Application of the maximum entropy method to absorption kinetic rate processes

Ablonczy, Zs.; Lukács, András; Papp, É.

doi:10.1016/s0301-4622(02)00379-4

Cited by 18 publications

(7 citation statements)

References 19 publications

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“…For obvious reasons it is important to be able to distinguish between both situations on objective grounds. This goal has been treated in various papers, but mainly using empirical 28,57 or semi-empirical criteria, 58 likely to be useful and applicable to a limited subset of lifetime distributions.…”

Section: Resultsmentioning

confidence: 99%

Practical Aspects of the Maximum Entropy Inversion of the Laplace Transform for the Quantitative Analysis of Multi-Exponential Data

Lórenz-Fonfrı́a

Kandori

2007

Appl Spectrosc

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The number, position, area, and width of the bands in a lifetime distribution give the number of exponentials present in time-resolved data and their time constants, amplitudes, and heterogeneities. The maximum entropy inversion of the Laplace transform (MaxEnt-iLT) provides a lifetime distribution from time-resolved data, which is very helpful in the analysis of the relaxation of complex systems. In some applications both positive and negative values for the lifetime distribution amplitudes are physical, but most studies to date have focused on positive-constrained solutions. In this work, we first discuss optimal conditions to obtain a sign-unrestricted maximum entropy lifetime distribution, i.e., the selection of the entropy function and the regularization value. For the selection of the regularization value we compared four methods: the chi2 criterion and Bayesian inference (already used in sign-restricted MaxEnt-iLT), and the L-curve and the generalized cross-validation methods (not yet used in MaxEnt-iLT to our knowledge). Except for the frequently used chi2 criterion, these methods recommended similar regularization values, providing close to optimum solutions. However, even when an optimal entropy function and regularization value are used, a MaxEnt lifetime distribution will contain noise-induced errors, as well as systematic distortions induced by the entropy maximization (regularization-induced errors). We introduce the concept of the apparent resolution function in MaxEnt, which allows both the noise and regularization-induced errors to be estimated. We show the capability of this newly introduced concept in both synthetic and experimental time-resolved Fourier transform infrared (FT-IR) data from the bacteriorhodopsin photocycle.

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Section: Resultsmentioning

confidence: 99%

Practical Aspects of the Maximum Entropy Inversion of the Laplace Transform for the Quantitative Analysis of Multi-Exponential Data

Lórenz-Fonfrı́a

Kandori

2007

Appl Spectrosc

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“…Owing to the small dimensions of the aluminum polycations, and to obtain satisfactory data for fitting, correlograms were averaged for a minimum of 1 min per run on the Zetasizer and 5 min on the 90plus, with at least four repetitions for each sample. Data treatment was performed using a software that was provided by the manufacturers, and correlograms were additionally fitted with Clementine, a toolbox developed to model decay kinetics using either maximum entropy or least-squares fitting. , …”

Section: Methodsmentioning

confidence: 99%

“…Data treatment was performed using a software that was provided by the manufacturers, and correlograms were additionally fitted with Clementine, a toolbox developed to model decay kinetics using either maximum entropy or least-squares fitting. 31,32 ■ RESULTS AND DISCUSSION Effect of Glycine on the Isomerization Kinetics: In Situ 27 Al NMR and Ferron Measurements. With 27 Al NMR, Al 13 isomerization is demonstrated and quantified by fitting the 63 ppm peak attributed to the tetrahedrally coordinated aluminum core of ε-Al 13 , and fitting of the 70 ppm peak attributed to the tetrahedrally coordinated aluminum cores of Al 30 .…”

Section: Inorganic Chemistrymentioning

confidence: 99%

Impact of Amino Acids on the Isomerization of the Aluminum Tridecamer Al₁₃

et al. 2017

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The stability of the Keggin polycation ε-Al is monitored by Al NMR and ferron colorimetric assay upon heating aluminum aqueous solutions containing different amino acids with overall positive, negative, or no charge at pH 4.2. A focus on the effect of the amino acids on the isomerization process from ε- to δ-Al is made, compared and discussed as a function of the type of organic additive. Amino acids such as glycine and β-alanine, with only one functional group interacting relatively strongly with aluminum polycations, accelerate isomerization in a concentration-dependent manner. The effect of this class of amino acids is also found increasing with the pK of their carboxylic acid moiety, from a low impact from proline up to more than a 15-fold increased rate from the stronger binders such as glycine or β-alanine. Amino acids with relatively low C-terminal pK, but bearing additional potential binding moieties such as free alcohol (hydroxyl group) moiety of serine or the amide of glutamine, speed the isomerization comparatively and even more than glycine or β-alanine, glutamine leading to the fastest rates observed so far. With aspartic and glutamic acids, changes in aluminum speciation are faster and significant even at room temperature but rather related to the reorganization toward slow reacting complexed oligomers than to the Al isomerization process. The linear relation between the apparent rate constant of isomerization and the additive concentration points to a first-order process with respect to the additives. Most likely, the dominant process is an accelerated ε-Al dissociation, increasing the probability of δ isomer formation.

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“…The second law for isolated systems shows that the excess entropy, ∆S=S−S eq ≤ 0, increases monotonically in time, d(∆S)/dt ≥ 0. Therefore it plays the role of Lyapunov function, and expresses of global stability (Tarbell, 1977;Bernstein et al, 1993;Ablonczy et al, 2003); equilibrium state is a global attractor, so that an isolated system is globally stable. Deviations from stationary state lead to decrease in entropy production.…”

Section: Stability and Entropy Productionmentioning

confidence: 99%

Transport and Rate Processes

Demi̇rel

2014

Nonequilibrium Thermodynamics

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Application of the maximum entropy method to absorption kinetic rate processes

Cited by 18 publications

References 19 publications

Practical Aspects of the Maximum Entropy Inversion of the Laplace Transform for the Quantitative Analysis of Multi-Exponential Data

Practical Aspects of the Maximum Entropy Inversion of the Laplace Transform for the Quantitative Analysis of Multi-Exponential Data

Impact of Amino Acids on the Isomerization of the Aluminum Tridecamer Al₁₃

Transport and Rate Processes

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Application of the maximum entropy method to absorption kinetic rate processes

Cited by 18 publications

References 19 publications

Practical Aspects of the Maximum Entropy Inversion of the Laplace Transform for the Quantitative Analysis of Multi-Exponential Data

Practical Aspects of the Maximum Entropy Inversion of the Laplace Transform for the Quantitative Analysis of Multi-Exponential Data

Impact of Amino Acids on the Isomerization of the Aluminum Tridecamer Al13

Transport and Rate Processes

Contact Info

Product

Resources

About

Impact of Amino Acids on the Isomerization of the Aluminum Tridecamer Al₁₃