Showing papers on "Rate equation published in 1994"
TL;DR: In this article, a rate law that integrates the effects of temperature, pH, ionic strength, and saturation conditions on the overall dissolution and precipitation rates of minerals is proposed, with special attention to the important effects of deviation from equilibrium on the rates of mineral-water reactions.
682 citations
TL;DR: In this article, the dynamic processes of reverse saturable absorption (RSA) in a solution of C60 are studied in detail by use of rate equations and the light-propagation equation for a five-energy-level model.
Abstract: The dynamic processes of reverse saturable absorption (RSA) in a solution of C60 are studied in detail by use of rate equations and the light-propagation equation for a five-energy-level model. The RSA experimental results for C60 in toluene solution with a nanosecond–picosecond Nd:YAG laser at 532 nm are consistent with the theoretical simulations. Effects of sample concentration and thickness on RSA and contributions of the singlet and triplet excited states to RSA for various laser-pulse widths and wavelengths are also analyzed. Finally, an all-optical switch based on excited-state nonlinear absorption and the pump-probe technique is implemented.
109 citations
TL;DR: In this article, the utility of the rate equation treatment of nucleation and growth with critical size i ≥ 1 for both isotropic and strongly anisotropic diffusion is illustrated.
Abstract: We illustrate the utility of the ‘‘mean‐field’’ rate equation treatment of nucleation and growth with critical size i≥1 for both isotropic and strongly anisotropic diffusion. Some comparison is made of rate equation predictions for mean densities and size distributions of stable islands with predictions from ‘‘exact’’ simulations for the low coverage precoalescence regime. We also consider island separation distributions, depletion effects, and associated splitting of kinematic diffraction profiles. We necessarily treat other issues via simulations. These include analysis of (i) transitions in island shape from compact to dendritic, as observed for Pt/Pt(111), and extraction of associated edge diffusion barriers; and (ii) adlayer percolation, which sometimes mediates the population of higher layers. We also briefly comment on nucleation and growth behavior in the specific systems M/M(100) with M=Fe, Pd, Au, Cu, Ni, and Ag.
101 citations
TL;DR: In this paper, a large-scale apparatus was used to evaluate the effect of particle size on the spontaneous heating of a coal stockpile, where coal with various ranges of particle sizes (between 2 and 50 mm in diameter) was oxidized in a cylinder of 3m length and 0.3m diameter.
80 citations
TL;DR: In this paper, a differential scanning calorimeter was used to monitor the reaction kinetics of an epoxy-based vinyl ester resin and a new graphical estimation technique was proposed for the determination of the kinetic parameters describing an autocatalytic reaction.
Abstract: A new graphical estimation technique is proposed for the determination of the kinetic parameters describing an autocatalytic reaction. A differential scanning calorimeter was used to monitor the reaction kinetics of an epoxy-based vinyl ester resin. The method utilizes information from a zero initial reaction rate, conversation at vitrification, the ratio of reaction rate constants under different isothermal conditions, and characteristics of the phenomenological kinetic model with assumptions being made about the overall reaction order. By fitting data to the integrated reaction rate equation with adjustments for the isothermal conditions, the kinetic parameters are estimated without using a linear or nonlinear regression method. Different kinetic parameters can be estimated from data before and after the gel point which was obtained from the relationship between the glass transition temperature and the degree of cure.
65 citations
TL;DR: In this paper, a consistent data base of reaction pathways, kinetics, and mechanisms for catalytic hydrogenation of one-, two-, three-, and four-fused aromatic ring compounds allowed for correlation of their Langmuir-Hinshelwood-Hougen-Watson (LHHW) rate law parameters with molecular structure.
62 citations
TL;DR: The reaction of atomic nickel with water in the gas phase has been investigated by kinetic studies under static pressure conditions near room temperature, and by accurate quantum chemical calculations as discussed by the authors, and experimental and theoretical results are consistent with a reaction mechanism involving formation of a weakly bound nickel-water adduct, which may react further by oxidative addition of nickel to the O-H bond of water to form the insertion product HNiOH.
Abstract: The reaction of atomic nickel with water in the gas phase has been investigated by kinetic studies under static pressure conditions near room temperature, and by accurate quantum chemical calculations. Experimental and theoretical results are consistent with a reaction mechanism involving formation of a weakly bound nickel–water adduct, which may react further by oxidative addition of nickel to the O–H bond of water to form the insertion product HNiOH. Experimental estimates of reaction energetics have been made by using unimolecular reaction theory calculations to model rate coefficients obtained by fitting kinetic data to a simple rate equations model. These experimental estimates are in agreement with the theoretical results, and indicate that the insertion product is bound by at least 20–25 kcal/mol, relative to nickel plus water. There is also agreement that the barrier to oxidative addition is no greater than 1–2 kcal/mol, and may be smaller. This theoretical result was obtained only at the highest ...
46 citations
TL;DR: In this article, a surface sulfur layer was identified on pyrite surfaces during transpassive oxidation using cyclic voltammetry, in situ laser Raman spectroscopy and potentiostatic measurements.
45 citations
TL;DR: In this paper, the reaction between black carbon, in the form of n-hexane soot, and NO 2 /N 2 O 4 has been studied at low nitrogen oxide pressures (9-35 ppm) and under the influence of simulated solar radiation.
36 citations
TL;DR: In this paper, the authors describe reversible non-linear copolymerizations with arbitrarily great numbers of monomers specifying the stoichiometric coefficients of the reactions involving end-groups and present rate equations for the vectorial generating function or discrete transform of the distribution of end groups and repeating units and its derivatives with respect to logarithms of Laplace parameters.
35 citations
TL;DR: In this paper, the Nernst-Planck equation was used to describe fluxes of chemical species and the method of singular value decomposition of a scaled stoichiometric matrix was used for qualitative analysis of model equations in order to obtain manageable description of systems with fast and slow reactions.
TL;DR: In this paper, a general plane wave theory for diode-pumped solid state lasers was developed for arbitrary saturation and outcoupling, and the model is based on the steady state rate equations for a two-manifold system coupled to the growth of the laser field and the depletion of the pump.
TL;DR: In this paper, an approach for including solvent effects in variational transition state theory calculations of rate constants for activated chemical reactions in solution is presented, and the focus is on methods capable of first-principles predictions of reaction rate constants from interatomic potential energy surfaces.
Abstract: An approach is outlined for including solvent effects in variational transition state theory calculations of rate constants for activated chemical reactions in solution. The focus is on methods capable of first-principles predictions of reaction rate constants from interatomic potential energy surfaces. The approach separates the system into a cluster model that is treated explicitly and the ‘solvent’ that is treated approximately, and includes both equilibrium solvation effects on interaction energies and non-equilibrium effects that enter through a solvent friction model. We discuss methods used to included quantum-mechanical effects on bound vibrational motions and quantum-mechanical effects on motion along a reaction coordinate (e.g. quantum tunnelling).
TL;DR: In this paper, the statistical nonequilibrium thermodynamic theory of diffusion-influenced reactions is employed to study reversible excimer formation in solution, and three types of rate coefficients for bimolecular excimer forming are discussed: (i) molecular rate coefficients defined by one-way reactive fluxes, (ii) phenomenological rate constants based on form of the macroscopic rate equations, and (iii) modified, time-dependent rate coefficients.
Abstract: The statistical nonequilibrium thermodynamic theory of diffusion‐influenced reactions is employed to study reversible excimer formation in solution. Three types of rate coefficients for bimolecular excimer formation are discussed: (i) molecular rate coefficients defined by one‐way reactive fluxes, (ii) phenomenological rate constants based on form of the macroscopic rate equations, and (iii) modified, time‐dependent phenomenological rate coefficients. Relations are derived linking: (i) the molecular rate coefficients for reversible and irreversible excimer formation rates, and (ii) the steady‐state molecular rate constant and the Laplace transform of the time resolved irreversible rate coefficient. The relationship between the present approach and the microscopic–stochastic theory of excimer formation is discussed.
TL;DR: The mechanism of tungsten chemical vapor deposition (CVD) using hydrogen reduction of Tungsten hexafluoride is reviewed in this paper, with emphasis on the relevant fundamental surface chemistry and kinetics.
15 Oct 1994-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: Differential scanning calorimetry was applied to the study of high temperature kinetics of TiAl 3 formation from the constituent metal powders as mentioned in this paper, and the effects of various experimental parameters on the reaction kinetics were determined.
Abstract: Differential scanning calorimetry was applied to the study of high temperature kinetics of TiAl 3 formation from the constituent metal powders. The reaction proceeds at a measurable rate above the melting point of aluminum. The effects of various experimental parameters on the reaction kinetics were determined. The heating rate affects the exothermic reaction temperature. In the temperature range 690–740°C, the rate equation obeys the Prout-Tompkins equation and the activation energy and pre-exponential factor are 149 kJ mol −1 and 1.2×10 6 s −1 respectively. In the temperature range 750–900°C, the rate equation obeys a second-order rate equation with an activation energy of 517 kJ mol −1 and a pre-exponential factor of 1.9×10 23 s −1 . These kinetics parameters represent true intrinsic values because they are directly determined by eliminating any heat transfer effects.
TL;DR: In this article, the Gibbs-Thomson equation for the chemical potential of spherical drops and the accepted driving force for neck growth between two spherical particles was derived. But the authors did not consider the influence of particle size and shape on the free energies of particles of anisotropic specific surface free energies.
Abstract: An equation is derived that describes the influence of particle size and shape on the free energies of particles of anisotropic specific surface free energies. When the specific surface free energy is isotropic, the general equation reduces directly to the Gibbs-Thomson equation for the chemical potential of spherical drops and predicts the accepted driving force for neck growth between two spherical particles. The general equation is also used to obtain equations for the chemical potentials of particles of non-equilibrium shapes and to derive alternate rate equations for different possible rate-controlling steps of mass transport when faceted [100] ridge/channel arrays etched into a [100] single-crystal surface decrease in depth to reduce the surface free energy. Edge free energies are suggested to sometimes play important roles in determining the sequence of shape changes that occur when particles of non-equilibrium shapes and to derive alternate rate equations for different possible rate-controlling steps of mass transport when faceted [100] ridge/channel arrays etched into a [100] single-crystal surface decrease in depth to reduce the surface free energy. Edge free energies are suggested to sometime play important roles in determining the sequence of shape changes that occur when particles of non-equilibrium shapes are annealed.
TL;DR: In this paper, a general equation for the time-dependent amplitudes of the modes of the electromagnetic field of a semiconductor laser is derived in the small-signal approximation.
Abstract: A quite general equation for the time-dependent amplitudes of the modes of the electromagnetic field of a semiconductor laser is derived in the small-signal approximation. It is shown that the modes fulfil a general orthogonality relation that follows directly from Maxwell's equations. The dependence of the dielectric function on temporally varying carrier densities is taken into account. The local changes of the carrier densities lead to a coupling of different modes. The equations for the mode amplitudes are used to derive rate equations for the photon number and the phase of a mode. >
TL;DR: An improved expression for the time-bandwidth product (DeltatDeltaf) of picosecond optical pulses from gain-switched semiconductor lasers was obtained by a series of numerical simulations based on rate equations without making any assumption for a particular pulse shape and chirp condition.
Abstract: An improved expression for the time-bandwidth product (DeltatDeltaf) of picosecond optical pulses from gain-switched semiconductor lasers was obtained by a series of numerical simulations based on rate equations without making any assumption for a particular pulse shape and chirp condition. The relation can be expressed by [Equation] as a function of the linewidth-enhancement factor alpha. The influence of the spontaneous emission factor beta on the relation is also examined.
24 Jul 1994
TL;DR: In this paper, the growth mechanism of polypyrrole has been studied in acetonitrile by kinetic and spectroelectrochemical measurements, and the results indicate that the polymerization reaction reaction rate is 1 3 ∼ 1 2 order with respect to the pyrrole concentration and 1 3 order to the amount of poly pyroxide.
Abstract: The growth mechanism of polypyrrole has been studied in acetonitrile by kinetic and spectroelectrochemical measurements. The results indicate that the polymerization reaction rate is 1 3 ∼ 1 2 order with respect to the pyrrole concentration and 1 3 order with respect to the amount of polypyrrole. In-Situ spectroelectrochemical studies at lower pyrrole concentrations indicate that reasonably high steady state concentrations of trimeric and tetrameric species are maintained during the polymerization reaction. From these observations, we conclude that: (1) both the monomer and polymer films are important for the growth (from the rate equation), (2) the formation of dimeric species appears to present the rate limiting step for the reaction (from the reaction order), (3) polymers grow in one-dimension, and (4) further growth of polymers from trimeric and tetrameric species requires a high monomer concentration.
TL;DR: End-linked tetrafunctional model networks were simulated using the bond-fluctuation algorithm and the kinetics of network formation was studied and compared with the solution of the rate equation for a four-step process.
Abstract: End-linked tetrafunctional model networks were simulated using the bond-fluctuation algorithm. The kinetics of network formation was studied and compared with the solution of the rate equation for a four-step process. A crossover from diffusion-controlled to reaction-controlled time behavior depending on the reaction speed was observed. For a reaction probability of 10−3 per movement of an unreacted chain end and a cross-linker into nearest neighbor position, the rate equation gives a satisfactory description of the kinetics of the reaction.
The evolution of the largest cluster as well as local imperfections of the network were considered in detail. The evolution of the cyclic rank differs from the model of Queslel and Mark.
The mobility of cross-links of different functionality was measured.
TL;DR: In this paper, the authors investigated the kinetics for the aqueous alkaline hydrolysis of 1,3,5,7-tetraaza-1,3-5,5-7-Tetranitrocyclooctane (HMX) and the temperature dependence of the rate constants.
TL;DR: In this paper, the authors proposed an equation of the form: dX/dT=A0/a2(a1/a 2)mexp ⊆(−E0/RT)f(X)n, where A0 and E0 are temperature independent rate parameters, a1 is the heating rate at which the kinetic parametersA0 and e0 have been calculated, a2 is any other heating rate for which the prediction is to be made, and m is an exponent.
Abstract: Thermogravimetric (TG) data is useful for determining the decomposition temperatures and rates of solid materials. Reaction rate parameters such as activation energy (E) and pre-exponential factor (A) can be determined from constant heating rate data using a simplified Arrhenius equation. Unfortunately, there is a wide variation in these parameters, reported in the literature for each substance, depending on the heating rate used among other factors. As a result there is no agreement on the data to be used in extrapolation to other conditions.
We have measured the decomposition of cellulose at various heating rates and found that the present form of rate equation explains data only at a single heating rate at which the parameters have been determined. These parameters fail to explain the decomposition data obtained at other heating rates.
In this paper we propose an equation of the form: dX/dT=A0/a2(a1/a2)mexp(−E0/RT)f(X)n, where A0 and E0 are temperature independent rate parameters, a1 is the heating rate at which the kinetic parametersA0 and E0 have been calculated, a2 is any other heating rate for which the prediction is to be made, and m is an exponent. This equation is consistent with the original Arrhenius equation and is able to explain the TG data over a wide range of heating rates.
TL;DR: By fitting the appropriate rate equation to the data it is possible to determine the maximum velocity and Michaelis constant for both forward and reverse reaction from experiments conducted in one direction only.
TL;DR: The commonly assumed quasiequilibrium particle distribution with the same quasi-Fermi-level for all quantum-dot carriers in the same energy (conduction or valence) band is found not to be valid for a wide range of temperatures at the inversion populations and bound energy separations used in the literature.
Abstract: The commonly assumed quasiequilibrium particle distribution with the same quasi-Fermi-level for all quantum-dot carriers in the same energy (conduction or valence) band is found not to be valid for a wide range of temperatures at the inversion populations and bound energy separations (greater than a LO phonon energy) used in the literature. Bound state occupation factors obtained from the steady state solution of rate equations describing the ionization balance in room-temperature 100-\AA{}-radius GaAs quantum dots whose centers are separated by 400 \AA{} are found to be very different from the quasiequilibrium distribution used in an example from the literature. In such quantum dots, bound state transitions result from collisions between charged particles via the Coulomb interaction, and from interband and intraband radiative processes. The critical free electron concentration above which collisional processes can establish a quasiequilibrium in the conduction band is found to exceed ${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. Our numerical solution is in good agreement with Pitaevskii's model from atomic physics of an electron random walk in energy as modeled by a Fokker-Planck equation. In our simple model, electrons are captured into a bound conduction band state via three-body recombination and phonon emission, and drop into lower energy bound states via a series of collisional deexcitations before combining with a valence band hole. Solution of the rate equations is standard in numerical studies of stimulated emission in atomic plasmas, but our present discussion is, to our knowledge, the first in the literature on semiconductor quantum-dot lasers.
TL;DR: In this paper, the reduction rate of cupric ions under UV light irradiation in the CuSO4+methanol+TiO2 system has been investigated and the parameters studied include the Cu2+ concentration, MeOH concentration, TiO2 content, light intensity, temperature and pH effects.
Abstract: Photoelectrochemical reduction of cupric ions under UV light irradiation in the CuSO4+methanol+TiO2 system has been investigated. The parameters studied include the Cu2+ concentration, MeOH concentration, TiO2 content, light intensity, temperature and pH effects. Two phenomena were noteworthy. The first is that the reduction rate of cupric ions can be divided into two stages, i.e. a slow stage and a rapid stage. The second phenomenon is that the time—conversion curves show little concavity. Analyses were performed via electron—hole pair generation, separation, capture, recombination and deposit chemical dissolution. The two-stage phenomenon can be attributed to the pH change of the system during the reaction. The concavity of the reaction curves is mainly affected by efficient electron—hole separation resulting from the metallic copper deposit. An apparent reaction rate equation for the rapid stage also has been derived. Dominant factors which affect the electrochemical reaction are the methanol adsorption, light absorption, temperature and pH of the system.
TL;DR: In this paper, the kinetics of irreversible coagulation phenomena in spatially homogeneous systems are formulated in terms of a multivariate stochastic process, governed by a master equation for the joint probability distribution of the numbers of reacting species.
Abstract: The kinetics of irreversible coagulation phenomena in spatially homogeneous systems is formulated in terms of a multivariate stochastic process. The latter is governed by a master equation for the joint probability distribution of the numbers of reacting species. An efficient numerical algorithm is used to simulate the complete time evolution of the stochastic process. The method is illustrated by simulating the coagulation reaction with configuration-dependent reaction kernels, Kij = (ij)ω, for clusters of mass i and j with 1/2 < ω ⩽ 1, which are designed to model gelation phenomena. It is demonstrated that the stochastic simulation allows the determination of critical exponents and the gel point directly from the master equation. The results are compared to predictions of the rate equation approach to the sol-gel transition.
TL;DR: In this article, a rate equation that reproduces the pattern of nearly symmetric abundance distributions observed in coalescence with high laser fluence and also to the strongly asymmetric case with low fluence was proposed.
TL;DR: In this article, a vertical cavity surface emitting laser with a vertically integrated detuned cavity is proposed and analyzed, and the theory predicts the laser will show the usual relaxation oscillation response near f/sub r/, and a relatively constant response throughout the microwave and millimeter wave bands.
Abstract: A vertical cavity surface emitting laser with a vertically integrated detuned cavity is proposed and analyzed. Intensity modulation is achieved by changing the refractive index inside the detuned cavity. It is expected that standard methods of dynamic analysis (the rate equations) will be unsuitable for this structure, so a new method of analysis in which optical sidebands are calculated separately is used. The theory predicts the laser will show the usual relaxation oscillation response near f/sub r/, and a relatively constant response throughout the microwave and millimeter wave bands. This is in contrast to direct modulation, in which the response beyond f/sub r/ declines at the rate 40 dB/decade. It is also in contrast to the Q-modulation of lasers for which the rate equations apply, in which case the decline is 20 dB/decade. >