Accepted Manuscript Thermodynamic Parameters for Adsorption Equilibrium of Heavy Metals and Dyes from Wastewaters Xiang Liu, D.J. Lee PII: DOI: Reference:
S0960-8524(13)01893-2 http://dx.doi.org/10.1016/j.biortech.2013.12.053 BITE 12776
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Bioresource Technology
Please cite this article as: Liu, X., Lee, D.J., Thermodynamic Parameters for Adsorption Equilibrium of Heavy Metals and Dyes from Wastewaters, Bioresource Technology (2013), doi: http://dx.doi.org/10.1016/j.biortech. 2013.12.053
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Thermodynamic Parameters for Adsorption Equilibrium of Heavy Metals and Dyes from Wastewaters 1
Xiang Liu1,2 and D. J. Lee1,2,3*
Department of Environmental Engineering, Fudan University, Shanghai, China Department of Chemical Engineering, National Taiwan University of Science and Technology, Taipei, 106 Taiwan 3 Department of Chemical Engineering, National Taiwan University, Taipei, 106 Taiwan * Author for correspondence Tel: +886-2-2363-5632, Fax:+886-2-2362-3040; E-mail: [email protected] 2
ABSTRACT This meta-analysis evaluates adsorption studies that report thermodynamic parameters for heavy metals and dyes from wastewaters. The adsorbents were derived from agricultural waste, industrial wastes, inorganic particulates, or some natural products. The adsorption mechanisms, derivation of thermodynamic relationships, and possible flaws made in such evaluation are discussed. This analysis shows that conclusions from the examined standard enthalpy and entropy changes are highly contestable. The reason for this flaw may be the poor physical structure of adsorbents tested, such that pore transport controlled the solute flux, leaving a surface reaction process near equilibrium. Keywords: Adsorption, thermodynamics, heavy metal, dye, low-cost adsorbent, equilibrium
1. Introduction Heavy metals and dyes are pollutants found in various industrial wastewaters. Methods for removing metals or dyes from a water stream include adsorption, a highly effective and economical process when the appropriate adsorbents are applied. The search for low-cost adsorbents, preferably derived from locally available waste materials, has become a primary research focus (Annadurai et al., 2002; Volesky and Holan, 1995; Gadd, 1993; Ho, 2006; Sheng et al., 2004; Vijayaraghavan et al., 2008; Wang and Chen, 2009; Guibal et al., 1998; Chang et al., 1997; Aksu, 2005; Chojnacka et al., 2010; Hossain et al., 1
2012). To date, thousands of studies have used countless adsorbents to remove heavy metals or dyes (Saini and Melo, 2013; Park et al., 2012; Fernandez et al., 2012; Bulgariu et al., 2012; Flores-Garmica et al., 2013; Ye et al., 2013; Lou et al., 2013; Wang et al., 2013; Wang et al., 2013; Wang et al., 2013; Yu et al., 2013). The effectiveness of biosorption processes to remove pollutants from wastewaters has recently been investigated (Mishra and Malik, 2013; Promies et al., 2013; Patel, 2012; Vithanage et al., 2012; Asgher, 2012; Mudhoo et al., 2012; Kikuchi and Tanaka, 2012; Hubbe et al., 2012; Julinova and Slavik, 2012; Das, 2012; Kanmani et al., 2012). A biomass typically exists with excess extracellular polymeric substances (EPS) that have a strong affinity for heavy metals (Zhang et al., 2012; 2013; Lin et al., 2013). Adsorption quantities and adsorption rates are two most important performance indices of any adsorption system. In a well-mixed reactor, the external mass transfer resistance of a solute to the surface of an adsorbent is low. The interaction between a solute and adsorbent surface “sites” is controlled by the quantity and rate of uptake of the solute. Interaction between a solute and surface site is a complicated function of all process parameters (Volesky, 2007). Thermodynamic parameters are the focus of engineering evaluations that assess the uptake of adsorbents, hopefully providing insight into adsorption mechanisms for further use to modify and optimize processes. Most studies estimated changes in free energy (∆G0), enthalpy (∆H0), and entropy (∆S0) under standard states based on a set of temperature-dependent equilibrium adsorption quantities. However, Ramesh et al. (2005) identified the probable flaws in many adsorption studies when they assessed their thermodynamic parameters. This review surveyed current literature and confirmed the findings by Ramesh et al. (2005). The use of single set of equilibrium constants versus testing temperature data to evaluate thermodynamic parameters is questioned.
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2. Adsorption tests Each year numerous studies are published on all aspects of biosorption. In 2012, 916 papers were published on the Web of Science (WoS) database on subject of “biosorption”, compared with only 20 in 1990. The total number of citations for biosorption papers exceeded 130,000 hits, with more than 21000 citations in 2012 alone. India and China account for about 33% of all biosorption papers. Table S1 lists the biosorption studies that reported their thermodynamic parameters. Although this list is not exhaustive, a discussion should be sufficient in identifying trends in biosorption equilibrium studies. In these studies, numerous metal ions were tested as the adsorbate (Cd2+, Cr6+, Ni2+, Cu2+, Pb2+, Cr3+,Sb3+, Sb5+, Hg+ Al3+, Se4+,Sb3+, Zn2+, Mn2+, Co 2+, Sr2+, Fe3+, Cs+, Au 3+, As5+), with adsorption of Cu2+, Cr6+, Pb2+, and Cd 2+ studies most likely attributable to environmental concerns of these heavy metals in industrial effluents. In dye adsorption studies, many dyes have been tested (methylene blue (MB), reactive dye yellow 42, red 45, blue 19, blue 49, malachite green, methyl orange, eriochrome black T, direct red-31, direct orange-26, rhodamine B, basic green 4, reactive black 5, basic red 46, basic yellow 28), with MB as the most widely studied. A WoS search identified over 450 studies published in the last decade. Most adsorbents tested were from “wastes,” and agricultural or natural products (coir pith carbon, pine tree bark, meranti wood, Moringa oleifera bark, Moringa oleifera leaves powder, Candida albicans biomass, tea factory waste, dehydrated wheat bran carbon, dehydrated peanut hull, modified oak sawdust, Agave lechuguilla biomass, chitin, Aspergillus niger, wheat shells, kaolinite clay, diatomite, moss (Drepanocladus revolvens) biomass, brown algae (Padina pavonica) biomass, green algae (Cladophora hutchinsiae) biomass, Lichen (Physcia tribacia) biomass, Penicillium simplicissimum, vermiculite, dolomite, Citrus sinensis, olive tree pruning waste, magnetic chitosan resin,
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Tamarindus indica seed powder, mushroom biomass (Agaricus bisporus), seed husk of Calophyllum inophyllum, chestnut shell, mycelial biomass (Streptomyces rimosus), rice husk, Cinnamomum camphora leaf powder, Acidithiobacillus ferrooxidans BY-3, coffee grounds, inactivated sewage sludge, Mansonia wood sawdust, anaerobic sludge, Ananas comosus (pineapple) leaf powder, walnut hull, macrofungus (Lactarius scrobiculatus) biomass, pine bark, Acacia leucocephal bark, olive oil industry waste, coconut copra meal, Corynebacterium glutamicum waste biomass, lichen (Cladonia furcata) biomass, chaff, phoenix tree leaves, neem oil cake (NOC), guava (Psidium guajava) leaf powder, and Ficus religiosa leaves. These studies emphasized the recycling process from waste to resource to fit the green targets of sustainable development. The number of adsorbate-adsorbent pairs for study is infinite. Understanding the adsorption mechanism provides basic information on how a system responds to changes in process parameters and clues on how the efficiency of an existing system can be further improved.
3. Adsorption mechanisms Affinity, which induces adsorption of a solute on an adsorbent surface, is a key focus in adsorption studies. Heavy metals ions are hydrophilic, charged solutes, while dyes are organic compounds with light-emitting groups with very different levels of acidity in water and molecular weight. The proposed adsorption mechanisms were ion exchange, surface adsorption, chemisorption, complexation and adsorption+complexation.
3.1 Adsorption of copper ions This discussion takes adsorption systems adsorbing Cu 2+ as an example. Argun et al. (2007) used oak sawdust to adsorb Cu2+ and noted that Cu2+ ions were bound to that
4
active surface on the sawdust by O2− ions and this action released H+ into the solution. Dursun (2006), who used Aspergillus niger to adsorb Cu2+, noted that under highly acidic pH, the overall surface charge on cells was positive and metal cations and protons compete for binding sites on cell walls, resulting in low metal uptake. At low pH values, cell wall ligands are closely associated with H3O+, restricting access to ligands. Nhattacharyya and Gupta (2011) applied mineral powders to adsorb Cu2+. At pH 6.0, the Cu(II) hydroxide precipitates. Chowdhurry and Saha (2011), who applied Tamarindus indica seed to adsorb Cu 2+, noted that by Fourier transform infrared spectroscopy (FTIR) spectral analysis various functional groups, such as NH2, OH, and CO are involved in Cu2+ biosorption. Ertugay and Bayhan (2010) applied a mushroom biomass to adsorb Cu2+; at pH values of 2, 4, 5 and 6, the zeta potentials of A. bisporus were -5.18, -5.2, -12.2 and -8.12 mV, respectively, such that copper ions were attracted to the surface of {what?} by electrostatic forces. Yao et al. (2010) used chestnut shell to adsorb Cu 2+, noting that C=O, –COO− and C–O bonds on the shell surface participated in copper binding. At pH>pHZPC (4.9 for the chestnut shell), adsorption of Cu 2+ was nearly complete due to the ion exchange reaction with dissociated –COOH groups (pKa=3.8–5.0) on the shell surface. Chen et al, (2010) asserted that ion-exchange and surface complexation were responsible to the accounted for adsorption of Cu 2+ ions by Cinnamomum camphora leaves. Ofomaj et al. (2010), who used Mansonia wood sawdust to adsorb Cu2+, demonstrated that copper uptake was low at low pH, and as pH increased the amount of copper ions adsorbed increased. In using Moringa oleifera leaves to adsorb Cu2+, Reddy et al. (2012) determined that Cu(II) was adsorbed mainly by active groups such as hydroxyl groups ( OH) and carboxylic groups (COO−). At pH3, the carboxyl group became COO−, and metal adsorption increased and peaked at around pH 4.0–6.0. For heavy metal ions other than copper ions, mean biosorption energy calculated using Dubinin–Radushkevich isotherm models suggested that biosorption of Se4+ and Sb3+ onto a biomass was determined by an ion exchange mechanism (Tuzen and Sarı, 2010; Uluozlu et al., 2010). Similar modeling methods indicated that the binding of chromium species to the Agave lechuguilla biomass was caused by interactions between metal ions and functional groups, such as carboxyl groups, on the surface of the bioadsorbent (Romero-Gonzalez et al., 2005, 2006). The carboxyl, amine, and hydroxyl groups on the biomass surface were involved in adsorption of Pb2+ ions (Lawal et al., 2010; Yan et al., 2010). Ion exchange between lignin, tannins, cellulosic compounds, and heavy metals, according to Ho et al. (2002), dominated in the use of agricultural waste as an adsorbent. Ion exchange during adsorption of Hg2+ onto a flax shive and then the chemical reduction of adsorbed Hg2+ to Hg0 by lignin and humic compounds occurred (Shukla et al., 2002). Ion exchange and hydrogen bonding induced adsorption of heavy metal ions by sawdust (Gupta et al., 2003).
3.2 Adsorption of methylene blue Methylene blue, a cationic dye, is a typical adsorbate. Han et al. (2006), who used wheat chaff to adsorb MB, determined that the adsorbent surface at low pH was enriched with protons competing with MB for adsorption sites. At a high pH, the surface charge of chaff is negative, enhancing MB adsorption. Han et al. (2007) used leaves from the phoenix tree to adsorb MB, arguing that the negative surface charge of leaves enhance MB adsorption. Kavitha and Namasivayam (2007), who applied coir to adsorb MB, noted that at pH 2, positively charged surface sites on coir do not promote adsorption of dye
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cations due to electrostatic repulsion. At a high pH, OH- on the coir surface favored adsorption of cationic dye molecules. Spent activated clay was used by Weng and Pan (2007) to adsorb MB; when the solution was pH>pHZPC, the negatively charged adsorbent surface enhanced adsorption of the MB dye. They argued that the adsorption degree was related to the development of a pH-dependent charge on the edges of adsorbent due to acid and base reactions on surface groups. Ponnusami et al. (2008), who used Guava leaf powder to adsorb MB, proposed that the surface of the adsorbent becomes negative at pH>pHZPC, enhancing adsorption. Oliveira et al. (2008) used coffee husks to adsorb MB, claiming that the low uptake of MB under the acidic condition was due to competition between excess protons and MB for adsorption. At pH>pHZPC, which was in the range of 4.3–4.5, the adsorbent surface became predominantly negatively charged, enhancing the electrostatic attraction between surface and MB cations. In using montmorillonite clay to adsorb MB, Almeida et al. (2009) noted that adsorption of MB on the clay surface was primarily influenced by the surface charge on the adsorbent. Silanol groups on the clay surface became increasingly deprotonated as the pH of the adsorption system increased, thereby increasing the number of negatively charged adsorbent sites. Reduced adsorption of MB under an acidic pH reflects the presence of excess H+ ions that compete with dye cations for adsorption sites. Ozer and Dursun (2007) applied dehydrated wheat bran carbon and dehydrated peanut hull to adsorb MB. The pH was not dependent on the adsorption quantity of MB on these adsorbents, and they claimed that the anionic groups formed during dehydration of wheat bran by sulphuric acid accounted for adsorption of MB. In applying wheat shells to adsorb MB, Bulut and Aydim (2006) noted that adsorption quantities of MB by wheat shells were significantly affected by pH at pH 2–4, but were not dependent on pH at pH 5–9. They asserted that the ion exchange mechanism was related to adsorption quantity. Barka et al. (2011), who applied Scolymus hispanicus
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L. to adsorb MB, noted that the isoelectric point of the adsorbent was about pH 5.2. Thus, at pH5.2, the ionic state of ligands, such as carboxyl, phosphoryl, sulfhydryl, and hydroxyl, and amino groups has negatively charged surfaces to enhance MB adsorption. In other dye studies, ion exchange was the predominant adsorption mechanism. Adsorption of direct orange-26 and direct red-31 dyes on rice husk (Safa and Bhatti, 2011), malachite green on clayey soil (Saha et al., 2010), and methyl orange on volcanic mud (Jalil et al., 2010) was via chemisorption. Adsorption of four reactive dyes on Citrus sinensis waste biomass (Asgher and Bhatti, 2012), and MB on montmorillonite clay (Almeida et al., 2009) was physisorption. In summary, all studies reported that solution pH significantly affected adsorption behavior, likely via competition of protons with ions on the charged adsorbent surface. The spectroscopic technique was commonly used to identify the key functional groups or compounds, such as proteins, polysaccharides and lipids that had an affinity for the adsorbate. These FTIR studies were conducted using dry samples, and the results of which may be misleading if other reactions on functional groups occurred during drying and pre-treatments.
4. Thermodynamics parameters of adsorption equilibrium 4.1 Evaluation of adsorption equilibrium parameters Many adsorbate-adsorbent pairs exist and studying them all is not cost effective. To incorporate complex microscopic interactions, adsorption studies focused on adsorption thermodynamics to identify the affinity of adsorbent for the adsorbate. Without detailed information how the solute, adsorbent, and solution interact, a
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macroscopic view of adsorption using the Langmuir model is as follows: q = qm
KC j (aq ) 1 + KC j ( aq )
(1)
where q and q m are the adsorbate and maximum adsorbate quantities, respectively; Cj(aq) is the solute concentration (mol L-1); and K is the Langmuir equilibrium constant. Fitting using the Langmuir model with isotherm data is used to estimate the qm, which characterizes the adsorption capacity of an adsorbent, and K, which characterizes the affinity of a solute for the adsorbent surface. With the fitted parameters, the standard Gibbs process of free energy of adsorption is as follows: ∆G 0 = − RT ln K ad
(2)
where Kad is the adsorption equilibrium constant (dimensionless). The isosteric heat of adsorption can be derived as follows: ∆H 0 = R
d ln K ad d (1 / T )
(3)
Consequently, when adsorption capability increases with temperature, ∆H0>0, the process is endothermic; otherwise, it is exothermic. Based on Eqs. (2) and (3), the entropy change of adsorption can be derived as follows:
∆G 0 ∆H 0 − − ∆S = − T T 0
(4)
Apparently, Eq. (4) is equivalent to Eq. (3) with no additional information extractable when using either equation.
4.1 Adsorption equilibrium parameters of copper ions With adsorption of Cu2+ as an example for discussion, Reddy et al. (2012) applied
Moringa oleifera leaves to adsorb Cu 2+ and noted that ∆H0=12.76 kJ/mol and ∆S0=52.6 J/mole-K, claiming that their adsorption was endothermic and some structural changes 9
occurred in the adsorbate and adsorbent. Argun et al. (2007), who applied oak sawdust to adsorb Cu 2+, noted that∆H0=4.331 kJ/mol and ∆S0=24 J/mole-K. They proposed that the positive entropy change was due to the redistribution of energy between adsorbate and adsorbent. In applying Aspergillus niger to adsorb Cu2+, Dursun (2006) determined that ∆H0=28.9 kJ/mol and ∆S0=168 J/mole-K. Adsorption in this study was endothermic and the randomness at the solid/solute interface was increased. Bhattacharyya and Gupta (2011) applied mineral powers to adsorb Cu2+; ∆H0 ranged at 30.7–45.7 kJ/mol and ∆S0= 86.8–334.5 J/mole-K. They claimed that positive entropy change was caused by the increased randomness of Cu(II) ions being adsorbed, by the release of other ions from the solid surface to the solution, or by partial desolvation of metal ions. Chowdhurry and Saha (2011), who applied Tamarindus indica seed to adsorb Cu 2+, determined that ∆H0=64.086 kJ/mol and ∆S0=240.50 J/mole-K, and claimed that biosorption was endothermic and the degree of freedom of the adsorbed species was increased. In applying mushroom biomass to adsorb Cu2+, Ertugay and Bayhan (2010) noted that ∆H0=-11.64 kJ/mol and ∆S0=-35.5 J/mole-K. These authors identified a low ∆G0 (-0.2 to -1.29 kJ/mol) and claimed that this process was physical adsorption. Yao et al. (2010), in applying chestnut shell to adsorb Cu2+, showed that ∆H0=-17.423 kJ/mol and ∆S0=-54.667 J/mole-K, and argued that adsorption was exothermic and the process was not driven by entropy. Chen et al. (2010) studied the adsorption of Cu2+ ions by
Cinnamomum camphora leaf powder, noting that ∆H0=8.0509 kJ/mol and ∆S0=92.49 J/mole-K. They also demonstrated that the process was endothermic and the randomness of the solid/solute interface was increased during adsorption. Ofomaj et al. (2010) applied Mansonia wood sawdust to adsorb Cu2+. As ∆H0=15.019 kJ/mol and ∆S0=-0.1096 J/mole-K, these authors proposed that the process was endothermic and the randomness of solid/solute interface was slightly reduced during adsorption. Both Chen et al. (2007)
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and Teker and Imamoglu (1999) applied carbon nanotubes to adsorb Th(IV) or activated carbon from rice hulls to adsorb Cu2+ and Cd2+. The positive entropy change likely indicated changes in the structure of adsorbents during adsorption. However, this interpretation has no experimental proof.
4.3 Adsorption equilibrium parameters of MB Kavitha and Namasivayam (2007) noted that ∆H0=30.88 kJ/mol and ∆S0=117.2 J/mole-K in their coir-MB system, and they reported that the reaction was endothermic and the randomness at the solid/solution interface was increased during adsorption. Weng and Pan (2007) showed that ∆H0=12.18 kJ/mol and ∆S0=154 J/mole-K in their activated clay-MB system and showed that the reaction was endothermic. With ∆H0=145 kJ/mol and ∆S0=492 J/mole-K in their montmorillonite clay-MB system, Almeida et al. (2009) reported that degree of freedom in the system increased as a result of adsorption of the MB molecule. According to Ozer and Dursun (2007), ∆H0=53.42 kJ/mol and ∆S0=272 J/mole-K in their wheat bran carbon and MB system and the randomness at the adsorbent-solution interface was increased during adsorption. In their peanut-hull-MB system, ∆H0=20.05 kJ/mol and ∆S0=155 J/mole-K, and Ozer et al. (2007) stated that the randomness at the adsorbent-solution interface was increased during adsorption. Bulut and Aydin (2006) determined that ∆H0=33.41 kJ/mol and ∆S0=185 J/mole-K in their wheat-shell-MB system, and stated that adsorption was endothermic and the positive entropy change reflected the affinity of the adsorbent for MB. According to Barka et al. (2011), ∆H0=-19.79 kJ/mol and ∆S0=-53.98 J/mole-K in their plant-MB system, and reported that adsorption was exothermic and the randomness at the solid/solution interface was reduced during adsorption. In their chaff-MB system, ∆H0=+2.41 kJ/mol and ∆S0=-34.4 J/mole-K, and Han et al. (2006) showed that their system was mildly
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endothermic and the randomness at the solid/solution interface was decreased during adsorption. Han et al. (2007) noted that ∆H0=7.77 kJ/mol and ∆S0=-40.0 J/mole-K in their tree-leaf-MB system, and demonstrated that their system was endothermic and the randomness at the solid/solute interface was decreased. According to Oliveira et al. (2008), ∆H0=17.693 kJ/mol and ∆S0=33.1 J/mole-K in their coffee-husk-MB system. Additionally, adsorption was endothermic and the randomness at the solid/solution interface was increased. Ponusami et al. (2008) showed that ∆H0=33.2 kJ/mol and ∆S0=192.966 J/mole-K in their guava-leaf-MB system, and they concluded that the reaction was endothermic and the randomness of the solid/solution interface was increased.
5. Discussion 5.1 Adsorption equilibrium models Detailed discussion of adsorption mechanisms for a specific system is an exhausting task. Volesky (2007) attempted to identify interactions between individual functional groups and solute molecules in order to predict adsorption behavior without conducting time-consuming experiments. Many phonological models were proposed to “re-invent” the Langmuir model. For example, the adsorption equilibrium, according to Blandamer et al. (1998), of adsorbate molecules j in aqueous solution to sites on an adsorbent originally occupied by water molecules is the following exchange mechanism:
j(aq) + H 2 O(ad ) ↔ j(ad ) + H 2 O(aq) ,
(5)
where aq and ad are the aqueous state and adsorbed state, respectively. When equilibrium is reached, the chemical potentials of both adsorbate molecules and the free solute should be the same. Restated, µj(ad)=µj(aq), where µj is the chemical potential of solute j. Hence, 12
the standard Gibbs free energy of the adsorption process can be modeled as follows:
∆G 0 = µ 0j (ad ) − µ 0j (aq ) = − RT ln K ad ,
(6)
where µj0(ad) is the chemical potential of an ideal adsorbate on an ideal adsorbent (no adsorbate-adsorbate interactions) with half surface coverage of the adsorbent (θ=1/2), and
µj0(aq) is the chemical potential of a solute at a unit concentration (Cr=1 mol/L). At low solute concentration limit and assuming that the solute-adsorbent site interaction can be a functional form of θ/(1-θ), the following expression can apply: K ad =
θC r (1 − θ )C j (aq)
,
(7)
where Ce is the solute concentration, and Cr is a reference concentration for the standard state of the aqueous phase. Clearly, by taking θ=q/qm and Cr=1 mol L-1, Eq. (7) is identical to Eq. (1) with K having the dimension of L mol-1. Restated, the Langmuir model is valid in light of the chemical reaction model (Eq. (5)) under the assumption of an ideal solute, solvent, adsorbate, and very diluted solution (Cj(aq)0), and the the Langmuir model is applicable to solute-adsorbent interactions. Additionally, the solute concentration should be in the unit mol L-1, regardless of the dimensions of q and qm. The K values acquired using L mol-1 can be used directly in Eq. (3) to estimate the change in standard free energy. Also, ∆G0 in Eq. (6) indicates that the process for 1 mole of solute molecules at a concentration of 1 mol L-1 are adsorbed onto an ideal adsorbent at 50% of the surface coverage. Take a typical biosorption study with an adsorbent of surface area of 50 m2 g-1, qm=50 mg g-1 and a solute molecular weight of 100 g mol-1. The adsorbate-adsorbate distance on the adsorbent surface is then approximately 1 nm, roughly seven times the radius of copper ions. Hence, the ideal adsorbate assumption is valid for Cu2+ systems. For an adsorbate with large size and excellent adsorption ability, adsorbate-adsorbate 13
interactions may be significant, such that complicated adsorption models should be adopted. Since most adsorption studies that used low-cost adsorbents had low to medium adsorbate uptake, the ideal adsorbate approximation is very likely applicable to thermodynamic studies.
5.2 Evaluation of thermodynamic parameters
When evaluating the thermodynamic parameters of adsorption system, the first step is to select the standard state. A standard state at Cr=1 mol L-1 is commonly adopted. Restated, when Ce is in the unit of mol L-1, Kad becomes dimensionless. However, when another standard state, Ct1=1 mmol L-1, is chosen, the free energy change becomes
C ∆G10 = µ 0j (ad ) − µ 0j (aq,1) = − RT ln K ad ,1 = ∆G 0 − RT ln r1 Cr
(8)
For instance, in one study, the researchers originally applied Cr=1 mol L-1, and concluded that at 298 K their system had K=10 L mol-1, giving ∆G 0 =-2.48 J mol-1, a weakly favorable adsorption. If the researchers adopted Cr,1=1 mmol L-1 rather than 1 mole L-1 as the standard state, with the former being more realistic than the latter in field applications, their ∆G10 became 4.96 kJ mol-1, indicating an unfavorable adsorption system. Apparently, the difference of 3RT in using 1 mol L-1 or 1 mmol L-1 as standard states is derived from mixing loss of free energy via entropy production. Assessing whether adsorption is favorable by the sign of free energy change alone is not universally applicable. Some authors assessed the thermodynamic parameters of adsorption at three or four temperatures, from which the ∆H0 and ∆S0 values were evaluated by fitting Eqs. (3) and (4). If the authors identified a positive ∆H0 and a positive ∆S0, they would conclude that adsorption was endothermic and the “randomness” of the solid/solute interface increased 14
during adsorption. Opposite conclusions were drawn when the authors identified a negative ∆H0 and a negative ∆S0. Why an adsorption reaction is endothermic or exothermic or how the randomness of the solid/solution interface is increased or decreased during adsorption remains unexplained. Some authors inferred that the positive entropy change during adsorption is the result of structural changes to the solute or adsorbent or the release of other ions by an ion exchange mechanism by the solute, without experimental or theoretical proof. Figure 1 shows the thermodynamic parameters collected from adsorption studies
(Table S1), which reveal an enthalpy-entropy compensation effect. Restated, the ∆S0-∆H0 pairs from very different adsorption systems have a linear relationship with the slope of 1/TC, giving TC=300 K. The enthalpy-entropy compensation was widely discussed for dissolution of a hydrophobic substance into water, micelle formation, and protein unfolding (Liu and Guo, 2001; Lee, 1995; Lee and Hwang, 1996; Dunitz, 1995; Hercigonja et al., 2012). The compensation effect for transferring a hydrophobic group from an oil pool to water was regarded as the net effect for disintegration of a structured water layer around a hydrophobic group. That is, since water molecules around a hydrophobic group form an orderly network that prevents individual water molecules from contacting the hydrophobic surface, entropy change via transferring a hydrophobic group from water to an oil pool is positive (increases system randomness). However, the existence of enthalpy-entropy compensation has been questioned (Melander, 1994; Bornish-Bowden, 2002). Dunitz (1995) argued that for any reaction system with weak intermolecular interaction, enthalpy-entropy compensation exists. However, some have argued that, based on Eq. (4), enthalpy-entropy compensation is present only when ∆G0 is nearly constant. If ∆G0 is near zero, as in almost all equilibrium systems, ∆H0 is proportional to ∆S0 over a narrow temperature range. 15
Entropy changes during adsorption has four steps: (1) remove the solute from the solution with breakdown of solute-water interactions; (2) close the cavity with establishment of water-water interactions; (3) create a cavity adjacent to an adsorption site with breakdown of the water-surface and water-water interactions; and (4) establish solute-surface interactions with the solute to form an adsorbate. Steps (2) and (3) reorganize the creation of water structure as a combined compensation and non-compensation process (Lee, 1994). Step (1) depends on solute-water interactions. For a hydrophilic substance, this process is not favorable as ∆H0>0 and ∆S0 is close to 0; for a hydrophobic substance, ∆H0 and ∆S0 are both lose to 0. Step (2) is a spontaneous process with ∆H00. Step (3) has ∆H0>0 and ∆S0
S0960-8524(13)01893-2 http://dx.doi.org/10.1016/j.biortech.2013.12.053 BITE 12776
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Bioresource Technology
Please cite this article as: Liu, X., Lee, D.J., Thermodynamic Parameters for Adsorption Equilibrium of Heavy Metals and Dyes from Wastewaters, Bioresource Technology (2013), doi: http://dx.doi.org/10.1016/j.biortech. 2013.12.053
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Thermodynamic Parameters for Adsorption Equilibrium of Heavy Metals and Dyes from Wastewaters 1
Xiang Liu1,2 and D. J. Lee1,2,3*
Department of Environmental Engineering, Fudan University, Shanghai, China Department of Chemical Engineering, National Taiwan University of Science and Technology, Taipei, 106 Taiwan 3 Department of Chemical Engineering, National Taiwan University, Taipei, 106 Taiwan * Author for correspondence Tel: +886-2-2363-5632, Fax:+886-2-2362-3040; E-mail: [email protected] 2
ABSTRACT This meta-analysis evaluates adsorption studies that report thermodynamic parameters for heavy metals and dyes from wastewaters. The adsorbents were derived from agricultural waste, industrial wastes, inorganic particulates, or some natural products. The adsorption mechanisms, derivation of thermodynamic relationships, and possible flaws made in such evaluation are discussed. This analysis shows that conclusions from the examined standard enthalpy and entropy changes are highly contestable. The reason for this flaw may be the poor physical structure of adsorbents tested, such that pore transport controlled the solute flux, leaving a surface reaction process near equilibrium. Keywords: Adsorption, thermodynamics, heavy metal, dye, low-cost adsorbent, equilibrium
1. Introduction Heavy metals and dyes are pollutants found in various industrial wastewaters. Methods for removing metals or dyes from a water stream include adsorption, a highly effective and economical process when the appropriate adsorbents are applied. The search for low-cost adsorbents, preferably derived from locally available waste materials, has become a primary research focus (Annadurai et al., 2002; Volesky and Holan, 1995; Gadd, 1993; Ho, 2006; Sheng et al., 2004; Vijayaraghavan et al., 2008; Wang and Chen, 2009; Guibal et al., 1998; Chang et al., 1997; Aksu, 2005; Chojnacka et al., 2010; Hossain et al., 1
2012). To date, thousands of studies have used countless adsorbents to remove heavy metals or dyes (Saini and Melo, 2013; Park et al., 2012; Fernandez et al., 2012; Bulgariu et al., 2012; Flores-Garmica et al., 2013; Ye et al., 2013; Lou et al., 2013; Wang et al., 2013; Wang et al., 2013; Wang et al., 2013; Yu et al., 2013). The effectiveness of biosorption processes to remove pollutants from wastewaters has recently been investigated (Mishra and Malik, 2013; Promies et al., 2013; Patel, 2012; Vithanage et al., 2012; Asgher, 2012; Mudhoo et al., 2012; Kikuchi and Tanaka, 2012; Hubbe et al., 2012; Julinova and Slavik, 2012; Das, 2012; Kanmani et al., 2012). A biomass typically exists with excess extracellular polymeric substances (EPS) that have a strong affinity for heavy metals (Zhang et al., 2012; 2013; Lin et al., 2013). Adsorption quantities and adsorption rates are two most important performance indices of any adsorption system. In a well-mixed reactor, the external mass transfer resistance of a solute to the surface of an adsorbent is low. The interaction between a solute and adsorbent surface “sites” is controlled by the quantity and rate of uptake of the solute. Interaction between a solute and surface site is a complicated function of all process parameters (Volesky, 2007). Thermodynamic parameters are the focus of engineering evaluations that assess the uptake of adsorbents, hopefully providing insight into adsorption mechanisms for further use to modify and optimize processes. Most studies estimated changes in free energy (∆G0), enthalpy (∆H0), and entropy (∆S0) under standard states based on a set of temperature-dependent equilibrium adsorption quantities. However, Ramesh et al. (2005) identified the probable flaws in many adsorption studies when they assessed their thermodynamic parameters. This review surveyed current literature and confirmed the findings by Ramesh et al. (2005). The use of single set of equilibrium constants versus testing temperature data to evaluate thermodynamic parameters is questioned.
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2. Adsorption tests Each year numerous studies are published on all aspects of biosorption. In 2012, 916 papers were published on the Web of Science (WoS) database on subject of “biosorption”, compared with only 20 in 1990. The total number of citations for biosorption papers exceeded 130,000 hits, with more than 21000 citations in 2012 alone. India and China account for about 33% of all biosorption papers. Table S1 lists the biosorption studies that reported their thermodynamic parameters. Although this list is not exhaustive, a discussion should be sufficient in identifying trends in biosorption equilibrium studies. In these studies, numerous metal ions were tested as the adsorbate (Cd2+, Cr6+, Ni2+, Cu2+, Pb2+, Cr3+,Sb3+, Sb5+, Hg+ Al3+, Se4+,Sb3+, Zn2+, Mn2+, Co 2+, Sr2+, Fe3+, Cs+, Au 3+, As5+), with adsorption of Cu2+, Cr6+, Pb2+, and Cd 2+ studies most likely attributable to environmental concerns of these heavy metals in industrial effluents. In dye adsorption studies, many dyes have been tested (methylene blue (MB), reactive dye yellow 42, red 45, blue 19, blue 49, malachite green, methyl orange, eriochrome black T, direct red-31, direct orange-26, rhodamine B, basic green 4, reactive black 5, basic red 46, basic yellow 28), with MB as the most widely studied. A WoS search identified over 450 studies published in the last decade. Most adsorbents tested were from “wastes,” and agricultural or natural products (coir pith carbon, pine tree bark, meranti wood, Moringa oleifera bark, Moringa oleifera leaves powder, Candida albicans biomass, tea factory waste, dehydrated wheat bran carbon, dehydrated peanut hull, modified oak sawdust, Agave lechuguilla biomass, chitin, Aspergillus niger, wheat shells, kaolinite clay, diatomite, moss (Drepanocladus revolvens) biomass, brown algae (Padina pavonica) biomass, green algae (Cladophora hutchinsiae) biomass, Lichen (Physcia tribacia) biomass, Penicillium simplicissimum, vermiculite, dolomite, Citrus sinensis, olive tree pruning waste, magnetic chitosan resin,
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Tamarindus indica seed powder, mushroom biomass (Agaricus bisporus), seed husk of Calophyllum inophyllum, chestnut shell, mycelial biomass (Streptomyces rimosus), rice husk, Cinnamomum camphora leaf powder, Acidithiobacillus ferrooxidans BY-3, coffee grounds, inactivated sewage sludge, Mansonia wood sawdust, anaerobic sludge, Ananas comosus (pineapple) leaf powder, walnut hull, macrofungus (Lactarius scrobiculatus) biomass, pine bark, Acacia leucocephal bark, olive oil industry waste, coconut copra meal, Corynebacterium glutamicum waste biomass, lichen (Cladonia furcata) biomass, chaff, phoenix tree leaves, neem oil cake (NOC), guava (Psidium guajava) leaf powder, and Ficus religiosa leaves. These studies emphasized the recycling process from waste to resource to fit the green targets of sustainable development. The number of adsorbate-adsorbent pairs for study is infinite. Understanding the adsorption mechanism provides basic information on how a system responds to changes in process parameters and clues on how the efficiency of an existing system can be further improved.
3. Adsorption mechanisms Affinity, which induces adsorption of a solute on an adsorbent surface, is a key focus in adsorption studies. Heavy metals ions are hydrophilic, charged solutes, while dyes are organic compounds with light-emitting groups with very different levels of acidity in water and molecular weight. The proposed adsorption mechanisms were ion exchange, surface adsorption, chemisorption, complexation and adsorption+complexation.
3.1 Adsorption of copper ions This discussion takes adsorption systems adsorbing Cu 2+ as an example. Argun et al. (2007) used oak sawdust to adsorb Cu2+ and noted that Cu2+ ions were bound to that
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active surface on the sawdust by O2− ions and this action released H+ into the solution. Dursun (2006), who used Aspergillus niger to adsorb Cu2+, noted that under highly acidic pH, the overall surface charge on cells was positive and metal cations and protons compete for binding sites on cell walls, resulting in low metal uptake. At low pH values, cell wall ligands are closely associated with H3O+, restricting access to ligands. Nhattacharyya and Gupta (2011) applied mineral powders to adsorb Cu2+. At pH 6.0, the Cu(II) hydroxide precipitates. Chowdhurry and Saha (2011), who applied Tamarindus indica seed to adsorb Cu 2+, noted that by Fourier transform infrared spectroscopy (FTIR) spectral analysis various functional groups, such as NH2, OH, and CO are involved in Cu2+ biosorption. Ertugay and Bayhan (2010) applied a mushroom biomass to adsorb Cu2+; at pH values of 2, 4, 5 and 6, the zeta potentials of A. bisporus were -5.18, -5.2, -12.2 and -8.12 mV, respectively, such that copper ions were attracted to the surface of {what?} by electrostatic forces. Yao et al. (2010) used chestnut shell to adsorb Cu 2+, noting that C=O, –COO− and C–O bonds on the shell surface participated in copper binding. At pH>pHZPC (4.9 for the chestnut shell), adsorption of Cu 2+ was nearly complete due to the ion exchange reaction with dissociated –COOH groups (pKa=3.8–5.0) on the shell surface. Chen et al, (2010) asserted that ion-exchange and surface complexation were responsible to the accounted for adsorption of Cu 2+ ions by Cinnamomum camphora leaves. Ofomaj et al. (2010), who used Mansonia wood sawdust to adsorb Cu2+, demonstrated that copper uptake was low at low pH, and as pH increased the amount of copper ions adsorbed increased. In using Moringa oleifera leaves to adsorb Cu2+, Reddy et al. (2012) determined that Cu(II) was adsorbed mainly by active groups such as hydroxyl groups ( OH) and carboxylic groups (COO−). At pH3, the carboxyl group became COO−, and metal adsorption increased and peaked at around pH 4.0–6.0. For heavy metal ions other than copper ions, mean biosorption energy calculated using Dubinin–Radushkevich isotherm models suggested that biosorption of Se4+ and Sb3+ onto a biomass was determined by an ion exchange mechanism (Tuzen and Sarı, 2010; Uluozlu et al., 2010). Similar modeling methods indicated that the binding of chromium species to the Agave lechuguilla biomass was caused by interactions between metal ions and functional groups, such as carboxyl groups, on the surface of the bioadsorbent (Romero-Gonzalez et al., 2005, 2006). The carboxyl, amine, and hydroxyl groups on the biomass surface were involved in adsorption of Pb2+ ions (Lawal et al., 2010; Yan et al., 2010). Ion exchange between lignin, tannins, cellulosic compounds, and heavy metals, according to Ho et al. (2002), dominated in the use of agricultural waste as an adsorbent. Ion exchange during adsorption of Hg2+ onto a flax shive and then the chemical reduction of adsorbed Hg2+ to Hg0 by lignin and humic compounds occurred (Shukla et al., 2002). Ion exchange and hydrogen bonding induced adsorption of heavy metal ions by sawdust (Gupta et al., 2003).
3.2 Adsorption of methylene blue Methylene blue, a cationic dye, is a typical adsorbate. Han et al. (2006), who used wheat chaff to adsorb MB, determined that the adsorbent surface at low pH was enriched with protons competing with MB for adsorption sites. At a high pH, the surface charge of chaff is negative, enhancing MB adsorption. Han et al. (2007) used leaves from the phoenix tree to adsorb MB, arguing that the negative surface charge of leaves enhance MB adsorption. Kavitha and Namasivayam (2007), who applied coir to adsorb MB, noted that at pH 2, positively charged surface sites on coir do not promote adsorption of dye
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cations due to electrostatic repulsion. At a high pH, OH- on the coir surface favored adsorption of cationic dye molecules. Spent activated clay was used by Weng and Pan (2007) to adsorb MB; when the solution was pH>pHZPC, the negatively charged adsorbent surface enhanced adsorption of the MB dye. They argued that the adsorption degree was related to the development of a pH-dependent charge on the edges of adsorbent due to acid and base reactions on surface groups. Ponnusami et al. (2008), who used Guava leaf powder to adsorb MB, proposed that the surface of the adsorbent becomes negative at pH>pHZPC, enhancing adsorption. Oliveira et al. (2008) used coffee husks to adsorb MB, claiming that the low uptake of MB under the acidic condition was due to competition between excess protons and MB for adsorption. At pH>pHZPC, which was in the range of 4.3–4.5, the adsorbent surface became predominantly negatively charged, enhancing the electrostatic attraction between surface and MB cations. In using montmorillonite clay to adsorb MB, Almeida et al. (2009) noted that adsorption of MB on the clay surface was primarily influenced by the surface charge on the adsorbent. Silanol groups on the clay surface became increasingly deprotonated as the pH of the adsorption system increased, thereby increasing the number of negatively charged adsorbent sites. Reduced adsorption of MB under an acidic pH reflects the presence of excess H+ ions that compete with dye cations for adsorption sites. Ozer and Dursun (2007) applied dehydrated wheat bran carbon and dehydrated peanut hull to adsorb MB. The pH was not dependent on the adsorption quantity of MB on these adsorbents, and they claimed that the anionic groups formed during dehydration of wheat bran by sulphuric acid accounted for adsorption of MB. In applying wheat shells to adsorb MB, Bulut and Aydim (2006) noted that adsorption quantities of MB by wheat shells were significantly affected by pH at pH 2–4, but were not dependent on pH at pH 5–9. They asserted that the ion exchange mechanism was related to adsorption quantity. Barka et al. (2011), who applied Scolymus hispanicus
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L. to adsorb MB, noted that the isoelectric point of the adsorbent was about pH 5.2. Thus, at pH5.2, the ionic state of ligands, such as carboxyl, phosphoryl, sulfhydryl, and hydroxyl, and amino groups has negatively charged surfaces to enhance MB adsorption. In other dye studies, ion exchange was the predominant adsorption mechanism. Adsorption of direct orange-26 and direct red-31 dyes on rice husk (Safa and Bhatti, 2011), malachite green on clayey soil (Saha et al., 2010), and methyl orange on volcanic mud (Jalil et al., 2010) was via chemisorption. Adsorption of four reactive dyes on Citrus sinensis waste biomass (Asgher and Bhatti, 2012), and MB on montmorillonite clay (Almeida et al., 2009) was physisorption. In summary, all studies reported that solution pH significantly affected adsorption behavior, likely via competition of protons with ions on the charged adsorbent surface. The spectroscopic technique was commonly used to identify the key functional groups or compounds, such as proteins, polysaccharides and lipids that had an affinity for the adsorbate. These FTIR studies were conducted using dry samples, and the results of which may be misleading if other reactions on functional groups occurred during drying and pre-treatments.
4. Thermodynamics parameters of adsorption equilibrium 4.1 Evaluation of adsorption equilibrium parameters Many adsorbate-adsorbent pairs exist and studying them all is not cost effective. To incorporate complex microscopic interactions, adsorption studies focused on adsorption thermodynamics to identify the affinity of adsorbent for the adsorbate. Without detailed information how the solute, adsorbent, and solution interact, a
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macroscopic view of adsorption using the Langmuir model is as follows: q = qm
KC j (aq ) 1 + KC j ( aq )
(1)
where q and q m are the adsorbate and maximum adsorbate quantities, respectively; Cj(aq) is the solute concentration (mol L-1); and K is the Langmuir equilibrium constant. Fitting using the Langmuir model with isotherm data is used to estimate the qm, which characterizes the adsorption capacity of an adsorbent, and K, which characterizes the affinity of a solute for the adsorbent surface. With the fitted parameters, the standard Gibbs process of free energy of adsorption is as follows: ∆G 0 = − RT ln K ad
(2)
where Kad is the adsorption equilibrium constant (dimensionless). The isosteric heat of adsorption can be derived as follows: ∆H 0 = R
d ln K ad d (1 / T )
(3)
Consequently, when adsorption capability increases with temperature, ∆H0>0, the process is endothermic; otherwise, it is exothermic. Based on Eqs. (2) and (3), the entropy change of adsorption can be derived as follows:
∆G 0 ∆H 0 − − ∆S = − T T 0
(4)
Apparently, Eq. (4) is equivalent to Eq. (3) with no additional information extractable when using either equation.
4.1 Adsorption equilibrium parameters of copper ions With adsorption of Cu2+ as an example for discussion, Reddy et al. (2012) applied
Moringa oleifera leaves to adsorb Cu 2+ and noted that ∆H0=12.76 kJ/mol and ∆S0=52.6 J/mole-K, claiming that their adsorption was endothermic and some structural changes 9
occurred in the adsorbate and adsorbent. Argun et al. (2007), who applied oak sawdust to adsorb Cu 2+, noted that∆H0=4.331 kJ/mol and ∆S0=24 J/mole-K. They proposed that the positive entropy change was due to the redistribution of energy between adsorbate and adsorbent. In applying Aspergillus niger to adsorb Cu2+, Dursun (2006) determined that ∆H0=28.9 kJ/mol and ∆S0=168 J/mole-K. Adsorption in this study was endothermic and the randomness at the solid/solute interface was increased. Bhattacharyya and Gupta (2011) applied mineral powers to adsorb Cu2+; ∆H0 ranged at 30.7–45.7 kJ/mol and ∆S0= 86.8–334.5 J/mole-K. They claimed that positive entropy change was caused by the increased randomness of Cu(II) ions being adsorbed, by the release of other ions from the solid surface to the solution, or by partial desolvation of metal ions. Chowdhurry and Saha (2011), who applied Tamarindus indica seed to adsorb Cu 2+, determined that ∆H0=64.086 kJ/mol and ∆S0=240.50 J/mole-K, and claimed that biosorption was endothermic and the degree of freedom of the adsorbed species was increased. In applying mushroom biomass to adsorb Cu2+, Ertugay and Bayhan (2010) noted that ∆H0=-11.64 kJ/mol and ∆S0=-35.5 J/mole-K. These authors identified a low ∆G0 (-0.2 to -1.29 kJ/mol) and claimed that this process was physical adsorption. Yao et al. (2010), in applying chestnut shell to adsorb Cu2+, showed that ∆H0=-17.423 kJ/mol and ∆S0=-54.667 J/mole-K, and argued that adsorption was exothermic and the process was not driven by entropy. Chen et al. (2010) studied the adsorption of Cu2+ ions by
Cinnamomum camphora leaf powder, noting that ∆H0=8.0509 kJ/mol and ∆S0=92.49 J/mole-K. They also demonstrated that the process was endothermic and the randomness of the solid/solute interface was increased during adsorption. Ofomaj et al. (2010) applied Mansonia wood sawdust to adsorb Cu2+. As ∆H0=15.019 kJ/mol and ∆S0=-0.1096 J/mole-K, these authors proposed that the process was endothermic and the randomness of solid/solute interface was slightly reduced during adsorption. Both Chen et al. (2007)
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and Teker and Imamoglu (1999) applied carbon nanotubes to adsorb Th(IV) or activated carbon from rice hulls to adsorb Cu2+ and Cd2+. The positive entropy change likely indicated changes in the structure of adsorbents during adsorption. However, this interpretation has no experimental proof.
4.3 Adsorption equilibrium parameters of MB Kavitha and Namasivayam (2007) noted that ∆H0=30.88 kJ/mol and ∆S0=117.2 J/mole-K in their coir-MB system, and they reported that the reaction was endothermic and the randomness at the solid/solution interface was increased during adsorption. Weng and Pan (2007) showed that ∆H0=12.18 kJ/mol and ∆S0=154 J/mole-K in their activated clay-MB system and showed that the reaction was endothermic. With ∆H0=145 kJ/mol and ∆S0=492 J/mole-K in their montmorillonite clay-MB system, Almeida et al. (2009) reported that degree of freedom in the system increased as a result of adsorption of the MB molecule. According to Ozer and Dursun (2007), ∆H0=53.42 kJ/mol and ∆S0=272 J/mole-K in their wheat bran carbon and MB system and the randomness at the adsorbent-solution interface was increased during adsorption. In their peanut-hull-MB system, ∆H0=20.05 kJ/mol and ∆S0=155 J/mole-K, and Ozer et al. (2007) stated that the randomness at the adsorbent-solution interface was increased during adsorption. Bulut and Aydin (2006) determined that ∆H0=33.41 kJ/mol and ∆S0=185 J/mole-K in their wheat-shell-MB system, and stated that adsorption was endothermic and the positive entropy change reflected the affinity of the adsorbent for MB. According to Barka et al. (2011), ∆H0=-19.79 kJ/mol and ∆S0=-53.98 J/mole-K in their plant-MB system, and reported that adsorption was exothermic and the randomness at the solid/solution interface was reduced during adsorption. In their chaff-MB system, ∆H0=+2.41 kJ/mol and ∆S0=-34.4 J/mole-K, and Han et al. (2006) showed that their system was mildly
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endothermic and the randomness at the solid/solution interface was decreased during adsorption. Han et al. (2007) noted that ∆H0=7.77 kJ/mol and ∆S0=-40.0 J/mole-K in their tree-leaf-MB system, and demonstrated that their system was endothermic and the randomness at the solid/solute interface was decreased. According to Oliveira et al. (2008), ∆H0=17.693 kJ/mol and ∆S0=33.1 J/mole-K in their coffee-husk-MB system. Additionally, adsorption was endothermic and the randomness at the solid/solution interface was increased. Ponusami et al. (2008) showed that ∆H0=33.2 kJ/mol and ∆S0=192.966 J/mole-K in their guava-leaf-MB system, and they concluded that the reaction was endothermic and the randomness of the solid/solution interface was increased.
5. Discussion 5.1 Adsorption equilibrium models Detailed discussion of adsorption mechanisms for a specific system is an exhausting task. Volesky (2007) attempted to identify interactions between individual functional groups and solute molecules in order to predict adsorption behavior without conducting time-consuming experiments. Many phonological models were proposed to “re-invent” the Langmuir model. For example, the adsorption equilibrium, according to Blandamer et al. (1998), of adsorbate molecules j in aqueous solution to sites on an adsorbent originally occupied by water molecules is the following exchange mechanism:
j(aq) + H 2 O(ad ) ↔ j(ad ) + H 2 O(aq) ,
(5)
where aq and ad are the aqueous state and adsorbed state, respectively. When equilibrium is reached, the chemical potentials of both adsorbate molecules and the free solute should be the same. Restated, µj(ad)=µj(aq), where µj is the chemical potential of solute j. Hence, 12
the standard Gibbs free energy of the adsorption process can be modeled as follows:
∆G 0 = µ 0j (ad ) − µ 0j (aq ) = − RT ln K ad ,
(6)
where µj0(ad) is the chemical potential of an ideal adsorbate on an ideal adsorbent (no adsorbate-adsorbate interactions) with half surface coverage of the adsorbent (θ=1/2), and
µj0(aq) is the chemical potential of a solute at a unit concentration (Cr=1 mol/L). At low solute concentration limit and assuming that the solute-adsorbent site interaction can be a functional form of θ/(1-θ), the following expression can apply: K ad =
θC r (1 − θ )C j (aq)
,
(7)
where Ce is the solute concentration, and Cr is a reference concentration for the standard state of the aqueous phase. Clearly, by taking θ=q/qm and Cr=1 mol L-1, Eq. (7) is identical to Eq. (1) with K having the dimension of L mol-1. Restated, the Langmuir model is valid in light of the chemical reaction model (Eq. (5)) under the assumption of an ideal solute, solvent, adsorbate, and very diluted solution (Cj(aq)0), and the the Langmuir model is applicable to solute-adsorbent interactions. Additionally, the solute concentration should be in the unit mol L-1, regardless of the dimensions of q and qm. The K values acquired using L mol-1 can be used directly in Eq. (3) to estimate the change in standard free energy. Also, ∆G0 in Eq. (6) indicates that the process for 1 mole of solute molecules at a concentration of 1 mol L-1 are adsorbed onto an ideal adsorbent at 50% of the surface coverage. Take a typical biosorption study with an adsorbent of surface area of 50 m2 g-1, qm=50 mg g-1 and a solute molecular weight of 100 g mol-1. The adsorbate-adsorbate distance on the adsorbent surface is then approximately 1 nm, roughly seven times the radius of copper ions. Hence, the ideal adsorbate assumption is valid for Cu2+ systems. For an adsorbate with large size and excellent adsorption ability, adsorbate-adsorbate 13
interactions may be significant, such that complicated adsorption models should be adopted. Since most adsorption studies that used low-cost adsorbents had low to medium adsorbate uptake, the ideal adsorbate approximation is very likely applicable to thermodynamic studies.
5.2 Evaluation of thermodynamic parameters
When evaluating the thermodynamic parameters of adsorption system, the first step is to select the standard state. A standard state at Cr=1 mol L-1 is commonly adopted. Restated, when Ce is in the unit of mol L-1, Kad becomes dimensionless. However, when another standard state, Ct1=1 mmol L-1, is chosen, the free energy change becomes
C ∆G10 = µ 0j (ad ) − µ 0j (aq,1) = − RT ln K ad ,1 = ∆G 0 − RT ln r1 Cr
(8)
For instance, in one study, the researchers originally applied Cr=1 mol L-1, and concluded that at 298 K their system had K=10 L mol-1, giving ∆G 0 =-2.48 J mol-1, a weakly favorable adsorption. If the researchers adopted Cr,1=1 mmol L-1 rather than 1 mole L-1 as the standard state, with the former being more realistic than the latter in field applications, their ∆G10 became 4.96 kJ mol-1, indicating an unfavorable adsorption system. Apparently, the difference of 3RT in using 1 mol L-1 or 1 mmol L-1 as standard states is derived from mixing loss of free energy via entropy production. Assessing whether adsorption is favorable by the sign of free energy change alone is not universally applicable. Some authors assessed the thermodynamic parameters of adsorption at three or four temperatures, from which the ∆H0 and ∆S0 values were evaluated by fitting Eqs. (3) and (4). If the authors identified a positive ∆H0 and a positive ∆S0, they would conclude that adsorption was endothermic and the “randomness” of the solid/solute interface increased 14
during adsorption. Opposite conclusions were drawn when the authors identified a negative ∆H0 and a negative ∆S0. Why an adsorption reaction is endothermic or exothermic or how the randomness of the solid/solution interface is increased or decreased during adsorption remains unexplained. Some authors inferred that the positive entropy change during adsorption is the result of structural changes to the solute or adsorbent or the release of other ions by an ion exchange mechanism by the solute, without experimental or theoretical proof. Figure 1 shows the thermodynamic parameters collected from adsorption studies
(Table S1), which reveal an enthalpy-entropy compensation effect. Restated, the ∆S0-∆H0 pairs from very different adsorption systems have a linear relationship with the slope of 1/TC, giving TC=300 K. The enthalpy-entropy compensation was widely discussed for dissolution of a hydrophobic substance into water, micelle formation, and protein unfolding (Liu and Guo, 2001; Lee, 1995; Lee and Hwang, 1996; Dunitz, 1995; Hercigonja et al., 2012). The compensation effect for transferring a hydrophobic group from an oil pool to water was regarded as the net effect for disintegration of a structured water layer around a hydrophobic group. That is, since water molecules around a hydrophobic group form an orderly network that prevents individual water molecules from contacting the hydrophobic surface, entropy change via transferring a hydrophobic group from water to an oil pool is positive (increases system randomness). However, the existence of enthalpy-entropy compensation has been questioned (Melander, 1994; Bornish-Bowden, 2002). Dunitz (1995) argued that for any reaction system with weak intermolecular interaction, enthalpy-entropy compensation exists. However, some have argued that, based on Eq. (4), enthalpy-entropy compensation is present only when ∆G0 is nearly constant. If ∆G0 is near zero, as in almost all equilibrium systems, ∆H0 is proportional to ∆S0 over a narrow temperature range. 15
Entropy changes during adsorption has four steps: (1) remove the solute from the solution with breakdown of solute-water interactions; (2) close the cavity with establishment of water-water interactions; (3) create a cavity adjacent to an adsorption site with breakdown of the water-surface and water-water interactions; and (4) establish solute-surface interactions with the solute to form an adsorbate. Steps (2) and (3) reorganize the creation of water structure as a combined compensation and non-compensation process (Lee, 1994). Step (1) depends on solute-water interactions. For a hydrophilic substance, this process is not favorable as ∆H0>0 and ∆S0 is close to 0; for a hydrophobic substance, ∆H0 and ∆S0 are both lose to 0. Step (2) is a spontaneous process with ∆H00. Step (3) has ∆H0>0 and ∆S0
