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Arrhenius Equation

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Jose Carlos Pinto – 1st expert on this subject based on the ideXlab platform

  • optimum reference temperature for reparameterization of the Arrhenius Equation part 2 problems involving multiple reparameterizations
    Chemical Engineering Science, 2008
    Co-Authors: Marcio Schwaab, Livia Pereira Lemos, Jose Carlos Pinto

    Abstract:

    Abstract Existence of high parameter correlations is one of the major problems during parameter estimation. This is particularly true when the mathematical model presents one or more kinetic constants that depend on temperature, as defined by the Arrhenius Equation. In a recent work, Schwaab and Pinto [2007. Optimum reference temperature for reparameterization of the Arrhenius Equation. Part 1: problems involving one kinetic constant. Chemical Engineering Science 62, 2750–2764] showed that an optimum reference temperature can be defined for reparameterization of the Arrhenius Equation and elimination of parameter correlation, when the model contains a single kinetic constant. However, when the model contains more than one kinetic constant, the number of parameter correlations is larger than the number of reference temperatures that can be defined; consequently, it becomes impossible to eliminate all the parameter correlations simultaneously. For this reason, in this work different norms are defined for the parameter correlation matrix and are used to allow for minimization of the parameter correlations through manipulation of reference temperatures. Three parameter estimation problems are used to illustrate the use of the proposed two-step parameter estimation procedure and to show that the minimization of parameter correlations and relative errors are indeed possible through proper manipulation of reference temperatures in problems involving multiple model parameters.

  • optimum reference temperature for reparameterization of the Arrhenius Equation part 1 problems involving one kinetic constant
    Chemical Engineering Science, 2007
    Co-Authors: Marcio Schwaab, Jose Carlos Pinto

    Abstract:

    The Arrhenius Equation is one of the most well-known Equations in the chemical field and is widely used to describe the temperature dependence of kinetic constants. This Equation contains two parameters, the frequency factor and the activation energy, which are usually estimated from experimental data. However, the correlation between the two parameter estimates is usually very high and in many cases is practically equal to one. This makes the precise identification of the parameter values very difficult. The high parameter correlation can be diminished through reparameterization of the Arrhenius Equation and definition of a reference temperature. For problems involving a single kinetic constant, it is shown here both analytically and through numerical examples that the proper definition of the reference temperature allows for estimation of the parameters of the Arrhenius Equation without correlation and with minimum relative error, leading to improvement of the parameter estimation procedure.

Aleksander Shkurenko – 2nd expert on this subject based on the ideXlab platform

  • A quantum mechanical alternative to the Arrhenius Equation in the interpretation of proton spin–lattice relaxation data for the methyl groups in solids
    Physical Chemistry Chemical Physics, 2015
    Co-Authors: Piotr Bernatowicz, Aleksander Shkurenko, Agnieszka Osior, Bohdan Kamieński, Sławomir Szymański

    Abstract:

    The theory of nuclear spin–lattice relaxation in methyl groups in solids has been a recurring problem in nuclear magnetic resonance (NMR) spectroscopy. The current view is that, except for extreme cases of low torsional barriers where special quantum effects are at stake, the relaxation behaviour of the nuclear spins in methyl groups is controlled by thermally activated classical jumps of the methyl group between its three orientations. The temperature effects on the relaxation rates can be modelled by Arrhenius behaviour of the correlation time of the jump process. The entire variety of relaxation effects in protonated methyl groups have recently been given a consistent quantum mechanical explanation not invoking the jump model regardless of the temperature range. It exploits the damped quantum rotation (DQR) theory originally developed to describe NMR line shape effects for hindered methyl groups. In the DQR model, the incoherent dynamics of the methyl group include two quantum rate (i.e., coherence-damping) processes. For proton relaxation only one of these processes is relevant. In this paper, temperature-dependent proton spin–lattice relaxation data for the methyl groups in polycrystalline methyltriphenyl silane and methyltriphenyl germanium, both deuterated in aromatic positions, are reported and interpreted in terms of the DQR model. A comparison with the conventional approach exploiting the phenomenological Arrhenius Equation is made. The present observations provide further indications that incoherent motions of molecular moieties in the condensed phase can retain quantum character over much broader temperature range than is commonly thought.

  • a quantum mechanical alternative to the Arrhenius Equation in the interpretation of proton spin lattice relaxation data for the methyl groups in solids
    Physical Chemistry Chemical Physics, 2015
    Co-Authors: Piotr Bernatowicz, Aleksander Shkurenko, Agnieszka Osior, Bohdan Kamienski, Slawomir Szymanski

    Abstract:

    The theory of nuclear spin–lattice relaxation in methyl groups in solids has been a recurring problem in nuclear magnetic resonance (NMR) spectroscopy. The current view is that, except for extreme cases of low torsional barriers where special quantum effects are at stake, the relaxation behaviour of the nuclear spins in methyl groups is controlled by thermally activated classical jumps of the methyl group between its three orientations. The temperature effects on the relaxation rates can be modelled by Arrhenius behaviour of the correlation time of the jump process. The entire variety of relaxation effects in protonated methyl groups have recently been given a consistent quantum mechanical explanation not invoking the jump model regardless of the temperature range. It exploits the damped quantum rotation (DQR) theory originally developed to describe NMR line shape effects for hindered methyl groups. In the DQR model, the incoherent dynamics of the methyl group include two quantum rate (i.e., coherence-damping) processes. For proton relaxation only one of these processes is relevant. In this paper, temperature-dependent proton spin–lattice relaxation data for the methyl groups in polycrystalline methyltriphenyl silane and methyltriphenyl germanium, both deuterated in aromatic positions, are reported and interpreted in terms of the DQR model. A comparison with the conventional approach exploiting the phenomenological Arrhenius Equation is made. The present observations provide further indications that incoherent motions of molecular moieties in the condensed phase can retain quantum character over much broader temperature range than is commonly thought.

Slawomir Szymanski – 3rd expert on this subject based on the ideXlab platform

  • a quantum mechanical alternative to the Arrhenius Equation in the interpretation of proton spin lattice relaxation data for the methyl groups in solids
    Physical Chemistry Chemical Physics, 2015
    Co-Authors: Piotr Bernatowicz, Aleksander Shkurenko, Agnieszka Osior, Bohdan Kamienski, Slawomir Szymanski

    Abstract:

    The theory of nuclear spin–lattice relaxation in methyl groups in solids has been a recurring problem in nuclear magnetic resonance (NMR) spectroscopy. The current view is that, except for extreme cases of low torsional barriers where special quantum effects are at stake, the relaxation behaviour of the nuclear spins in methyl groups is controlled by thermally activated classical jumps of the methyl group between its three orientations. The temperature effects on the relaxation rates can be modelled by Arrhenius behaviour of the correlation time of the jump process. The entire variety of relaxation effects in protonated methyl groups have recently been given a consistent quantum mechanical explanation not invoking the jump model regardless of the temperature range. It exploits the damped quantum rotation (DQR) theory originally developed to describe NMR line shape effects for hindered methyl groups. In the DQR model, the incoherent dynamics of the methyl group include two quantum rate (i.e., coherence-damping) processes. For proton relaxation only one of these processes is relevant. In this paper, temperature-dependent proton spin–lattice relaxation data for the methyl groups in polycrystalline methyltriphenyl silane and methyltriphenyl germanium, both deuterated in aromatic positions, are reported and interpreted in terms of the DQR model. A comparison with the conventional approach exploiting the phenomenological Arrhenius Equation is made. The present observations provide further indications that incoherent motions of molecular moieties in the condensed phase can retain quantum character over much broader temperature range than is commonly thought.