Comparison of regression models for obtaining parameters of the adsorption isotherm of Langmuir's equation by method of modeling computer

Abstract

To obtain estimates of parameters of Langmuir adsorption isotherm from experimental data, re-searchers often use one of several linearized forms of the original non-linear equation to perform regression analysis. This technique has the advantage of calculation simplicity. However, by linearization, it ignores several fundamental prerequisite of the used least squares regression method, which can potentially lead to misleading results with higher level of uncertainties. In the last few decades, several suggestions for im-provement have been made, one of which is using the non-linear regression technique, which can be done using merely Microsoft Excel. In this work, we performed a standard experiment of constructing the Lang-muir adsorption isotherm of ions Pb2+ on montmorillonite clays from various regions (Polyanka, Nelidovka – Belgorod, Russia and Lam Dong – Vietnam), then compared the parameter estimates, obtained using least squares method on two traditional linear forms and one non-linear form of the equation. After that, we con-structed 104 similar experiments on computer using Monte-Carlo simulation method, each one is performed on various levels of measurement errors, using identical data from the real experiment. Distribution curves and statistical characteristics (median and standard deviation) of the obtained parameter estimates have been calculated and compared for different regression models and different sorbents. The errors in estimating the parameters grow up almost linearly with the measurement errors for all regression models, and the non-linear model has the lowest slope coefficients for both parameters. It has been concluded that the non-linear regres-sion model is far more accurate and reliable, therefore it is recommended using in research practice.