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Vasanth K Kumar - One of the best experts on this subject based on the ideXlab platform.
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Isotherms and thermodynamics by linear and non linear regression analysis for the sorption of methylene blue onto activated carbon comparison of various error functions
Journal of Hazardous Materials, 2008Co-Authors: Vasanth K Kumar, K Porkodi, Fernando RochaAbstract: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.
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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
Journal of Hazardous Materials, 2008Co-Authors: Vasanth K Kumar, K Porkodi, Fernando RochaAbstract: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 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), 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, 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.
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Isotherms for malachite green onto rubber wood hevea brasiliensis sawdust comparison of linear and non linear methods
Dyes and Pigments, 2007Co-Authors: Vasanth K Kumar, S SivanesanAbstract:Abstract Comparison of linear least-squares method and a trial and error non-linear method of estimating the isotherm parameters was examined to the experimental equilibrium data of Malachite Green, a basic dye onto rubber wood sawdust. The experimental data were fitted to Langmuir, Freundlich and Redlich–Peterson Isotherms. The four different linearized forms of Langmuir Isotherms are also discussed. Langmuir isotherm parameters obtained from the four Langmuir linear equations are different but they are the same by using non-linear Langmuir equation. The best-fitting Isotherms are Langmuir and Redlich–Peterson. Present investigation showed that the non-linear method is more appropriate method to determine the isotherm parameters. Langmuir is a special case of Redlich–Peterson when the constant ‘g’ equals to unity.
Fernando Rocha - One of the best experts on this subject based on the ideXlab platform.
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Isotherms and thermodynamics by linear and non linear regression analysis for the sorption of methylene blue onto activated carbon comparison of various error functions
Journal of Hazardous Materials, 2008Co-Authors: Vasanth K Kumar, K Porkodi, Fernando RochaAbstract: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.
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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
Journal of Hazardous Materials, 2008Co-Authors: Vasanth K Kumar, K Porkodi, Fernando RochaAbstract: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 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), 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, 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.
Andreas Seidelmorgenstern - One of the best experts on this subject based on the ideXlab platform.
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single component and competitive adsorption of propane carbon dioxide and butane on vycor glass
Chemical Engineering Science, 2008Co-Authors: J Cermakova, A Markovic, Petr Uchytil, Andreas SeidelmorgensternAbstract:Equilibrium of gas phase adsorption on Vycor glass has been investigated. Adsorption Isotherms for propane, carbon dioxide and butane as pure gases, binary mixtures and ternary mixtures were determined experimentally as a function of temperature using a volumetric method. The single-component Isotherms were described with the Langmuir and Freundlich equations. Additionally, a second order isotherm based on statistical thermodynamics and an isotherm equation based on vacancy solution theory taking into account real phase behavior were used for fitting single-component equilibrium data. In order to describe the measured partial Isotherms for binary mixtures, at first simple extensions of the single-component isotherm models were used, i.e., the conventional competitive Langmuir model and a multi-Freundlich equation based on the ideal adsorbed solution theory (IAS). Since these two simple isotherm models failed to represent the unusual competitive behavior observed, three model extensions using additional mixture parameters were applied, i.e., two modified multi-Langmuir equations based on: (a) statistical thermodynamics and (b) vacancy solution theory and a modified multi-Freundlich IAS model correcting spreading pressure uncertainties. These three model equations were found to be capable to describe the observed behavior better. Finally, the measured partial adsorption equilibrium data of the ternary system were correlated based on the extended equations using the determined additional binary parameters. The results obtained reveal the difficulty to predict accurately multi-component adsorption equilibria.
Stephan Scholl - One of the best experts on this subject based on the ideXlab platform.
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Inverse ideal adsorbed solution theory for calculation of single-component adsorption equilibria from mixture Isotherms supported by adsorption equilibrium distribution
Adsorption, 2019Co-Authors: Friederike Stehmann, Dave Hartig, Stephan SchollAbstract:Adsorption isotherm data of methanol, ethanol, and dimethyl carbonate were determined via headspace experiments on two activated carbons (RB 4 from CABOT Norit and SC 40 from SilCarbon) at different temperatures. However, dimethyl carbonate (DMC) showed a significant decomposition to methanol and CO_2 during the adsorption experiments. Hence, the measured isotherm data for DMC were always two-component isotherm data assuming CO_2 as non-adsorbing component. Thus, ideal adsorbed solution theory (IAST) was inverted to determine the single-component isotherm of DMC using two-component isotherm data and the known single component isotherm of methanol. The inverse IAST was supported by the calculation of the adsorption equilibrium distribution. This calculation was done with the expectation maximization method and results were used to determine the most probable isotherm equations to initialize the inverse IAST calculation. The methodology was validated for mixtures of methanol and ethanol where both single-component Isotherms were known. Finally, single-component Isotherms were calculated for DMC on RB 4 and SC 40 at different temperatures.
Alexander V Neimark - One of the best experts on this subject based on the ideXlab platform.
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using in situ adsorption dilatometry for assessment of micropore size distribution in monolithic carbons
Carbon, 2016Co-Authors: Pio Kowalczyk, Christia Alze, Gudru Reichenaue, Artur P. Terzyk, Pio A Gaude, Alexander V NeimarkAbstract:We demonstrate that in-situ adsorption dilatometry provides a new opportunity for structural characterization of microporous carbons. We present experimental results for CO2 adsorption at 293 K and in-situ deformation obtained by dilatometry on a synthetic monolithic carbon sample. The carbon deformation in the course of adsorption is non-monotonic: the strain isotherm shows the sample contraction at low adsorption followed by progressive expansion. To evaluate structural and mechanical properties of the sample from the experimental adsorption and strain Isotherms, a kernel of theoretical adsorption Isotherms is obtained with the grand canonical Monte Carlo simulation of CO2 adsorption in a series of carbon micropores ranging from 0.22 to 2.0 nm. The respective kernel of adsorption stress Isotherms is constructed using the thermodynamic model of adsorption stress. The pore volume and surface area distributions were calculated independently from a) the experimental excess adsorption isotherm by deconvoluting the generalized adsorption equation and b) the experimental strain isotherm by using the kernel of adsorption stress Isotherms. The proposed method of determining the pore size distribution from the strain isotherm validates the thermodynamic model of adsorption stress in micropores and provides additional information about the sample material with respect to mechanical properties of the microporous matrix.
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evaluation of pore structure parameters of mcm 41 catalyst supports and catalysts by means of nitrogen and argon adsorption
Journal of Physical Chemistry B, 1997Co-Authors: P I Ravikovitch, Di Wei, Weite Chueh, Gary L Haller, Alexander V NeimarkAbstract:A new method has been used to obtain pore size characteristics of MCM-41 catalyst supports and vanadium-substituted MCM-41 catalysts. The approach is based on the nonlocal density functional theory (NLDFT) model for nitrogen and argon adsorption in MCM-41, proposed recently. Samples with pore sizes varying from ca. 25 to 37 A were prepared by hydrothermal synthesis. Two synthesis procedures employing different sources of V were used to prepare V/MCM-41 catalysts. The samples were characterized by X-ray diffraction (XRD). N2 and Ar adsorption Isotherms at 77 K were measured starting from the relative pressure P/P0 = 1 × 10-5. Analysis of adsorption Isotherms was carried out in two stages. The first stage implies comparison of a given isotherm with a reference isotherm measured on a well-characterized sample of MCM-41 with uniform pores. From such a comparison, micropore volume, specific surface area of mesopores, and the point of the beginning of the capillary condensation are determined. In the second sta...
