion paper in this issue illustrates this coupling with experiments where quartz and olivine react to form enstatite reaction rims under ambient conditions of 1 GPa and 1000 � C. It has been demonstrated that for identical run conditions, the thickness of the reaction rims depends on whether quartz grains are embedded in an olivine matrix or olivine grains are included in a quartz matrix. The experimental conditions, the nature of the results, and the large volume change of the reaction ()6%) leave only viscous creep as a viable matrix response to the reaction progress. A model is developed for this reaction, which combines diffusion of chemical components through the growing rim and viscous creep of the matrix. The resulting rate law for reaction rim growth in spherical geometry shows that the progress rate is proportional to the reaction overstepping and controlled by the slower of the two competing processes; either diffusion or creep. If diffusion is rate limiting the usual linear proportionality between rim growth and ffiffi p results. However, if viscous creep is rate limiting, then the reaction rates are reduced and may become effectively creep controlled. With respect to the experiments in the companion paper it is inferred that the effective viscosity of the two matrix materials, i.e. polycrystalline quartz and olivine, differ by approximately one order of magnitude with the quartz being the stronger one. The absolute values of the inferred viscosities correspond well to published flow laws. The rheological properties of natural rocks are well within the parameter range for which significant mechanical control on reaction rim growth is expected. This implies that for the interpretation of natural reaction rims and corona structures both diffusion and mechanical control need to be considered. In addition the mechanical effect also needs to be considered when interdiffusion coefficients are retrieved from rim growth experiments. This should also be considered for geospeedometry analyses. Furthermore, the control on reaction rate because of slow creep of the matrix is expected to be even more important, compared to the experiments, under colder crustal conditions and may contribute substantially to the frequent observation of only partially completed reactions. We suggest that this phenomenon is referred to as mechanical closure, which may be an important mechanism in the kinetic displacement of the boundaries between the stability fields of phase assemblages.

Modeling Study of the Sorption-Enhanced Reaction Process for CO2 Capture. II. Application to Steam-Methane Reforming

Abstract: In this paper, the reactor model introduced in part I will be verified using the results of an analytical solution for the increase of CH4 conversion over the bed and validated using the results of sorption-enhanced steam-methane reforming laboratory-scale experiments. An experimentally derived rate equation for the steam-methane reforming reaction is used, a literature rate equation for the water−gas shift reaction. An overview of modeling work on the sorption-enhanced reaction process for steam-methane reforming performed by other groups is presented. The CH4 and CO2 profiles obtained from laboratory-scale experiments are quite satisfactorily described using a Freundlich isotherm. A sensitivity analysis shows that both the CH4 and CO2 profiles are sensitive to the adopted isotherm model and its parameters. In addition to that, the CH4 and CO2 profiles are sensitive to the diffusion coefficient. Neither profile is sensitive to the particle size or the heat of adsorption.

Kinetics of Deposition of Cu Thin Films in Supercritical Carbon Dioxide Solutions from a F-Free Copper(II) β -Diketone Complex

Abstract: Kinetics of deposition of Cu thin films in supercritical carbon dioxide solutions from copper bis(di-isobutyrylmethanate) {Cu[(CH 3 ) 2 CH(CO)CH(CO)CH(CH 3 ) 2 ] 2 }, Cu(dibm) 2 ), a F-free copper(II) complex, via hydrogen reduction were studied. A flow-type reaction system was employed to control each deposition parameter independently and at a constant value. Apparent activation energies for Cu growth were determined for a temperature range of 200―260°C as a function of hydrogen concentration. The determined values varied from 0.35 to 0.63 eV and decreased as hydrogen concentration increased. At a deposition temperature of 200°C, growth rate followed a Langmuir-type dependence against Cu(dibm) 2 and hydrogen concentrations, showing first-order dependence at lower concentrations and zero-order dependence at higher concentrations. At a higher deposition temperature of 240°C, no saturation in the growth rate was observed. A Langmuir―Hinshelwood-type growth mechanism was discussed, and a rate equation for growth was proposed, taking into account the temperature dependence of both the rate constant of the rate-determining reaction and adsorption equilibrium constants. The hydrogen concentration dependence of the apparent activation energy for Cu growth was discussed with this rate equation.

Optical limiting for microsecond pulses

Abstract: We present a dynamical theory of nonlinear absorption and propagation of laser pulses with duration in the microsecond time domain. The general theory is applied to fullerene C(60) because of its good optical limiting properties, namely, a rather low ground state absorption and a strong triplet-triplet absorption. It is shown that sequential absorption involving strong triplet-triplet transitions is the major mechanism of nonlinear absorption. The intrinsic hierarchy of time scales makes an adiabatic solution of the coupled rate equations valid, which therefore can be reduced to a single dynamical equation for the ground state population. The slow evolution of this population is defined by an effective rate of population transfer to the triplet state and by the pulse duration. The propagation effect plays an important role in the optical power limiting performance. The intensity of the field as well as the population of the triplet state decreases during the pulse propagation, and a weakened nonlinear sequential two-photon absorption is followed by a linear one-photon absorption which gradually becomes the dominating process. The competition between these qualitatively different processes depends on the field intensity, the length of the absorber, and the concentration. The pulse propagation is studied by solving numerically the two-dimensional paraxial field equation together with the effective rate equation for the ground state population.

Drug Stability and Degradation Studies

Abstract: Publisher Summary This chapter discusses the basic treatments of drug degradation studies, including kinetics, pathways, important factors, and typical practices for assessing both chemical and physical stability of pharmaceutical compounds. Chemical degradation reactions of pharmaceuticals follow the well-established treatments of chemical kinetics. When a chemical reaction starts, the concentrations of reactants and products change with time until the reaction reaches completion or equilibrium. The concentrations of the reactants decrease, while those of the products increase over time. Therefore, the rate of a reaction can be represented either by the decreasing change in the concentration of a reactant or the increasing change in the concentration of a product with respect to time. Many reactions involve more than a single step, and are known as complex reactions. Depending on the reaction schemes, and the magnitude of respective rate constants, the overall kinetics may be approximated by zero-, first- or second-order rate equations. Water is ubiquitously present as atmospheric moisture, and has a profound effect on solid-state reactions. Water can act as a reactant, and be involved in the reaction itself, such as in hydrolytic reactions, and also it is an excellent plasticizer; it increases molecular mobility of reactants and enhances drug degradation.

Time-Resolved Studies of a Rolled-Up Semiconductor Microtube Laser

Abstract: We report on lasing in rolled-up microtube resonators. Time-resolved studies on these semiconductor lasers containing GaAs quantum wells as optical gain material reveal particularly fast turn-on-times and short pulse emissions above the threshold. We observe a strong red-shift of the laser mode during the pulse emission which is compared to the time evolution of the charge-carrier density calculated by rate equations.

Density functional study of the high-temperature oxidation of o-, m- and p-xylyl radicals.

Abstract: Theoretical calculations at the CBS-QB3 level of theory have been performed to investigate the potential energy surface for the reaction of o-, m- and p-xylyl with molecular oxygen. The differences of the relative potential energies for the products and the transition states of o-, m- and p-xylyl with molecular oxygen were found to be within 8.5 kJ/mol at the CBS-QB3 level of theory. Although the reaction of m- and p-xylyl radicals with molecular oxygen have the same reaction pathways and also the same reaction thermochemistry as that of benzyl radicals, the o-xylylperoxy radicals formed by the reaction of o-xylyl + O2 had an additional intramolecular isomerization pathway to form the o-xylyl hydroperoxy radicals. The rate constants and the product branching ratios for the o-xylyl + O2 and its subsequent reactions were evaluated by the RRKM and master equation analysis. Possible roles for these reaction pathways on the combustion of o-xylenes are discussed.

A rigorous foundation of the diffusion-influenced bimolecular reaction kinetics.

Abstract: We formulate a general theory of the diffusion-influenced kinetics of irreversible bimolecular reactions occurring in the low concentration limit. Starting from the classical Liouville equation for the reactants and explicit solvent molecules, a formally exact expression for the bimolecular reaction rate coefficient is derived; the structures of reactant molecules and the sink functions may be arbitrarily complicated. The present theoretical formulation shows clearly how the well-known Noyes and Wilemski-Fixman rate theories are related and can be improved in a systematic manner. The general properties of the rate coefficient such as the long-time behavior and the upper and the lower bounds are analyzed. When the reaction can occur at a range of distance, the non-Markovianity of repeated encounter events between a reactant pair becomes significant and either the Noyes theory or the Wilemski-Fixman theory fails. The present theory provides a practical method for calculating the rate expression for such reactions, which improves significantly on the Wilemski-Fixman theory.

Modeling the temperature characteristics of InAs/GaAs quantum dot lasers

Abstract: A systematic investigation of the temperature characteristics of quantum dot lasers emitting at 1.3 μm is reported. The temperature dependence of carrier lifetime, radiative efficiency, threshold current, differential efficiency, and gain is measured, and compared to the theoretical results based on a rate equation model. The model accurately reproduces all experimental laser characteristics above room temperature. The degradation of laser characteristics with increasing temperature is clearly shown to be associated to the thermal escape of holes from the confined energy levels of the dots toward the wetting layer and the nonradiative recombination therein.

Measurement of the intersystem crossing rate in aluminum tris(8-hydroxyquinoline) and its modulation by an applied magnetic field

Abstract: The rate constant for intersystem crossing in aluminum tris(8-hydroxyquinoline) was measured using the time dependence of the luminescence under high excitation intensity and modeling using a rate equation approach. Under high illumination levels intersystem crossing results in the transfer of singlets into triplets, which due to their long lifetime effectively remove molecules from participating in photoluminescence. The intersystem crossing rate was found to be ∼2.2×104 s−1 at 80 K. The presence of a magnetic field was found to increase the rate constant by ∼10% with applied fields of ∼100 mT.

Energy transfer rates and population inversion of I411/2 excited state of Er3+ investigated by means of numerical solutions of the rate equations system in Er:LiYF4 crystal

Abstract: In this work, we present the spectroscopic properties of LiYF4 (YLF) single crystals activated by high doping of erbium ions. The most important processes that lead to the up-conversion erbium emissions in the infrared region were identified. A time-resolved luminescence spectroscopy technique was employed to measure the luminescence decays and to determine the most important mechanisms involved in the up-conversion processes that populate the S43/2 excited state. A study of the energy transfer up-conversion (ETU) processes in Er:YLF showed that an ETU rate can be obtained from the I411/2 (ETU1) and S43/2 (ETU2) up-conversion luminescence transient analysis, i.e., from best fittings of the acceptor state luminescence. An analysis of the ETU rate dependence on the wavelength and intensity of pulsed laser excitations allowed us to obtain the ETU rate constants from the lower (I413/2) and upper (I411/2) laser levels to use them in the numerical solutions of the rate equation system for the Er-doped YLF cryst...