Kinetic and Equilibrium Models of Adsorption

Abstract

In adsorption study, isotherms and kinetics of adsorption process provide pieces of information underlying the mechanisms and dynamics of the process. Several equilibrium and kinetic models are usually employed for performing the experimental design of an adsorption system. In this chapter, the Langmuir, Freundlich, Sips, Liu, Redlich-Peterson nonlinear equations, as well as other unusual isotherm models (Hill, Khan, Radke-Prausnitz, Toth) are discussed. For the kinetics of adsorption, the pseudofirst-order, pseudo-second-order, general-order, Avrami fractionary order, and Elovich chemisorption models are explained. The importance of statistical parameters such as coefficient of determination (R 2 ), adjusted coefficient of determination (R 2 adj ), and standard deviation (root of mean square error) are highlighted. The usage of linearized and nonlinearized equations are illustrated and explained. Some common mistakes commonly committed in the literature using linearized equilibrium and kinetic adsorption models as well as other polemic points in adsorption research are pointed out. Analytical techniques together with thermodynamical data of enthalpy and entropy changes are needed to ascertain if an adsorption process is a chemical or a physical process.

Removal of Orange 2G Dye from Aqueous Solutions Using TiO2-Based Nanoparticles: Isotherm and Kinetic Studies

“…4. The first zone was attributed to the diffusional process of the dye on the sorbent surface; hence, it was the fastest adsor- zone) could be regarded as the diffusion through smaller pores, which is followed by the establishment of equilibrium [24,25]. From the slope of the linear portion of the second zone it was possible to determine intraparticle diffusion rate constant (Kid) which is 1.9834 mg g -1 min -½ and thickness boundary layer (C) which is 7.7222 mg g -1 .…”

Al-Waste-Based Zeolite Adsorbent Used for the Removal of Ammonium from Aqueous Solutions

“…where q max (mg/g) is the maximum adsorption capacity of the zeolite, C e (mg/L) is the ammonium concentration at equilibrium, k T (L/mg) is the Toth isotherm constant, and n (dimensionless) is the Toth exponent [33].…”

Comments on the paper: a critical review of the applicability of Avrami fractional kinetic equation in adsorption-based water treatment studies

“…Similarly, Lima et al [16] reported that the authors attribute wrongly ca. 99% of the mechanism of adsorption just based on one of the four forms of the linearized pseudo-second-order kinetic model [16].…”

“…The main intention of such article was to present an alternative equation for calculating kinetic parameters of the interaction that occurred, at a glance in multi-step features, in chitosan-based materials/aqueous solutions interfaces. Secondly, the authors think that the mechanism of adsorption does not just agree with a simple kinetic equation such as pseudo-first-order, pseudo-secondorder, Elovich chemisorption model, and other kinetic models [16]. A given well-established mechanism of adsorption should be certified after the use of several analytical techniques (FTIR, SEM, N 2 adsorption/ desorption curves, Raman spectroscopy, TGA/DTA, DSC, NMR of 29 Si and 13 C at solid state, XRD, pH pzc , CHN analysis, and solution calorimetry analysis) to support the adsorption experimental data (kinetics and equilibrium) [17][18][19][20][21][22][23][24][25], instead of establishing a mechanism of adsorption on a simple kinetic model [17][18][19][20][21][22][23][24][25], as many authors have done in the adsorption studies reported in the literature [16].…”