Isotherms and thermodynamics by linear and non-linear regression analysis for the sorption of methylene blue onto activated carbon: comparison of various error functions

A new approach in regression analysis for modeling adsorption isotherms

Numerous regression approaches to isotherm parameters estimation appear in the literature. The real insight into the proper modeling pattern can be achieved only by testing methods on a very big number of cases. Experimentally, it cannot be done in a reasonable time, so the Monte Carlo simulation method was applied. The objective of this paper is to introduce and compare numerical approaches that involve different levels of knowledge about the noise structure of the analytical method used for initial and equilibrium concentration determination. Six levels of homoscedastic noise and five types of heteroscedastic noise precision models were considered. Performance of the methods was statistically evaluated based on median percentage error and mean absolute relative error in parameter estimates. The present study showed a clear distinction between two cases. When equilibrium experiments are performed only once, for the homoscedastic case, the winning error function is ordinary least squares, while for the case of heteroscedastic noise the use of orthogonal distance regression or Margart's percent standard deviation is suggested. It was found that in case when experiments are repeated three times the simple method of weighted least squares performed as well as more complicated orthogonal distance regression method.

Feasibility of electrochemical degradation of pharmaceutical pollutants in different aqueous matrices: optimization through design of experiments

Electrochemical degradation of different effluents polluted with carbamazepine, a well-known refractory pharmaceutical contaminant, was addressed in this article. Ultrapure water (Milli-Q(TM) technology), surface water from a lake and urban wastewater were the matrices used to evaluate the feasibility of performing the electro-oxidation of carbamazepine. Specific designs of experiments were planned for each of the aqueous media. The initial carbamazepine concentration and the electric current density were considered as the operational variables. Although the optimal values of both variables follow the same trend in the three cases, significant differences are observed regarding the comparative influence of each variable on the degradation of carbamazepine.

Parameterized SVM for personalized drug concentration prediction

This paper proposes a parameterized Support Vector Machine (ParaSVM) approach for modeling the Drug Concentration to Time (DCT) curves. It combines the merits of Support Vector Machine (SVM) algorithm that considers various patient features and an analytical model that approximates the predicted DCT points and enables curve calibrations using occasional real Therapeutic Drug Monitoring (TDM) measurements. The RANSAC algorithm is applied to construct the parameter library for the relevant basis functions. We show an example of using ParaSVM to build DCT curves and then calibrate them by TDM measurements on imatinib case study.

Distinctive sorption mechanisms of 4-chlorophenol with black carbons as elucidated by different pH

Black carbon (BC) has been considered as an important sorbent in the environment in recent years due to its high sorption capacity and unique sorption behavior. Sorption characteristics of black carbons from two main sources were investigated to get a better understanding of organic chemical fate in the environment. The present study showed sorption mechanisms of 4-chlorophenol, a common organic contaminant in the surroundings, in two kinds of black carbons, soot surrogate (BC1) and environmental char (BC2) derived from rice straw. Sorption capacity of 4-chlorophenol was much higher in BC1 than on BC2 due to the larger surface area of BC1. However, the surface-area normalized sorption coefficients (sorption capacity per surface area) of BC2 were higher than those of BC1, indicating electrostatic attraction and actions of polar foundational groups on BC2 can react with 4-chlorophenol. With increasing temperature, sorption of BC1 decreased but the sorption of BC2 significantly increased at pH 10 and only slightly increased at pH 4. An exothermic sorption reaction was found for BC1; however, an endothermic reaction of chemical sorption occurred on BC2 at pH 10 due to the electrostatic attraction. At pH4, sorption capacity of BC2 decreased and the small positive sorption enthalpy indicated that less electrostatic attractions occurred because of the neutral form of 4-chlorophenol and the domination of mainly hydrophobic interactions.

Application of activated carbon derived from 'waste' bamboo culms for the adsorption of azo disperse dye: kinetic, equilibrium and thermodynamic studies

The utilization of activated carbon derived from 'waste' bamboo culms (BAC) for the removal of Disperse Red 167 (DR167), an azo disperse dye, was investigated. Studies of the properties of the adsorbent, the effect of contact time, the initial pH of the solution, the initial concentration of the dye solution and temperature indicated that a low initial pH or concentration of dye solution favors the adsorption process; temperature exerts a greater effect on the removal of azo disperse red 167 dye from aqueous solution. Kinetic and isotherm data were fitted to five non-linear kinetic and nine non-linear isotherm equations. In addition, the fits were evaluated in terms of the non-linear coefficient, Chi-square test, Marquardt's percent standard deviation error function and small-sample-corrected Akaike Information Criterion (AICc) methodology. The results showed that the AICc analysis was the best statistical tool for analyzing the data, the intra-particle diffusion and the pseudo-first-order models played important roles in the controlling rate step, and the Temkin equation best described the BAC isotherm data. Furthermore, the thermodynamic analysis indicated that the adsorption was a spontaneous, endothermic, entropy-increasing and physical process. Two types of commercial activated carbon, Filtrasorb 400 and Filtrasorb (F400 and F300), were used as contrast adsorbents. The contrast experiments revealed that BAC exhibits similar properties to F400 and F300. The utilization of bamboo wastes as carbon precursors is feasible.

Adsorptive removal of methylene blue by agar: effects of NaCl and ethanol

Adsorption of methylene blue (MB) on agar was investigated as a function of temperature (308-328 K), different concentrations of NaCl and HCl and various weight percentages of binary mixtures of ethanol with water. It was observed that the maximum experimental adsorption capacity, qm, exp, in water is up to 50 mg g-1 and decreases with increase in weight percentage of ethanol and NaCl and HCl concentration compared to that of water. Analysis of data using ARIAN model showed that MB adsorbs as monomer and dimer on the surface of agar. Binding constants of MB to agar were calculated using the Temkin isotherm. The process is exothermic in water and other solutions. The mean adsorption energy (E) value indicated binding of MB to agar is chemical adsorption. Kinetics of this interaction obeys from the pseudo-second-order model and diffusion of the MB molecules into the agar is the main rate-controlling step.

Equilibrium and kinetic studies on free cyanide adsorption from aqueous solution by activated carbon

Adsorption equilibrium and kinetics of free cyanide onto activated carbon were investigated in the batch tests, and the effects of contact time (1-72 h) and initial cyanide concentrations in the range of 102-532 mg/L were studied. Linear regression was used to determine the best fit of equilibrium and kinetics expressions. The two-parameter models including Freundlich, Dubinin-Radushkevich, Temkin and four different linearized forms of Langmuir and three-parameter models including Redlich-Peterson and Koble-Corrigan were employed for fitting the equilibrium data and it was found that, three-parameter models fitted the data better than the two-parameter models and among the three-parameter models the equilibrium data are best represented by Koble-Corrigan model. A number of kinetic models including fractional power, zero order, first order, pseudo-first order, Elovich, second order, intraparticle diffusion and four different linearized forms of pseudo-second order models were tested to fit the kinetic data. The latter was found to be consistent with the data. Intraparticle diffusion plots show that the adsorption process of free cyanide is a two steps process. In the first step, the adsorption of cyanide is fast while in the second step, cyanide adsorption slows down.