2.5.3.1 Adsorption Isotherms
An adsorption isotherm governs the retention of an adsorbate from an aqueous phase to a solid phase at constant pH and temperature. These mathematical correlations depict graphical expression of solid phase concentrations against the residual concentration. The isotherms are important in design and industrial application of adsorption systems. Foo and Hameed (2010) reviewed many isotherms such as Brunauer–Emmett–Teller (BET), Redlich–
Peterson, Dubinin–Radushkevich, etc. but the Langmuir and Freundlich adsorption Isotherms, given in Equations 2.18 and 2.19, are commonly used to determine the adsorption capacity of different adsorbents (Foo and Hameed, 2010).
50 solute adsorbed, Ce = residual liquid phase concentration at equilibrium (mg/l), b = Langmuir adsorption coefficient; K, n = empirical Freundlich constants
Linear fits of either Langmuir or Freundlich or both isotherms appear to offer satisfactory interpretation of the mechanism of adsorption process and evaluation of slag capacity of single solutes. On the basis of regression coefficients (R2), Langmuir isotherm was better fitted to adsorption data than Freundlich isotherm for Pb2+ ion adsorption (Lopez et al., 1995) as well as Cu2+, Pb2+, Zn2+, Cd2+, Cr3+ adsorption (Lopez-Delgado et al., 1998) by BF sludge. In other articles Freundlich isotherm gave a better description of Cu2+, Ni2+ and Zn2+
adsorption by BFS (Dimitrova, 1996). Further, Dimitrova and Mehandgiev (1998) found Pb2+
ion adsorption by BFS to fit Freundlich adsorption isotherm well, while Curkovic et al (2001) established that Langmuir isotherm was a better model to describe Pb2+ and Cu2+ adsorption on EAF slag than that of Freundlich. Other applications of Langmuir Isotherm are Pb2+ and Cu2+ ion adsorption with iron and steel slags (Feng et al., 2004), better fits of Langmuir than Freundlich isotherms have been reported for Cu2+ ion adsorption by slags (Kim et al., 2008) and Pb2+ ion adsorption by steel slag (Liu et al., 2010). However, complex interaction of metal ions with slag surfaces and hydrolysis products make it difficult to interpret and predict multicomponent adsorption data.
51
Multisolute adsorption may be complicated by the effects of interaction and competition between solutes and adsorbent (McKay, 1991). The use of multicomponent adsorption models such as non-modified and modified Langmuir, extended Langmuir and Freundlich etc. have been published but Ahmaruzzaman (2011) argued that one cannot obtain a meaningful physical interpretation of the mechanism of the adsorption process with such.
Xue et al (2009) applied extended constant-capacitance surface complexation model to describe adsorption of Cu2+, Cd2+, Pb2+ and Zn2+ ions by BOF. This model proposes an ion exchange process at low pH on permanent charge sites, and formation of metal complexes on variable charge sites (surface hydroxyl groups) at high pH. The model provided good fits of adsorption data for all metal ions in both single and multisolute systems. However, lack of good fits in multisolutes particularly for Cu2+ and Pb2+ ions was attributed to complicated surface chemistry of these metal ions that probably involved surface co-precipitation and/or formation of multi-solute adsorbates. The authors proposed direct methods such as extended X-ray absorption fine structure spectroscopy (EXAFS) to determine the mechanism of adsorption in multisolute systems.
2.5.3.2 Kinetic models
The rate of solute adsorption is controlled by three classical steps, i.e., external diffusion across liquid film that surrounds adsorbent particles, pore diffusion in the internal pore sites of the adsorbent and adsorption step which may involve physisorption, chemisorption, ion exchange, precipitation, complexation (Qiu et al., 2009). The overall rate of kinetic process is then determined by the rate of the slowest step (Dabrawski, 2001). The use of pseudo first order, pseudo second order and Elovich’s rate equations based on chemical adsorption as well as intra particle diffusion and Boyd’s film diffusion models appear frequently in
52
literature to analyse the kinetics of adsorption. A summary of commonly used kinetic models is given in Table 2.5 below.
Table 2.5: Some of the commonly used kinetic models Rate
Equation
Differential Non Linear Linear transformations Linearized plots
Where (Qt, Qe) = amount of metal ions adsorbed per unit weight of adsorbent (mg/g) at any time t (min) and at equilibrium respectively, k1 is first order adsorption constant (mg/g min), h = kQ2e = second order initial adsorption rate (mg/g min); a = desorption constant (g/mg), α
= initial adsorption rate (mg/g min), ki = intraparticle diffusion rate constant (mg/g min-1/2), k2 is second order adsorption constant (mg/g min)
Several researchers have applied chemical and diffusion models to analyse the kinetics of different adsorption systems. Liu et al (2009) observed an initially high rate of Cr3+ ion adsorption by steel slag, and attributed it to the availability of large surface area at the start of the adsorption process. However, as adsorption progressed, adsorption sites probably
53
become exhausted and the rate of adsorption become controlled by the rate at which Cr3+
ions diffused from exterior to the interior sites of slag particles. Curkovic et al (2001), Dimitrova (1996) and others (Huifen et al., 2011; Motsi et al., 2009; Xue et al., 2009) have reported a kinetically fast initial adsorption step followed by slower second phase during adsorption of various metal ions with slags and zeolites. Dimitrova (1996) attributed limited mass transfer kinetics of Cu2+, Ni2+ and Zn2+ ions to low rates of internal solute diffusion inside BFS structure. Slower kinetics were also evident in solutions of high solute concentrations. The authors suggested that possible formation of sparingly soluble silicate complexes and precipitates on slag surfaces decreased solute diffusion rates by limiting solute access to the internal slag structure.
Feng et al (2004) studied the kinetics of Cu2+ and Pb2+ ion adsorption. Pb2+ ions adsorbed faster and higher than Cu2+ ions in both slags. Iron slag had higher loading capacity than steel slag possibly due to higher CaO content, % porosity and specific surface area. The data was fitted to pseudo second order kinetic model where the rate constant increased with pH for slag with high CaO, suggesting that adsorption rate was probably controlled by CaO content. Liu et al (2010) reported that the pseudo second order kinetic equation gave a better linear fit of data for Pb2+ ion adsorption by steel slag than pseudo first order equation.