Kinetic, Isotherm, and Thermodynamic Studies for Batch Adsorption of Metals and Anions, and Management of Adsorbents after the Adsorption Process

Table of Contents:

Deepak Gusain

Durban University of Technology

Shikha Dubey and Yogesh Chandra Sharma

IIT(BHU), Varanasi

Faizal Bux

Durban University of Technology


  • 8.1 Kinetic Study................................................................................................250
  • 8.2 Isotherm Study..............................................................................................252
  • 8.3 Thermodynamics..........................................................................................254
  • 8.4 Management of Adsorbent after the Adsorption Process.............................258
  • 8.4.1 Use as a Catalyst...............................................................................260
  • 8.4.2 Use for the Production of Ceramics..................................................260
  • 8.4.3 Use as a Fertilizer.............................................................................260
  • 8.5 Economic Viability: Desorption vs Disposal...............................................262
  • 8.6 Conclusion....................................................................................................265

This chapter includes the study of kinetic and isotherm model for metals and

anions. The kinetic and isotherm data can be fitted by either linear curve fitting or nonlinear curve fitting. The kinetic and isotherm model can be estimated by the coefficient-of-determination values, chi-square values, and closeness of experimental and theoretical data. Thermodynamic parameters are also evaluated in this chapter, and thermodynamic data depicted the physisorption or chemisorption nature of the adsorption process and the endothermic or exothermic nature of adsorption. In addition, management of an adsorbent post its use is also discussed.

Kinetic Study

The adsorption process is governed by four steps: (a) bulk diffusion or mass transfer, (b) film diffusion or boundary layer diffusion, (c) pore diffusion, and (d) physical or chemical reaction. The first step can be completely ignored or significantly reduced (Wang, Shi, Pan, et al. 2020; Tan and Hameed 2017) in batch adsorption conditions due to stirring. The mass transfer resistance during stirring can be reduced by stirring (Tan and Hameed 2017).

The second step is directly proportional to the concentration of ions and the specific surface area of the adsorbent. The third step, i.e. pore diffusion, is controlled by pore structure, pore size, pore volume, and the size and structure of the adsorbate.

The last step is a physical or chemical reaction, which is quite fast. So, the first and last steps can be ignored in kinetics and the rate is mainly determined by both the second and third steps. If there is a linear relationship between the adsorbate uptake rate and t(l/2), then it can be concluded that only pore diffusion is the rate-controlling step. Therefore, determination of the slowest step or rate-controlling step helps us in determining the rate of adsorbate uptake. The study of adsorbate uptake rate is known as kinetic study in adsorption.

The kinetic study for adsorption was conducted by fitting the kinetic data on the pseudo-first-order model (Panneerselvam et al. 2011; Alijani and Shariatinia 2017; Nashine and Tembhurkar 2016; Yan, Kong, et al. 2015; Kyzas et al. 2016), pseudo-second-order model (Zhang et al. 2014; Liu and Zhang 2015; Namasivayam and Sangeetha 2006; Li et al. 2009), intra-particle diffusion model (Guo et al. 2016; Ngah and Fatinathan 2010), and Weber-Morris model (Sankararamakrishnan et al. 2014).

The best kinetic model is selected on the basis on the coefficient of determination (R2) obtained during curve fitting analysis of kinetic data. The fitting of the data is analyzed with linear (Ngah and Fatinathan 2010; Sani et al. 2017; Zhu and Li 2015; Liu, Zhu, et al. 2013; Hao et al. 2010) and nonlinear curve fitting analyses (Jian et al. 2015; Qi et al. 2015; Zhang, Gao, et al. 2013; Yu, Ma, et al. 2015; Zhou et al. 2017; Özlem Kocaba§-Atakli and Yiiriim 2013; Hossain et al. 2012). However, in the case of adsorption of cesium on nickel oxide-grafted andic soil, the coefficient of determination was 1, and it was difficult to determine, on the basis of the coefficient of determination, whether the system followed the pseudo-first-order or pseudo-second-order model (Ding et al. 2013). In the case of nickel adsorption with polyvinyl alcohol-based chelating sponge, the system followed both the pseudo-first-order and pseudo-second-order models, and this led to the conclusion in the research article that the system followed the intra-particle diffusion process as the rate-limiting step of adsorption in the solution (Cheng et al. 2014). In addition, the closeness of experimental and theoretical adsorbed amounts is also used for the determination of the most suitable kinetic model (Namasivayam and Sangeetha 2006). Jiang et al. (2013) recommended the use of data on the initial fast rate of adsorption for fitting the kinetic model. It was suggested that the whole kinetic data are not able to fit the pseudo-first-order model, and the model is applicable only for rapid initial stage of adsorption.

The better fit of kinetic data on the pseudo-second-order model follow-up is taken as a proxy for chemisorption (Zhang, Liu, Jiang, et al. 2015; Jin et al. 2017; Zhong et al. 2016; Zha et al. 2014; Venkateswarlu and Yoon 2015b; Huang, Yang, et al. 2015; Roushani et al. 2017; Chen, Shah, et al. 2017; Zeng et al. 2015; Yang, Liu, et al. 2017; Tan. Liu, et al. 2015; Dolatyari et al. 2016; Zhang, Li, et al. 2012; Chen, Zhang, Li, et al. 2016; Chen, Shu, et al. 2017; Wang, Yu, et al. 2017; Zhu et al. 2017; Yu et al. 2013; Tang and Zhang 2016; Wu et al. 2017; Kundu et al. 2017; Zhao and Feng 2016; Usman et al. 2016; Wan et al. 2012; Guo, Su, et al. 2017; Cheng et al. 2014; Liu, Yuan, et al. 2017). The rate of adsorption was fast during the initial stages (Idris 2015; Cheng et al. 2012; Zhao and Feng 2016; Ganesan, Kamaraj, and Vasudevan 2013; Ebrahimi-Gatkash et al. 2017; Hu et al. 2015). The high rate of adsorption was attributed to the high concentration gradient, high availability of the adsorption sites (Anirudhan et al. 2016; Nunell et al. 2015), and passive process of adsorption (Chen, Shu, et al. 2017), e.g. the rate of adsorption increased with an increase in the concentration of uranyl ions on nano-magnesium hydroxide (Chen, Zhuang, et al. 2014). However, in the case of adsorption of manganese with diethylenetriamine-modified silica, the highest initial rate of adsorption was found at the lowest concentration, i.e. lOppm (Idris 2015), but in the case of adsorption of nitrate with hydrous bismuth oxide, the adsorption rate was faster in the intermediate concentration range of 28-42 mgN/L as compared to the low (14 mgN/L) and high (56 mgN/L) concentrations. The high rate of adsorption during the initial adsorption of strontium with Na-montmorillonite was attributed to ion exchange or chemical sorption (Yu, Mei, et al. 2015).

The kinetics of U(VI) removal by bovine serum-coated graphene oxide is expected to occur in two parts: the first part is chelation and the second part is intra-particle diffusion (Yang, Liu, et al. 2017). The chelation is confirmed by the merging of a new peak in FTIR spectra at 912cm1 (O=U=O) and redshift that occurred at 1650cm"1. This is attributed to chelation between U(VI) and the COOH group. The chelation is also confirmed by the XPS data. The N and О Is peak shifted to higher energy after adsorption. This suggested the binding of N- and О-containing groups of the adsorbent with uranyl species. The change in binding energy was more in N (1 eV) than in О (0.5 eV). This suggests that the primary group responsible for chemical bond formation is nitrogen and suggests more stability of bond formation with the N-containing groups.

The rate of adsorption varied with temperature and modification of the adsorbent. The rate of adsorption for selenate removal with Mg-Al layered double hydroxide increased with an increase in the temperature (Kameda et al. 2014). Mercury(II) adsorption on the graphene oxide (GO)-iron oxide (Fe,O4) magnetic nanoparticle composite (GOMNP) exhibited different mechanisms at varying temperatures. At 20°C, the adsorption mechanism followed pseudo-second-order kinetics, while at higher temperatures, intra-particle diffusion governed the sorption mechanism

(Diagboya et al. 2015). The rate of adsorption was faster after the modification of magnetic mesoporous carbon with polyacrylic acid (Zeng et al. 2015). The faster rate of adsorption was due to the blocking of pores by functionalization. The blocking of pores led to the reduced diffusion path length and decreased diffusion of the adsorbate into the inner surface and pores of the adsorbent.

The concentration also alters the kinetics of the adsorption process. The rate of adsorption of uranyl ion on nano-magnesium hydroxide increased with an increase in the concentration (Chen, Zhuang, et al. 2014). Similarly, an increase in the concentration of manganese led to a decline in the pseudo-second-order rate constant (Idris 2015). The decrease in the adsorption rate constant with an increase in the concentration is attributed to increased occupation of the active sites on the surface of the adsorbent by adsorbates (Idris 2015).

Isotherm Study

An adsorption isotherm is a quantitative method to characterize adsorbate equilibrium between the aqueous and solid phases at a constant ambient temperature (Tong et al. 2019). The Langmuir (Zhang et al. 2014; Liu and Zhang 2015; Anirudhan et al. 2009; Li et al. 2009), Freundlich (Guo, Su, et al. 2017; Cheng et al. 2014; Ren, Zhang, et al. 2011; Yazdani et al. 2016), Dubinin-Radushkevich (D-R) (Ngah and Fatinathan 2010; Zhang, Li, et al. 2010; Zhang, Zhu, et al. 2010; Katal. Baei, et al. 2012), Sips (Alatalo et al. 2015; Anirudhan et al. 2016; Reddy and Lee 2013b), and Redlich-Peterson (Kumari et al. 2015; Li, Li, et al. 2012) isotherm models were applied to fit the adsorption isotherm data. In addition, other models were also used, such as the Temkin isotherm model (two-parameter) (Boulaiche et al. 2019; Chakraborty et al. 2019; Bezzina et al. 2020), Flory-Huggins isotherm model (two-parameter) (Arrousse et al. 2020; Jalees et al. 2019), Hill isotherm model (two-parameter) (Lin et al. 2019; Abdelwaheb et al. 2019), Halsey isotherm model (two-parameter) (Ramadoss and Subramaniam 2019; Amin et al. 2019; Shahnaz et al. 2020), and Jovanovic isotherm model (two-parameter) (Karoui et al. 2020; Ghaleh et al. 2020).

Each isotherm model has its own assumption. The Langmuir isotherm is based on the assumption that only one site is available for each adsorbate. The total number of sites is limited, and each adsorbate has the same affinity for each site and does not interfere with the binding of other adsorbates.

The Freundlich isotherm is based on variable kinds of adsorption sites present on the adsorbent (Tong et al. 2019). In this adsorption model, adsorption heat and affinities do not need to be uniformly distributed (opposite to the Langmuir isotherm model) on the heterogeneous surface. There is an exponential decline in adsorption energy with subsequent occupation of adsorption sites (Al-Ghouti and Da'ana 2020).

The Temkin isotherm model is used for the description of adsorption of hydrogen on platinum electrodes, under acidic conditions. It avoids extremely high and low concentrations of the adsorbate (Al-Ghouti and Da’ana 2020). This model assumes that adsorption acts as a function of temperature of all molecules, and adsorption heat of all molecules existing in the layer declines linearly rather than logarithmically with increase in coverage of adsorbent surface.

The Sips isotherm is a combination of both the Langmuir and Freundlich isotherm models and is dependent upon the concentration of the solution where at low concentrations, it favors the Freundlich isotherm, and at the high concentrations, it fits the Langmuir isotherm model (Al-Ghouti and Da’ana 2020).

The Redlich-Peterson model is also a hybrid model of the Langmuir and Freundlich isotherms with three parameters. This isotherm has an exponential function of concentration in the denominator (equilibrium concentration) and varies linearly with equilibrium in the numerator (Al-Ghouti and Da’ana 2020). At high concentrations, it follows mainly the Freundlich isotherm model, and at low concentrations, it follows the Langmuir isotherm model. However, two isotherms, i.e. Langmuir and Freundlich, are predominantly in use.

The coefficient of determination was used to find out the suitable isotherm (Jain et al. 2014; Mohammadi et al. 2014, 2015; Mangaleshwaran et al. 2015; Liu. Yuan, et al. 2017; Kandah and Meunier 2007; Gupta et al. 2014; Saleem et al. 2016). The isotherm data can be fitted with both linear (Sani et al. 2017; Zhu and Li 2015; SenthilKumar et al. 2011; Fouladgar et al. 2015; Pizarro et al. 2015; Lee et al. 2016; Hao et al. 2010; Ren, Zhang, et al. 2011; Alijani and Shariatinia 2017; Vu et al. 2015; Sankararamakrishnan et al. 2014) and nonlinear curve fitting analyses (Hossain et al. 2012; Özlem Kocaba§-Atakh and Yiiriim 2013; Sheng et al. 2010; Zhang, Liu, Wu, et al. 2015; Martinson and Reddy 2009; Zhang, Gao, et al. 2013; Yu, Ma, et al. 2015; Jian et al. 2015; Tang et al. 2013; Zhang, Ren, et al. 2013). The decent fitting of isotherm data on both the Langmuir and Freundlich isotherms makes it difficult to suggest the best adsorption isotherm, e.g. nickel adsorption with nano-alumina (Srivastava et al. 2011) and Fe3O4-impregnated tea waste (Panneerselvam et al.

2011) . However, the decent fitting of isotherm data on both the Langmuir and Freundlich isotherms for adsorption of uranyl ions on ammonia-modified graphene oxide suggested that it followed both chemisorption and physisorption (Verma and Dutta 2015).

In the case of adsorption of cobalt with nanocellulose/nanobentonite composite, the value of coefficient of determination for the Langmuir, Freundlich, and Sips isotherms was larger than 0.9 (Anirudhan et al. 2016). However, a lower value of y2 (chi-square) was used as an additional factor for comparison. The lower value of y2 in the Sips isotherm suggests the follow-up of this model by the isotherm data. Hence, the system follows the monolayer adsorption at a lower concentration and multilayer adsorption at a higher concentration.

The isotherm data for chromium removal with magnetite hollow microspheres followed the Freundlich isotherm at a low initial concentration, i.e. 10 mg/1, but at 20 mg/1, it started to deviate from the Langmuir isotherm, and at 40 mg/1, it followed the Langmuir isotherm with a much higher adsorption capacity, i.e. 180 mg/g (Liu et al.

2012) . The biphasic behavior is attributed to hollow magnetite microspheres, where the surface complexation of Cr with Fe on the surface hollow structure provided an accessible pathway into the interior of magnetite hollow microspheres.

The Redlich-Peterson isotherm explains the adsorption of Cr(VI) on Fe,O4@ poly(m-phenylenediamine) core shell better than the Langmuir and Freundlich. This suggests that the reduction-sorption process was the hybrid process (nonlinear) (Wang, Zhang, et al. 2015).

The mean energy values calculated from the D-R isotherm model were used as theoretical evidence for the mechanism of adsorption (Chen, Zhang, Li, et al. 2016). The mean adsorption energy of less than 8 kJ/mol suggested the physical nature of adsorption (Javadian 2014; Mukhopadhyay et al. 2017; Azari et al. 2015; Elwakeel and Guibal 2015). The mean energy value between 8 and 16 kJ/mol is indicative of the ion exchange process (Duranoglu et al. 2012; Gonzalez and Pliego-Cuervo 2014) or physical/chemical adsorption (Zhu et al. 2017), and that more than 16 kJ/mol is indicative of chemisorption (Mukhopadhyay et al. 2017).

The adsorption of chromium on amino-functionalized titanate nanotubes and protonated titanate nanotubes follows the Langmuir isotherm model (Wang, Liu, et al.

2013). The adsorption capacity for amino-functionalized titanate nanotubes is much larger (153.85 mg/g) than for protonated titanate nanotubes. This suggests that the amino groups act as an important factor in the adsorption of chromium.

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