Showing papers on "Rate equation published in 2017"
TL;DR: In this paper, the authors presented a study of kinetics of soybean methanolysis using CKD as a heterogeneous catalyst, where all reactions took place at a constant methanol to oil molar ratio of 12:1 and catalyst loading of 3.5%.
Abstract: Biodiesel may be produced through transesterification reaction between triglycerides and light alcohols in presence of different catalysts. This paper presents a study of kinetics of soybean methanolysis using cement kiln dust (CKD) as a heterogeneous catalyst. All reactions took place at a constant methanol to oil molar ratio of 12:1 and catalyst loading of 3.5%. The study consists of three phases; the first one is to consider the reaction following irreversible homogeneous kinetic models (1st and 2nd orders) due to using high excess of methanol. The second is to add the backward reaction term to the power law models. Finally, models for heterogeneous catalysts such as Eley–Rideal and Langmuir–Hinshelwood models are suggested to describe reaction kinetics. Least squares method, Runge–Kutta methods for ordinary differential equations and Levenberg–Marquardt algorithm for minimizing objective function were used to obtain the parameters of each suggested model in each phase. Calculation of determination coefficient (R 2 ) and minimization of squared error summation method were used to determine which model is the best one to fit the experimental data. Eley–Rideal kinetic model was the best model amongst the suggested models. Fisher and Chi-square criteria were used to check the reliability of generated rate equation. The rate differential equation was solved to obtain the main engineering factors controlling the reaction.
59 citations
TL;DR: In this paper, a mesoscopic model of a chemically active colloidal particle which on certain parts of its surface promotes chemical reactions in the surrounding solution is studied, in which only electrically neutral species are present in the solution and on chemical reactions which are described by first order kinetics.
Abstract: We study a mesoscopic model of a chemically active colloidal particle which on certain parts of its surface promotes chemical reactions in the surrounding solution. For reasons of simplicity and conceptual clarity, we focus on the case in which only electrically neutral species are present in the solution and on chemical reactions which are described by first order kinetics. Within a self-consistent approach we explicitly determine the steady state product and reactant number density fields around the colloid as functionals of the interaction potentials of the various molecular species in solution with the colloid. By using Teubner's reciprocal theorem, this allows us to compute and to interpret -- in a transparent way in terms of the classical Smoluchowski theory of chemical kinetics -- the external force needed to keep such a catalytically active colloid at rest (\textit{stall} force) or, equivalently, the corresponding velocity of the colloid \textit{if} it is free to move. We use the particular case of triangular-well interaction potentials as a benchmark example for applying the general theoretical framework developed here. For this latter case, we derive explicit expressions for the dependences of the quantities of interest on the diffusion coefficients of the chemical species, the reaction rate constant, the coverage by catalyst, the size of the colloid, as well as on the parameters of the interaction potentials. These expressions provide a detailed picture of the phenomenology associated with catalytically-active colloids and self-diffusiophoresis.
59 citations
TL;DR: For both systems, the corresponding large deviations are calculated and it is shown that under the condition of detailed balance, the large deviations enables us to derive a non-linear relation between thermodynamic fluxes and free energy driving force.
Abstract: We study stochastic interacting particle systems that model chemical reaction networks on the microscopic scale, converging to the macroscopic reaction rate equation. One abstraction level higher, we also study the ensemble of such particle systems, converging to the corresponding Liouville transport equation. For both systems, we calculate the corresponding large deviations and show that under the condition of detailed balance, the large deviations enables us to derive a non-linear relation between thermodynamic fluxes and free energy driving force.
57 citations
TL;DR: It is demonstrated that the relative composition of free electrons and H2O2 in the optical breakdown plasma may be controlled by changing the pulse energy and duration, which may make it possible to tune the size and dispersity of AuNPs and other metal nanoparticle products synthesized with femtosecond laser-based methods.
Abstract: Free electrons and H2O2 formed in an optical breakdown plasma are found to directly control the kinetics of [AuCl4]− reduction to form Au nanoparticles (AuNPs) during femtosecond laser-assisted synthesis of AuNPs. The formation rates of both free electrons and H2O2 strongly depend on the energy and duration of the 800 nm laser pulses over the ranges of 10–2400 μJ and 30–1500 fs. By monitoring the conversion of [AuCl4]− to AuNPs using in situ UV–vis spectroscopy during laser irradiation, the first- and second-order rate constants in the autocatalytic rate law, k1 and k2, were extracted and compared to the computed free electron densities and experimentally measured H2O2 formation rates. For laser pulse energies of 600 μJ and lower at all pulse durations, the first-order rate constant, k1, was found to be directly proportional to the theoretically calculated plasma volume, in which the electron density exceeds the threshold value of 1.8 × 1020 cm–3. The second-order rate constant, k2, was found to correlate...
48 citations
TL;DR: In this article, a mathematical formalism of nonequilibrium thermodynamics for chemical reaction models with N species, M reactions, and general rate law was studied, and a generalized macroscopic chemical free energy function and its associated balance equation with nonnegative source and sink were presented.
Abstract: This paper studies a mathematical formalism of nonequilibrium thermodynamics for chemical reaction models with N species, M reactions, and general rate law. We establish a mathematical basis for J. W. Gibbs’ macroscopic chemical thermodynamics under G. N. Lewis’ kinetic law of entire equilibrium (detailed balance in nonlinear chemical kinetics). In doing so, the equilibrium thermodynamics is then naturally generalized to nonequilibrium settings without detailed balance. The kinetic models are represented by a Markovian jumping process. A generalized macroscopic chemical free energy function and its associated balance equation with nonnegative source and sink are the major discoveries. The proof is based on the large deviation principle of this type of Markov processes. A general fluctuation dissipation theorem for stochastic reaction kinetics is also proved. The mathematical theory illustrates how a novel macroscopic dynamic law can emerges from the mesoscopic kinetics in a multi-scale system.
47 citations
TL;DR: Based on the thermodynamics properties of the Fe-CO-CO 2 system, CO/CO 2 mixtures in different volume ratios can decouple the reduction of Fe 2 O 3 into three relatively independent steps as mentioned in this paper.
45 citations
TL;DR: In this paper, a rate equation for the photocatalytic reaction has been developed from the experimental results obtained with the single stack operated under different ethanol partial pressures, light irradiation intensities and contact times.
Abstract: Silicone microreactors containing microchannels of 500 µm width in a single or triple stack configuration have been manufactured, coated with an Au/TiO2 photocatalyst and tested for the photocatalytic production of hydrogen from water-ethanol gaseous mixtures under UV irradiation. Computational fluid dynamics (CFD) simulations have revealed that the design of the distributing headers allowed for a homogeneous distribution of the gaseous stream within the channels of the microreactors. A rate equation for the photocatalytic reaction has been developed from the experimental results obtained with the single stack operated under different ethanol partial pressures, light irradiation intensities and contact times. The hydrogen photoproduction rate has been expressed in terms of a Langmuir-Hinshelwood-type equation that accurately describes the process considering that hydrogen is produced through the dehydrogenation of ethanol to acetaldehyde. This equation incorporates an apparent rate constant (kapp) that has been found to be proportional to the intrinsic kinetic rate constant (k), and that depends on the light intensity (I) as follows: kapp = k·I0.65. A three-dimensional isothermal CFD model has been developed in which the previously obtained kinetic equation has been implemented. The model adequately describes the production of hydrogen of both the single and triple stacks. Moreover, the specific hydrogen productions (i.e. per gram of catalyst) are very close for both stacks thus suggesting that the scaling-up of the process could be accomplished by simply numbering-up. However, small deviations between the experimental and predicted hydrogen production suggest that a fraction of the radiation is absorbed by the microreactor components which should be taken into account for scaling-up purposes.
40 citations
TL;DR: In this paper, the dissolution rate of a nuclear waste glass is investigated under high flow conditions such that saturation with respect to alteration products is avoided. But, it appears that a single rate constant, an intrinsic rate constant is consistent with the data.
35 citations
TL;DR: In this article, the polarization of the electronic and nuclear spin in a single nitrogen vacancy center in diamond was discussed, and a rate equation model was formulated to explain the effect of the laser pulse on the spin system.
Abstract: Initializing a set of qubits to a given quantum state is a basic prerequisite for the physical implementation of quantum-information protocols. Here, we discuss the polarization of the electronic and nuclear spin in a single nitrogen vacancy center in diamond. Our initialization scheme uses a sequence of laser, microwave and radio-frequency pulses, and we optimize the pumping parameters of the laser pulse. A rate equation model is formulated that explains the effect of the laser pulse on the spin system. We have experimentally determined the population of the relevant spin states as a function of the duration of the laser pulse by measuring Rabi oscillations and Ramsey-type free-induction decays. The experimental data have been analyzed to determine the pumping rates of the rate equation model.
34 citations
TL;DR: In this paper, a Langmuir-Hinshelwood-type equation of the electron-hole pair is derived for all light intensity values and reproduce the three typical dependences of reaction rate on light intensity.
31 citations
TL;DR: In this article, a reaction rate model for a unit reaction area in Ni-YSZ anodes of solid oxide fuel cells (SOFCs) has been proposed for analytical analysis of ammonia-fed SOFCs.
TL;DR: In this article, boundary layer flow of carbon nanotubes over a curved stretching surface is examined and analyzed for different involved parameters, such as temperature, concentration, skin friction coefficient and Nusselt number.
Abstract: Present analysis examines boundary layer flow of carbon nanotubes over a curved stretching surface. Instead of classical Fourier law we employed Cattaneo-Christov heat flux theory. The heterogeneous reaction taking place on the wall surface are given by isothermal cubic autocatalytic kinetics. The homogeneous reaction occurring in the ambient fluid are governed by first order kinetics. Appropriate transformations are employed to obtain system of nonlinear ordinary differential equations. Convergent series solution are obtained. Single and multi wall carbon nanotubes are used. Water is taken as a base fluid. Fluid flow, temperature, concentration, skin friction coefficient and Nusselt number are examined and analyzed for different involved parameters.
TL;DR: In this paper, a framework that enables finite-element modeling of nucleation, growth, and amorphization processes in phase-change memory devices using a single rate equation that tracks evolution of local crystal density at each mesh point is presented.
Abstract: We have constructed a framework that enables finite-element modeling of nucleation, growth, and amorphization processes in phase-change memory devices using a single rate equation that tracks evolution of local crystal density at each mesh point. The rate equation, current continuity equation, and Fourier heat transfer equation are solved simultaneously to perform electro-thermal simulations that capture the device dynamics during set and reset operations. The functionality of this framework is demonstrated through simulation of various set and reset operations and consecutive set/reset cycles of a mushroom cell using temperature and crystallinity dependent parameters for Ge2Sb2Te5.
TL;DR: In this paper, a hierarchical multiscale approach based on a micro-kinetic model enabling to predict temperature, pressure and species generated during the thermite reaction of Al nanoparticles mixed with CuO nanoparticles is presented.
TL;DR: In this article, a proper mathematical model allows the utilization of the differential and/or the integral methods of kinetic analysis, which can take into account not only the momentum and the mass balances, but also the radiative transfer equation.
TL;DR: In this article, the reduction of Fe2O3 by H2 was conducted in a thermogravimetric analyzer at 973 − 1172 K. The activation energy is 36.74 − 1.09 −kJ−1.
Abstract: Low-grade hydrogen-containing gases can be converted into high-value pure hydrogen by chemical-looping hydrogen generation. Iron-based oxygen carrier is believed to be the most suitable oxygen carrier for CLHG. It is essential to investigate the reduction mechanism and kinetics of Fe2O3 with hydrogen. The reduction of Fe2O3 by H2 was conducted in a thermogravimetric analyzer at 973–1172 K. The phase analysis of reduction products in different reduction stages illustrated that Fe2O3 → Fe3O4 and Fe3O4 → FeO proceed simultaneously; hence, the reduction process is a two-step reaction, in the sequence of Fe2O3 → FeO and FeO → Fe. To investigate the reaction mechanisms for the two steps, the Hancock–Sharp method and the nonlinear fitting approach were applied to select the kinetic models. The reaction mechanisms of Fe2O3 → FeO can be described by nucleation and growth model. The activation energy is 36.74 ± 1.09 kJ mol−1, and reaction rate equation derived from Arrhenius law is estimated for Fe2O3 → FeO. As for FeO → Fe, the first stage is controlled by the phase-boundary reaction, and the oxygen diffusion affects the last stage of the reduction process.
TL;DR: In this article, the authors investigated the distribution of reaction rate during convective heat transfer with endothermic chemical reaction in channel using a 2D model and found that the reaction rate near wall was much higher than that in the core flow region, and there was a dramatic increase in reaction rate in very thin layer near the wall.
TL;DR: This work uses an integrated probability flux balance method to derive the cNESS turnover rate for a conformation-modulated enzymatic reaction, and extends the traditional Michaelis-Menten rate equation to a generalized form, which includes non-MM corrections induced by conformational population currents within combined cyclic kinetic loops.
Abstract: In a conformational nonequilibrium steady state (cNESS), enzyme turnover is modulated by the underlying conformational dynamics. On the basis of a discrete kinetic network model, we use an integrated probability flux balance method to derive the cNESS turnover rate for a conformation-modulated enzymatic reaction. The traditional Michaelis–Menten (MM) rate equation is extended to a generalized form, which includes non-MM corrections induced by conformational population currents within combined cyclic kinetic loops. When conformational detailed balance is satisfied, the turnover rate reduces to the MM functional form, explaining its general validity. For the first time, a one-to-one correspondence is established between non-MM terms and combined cyclic loops with unbalanced conformational currents. Cooperativity resulting from nonequilibrium conformational dynamics can be achieved in enzymatic reactions, and we provide a novel, rigorous means of predicting and characterizing such behavior. Our generalized M...
TL;DR: The H-atom product yields of the C(1D) + CH4 reaction agree with the results of earlier crossed-beam experiments at higher collision energy, and comparison with earlier work involving the same singlet C3H6 potential energy surface allows conclusions to be drawn.
Abstract: The reactions of atomic carbon in its first excited 1D state with both CH4 and C2H6 have been investigated using a continuous supersonic flow reactor over the 50–296 K temperature range. C(1D) atoms were generated in situ by the pulsed laser photolysis of CBr4 at 266 nm. To follow the reaction kinetics, product H atoms were detected by vacuum ultraviolet laser-induced fluorescence at 121.567 nm. Absolute H-atom yields for both reactions were determined by comparison with the H-atom signal generated by the reference C(1D) + H2 reaction. Although the rate constant for the C(1D) + CH4 reaction is in excellent agreement with earlier work at room temperature, this process displays a surprising reactivity increase below 100 K. In contrast, the reactivity of the C(1D) + C2H6 system decreases as the temperature falls, obeying a capture-type rate law. The H-atom product yields of the C(1D) + CH4 reaction agree with the results of earlier crossed-beam experiments at higher collision energy. Although no previous dat...
TL;DR: In this paper, the authors demonstrate the strong resonant two photon absorption coefficient ≈71 ± 5 cm/GW at 532 nm in α-NiMoO4 nanoparticles prepared by a facile hydrothermal method, which suggests that they can be utilized as passive optical limiters.
Abstract: In this manuscript, we demonstrate the strong resonant two photon absorption coefficient ≈71 ± 5 cm/GW at 532 nm in α-NiMoO4 nanoparticles prepared by a facile hydrothermal method. Strikingly, we have obtained the optical limiting onset threshold fluence (FON) of 36 mJ/cm2 for the linear transmittance of 0.64 with an excellent two photon absorption cross section (38 × 10−45 cm4 s), which suggests that they can be utilized as passive optical limiters. To explain the observed effects, we present a two-level rate equation model and numerically simulated the Z-scan peak shape, which is in good agreement with the experimental data. Further, we also show the normalized population density of the carriers in excited and ground states.
TL;DR: In this article, a base-catalyzed hydrolysis of coumalic acid (COU) in binary aqueous-methanol and acyclic acid mixtures has been studied kinetically at a temperature range from 283 to 313 K.
TL;DR: In this paper, the authors examined in detail the rates of energy transfer relevant to the 5I5 → 5I6 transition (at 3930nm) in Ho3+-doped InF3 glass as a function of the HO3+ concentration.
TL;DR: In this paper, the authors describe the kinetics and thermodynamics of copolymers undergoing recombination reactions, which are important for prebiotic chemistry, and compare the predictions of both approaches for the relaxation of thermodynamic quantities towards equilibrium.
Abstract: We describe the kinetics and thermodynamics of copolymers undergoing recombination reactions, which are important for prebiotic chemistry. We use two approaches: the first one, based on chemical rate equations and the mass-action law describes the infinite size limit, while the second one, based on the chemical master equation, describes systems of finite size. We compare the predictions of both approaches for the relaxation of thermodynamic quantities towards equilibrium. We find that for some choice of initial conditions, the entropy of the sequence distribution can be lowered at the expense of increasing the entropy of the length distribution. We consider mainly energetically neutral reactions, except for one simple case of non-neutral reactions.
TL;DR: In this paper, a simple and interesting method is presented for analyzing the effect of adsorbent mass on the rate of adsorption process, which is based on the plot of the normalized adsorbed amount q e - q q e, versus the normalized time scale t [ m ] n.
TL;DR: It is shown that for lasers with highly damped relaxation oscillations, such resonances can be obtained and lead to spontaneous mode-locking and two different laser types are analysed experimentally yielding qualitatively identical dynamics.
Abstract: Multiple time scales appear in many nonlinear dynamical systems. Semiconductor lasers, in particular, provide a fertile testing ground for multiple time scale dynamics. For solitary semiconductor lasers, the two fundamental time scales are the cavity repetition rate and the relaxation oscillation frequency which is a characteristic of the field-matter interaction in the cavity. Typically, these two time scales are of very different orders, and mutual resonances do not occur. Optical feedback endows the system with a third time scale: the external cavity repetition rate. This is typically much longer than the device cavity repetition rate and suggests the possibility of resonances with the relaxation oscillations. We show that for lasers with highly damped relaxation oscillations, such resonances can be obtained and lead to spontaneous mode-locking. Two different laser types--a quantum dot based device and a quantum well based device-are analysed experimentally yielding qualitatively identical dynamics. A rate equation model is also employed showing an excellent agreement with the experimental results.
TL;DR: This work presents the highest repetition rate and shortest pulse width which are achieved by an electric-optic LGS Q-switching at the wavelength of 1.34 μm, and it enriches the material categories for generating the high repetition rate pulsed laser.
Abstract: An electro-optically Q-switched pulsed laser at 134 μm with a repetition rate of 100 kHz applying optically active langasite (La3Ga5SiO14) crystal has been reported With Nd:YVO4 as laser crystal, the electro-optically Q-switched pulsed lasers were obtained with the maximum repetition rate of 100 kHz, maximum average output power of 242 W, and a minimum pulse width of 24 ns Based on the theory of rate equations, the optimal pulse energy of the electro-optical Q-switching could be calculated The experimental results have been found to be matched well with the theoretical calculations To the best of our knowledge, this work presents the highest repetition rate and shortest pulse width which are achieved by an electric-optic LGS Q-switching at the wavelength of 134 μm, and it enriches the material categories for generating the high repetition rate pulsed laser
TL;DR: An efficient approach to obtain the branching ratio from a given set of rate equations is introduced, derived from a recently proposed rate constant matrix contraction (RCMC) method, and termed full‐ RCMC (f‐RCMC).
Abstract: The branching ratio of unimolecular decomposition can be evaluated by solving the rate equations Recent advances in automated reaction path search methods have enabled efficient construction of the rate equations based on quantum chemical calculations However, it is still difficult to solve the rate equations composed of hundreds or more elementary steps This problem is especially serious when elementary steps that occur in highly different timescales coexist In this article, we introduce an efficient approach to obtain the branching ratio from a given set of rate equations It has been derived from a recently proposed rate constant matrix contraction (RCMC) method, and termed full-RCMC (f-RCMC) The f-RCMC gives the branching ratio without solving the rate equations Its performance was tested numerically for unimolecular decomposition of C3 H5 and C4 H5 Branching ratios obtained by the f-RCMC precisely reproduced the values obtained by numerically solving the rate equations It took about 95 h to solve the rate equations of C4 H5 consisting of 234 elementary steps In contrast, the f-RCMC gave the branching ratio in less than 1 s The f-RCMC would thus be an efficient alternative of the conventional kinetic simulation approach © 2016 Wiley Periodicals, Inc
TL;DR: In this article, a kinetic model derived from the classical Sestak-Berggren equation was established to simulate the isothermal gasification process of coal char with different partial pressures of H 2 O, CO 2 and their mixtures.
27 Nov 2017
TL;DR: In this article, a rate equation model was used to analyze the competition between the dark exciton pseudospin relaxation and the decay of the light exciton population into the localized states.
Abstract: Optical orientation of localized/bound excitons is shown to be effectively enhanced by the application of magnetic fields as low as 20 mT in monolayer WS2. At low temperatures, the evolution of the polarization degree of different emission lines of monolayer WS2 with increasing magnetic fields is analyzed and compared to similar results obtained on a WSe2 monolayer. We study the temperature dependence of this effect up to K for both materials, focusing on the dynamics of the valley pseudospin relaxation. A rate equation model is used to analyze our data and from the analysis of the width of the polarization dip in magnetic field we conclude that the competition between the dark exciton pseudospin relaxation and the decay of the dark exciton population into the localized states are rather different in these two materials which are representative of the two extreme cases for the ratio of relaxation rate and depolarization rate.
TL;DR: In this article, a method for the identification of the reaction kinetic model using isothermal calorimetric data and additional measurement of the rate of pressure change in a constant volume of a calorific vessel is described.