Topic
Rate equation
About: Rate equation is a research topic. Over the lifetime, 4249 publications have been published within this topic receiving 90524 citations. The topic is also known as: rate law.
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TL;DR: In this article, it was shown that the rate of integration at a kink is of the order of one thousandth of the speed of dehydration of the cation, which is due to the activation energy of diffusion, as an ion, in order to integrate, must dehydrate and make a diffusional jump.
449 citations
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TL;DR: The theory of absolute reaction rates for condensed phases was developed in this article, where the rate of a reaction of any order in any phase where the slow process is the passage over an energy barrier consists of the product of a transmission coefficient κ, a frequency kT/h, an equilibrium constant between an activated complex and the reactants and an activity coefficient factor.
Abstract: The theory of absolute reaction rates is developed for condensed phases. The equation for the rate of a reaction of any order in any phase where the slow process is the passage over an energy barrier consists of the product of a transmission coefficient κ, a frequency kT/h, an equilibrium constant between an activated complex and the reactants and an activity coefficient factor. Previous theories of reaction rates such as Bronsted's, the collision theory of Mc C. Lewis, etc., are seen to be special cases of the general theory. A variety of examples are considered.
385 citations
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TL;DR: In this paper, the rate equations for a microcavity semiconductor laser are solved and the steady-state behavior of the laser and some of its dynamic characteristics are investigated, and it is shown that by manipulating the mode density and the spontaneous decay rates of the cavity modes, the threshold gain can be decreased and the modulation speed can be improved.
Abstract: The rate equations for a microcavity semiconductor laser are solved and the steady-state behavior of the laser and some of its dynamic characteristics are investigated. It is shown that by manipulating the mode density and the spontaneous decay rates of the cavity modes, the threshold gain can be decreased and the modulation speed can be improved. However, in order to fully exploit the possibilities which the modification of the spontaneous decay opens up, the active material volume in the cavity must be smaller than a certain value. Threshold current using different definitions, population inversion factor, L-I curves, linewidth, and modulation response are discussed. >
363 citations
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TL;DR: The catalytic oxidation of carbon monoxide on a platinum surface was studied by scanning tunneling microscopy and the kinetic parameters were obtained, and their values agree well with data from macroscopic measurements.
Abstract: The catalytic oxidation of carbon monoxide (CO) on a platinum (111) surface was studied by scanning tunneling microscopy The adsorbed oxygen atoms and CO molecules were imaged with atomic resolution, and their reactions to carbon dioxide (CO 2 ) were monitored as functions of time The results allowed the formulation of a rate law that takes the distribution of the reactants in separate domains into account From temperature-dependent measurements, the kinetic parameters were obtained Their values agree well with data from macroscopic measurements In this way, a kinetic description of a chemical reaction was achieved that is based solely on the statistics of the underlying atomic processes
358 citations
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TL;DR: In this paper, the authors used a 9-carbon model compound to describe a proposed mechanism for homoepitaxial growth of diamond from methyl radicals on a hydrogenated, electrically neutral (100) surface.
Abstract: We use a 9‐carbon model compound to describe a proposed mechanism for homoepitaxial growth of diamond from methyl radicals on a hydrogenated, electrically neutral (100) surface. We estimate enthalpy and entropy changes for each step in the mechanism using group additivity methods, taking into account the types of bonding and steric repulsions found on the (100) surface. Rate constants are estimated based on analogous reactions for hydrocarbon molecules, while gas phase species concentrations are taken from our previous measurements. The rate equations are then integrated. The method, which contains no adjustable parameters or phenomenological constants, predicts a growth rate of between 0.06 and 0.6 μm/h, depending on the local details of the surface. Uncertainties related to the use of a model compound rather than diamond are discussed. The analysis demonstrates that the proposed mechanism is feasible.
350 citations