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The interaction among Xanthan (XANT) and three azo dyes: Direct blue 1 (DB1), Direct red 81 (DR81), and Direct black 22 (DB22) was studied. The Xanthan-dye-Al product was formed after the addition of AlCl3 to a Xanthan-Dye adduct containing solution. It was proposed that polyhydroxyoxoaluminum clusters named CAL-13 and CAL-30 react with this adduct producing a Xanthanate aluminum network, XANT-Al, and as a consequence a decrease in dye concentration in an aqueous medium was observed. The removal efficiencies obtained were the following: DB1 (99 %), DB22 (99 %) and DR81 (94 %), demonstrating that this dye removal method is very efficient. The Zimm-Bragg model adequately described the experimental data and the order observed in the Ku (nucleation) and U (aggregation) parameters from this model was the following: DB1>DB22> DR81. Evidence suggests that physicochemical properties of dyes such as charge, molecular weight, aggregation ability and the capacity of XANT-Al to trap dye molecules are involved in the high removal values. Moreover, the dye binding mechanisms include: electrostatic, hydrogen bonding and hydrophobic interactions that determine the magnitude of the parameters Ku and U. These findings suggest that the XANT polymer is a good option to remove azo dyes from an aqueous medium.

A novel stochastic model is proposed to characterize the adsorption kinetics of pollutants including dyes (direct red 80 and direct blue 1), fluoride ions, and cadmium ions removed by calcium pectinate (Pec-Ca), aluminum xanthanate (Xant-Al), and reed leaves, respectively. The model is based on a transformation over time following the Ornstein–Uhlenbeck stochastic process, which explicitly includes the uncertainty involved in the adsorption process. The model includes stochastic versions of the pseudo-first-order (PFO), pseudo-second-order (PSO), and pseudo- n -order (PNO) models. It also allows the estimation of the adsorption parameters, including the maximum removal capacity ( q e ), the adsorption rate constant ( k n ), the reaction pseudoorder ( n ), and the variability σ 2 . The model fitted produced R 2 values similar to those of the nonstochastic versions of the PFO, PSO, and PNO models; however, the obtained values for each parameter indicate that the stochastic model better reproduces the experimental data. The q e values of the Pec-Ca-dye, Xant-Al-fluoride, and reed leaf-Cd+2 systems ranged from 2.0 to 9.7, 0.41 to 1.9, and 0.04 and 0.29 mg/g, respectively, whereas the values of k n ranged from 0.051 to 0.286, 0.743 to 75.73, and 0.756 to 8.861 (mg/g)1-n/min, respectively. These results suggest a variability in the parameters q e and k n inherent to the natures of the adsorbate and adsorbent. The obtained n values ranged from 1.13 to 2.02 for the Pec-Ca-dye system, 1.0–3.5 for the Xant-Al-fluoride system, and 1.8–3.8 for the reed leaf-Cd+2 system. These ranges indicate the flexibility of the stochastic model to obtain fractional n values, resulting in high R 2 values. The variability in each system was evaluated based on σ 2 . The developed model is the first to describe pollutant removal kinetics based on a stochastic differential equation.

In this paper, a new Estimation of Distribution Algorithm (EDA) is presented. The proposed algorithm employs a dependency tree as a graphical model and bivariate copula functions for modeling relationships between pairwise variables. By selecting copula functions it is possible to build a very flexible joint distribution as a probabilistic model. The experimental results show that the proposed algorithm has a better performance than EDAs based on Gaussian assumptions.

Palabras clave: agregación, grupos funcionales, gelificación RESUMEN Los colorantes azo representan entre 60 y 75 % de los colorantes producidos actualmente. Se utilizan ampliamente en la industria cosmética, del papel, optoelectrónica, textil, etc. Desafortunadamente una vez utilizados, debido a su alta resistencia a tratamientos convencionales de aguas residuales, contaminan los cuerpos de agua donde son descargados. En este reporte se utiliza alginato de sodio (ALG) para remover los colorantes azo rojo directo 80 (RD80), rojo congo (Rcongo) y rojo de metilo (Rmetilo). Estudios de espectroscopía UV-visible, FTIR y Raman ayudaron a elucidar los tautómeros involucrados en su remoción. Los porcentajes de remoción fueron: RD80 (99.9 % a pH = 12 y fuerza iónica= 0.1 M), Rcongo (99.7 % a pH = 12 y fuerza iónica = 0.1 M) y Rmetilo (14.9 % a pH = 7 y fuerza iónica = 0.1 M). El modelo de Zimm-Bragg describe adecuadamente las isotermas experimentales, sugiriendo la importancia de la agregación de los colorantes en su eficiencia de remoción. Adicionalmente, se comparó la eficiencia de remoción de siete colorantes azo y se encontró que moléculas con peso molecular elevado, con alta planaridad y carga positiva mostraron las mayores eficiencias de remoción. Lo anterior permite predecir cualitativamente a partir de las estructuras de colorantes azo, cuál de ellos será removido más eficientemente con el ALG.