Rate Equations Research Articles

Properties and mechanism of uranium adsorption on single-sided fluorinated graphene: A first-principles study

Functionalized two-dimensional materials have been widely explored as possible candidates to adsorb radioactive nuclide due to their large specific surface and tunable properties. In this work, single-sided fluorinated graphene (ssFG) with different fluorinated rates have been predicted to be an effective adsorbent for uranium atoms using density functional theory (DFT) simulations. The linear response method was used to obtain a more accurate Hubbard U value (3.1 eV) of the 5f orbital of the uranium atom. Our calculated results show that uranium atoms were energetically favorable adsorbed on the C2F, C6F, C8F ssFGs, and their adsorption energies are 3.45, 1.20, and 1.12 eV, respectively. The electronic analysis, such as the density of states, charge transfer and differential charge density suggest that the uranium atom has the strongest chemisorption with the substrate C2F. C2F also exhibits excellent performance in terms of the adsorption capacity of uranium atoms. In addition, the critical temperature for the adsorption-desorption transition of uranium atoms was predicted to be 632 K by the adsorption rate equation. The results suggest that ssFG, especially C2F, was a promising material for uranium adsorption, have promising application in nuclear waste disposal, extraction of uranium from seawater, uranium detection, etc.

Facile Access to Organostibines via Selective Organic Superbase Catalyzed Antimony‐Carbon Protonolysis

The selective formation of antimony‐carbon bonds via organic superbase catalysis under metal‐ and salt‐free conditions is reported. This novel approach utilizes electron‐deficient stibine, Sb(C6F5)3, to give upon base‐catalyzed reactions with weakly acidic aromatic and heteroaromatic hydrocarbons access to a range of new aromatic and heteroaromatic stibines, respectively, with loss of C6HF5. Also, the significantly less electron‐deficient stibines, Ph2SbC6F5 and PhSb(C6F5)2 smoothly underwent base‐catalyzed exchange reactions with a range of terminal alkynes to generate the stibines of formulae PhSb(C≡CPh)2, and Ph2SbC≡CR [R = C6H5, C6H4‐NO2, COOEt, CH2Cl, CH2NEt2, CH2OSiMe3, Sb(C6H5)2], respectively. These formal substitution reactions proceed with high selectivity as only the C6F5 groups serve as a leaving group to be liberated as C6HF5 upon formal proton transfer from the alkyne. Kinetic studies of the base‐catalyzed reaction of Ph2SbC6F5 with phenyl acetylene to form Ph2SbC≡CPh and C6HF5 suggested the empirical rate law to exhibit a first‐order dependence with respect to the base catalyst, alkyne and stibine. DFT calculations support a pathway proceeding via a concerted σ‐bond metathesis transition state, where the base catalyst activates the Sb‐C6F5 bond sequence through secondary bond interactions.

Facile Access to Organostibines via Selective Organic Superbase Catalyzed Antimony-Carbon Protonolysis.

The selective formation of antimony-carbon bonds via organic superbase catalysis under metal- and salt-free conditions is reported. This novel approach utilizes electron-deficient stibine, Sb(C6F5)3, to give upon base-catalyzed reactions with weakly acidic aromatic and heteroaromatic hydrocarbons access to a range of new aromatic and heteroaromatic stibines, respectively, with loss of C6HF5. Also, the significantly less electron-deficient stibines, Ph2SbC6F5 and PhSb(C6F5)2 smoothly underwent base-catalyzed exchange reactions with a range of terminal alkynes to generate the stibines of formulae PhSb(C≡CPh)2, and Ph2SbC≡CR [R = C6H5, C6H4-NO2, COOEt, CH2Cl, CH2NEt2, CH2OSiMe3, Sb(C6H5)2], respectively. These formal substitution reactions proceed with high selectivity as only the C6F5 groups serve as a leaving group to be liberated as C6HF5 upon formal proton transfer from the alkyne. Kinetic studies of the base-catalyzed reaction of Ph2SbC6F5 with phenyl acetylene to form Ph2SbC≡CPh and C6HF5 suggested the empirical rate law to exhibit a first-order dependence with respect to the base catalyst, alkyne and stibine. DFT calculations support a pathway proceeding via a concerted σ-bond metathesis transition state, where the base catalyst activates the Sb-C6F5 bond sequence through secondary bond interactions.

An encompassed representation of timescale hierarchies in first-order reaction network

Complex networks are pervasive in various fields such as chemistry, biology, and sociology. In chemistry, first-order reaction networks are represented by a set of first-order differential equations, which can be constructed from the underlying energy landscape. However, as the number of nodes increases, it becomes more challenging to understand complex kinetics across different timescales. Hence, how to construct an interpretable, coarse-graining scheme that preserves the underlying timescales of overall reactions is of crucial importance. Here, we develop a scheme to capture the underlying hierarchical subsets of nodes, and a series of coarse-grained (reduced-dimensional) rate equations between the subsets as a function of time resolution from the original reaction network. Each of the coarse-grained representations guarantees to preserve the underlying slow characteristic timescales in the original network. The crux is the construction of a lumping scheme incorporating a similarity measure in deciphering the underlying timescale hierarchy, which does not rely on the assumption of equilibrium. As an illustrative example, we apply the scheme to four-state Markovian models and Claisen rearrangement of allyl vinyl ether (AVE), and demonstrate that the reduced-dimensional representation accurately reproduces not only the slowest but also the faster timescales of overall reactions although other reduction schemes based on equilibrium assumption well reproduce the slowest timescale but fail to reproduce the second-to-fourth slowest timescales with the same accuracy. Our scheme can be applied not only to the reaction networks but also to networks in other fields, which helps us encompass their hierarchical structures of the complex kinetics over timescales.

A theoretical description for competitive adsorption at the Solid/Solution interface

Wastewaters usually contain several solutes, and the adsorption process for removing pollutants from the solutions is usually competitive. Kinetic modeling of adsorption systems is a useful tool to obtain some information about the behavior of the system at the same time or in the future. The provided rate equations for binary adsorption are in differential form, and their solutions are approximated numerically using computers. In the present work, the kinetics of competitive adsorption at the solid/solution interface is studied. The new equation shows an exponential relation between time and surface coverage. This new equation is the first analytical solution of the kinetics Langmuir model of competitive adsorption. The simulated and experimental data confirm the provided equation is suitable to study the rate of binary adsorption.

Theoretical study on the mechanism of alcohol photooxidation on Nb2O5 surface.

Theoretical modeling of the solid-state photocatalysis is one of the important issues as various useful photocatalysts have been developed to date. In this work, we investigated the mechanism of the alcohol photooxidation on niobium oxide (Nb2O5) which was experimentally developed, using the density functional theory (DFT)/time-dependent (TD)DFT calculations based on the cluster model. The alcohol adsorption and the first hydrogen transfer from hydroxy group to surface occur in the ground state, while the second hydrogen transfer from CH proceeds in the excited states during the photoirradiation of UV or visible light. The spin crossing was identified and the low-lying triplet states were solved for the reaction pathway. The photoabsorption in the visible light region was characterized as the charge transfer transition from O 2p of alcohol to Nb 4d of the Nb2O5 surface. The spin density and the natural population analysis indicated the generation of spin density in the moiety of carbonyl compound and its dissipation to the interface of the surface, which partly explains the electron paramagnetic resonance measurement. It was confirmed that the rate determining step is the desorption of carbonyl compound and water molecule in agreement with the experimental rate equation analysis. The present findings with the theoretical modeling will provide useful information for the further studies of the solid-state photocatalysis.

How Metal/Insulator Interfaces Enable an Enhancement of the Hydrogen Evolution Reaction Kinetics

AbstractThe nanostructuring of electrodes is a common way of increasing electrocatalytic activity. Yet, the fact that the presence of insulating material in nanostructured composites can have a positive effect on efficiency was an unexpected recent finding. The rate enhancement has been linked to different electric fields at the insulator and metal interfaces, facilitating enhanced transport of reaction products into the bulk electrolyte. In this article, we further uncover the origin of the rate enhancement with parameter studies and simulations. We experimentally investigate various parameter dependencies of the alkaline Hydrogen Evolution Reaction (HER) on well‐defined nanometer‐sized Au arrays embedded in a silicon nitride insulating layer. We find a significant enhancement of the HER for all experimental conditions and opposite activity trends with pH, electrolyte concentration and the cationic species compared to a continuous Au electrode. Using a mean field model, we quantify the electrostatic interfacial pressure above the Au and the insulator patches. Combining the double layer simulations with rate equations, we demonstrate that all parameter variations can be consistently explained by the fact that the double layer structure above the insulator patches is much less rigid than above the metal islands and is independent of the applied potential.

Deep bed filtration and formation damage by particles with distributed properties

Current models for deep bed filtration describe particles with uniform properties. Yet, the sizes, densities, and mineral composition of particles vary significantly in the same injection well. The aim of this work is to provide an effective mathematical model for water injection of particles with distributed properties and formation damage prediction. We average the set of traditional population balance equations for single-property particles and obtain one upscaled equation. The upscaled equation for particle retention rate contains a non-linear function of suspended concentration, which we call the 'suspension function'. We derive analytical solutions for the upscaled equation for linear (coreflood) and radial (well injectivity) flows. Then we treat lab coreflood data to determine the model suspension function and provide a model for well injectivity prediction. The retention profile for the flow of uniform particles has an exponential form. Frequently reported in the literature, hyper-exponential forms have been hypothetically explained by multiple particle properties. The inverse solution allows revealing the individual filtration coefficients for binary mixtures from total breakthrough concentrations during coreflood. Treatment of the data from lab experiments reveals individual filtration coefficients that belong to common intervals. For the first time, deep bed filtration of particles with distributed properties is upscaled and presented using a single equation that reflects the particle property distribution. This equation provides an effective mathematical model for tuning lab coreflood data, determines the model function, and uses it for injectivity decline prediction.

Kinetics and mechanism of the gas-phase reaction of the hydroxyl radical with meta-aminotoluene compound.

An ab initio investigation into the potential energy landscape of the meta-aminotoluene + •OHreaction has been conducted in this study. The calculated results reveal that the reaction channel leading to the product (NHC6H4CH3 + H2O) prevails under the 300-1700K temperature range, while the reaction path forming the product (NH2C6H4CH2 + H2O) dominates in the higher-temperature region (T ≥ 1800K). Within the specified temperature range, the product branching ratio for the former declines from 48 to 30%, while the latter shows an increase, reaching 29%. The overall second-order rate constants of the titled reaction obtained at the pressure 760Torr (N2) can be illustrated by the modified Arrhenius expression of ktotal = 1.46 × 10-13 T0.58 exp[(-0.759kcal.mol-1)/RT] cm3 molecule-1s-1 and ktotal = 1.86 × 10-22 T3.24 exp[(-5.086kcal.mol-1)/RT] cm3 molecule-1s-1, covering the temperature range of T = 300-600K and T > 600K, respectively. The total rate constant at the ambient conditions in this work, 1.43 × 10-11 cm3 molecule-1s-1, has been found to be roughly one order of magnitude lower than the available experimental data, ~ 1.2 × 10-10 cm3 molecule-1s-1, measured by Atkinson et al., Rinke et al., and Witte et al., or the theoretical value, 4.4 × 10-10 cm3 molecule-1s-1, and calculated by Abdel-Rahman and co-workers for the aniline + •OH reaction. The structures of reactants, transition states, intermediate states, and products of the meta-aminotoluene + •OHreaction are calculated with the aug-cc-pVTZ basis set and the methods DFT/B3LYP and CCSD(T). The rate constants and branching ratios in the 300-2000K temperature range are calculated with the statistical theoretical TST and RRKM master equation computations including tunneling corrections, with potential energy surface constructed by the CCSD(T)//B3LYP/aug-cc-pVTZ approach.

Photochemistry of plateau lake-derived dissolved organic matter: Reactive species generation and effects on 17β-estradiol photodegradation

Naturally strong ultraviolet irradiation at high altitudes causes photobleaching of plateau lake DOM (P-DOM) and affects its photochemical activity. However, the photoreactivity of P-DOM has remained unclear under natural photobleaching condition. Here, six P-DOM samples isolated from plateau lakes in Yunnan Province, China as well as two reference DOM as comparisons were used to explore the photogeneration of reactive species (RS) and their effects on 17β-estradiol photodegradation. Compared with SRHA/SRFA, P-DOM has lower aromaticity, average molecular weight, and electron-donating capacity. The quantum yields of triplet state P-DOM (3P-DOM*), 1O2, and ∙OH produced in P-DOM solutions were greatly higher than those of reference DOM. The RS quantum yields had positive linear correlations with E2/E3 and SR, whereas were negatively linear correlated with SUVA25. Radical quenching experiments showed that 3P-DOM* was the prominent RS for 17β-estradiol photodegradation, and its contribution exceeded 70% for each of P-DOM. 3P-DOM*-mediated photodegradation was mainly attributed to the electron-transfer reactions with an average second-order rate constant of 4.62 × 109 M-1s-1, indicating the strong photoreactivity towards 17β-estradiol. These findings demonstrate that P-DOM is an efficient photosensitizer for RS production, among which 3P-DOM* may play an important role in enhanced photodegradation for organic micropollutants in plateau lake enriched with DOM.

Fructooligosaccharides: Production by recombinant fructosyltransferase from Festuca arundinacea in a continuous reactor and kinetic modeling profile

In the quest for maximum conversion of sucrose into 1-kestose using fructosyltransferases in a continuous reactor, consideration of the reversible reactions at competing concentrations of sucrose and 1-kestose is crucial. In this study, a kinetic model based on a combined approach of rapid equilibrium and steady-state kinetics was developed to predict the profile of FOS production using recombinant sucrose: sucrose 1-fructosyltransferase from Festuca arundinacea produced in Pichia pastoris. The purified enzyme selectively converted sucrose into 1-kestose with a final yield of 0.66 g/g sucrose consumed. The reaction rate laws adequately described the kinetic profile of the substrate and the products and accurately predicted the composition of the reaction mixture. The model was fitted to experimental data obtained at three enzyme dosages and three initial sucrose concentrations. The model could predict the effect of substrate concentration on initial rate kinetics, half-saturation constant, and transferase to hydrolase ratio. For the known values of initial sucrose and enzyme concentration, the optimum reaction time and the required dilution rate were predicted for the development of a continuous process to produce 1-kestose-enriched short-chain FOS. A volumetric productivity of ∼110 g/L/h of 1-kestose with 40 % carbohydrate composition in the permeate flux was demonstrated.

Restriction on molecular fluxionality by substitution: A case study for the 1,10-dicyanobullvalene.

We show herein that 1,10-dicyano substitution restricts the paragon fluxionality of bullvalene to just 14 isomers which isomerize along a single cycle. The restricted fluxionality of 1,10-dicyanobullvalene (DCB) is investigated by means of: (i) Bonding analyses of the isomer structures using the adaptive natural density partitioning (AdNDP). (ii) Quantum dynamical simulations of the isomerizations along the cyclic intrinsic reaction coordinate of the potential energy surface (PES). The PES possesses 14 equivalent potential wells supporting 14 isomers which are separated by 14 equivalent potential barriers supporting 14 transition states. Accordingly, at low temperatures, DCB appears as a hindered molecular rotor, without any delocalization of the wavefunction in the 14 potential wells, without any nuclear spin isomers, and with completely negligible tunneling. These results are compared and found to differ from those for molecular boron rotors. (iii) Born-Oppenheimer molecular dynamics (BOMD) simulations of thermally activated isomerizations. (iv) Calculations of the rate constants in the frame of transition state theory (TST) with reasonable agreement achieved with the BOMD results. (v) Simulations of the equilibration dynamics using rate equations for the isomerizations with TST rate coefficients. Accordingly, in the long-time limit, isomerizations of the 14 isomers, each with Cs symmetry, approach the "14 Cs → C7v" thermally averaged structure. This is a superposition of the 14 equally populated isomer structures with an overall C7v symmetry. By extrapolation, the results for DCB yield working hypotheses for so far un-explored properties e.g. for the equilibration dynamics of C10H10.

Modeling of heat conduction through rate equations

AbstractStarting from a classical thermodynamic approach, we derive rate-type equations to describe the behavior of heat flow in deformable media. Constitutive equations are defined in the material (Lagrangian) description where the standard time derivative satisfies the principle of objectivity. The statement of the Second Law is formulated in the classical form and the thermodynamic restrictions are then developed following a variant of the Coleman-Noll procedure where the entropy production too is given by a non-negative constitutive equation. Both the free energy and the entropy production are assumed to depend on a common set of independent variables involving, in addition to temperature, both temperature gradient and heat-flux vector together with their time derivatives. This approach results in rate-type constitutive function for the heat flux that are intrinsically consistent with the Second Law and easily amenable to analysis. In addition to providing already known models (e.g., Maxwell-Cattaneo-Vernotte’s and Jeffreys-like heat conductors), this scheme allows the formulation of new models of heat transport that are likely to apply also in nanosystems. This is consistent with the fact that higher-order time derivatives of the heat flux are in order when high-rate regimes occur.

Magnetic nanoparticles in square-wave fields for breakthrough performance in hyperthermia and magnetic particle imaging

Driving immobilized, single-domain magnetic nanoparticles at high frequency by square wave fields instead of sinusoidal waveforms leads to qualitative and quantitative improvements in their performance both as point-like heat sources for magnetic hyperthermia and as sensing elements in frequency-resolved techniques such as magnetic particle imaging and magnetic particle spectroscopy. The time evolution and the frequency spectrum of the cyclic magnetization of magnetite nanoparticles with random easy axes are obtained by means of a rate-equation method able to describe time-dependent effects for the particle sizes and frequencies of interest in most applications to biomedicine. In the presence of a high-frequency square-wave field, the rate equations are shown to admit an analytical solution and the periodic magnetization can be therefore described with accuracy, allowing one to single out effects which take place on different timescales. Magnetic hysteresis effects arising from the specific features of the square-wave driving field results in a breakthrough improvement of both the magnetic power released as heat to an environment in magnetic hyperthermia treatments and the magnitude of the third harmonic of the frequency spectrum of the magnetization, which plays a central role in magnetic particle imaging.

Efficient and accurate parameter extraction for quantum-well DFB lasers: a comprehensive approach integrating multiple mathematical models

This study proposes an efficient and accurate method for parameter extraction of quantum well distributed feedback (DFB) lasers by combining the rate equation model, finite element method, transmission matrix method, and traveling wave model (TWM). By fabricating and measuring the companion Fabry-Perot (FP) lasers, material and structural parameters common with the target DFB laser are extracted efficiently. All the intrinsic parameters of the DFB laser are accurately extracted by integrating multiple mathematical models, and the possibility of multiple solutions is avoided. From the extracted parameters, the output characteristics of the DFB laser are simulated using the TWM. The simulation results agree closely with the experimental results, proving the feasibility and accuracy of the proposed method.

Simulation of a catalytic deoxygenation reaction of fatty acids to produce biohydrocarbons and evaluation of the influence of reaction parameters on the conversion and selectivity of products

Nowadays, there has been an urgency in the search for sustainable energy sources, such as those derived from biomass. This search is not only limited to minimizing greenhouse gas emissions but is also related to the increasing scarcity of fossil fuels. This work aims to investigate and analyze the production of bio-hydrocarbons from fatty acids through the simulation of the deoxygenation reaction by the DWSim software. In this simulation, a continuous catalytic deoxygenation reactor of the stirred tank with fluidized bed type was selected, aiming to understand the influence of operating parameters on this reaction. The parameters evaluated were temperature, pressure, hydrogen feed, and catalyst mass. For this simulation, hydrogen and stearic acid were chosen as feedstocks, focusing on the heptadecane and octadecane production. The rate law was chosen based on an extensive literature review, as well as reaction conditions. The kinetic model used as a reference was based on reactions of stearic acid and hydrogen in the presence of NiMo/Al2O3 as a catalyst. A stearic acid feed of 2.4 x 104 m3 year-1 was used as a base, representing the average feed of fatty raw material practiced in biodiesel plants located in the state of Minas Gerais, Brazil. From the variation of these parameters for a sensitivity analysis, with conversion as the key response, the following optimal operating conditions were defined: temperature of 650 K, pressure of 50 bar, molecular hydrogen feed of 4.1 x 10-3 m³ s-1, and catalyst mass of 8 kg. Under these new circumstances, the conversion of stearic acid reached a value of 99.23 %. The simulation of this reaction allowed us to understand the effect of the main reaction parameters on the reaction products, proved to be an important and robust tool to be used in projects and feasibility analyses of plants and biorefineries.

Construction of a screening system for lipid-derived radical inhibitors and validation of hit compounds to target retinal and cerebrovascular diseases

Recent studies have highlighted the indispensable role of oxidized lipids in inflammatory responses, cell death, and disease pathogenesis. Consequently, inhibitors targeting oxidized lipids, particularly lipid-derived radicals critical in lipid peroxidation, which are known as radical-trapping antioxidants (RTAs), have been actively pursued. We focused our investigation on nitroxide compounds that have rapid second-order reaction rate constants for reaction with lipid-derived radicals. A novel screening system was developed by employing competitive reactions between library compounds and a newly developed profluorescence nitroxide probe with lipid-derived radicals to identify RTA compounds. A PubMed search of the top hit compounds revealed their wide application as repositioned drugs. Notably, the inhibitory efficacy of methyldopa, selected from these compounds, against retinal damage and bilateral common carotid artery stenosis was confirmed in animal models. These findings underscore the efficacy of our screening system and suggest that it is an effective approach for the discovery of RTA compounds.

Microscopic mechanism and effect analysis of polymer modifiers on embrittlement and viscosity behaviour of asphalt

To support the research and development of asphalt binder with low embrittlement point in cold areas, the microscopic mechanism and effect of polymer modifier on embrittlement and viscosity of asphalt were analysed by molecular dynamics method. The mixed molecular models of three polymer modified asphalt commonly used in cold areas and the interactive molecular models of each component of asphalt and modifier were established. The micromechanical properties of high-content polymer modified asphalt were studied by three important indices, namely brittleness point, shear viscosity and elastic modulus, and the interaction behaviour of each component of asphalt and modifier molecules was analysed by the layer model. The following conclusions were obtained: The brittleness point of modified asphalt can be decreased by increasing the polymer modifier content, with a notable reduction of 25.54 % observed when the content reaches 7.5 %. However, this is accompanied by a subsequent increase in shear viscosity at mixing temperatures, with the highest increase reaching 16.9 %. At low temperature environment, the diffusion rate of the modifier is closely related to its own type, temperature and the type of asphalt components, and in different modified asphalt, the law of the diffusion rate of each asphalt component is not completely consistent, so it is necessary to fully consider the influence of the proportion of asphalt components, and choose the modifier sensitive to the corresponding components. The above research results have an important guiding role in the scientific formulation of the design and test scheme of low-brittleness-point asphalt binder and the completion of the research and development of low-brittleness-point asphalt binder for cold areas.

High energy and high repetition rate QCW-LD end-pumped electro-optical Q-switched Yb:YAG laser

The quasi-continuous wave laser diode (QCW-LD) pumping is considered as the most efficient way for generating high energy nanosecond pulsed laser with repetition rate ranging from 50 to 1000 Hz. Here, a high efficiency, high repetition rate and high energy QCW-LD end-pumped electro-optical (EO) Q-switched Yb:YAG laser was demonstrated. The shortest pulse duration of 17.4 ns with a maximum single pulse energy of 5.1 mJ was obtained at the repetition rate of 100 Hz. As the repetition rate increases up to 500 Hz, the maximum output single pulse energy was obtained to be 5.38 mJ with the pulse width of 18.7 ns, corresponding to the slope efficiency of 21.6% and beam quality factor of M x 2=1.04, and M y 2=1.01. In addition, a theoretical study was carried by numerical simulation of the rate equations, and the results were agreed well with the experimental ones. The results show that QCW-LD pumping with Yb-doped crystals is a promising way for highly efficient, high-energy and high repetition rate nanosecond pulsed laser generation.

Novel semi-analytical model for solving the C*-integral of specimens with mode-I crack under various constraints

The energy rate line integral C* is an essential fracture parameter that characterizes the stress and strain rate field intensity at a crack tip for materials undergoing creep deformation, and is also a crucial parameter describing the creep crack growth rate. This study proposes a method for determining the characteristic parameters of the creep displacement rate model for specimens with mode-I crack under various constraints. Based on the displacement rate model, a semi-analytical model of the C*-integral related to the displacement rate, load, specimen sizes, and Norton's law parameters of materials is proposed. Furthermore, finite element analysis (FEA) models were established for compact tension (CT), single-edged notched bending (SEB), C-shaped tension (CST), and single-edge notched tension (SET) specimens, and the proposed models were verified using FEA results and those predicted by the ASTM method. The explicit correlation between the creep displacement rate and crack length a in the model can contribute to developing novel testing methods for real-time crack length and creep crack growth rate.