A critical review of the model fitting quality and parameter stability of equilibrium adsorption models

• Published in: Advances in colloid and interface science Vol. 262; pp. 50 - 68
• Main Authors: Peng, Mengsu, Nguyen, Anh V., Wang, Jianlong, Miller, Reinhard
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01.12.2018
• Subjects: Curve fitting; Gibbs thermodynamics; Least-square method; Regression analysis; Surface tension; Surfactant; Gibbs thermodynamics; Surface tension; Regression analysis; Surfactant; Least-square method; Curve fitting
• ISSN: 0001-8686; 1873-3727; 1873-3727
• DOI: 10.1016/j.cis.2018.10.001

We reviewed eight commonly used equilibrium adsorption models and examined their underlying assumptions, fitting qualities, and parameter stabilities. We compared several objective functions that have been applied to curve fitting analysis and a few statistics tests that have been performed to evaluate regression quality. The iteratively reweighted least squares algorithm was selected as the most suitable regression method for adsorption models in the presence of heteroscedasticity. The fraction of unexplained variance was selected to indicate the model fitting quality. Two sources of parameter instability were identified: residue instability and function instability. While the definition of the instability caused by residue is well established, we are the first to consider the instability caused by an adsorption model. The models discussed in this article can be applied to many surfactants, such as normal alcohols, polyglycol ethers, and sodium dodecyl sulfate at different salt concentrations. Our results show that both the model fitting quality and parameter instability increase with the number of parameters subject to curve fitting. For the Frumkin-type of reorientation model, the parameter instability can be as high as 25%. The high degree of instability in some complicated adsorption models may invalidate the estimated parameters. Therefore, additional measurements or simulations are required for complicated models to extract reliable model parameters. [Display omitted] •Classic, reorientation and ionic equilibrium surface tension models are reviewed.•Methods of curve fitting and evaluating are compared.•A rigorous definition of parameter instability is proposed.•Fitting qualities and stabilities of different models are discussed.•Potential solutions for parameter instability are considered.