Determination of optimum isotherm and kinetic models for phosphate sorption onto iron oxide nanoparticles: nonlinear regression with various error functions

Jeong Ann Park, Jae Hyun Kim, Jin Kyu Kang, Jeong Woo Son, In Geol Yi, Song Bae Kim, Sang-Hyup Lee, Jae Woo Choi, Chang Gu Lee

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The aim of this study was to determine optimum kinetic and isotherm models for phosphate (P) sorption onto iron oxide nanoparticles through nonlinear regression analysis. Equilibrium batch experiments were conducted at the experimental conditions of initial P concentration = 0.5–20 mg/L, adsorbent doses = 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6 g/L, and shaking time = 24 h. Kinetic batch experiments were also performed at the experimental conditions of initial P concentrations = 1, 2, 4, 6, 8, and 10 mg/L, adsorbent dose = 0.6 g/L, and shaking time = 10 min–24 h. Six isotherm models (Langmuir, Freundlich, Temkin, Redlich–Peterson, Khan, and Sips) were used to analyze the equilibrium data through nonlinear regression analysis. Three kinetic models (pseudo-first-order, pseudo-second-order, and Elovich) were used to analyze the kinetic data through nonlinear regression. Error functions including the sum of the squared errors, hybrid fractional error function (HYBRID), average relative error, Marquardt’s percent standard deviation, and sum of the absolute errors (EABS) were used to minimize the error distribution between experimental data and predicted model fits in the optimization process. To compare the five error values, the results of each set were normalized and summed. Considering both coefficient of determination (R2) and Chi-square (χ2), the Redlich–Peterson (Freundlich) model was found to provide the best fit to the experimental data in the equilibrium model analyses, and the optimum parameter values were obtained by the HYBRID error function with the parameter values of KR/aR= 3.59–4.15 mg/g and g = 0.69–0.89 from the Redlich–Peterson model. Considering both R2 and χ2, the Elovich (or pseudo-second-order) model was found to provide the best fit to the kinetic data in the kinetic model analyses, and the optimum parameter values produced by the EABS error function with the parameter values of α = (3.60 × 105)–(4.80 × 106) mg/g/h and β = 4.43–13.07 g/mg from the Elovich model.

Original languageEnglish
Pages (from-to)3107-3118
Number of pages12
JournalDesalination and Water Treatment
Volume57
Issue number7
DOIs
Publication statusPublished - 2016 Feb 7

Keywords

  • Error function
  • Iron oxide nanoparticle
  • Isotherm model
  • Kinetic model
  • Nonlinear regression
  • Phosphate sorption

ASJC Scopus subject areas

  • Pollution
  • Water Science and Technology
  • Ocean Engineering

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