Determination Of Kinetic Rate Constants Research Articles

Segmented flow capillary microreactors for determination of kinetic rate constants of reactive zinc extraction system

Conventional techniques for kinetic rate constant acquisition are limited by diffusive transport, which can be well addressed by microfluidic techniques. Segmented flow capillary microreactors were used for the first time in this study to obtain kinetic rate constants for a reactive zinc extraction system. The influences of initial zinc ion concentration, total flow velocity, pH of the aqueous phase, and ionic strength on the kinetic rate constant determination were investigated. The control regimes were determined with the ratio of reaction to total resistance R, and the Hatta number. The kinetic rate constants obtained at low initial zinc concentrations, low acidity and high flow velocities exhibited minor deviations, indicating that the zinc sulfate/D2EHPA system could be under the kinetic control regime with the capillary microreactors, which also demonstrated the viability of the segmented flow approach. The kinetic rate constant data obtained with the segmented flow capillary microreactor from this work were much higher than those obtained from previous studies, which may be attributed to the fact that the microreactor minimizes the influence of diffusive transport. The purpose of this work was to provide reliable kinetic data of the reactive zinc extraction system and to verify the efficiency and superiority of the segmented flow microreactor approach over other techniques.

UV-LED fluence determination by numerical method for microbial inactivation studies

The Ultraviolet Light-Emitting Diode (UV-LED) is a new UV source suitable for small to mid-size water disinfection units. The design of a UV-LED reactor entails the integration of hydrodynamics, radiation, and kinetics data. The kinetics of microbial inactivation are necessary for UV-LED reactor design and the determination of kinetic rate constants depends on the accuracy of fluence rate measurement. However, there is not an easy way to measure the fluence rate inside a solution. In this study, a computational method is proposed to calculate irradiance and fluence rate based on the LED’s relative radiation profile and its radiant power, which are two standard pieces of information available in an LED’s datasheet. UV-LED was modeled as a polychromatic point source with a specific radiation profile and the fluence rate was calculated by solving the Radiative Transfer Equation by considering the refraction, reflection, and absorption of the medium. The irradiance and fluence rate predictions on the surface of the water were evaluated successfully by radiometry and actinometry measurements, respectively. The fluence rate imposed by 265-nm UV-LED and 275-nm UV-LED in Petri dishes with internal diameters of 5 cm and 9 cm were measured using biodosimetry with E. coli and MS2, when the UV-LED germicidal factor was obtained by considering the LED emission spectrum and the microorganism action spectra. Biodosimetry experiments using E. coli and MS2 at exposure times over 200 s indicated a close agreement between the simulation and experimental data. Such results are indicating the kinetic rate constants of a microorganism can be estimated without performing kinetic study using the action spectrum of microorganisms. Further, the results showed the proposed method can be applied for fluence rate determination for any LED’s radiation profile, LED position, and the experimental apparatus’s regardless of the availability of the action spectrum of microorganisms.

Removal efficiencies and kinetic rate constants of xenobiotics by ozonation in tertiary treatment.

This study gives a full overview of the chemical oxidation by ozone of selected xenobiotics usually present in effluents of conventional wastewater treatment plants. A qualitative and quantitative overview of literature data was made, and describes the ozonation efficiency and processes for the elimination of 12 xenobiotics (pesticides and pharmaceuticals). A database was built, compiling literature results of experimental ozonation assays in laboratory and real-scale conditions. Special attention was paid to selecting the data and compiling reliable results on removal efficiencies and kinetic parameters. An original study was performed in a semi-batch reactor applying ozone on secondary effluent spiked beforehand with a cocktail of 12 xenobiotics. The results of this study were compared with the literature data to evaluate the influence of the kinetic competition of xenobiotics in spiked wastewater in the determination of kinetic rate constants. These 12 xenobiotics were classified into three groups (high-/medium-/low-oxidizable) according to the ranges of their direct kinetic rate constants (kO3). A best effective ozone dose between 0.2 and 0.4 gO3 gDOC-1 is proposed for the elimination of xenobiotics. The predominant elimination pathway between direct and indirect oxidation was identified for each xenobiotic.

Modelling of interfacial mass transfer in microfluidic solvent extraction: part I. Heterogenous transport

An investigation of molecular diffusion of solutes across water/oil interfaces in a Y-Y-shaped microchannel with an integrated guide structure is presented. Finite volume numerical simulations were compared with experimental literature data. Analytical approaches including an infinite composite medium model, phase-specific mass transfer coefficient models, and a static transfer cell model were also assessed. An increase in accuracy for the mass transfer coefficient models was achieved by using local coefficients as opposed to length-averaged expressions. The static transfer cell model was shown to improve when based on the interfacial contact time, as opposed to the organic phase residence time. The results presented in this work have immediate application to the determination of kinetic rate constants in reactive mass transfer systems, as considered in Part II of this study (Ciceri et al. Microfluid Nanofluid, 2012).

Effects of the anion salt nature on the rate constants of the aqueous proton exchange reactions

The proton-transfer ground-state rate constants of the xanthenic dye 9-[1-(2-methyl-4-methoxyphenyl)]-6-hydroxy-3H-xanthen-3-one (TG-II), recovered by Fluorescence Lifetime Correlation Spectroscopy (FLCS), have proven to be useful to quantitatively reflect specific cation effects in aqueous solutions (J. M. Paredes, L. Crovetto, A. Orte, J. M. Alvarez-Pez and E. M. Talavera, Phys. Chem. Chem. Phys., 2011, 13, 1685-1694). Since these phenomena are more sensitive to anions than to cations, in this paper we have accounted for the influence of salts with the sodium cation in common, and the anion classified according to the empirical Hofmeister series, on the proton transfer rate constants of TG-II. We demonstrate that the presence of ions accelerates the rate of the ground-state proton-exchange reaction in the same order than ions that affect ion solvation in water. The combination of FLCS with a fluorophore undergoing proton transfer reactions in the ground state, along with the desirable feature of a pseudo-dark state when the dye is protonated, allows one unique direct determination of kinetic rate constants of the proton exchange chemical reaction.

On bubble column reactor design for the determination of kinetic rate constants in gas-liquid systems

The design of a semibatch bubble column reactor with its mathematical description is proposed for the study of ozonation reactions. The mathematical model used to describe the gas–liquid mass transfer rate in the reactor is based on the unstationary film theory and the resulting model is theoretically analysed to identify its relevant parameters. After its structural identifiability analysis, the parameters are reduced to five, that is, the gas hold-up, the ratio of diffusivities of the reacting species, the volumetric mass transfer coefficient and two time constants related with the kinetic rate constant. From the sensitivity analysis of this reduced model, we conclude that it is not sensible to the gas hold-up and the diffusivity ratio of the reacting species for optimization purposes in moderate and slow kinetic regimes. The model is tested with the reaction between the ozone and the azo-compound Acid Red 27. The experimental data match quite well the model allowing the estimation of the volumetric mass transfer coefficient together with the kinetic constant. The kinetic rate constant for the direct reaction between the ozone and the Acid Red 27 is estimated in k2 = 3723 ± 127 M−1 s−1 at 21.2 ± 0.5°C. The self-coherence of the model, the absence of hypothesis about the state of the film together with the proposed optimization procedure, allows to consider the proposed methodology as a viable alternative for the study of gas–liquid systems in semi-batch bubble columns reactors in comparison with classical approaches. La conception d'un reacteur semi-continu de type colonne a bulles avec sa description mathematique est proposee pour l'etude des reactions d'ozonation. Le modele mathematique utilise pour decrire le taux de transfert de masse gaz–iquide dans le reacteur est fonde sur la theorie des pellicules en regime instationnaire et une analyse theorique du modele en resultant est faite pour identifier ses parametres pertinents. Apres l'analyse d'identifiabilite structurale, les parametres sont reduits a cinq, c.-a-d., la retenue de gaz, le rapport de diffusivite des especes en reaction, le coefficient volumetrique de transfert de masse et deux constantes de temps liees a la constante du taux cinetique. A partir de l'analyse de sensibilite de ce modele reduit, nous concluons qu'il n'est pas sensible a la retenue de gaz et au rapport de diffusivite des especes de reaction pour les besoins d'optimisation. Le modele est examine par rapport a la reaction entre l'ozone et l'azocompose acide rouge 27. Les donnees experimentales s'accordent tout a fait au modele permettant l'estimation du coefficient volumetrique de transfert de masse ainsi que de la constante cinetique. La constante de taux cinetique pour la reaction directe entre l'ozone et l'acide rouge 27 est estime a k2 = 3723 ± 127 1/(M.s) a 21,2 ± 0,5°C. L'auto-coherence du modele, l'absence d'hypothese relative a l'etat de la pellicule, ainsi que le processus d'optimisation propose, nous permettent de considerer la methodologie proposee comme une alternative viable pour l'etude des systemes gaz-liquides dans des reacteurs semi-continus de type colonne a bulles comparee aux approches classiques.

Kinetic of benzotriazole oxidation by ozone and hydroxyl radical

Ozonation experiments were performed in batch reactors in order to determine the rate constants for the reaction of molecular ozone and OH radicals with benzotriazole (BT) at different pHs. The first group of ozonation experiments was carried out for the determination of the rate constant for the direct reactions between ozone and BT. Two different kinetic models were used for the determination of kinetic rate constants: (i) the log-reduction of BT with ozone in excess, (ii) the competition kinetic model. The second-order rate constants for BT with molecular ozone were determined to be 36.4 ± 3.8 M −1 s −1 and 18.4 ± 0.8 M −1 s −1 at pH 2 from the two methods respectively. With the competition method, the value at pH 5 was found to be 22.0 ± 2.0 M −1 s −1. In a following stage, the reaction of BT with OH radicals was investigated at pH values ranging from 2 to 10.2. Using a method involving two probe compounds during the ozonation, the second-order rate constants of the BT reaction with hydroxyl radicals were determined. The rate constants were found to vary from 6.2 × 10 9 M −1 s −1 at pH 10.2 to 1.7 × 10 10 M −1 s −1 at pH 2.

Inverse determination of kinetic rate constants for transesterification of vegetable oils

We present an inverse procedure for determining the rate constants for the kinetic equations that describe the transesterification reaction used to produce biodiesel from vegetable oils. In this approach, we require a mathematical model and its corresponding computer implementation, an experimental setup for taking experiment data and a numerical optimization procedure are used to determine the rate constants. A continuous laminar flow microreactor concept is considered due the simplicity of the design, the precise controllability of the flow conditions and the accuracy of the corresponding numerical model.

Molecular interactions in the insulin-like growth factor (IGF) axis: a surface plasmon resonance (SPR) based biosensor study

This review describes a comprehensive analysis of a surface plasmon resonance (SPR)-based biosensor study of molecular interactions in the insulin-like growth factor (IGF) molecular axis. In this study, we focus on the interaction between the polypeptide growth factors IGF-I and IGF-II with six soluble IGF binding proteins (IGFBP 1-6), which occur naturally in various biological fluids. We have describe the conditions required for the accurate determination of kinetic rate constants for these interactions and highlight the experimental and theoretical pitfalls, which may be encountered in the early stages of such a study. We focus on IGFBP-5 and describe a site-directed mutagenesis study, which examines the contribution of various residues in the protein to high affinity interaction with IGF-I and -II. We analyse the interaction of IGFBP-5 (and IGFBP-3) with heparin and other biomolecules and describe experiments, which were designed to monitor multi-protein complex formation in this molecular axis.

Determination of kinetic rate constants for 2-[18F]fluoro-2-deoxy-D-glucose and partition coefficient of water in conscious macaques and alterations in aging or anesthesia examined on parametric images with an anatomic standardization technique.

Kinetic rate constants for 2-[18F]fluoro-2-deoxy-d-glucose (FDG) and the tissue-blood partition coefficient of water were determined using dynamic positron emission tomography in conscious macaques, and alterations in these parameters in aging or anesthesia were also examined. The parameters were estimated on a pixel-by-pixel basis using an anatomic standardization technique; group differences were then examined on the parametric images from the young, aged, and anesthesia groups. For the conscious condition, seven young and seven aged male rhesus macaques were used; six young male rhesus macaques were used for the isoflurane anesthesia condition. H2 15O and FDG were used as tracers. The kinetic parameters were estimated by a nonlinear least-square fitting procedure with compartment models including terms for the cerebral blood volume (CBV) and time delay of the input function. Cerebral blood flow (CBF) and cerebral metabolic rate of glucose (CMRglc) were also calculated from the estimated parameters. In the aged group, glucose phosphorylation was decreased more than glucose transport, and the occipital cortex was the most affected region where reduction in CBV, CMRglc, and CBF were also observed. In the anesthesia group, glucose transport was decreased; however, glucose phosphorylation was not affected except for the occipital pole. The occipital cortex was also the most affected region. The tissue-blood partition coefficient of water was decreased globally.

Tracing Ni, Cu, and Zn kinetics and equilibrium partitioning between dissolved and particulate phases in South San Francisco Bay, California, using stable isotopes and high-resolution inductively coupled plasma mass spectrometry

Additions of the low occurrence stable isotopes 61Ni, 65Cu, and 68Zn were used as tracers to determine the exchange kinetics of metals between dissolved and particulate forms in laboratory studies of natural water and suspended sediments from South San Francisco Bay, CA. Dissolved metal isotope additions were made so that the isotope ratios (rather than total metal partitioning) were significantly altered from initial ambient conditions. Dissolved metal concentrations were determined using an organic ligand sequential extraction technique followed by analysis with high-resolution inductively coupled plasma mass spectrometry (HR-ICPMS). Exchangeable particulate concentrations were extracted using a 20% acetic acid leach followed by determination using HR-ICPMS. Equilibrium and kinetic sorption parameters were quantified according to a general model for trace metal partitioning assuming pseudo-first-order kinetics. Partition coefficients (K D) were tracked as a function of time over the fortnight experiment. For Ni, Cu, and Zn the initial ambient K D values were found to be 10 3.65, 10 3.88, and 10 4.52 L kg −1, respectively. As a result of the dissolved metal isotope additions, the partition coefficients for all three metals dropped and then increased back to near ambient K D values after 14 days. Curve-fitting concentration versus time profiles from both dissolved and exchangeable particulate data sets allowed determination of kinetic rate constants. The best estimates of forward and backward kinetic rate constants for Ni, Cu, and Zn respectively are k′ f = 0.03, 0.07, 0.12 d −1 and k b = 0.13, 0.12, 0.15 d −1. These results predict that sorption equilibria in South Bay should be reached on the order of a month for Ni, on the order of 3 weeks for Cu, and on the order of 2 weeks for Zn. Together, the dissolved and exchangeable particulate data indicate more sluggish sorption kinetics for Ni than for Cu and Zn and suggest that different chemical forms control the speciation of these three metals in South Bay. Order of magnitude metal sorption exchange rates were estimated using these kinetic results. These calculations indicate that sorption exchange between dissolved and suspended particulate phases can cause dynamic internal cycling of these metals in South San Francisco Bay.

Determination of active concentrations and association and dissociation rate constants of interacting biomolecules: an analytical solution to the theory for kinetic and mass transport limitations in biosensor technology and its experimental verification.

Accurate determination of kinetic rate constants for interacting biomolecules requires knowledge of the active concentrations of the participating molecules. Also, in other biomedical and clinical applications, sensitive, precise and accurate methods are needed to determine the concentration of biologically active molecules, which frequently constitute only a fraction of the total molecular pool. Here we report a novel development of the approach to determining active concentrations based on surface plasmon resonance (SPR) technology. The method relies on changes in binding rates with varying flow rates under conditions of partial mass transport, and does not require standards of known concentrations, given that the molecular mass of the molecule of interest is known. We introduce an analytical solution to the differential equations describing the formation of a 1:1 bimolecular complex, taking into account both the association and dissociation reactions, under partial mass transport limitations. This solution can be used in global fitting to binding curves obtained at different flow rates. The accuracy, precision, and sensitivity of this approach were determined in experiments involving binding of tyrosine-phosphorylated recombinant proteins to anti-phosphotyrosine antibodies, where the active concentration could be determined independently by in vitro phosphorylation with (33)P. There was an excellent agreement between the active concentrations determined by the analytical SPR-based method and by determination of the level of radioactivity of the phosphorylated protein. The SPR-based method allows determination of protein concentrations at picomolar levels. A procedure for accurate determinations of association and dissociation rate constants, based on the analytical solution of the mass transport and binding theory, is outlined.

An Adaptation of Kubista's Method for Spectral Curve Deconvolution

A chemometric approach to spectral curve deconvolution is described, evaluated, and applied to micellar systems. The technique is based on the method of principal component analysis of a spectral matrix followed by transformation of the abstract vectors into real spectra and concentrations. The approach reported here is similar to that of Kubista et al. (Anal. Chem. 1993, 65, 994-998). In the present study, however, more spectral information is known about the system of interest. This information is included in the deconvolution, which should, in general, increase the reliability of the method. From this method we obtain very reliable (noise-insensitive) λ(max) values of indicator molecules in the micellar pseudophase free from contributions of the indicator in the aqueous phase. The water-to-micelle partition coefficients are also determined. The effects of noise and the extent of indicator partitioning on the reliability of the method are evaluated using model data. The application of the method to the study of eight indicators in a prototypical micellar system (sodium dodecyl sulfate) is presented. Extension of the method to other types of chemical studies such as the determination of kinetic rate constants and product spectra is briefly discussed.

Determination of Kinetic Rate Constants for the Binding of Inhibitors to HIV-1 Protease and for the Association and Dissociation of Active Homodimer

Association and dissociation rate constants for a competitive inhibitor of HIV-1 protease were determined by a novel method employing a pair of integrated rate equations. This method, termed the paired progress curve method, is both rapid and reproducible. Progress curves, taken at a single concentration of inhibitor, are analyzed simultaneously to determine association and dissociation rate constants, the concentration of active sites, and the catalytic rate constant. The method is applied to BILA 398, a compound for which the cocrystal structure with HIV-2 protease has been reported recently [Tong, L., et al. (1993) Proc. Natl. Acad. Sci. U.S.A. 90, 8387-8391]. This compound exhibited an association constant of 1.6 x 10(7) M-1 s-1 and a dissociation constant of 1.0 x 10(-4) s-1 corresponding to a binding affinity constant of 6.4 x 10(-12) M. During the course of the analysis, nonlinearity was observed in control reactions containing enzyme and substrate only. This was subsequently shown to be due to a reversible inactivation process resulting from enzyme dilution. Integrated rate equations were developed on the basis of the dissociation of active dimeric enzyme during dilution and a reassociation of dilute monomers following the addition of substrate. The equations were modeled to the data, yielding a dissociation constant of 1.9 x 10(-3) s-1 and an association constant of 9.2 x 10(5) M-1 s-1 for the monomer-dimer interconversion process. This corresponds to an equilibrium constant of 4 x 10(-9) M for the dimerization of HIV-1 protease.

Vibrational energy transfer and relaxation processes in CH 3Br. A detailed kinetic analysis of the lower vibrational levels

Energy transfer processes among the lower vibrational levels in CH 3Br have been examined in an attempt to obtain information about the magnitude of the rate constants coupling these levels with one another and coupling ν 3 and ν 6 to the ground state. We conclude that there is a significant direct deactivation of both ν 3 and ν 6 to the ground state for CH 3Br-CH 3Br collisions. The magnitude of V-V rate constants for CH 3Br-CH 3Br and CH 3Br-rare gas interactions are discussed. In the course of these studies, a numerical method has been developed which allows for the determination of kinetic rate constants from measured rates by iterative solution of the coupled set of kinetic equations. Propagation of error from experimental rates to kinetic rate constants has been explicitly considered. The impact of our kinetic analysis and resulting conclusions on previous studies of the methyl halides is also discussed.

The complete determination of kinetic rate constants for coupled chemical reaction by means of relaxation spectroscopy

A method of analysis is proposed for chemical relaxation spectra permitting determination of the complete set of rate constants for a coupled multistep reaction. The essential feature is the construction of a “correlation” matrix from transient multispectral experimental data. The analysis requires only integration, matrix inversion, and matrix multiplication.

A numerical experiment on the determination of kinetic rate constants in the presence of diffusion

Two chemicals,A andB, are allowed to diffuse together and a reaction described by $$A + B\mathop \rightleftharpoons \limits_{K_{ - 1} }^{K_1 } C$$ is allowed to proceed. This system is described mathematically by a system of partial differential equations. A numerical procedure is presented to find the rate constants ofK 1 andK −1. A systematic analysis of the effects of errors is also presented.

Determination of kinetic rate constants in electrochemically initiated anionic polymerization of 1,3‐butadiene

AbstractThe rate constants for electrochemically initiated polymerization were determined by employing a pulsing technique. An electrochemical titration was conducted in which polymer chains were initiated electrochemically, propagated in the absence of current, and terminated electrochemically. The concentrations of supporting electrolyte and monomer were chosen to correspond to those employed in electropolymerization syntheses. The temperature range −10°C to −72°C gave kp = 1.45 × 102 exp {2600/RT}. The Arrhenius parameters are compared to those from previous studies and are interpreted in terms of ion‐pair propagation. Precise control of molecular weight distributions is implicit from an accurate knowledge of the kinetic parameters and is reported separately.

Analysis of a procedure for the determination of kinetic rate constants.

This paper is concerned with a mathematical analysis of the modified Guggenheim procedure. Theorems concerning the solutions of the differential equations which describe the general reaction $$E + SB\xrightarrow{{k_2 }}C + X, C\xrightarrow{{k_3 }}E + D$$ are derived and are used in a general discussion of the validity of the procedure. Numerical results are given to illustrate the general assertions and to obtain the range of values ofE 0 andS 0 for which the procedure is valid and enzymatic reaction such as α-chymotrypsin.