Nonexponential Kinetics of Surface Chemical Reactions

Snopok, B. A.

doi:10.1007/s11237-014-9351-0

Cited by 21 publications

(26 citation statements)

References 148 publications

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“…These last years the Brouers-Sotolongo fractal kinetics model [1], referred as BSf model in the following, has been invoked and used in a number of problems: in biosorption kinetics [2], non exponential kinetics of surface chemical reactions [3], adsorption on mesoporous carbons [4] [5] and spin dynamics in magnetic systems [6].…”

Section: Introductionmentioning

confidence: 99%

The Fractal (BSf) Kinetics Equation and Its Approximations

Brouers¹

2014

JMP

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We discuss the Brouers-Sotolongo fractal (BSf) kinetics model. This formalism interpolates between the first and second order kinetics. But more importantly, it introduces not only a fractional order n but also a fractal time parameter a which characterizes the time variation of the rate constant. This exponent appears in non-exponential relaxation and complex reaction models as demonstrated by the extended use of the Weibull and Hill kinetics which are the two most popular approximations of the BSf (n, a) kinetic equation as well in non-Debye relaxation formulas. We show that the use of nonlinear programs allows an easy and precise fitting of the data yielding the BSf parameters which have simple physical interpretations.

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Section: Introductionmentioning

confidence: 99%

The Fractal (BSf) Kinetics Equation and Its Approximations

Brouers¹

2014

JMP

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“…Note that Equation (4) of the previous set of equations has the diffusive term, i.e., D = 0, which promotes the spreading of the system. Equation (5) has no diffusive term and leads the particles to the rest, in contrast to Equation (4). Consequently, this system of equations can be related to the following process: diffusion pauses as expected.…”

Section: Diffusion and Pausesmentioning

confidence: 93%

“…Nowadays, anomalous diffusion plays an important role in the understanding of several phenomena, e.g., in biology [1][2][3][4], engineering [5,6], and physics [7][8][9]. Among them, we have the transport through the porous media [10,11], dynamic processes in protein folding [12], infiltration [13], single particle tracking [14], electrical response [15,16], and diffusion on fractals [17].…”

Section: Introductionmentioning

confidence: 99%

Intermittent Motion, Nonlinear Diffusion Equation and Tsallis Formalism

Lenzi

Silva

Lenzi

et al. 2017

Entropy

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Abstract:We investigate an intermittent process obtained from the combination of a nonlinear diffusion equation and pauses. We consider the porous media equation with reaction terms related to the rate of switching the particles from the diffusive mode to the resting mode or switching them from the resting to the movement. The results show that in the asymptotic limit of small and long times, the spreading of the system is essentially governed by the diffusive term. The behavior exhibited for intermediate times depends on the rates present in the reaction terms. In this scenario, we show that, in the asymptotic limits, the distributions for this process are given by in terms of power laws which may be related to the q-exponential present in the Tsallis statistics. Furthermore, we also analyze a situation characterized by different diffusive regimes, which emerges when the diffusive term is a mixing of linear and nonlinear terms.

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“…This opens the way for the direct optimization of the procedure of response space parameterization and finding the best time interval for the formation of CI with maximum information content. Correct application of the kinetic discrimination effect makes it possible to essentially increase the efficiency of cross-selective sensor arrays for gas analysis [25,40,[127][128][129][130][131].…”

Section: Multisensor Array Response Parameterizationmentioning

confidence: 99%