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The Scientific World Journal
Volume 2014 (2014), Article ID 930879, 17 pages
http://dx.doi.org/10.1155/2014/930879
Research Article

A New Approach in Regression Analysis for Modeling Adsorption Isotherms

1Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, 11000 Belgrade, Serbia
2Faculty of Civil Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia
3Vinča Institute of Nuclear Sciences, University of Belgrade, P.O. Box 522, 11001 Belgrade, Serbia

Received 30 August 2013; Accepted 4 November 2013; Published 30 January 2014

Academic Editors: G. Ding, C. Kordulis, and C. Waterlot

Copyright © 2014 Dana D. Marković et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. T. Yang, Adsorbents: Fundamentals and Applications, John Wiley & Sons, Hoboken, NJ, USA, 2003.
  2. M. Joshi, A. Kremling, and A. Seidel-Morgenstern, “Model based statistical analysis of adsorption equilibrium data,” Chemical Engineering Science, vol. 61, no. 23, pp. 7805–7818, 2006. View at Publisher · View at Google Scholar · View at Scopus
  3. G. Alberti, V. Amendola, M. Pesavento, and R. Biesuz, “Beyond the synthesis of novel solid phases: review on modelling of sorption phenomena,” Coordination Chemistry Reviews, vol. 256, no. 1-2, pp. 28–45, 2012. View at Publisher · View at Google Scholar · View at Scopus
  4. K. Y. Foo and B. H. Hameed, “Insights into the modeling of adsorption isotherm systems,” Chemical Engineering Journal, vol. 156, no. 1, pp. 2–10, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. O. M. Akpa and E. I. Unuabonah, “Small-sample corrected akaike information criterion: an appropriate statistical tool for ranking of adsorption isotherm models,” Desalination, vol. 272, no. 1–3, pp. 20–26, 2011. View at Publisher · View at Google Scholar · View at Scopus
  6. M. I. El-Khaiary, “Least-squares regression of adsorption equilibrium data: comparing the options,” Journal of Hazardous Materials, vol. 158, no. 1, pp. 73–87, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. M. I. El-Khaiary and G. F. Malash, “Common data analysis errors in batch adsorption studies,” Hydrometallurgy, vol. 105, no. 3-4, pp. 314–320, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. K. V. Kumar, K. Porkodi, and F. Rocha, “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, vol. 151, no. 2-3, pp. 794–804, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. K. V. Kumar, K. Porkodi, and F. Rocha, “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, vol. 150, no. 1, pp. 158–165, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. M. C. Ncibi, “Applicability of some statistical tools to predict optimum adsorption isotherm after linear and non-linear regression analysis,” Journal of Hazardous Materials, vol. 153, no. 1-2, pp. 207–212, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. G. Limousin, J. P. Gaudet, L. Charlet, S. Szenknect, V. Barthès, and M. Krimissa, “Sorption isotherms: a review on physical bases, modeling and measurement,” Applied Geochemistry, vol. 22, no. 2, pp. 249–275, 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. C. H. Giles, D. Smith, and A. Huitson, “A general treatment and classification of the solute adsorption isotherm. I. Theoretical,” Journal of Colloid And Interface Science, vol. 47, no. 3, pp. 755–765, 1974. View at Google Scholar · View at Scopus
  13. C. Hinz, “Description of sorption data with isotherm equations,” Geoderma, vol. 99, no. 3-4, pp. 225–243, 2001. View at Publisher · View at Google Scholar · View at Scopus
  14. K. V. Kumar, C. Valenzuela-Calahorro, J. M. Juarez, M. Molina-Sabio, J. Silvestre-Albero, and F. Rodriguez-Reinoso, “Hybrid isotherms for adsorption and capillary condensation of N2 at 77 K on porous and non-porous materials,” Chemical Engineering Journal, vol. 162, no. 1, pp. 424–429, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. I. Langmuir, “The constitution and fundamental properties of solids and liquids—part I: solids,” The Journal of the American Chemical Society, vol. 38, no. 2, pp. 2221–2295, 1916. View at Google Scholar · View at Scopus
  16. H. M. F. Freundlich, “Over the adsorption in solution,” Journal of Physical Chemistry, vol. 57, pp. 385–471, 1906. View at Google Scholar
  17. D. D. Do, Adsorption Analysis: Equilibria and Kinetics, Imperial College Press, London, UK, 1998.
  18. O. Redlich and D. L. Peterson, “A useful adsorption isotherm,” Journal of Physical Chemistry, vol. 63, no. 6, pp. 1024–1026, 1959. View at Google Scholar · View at Scopus
  19. R. Sips, “On the structure of a catalyst surface,” Journal of Chemical Physics, vol. 16, no. 5, pp. 490–495, 1948. View at Publisher · View at Google Scholar
  20. D. Jukić, K. Sabo, and R. Scitovski, “Total least squares fitting Michaelis-Menten enzyme kinetic model function,” Journal of Computational and Applied Mathematics, vol. 201, no. 1, pp. 230–246, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. J. C. Miller and J. N. Miller, Statistics and Chemometrics for Analytical Chemistry, Pearson Prentice Hall, Edinburgh, UK, 5th edition, 2005.
  22. N. R. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, Cambridge, UK, 2nd edition, 2002.
  23. A. G. Asuero and G. González, “Fitting straight lines with replicated observations by linear regression. III. Weighting data,” Critical Reviews in Analytical Chemistry, vol. 37, no. 3, pp. 143–172, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. L. S. Matott and A. J. Rabideau, “ISOFIT—a program for fitting sorption isotherms to experimental data,” Environmental Modelling and Software, vol. 23, no. 5, pp. 670–676, 2008. View at Publisher · View at Google Scholar · View at Scopus
  25. A. Martínez, F. J. del Río, J. Riu, and F. X. Rius, “Detecting proportional and constant bias in method comparison studies by using linear regression with errors in both axes,” Chemometrics and Intelligent Laboratory Systems, vol. 49, no. 2, pp. 179–193, 1999. View at Publisher · View at Google Scholar · View at Scopus
  26. B. Carmichael and A. Coën, “Asset pricing models with errors-in-variables,” Journal of Empirical Finance, vol. 15, no. 4, pp. 778–788, 2008. View at Publisher · View at Google Scholar · View at Scopus
  27. T. Söderström, K. Mahata, and U. Soverini, “Identification of dynamic errors-in-variables models: approaches based on two-dimensional ARMA modeling of the data,” Automatica, vol. 39, no. 5, pp. 929–935, 2003. View at Publisher · View at Google Scholar · View at Scopus
  28. M. Tod, A. Aouimer, and O. Petitjean, “Estimation of pharmacokinetic parameters by orthogonal regression: comparison of four algorithms,” Computer Methods and Programs in Biomedicine, vol. 67, no. 1, pp. 13–26, 2002. View at Publisher · View at Google Scholar · View at Scopus
  29. E. Voigtman, “Limits of detection and decision—part 3,” Spectrochimica Acta B, vol. 63, no. 2, pp. 142–153, 2008. View at Publisher · View at Google Scholar · View at Scopus
  30. A. Sayago, M. Boccio, and A. G. Asuero, “Fitting straight lines with replicated observations by linear regression: the least squares postulates,” Critical Reviews in Analytical Chemistry, vol. 34, no. 1, pp. 39–50, 2004. View at Publisher · View at Google Scholar · View at Scopus
  31. F. C. Wu, B. L. Liu, K. T. Wu, and R. L. Tseng, “A new linear form analysis of Redlich-Peterson isotherm equation for the adsorptions of dyes,” Chemical Engineering Journal, vol. 162, no. 1, pp. 21–27, 2010. View at Publisher · View at Google Scholar · View at Scopus
  32. R. I. Yousef, B. El-Eswed, and A. H. Al-Muhtaseb, “Adsorption characteristics of natural zeolites as solid adsorbents for phenol removal from aqueous solutions: kinetics, mechanism, and thermodynamics studies,” Chemical Engineering Journal, vol. 171, no. 3, pp. 1143–1149, 2011. View at Publisher · View at Google Scholar · View at Scopus
  33. D. D. Maksin, A. B. Nastasović, A. D. Milutinović-Nikolić et al., “Equilibrium and kinetics study on hexavalent chromium adsorption onto diethylene triamine grafted glycidyl methacrylate based copolymers,” Journal of Hazardous Materials, vol. 209-210, pp. 99–110, 2012. View at Publisher · View at Google Scholar · View at Scopus
  34. MATLAB Release, The MathWorks, Natick, Mass, USA, 2007.
  35. J. Poch and I. Villaescusa, “Orthogonal distance regression: a good alternative to least squares for modeling sorption data,” Journal of Chemical and Engineering Data, vol. 57, no. 2, pp. 490–499, 2012. View at Publisher · View at Google Scholar · View at Scopus
  36. B. M. Jovanović, V. L. Vukašinović-Pešić, and L. V. Rajaković, “Enhanced arsenic sorption by hydrated iron (III) oxide-coated materials—mechanism and performances,” Water Environment Research, vol. 83, no. 6, pp. 498–506, 2011. View at Google Scholar
  37. B. M. Jovanović, V. L. Vukašinović-Pešić, N. Dj. Veljović, and L. V. Rajaković, “Arsenic removal from water using low-cost adsorbents—a comparative study,” Journal of Serbian Chemical Society, vol. 76, pp. 1437–1452, 2011. View at Google Scholar
  38. L. V. Rajaković, D. D. Marković, V. N. Rajaković-Ognjanović, and D. Z. Antanasijević, “Review: the approaches for estimation of limit of detection for ICP-MS trace analysis of arsenic,” Talanta, vol. 102, pp. 79–87, 2012. View at Publisher · View at Google Scholar
  39. H. Huang and G. A. Sorial, “Statistical evaluation of an analytical IC method for the determination of trace level perchlorate,” Chemosphere, vol. 64, no. 7, pp. 1150–1156, 2006. View at Publisher · View at Google Scholar · View at Scopus