Showing papers on "Rate equation published in 2016"

Automated prediction of catalytic mechanism and rate law using graph-based reaction-path sampling

Abstract: In a recent article [J. Chem. Phys. 2015, 143, 094106], we introduced a novel graph-based sampling scheme which can be used to generate chemical reaction paths in many-atom systems in an efficient and highly automated manner. The main goal of this work is to demonstrate how this approach, when combined with direct kinetic modeling, can be used to determine the mechanism and phenomenological rate law of a complex catalytic cycle, namely cobalt-catalyzed hydroformylation of ethene. Our graph-based sampling scheme generates 31 unique chemical products and 32 unique chemical reaction pathways; these sampled structures and reaction paths enable automated construction of a kinetic network model of the catalytic system when combined with density functional theory (DFT) calculations of free energies and resultant transition-state theory rate constants. Direct simulations of this kinetic network across a range of initial reactant concentrations enables determination of both the reaction mechanism and the associate...

Rate Law Analysis of Water Oxidation and Hole Scavenging on a BiVO4 Photoanode

Abstract: Spectroelectrochemical studies employing pulsed LED irradiation are used to investigate the kinetics of water oxidation on undoped dense bismuth vanadate (BiVO4) photoanodes under conditions of photoelectrochemical water oxidation and compare to those obtained for oxidation of a simple redox couple. These measurements are employed to determine the quasi-steady-state densities of surface-accumulated holes, ps, and correlate these with photocurrent density as a function of light intensity, allowing a rate law analysis of the water oxidation mechanism. The reaction order in surface hole density is found to be first order for ps 1 nm–2. The effective turnover frequency of each surface hole is estimated to be 14 s–1 at AM 1.5 conditions. Using a single-electron redox couple, potassium ferrocyanide, as the hole scavenger, only the first-order reaction is observed, with a higher rate constant than that for water oxidation. These results are discussed in terms of catalysis by BiV...

Marcus Bell-Shaped Electron Transfer Kinetics Observed in an Arrhenius Plot

Abstract: The Marcus theory of electron transfer predicts a bell-shaped dependence of the reaction rate on the reaction free energy. The top of the “inverted parabola” corresponds to zero activation barrier when the electron-transfer reorganization energy and the reaction free energy add up to zero. Although this point has traditionally been reached by altering the chemical structures of donors and acceptors, the theory suggests that it can also be reached by varying other parameters of the system including temperature. We find here dramatic evidence of this phenomenon from experiments on a fullerene–porphyrin dyad. Following photoinduced electron transfer, the rate of charge recombination shows a bell-shaped dependence on the inverse temperature, first increasing with cooling and then decreasing at still lower temperatures. This non-Arrhenius rate law is a result of a strong, approximately hyperbolic temperature variation of the reorganization energy and the reaction free energy. Our results provide potentially th...

Kinetics of nanocrystal synthesis in a microfluidic reactor: theory and experiment

Abstract: The processes occurring during nanocrystal nucleation and growth are currently not well understood Herein, we theoretically and experimentally investigate the growth kinetics in colloidal nanocrystal synthesis Using a novel microfluidic reactor integrating independent modules for nucleation and growth, we demonstrate the controlled, direct synthesis of high quality nanocrystals in high yield For CdSe nanocrystals, we find that size tuning solely by variation of the reaction time and temperature does not yield product populations of optimal size dispersion or yield Instead, we present an improved method for the synthesis of bespoke nanocrystals that relies on the controlled addition of precise amounts of additional precursor subsequent to nucleation and fine tuning of the reaction time and temperature in the second stage Real-time spectroscopic monitoring of the produced crystals in conjunction with kinetic simulations confirms the close correspondence between the model and the experiment and elegantly quantifies the effects of temperature, concentration, additives and surfactants on conversion, growth and diffusion rates within the model framework We show that the conversion of the precursor to a monomer follows a first order rate law and that the growth rate has a stronger temperature dependence than the conversion rate Moreover, the surfactant concentration retards the reaction by inhibiting diffusion to the growing crystals whilst maintaining a uniform conversion rate Finally, we demonstrate that diphenylphosphine, a common additive in CdSe synthesis, enhances the reaction rate by accelerating precursor conversion

Study of hydrogen isotopes behavior in tungsten by a multi trapping macroscopic rate equation model

Abstract: Density functional theory (DFT) studies show that in tungsten a mono vacancy can contain up to six hydrogen isotopes (HIs) at 300 K with detrapping energies varying with the number of HIs in the vacancy. Using these predictions, a multi trapping rate equation model has been built and used to model thermal desorption spectrometry (TDS) experiments performed on single crystal tungsten after deuterium ions implantation. Detrapping energies obtained from the model to adjust temperature of TDS spectrum observed experimentally are in good agreement with DFT values within a deviation below 10%. The desorption spectrum as well as the diffusion of deuterium in the bulk are rationalized in light of the model results.

Mechanism of dynamic plasma motion in internal modification of glass by fs-laser pulses at high pulse repetition rate.

Abstract: Evolution of free-electron density in internal modification of glass by fs-laser pulses at high pulse repetition rates is simulated based on rate equation model, which is coupled with thermal conduction model in order to incorporate the effect of thermal ionization Model shows that highly absorbing small plasma generated near the geometrical focus moves toward the laser source periodically to cover the region, which is much larger than focus volume The simulated results agree qualitatively with dynamic motion of plasma produced in internal modification of borosilicate glass by fs-laser pulses at 1 MHz through the observation using high-speed video camera The paper also reveals the physical mechanism of the internal modification of glass when heat accumulation is significant

Accurate modeling of high-repetition rate ultrashort pulse amplification in optical fibers.

Abstract: A numerical model for amplification of ultrashort pulses with high repetition rates in fiber amplifiers is presented. The pulse propagation is modeled by jointly solving the steady-state rate equations and the generalized nonlinear Schrodinger equation, which allows accurate treatment of nonlinear and dispersive effects whilst considering arbitrary spatial and spectral gain dependencies. Comparison of data acquired by using the developed model and experimental results prove to be in good agreement.

High-gain polymer optical waveguide amplifiers based on core-shell NaYF4/NaLuF4: Yb3+, Er3+ NPs-PMMA covalent-linking nanocomposites.

Abstract: Waveguide amplifiers have always been significant key components for optical communication. Unfortunately, the low concentration of rare earth ions doped in the host material and the inadequate optimization of the waveguide structure have been the common bottleneck limitations. Here, a novel material, NaYF4/NaLuF4: 20% Yb3+, 2% Er3+ nanoparticle-Polymeric Methyl Methacrylate covalent-linking nanocomposite, was synthesized. The concentrations of Er3+ and Yb3+ doping increased an order of magnitude. Under a 980 nm laser excitation, highly efficient emission at 1.53 μm was obtained. The characteristic parameters of the single mode waveguide were carefully designed and optimized by using a finite difference method. A formulized iteration method is presented for solving the rate equations and the propagation equations of the EYCDWA, and both the steady state behavior and the gain were numerically simulated. The optimal Er3+ and Yb3+ concentrations are 2.8 × 1026 m-3 and 2.8 × 1027 m-3, and the optimal waveguide length is 1.3 cm. Both theoretical and experimental results indicated that, for an input signal power of 0.1 mW and a pump power of 400 mW, a net gain of 15.1 dB at 1530 nm is demonstrated. This result is the highest gain ever reported in polymer-based waveguide amplifiers doped with inorganic Er3+-Yb3+ codoped nanocrystals.

Evaluation of rate law approximations in bottom-up kinetic models of metabolism

Abstract: The mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question. In this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction mass action rate law that removes the role of the enzyme from the reaction kinetics. We utilized in vivo data for the human red blood cell to compare the effect of rate law choices against the backdrop of physiological flux and concentration differences. We found that the Michaelis-Menten rate law with measured enzyme parameters yields an excellent approximation of the full system dynamics, while other assumptions cause greater discrepancies in system dynamic behavior. However, iteratively replacing mechanistic rate laws with approximations resulted in a model that retains a high correlation with the true model behavior. Investigating this consistency, we determined that the order of magnitude differences among fluxes and concentrations in the network were greatly influential on the network dynamics. We further identified reaction features such as thermodynamic reversibility, high substrate concentration, and lack of allosteric regulation, which make certain reactions more suitable for rate law approximations. Overall, our work generally supports the use of approximate rate laws when building large scale kinetic models, due to the key role that physiologically meaningful flux and concentration ranges play in determining network dynamics. However, we also showed that detailed mechanistic models show a clear benefit in prediction accuracy when data is available. The work here should help to provide guidance to future kinetic modeling efforts on the choice of rate law and parameterization approaches.

Modeling blue to UV upconversion in β-NaYF4:Tm3+

Abstract: Samples of 0.01% and 0.3% Tm3+-doped β-NaYF4 show upconverted UV luminescence at 27 660 cm−1 (361 nm) after blue excitation at 21 140 cm−1 (473 nm). Contradictory upconversion mechanisms in the literature are reviewed and two of them are investigated in detail. Their agreement with emission and two-color excitation experiments is examined and compared. Decay curves are analyzed using the Inokuti–Hirayama model, an average rate equation model, and a microscopic rate equation model that includes the correct extent of energy transfer. Energy migration is found to be negligible in these samples, and hence the average rate equation model fails to correctly describe the decay curves. The microscopic rate equation model accurately fits the experimental data and reveals the strength and multipolarity of various interactions. This microscopic model is able to determine the most likely upconversion mechanism.

An advanced reaction model determination methodology in solid-state kinetics based on Arrhenius parameters variation

Abstract: The Arrhenius parameters variation with the conversion degree of reaction is generally due to the overlapping of parallel or consecutive reactions, and the solution of the problem must imply the deconvolution of the overlapping reaction rather than fitting the experimental curve by assuming variable kinetic parameters. The reaction model determination methods are based on the choice of constant Arrhenius parameters and the use of approximations. To solve this major limitation, a new method for the determination of reaction model based on the Arrhenius parameters variation was proposed. This method appears to accurately simulate single-step as well as multi-step reactions kinetics. The proposed method is based on the general rate equation. The method was validated on artificial data calculated for the various dependences of kinetic parameters on conversion. Then, the method was applied for the non-isothermal crystallization kinetics of the amorphous dehydrated Cu4SO4(OH)6, i.e., Cu4SO4O3 to CuO and CuO·CuSO4 in the nano–scale range. The results were compared with the well-known reaction model determination methods and interpreted.

Injection-induced, tunable all-optical gating in a two-state quantum dot laser.

Abstract: We demonstrate a tunable all-optical gating phenomenon in a single-section quantum dot laser. The free-running operation of the device is emission from the excited state. Optical injection into the ground state of the material can induce a switch to emission from the ground state with complete suppression of the excited state. If the master laser is detuned from the ground-state emitting frequency, a periodic train of ground-state dropouts can be obtained. These dropouts act as gates for excited-state pulsations: during the dropout, the gate is opened and gain is made available for the excited state, and the gate is closed again when the dropout ends. Numerical simulations using a rate equation model are in excellent agreement with experimental results.

Modulation response of nanolasers: what rate equation approaches miss

Abstract: Rate equation approaches are a standard method to describe and examine the modulation dynamics of various semiconductor lasers, including nanolasers with high spontaneous emission rates. Using the more complex Bloch equation model we investigate the impact of the internal timescales on the stability and the modulation response. We demonstrate the limitation of rate equation approaches for systems where photon decay rate and polarization decay have similar orders of magnitude.

Kinetic rate laws invariant to scaling the mineral formula unit

Abstract: A modified form of the kinetic rate law for mineral dissolution and precipitation is proposed that is invariant to a scale transformation of the mineral formula unit. The scale factor appears in both the affinity factor determining the extent of disequilibrium and in the prefactor term, which multiplies the affinity factor. The form of the rate law is obtained by imposing invariance of the reactive transport equations on scaling the mineral formula unit, a basic requirement of all kinetic rate laws describing mineral reactions. This requirement is shown to be consistent with the Horiuti-Temkin formulation of the overall reaction rate for stationary-state conditions. The overall rate law is derived by summing a network of elementary reaction steps each weighted by a stoichiometric number giving the rate of the ith intermediate step relative to the overall reaction rate. However, it is noted that current formulations of mineral kinetic rate laws are more empirically based and do not always satisfy the requirement that the elementary reaction steps defining a reaction mechanism sum to form the overall reaction. In addition, there appears to be confusion in the literature between the Temkin average stoichiometric number and the scale factor related to the mineral formula unit, which are shown to be two distinct quantities. Finally, it is noted that in recent numerical simulations modeling sequestration of supercritical CO2 in deep geologic formations, different chemical formulas for oligoclase have been used related by a scale factor of five without taking into account the scale factor in the kinetic rate law. This oversight could result in potentially significantly larger oligoclase dissolution rates, and exaggerated CO2 mineralization through precipitation of dawsonite.

Kinetics of Ge(IV) Extraction Using a Microstructured Membrane Contactor

Abstract: For hydrometallurgical metal extraction, the mass transfer by diffusion is additionally coupled with a chemical reaction of the metal ion with the extractant molecule, usually at the interface. Consequently, the kinetics is either limited by diffusion or chemical reaction (or both, respectively, in a mixed regime). Conventional methods for determining the extraction kinetics often lead to a misinterpretation, especially for fast reactions, and an isolated view of the interfacial reaction is restricted. With a new microcontactor setup, it is possible to perform a comprehensive kinetic analysis with very low sample volumes compared to established methods. Additionally, it is possible to quantify all individual mass transfer resistances and identify the extraction regime with the developed mass transfer model. The chemical reaction part is investigated isolated, to derive rate laws and kinetic constants. The methodology is discussed for the extraction of Ge(IV) from aqueous solutions with the two extractants 5,8-diethyl-7-hydroxydodecan-6-oxime (LIX 63) and 7-(4-ethyl-1-methyloctyl)-8-hydroxyquinoline (Kelex 100). It was found that the extraction with LIX 63 is reaction limited and with Kelex 100 the reaction resistance is in the same order of magnitude as the diffusion resistances. The obtained results provide fundamental kinetic data for the design of solvent extraction equipment.

Thermal Degradation Rate of 2-Amino-2-methyl-1-propanol to Cyclic 4,4-Dimethyl-1,3-oxazolidin-2-one: Experiments and Kinetics Modeling

Abstract: Employing experimental kinetics data collected in this study, a power law rate equation for the thermal degradation of 2-amino-2-methyl-1-propanol (AMP) to 4,4-dimethyl-1,3-oxazolidin-2-one (DMOZD) as a function of amine and CO2 concentration in the solution is introduced. The rate experiments were carried out at 120, 135, and 150 °C. Kinetic data was collected to extract the initial rate equation from aqueous solutions of 1.12, 1.68, 2.24, and 3.36 M, AMP and CO2 loadings from 0.17 to 0.7, molCO2/molAMP. Since the rate equation is based on the initial reactions in the solution, the output from the kinetic model can be used to estimate the thermal degradation rate of AMP as a whole and DMOZD formation rate at the onset of the reaction, as this cyclic compound can be considered as the primary initial thermal degradation product. The power with respect to AMP and CO2 concentration in the kinetic model, and activation energy and pre-exponential factor, were calculated and introduced in this work. AMP degrada...

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Palladium(II)-catalyzed oxidation of l-tryptophan by hexacyanoferrate(III) in perchloric acid medium: a kinetic and mechanistic approach

Abstract: The catalytic effect of palladium(II) on the oxidation of l-tryptophan by potassium hexacyanoferrate(III) has been investigated spectrophotometrically in aqueous perchloric acid medium. A first order dependence in [hexacyanoferrate(III)] and fractional-first order dependences in both [l-tryptophan] and [palladium(II)] were obtained. The reaction exhibits fractional-second order kinetics with respect to [H +]. Reaction rate increased with increase in ionic strength and dielectric constant of the medium. The effect of temperature on the reaction rate has also been studied and activation parameters have been evaluated and discussed. Initial addition of the reaction product, hexacyanoferrate(II), does not affect the rate significantly. A plausible mechanistic scheme explaining all the observed kinetic results has been proposed. The final oxidation products are identified as indole-3-acetaldehyde, ammonium ion and carbon dioxide. The rate law associated with the reaction mechanism is derived.

A kinetic model for GaAs growth by hydride vapor phase epitaxy

Abstract: Precise control of the growth of III-V materials by hydride vapor phase epitaxy (HVPE) is complicated by the fact that the growth rate depends on the concentrations of nearly all inputs to the reactor and also the reaction temperature. This behavior is in contrast to metalorganic vapor phase epitaxy (MOVPE), which in common practice operates in a mass transport limited regime where growth rate and alloy composition are controlled almost exclusively by flow of the Group III precursor. In HVPE, the growth rate and alloy compositions are very sensitive to temperature and reactant concentrations, which are strong functions of the reactor geometry. HVPE growth, particularly the growth of large area materials and devices, will benefit from the development of a growth model that can eventually be coupled with a computational fluid dynamics (CFD) model of a specific reactor geometry. In this work, we develop a growth rate law using a Langmuir-Hinshelwood (L-H) analysis, fitting unknown parameters to growth rate data from the literature that captures the relevant kinetic and thermodynamic phenomena of the HVPE process. We compare the L-H rate law to growth rate data from our custom HVPE reactor, and develop quantitative insight into reactor performance, demonstrating the utility of the growth model.

An Analytical Framework for Studying Small-Number Effects in Catalytic Reaction Networks: A Probability Generating Function Approach to Chemical Master Equations.

Abstract: Cell activities primarily depend on chemical reactions, especially those mediated by enzymes, and this has led to these activities being modeled as catalytic reaction networks. Although deterministic ordinary differential equations of concentrations (rate equations) have been widely used for modeling purposes in the field of systems biology, it has been pointed out that these catalytic reaction networks may behave in a way that is qualitatively different from such deterministic representation when the number of molecules for certain chemical species in the system is small. Apart from this, representing these phenomena by simple binary (on/off) systems that omit the quantities would also not be feasible. As recent experiments have revealed the existence of rare chemical species in cells, the importance of being able to model potential small-number phenomena is being recognized. However, most preceding studies were based on numerical simulations, and theoretical frameworks to analyze these phenomena have not been sufficiently developed. Motivated by the small-number issue, this work aimed to develop an analytical framework for the chemical master equation describing the distributional behavior of catalytic reaction networks. For simplicity, we considered networks consisting of two-body catalytic reactions. We used the probability generating function method to obtain the steady-state solutions of the chemical master equation without specifying the parameters. We obtained the time evolution equations of the first- and second-order moments of concentrations, and the steady-state analytical solution of the chemical master equation under certain conditions. These results led to the rank conservation law, the connecting state to the winner-takes-all state, and analysis of 2-molecules M-species systems. A possible interpretation of the theoretical conclusion for actual biochemical pathways is also discussed.

Rate equation of steam-methane reforming reaction on Ni-YSZ cermet considering its porous microstructure

Abstract: The steam-methane reforming reaction on a Ni-YSZ (yttria-stabilized zirconia) cermet was experimentally investigated in the temperature range of 650 to 750°C. We examined the effects of the partial pressures of methane and steam in the supply gas on the reaction rate. The porous microstructure of the Ni-YSZ cermet was quantified using an FIB-SEM technique. A power-law-type rate equation was obtained on the basis of the unit surface area of the Ni-pore contact surface in the cermet. The kinetics indicated a strong positive dependence on the methane partial pressure and a negative dependence on the steam partial pressure, in good agreement with the literature. The obtained rate equation successfully predicted the reaction characteristics of Ni-YSZ cermets having different microstructures.