LITERATURE REVIEW
2.1 Single component adsorption isotherm models
2.1.1 Single parameter isotherms
For adsorption on a uniform surface at sufficiently low concentrations such that all molecules are isolated from their nearest neighbours, the equilibrium relationship between fluid phase and adsorbed phase concentrations will be linear. This linear relationship is commonly known as Henry’s law (Ruthven, 1938) as presented in Table 2.1. This is the simplest model having a single parameter. This model is applicable at low effluent concentration only (Maurya & Mittal, 2010). Henry’s law model was applied to describe the experimental data obtained for the sorption of Hg(II) onto C. papaya (Basha et al., 2008).
This study revealed that this model completely failed to predict the equilibrium isotherm for biosorption of Hg(II). This might be due to the unavailability of sorption data in the lower range of Hg(II) concentration. Henry’s model was also applied to describe the experimental data obtained from the sorption of Methylene Blue and Rhodamin B on the surface of activated carbon and fungal biomass (Maurya & Mittal, 2006). This model again completely failed to predict the equilibrium isotherm of any of the adsorbate–adsorbent systems mainly due to unavailability of sorption data in the lower range of dye concentrations.
2.1.2 Two parameter isotherms
Langmuir isotherm model (Table 2.1) is the empirical model which assumes monolayer adsorption i.e. adsorbed layer is only one molecule thick. Adsorption occurs at fixed number of definite localized sites that are identical and equivalent, with no lateral interaction between adsorbed molecules, even on adjacent sites. Langmuir isotherm refers to homogeneous adsorption, which each molecule possess constant enthalpies and sorption
9 Table 2.1: Single component adsorption isotherm models.
Isotherm model
Number of parameter(s)
involved Mathematical Expressions General Remarks References
Henry’s Law 1 e h e
C K q
where Kh = Henry’s constant (L/g), qe = equilibrium uptake (mg/g), Ce = equilibrium concentration of adsorbate (mg/L)
Applicable at low effluent concentrations only
Very simple equation
Ruthven, 1938
Langmuir
model 2
e e m
e bC
bC q q
1
where qe = equilibrium uptake (mg/g), qm = maximum adsorbate uptake by adsorbent (mg/g), b = Langmuir adsorption constant (L/mg), Ce = adsorbate concentration in solution at equilibrium (mg/L)
Monolayer sorption
Homogeneous adsorption energy
Langmuir, 1918
Freundlich
model 2
en
e k C
q
1
where k = Freundlich constant, 1/n = adsorption intensity, Ce = adsorbate concentration in solution at equilibrium (mg/L), qe = equilibrium uptake (mg/g)
Simple expression
Empirical in nature
Heterogeneous adsorption energy
Freundlich, 1926
Brunauer- Emmer- Teller
(BET) model
2
s e BET e
s
e BET s e
C 1 C C + C C
C
× C
×
= q q
1
where CBET = BET adsorption isotherm (L/mg), Cs = adsorbate monolayer saturation concentration (mg/L), qs = theoretical isotherm saturation capacity (mg/g), qe = equilibrium
adsorption capacity (mg/g) and Ce = adsorbate concentration in solution at equilibrium (mg/L)
Multiple sorption
Applicable for gas phase adsorption
Bruanuer et al., 1938
Temkin
isotherm 2
e
e AC
b q RTln
where R = gas constant (8.314 J/mol K), T = absolute temperature (K), A and b = constants
Temperature dependent expression
Excellent for predicting the gas phase equilibrium
Basha et al., 2008;
Tempkin & Pyzhev, 1940
Table continued on next page...
Radushkevich (DR) isotherm
model
2 e
= DR model constant (mg/g), and R, T and Ce represent the gas constant (8.314 J/mol k), absolute temperature (K) and adsorbate equilibrium concentration (mg/L) respectively
expression Febrianto et al., 2009;
Foo & Hameed, 2010
Redlich–
Peterson (R-P) isotherm
model
3
g e R
e e R
C a
C q K
1
where KR = R-P isotherm constant (L/g), aR = constant (L/mg)g, g = an exponent having value between 0 and 1, Ce = equilibrium liquid phase concentration of the adsorbate (mg/L), qe = equilibrium adsorbate loading onto the adsorbent (mg/g)
Can be applied either in
homogeneous or heterogeneous systems
Empirical equation
Febrianto et al., 2009;
Redlich & Peterson, 1959
Sips model (Combination
of Langmuir and Freundlich)
3
e s
e s m
e bC
C b q q
1
where bs = Sips model isotherm constant (L/g), γ = Sips model exponent, qm = maximum adsorbate uptake by adsorbent (mg/g), Ce = adsorbate concentration in solution at equilibrium (mg/L)
Combination of Langmuir and Freundlich
Reduces to Freundlich at low concentrations
Predicts a monolayer adsorption capacity of Langmuir model at higher concentrations
Sips, 1948
Toth equation 3
T enT
nTe T max e
C b
C b
q q 1
1
where, qmax = maximum sorption capacity (mg/g), bT = sorption affinity parameter (L/mg), nT = heterogeneity parameter, Ce = adsorbate concentration in solution at equilibrium (mg/L), qe = equilibrium uptake (mg/g)
Improvement over Langmuir and Freundlich
Empirical equation
Toth, 1971
Table continued on next page...
11 Table 2.1 continues...
Radke-Prausnitz
isotherm model 3
1
R R B f R R
B f R R
e a r C
C r q a
where aR and rR = Radke–Prausnitz model constants, βR = Radke–Prausnitz model exponent, qe = equilibrium uptake (mg/g), Cf = equilibrium concentration of adsorbate in solution (mg/L)
Simple expression
Empirical
Uses three parameters Vijayaraghavan et al., 2006
Weber and van
Vliet 4 4
2 3 1
a Q a e
Q a
a
C
where a1, a2, a3 and a4 = Weber and van Vliet parameters
Successfully applied for adsorption of hydrocarbon on activated carbon
Maurya & Mittal, 2006
Fritz–
Schluender 5 ( 2)
1
2 ' 1
1
e e
e C
Q C
where α’1, α1, α2, β1 and β2 = Fritz- Schluender constants
Improvement over
Langmuir and Freundlich
Uses five parameters Maurya & Mittal, 2006
ideal and reversible adsorption, not restricted to the formation of monolayer. The Freundlich model for heterogeneous surface energy could be derived by assuming a logarithmic decrease in the heat of adsorption with the fraction of surface covered by the adsorbed solute (Freundlich, 1926). Freundlich isotherm has the ability to fit nearly all experimental adsorption-desorption data, and is especially excellent for fitting data from highly heterogeneous adsorbent systems (Foo & Hameed, 2009, 2010).
The Brunauer-Emmer-Teller (BET) model assumes that number of layers of adsorbate accumulates at the surface and that the Langmuir model applies to each layer (Bruanuer et al., 1938). The kinetics concept proposed by Langmuir is applied to this multiple layer process, that is the rate of adsorption on any layer is equal to the rate of desorption from that layer.
The BET equation is generally used for gas-phase adsorption, where multilayer adsorption is frequently encountered (Bruanuer et al., 1938; Foo & Hameed, 2010). Superb applicability of this model was shown for the biosorption of Cr(VI) using Lyngbya putealis exopolysaccharides, claiming multilayer adsorption occurring in the system (Kiran &
Kaushik, 2008). However, simple curve fitting procedure and high value of correlation coefficient was not valid enough to justify the occurrence of multilayer adsorption. Ideal assumptions within this model namely all sites are energetically identical along with no horizontal interaction between adsorbed molecules may be correct for heterogeneous material and simple non-polar gases but not for complex systems involving heterogeneous adsorbent such as biosorbents and metals. For that reason, this equation is unpopular in the interpretation of liquid phase adsorption data for complex solids.
Temkin isotherm (Table 2.1) was proposed to describe adsorption of hydrogen on platinum electrodes within acidic solutions (Basha et al., 2008; Tempkin & Pyzhev, 1940).
The derivation of the Temkin isotherm is based on the assumption that the decline of the heat of sorption as a function of temperature is linear rather than logarithmic. Temkin isotherm is excellent for predicting the gas phase equilibrium (Febrianto et al., 2009). In case of liquid phase adsorption especially in heavy metals adsorption using biosorbent, this model falls short in representing the equilibrium data (Febrianto et al., 2009). Adsorption in the liquid
do not necessarily organize in a tightly packed structure. The presence of solvent molecules and formation of micelles from adsorbed molecules add to the complexity of liquid phase adsorption. Numerous factors including pH, solubility of adsorbate in the solvent, temperature and surface chemistry of the adsorbent influence adsorption from liquid phase.
Since the basis of derivation for Temkin equation is a simple assumption, complex phenomenon involved in liquid phase adsorption is not taken into account by this equation (Febrianto et al., 2009) and as a result this equation is often not suitable for representation of experimental data in complex systems. Dubinin and his co-workers (Dubinin &
Radushkevich, 1947) conceived Dubinin–Radushkevich (DR) isotherm model for subcritical vapors in micropore solids where the adsorption process followed a pore filling mechanism onto energetically non-uniform surface (Foo & Hameed, 2009, 2010). The Dubinin–
Radushkevich (DR) model is excellent for interpreting organic compounds sorption equilibria (in gas phase condition) in porous solids (Foo & Hameed, 2009). DR model is rarely applied onto liquid-phase adsorption due to the complexities associated with other factors such as pH and ionic equilibria inherent in these systems. This approach was usually applied to distinguish the physical and chemical adsorption of metal ions (Apiratikul & Pavasant, 2008;
Febrianto et al., 2009; Vijayaraghavan et al., 2006).
2.1.3 Three parameter isotherms
Redlich-Peterson (R-P) isotherm model (Table 2.1) is a hybrid isotherm featuring both Langmuir and Freundlich isotherms, which incorporate three parameters into an empirical equation (Redlich & Peterson, 1959). The model has a linear dependence on concentration in the numerator and an exponential function in the denominator to represent adsorption equilibria over a wide concentration range, that could be applied either in homogeneous or heterogeneous systems due to its versatility. This model is quite popular for the prediction of heavy metals biosorption equilibria data (Febrianto et al., 2009). This model fits the experimental data accurately in several systems, namely adsorption of cadmium and nickel onto bagasse fly ash (Srivastava et al., 2006), biosorption of chromium using suspended and immobilized cells of Rhizopus arrhizus (Preetha & Viruthagiri, 2007) as well as sorption of lead onto peat (Ho, 2006).
Sips isotherm (Table 2.1) is a combined form of Langmuir and Freundlich expressions (Sips, 1948) deduced for predicting heterogeneous adsorption systems (Günay et
characteristic of the Langmuir isotherm. As a general rule, the equation parameters are governed mainly by the operating conditions such as the alteration of pH, temperature and concentration of adsorbate. Sips isotherm provides a reasonably accurate prediction of heavy metal biosorption experimental results with high value of correlation coefficient (R2) (Apiratikul & Pavasant, 2008; Febrianto et al., 2009; Vijayaraghavan et al., 2006).
Toth isotherm model (Table 2.1) is another empirical equation developed to improve Langmuir isotherm fittings (Toth, 1971) and useful in describing heterogeneous adsorption systems, while satisfying both low and high-end boundary of the concentration (Vijayaraghavan et al., 2006). Its correlation presupposes an asymmetrical quasi-Gaussian energy distribution with most of its sites have adsorption energy lower than the peak (maximum) or mean value. Vijayaraghavan et al. (2006) used this isotherm for describing adsorption equilibria of Ni(II) onto Sargassum wightii. Toth equation offered the best model for nickel biosorption data at all pH conditions examined. However this isotherm is still unable to predict the isotherm in a particular heterogeneous system as in the biosorption of Hg(II) into C. papaya (Basha et al., 2008). Vijayaraghavan et al. (2006) used Radke- Prausnitz isotherm model for modeling equilibria of adsorption of Ni(II) onto Sargassum wightii. The Ni(II) biosorption data did not correlate well with Radke-Prausnitz model.
2.1.4 Four parameter isotherm
The Weber and van Vliet model (Table 2.1) is an empirical equation having four parameters (Maurya & Mittal, 2006) and similar to the three-parameter isotherms it also expresses adsorption capacity as an explicit function of equilibrium concentration. It provided a poor fit in comparison to most of the isotherm models having two degrees of freedom used to describe biosorption equilibria of two cationic dyes on activated carbon (Maurya & Mittal, 2006). The applicability of the Weber and van Vliet model has also been reported to be less satisfactory compared to Langmuir and Freundlich (Ting & Mittal, 1999; Wang et al., 1997).
2.1.5 Five parameter isotherm
The Fritz-Schluender isotherm model (Table 2.1) is also an empirical equation of five degrees of freedom and successfully applied to liquid-phase adsorption of organic solute to the activated carbon surface (Maurya & Mittal, 2006). Maurya and Mittal (2006) applied sixteen numbers of adsorption isotherms to represent biosorption of two cationic dyes onto activated carbon. A comparison of the Fritz-Schluender isotherm model having the highest correlation coefficient with the most widely used isotherm models (i.e. Langmuir and Freundlich isotherm models) showed that there was improvement in the predictions by the Fritz-Schluender model over either the Langmuir or Freundlich model, but it was not substantial. Besides, application of the Fritz-Schluender model was not as simple. Thus, the Langmuir and Freundlich models could be used for predicting the adsorptive processes.
Many researchers have successfully employed Lamgmuir isotherm model for adsorption of heavy metals ions by various adsorbents. The applicability of the Langmuir isotherm were tested to describe Cd(II) adsorption by hematite and monolayer coverage (qm) was observed as 0.24, 0.23, and 0.22 mg/g at 20, 30, and 40 oC respectively at pH 9.2 (Singh et al., 1998). The applicability of the Langmuir, Freundlich, Redlich-Peterson and Temkin adsorption models were tested for Cu(II) adsorption by Tectona grandis L.f. leaves powder (Prasanna Kumar et al., 2006). Langmuir model interpreted the experimental data well with maximum adsorption capacity of 15.43 mg/g of Cu(II) ion. Equilibrium biosorption of Cd(II) and Cu(II) metal ions was investigated using wheat straw as an adsorbent (Dang et al., 2009).
Among the model tested, namely the Langmuir, Freundlich, Temkin and Dubinin- Radushkevich isotherms, the biosorption equilibrium for both Cd(II) and Cu(II) was best described by the Langmuir model.
Maurya and Mittal (2006) investigated the applicability of equilibrium isotherm models for biosorptive uptake of Methylene Blue and Rhodamin B (cationic dyes) on two types of macrofungi biosorbents and they compared results with adsorption on activated carbon. Results showed that in general the accuracy of models to fit experimental data improved with the degree of freedom (i.e. number of parameters in the expression). The Fritz-Schluender model gave the most accurate fit (R2 values in the range of 0.85–0.99) to all experimental data in comparison to other models used both for activated carbon and the biosorbent. But based on the study, Maurya and Mittal (2006) concluded that most widely