Showing papers on "Rate equation published in 2020"

Optical cycling, radiative deflection and laser cooling of barium monohydride (BaH)

Abstract: We present the first experimental demonstration of radiation pressure force deflection and direct laser cooling for barium monohydride (BaH) molecules resulting from multiple photon scattering. Despite a small recoil velocity (2.7 mm/s) and a long excited state lifetime (137 ns), we use 1060 nm laser light exciting the $X\rightarrow A$ electronic transition of BaH to deflect a cryogenic buffer-gas beam and reduce its transverse velocity spread. Multiple experimental methods are employed to characterize the optical cycling dynamics and benchmark theoretical estimates based on rate equation models as well as solutions of the Lindblad master equation for the complete multilevel system. Broader implications for laser cooling and magneto-optical trapping of heavy-metal-containing molecules with narrow transition linewidths are presented. Our results pave the way for producing a new class of ultracold molecules -- alkaline earth monohydrides -- via direct laser cooling and trapping, opening the door to realizing a new method for delivering ultracold hydrogen atoms (Lane 2015 \textit{Phys. Rev. A} 92, 022511).

Passively Q-switched near-infrared lasers with bismuthene quantum dots as the saturable absorber

Abstract: Bismuthene quantum dots (Bi-QDs) were synthesized via the liquid phase exfoliation (LPE) method for the passive Q-switching operation in near-infrared (NIR) region. The nonlinear optical properties of the prepared Bi-QDs were investigated by the open-aperture Z-scan technology. The modulation depths were 18.1% and 5.1% at 1.06 and 1.34 µm, respectively. Based on the Bi-QDs saturable absorber, passively Q-switched Nd:GdVO4 lasers operating at 4F3/2 → 2I11/2 and 4F3/2 → 2I13/2 transitions were demonstrated, showing the wideband optical modulation in NIR regime. For the 4F3/2 → 2I13/2 transition lasing at 1.34 µm, the shortest pulse duration of 155 ns was obtained with a repetition rate of 457 kHz. With respect to the 4F3/2 → 2I11/2 transition at 1.06 µm, the minimum pulse duration was 150 ns with a repetition rate of 424 kHz, leading to a single pulse energy of 261 nJ and a peak power of 1.68 W. In addition, the ground state absorption cross section and the excited state absorption cross section of Bi-QDs were also investigated for the first time. The impact of the excited state lifetime on the output parameters was numerically stimulated by the coupled rate equations. Our work confirmed that the trap state in Bi-QDs played an important role in the pulse generation mechanism.

Prediction of reversible lithium plating with a pseudo-3D lithium-ion battery model

Abstract: Fast charging of lithium-ion batteries remains one of the most delicate challenges for the automotive industry, being seriously affected by the formation of lithium metal in the negative electrode. Here we present a physicochemical pseudo-3D model that explicitly includes the plating reaction as side reaction running in parallel to the main intercalation reaction. The thermodynamics of the plating reaction are modeled depending on temperature and ion concentration, which differs from the often-used assumption of a constant plating condition of 0 V anode potential. The reaction kinetics are described with an Arrhenius-type rate law parameterized from an extensive literature research. At low temperatures not only the main processes (intercalation and solid-state diffusion) become slow, but also the plating reaction itself becomes slower. Using this model, we are able to predict typical macroscopic experimental observables that are indicative of plating, that is, a voltage plateau during discharge and a voltage drop upon temperature increase. A spatiotemporal analysis of the internal cell states allows a quantitative insight into the competition between intercalation and plating. Finally, we calculate operation maps over a wide range of C-rates and temperatures that allow to assess plating propensity as function of operating condition.

Rate Equation Modeling of Interband Cascade Lasers on Modulation and Noise Dynamics

Abstract: This work presents a rate equation model for interband cascade lasers, which is used for investigating modulation dynamics and optical noise properties. Through standard small-signal analysis of the rate equations, we analytically derive the resonance frequency, the damping factor, the relative intensity noise (RIN), and the frequency noise (FN) of the interband cascade lasers. It is shown that more cascading stages are beneficial for reaching a broad modulation bandwidth at a low pump current. On the other hand, fewer cascading stages are favorable to achieve low-RIN and low-FN (or narrow-linewidth) laser emission.

Two-photon absorption laser induced fluorescence: rate and density-matrix regimes for plasma diagnostics

Abstract: Two-photon Absorption Laser Induced Fluorescence (TALIF) technique employing nanosecond lasers is often used to measure space- and time-resolved distributions of key atomic and molecular radicals in reactive environments such as plasmas and combustions. Although the technique was applied for about four decades, particularly in high pressure non-equilibrium plasmas accurate measurements of species densities remain challenging. With atomic oxygen as an example, central aspects of the technique including the role of photon statistics and line profiles on the two-photon absorption rates, selection rules, spatial and temporal resolutions, photolytic and quenching effects, and absolute calibration methods are discussed. Simulations using rate equations which include non-depletion regime, 3-level and 6-level models are compared and criteria for non-saturation regimes are given for low- and high-pressure plasmas. Solutions of the density-matrix model, which include coherent excitation and Stark detuning phenomena, and the rate equation model are compared. The validity criteria for non-depletion and photolytic-free regimes and rate models are given. The nanosecond TALIF quench-free regime at high laser intensities is investigated using the density-matrix model. The two-photon cross-sections for O, H and N atomic radicals and their ratio with Kr and Xe rare gases used for calibrations are revisited and recommendations are proposed. For TALIF applying ultrafast lasers, the appropriate model for the fluorescence probability is discussed.

Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures.

Abstract: We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradient-flow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailed-balance steady state. The limit of large volumes is studied in the sense of evolutionary $$\Gamma $$ -convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels.

Time-Dependent Differential and Integral Quantum Yields for Wavelength-Dependent [4+4] Photocycloadditions.

Abstract: The [4+4] photocycloaddition of anthracene is one of most relevant photoreactions and is widely applied in materials science, as it allows to remote-control soft matter material properties by irradiation. However, highly energetic UV irradiation is commonly applied, which limits its application. Herein, the wavelength dependence of the photodimerization of anthracene is assessed for the first time, revealing that the reaction is induced just as effectively with mild visible light (410 nm). To fully establish [4+4] cycloadditions within defined chemical environments, a conceptual framework for the solution kinetics of the photo-dimerization up to long reaction times is established by developing a novel photoreaction rate law that is dependent on individual rate coefficients of the key reaction steps. These coefficients can be determined based on low conversion photochemical experiments. Both differential and integral quantum yields can subsequently be predicted that are strongly time-dependent, highlighting the need for a detailed reaction pathway analysis. The presented approach simplifies a complex photochemical scenario, making the photochemical anthracene dimerization, or potentially any other photochemical dimerization, amenable to a time-dependent understanding at the elementary reaction level.

A quantum optics approach to photoinduced electron transfer in cavities

Abstract: We study a simple model for photoinduced electron transfer reactions for the case of many donor-acceptor pairs that are collectively and homogeneously coupled to a photon mode of a cavity. We describe both coherent and dissipative collective effects resulting from this coupling within the framework of a quantum optics Lindblad master equation. We introduce a method to derive an effective rate equation for electron transfer, by adiabatically eliminating donor and acceptor states and the cavity mode. The resulting rate equation is valid both for weak and strong coupling to the cavity mode, and describes electronic transfer through both the cavity coupled bright states and the uncoupled dark states. We derive an analytic expression for the instantaneous electron transfer rate that depends non-trivially on the time-varying number of pairs in the ground state. We find that under proper resonance conditions, and in the presence of an incoherent drive, reaction rates can be enhanced by the cavity. This enhancement persists, and can even be largest, in the weak light-matter coupling regime. We discuss how the cavity effect is relevant for realistic experiments.

Auger-type process in ultrathin ReS2

Abstract: The dramatic enhancement of charge carrier interaction makes many-body effects of great prominence in two-dimensional materials. Here we report the defect-assisted Auger scattering combined with band-to-band Auger recombination as playing the dominant recovery mechanism in the charge carriers of atomically thin-layered ReS2. Time resolved transient absorption spectra investigation reveals two different decay processes over the visible and near- infrared range, which is attributed to the shallow and deep defects introduced by the existence of sulfur (S) vacancy. A rate equation system is invoked to rationalize our peculiar pump and temperature dependence of carrier dynamics quantitatively. These findings provide theoretical insights into the significant role played by nonradiative Auger processes and may pave the way for the development of diverse ReS2-based high performance photonic and optoelectronic devices.

Time Fractional Fisher–KPP and Fitzhugh–Nagumo Equations

Abstract: A standard reaction–diffusion equation consists of two additive terms, a diffusion term and a reaction rate term. The latter term is obtained directly from a reaction rate equation which is itself derived from known reaction kinetics, together with modelling assumptions such as the law of mass action for well-mixed systems. In formulating a reaction–subdiffusion equation, it is not sufficient to know the reaction rate equation. It is also necessary to know details of the reaction kinetics, even in well-mixed systems where reactions are not diffusion limited. This is because, at a fundamental level, birth and death processes need to be dealt with differently in subdiffusive environments. While there has been some discussion of this in the published literature, few examples have been provided, and there are still very many papers being published with Caputo fractional time derivatives simply replacing first order time derivatives in reaction–diffusion equations. In this paper, we formulate clear examples of reaction–subdiffusion systems, based on; equal birth and death rate dynamics, Fisher–Kolmogorov, Petrovsky and Piskunov (Fisher–KPP) equation dynamics, and Fitzhugh–Nagumo equation dynamics. These examples illustrate how to incorporate considerations of reaction kinetics into fractional reaction–diffusion equations. We also show how the dynamics of a system with birth rates and death rates cancelling, in an otherwise subdiffusive environment, are governed by a mass-conserving tempered time fractional diffusion equation that is subdiffusive for short times but standard diffusion for long times.

Traversing Dense Networks of Elementary Chemical Reactions to Predict Minimum-Energy Reaction Mechanisms

Abstract: Numerous different algorithms have been developed over the last few years which are capable of generating large, dense chemical reaction networks describing the inherent chemical reactivity of a collection of discrete molecules. For all elementary reactions in a given reaction network, reaction rate calculations, followed by direct micro-kinetic modelling, enables one to predict macroscopic outcomes (e.g. rate laws, product selectivity) based on atomistic input data. However, for chemical reaction networks containing thousands of reactant molecules, such simulations can be extremely time-consuming; in addition, the complex coupled time-dependence of molec- ular concentrations can present challenges when seeking essential mechanistic features. In this Article, we instead present an algorithm which seeks to predict the “most likely” reaction mechanism, or competing mechanisms, connecting any two user-selected reactant and product species, given a previously- generated reaction network as input. The approach is success- fully tested for reaction networks (containing tens of thousands of possible reactions) describing the carbon monoxide oxidation on platinum nanoparticles.

Alternative Kinetic Model of the Iodide–Iodate Reaction for Its Use in Micromixing Investigations

Abstract: The Villermaux-Dushman method, one of the most extensively used test reaction systems for micromixing characterization, has been widely criticized for years due to uncertainties regarding the incomplete dissociation of sulfuric acid and the proposed kinetic study by Guichardon et al. In this work, a renewed study of the kinetics of the iodide-iodate reaction is presented, using perchloric acid to avoid issues concerning incomplete acid dissociation. The experimental results are in good agreement with the fifth-order rate law for the iodide-iodate reaction. The reaction rate coefficient strongly depends on the ionic strength and can be modeled with a Davies-like equation. When implemented in the incorporation model, the kinetic model presented in this study can be used to estimate micromixing times that are in line with the theoretical engulfment time. This is observed in two different reactors with low and high intensities of mixing: an unbaffled stirred vessel and a rotor-stator spinning disk reactor. The results from the latter are also compared with the second Bourne reaction, giving very similar micromixing times. The kinetic model presented in this study in combination with strong monoprotic acids is suggested as an alternative to characterize micromixing behavior.

Effects of surfaces and macromolecular crowding on bimolecular reaction rates.

Abstract: Biological cells are complex environments that are densely packed with macromolecules and subdivided by membranes, both of which affect the rates of chemical reactions. It is well known that crowding reduces the volume available to reactants, which increases reaction rates, and also inhibits reactant diffusion, which decreases reaction rates. This work investigates these effects quantitatively using analytical theory and particle-based simulations. A reaction rate equation based on only these two processes turned out to be inconsistent with simulation results. However, accounting for diffusion inhibition by the surfaces of nearby obstacles, which affects access to reactants, it led to perfect agreement for reactions near impermeable planar membranes and improved agreement for reactions in crowded spaces. A separate model that quantified reactant occlusion by crowders, and extensions to a thermodynamic 'cavity' model proposed by Berezhkovskii and Szabo [25], were comparably successful. These results help elucidate reaction dynamics in confined spaces and improve prediction of in vivo reaction rates from in vitro ones.

Modular microreactor with integrated reflection element for online reaction monitoring using infrared spectroscopy

Abstract: We report on the fabrication of an internal reflection element (IRE) combined with a modular polymer microfluidic chip that can be used for attenuated total reflection (ATR) infrared spectroscopy. The IRE is fabricated from a silicon wafer. Two different polymers are used for the fabrication of the two types of modular microfluidic chips, namely polydimethylsiloxane (PDMS) and cyclic olefin copolymer (COC). The microfluidic chip is modular in the sense that several layers of mixing channels, using the herringbone mixer principle, and reactions chambers, can be stacked to facilitate the study of the desired reaction. A model Paal-Knorr reaction is carried out to prove that the chip works as intended. Furthermore, we highlight the strength of IR spectroscopy as a tool for reaction monitoring by identifying the peaks and showing the different reaction orders at the different steps of the Paal-Knorr reaction. The reduction of the aldehyde groups indicates a (pseudo) first order reaction whereas the vibrational modes associated with the ring formation indicate a zero order reaction. This zero order reaction can be explained with literature, where it is suggested that water acts as a catalyst during the dehydration step, which is the final step in the pyrrole ring formation.

Kinetic modelling of hydrogen transfer deoxygenation of a prototypical fatty acid over a bimetallic Pd60Cu40 catalyst: an investigation of the surface reaction mechanism and rate limiting step

Abstract: Herein, for the first time, we demonstrate a novel continuous flow process involving the application of tetralin as a hydrogen donor solvent for the catalytic conversion of oleic acid to diesel-like hydrocarbons, using an efficient and stable carbon-supported bimetallic PdCu catalyst. Using Pd60Cu40/C, where 60 : 40 is the molar ratio of each metal, at optimum reaction conditions (360 °C and WHSV = 1 h−1), 90.5% oleic acid conversion and 80.5% selectivity to C17 and C18 paraffinic hydrocarbons were achieved. Furthermore, a comprehensive mechanistic based kinetic modelling – considering power rate law, L–H and E–R models was conducted. Kinetic expressions derived from the three kinetic models were investigated in rate data fitting through nonlinear regression using a Levenberg–Marquardt algorithm. Based on the statistical discrimination criteria, the experimental data of the dehydrogenation reaction of tetralin were best fitted by an L–H rate equation assuming the surface reaction as the rate controlling step. In contrast, the kinetic data of the oleic acid deoxygenation reaction were well correlated with an L–H rate equation assuming single site adsorption of oleic acid with dissociative H2 adsorption. It was found that the rate limiting step of the overall reaction was the hydrogenation of oleic acid with an activation energy of 75.0 ± 5.1 kJ mol−1 whereas the dehydrogenation of tetralin had a lower activation energy of 66.4 ± 2.7 kJ mol−1.

Elementary reaction pathway study and a deduced macrokinetic model for the unified understanding of Ni-catalyzed steam methane reforming

Abstract: Ni-Catalyzed steam methane reforming (SMR) is widely used in energy and chemical engineering, but the confusion about vastly different SMR kinetic data has lasted for half a century. Towards solving the puzzle, the intrinsic mechanism of SMR is examined by performing density functional theory computations and transition state theory analyses on 80 elementary reaction steps involved in SMR over Ni(111). A microkinetic model is developed by combining the thermochemical data of the elementary reactions with a continuous stirring tank reactor model. The microkinetic model is used to investigate the reaction pathways, the rate determining steps and the abundances of surface species. Reaction rates predicted by the microkinetic model are in good agreement with the experimental data obtained under very different temperature and pressure conditions. An analytical expression of the SMR rate is derived based on the dominant reaction pathway and the abundances of surface species. The rate equation is verified to accurately reflect the microkinetic modeling. Applying the analytical rate equation yields a coherent explanation of the seemingly incompatible experimental data on the reaction orders of CH4, H2O and H2 and the activation energy of SMR. The rate equation is very useful for the optimization of the operating conditions of SMR.

A Revised Pseudo-Second Order Kinetic Model for Adsorption, Sensitive to Changes in Sorbate and Sorbent Concentrations

Abstract: Much contemporary research considers the development of novel sorbents for the removal of toxic contaminants. Whilst these studies often include experimental adsorption kinetics, modelling is normally limited to application of the pseudo-second order (PSO) rate equation, which provides no sensitivity towards changes in experimental conditions and thus no predictive capability. We demonstrate a relatively simple modification of the PSO model, with the final form dqt/dt = k’Ct(1-(qt/qe))^2 where k’=k2*(qe*^2)/C0*. We demonstrate that unlike the PSO model, this new rate equation provides first-order dependence upon initial sorbate concentration (observed experimentally as x=0.829±0.417), whilst rate constant k’ is significantly less sensitive to changes in C0 and Cs than PSO rate constant k2. We demonstrate that this model improves predictive capacity towards changes in C0 and Cs, particularly when qe is calculated using the Langmuir or Freundlich adsorption isotherm. Finally, we explore how the new rate constant, k’, responds to changes in sorbent morphology, identifying that particle radius is a better constraining parameter than surface area. In this new equation, the conditionality of the rate constant upon experimental conditions is significantly decreased, facilitating better comparison of new results with the literature.

A Master Equation for Photochemical Rates.

Abstract: Traditionally, the general photochemical rate equation could be integrated only at two limits (high concentration and low concentration). In this paper, the general photochemical equation has been integrated to yield a master equation that is valid for any chromophore concentration. Hence, in future, data for all concentrations can be utilized in deriving the incident photon flux and/or the quantum yield for a photochemical reaction. Unfortunately, the master equation can only be used for monochromatic light sources.

Multi-Objective Laser Rate Equation Based Parameter Extraction Using VCSEL Small Signal Response and RIN Spectra

Abstract: Rate equation parameters used to simulate semiconductor lasers must be carefully chosen in order to accurately model high-speed laser characteristics in optical link simulations. Previous parameter extraction methods have largely characterized these lasers through their small signal frequency response. We show that capturing both the small signal frequency response and relative intensity noise (RIN) spectrum of the laser is crucial for accurate parameter extraction. We present a multi-objective parameter extraction method alongside a stochastic rate equation model to account for a vertical cavity surface emitting laser's (VCSEL's) bandwidth and RIN characteristics. A genetic algorithm extracts VCSEL parameters from a set of experimentally measured small signal responses and RIN spectra at multiple drive currents. Through Pareto sorting we can extract a single set of parameters which accurately captures the laser's BW and RIN characteristics.

Optimization and reaction kinetics analysis for phosphorus removal in struvite precipitation process

Abstract: As a promising strategy to remove and recover phosphorus from wastewater, optimization of the struvite (MgNH4 PO4 .6H2 O) precipitation parameters is required to achieve desirable phosphorus removal efficiency. To tackle the challenges upon the precipitation optimization methods as three-level full factorial designs, and central composite design as well, Box-Behnken design was implemented to optimize different reaction parameters for phosphorus removal and recovery during struvite precipitation in the current study. Moreover, the reaction orders and the rate equation were all determined to reveal the reaction kinetics parameters of struvite precipitation. The results showed that the optimal operating parameters of pH, Mg/P ratio and N/P ratio were 9.82, 1.45, and 4.00, respectively, by which more than 95% of phosphorus removal efficiency could be achieved. In addition, it was found that pH and pH/(N/P) had the most influence on phosphorus removal efficiency among different individual factors and interactive items, respectively. The partial orders of PO4 -P, Mg2+ , and NH 4 + in kinetic rate equation were determined as 1.586, 0.930, and 1.236 while the rate constant k was 0.0167 ± 0.0014 mM-2.752 per minute by differential method. PRACTITIONER POINTS: Different reaction parameters were optimized by Box-Behnken design. pH and pH/(N/P) had the most influence on phosphorus removal efficiency among different individual factors and interactive items. The reaction orders and the rate equation were all determined to reveal the reaction kinetics parameters.

Density Functional Theory Based Micro- and Macro-Kinetic Studies of Ni-Catalyzed Methanol Steam Reforming

Abstract: The intrinsic mechanism of Ni-catalyzed methanol steam reforming (MSR) is examined by considering 54 elementary reaction steps involved in MSR over Ni(111). Density functional theory computations and transition state theory analyses are performed on the elementary reaction network. A microkinetic model is constructed by combining the quantum chemical results with a continuous stirring tank reactor model. MSR rates deduced from the microkinetic model agree with the available experimental data. The microkinetic model is used to identify the main reaction pathway, the rate determining step, and the coverages of surface species. An analytical expression of MSR rate is derived based on the dominant reaction pathway and the coverages of surface species. The analytical rate equation is easy to use and should be very helpful for the design and optimization of the operating conditions of MSR.

Modeling of intracavity-pumped Q-switched terahertz parametric oscillators based on stimulated polariton scattering.

Abstract: In this paper, the rate equations describing the operation of intracavity-pumped Q-switched terahertz parametric oscillators based on stimulated polariton scattering are given for the first time. The rate equations are obtained under the plane-wave approximation, the oscillating fundamental and Stokes waves are supposed to be round uniform beam spots. Considering the fact that the terahertz wave nearly traverses the pump and Stokes beams and using the coupled wave equations, the terahertz wave intensity is expressed as the function of the fundamental and Stokes intensities. Thus, the rate equations describing the evolution processes of the fundamental and Stokes waves are obtained in the first step. The THz wave properties are then obtained. Several curves based on the rate equations are generated to illustrate the effects of the nonlinear coefficient, the THz wave absorption coefficient, and pulse repetition rate on the THz laser characteristics. Taking the intracavity-pumped Mg:LiNbO3 TPO as an example, the THz frequency tuning characteristic and the dependences of the fundamental, Stokes, and THz wave powers on the incident diode pump power are calculated. The theoretical results are in agreement with the experimental results on the whole.