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 comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of methylene blue sorption by activated carbon. The r2 was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions, namely coefficient of determination (r2), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r2 was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K2 was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.

Comparison of various error functions in predicting the optimum isotherm by linear and non-linear regression analysis for the sorption of basic red 9 by activated carbon.

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of basic red 9 sorption by activated carbon. The r(2) was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions namely coefficient of determination (r(2)), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), the average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. Non-linear regression was found to be a better way to obtain the parameters involved in the isotherms and also the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r(2) was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K(2) was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.

Comments on "Biosorption of nickel from protonated rice bran".

This letter explains the appropriate way to calculate the parameters in pseudo first and second order kinetics, Langmuir and Freundlich isotherm.

Comments on "Removal of lead from aqueous solution using Syzygium cumini L.: equilibrium and kinetic studies".

This letter reports the importance and advantages of the constraints in the Redlich-Peterson isotherm exponent.

Comments on "equilibrium and kinetic studies for the biosorption system of copper(II) ion from aqueous solution using Tectona grandis L.f. leaves powder".

This letter reports the way to solve the Redlich-Peterson isotherm. In addition the importance of constraints for the Redlich-Peterson isotherm exponent was discussed in detail.

Comments on "Adsorption of 4-chlorophenol from aqueous solutions by xad-4 resin: isotherm, kinetic, and thermodynamic analysis".

This letter reports the importance and advantages of the constraints in the Redlich Peterson isotherm exponent.

Mass transfer, kinetics and equilibrium studies for the biosorption of methylene blue using Paspalum notatum.

Batch experiments were carried out for the sorption of methylene blue onto Paspalum notatum. The operating variables studied were initial dye concentration, initial solution pH, adsorbent dosage and contact time. Experimental equilibrium data were fitted to Freundlich, Langmuir and Redlich-Peterson isotherms by non-linear regression method. Six error functions was used to determine the optimum isotherm by non-linear regression method. The present study shows r2 as the best error function to determine the parameters involved in both two- and three-parameter isotherms. Langmuir isotherm was found to be the optimum isotherm for methylene blue onto P. notatum. The monolayer methylene blue sorption capacity of P. notatum was found to be 31 mg/g. The kinetics of methylene blue onto P. notatum was found to follow a pseudo second order kinetics. A Boyd plot confirms the external mass transfer as the rate-limiting step in the dye sorption process. The influence of initial dye concentration on the dye sorption process was represented in the form of dimensionless mass transfer numbers (Sh/Sc0.33) and was found to vary as C(0)-5x10(-6).

Equilibrium, kinetics and mechanism modeling and simulation of basic and acid dyes sorption onto jute fiber carbon: Eosin yellow, malachite green and crystal violet single component systems.

Batch experiments were carried out for the sorption of eosin yellow, malachite green and crystal violet onto jute fiber carbon (JFC). The operating variables studied are the initial dye concentration, initial solution pH, adsorbent dosage and contact time. Experimental equilibrium data were fitted to Freundlich, Langmuir and Redlich-Peterson isotherm by non-linear regression method. Langmuir isotherm was found to be the optimum isotherm for eosin yellow/JFC system and Freundlich isotherm was found to be the optimum isotherm for malachite green/JFC and crystal violet/JFC system at equilibrium conditions. The sorption capacities of eosin yellow, malachite green and crystal violet onto JFC according to Langmuir isotherm were found to 31.49 mg/g, 136.58 mg/g, 27.99 mg/g, respectively. A single stage batch adsorber was designed for the adsorption of eosin yellow, malachite green and crystal violet onto JFC based on the optimum isotherm. A pseudo second order kinetic model well represented the kinetic uptake of dyes studied onto JFC. The pseudo second order kinetic model successfully simulated the kinetics of dye uptake process. The dye sorption process involves both surface and pore diffusion with predominance of surface diffusion at earlier stages. A Boyd plot confirms the external mass transfer as the rate limiting step in the dye sorption process. The influence of initial dye concentration on the dye sorption process was represented in the form of dimensionless mass transfer numbers (Sh/Sc(0.33)) and was found to be agreeing with the expression:

Relation between some two- and three-parameter isotherm models for the sorption of methylene blue onto lemon peel.

Equilibrium uptake of methylne blue onto lemon peel was fitted to the 2 two-parameter isotherm models namely Freundlich and Langmuir and 3 six-parameter isotherm models namely Redlich-Peterson, Toth, Radke-Prausnitz, Fritz-Schluender, Vieth-Sladek and Sips isotherms by non-linear method. A comparison between two-parameter and three-parameter isotherms was reported. The best fitting isotherm was the Sips isotherm followed by Langmuir isotherm and Redlich-Peterson isotherm equation. Redlich-Peterson isotherm is a special case of Langmuir isotherm when the Redlich-Peterson isotherm constant g was unity. Radke-Prausnitz, Toth, Vieth-Sladek isotherm were the same when the Toth isotherm constant, n(T) and the Radke-Prausnitz isotherm, m(RP) are equal to unity and when the Vieth-Sladek isotherm constant, K(VS) equals zero. The sorption capacity of lemon peel for methylene blue uptake was found to be 29 mg/g.

Adsorption of dissolved Reactive red dye from aqueous phase onto activated carbon prepared from agricultural waste.

The adsorption of Reactive red dye (RR) onto Coconut tree flower carbon (CFC) and Jute fibre carbon (JFC) from aqueous solution was investigated. Adsorption studies were carried out at different initial dye concentrations, initial solution pH and adsorbent doses. The kinetic studies were also conducted; the adsorption of Reactive red onto CFC and JFC followed pseudosecond-order rate equation. The effective diffusion coefficient was evaluated to establish the film diffusion mechanism. Quantitative removal of Reactive red dye was achieved at strongly acidic conditions for both the carbons studied. The adsorption isotherm data were fitted well to Langmuir isotherm and the adsorption capacity were found to be 181.9 and 200 mg/g for CFC and JFC, respectively. The overall rate of dye adsorption appeared to be controlled by chemisorption, in this case in accordance with poor desorption studies.

Heterogeneous photocatalytic decomposition of Crystal Violet in UV-illuminated sol-gel derived nanocrystalline TiO2 suspensions.

Nanostructured TiO2 ultrafine powder (Ti-SG) 100% anatase phase prepared by the sol-gel method was used as a photocatalyst in the decomposition reaction of a basic dye, Crystal Violet (hexamethyl-p-rosaniline chloride), in water under UV light irradiation. Optimization of the photocatalyst's performance as a function of irradiation time, catalyst concentration, and solution pH was performed. The photoactivity was greatly dependent on the solution pH and it was effective for Crystal Violet to be degraded under basic conditions. The extent of photooxidation or -reduction of CV was discussed in terms of the Langmuir-Hinshelwood model. Results also indicated that the proper addition of H2O2 could improve the degradation rate, but excess H2O2 quenched the formation of OH*. Textural and photocatalytic characteristics of sol-gel derived TiO2 (Ti-SG) were compared with those of commercial P25, TiO2. The relative photonic efficiency of sol-gel derived TiO2 was found to be 2.77 with reference to phenol.

Adsorption of methylene blue onto jute fiber carbon: kinetics and equilibrium studies.

Jute fiber obtained from the stem of a plant was used to prepare activated carbon using phosphoric acid. Feasibility of employing this jute fiber activated carbon (JFC) for the removal of Methylene blue (MB) from aqueous solution was investigated. The adsorption of MB on JFC has found to dependent on contact time, MB concentration and pH. Experimental result follows Langmuir isotherm model and the capacity was found to be 225.64 mg/g. The optimum pH for the MB removal was found to be 5-10. The kinetic data obtained at different concentrations have been analyzed using a pseudo-first-order, pseudo-second-order equation, intraparticle diffusion and Elovich equation. Among the kinetic models studied, the intraparticle diffusion was the best applicable model to describe the adsorption of MB onto JFC.