Article

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

Faculty of Physics, Chair of Complex Systems H. Poincar, University of Havana, Cuba
Physica A: Statistical Mechanics and its Applications (Impact Factor: 1.72). 08/2005; DOI: 10.1016/j.physa.2005.12.062
Source: arXiv

ABSTRACT We derive a universal function for the kinetics of complex systems characterized by stretched exponential and/or power-law behaviors. This kinetic function unifies and generalizes previous theoretical attempts to describe what has been called “fractal kinetic”.The concentration evolutionary equation is formally similar to the relaxation function obtained in the stochastic theory of relaxation, with two exponents α and n. The first one is due to memory effects and short-range correlations and the second one finds its origin in the long-range correlations and geometrical frustrations which give rise to ageing behavior. These effects can be formally handled by introducing adequate probability distributions for the rate coefficient. We show that the distribution of rate coefficients is the consequence of local variations of the free energy (energy landscape) appearing in the exponent of the Arrhenius formula.The fractal (n,α) kinetic has been applied to a few problems of fundamental and practical importance in particular the sorption of dissolved contaminants in liquid phase. Contrary to the usual practice in that field, we found that the exponent α, which is implicitly equal to 1 in the traditional analysis of kinetic data in terms of first- or second-order reactions, is a relevant and useful parameter to characterize the kinetics of complex systems. It is formally related to the system energy landscape which depends on physical, chemical and biological internal and external factors.We discuss briefly the relation of the (n,α) kinetic formalism with the Tsallis theory of non-extensive systems.

Download full-text

Full-text

Available from: O. Sotolongo-Costa, Jun 23, 2015
1 Follower
 · 
130 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The adsorptive removal capacities of highly available Turbinaria turbinata alga and its derived carbonaceous products (i.e. pyrolyzed, physically and chemically activated carbons) were investigated in this study. Several textural and chemical characterizations were performed on the alga and its activated carbons (ACs). Besides, kinetics and isotherms assays were performed and modeled in order to monitor the sorption capacities and dynamic behaviors. The main results showed that the raw Turbinaria biomass has a non porous structure. Then, after thermo-chemical treatments, a porous matrix starts to develop and the total pore volume drastically increased from 0.001 cm3/g for the algal precursor (turb-raw) to 1.316 cm3/g for its derived chemically AC (turb-P1). As well, the specific surface area improved from m2/g for (turb-raw) to 1307 m2/g for (turb-P1). Consequently, the maximum sorption capacity went from 63 mg/g for the algal biomass up to 411 mg/g for the chemically ACs. Moreover, the removal rate was taken into consideration in order to set a more reliable and realistic approach to figure out the most efficient AC. Thus, based on those criteria, it was found that the chemically activated carbon “turb-P1” is the most efficient Turbinaria-derived sorbent to adsorb and remove methylene blue (MB) molecules from aqueous solutions with 169 g of the dye using 1 kg of raw alga (considering an AC production yield of 49%).
    Biochemical Engineering Journal 08/2012; 67:35-44. DOI:10.1016/j.bej.2012.05.008 · 2.37 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Dynamical disorder motivates fluctuating rate coefficients in phenomenological, mass-action rate equations. The reaction order in these rate equations is the fixed exponent controlling the dependence of the rate on the number of species. Here, we clarify the relationship between these notions of (dis)order in irreversible decay, n A → B, n = 1, 2, 3, …, by extending a theoretical measure of fluctuations in the rate coefficient. The measure, Jn-Ln (2)≥0, is the magnitude of the inequality between Jn, the time-integrated square of the rate coefficient multiplied by the time interval of interest, and Ln (2), the square of the time-integrated rate coefficient. Applying the inequality to empirical models for non-exponential relaxation, we demonstrate that it quantifies the cumulative deviation in a rate coefficient from a constant, and so the degree of dynamical disorder. The equality is a bound satisfied by traditional kinetics where a single rate constant is sufficient. For these models, we show how increasing the reaction order can increase or decrease dynamical disorder and how, in either case, the inequality Jn-Ln (2)≥0 can indicate the ability to deduce the reaction order in dynamically disordered kinetics.
    The Journal of Chemical Physics 02/2015; 142(6):064113. DOI:10.1063/1.4907629 · 3.12 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In the present work, the preparation of several chemically activated carbons (CACs) from marine Posidonia oceanica fibrous biomass was performed using various activating agents. The chemical activation was carried out using phosphoric acid (H3PO4), potassium hydroxide (KOH), zinc chloride (ZnCl2) and hydrogen peroxide (H2O2). The effects of those impregnating agents were investigated for all produced CACs via several chemical and structural analyses. The results showed that H3PO4 seems to induce the deepest impact on the P. oceanica fibres by providing the lowest conversion yield (16.9%). Besides, the pore analysis showed that two types of porosity were developed: (i) CACs characterized by an inner structure combining significant fraction of both mesopores and micropores (i.e. CAC-H3PO4, CAC-KOH and CAC-ZnCl2) and (ii) CAC-H2O2 with a large mesoporous structure and a small fraction of microporosity. Dealing with the RAMAN and XPS analysis, it was showed that the main carbon fraction is structurally organized (i.e. graphite), especially for the CAC-ZnCl2 sample. As for the isotherm and kinetic investigation, the experimental and modeling results revealed that CAC-H3PO4 was the best performing activated carbon by removing the highest methylene blue dye amount (137 mg/g) in the shortest time (1.3 h to reach the half reaction point).
    Journal of Analytical and Applied Pyrolysis 09/2014; 109. DOI:10.1016/j.jaap.2014.06.010 · 3.07 Impact Factor