Determination of the absolute concentration of O atoms and OH radicals in laboratory studies

The fast reaction of O atoms with NO₂ has been used in measurements of absolute concentrations of O atoms. Similarly, the reaction of H with NO₂ can be used to generate OH radicals in known concentrations. Relative concentrations of both O atoms and OH radicals have frequently been measured by resonance fluorescence determinations in the ultra-violet. It will be shown that the stoichiometry of these reactions is strongly dependent on the initial concentration of reactants and on the contact time (in the case of OH on secondary reactions as well), making it impossible to equate directly the loss of NO₂ with the loss of O atoms or the production of OH radicals. In the first part of this work a simple analytical mathematical method for the determination of the concentration of atomic oxygen will be developed. The method is based on the integrated second order kinetic equation, and the effect of the experimental conditions on the results is discussed. In the second part, the production of OH as a function of contact time and of the initial concentrations of H and NO₂ is examined using a five reaction mechanism. By careful choice of the initial concentrations of reactants it is possible to reproduce the experimental results using simplified analytical expressions for the concentration of OH and hence to calculate a calibration factor. The importance of carrying out the calibration measurements under the same experimental conditions as those employed in kinetic experiments is highlighted.     

The micro-optical ring electrode. 3: Transient photocurrent studies of photophysical-electrochemical and photophysical-chemical-electrochemical systems

The micro-optical ring electrode (MORE) is a photoelectrochemical device based on a ring microelectrode that uses the insulating material interior to the ring electrode as a light guide. In this paper, we describe the preparation and characterization of very thin ring MOREs with (ring inner radius)/(ring outer radius) > 0.99. Theoretically, we derive asymptotic analytical expressions for the time dependence of the diffusion-limited transient light-on photocurrent generated by two general types of photoelectrochemical systems: (a) the PE (photophysical-electrochemical) system, wherein the photoexcited species itself is directly detected on the ring; (b) the PCE (photophysical-chemical-electrochemical) system, wherein the photoexcited species undergoes a homogeneous electron transfer reaction prior to electrochemical detection. Experimentally, we establish that it is possible to use such MOREs to study the wavelength dependence of photocurrents derived from photoelectrochemically active systems, such as the Ru(bipy)3 2+/Fe3+ PCE system, demonstrating the potential utility of the MORE as a selective electroanalytical probe. We also use our expressions for the time dependence of photocurrents at the MORE to derive values for the photoelectrochemical kinetic parameters of this system, including the rate coefficient for the back reaction of photogenerated Ru(bipy)3 3+ (0.115 s(-1)) and the quantum efficiency for the primary redox products, Ru(bipy)3 3+ and Fe2+, escaping cage recombination, phi(CE) = 0.099.     

Dependence of diffusive permeation rates and selectivities on upstream and downstream pressures : IV. Computer simulation of nonideal systems

In previous papers we have shown that a semi-empirical thermodynamic—diffusive model appears to duplicate the behavior of the hexane/heptane/polyethylene system with regard to the effect of upstream and downstream pressure on rate and separation. In the present paper we present a numerical method for dealing with our model equations, which allows us to treat nonideal systems, and to make use of more general expressions describing the concentration dependence of diffusivity. This method is discussed in detail, and several typical simulation results are presented.     

Nonsteady-State Model for Kinetics of Radical Chain Polymerization. 1. Direct Photoinitiation and Thermal Initiation with Constant Monomer Concentration

Chain radical polymerization with direct photoinitiatlon or thermal initiation and constant monomer concentration has been theoretically studied by dealing precisely with the kinetic differential equations. The expressions for molecular size distribution, number- and weight-average degrees of polymerization, and their dependence on the reaction conditions are derived in analytical form. A computation program allowed easy calculation of these parameters concerned with the resultant polymer.     

New differential techniques for evaluating rate constants and ratios of rate constants. The behaviors of irreversible first-and pseudo-first-order reactions

A record of the time dependence of the difference between two signals, one proportional to the concentration of a reactant or product in one reaction mixture and the other proportional to the concentration of the same or a corresponding substance in another mixture in which the reaction is initiated at the same time as the first, makes it possible to obtain not only the ratio, but also the individual values, of the rate constants for the two reactions. The effects of the experimental variables on a number of measurable parameters are examined, the errors associated with a number of different ways of evaluating the rate constants and their ratio are discussed, and it is shown how conditions can be selected that should provide values whose precisions compare favorably with those attainable by other techniques.     

Cellulose and hemicellulose hydrolysis models for application to current and novel pretreatment processes

Acids catalyze the hydrolysis of cellulose and hemicellulose to produce sugars that organisms can ferment to ethanol and other products. However, advanced low- and no-acid technologies are critical if we are to reduce bioethanol costs to be competitive as a pure fuel. We believe carbohy drate oligomers play a key role in explaining the performance of such hydrolysis processes and that kinetic models would help us understand their role. Various investigations have developed reaction rate expressions based on an Arrhenius temperature dependence that is first order in substrate concentration and close to first order in acid concentration. In this article, we evaluate these existing hydrolysis models with the goal of providing a foundation for a unified model that can predict performance of both current and novel pretreatment process configurations.     

Relations between kinetic parameters of different column models for liquid chromatography applying core-shell particles

This article presents analytical solutions of the general rate model (GRM), the lumped kinetic model (LKM), and the simpler equilibrium dispersive model (EDM) for core-shell particles and linear adsorption isotherms. The solutions in the Laplace domain are applied to derive analytical expressions for the temporal moments of these models. The results provide relations between the model specific kinetic parameters by matching one or more of the temporal moments. Several case studies are considered for illustration. The results show that simpler models are in many cases as good as the most detailed GRM if their kinetic parameters fulfill the matching relations. Thus, it is possible to reliably predict elution profiles using the simpler models. The derived analytical expressions can also be utilized to efficiently estimate model parameters from experimentally observed elution profiles to further optimize core-shell particles and to identify suitable column sizes and operating conditions.     

Determining the radius and the apparent charge of a micelle from electrical conductivity measurements by using a transport theory: explicit equations for practical use

We propose here a procedure which combines experiments and simple analytical formulas that allows us to determine good estimations of the size and charge of ionic micelles above the critical micellar concentration (cmc). First, the conductivity of n-tetradecyltrimethylammonium bromide and chloride (TTABr and TTACl, respectively) aqueous solutions was measured at 25 degrees C, before and above their cmc. Then, an analytical expression for the concentration dependence of the conductance of an ionic mixture with three species (monomers, micelles, and counterions) was developed and applied to the analysis of the experiments. The theoretical calculations use the mean spherical approximation (MSA) to describe equilibrium properties. Here, we propose new expressions for the electrical conductivity, adapted to the case of electrolytes that are dissymmetric in size, and applicable up to a total surfactant concentration of 0.1 mol L(-1). Moreover, we show that they are good approximations of the corresponding numerical results obtained from Brownian dynamics simulations. Since the analytical formulas given in the present paper involve a small number of unknown parameters, they allow one to derive the size and charge of macroions in solution from conductivity measurements.     

Reduction of chemical reaction networks using quasi-integrals

We present a numerical method to identify possible candidates for quasi-stationary manifolds in complex reaction networks governed by systems of ordinary differential equations. Inspired by singular perturbation theory, we examine the ratios of certain components of the reaction rate vector. Those ratios that rapidly approach a nearly constant value define a slow manifold for the original flow in terms of quasi-integrals, that is, functions that are nearly constant along the trajectories. The dimensionality of the original system is thus effectively reduced without reliance on a priori knowledge of the different time scales in the system. We also demonstrate the relation of our approach to singular perturbation theory which, in its simplest form, is just the well-known quasi-steady-state approximation. In two case studies, we apply our method to oscillatory chemical systems: the 6-dimensional hemin-hydrogen peroxide-sulfite pH oscillator and a 10-dimensional mechanistic model for the peroxidase-oxidase (PO) reaction system. We conjecture that the presented method is especially suited for a straightforward reduction of higher dimensional dynamical systems where analytical methods fail to identify the different time scales associated with the slow invariant manifolds present in the system.     

The “fine structure” of the slow micellar relaxation mode and the aggregation rates in the range between a potential hump and well in the work of aggregation

An analytical expression has been derived for the quasi-stationary size distribution of surfactant aggregates in a micellar system approaching the final equilibrium state. In contrast to previously known relations, the derived expression takes into account variations in the concentration of monomers during the slow relaxation and enables one to determine the previously unknown fine structure of the linearized mode of slow relaxation, i.e., its dependence on the aggregation numbers in the range between the maximum and minimum of the work of aggregation. This dependence has been reliably confirmed by the numerical solution of the set of linearized Becker–Döering difference equations, which describe the molecular mechanism of the kinetics of micellization and micellar relaxation. In turn, the expression found for the relaxation mode makes it possible to refine the analogous “fine structure” of aggregation rates at different points of the same range between the maximum and minimum of the work of aggregation, in which the aggregation rates appear to be low but exhibit a nonmonotonic behavior. This behavior is also confirmed by the numerical solution of the Becker–Döering difference kinetic equations.     

Mathematical modelling of enzyme kinetics reaction mechanisms and analytical solutions of non-linear reaction equations

The boundary value problem in basic enzyme reactions is formulated and approximate expressions for substrate and product concentrations are presented. He’s variational iteration method is used to give approximate and analytical solutions of non-linear reaction equations containing a non-linear term related to enzymatic reaction. The relevant analytical solutions for the substrate, enzyme, substrate-enzyme and product concentration profiles are discussed in terms of dimensionless reaction diffusion parameters K, λ and e{\varepsilon}.     

Analytical expression of non steady-state concentration for the CE mechanism at a planar electrode

The analytical solutions of the non-steady-state concentrations of species at a planar microelectrode are discussed. The analytical expression of the kinetics of CE mechanism under first or pseudo-first order conditions with equal diffusion coefficients at planar electrode under non-steady-state conditions are obtained by using Homotopy perturbation method. These simple new approximate expressions are valid for all values of time and possible values of rate constants. Analytical equations are given to describe the current when the homogeneous equilibrium position lies heavily in favour of the electroinactive species. Working surfaces are presented for the variation of limiting current with a homogeneous kinetic parameter and equilibrium constant. In this work we employ the Homotopy perturbation method to solve the boundary value problem. Furthermore, in this work the numerical simulation of the problem is also reported using Scilab program. The analytical results are found to be in excellent agreement with the numerical results.     

Analytical expression of non-steady-state concentrations and current pertaining to compounds present in the enzyme membrane of biosensor

A mathematical model of trienzyme biosensor at an internal diffusion limitation for a non-steady-state condition has been developed. The model is based on diffusion equations containing a linear term related to Michaelis-Menten kinetics of the enzymatic reaction. Analytical expressions of concentrations and current of compounds in trienzyme membrane are derived. An excellent agreement with simulation data is noted. When time tends to infinity, the analytical expression of non-steady-state concentration and current approaches the steady-state value, thereby confirming the validity of the mathematical analysis. Furthermore, in this work we employ the complex inversion formula to solve the boundary value problem.     

On approximate analytical solutions of differential equations in enzyme kinetics using homotopy perturbation method

Homotopy perturbation method is used to extend the approximate analytical solutions of non-linear reaction equations describing enzyme kinetics for combinations of parameters for which solutions obtained in previous works are not valid. Also, by constructing a new homotopy, alternative approximate analytical expressions for substrate, substrate-enzyme complex and product concentrations are found. These first-order approximate solutions give more accurate results than the second-order approximations derived in previous works.     

Size-selective concentration and label-free characterization of protein aggregates using a Raman active nanofluidic device

Trace detection and physicochemical characterization of protein aggregates have a large impact in understanding and diagnosing many diseases, such as ageing-related neurodegeneration and systemic amyloidosis, for which the formation of protein aggregates is one of the pathological hallmarks. Here we demonstrate an innovative label-free method for detecting and characterizing small amounts of early stage protein aggregates using a Raman active nanofluidic device. Sub-micrometre channels formed by a novel elastomeric collapse technique enable the separation and concentration of matured protein aggregates from small protein molecules. The Raman enhancement by gold nanoparticle clusters fixed below a micro/nanofluidic junction allows characterization of intrinsic properties of protein aggregates at concentration levels (～fM) much lower than can be done with traditional analytical tools. With our device we show for the first time the concentration dependence of protein aggregation over these low concentration ranges. We expect that our method could facilitate definitive diagnosis and possible therapeutics of diseases at early stages.     

The possibility of using femtosecond IR spectroscopy to determine the composition of molecules in the gas phase

The possibility of using one method of femtosecond laser spectroscopy, IR pump-probe, is considered for analyzing the molecular composition of gas. The measured intramolecular relaxation time of the vibrational energy is proposed as an individual characteristic of molecules. A number of compounds of different classes having the molecular chromophore group C=O are investigated. It is shown that the characteristic relaxation times of the corresponding analytical signals in the resonant exciting of C=O vibrations are significantly different for different molecules (ten or more), making it possible to identify molecules in mixtures by means of temporal selection. The linear dependence of the analytical signal on the vapor pressure of the investigated compounds and the energy fluence of the exciting radiation is revealed. It is shown that the analytical signal is not dependent on the pressure of the buffer gas (nitrogen) up to 1 atm.     

Synergistic effects in mixtures of oppositely charged surfactants as calculated from the Poisson-Boltzmann theory: a comparison between theoretical predictions and experiments

Critical micelle concentrations in mixtures of an anionic surfactant and a cationic amphiphilic drug have been investigated using a model-independent procedure to quantify observed synergistic effects. Experimental results were compared with a theory based on the Poisson-Boltzmann mean field approximation of a charged interface with a diffuse layer of counterions. Explicit expressions for the activity coefficients from which the critical micelle concentration can be calculated and quantitatively predicted have been derived and excellent agreement between experimental data and theory was obtained. As a result, we demonstrate that it is possible to rationalize and predict the magnitude of synergism in mixtures of oppositely charged surfactants in the presence of added salt.     

Resonance of relaxation time in the temperature modulated Schlögl model

We show the possibility to accelerate-in a resonant way-a nonlinear chemical reaction by imposing a small temperature modulation. This classical resonance, which happens for particular modulation frequencies, is illustrated on the athermic cubic Schlogl model, which allows us to get analytical expressions for both the reaction relaxation time and the frequency-resonant delay.     

Effect of surface conduction–induced electromigration on current monitoring method for electroosmotic flow measurement

Current monitoring method for measurement of EOF in microchannels involves measurement of time-varying current while an electrolyte displaces another electrolyte having different conductivity due to EOF. The basic premise of the current monitoring method is that an axial gradient in conductivity of a binary electrolyte in a microchannel advects only due to EOF. In the current work, using theory and experiments, we show that this assumption is not valid for low concentration electrolytes and narrow microchannels wherein surface conduction is comparable with bulk conduction. We show that in presence of surface conduction, a gradient in conductivity of binary electrolyte not only advects with EOF but also undergoes electromigration. This electromigration phenomenon is nonlinear and is characterized by propagation of shock and rarefaction waves in ion concentrations. Consequently, in presence of surface conduction, the current–time relationships for forward and reverse displacement in the current monitoring method are asymmetric and the displacement time is also direction dependent. To quantify the effect of surface conduction, we present analytical expressions for current–time relationship in the regime when surface conduction is comparable to bulk conduction. We validate these relations with experimental data by performing a series of current monitoring experiments in a glass microfluidic chip at low electrolyte concentrations. The experimentally validated analytical expressions for current–time relationships presented in this work can be used to correctly estimate EOF using the current monitoring method when surface conduction is not negligible.     

Mass transport in micellar surfactant solutions: 2. Theoretical modeling of adsorption at a quiescent interface

Here, we apply the detailed theoretical model of micellar kinetics from part 1 of this study to the case of surfactant adsorption at a quiescent interface, i.e., to the relaxation of surface tension and adsorption after a small initial perturbation. Our goal is to understand why for some surfactant solutions the surface tension relaxes as inverse-square-root of time, 1/t(1/2), but two different expressions for the characteristic relaxation time are applicable to different cases. In addition, our aim is to clarify why for other surfactant solutions the surface tension relaxes exponentially. For this goal, we carried out a computer modeling of the adsorption process, based on the general system of equations derived in part 1. This analysis reveals the existence of four different consecutive relaxation regimes (stages) for a given micellar solution: two exponential regimes and two inverse-square-root regimes, following one after another in alternating order. Experimentally, depending on the specific surfactant and method, one usually registers only one of these regimes. Therefore, to interpret properly the data, one has to identify which of these four kinetic regimes is observed in the given experiment. Our numerical results for the relaxation of the surface tension, micelle concentration and aggregation number are presented in the form of kinetic diagrams, which reveal the stages of the relaxation process. At low micelle concentrations, "rudimentary" kinetic diagrams could be observed, which are characterized by merging of some stages. Thus, the theoretical modeling reveals a general and physically rich picture of the adsorption process. To facilitate the interpretation of experimental data, we have derived convenient theoretical expressions for the time dependence of surface tension and adsorption in each of the four regimes.