Statistical Analysis of Optimized Isotherm Model for Maxsorb III/Ethanol and Silica Gel/Water Pairs

Abstract

In this study, five error evaluation functions are used to calculate the error deviation between the experimental data and the predicted data for Maxsorb III/ethanol and RD silica gel/water pairs when the isotherm data fitted with six isotherm models. An error analysis based on the sum of normalized error (SNE) is performed to observe the effect of different error evaluation functions for the determination of isotherm parameters. On the basis of error values, Tòth isotherm provides less error compared to other models for both pairs. Error analysis using SNE advocates that HYBRID error evaluation function is suitable for D-A, Freundlich, and Hill models for both pairs whereas ARED error evaluation function is appropriate for Tòth and Langmuir models for Maxsorb III/ethanol pairs. However, RMSD for Redlich-Peterson and SSE for Tòth are appropriate for Maxsorb III/ethanol and silica gel/water pairs, respectively. Seven statistical tools are employed to predict the best isotherm model for the studied pairs. It is found that, except F-test, all other functions provide agreeable results for the better fitting of Tòth model for Maxsorb III/ethanol pair. More or less, similar findings are observed for the RD silica gel/water pair. Moreover, seven information criteria (IC's) are also performed in order to find the optimum isotherm model. On the basis of IC's, Tòth model provides less information loss compared to other models for the studied pairs.

A Statistical Approach to Determine Optimal Models for IUPAC-Classified Adsorption Isotherms

“…In this study, two error functions, namely the HYBRID and RMSD error functions, are used to optimize the parameters of the models. In our previous study [21], through analysis of the sum of normalized error (SNE), it was concluded that the HYBRID error function is appropriate to use for parameter optimization for almost all isotherm models. On the other hand, RMSD error function is frequently used by the researchers [21] for the optimization of parameters.…”

“…In our previous study [21], through analysis of the sum of normalized error (SNE), it was concluded that the HYBRID error function is appropriate to use for parameter optimization for almost all isotherm models. On the other hand, RMSD error function is frequently used by the researchers [21] for the optimization of parameters. Simultaneous use of these two error functions is considered in the current study for optimization since both of them are squared-type error function.…”

“…Sclove (1987) [57] proposed adjusted BIC (denoted by ABIC), based on the information from Rissanen (1978) [70] and Boekee and Buss (1981) [71]. Here, the form of the penalty term is, f (n,p) = pln[(n + 2)/24] [21,47]. Likewise, Bozdogan [61] proposed another modified version of BIC, namely CAIC using f (n,p) = p[ln(n) + 1).…”

“…Likewise, Bozdogan [61] proposed another modified version of BIC, namely CAIC using f (n,p) = p[ln(n) + 1). More explanation of information-based criteria can be found in our previous study [21]. In this paper, the information criterion (IC) as mentioned above is applied separately for comparing the selection rates of the competing models.…”

“…In the current study, two error functions, RMSD and hybrid fractional error deviation (HYBRID) used to optimize the parameters for Type-I(a) and Type-I(b) adsorption isotherm. Whereas, on the other hand only HYBRID error evaluation function is used for other types since authors [21] showed that HYBRID error was better than other errors for optimization of parameters. Parameter effect adjustment and information loss are considered in this investigation to find the optimal isotherm model for a particular type, which also makes it significant from the statistical analysis of the best-fitting model.…”