Generalized fractal kinetics in complex systems (application to biophysics and biotechnology)

Brouers, F.; Sotolongo‐Costa, Oscar

doi:10.1016/j.physa.2005.12.062

Cited by 137 publications

(92 citation statements)

References 29 publications

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“…Such slopes, p, near 0.5 are typical for IDM and seem to suggest initial sorption mechanism controlled by normal diffusion, whereas for p \ 0.5 we system shows super diffusion and for p \ 0.5-subdiffusion (Sharifi-Viand et al 2012) with such effects attributed to disordered structure of the porous media (Havlin and Ben-Avraham 2002). However, one has to say, that the Bangham plot may be written as uðtÞ ¼ 1 À exp½ÀðktÞ p which is mathematically equivalent to the Avrami (1939) and fractal (Brouers and Sotolongo-Costa 2006) kinetic equations. Moreover, similar type of initial adsorption rates (a * t p ) are present in the SRT model with LF heterogeneity, however, power coefficient p ¼ n=ð1 þ nÞ B 0.5, where 0 \ nB1 is the heterogeneity coefficient (Marczewski 2011).…”

Section: Preliminary Analysis-bangham Plotsmentioning

confidence: 93%

“…Recently, several new equations describing fractal-like adsorption model (Haerifar and Azizian 2012) were presented. Those equations were derived from IKL and empirical MOE as well as from SRT model by using fractal approach to kinetics (Brouers and Sotolongo-Costa 2006) introduced in order to account for complexity of adsorption systems but earlier developed by Erofeev co-workers as KEKAM theory (Avrami 1939). In this paper only fractallike MOE (f-MOE) will be used:…”

Section: Adsorption Kinetics In Non-ideal Systemsmentioning

confidence: 99%

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Adsorption and desorption kinetics of benzene derivatives on mesoporous carbons

2013

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Adsorption and desorption of benzoic and salicylic acids and phenol from a series of synthesized mesoporous carbons is measured and analyzed. Equilibrium adsorption isotherms are best described by the LangmuirFreundlich isotherm. Intraparticle diffusion and McKay's pore diffusion models, as well as mixed 1,2-order (MOE), integrated Langmuir kinetic equation (IKL), LangmuirFreundlich kinetic equation and recently derived fractallike MOE (f-MOE) and IKL models were compared and used to analyze adsorption kinetic data. New generalization of Langmuir kinetics (gIKL), MOE and f-MOE were used to describe desorption kinetics. Analysis of adsorption and desorption half-times shows simple relation to the size of carbon pores.

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Section: Preliminary Analysis-bangham Plotsmentioning

confidence: 93%

Section: Adsorption Kinetics In Non-ideal Systemsmentioning

confidence: 99%

Adsorption and desorption kinetics of benzene derivatives on mesoporous carbons

2013

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“…The stretched exponential (SE) equation was developed as a global kinetic equation by Kolmogorov, Erofeev, Kozeeva, Avrami, and Mampel, and it is called the KEKAM equation [35][36]. It is characterized by parameter A and rate coefficient k. For the purpose of this analysis, the following forms of the equation were used:…”

Section: Kinetic Equationsmentioning

confidence: 99%

“…First approach proposed by Busch et al [18] consider the combination of two first-order rate functions and represent the traditional approach to interpret experimental data in terms of fast and slow sorption process. The other empirical kinetic equations are: the pseudo-second-order kinetic equation (PSOE) proposed by Blanchard et al [31], in original time-integrated form [32]; Elovich equation developed to describe kinetics of chemisorption [33][34] and stretched exponential equation (SE) also known as the KEKAM equation [35][36].…”

Section: Introductionmentioning

confidence: 99%

Kinetics of methane and carbon dioxide sorption and sorption–induced expansion of coal – kinetic equations assessment

et al. 2016

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Abstract. The aim of this study was to investigate the ability of kinetic equations to describe the sorption kinetics and expansion rate of solid coal samples. In order to address his issue the sorption kinetics of methane and carbon dioxide on bituminous coals were studied. At the same time, the changes occurring in the sample's overall dimensions, which accompanied sorption processes, were monitored. Experiments were carried out at high pressure by means of the volumetric method on a cubicoid solid samples. Several literature-based modeling approaches and equations are proposed to fit the kinetic curves of gas deposition, as well as the adequate kinetics of coal swelling. First equation represents the traditional approach to interpret experimental data in terms of fast and slow sorption process and consider the combination of two first-order rate functions. The other empirical kinetic equations are: the pseudo-second-order kinetic equation (PSOE), Elovich equation and the stretched exponential equation (SE). Two of the four equations are suitable to describe the kinetics of methane and carbon dioxide sorption and have been successfully used to quantify the observed dilatometric phenomena rates. The stretched exponential equation gave the best fit to the experimental data.

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“…A Eq. (11) também ocorre em cinética química, em que p representa a concentração de um dado reagente [12]. Se λ(x) = b x, a Eq.…”

Section: Família De Equações Diferenciais Não Linearesunclassified

Equações não lineares, método WKB generalizado e aplicação à equação de Thomas-Fermi

Pedron¹,

Mendes²

2008

Rev. Bras. Ens. Fis.

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Uma família de equações diferenciais ordinárias não lineares com ordem arbitráriaé obtida no contexto da mecânica estatística não extensiva baseada na entropia de Tsallis.É desenvolvida explicitamente uma extensão do método WKB para equações de segunda ordem a qualé aplicada para resolver aproximadamente uma classe de equações que contém como caso particular a equação de Thomas-Fermi para umátomo livre e para umíon sujeito a um campo magnético intenso. Espera-se que o procedimento apresentado aqui possa serútil na discussão de outros processos não lineares. Palavras-chave: entropia de Tsallis, método WKB, equações diferenciais não lineares.A family of nonlinear ordinary differential equations with arbitrary order is obtained in the non-extensive statistical mechanics scenario based on the Tsallis entropy. It is developed explicitly a WKB-like method for second order equations and it is applied to solve approximately a class of equations that contains as special case the Thomas -Fermi equation for a free neutral atom and heavy ion subjected to a strong magnetic field. It is expected that the procedure presented here can be useful in the discussion of other nonlinear processes. Keywords: Tsallis entropy, WKB method, nonlinear differential equations. IntroduçãoEm geral, quando uma nova teoriaé empregada para investigar alguma situação física, surgem com ela conceitos que são usados em vários contextos diferentes daquele que ela foi originalmente proposta. Por exemplo, devido a mecânica quântica, idéias relacionadas ao princípio da incerteza foram largamente disseminadas nas mais diversasáreas do conhecimento. Outro exemplo advém dos estudos sobre transições de fase em sistemas termodinâmicos, que conduziu ao uso de conceitos de invariância de escala em inúmeros contextos. Mais recentemente, tem sido explorada uma nova forma entrópica, a entropia de Tsallis [1]que tem como caso limite a entropia de BoltzmannGibbs-Shannon (BGS)quando q → 1. Naturalmente, existem casos que ilustram como podem existir conceitos baseados em S q que não são necessariamente ligados a mecânica estatística no seu sentido tradicional. Neste trabalho será mostrado detalhadamente como uma dessas situações pode ocorrer. Uma propriedade curiosa de S q surge quando dois sistemas independentes (A e B) são considerados. Em tal situação, as probabilidades são decompostas na forma de produto e, daí, verifica-se queEssa relação mostra que o caráter não extensivo de S q reduz-se ao extensivo no limite q → 1, assim comoé esperado que aconteça com uma mecânica estatística baseada na entropia de Tsallis. Além disso, a propriedade de (pseudo) aditividade (Eq. (3)) permite interpretar oíndice entrópico q como um indicador do grau de não extensividade de S q . Devido a essa propriedade, a mecânica estatística generalizada, que está ba-

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Generalized fractal kinetics in complex systems (application to biophysics and biotechnology)

Cited by 137 publications

References 29 publications

Adsorption and desorption kinetics of benzene derivatives on mesoporous carbons

Adsorption and desorption kinetics of benzene derivatives on mesoporous carbons

Kinetics of methane and carbon dioxide sorption and sorption–induced expansion of coal – kinetic equations assessment

Equações não lineares, método WKB generalizado e aplicação à equação de Thomas-Fermi

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