Backward Reaction Rate Research Articles

Dynamic Interfacial Tension Measurement for the Kinetic Study of Eu(III) Extraction in the NaNO3/Tributyl Phosphate System Based on an Increase in Interfacial Tension.

We demonstrated for the first time that interfacial tension measurements can be used to evaluate the kinetics of the solvent extraction of metal ions. The Eu(III) extraction mechanism in the nitrate ion/tributyl phosphate (TBP) system was investigated on the basis of dynamic interfacial tension. Interestingly, the interfacial tension of the TBP droplet (γ) increased with Eu(III) extraction. This behavior can be explained by the electrocapillary effect. The time dependence of γ was kinetically analyzed, and we demonstrated that the rate-determining process was the interfacial reaction of Eu(III). Furthermore, the dependence of the mass transfer rate constant upon the concentration of the nitrate ions revealed that two nitrate ions were involved in the interfacial reaction during Eu(III) extraction. However, no change in the rate constant upon TBP concentration was observed, because the change in the TBP concentration did not affect the electrocapillary effect. We determined the forward and backward reaction rates to be k1 = (1.5 ± 0.7) × 10-6 m M-2 s-1 and k-MT = (6.9 ± 3.9) × 10-7 m s-1. Therefore, for the first time, we demonstrated that dynamic interfacial tension, which is involved in the electrocapillary effect, can be used to elucidate the kinetics of Eu(III) extraction. We expect that this study will attract the attention of researchers in several fields, including physical and analytical chemistry.

Electrodeposition Stability Landscape for Solid–Solid Interfaces

AbstractAs solid‐state batteries (SSBs) with lithium (Li) metal anodes gain increasing traction as promising next‐generation energy storage systems, a fundamental understanding of coupled electro‐chemo‐mechanical interactions is essential to design stable solid‐solid interfaces. Notably, uneven electrodeposition at the Li metal/solid electrolyte (SE) interface arising from intrinsic electrochemical and mechanical heterogeneities remains a significant challenge. In this work, the thermodynamic origins of mechanics‐coupled reaction kinetics at the Li/SE interface are investigated and its implications on electrodeposition stability are unveiled. It is established that the mechanics‐driven energetic contribution to the free energy landscape of the Li deposition/dissolution redox reaction has a critical influence on the interface stability. The study presents the competing effects of mechanical and electrical overpotential on the reaction distribution, and demarcates the regimes under which stress interactions can be tailored to enable stable electrodeposition. It is revealed that different degrees of mechanics contribution to the forward (dissolution) and backward (deposition) reaction rates result in widely varying stability regimes, and the mechanics‐coupled kinetics scenario exhibited by the Li/SE interface is shown to depend strongly on the thermodynamic and mechanical properties of the SE. This work highlights the importance of discerning the underpinning nature of electro‐chemo‐mechanical coupling toward achieving stable solid/solid interfaces in SSBs.

TO ISSUE INCREASING THE EFFICIENCY OF THE MASS TRANSFER PROCESS IN AGITATORS

This study investigates the impact of impeller design on the rate of esterification reaction in a batch reactor. Different impeller designs were tested and compared, including Backswept impeller, C-shaped, Double Blade impeller, and Pitched impeller. The results showed that the choice of impeller design has a significant effect on the rate of esterification reaction, with the Backswept impeller proving to be the most effective. In this work, it is aimed to investigate the esterification of acetic acid and methanol in a batch stirred reactor for the synthesis of methyl acetate. The temperature range of 303.15 K is examined, with sulphuric acid used as the homogeneous catalyst in varying concentrations of 0.0633 mol·L1 to 0.3268 mol·L-1. The feed molar ratio of acetic acid to methanol also varied from 1:1 to 1:4 to observe its influence on the reaction rate. The research delves into the effects of temperature, catalyst concentration, and reactant concentration on the reaction rate. The experimental data is correlated using a second-order kinetic rate equation, and the forward and backward reaction rate constants and activation energies are determined from the Arrhenius plot. The developed kinetic model is compared with previous models in literature. In order to find the most effective impeller for esterification reaction, diameter of impellers was accepted same in the constant volume and dimension of batch reactor. The obtained kinetic equation proves useful for the simulation of a reactive distillation column for the synthesis of methyl acetate. Keywords: the batch reactor, impeller, esterification, effectivity, mass transfer, mixing, mechanical mixers, Logarithmic Shear Rate, Eddy Diffusivity.

Effect of equilibrium constant for carbon dioxide recombination in hypersonic flow analysis

An equilibrium constant is an important parameter in regard to determining the backward reaction rate constant in chemical kinetics modeling for a hypersonic flow. Three common approaches for the equilibrium constant determination are based on the partition function, Gibbs free energy, and the experimental reaction rate measurement. The present study conducted a computational fluid dynamics (CFD) analysis with different equilibrium constant formulations in a thermochemical nonequilibrium hypersonic flow in order to study the influence of the equilibrium constant in carbon dioxide flow during the Martian entry. The equilibrium constant for the carbon dioxide molecule dissociation differs from one method to another among the reactions that are considered in the carbon dioxide flow. Three different flow conditions, which are based on the experimental data that is provided in the literature, are considered in the detailed comparison analysis using CFD. The variation of the flow properties in terms of pressure, temperature, and mass fraction along the stagnation line is compared for different cases of the equilibrium constant computation. The results that are obtained from the present study confirm that the equilibrium constant influences the numerical computation in the thermochemical nonequilibrium flow especially for the non-catalytic wall boundary condition.

Dynamics of two-step reversible enzymatic reaction under fractional derivative with Mittag-Leffler Kernel.

Chemical kinetics is a branch of chemistry that is founded on understanding chemical reaction rates. Chemical kinetics relates many aspects of cosmology, geology, and even in some cases of, psychology. There is a need for mathematical modelling of these chemical reactions. Therefore, the present research is based on chemical kinetics-based modelling and dynamics of enzyme processes. This research looks at the two-step substrate-enzyme reversible response. In the two step-reversible reactions, substrate combines with enzymes which is further converted into products with two steps. The model is displayed through the flow chart, which is then transformed into ODEs. The Atangana-Baleanu time-fractional operator and the Mittag-Leffler kernel are used to convert the original set of highly nonlinear coupled integer order ordinary differential equations into a fractional-order model. Additionally, it is shown that the solution to the investigated fractional model is unique, limited, and may be represented by its response velocity. A numerical scheme, also known as the Atangana-Toufik method, based on Newton polynomial interpolation technique via MATLAB software, is adopted to find the graphical results. The dynamics of reaction against different reaction rates are presented through various figures. It is observed that the forward reaction rates increase the reaction speed while backward reaction rates reduce it.

Rational Design Method Based on Techno-Economic Principles for Integration of Organic/Organic Pervaporation with Lipase Catalyzed Transesterification.

An engineering foundation is developed in this manuscript to allow the rational design of enzymatic transesterifications integrated with organic–organic pervaporation for the removal of methanol. In the first part, enzyme kinetics are elucidated for the solventless transesterification of two monoterpene alcohols with methyl acetate catalyzed by Novozym 435. Nonlinear regression revealed that three parameters (enzyme loading, forward and backward second-order reaction rate) sufficed to describe the entire conversion as a function of time. In the second part, a mathematical model for acetate ester production, integrated with organic–organic pervaporation, was developed based on a set of ordinary differential equations. To this end, empirical formulae for the pervaporation performance (of a PERVAP 2255-30 membrane and a standard HybSi® membrane) were established, relating methyl acetate and methanol flux to the methanol concentration in the reactor. The resulting digital twin, “PervApp”, allows us to study the influence of the key design parameters “enzyme loading” and “membrane surface” on, e.g., catalyst productivity. Finally, a techno-economic assessment is made for an annual production of 100 tons of geranyl acetate. The described methodology allows producers to shift from laborious, expensive and often disappointing trial-and-error approaches to the rational design of such integrated units.

Photochromic films prepared by solid state processing of disentangled ultrahigh molecular weight polyethylene and photochromic dyes composites

AbstractDisentangled ultrahigh molecular weight polyethylene (DPE) is a special grade of polyethylene (molecular weight, >106 Da) which can be processed by an environment friendly solid state process on counter rotating two roll mill (TRM) below the melt temperature of the polymer. This unique processing property of DPE was utilized to develop smart DPE photochromic films. Photochromic dye like 'Spirooxazine' or 'Spiropyran' has been mixed with DPE resin powder prior to film formation without altering the DPE properties. These films could change their optical appearances on exposure to UV‐light of wavelength 365 nm and the color change phenomenon of the films could also be replicated by sunlight. The color change observed is found to be reversible, that is, films could return to colorless form either spontaneously in dark or by thermal stimuli. Such smart property was imparted to DPE even at very low concentration (2,000 ppm) of photochromic dyes. Spectrophotometric studies were used to measure the rate of forward reaction with UV radiation and the rate of backward reaction in dark. In fact, DPE powder and photochromic dye composite was used to produce the compression molded disc to understand the color change phenomena. Moreover, it was observed that the photo‐degradation rate of dye, could be retarded ~30% by using amphoteric Zinc phthalate salt. TGA and DSC studies confirmed that the characteristics of DPE film remained almost unaltered even after with preparation of film photochromic dyes.

Analysis of catalytic heat transfer for a multi-species gas mixture

Stagnation point catalytic heat transfer model for a multi-species gas mixture has been developed in this work. The analysis extends the existing tertiary gas mixture catalytic model that assumes thermochemical equilibrium at the edge of a chemically frozen boundary layer. The catalytic heat transfer is computed numerically by solving the governing equations with matrix diagonalization and shooting methods. The present model is applied to compute the heat transfer for both tertiary gas mixture O-O2-Ar and quinary gas mixture O-O2-N-N2-Ar. For the case of the tertiary gas mixture, the present model predicts in the finite-catalytic region, the stagnation-point heat transfer due to recombination is similar with that of the existing models of Goulard and Park. In the highly-catalytic region, however, noticeable differences are observed owing to how the species mass fraction at the wall is computed. Unlike the Goulard approach treating the oxygen and nitrogen as a single recombination efficiency, in the case of the quinary gas mixture, the oxygen recombination efficiency needs to be decoupled with that of nitrogen. The present global model for the tertiary gas mixture is also compared with the Computational Fluid Dynamics (CFD) approach. The results suggest that the present model predicts a similar diffusive stagnation heat transfer to that of the CFD approach, within some acceptable range, when a zero backward reaction rate constant is assumed in the chemical reaction modeling.

Measuring reaction rates at equilibrium with the isotope doping method

Since the time of J. H. van’t Hoff [1], it has been known that chemical equilibrium is dynamic, meaning that at equilibrium, chemical reactions do not cease, but instead the forward and backward reaction rates are equal. The constant concentrations at equilibrium preclude the use of concentrations to measure reaction rates at equilibrium. Therefore, with the exception of a few special cases, no reaction rates at equilibrium have been published in the literature of chemistry, physics, or chemical engineering. Here we report dissolution and precipitation rates at equilibrium for quartz and barite with the isotope-doping method. Experimental data show that dissolution and precipitation rates are equal at equilibrium, indicating the principle of detailed balance (PDB) appear to be applicable at these experimental conditions. The PDB has been a cornerstone for irreversible thermodynamics and chemical kinetics for a long time, and its wide application in geochemistry has mostly been implicit and without experimental testing of its applicability. Nevertheless, many extrapolations based on PDB without experimental validation have far reaching impacts on society’s mega environmental enterprises. The isotope doping method appears to able to test its applicability for a variety of minerals at a wide range of conditions.

An innovative approach for storing low-grade thermal energy using liquid phase thermoreversible reaction

This study investigates the potential of “methanol+acetaldehyde↔hemiacetal” as a liquid phase thermoreversible reaction for long-term storing of low-grade thermal energy to overcome the mismatch between energy supply and demand. Both forward and backward reactions are studied experimentally and the technical issues associated with employing such a system are discussed. Methanol and acetaldehyde would react via an exothermic reaction (-ΔHr=31.8kJmoleor104.7kWhm3) at low temperature range (<15 °C) and atmospheric pressure, with a high reaction rate (k=26.26×102exp-4099T). The regeneration of parent reactants with high purity occurs at 48 °C which can easily be delivered using low-grade heat. The low operating temperature required for forward reaction and the reduction in backward reaction rate caused by methanol accumulated are the main engineering challenges. These technical problems need to be solved before this reaction could be utilised commercially.

Determination of Equilibrium Constant and Relative Brightness in FRET-FCS by Including the Third-Order Correlations.

Fluorescence correlation spectroscopy (FCS) encodes the information on the equilibrium constant (K), the relative fluorescence brightness of fluorophore (Q), and the forward and backward reaction rate constants (k+ and k-) on a physical or chemical relaxation. However, it has been a long-standing problem to completely resolve the FCS data to get the thermodynamic and kinetic information. Recently, we have solved the problem for fluorescence autocorrelation spectroscopy (FACS). Here, we extend the method to fluorescence cross-correlation spectroscopy (FCCS), which appears when FCS is coupled with fluorescence resonance energy transfer (FRET). Among 12 total second-order and third-order pre-exponential factors in a relaxation process probed by the FRET-FCS technique, 3 are independent. We presented and discussed 3 sets of explicit solutions to use these pre-exponential factors to calculate K and Q. Together with the relaxation time, the acquired K will allow people to obtain k+ and k-, so that the goal of deciphering the FRET-FCS data will be fully reached. The theory is verified by extensive computer simulations and tested experimentally on a system of oligonucleotide hybridization.

Isotope exchange reactions involving HCO+ with CO: A theoretical approach

Aims. We aim to investigate fractionation reactions involved in the 12C/13C, 16O/18O, and 17O balance. Methods. Full-dimensional rovibrational calculations were used to compute numerically exact rovibrational energies and thermal equilibrium conditions to derive the reaction rate coefficients. A nonlinear least-squares method was employed to represent the rate coefficients by analytic functions. Results. New exothermicities are derived for 30 isotopic exchange reactions of HCO+ with CO. For each of the reactions, we provide the analytic three-parameter Arrhenius-Kooij formula for both the forward reaction and backward reaction rate coefficients, that can further be used in astrochemical kinetic models. Rotational constants derived here for the 17O containing forms of HCO+ may assist detection of these cations in outer space.

Upscaling multicomponent transport in porous media with a linear reversible heterogeneous reaction

The upscaling process of multicomponent mass transfer and reaction in a rigid and homogeneous porous media was carried out using the method of volume averaging. The first-order reversible reaction which occurs at the solid-fluid interface was considered in this paper. The corresponding macroscopic governing equations were derived from the system dynamics at the pore scale. The effective coefficients were obtained by solving the associated closure problems. This study shows that if the backward reaction rate constant at the microscale is small enough, i.e. k-→0, the obtained upscaled model is in accordance with the macroscopic model derived from the first-order irreversible heterogeneous reaction case which was extensively investigated in the literature. The influence of reaction rates on the effective parameters in the macroscopic equations was also investigated. It has been found that both forward and backward reaction rates have significant influence on the effective diffusivities and effective reaction rates in the macroscopic equations. The established equations were successfully verified by the comparison of the direct numerical calculations.

Back Extraction of HCl from TOA Dissolved in N-Octanol by Aqueous Ammonia in a Microchannel Device

To recover the extractant in the preparation of KH2PO4 using the extraction method, studies for the back extraction of HCl by aqueous ammonia from TOA (trioctylamine) dissolved in n-octanol were conducted. First, the reaction of HCl back extraction from TOA in n-octanol with aqueous ammonia was examined in shaking flasks and the equilibrium of this reaction was validated. The equilibrium constant of the stripping reaction was determined in the temperature range of 297.7-318.2 K and the reaction enthalpy was found to be -17.8 kJ/mol indicating that the stripping reaction was exothermic. Then kinetic experiments were performed in a microchannel device with the elimination of mass transfer limitations, as demonstrated by the experimental results. A kinetic model was established to obtain the forward and backward interfacial reaction rate constants with the help of the obtained equilibrium constant of the stripping reaction. This model described the measured data well and predicted correctly the change of HCl concentration in the oil phase along with the residence time in our experiments. Furthermore, the activation energy for the forward (8.21 kJ/mol) and backward (26.0 kJ/mol) reaction was determined and subsequently the forward and backward interfacial reaction rate constants were determined in the temperature range of 298.7-313.2 K.

Etching of Silicon Nitride in 3D NAND Structures

3D NAND structures present a unique difficulty in semiconductor device manufacturing. One method of production consists of cylindrical structures made of alternating layers of silicon dioxide (SiO2) and silicon nitride (SiN) with a core of SiO2. As part of the device manufacturing process the SiN is etched away, leaving the SiO2 core with disc-shaped SiO2 fins. Due to material selectivity requirements of etching only the SiN while leaving the SiO2 unchanged, the process of choice is often immersion in a high-concentration hot phosphoric acid (H3PO4) bath with a silica additive to inhibit SiO2 etching, which with proper tuning can have selectivity of greater than 100:1 for etching SiN:SiO2. Like all wet etch processes, uniformity of the process is a constant concern. One of our goals in this paper is to show how we use experimental measurements and simulations to better understand what parameters have the most effect on the process, and how we can use that knowledge to improve the process. Experimentally we have measured the etch rate of blanket SiN and SiO2 wafers. We fit the etch rate data to Arrhenius models to quantify the etch rate of SiN and SiO2 films. Simulations of the etch process on both blanket wafers and patterned wafers showed that the etch rate is the same and doesn’t depend on feature geometry. In this paper we propose a simple chemical reaction and diffusion mechanism that explains the experimental observations of the etched structures. The uniformity of the SiN etching between the top and the bottom of the 3D NAND stacks indicates that the reaction rate is much slower than the rate of diffusion of reactants and products into and out of the structure, so the etching is a reaction-controlled mechanism. This indicates within-wafer uniformity and wafer-to-wafer uniformity variations as being primarily due to differences of temperature within the bath. We also conducted simulations of the etching of the SiN in the 3D NAND structure and the liquid flow in the bath to model and explain this mechanism. In these simulations we varied the rate of the surface reaction of H3PO4 etching SiN, and showed that for a fast reaction rate that the structure would etch from the top to the bottom as the overall reaction rate become diffusion limited, while for a slow reaction rate the entire structure would etch uniformly, showing it to be a reaction limited process. Another issue with SiN etching in an H3PO4 bath is that the etch rate of SiO2 depends highly on the concentration of silica, in fact the bath is generally pre-seeded with silica in order to achieve a lower SiO2 etch rate, though if above a critical concentration deposition is known to occur. Based on a study of silica chemistry, it may be possible for silica deposition to occur even when below the critical concentration. This would be a film that would grow on a SiO2 surface but would later dissolve back into solution. We propose a mechanism that explains the formation and later disappearance of the growth film on the SiO2 surface as a result of the etching of the SiN and the formation of silica byproducts into a sol/gel network. Sol/gels have the unique property of their ability to form in an area of locally high flux, and then later dissolve over a much longer time scale. The difference in forward and backward reaction rates of the sol/gel film formation and disillusion, respectively, are such that the system is never in equilibrium. Thus, even though all the silica can dissolve in the phosphoric acid at equilibrium, the silica formed from the SiN etching forms into a sol/gel polymer network that only slowly dissolves after SiN etching has stopped. We discuss the implications of this sol/gel oxide film for further process improvement. With better theoretical understanding of the SiN etching and possible silica sol/gel formation and dissolution process, we now have tools to better optimize the phosphoric acid bath, improving both etching uniformity and necessary process time. Figure 1

Effects of reversible chemical reaction on Li diffusion and stresses in spherical composition-gradient electrodes

Composition-gradient electrode materials have been proven to be one of the most promising materials in lithium-ion battery. To study the mechanism of mechanical degradation in spherical composition-gradient electrodes, the finite deformation theory and reversible chemical theory are adopted. In homogeneous electrodes, reversible electrochemical reaction may increase the magnitudes of stresses. However, reversible electrochemical reaction has different influences on stresses in composition-gradient electrodes, resulting from three main inhomogeneous factors—forward reaction rate, backward reaction rate, and reaction partial molar volume. The decreasing transition form of forward reaction rate, increasing transition form of backward reaction rate, and increasing transition form of reaction partial molar volume can reduce the magnitudes of stresses. As a result, capacity fading and mechanical degradation are reduced by taking advantage of the effects of inhomogeneous factors.

Microwave assisted process intensification of lipase catalyzed transesterification of 1,2 propanediol with dimethyl carbonate for the green synthesis of propylene carbonate: Novelties of kinetics and mechanism of consecutive reactions

Green chemistry inherently hinges on process intensification through catalysis and waste minimization. The synergism of enzyme catalysis with microwave irradiation was studied systematically in this work for a consecutive reaction about which no literature report exists. Transesterification reaction of renewable starting materials (1,2 propanediol and dimethyl carbonate) was studied as a new strategy for environmentally benign route of cyclic carbonate synthesis in non aqueous media. A variety of supported enzymes were considered including Lipozyme RM IM, Lipozyme TL IM, Amano and Candida antarctica (Novozyme 435) among which Novozym 435 was the best. Both reactions occur under the influence of enzyme and also are enhanced by microwave irradiation. Thus, the example reported here serves as the first of its kind. The studies cover influence of different process parameters on reaction rate and selectivity of propylene carbonate and include agitation speed, solvent, loading of catalyst, reactant concentration (mole ratio) and temperature. A novel kinetic model was developed by finding forward and backward reaction rate constants for each step of the reaction. Microwave irradiation not only increases reaction rate but also improves the thermal stability of enzyme. Maximum conversion of 93% was obtained in 6h using 250mg of enzyme loading with 1 and 3mmol of 1,2 propanediol and dimethyl carbonate in 15mL solution made up with 1,4-dioxane as solvent at 70°C as compared to 54.4% conversion under conventional heating, thus proving the synergism between microwave irradiation and lipase. The enzyme is reusable and the results are novel.

The thermodynamic driving force for kinetics in general and enzyme kinetics in particular.

The thermodynamic driving force of a reaction is usually taken as the chemical potential difference between products and reactants. The forward and backward reaction rates are then related to this force. This procedure is of very limited validity, as the resulting expression contains no kinetic factor and gives little information on reaction kinetics. The transformation of the reaction rate as a function of concentration (and temperature) into a function of chemical potential should be more properly performed, as illustrated by a simple example of an enzymatic reaction. The proper thermodynamic driving force is the difference between the exponentials of the totaled chemical potentials of reactants and products.

Numerical analysis of transport and retardation for cesium in crushed granite using multi-stage advection–dispersion column experiments

In this study, a systematic analysis of cesium through crushed granite (0.297–0.840 mm) was constructed where synthetic groundwater and seawater were employed as the liquid phase. To build such models, multi-stage advection–dispersion column tests were conducted in order to determine the major transport processes and the calibration/validation of the hypothesized reactive transport models. The experimental breakthrough curves (BTCs) for HTO and Cs were both matched with their corresponding numerical BTCs by adjusting reaction and transport parameters such as forward or backward reaction rate constants (kf or kb), dispersivity (α), and porosity(θ).

Microkinetic evaluation of normal and inverse kinetic isotope effects during methane steam reforming to synthesis gas over a Ni/NiAl2O4 model catalyst

A microkinetic model was developed and applied to simulate an extensive experimental dataset on methane steam reforming. The data set consisted of 537 data points, and was collected over a Ni/NiAl2O4 catalyst at 843, 858, and 873K in a wide steam-to-carbon ratio range between 0.2 and 7.1. A microkinetic engine modeling tool was applied for the construction and parameter estimation of an elementary step network consisting of 12 reversible reactions. Specific reaction pathways were implemented for the formation of CO and CO2, respectively. The model qualitatively if not quantitatively explains inverse and normal isotope effects experimentally observed at low and high S/C ratios, respectively, and is thermodynamically consistent. A combination of the approach to partial equilibrium (i.e. whether the elementary step proceeds forward or backward) and net rate (i.e. the difference between forward and backward reaction rate) provides novel insight into the oxidation mechanism of CHx and CHxO surface species.