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Predicting Solute Adsorption on Activated Carbon: Phenol Irena Efremenko*,† and Moshe Sheintuch Department of Chemical Engineering, Technion, Israel Institute of Technology, Haifa 32000, Israel ReceiVed August 1, 2005. In Final Form: NoVember 14, 2005 Activated carbon (AC), the most widely used adsorbent in water and in wastewater treatment, comprises a high surface area of very small, convoluted and interconnected pores. Despite the wide use of AC, there is little fundamental atomic-level understanding of its adsorption capacity and selectivity as well as its pore structure. The purpose of this work is to suggest the methodology for calculation of equilibrium adsorption capacity of common water organic pollutants and use it for phenol as a model. The effects of various functional groups, pore size, and coverage on thermodynamics of phenol adsorption from the gas phase and from water media are calculated using molecular mechanics (MM) and density functional theory (DFT) approaches.
1. Introduction Activated carbon (AC) is widely used in water and wastewater treatment primarily as an adsorbent for the removal of relatively low levels of organic and inorganic contaminants via transfer from the dissolved phase to the solid carbon surface. Its high absorptive properties are primarily due to extensive porosity and very large available surface area. In fact, the surface area per gram of material can range from 500 to 1400 square meters, and values as high as 2500 m2/g have been reported.1 Knowing its adsorption capacity and adsorption isotherms is a prerequisite for any technological application. This information is typically obtained experimentally and as such is limited to the carbon used with the pretreatment applied. Each kind of pretreatment usually induces a variety of changes in chemical and physical properties of AC that makes atomic level structure-property ascription difficult. Recent advances in computational chemistry may be implemented to predict absorptive properties of AC with well-defined structure, which can be further used for adsorbent and pretreatment optimization. This will require the following information and approaches: (i) Characterize the structure of AC and calculate the maximal (geometrical) capacity for adsorption of a certain component. (ii) Calculate the changes in the enthalpy (∆H), entropy (∆S), and Gibbs free energy (∆G) for adsorption from the gas-phase and then from the liquid-phase. (iii) Use this information to calculate the adsorption equilibrium and the isotherm. We avoid addressing here the more difficult problem of adsorption kinetics. Activated carbon’s porous structure is not fully understood. It consists generally of small graphite crystallites with highly disordered, irregular, rough, and heterogeneous surfaces. In general, activated carbon is sometimes described as having a “crumpled” layered surface, in which flat sheets are broken and curved back upon themselves. Recent results show that AC porous structures may be comprised of carbon nanotubes.2 Most forms of activated carbon are nonpolar in nature, so they have the greatest affinity for other nonpolar substances. The AC surface * To whom correspondence should be addressed. E-mail:
[email protected]. † Current address: Department of Organic Chemistry, Weizmann Institute of Science, Rehovot 76100, Israel. (1) Cheremisinoff, P. N.; Angelo, C. M. Carbon Adsorption Applications. Carbon Adsorption Handbook; Ann Arbor Science Publishers: Ann Arbor, MI, 1980; pp 1-54.
structure is highly complex and depends on the raw material used to produce it, the method of production, and pretreatment. The “zigzag” configuration of edges of carbon layers is the most common in a wet environment.3,4 Pretreatment of activated carbon by acids or bases causes reorganization of their porous5 and surface6-8 structures and can affect its capacity dramatically.9 Depending on the AC nature, pretreatment, and application history, a multitude of surface functional groups and surface ensembles are formed, so that the determination of the local AC surface structure, and specifically of the active sites for adsorption of molecules with various natures, is not straightforward. Usually, high adsorption activity of activated carbon is attributed to the surface functional groups. The infrared study10 indicates that the most common oxygen functional groups on carbon materials are CdO in lactones and carboxylic anhydrides (stretching frequency 1750 cm-1), quinone and ceto-enol groups (1600 cm-1), and C-O group in ethers, lactones, phenols, and carboxylic anhydrides (a broad band centered around 1250 cm-1). It has been shown that gas phase oxidation of activated carbons increases mainly the concentration of hydroxyl and carbonyl surface groups, whereas oxidation in the liquid phase increases especially the concentration of carboxylic acids. Due to the presence of a polar -OH group, a phenol molecule is able to form hydrogen bonds with surface functional groups. On the other hand, the aromatic ring of the molecule determines its ability to have hydrophobic interactions. Phenol adsorption on AC was studied experimentally in refs 11-14. Despite the wide use of AC as adsorbents and catalyst (2) Pfeifer, P.; Ehrburger-Dolle, F.; Rieker, T. P.; Gonza´lez, M. T.; Hoffman, W. P.; Molina-Sabio, M.; Rodrı´guez-Reinoso, F.; Schmidt, P. W.; Voss, D. J. Phys. ReV. Lett. 2002, 88, 115502. (3) Hennig, G. R. Chem. Phys. Carbon 1966, 2, 1. (4) Boehm, H. P. AdV. Catalysis 1966, 16, 179. (5) Pfeifer, P.; Ehrburger-Dolle, F.; Rieker, T. P.; Gonza´lez, M. T.; Hoffman, W. P.; Molina-Sabio, M.; Rodrı´guez-Reinoso, F.; Schmidt, P. W.; Voss, D. J. Phys. ReV. Lett. 2002, 88 115502. (6) Voll, M.; Boehm, H. P. Carbon 1971, 9, 473. (7) Voll, M.; Boehm, H. P. Carbon 1970, 8, 741. (8) Boehm, H. P. Carbon 2002, 40, 145. (9) Boehm, H. P. Carbon 1994, 32, 2, 759. (10) Figueiredo, J. L.; Pereira, M. F. R.; Freitas, M. M. A.; O Ä rfa˜o, J. J. M. Carbon 1999, 37, 1379. (11) Sheindorf, C.; Rebhum, M.; Sheintuch, M. J. Colloid Interface Sci. 1981, 79, 136. (12) Sheindorf, C.; Rebhum, M.; Sheintuch, M. Water Res. 1982, 16, 357. (13) Matatov-Meytal, Yu. I.; Sheintuch, M. Ind. Chem. Eng. Res. 1997, 36, 4374. (14) Matatov-Meytal, Yu. I.; Sheintuch, M. Ind. Chem. Eng. Res. 2000, 39, 18.
10.1021/la052100u CCC: $33.50 © 2006 American Chemical Society Published on Web 03/10/2006
Predicting Solute Adsorption on AC: Phenol
supports, there is little fundamental understanding of its adsorption capacity and selectivity. Optimization of its surface structure and operation conditions requires detailed knowledge of the activity of various adsorption sites and surface functional groups. In the present work, the effects of various functional groups, pore size, and coverage on thermodynamics of phenol adsorption from the gas phase and from water media are calculated using molecular mechanics (MM) and density functional theory (DFT) approaches. Obtained thermodynamic parameters are further used for prediction of storage capacity using a well-known expression of adsorption and gas-liquid equilibria. This work continues along the lines of related studies in our group that were aimed at explaining transport through a carbon membrane15,16 and hydrogen storage in carbon nanotubes.17 The present work was motivated by our interest in adsorption on AC11,12 and regenerative procedures using catalytic agents that were deposited on the AC.13,14 The structure of this work is as follows. In the next section, the computational methods and models are outlined. Thermodynamics of phenol adsorption from the gas phase and from aqueous solution on surface functional groups, on graphite planes of the AC surface, and in narrow pores are presented in sections 3-5. In section 6, the obtained thermodynamic parameters are applied for predicting adsorption capacity of AC toward phenol. Section 7 concludes the manuscript.
2. Computational Methods and Models Phenol adsorption on activated carbon is governed by van der Waals and Coulomb interactions. Other important effects that should be considered in relation to phenol adsorption from water solution are the solvation energy of its molecule and possible concurrent adsorption of water molecules. To represent van der Waals interactions, we applied molecular mechanics (MM) modeling using the universal force field (UFF) parameters of Rappe et al.18,19 This approach was proven to accurately represent both short- and long-range interactions in the absence of chemical interactions (breaking of existing chemical bonds and formation of new chemical bonds). Accurate representation of the Coulomb interactions and solvation effects requires the correct description of electron density distribution on interacting centers. For this aim, we performed density functional theory (DFT) calculations using the B3LYP functional, which combines the Becke-320 exchange functional and the Lee-Yang-Parr correlation functional21 and the standard cc-pVDZ basis set.22 All calculations were performed using the Gaussian 98 package from Gaussian Inc.23 The geometries were fully optimized in both MM and DFT calculations. The minimum energy geometries were determined to be true minima by the absence of imaginary frequencies in the calculated vibrational spectrum. The adsorption energies are not corrected for the basis set superposition error. Zero-point energies (ZPEs) and thermal contributions to thermodynamic functions were computed from DFT or MM optimized structures and harmonic frequencies by using the rigid rotor/harmonic oscillator approximation and the standard expressions for an ideal gas in the canonical ensemble at 298.15 K and (15) Sznejer, G. A.; Efremenko, I.; Sheintuch, M. AIChE J. 2004, 50, 596. (16) Efremenko, I.; Sheintuch, M. Chem. Eng. Sci. 2004, 59 2013. (17) Efremenko, I.; Sheintuch, M. Langmuir 2005, 21, 6282. (18) Rappe, A. K.; Goddard, W. A. J. Phys. Chem. 1991, 95, 3358. (19) Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A.; Skiff, W. M. J. Am. Chem. Soc. 1992, 114, 10024. (20) Becke, A. D., J. Chem. Phys. 1993, 98, 5648. (21) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV B 1998, 37, 785. (22) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007. (23) Frisch, M. J. et al. Gaussian 98, revision A.7; Gaussian, Inc.: Pittsburgh, PA, 1998.
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1 atm. Thermodynamic parameters of phenol adsorption were calculated as a difference between the corresponding values of the system with optimal position of a molecule inside a nanotube and those of the corresponding separated components. Effect of water solvent was simulated at the DFT level of theory using the self-consistent isodensity polarized continuum model (SCI-PCM).24 In this method, the solvent is taken as a continuum of uniform dielectric constant ) 78.39, the reaction field, where the solute is placed in a spherical cavity within the solvent field. The solute cavity is developed in a self-consistent procedure using the calculated electron density of the solute: A dipole in the molecule induces a dipole in the medium, and the electric field applied by the solvent dipole in turn interacts with the molecular dipole, leading to the net stabilization. The solute cavity was defined by an isodensity surface of 0.0004 au. In MM calculations, flat graphite surface was modeled by one-layer polyaromatic cluster C146H32. Nanopores of various diameters were modeled by zigzag carbon nanotubes varying in size from (12,0) to (24,0) that corresponds to the pore diameters (D), defined as a distance between the centers of the opposite C atoms, from 9.4 to 18.8 Å. The length of nanotubes was set to 7.1 Å (8 carbon layers) with outer C atoms being saturated with hydrogen. In DFT calculations, the smallest C6H5 and C10H8 clusters saturated by functional groups were used. The adsorption energy for a single adsorbed molecule was calculated as a difference between the energy of the system and the energy of the corresponding separated components. Adsorption energy of nth molecule (coverage dependence) was calculated with respect to the system “adsorbent + (n-1) adsorbed molecules”.
3. Adsorption Positions 3.a. Adsorption from the Gas Phase. MM calculations showed that, although all AC surface functional groups are capable to phenol adsorption at low temperatures (∆H < 0), the entropic effect leads to an increase of the Gibbs free energy at higher temperatures. Figure 1 shows the adsorption centers we found to be active to phenol adsorption at 298 K. Both energetic results and optimized geometries indicate that the phenol adsorption occurs mainly on the graphite planes of the AC surface and in small pores while existence of surface functional groups is less important, especially at high temperatures. In order for the description of Coulomb interactions to be accurate, we compared phenol interaction with the most common functional groups on AC surface calculated by MM and DFT methods (Table 1). DFT results confirm the above conclusion that phenol adsorption on surface functional groups is energetically favorable only at low temperatures; at room temperatures, entropy effect makes the interaction unfavorable for all functional groups tested except for the carboxylic group, which is characterized by the highest polarity. For functional groups with low polarity, MM adsorption energies are close to those obtained by the DFT method, whereas for the highly polar acidic group, the MM interaction energy is significantly smaller than that calculated using DFT. On the large clusters presented in Figure 1, the molecule is usually adsorbed parallel to the graphite plane independent of the nature of the functional groups. That again indicates that hydrophobic adsorption due to van der Waals interaction prevails. Based on these calculations, the most favorable surface sites for gas-phase room-temperature phenol adsorption are those containing carboxylic anhydrides OdCsOsCdO or carboxylic acid COOH (∆G ) -2.3 kcal/mol) groups, nanopores of (24) Foresman, B.; Keith, T. A.; Wiberg, K. B.; Snoonian, J.; Frisch, M. J. J. Phys. Chem. 1996, 100, 16098.
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Figure 1. Structure of phenol adsorption complexes in the most stable sites of an AC surface and the corresponding to thermodynamic parameters at 298 K (∆H, kcal/mol, ∆S, cal/mol‚K, and ∆G, kcal/mol, calculated by MM method.) Table 1. DFT Optimized Geometries of the Phenol Interaction Complexes with the Most Common Functional Groups on AC Surface, Hydrogen Bond Lengths (dO-H), and the Corresponding Thermodynamic Parameters (∆H, kcal/mol, ∆S, cal/mol‚K, and ∆G, kcal/mol) at 298 Ka
a The latter are compared with the corresponding MM data calculated for the same systems (MM) and for large polyaromatic cluster C146H32 (similar to those presented in Figure 1) with the same functional groups (MM, ref).
molecular dimensions (∆G ) -14.7 kcal/mol), and the regular graphite planes of the AC surface (∆G ) -3.1 kcal/mol). 3.b. Adsorption from Water Solution. Phenol adsorption in water media becomes energetically less favorable due to the stabilization of the dissolved species by interaction with the
solvent (calculated ∆G298 solv ) 4.97 kcal/mol in comparison with the corresponding experimental value of 6.6 kcal/mol25). (25) CRC Handbook of Chemistry and Physics, 85th ed.; CRC Press: Boca Raton, FL, 2004-2005.
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Table 2. Adsorption of Water Molecule from the Gas Phase and from Water Media at 298 Ka
a DFT optimized geometries of the water interaction complexes with the most common functional groups on AC surface, their solvation energies (Esolv., kcal/mol) and Gibbs free energies (∆Gsolv., kcal/mol), the corresponding binding energies (BE, kcal/mol), length of the hydrogen bond (d, Å), and thermodynamic parameters (∆H298, kcal/mol, ∆S298, kcal/mol, and ∆G298, kcal/mol).
Figure 2. Pore size dependence of thermodynamic parameters for phenol adsorption from the gas phase (∆H, kcal/mol, ∆S, cal/mol‚K, and ∆G, kcal/mol) at 298 K. Values on the right axis correspond to the adsorption on flat graphite surface (pore diameter D tends to infinity).
Moreover, highly polar solvent molecules are able to adsorb either on the AC surface or the functional groups. Thermodynamic parameters for adsorption of water molecules from the gas phase and from water media are presented in Table 2. One can see that the presence of the solvent molecules significantly changes the geometry, energetics, and thermodynamics of the adsorption. As in the case of phenol adsorption, the strongest interaction occurs between water molecule and acidic functional group; this group is the only one for which ∆G298 < 0. Adsorption of water molecule on this functional group from the gas phase (∆G298 ) -4.59 kcal/mol) is energetically more favorable than adsorption of phenol molecule (∆G298 ) -2.26 kcal/mol). A similar tendency should be anticipated for all highly polar surface functional groups as water molecules have more ionic nature than phenol. Taking into account the much higher concentration of water molecules in the solution than that of the solute (the molar fraction of phenol at concentration of 10 ppm is 0.19 × 10-5), our results indicate that phenol interaction with surface functional groups is negligible due to the competitive water adsorption. Thus, phenol adsorption will not be benefited from functionalization of AC surface during pretreatment.
4. Pore Size Dependence 4.a. Adsorption from the Gas Phase. Due to its preferentially hydrophobic nature, a phenol molecule shows high affinity to nonpolar adsorption sites on the AC surface. Such interactions originate from van der Waals forces and, therefore, are better modeled by the MM method. Depending on the nature of the sorbent, most sites of this type are located either in the nano-, micro-, or mesopores. Based on the experimental results,2 such pores are represented in our calculations by zigzag carbon nanotubes of various radii. Enthalpy of phenol adsorption shows weak dependence on the pore diameter; it changes from -23.9 to -18.1 kcal/mol with increasing pore diameter from 9.4 to 18.8 Å and approaches the ∆H value on flat graphite surface of -14.7 kcal/mol (Figure 2). The ∆G changes show a similar trend, but due to the high sensitivity of the entropy term to specific geometry of the adsorption site, ∆G increases nonuniformly with increasing pore diameter. 4.b. Adsorption from Water Solution. The interaction of water molecules with the hydrophobic adsorption sites of a flat graphite surface or of a carbon nanopores is much weaker than that of phenol (∆H lies in the -2.0 to -2.5 kcal/mol range). The
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Figure 3. Coverage dependence of thermodynamic parameters for phenol adsorption from gas phase on a flat graphite surface at 298 K calculated as ∆Gn ) Gn - Gn-1 - Gphenol, etc. Up to 5 molecules adsorb directly to the surface, whereas the 6th molecule is adsorbed in the second layer.
Figure 4. Coverage dependence of thermodynamic parameters for gas-phase phenol adsorption within a carbon nanopore of 15.66 Å in diameter (298 K, calculated as in Figure 3).
interaction becomes energetically unfavorable if it is accompanied by the destruction of water solvation sphere, i.e., adsorption of H2O molecules on the AC-water interface is not stable even at low temperatures. Water adsorption on nonpolar sites of the AC surface, either from the gas or the aqueous phase, is characterized by positive ∆G due to the entropic effects. Therefore, the interaction of phenol with water molecules within the narrow pores could be neglected, and thermodynamics of phenol adsorption from water solution could by directly derived from the data of gas-phase adsorption (Figure 2) by subtracting the corresponding thermodynamic parameters characterizing solvation of a phenol molecule (∆H ) -4.90 kcal/mol, ∆S ) 0.25 cal/mol K and ∆G ) -4.97 kcal/mol at 298.15 K at the applied DFT level of theory). Phenol adsorption in carbon nanopores at room temperature is characterized by ∆G < 0,
whereas in wider pores, in which curvature of pore walls is negligible, adsorption from water media at room temperature becomes thermodynamically unfavorable.
5. Coverage Dependence 5.a. Adsorption from the Gas Phase. Interactions between chemisorbed molecules are usually repulsive; physisorption, in the absence of steric restrictions, on the other hand, is often characterized by slight attraction. Analysis of the adsorption geometries and corresponding thermodynamic parameters for phenol adsorption on flat graphite plane of AC surface (Figure 3) indicate that at low coverage the interaction between adsorbed molecules is negligible; slight fluctuations in ∆H values should be attributed to the cluster boundary effect. However, entropy decreases with increasing coverage so that ∆G298 increases and
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Figure 5. Coverage dependence of thermodynamic parameters for gas-phase water adsorption within a carbon nanopore of 15.66 Å in diameter (298 K, calculated as in Figure 3).
becomes positive near the monolayer coverage. Interaction of the second-layer phenol molecules with phenol molecules directly adsorbed on graphite plane of AC surface is slightly stronger than the phenol-AC interaction (BE ) 15.89 and 15.16 kcal/mol, respectively) as it is additionally stabilized by Coulomb interactions between polar OH groups. At room temperature, however, formation of the second layer is thermodynamically less favorable than direct adsorption on a graphite plane due to the entropy effect (∆G298 ) -6.53 and -3.53 kcal/mol, respectively). Interaction between adsorbed molecules within narrow pores is slightly attractive (∼1-2.2 kcal/mol per a pair). Formation of such weak bonds is accompanied by an increase in entropy so that ∆G298 notably decreases with increasing coverage. Figure 4 presents the thermodynamics of phenol adsorption within cylindrical nanopore of 15.66 Å in diameter with increasing number of phenol molecules in the cross-section. At low temperature, the optimal loading in such a pore is 4 phenol molecules, whereas at room temperature, the entropy factor decreases the optimal loading to 3 molecules, however adsorption of 4 molecules is still thermodynamically stable. 5.b. Adsorption from Water Solution. Formation of hydrogen bonds between water molecules adsorbed within the narrow pores can stabilize water adsorption. Therefore, we studied the coverage dependence of the thermodynamic parameters for water adsorption (Figure 5). The results confirmed the above conclusion that room-temperature water-adsorption is thermodynamically unfavorable in narrow pores and the interaction of phenol with water molecules could be ignored. The interaction of the phenol molecules adsorbed on graphite planes of AC surface with the solution cannot be neglected. The adsorption geometries presented in Figure 3 suggest that at low coverage the solvation energy could be approximated as onehalf of the solvation energy of a phenol molecule in solution as half of the surface of adsorbed phenol molecule remains available for interaction with the solvent.
6. Adsorption Capacity 6.a. Maximal Adsorption Capacity. For engineering purposes, adsorption should be characterized for its capacity and its rate: The adsorption rate is masked by external mass transfer,
Figure 6. Two projections of the Connolly surface (solvent accessible area) of a phenol molecule (a) and side view of the Connolly surface of a phenol molecule adsorbed within a cylindrical carbon nanopore of 10.96 Å diameter (b).
the transfer of solute from the bulk liquid to the surface layer of fluid around a particle, and by diffusion within the pore. These processes are rather slow. In the present work, we do not consider adsorption kinetics and estimate AC storage capacity at the equilibrium with solution. Phenol adsorption on AC surface is controlled by thefollowing main factors:26 (i) Surface Area of ActiVated Carbon, which Determines the Number of Adsorption Sites. Several authors have documented the fact that large molecules tend to be more sorbable than small molecules. This effect arises from the nature of the van der Waals interaction. To maximize the interaction area and, correspondingly, to increase the interaction energy, adsorbed phenol molecules are oriented parallel to flat graphite planes on AC surface (Figure 2) or to pore walls (Figure 4). The size of a phenol molecule upon physisorption could be approximated by ellipsoid of 7.86 × 7.85 × 3.49 Å dimension (Figure 6). Assuming that whole AC surface is available for adsorption that leads to the maximal adsorption capacity of AC with surface area S (m2/g) to be Cmax ) 3.23 × 10-4 × S (g phenol/g AC). (ii) Pore Size, which Determines the Accessibility of Surface Sites for Phenol Molecules. The complex internal surface area of AC is usually divided into three components: micropores (of diameters less than 2 nm) that constitute the largest portion of the carbon’s surface area, mesopores (2-50 nm), and macropores (>50 nm).27 Many studies document cases in which large (26) ActiVated carbon adsorption for wastewater treatment; Perrich, J. R., Ed.; CRC Press: Boca Raton, FL, 1981.
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θ ) KApA/(1 + KApA)
(1)
where pA, the partial-pressure of component A, is described with
K A pA )
a2S0(T) exp(∆Edes/kT)pA νx2πmkT a2λn
Figure 7. Size dependence of accessibility of the pore surface for phenol adsorption.
molecules adsorption is inhibited, mostly due to “screening” or “sieving” by smaller pores. Our calculations indicate that phenol adsorption in cylindrical pores smaller than 9.4 Å in diameter is limited by steric restrictions. Therefore, only micropores with diameter larger than 1 nm are available for phenol adsorption. Figure 6b also demonstrates that, due to geometric considerations, the inner surface of narrow pores could be only partially available for adsorption. From geometric considerations, we conclude that from 60 to 100% of the surface could be occupied by adsorbed phenol molecules in cylindrical nanopores with diameter between 1 and 2 nm, whereas in meso- and macropores most of the surface area is accessible for adsorption (Figure 7). (iii) Solubility of Solute in Aqueous Solution. That determines the relative stability of adsorbed and solvated phenol molecules. Our calculations show that water and phenol molecules are adsorbed on different sites of AC surface. As it is described above, in calculations of adsorption capacity, we take into account calculated solvation energy for a phenol molecule in bulk solution, half of the solvation energy for a molecule adsorbed on the solid-liquid interphase and consider a molecule adsorbed within nanopore as nonsolvated. (iV) pH. Due to negligible phenol interaction with surface functional groups in water media and negligible interaction of ionic species with hydrophobic adsorption sites on AC surface (see above), pH is expected mainly to affect adsorption kinetics rather than thermodynamics; therefore, pH effect is not considered in the present work. (V) Temperature. Because adsorption interactions are usually exothermic, high temperatures would seem to inhibit adsorption capacity, but this is not usually found to be a factor in most systems.26 This can be accounted for when considering that the temperature inhibits the capacity but it accelerates the diffusion of solute into narrow pores. 6.b. Computing the Adsorption Isotherm. The adsorption isotherm can be predicted from thermodynamic consideration, equating the chemical potential of the two (adsorbed and solution) phases or from dynamics considerations, equating the rates of steps involved: evaporation, adsorption, desorption, and condensation. Both approaches should yield, of course, the same results. Since most previous results treated the gas-adsorbed phase equilibrium, we will discuss it first and then introduce the gas-liquid equilibrium to obtain a liquid-adsorbed phase adsorption isotherm. The equilibrium of a gas and an adsorbed regular-lattice phase, in the context of a Langmuir isotherm, is summarized by Chorhendorff28 and Yang29 to show that the coverage follows (27) Bansal, R. C.; Jean-Baptiste, D.; Fritz, S. ActiVe Carbon; Marcel Dekker: New York, 1988. (28) Chorkendorff, I.; Niemantsverdriet, J. W. Concepts of modern catalysis and kinetics; Wiley-VCH: New York, 2003.
) kT S (T) exp(∆Edes/kT) (2) hν 0
where a2 is the area of a site, λ ) h/(2πmkT)1/2 is the thermal de-Broglie wavelength, n ) pA/kT is the gas-phase density, S0 is the sticking coefficient that express entropy effects, and ∆Edes is the activation energy for desorption. For nonactivated adsorption ∆Edes ) -∆H. For the common case of kT/hν ) 1, and defining S0 ) exp(∆S/k), the equation is reduced to
KApA ) a2λn exp(∆G/kT)
(3)
A similar equation can be derived by equating the adsorption and desorption rates.15-17 The adsorption in a cylindrical pore is more complex since it involves packing within the pore. We assume here that in equilibrium it can be viewed as layers with equal coverage at each layer. We should modify the expression above to a case of adsorption in a tube (or rather its mouth). If the pore cross section is Sn and it can pack i molecules of species A (or Sn/i per molecule), then
KApA ) (Sn/i) λn exp(∆G/kT)
(4)
and θ is calculated accordingly. The linear density (molecules/ length) in the pore can be calculated and a comparison of kinetic17 and thermodynamic approaches30,31 is outlined elsewhere.17 The equilibrium of a gas-phase and a liquid ideal solution of solute mole fraction xA in a solvent is described by
pA ) P0AxA
(5)
where P0A is the vapor pressure of the pure solute (P0A ) 41.744 Pa at 298 K for phenol25). For nonideal solution, due to solutesolvent interaction, pA ) P0AxA exp(∆Gsol/kT) and overall adsorption is given by θ (eq 1) with
KApA ) KAP0AxA exp(-∆Gsol/kT) ) (Sn/i)λn0AxA exp((∆G - ∆Gsol)/kT) ) Kxx (6) It may be more convenient to use experimental Henry’s law values, HpA ) xA, which already incorporate the nonideality of the solution. In that case, we can still use eq 6 with n0A ) 1/HkT and ∆Gsol ) 0. The latter approach is applied in the present work. Very often organics adsorption on AC is best described by the Freundlich isotherm.11,12,29 This is usually attributed to powerlaw distribution of energies. Yang29 derived the adsorption parameter (Kf) in θ ) KfP1/n from statistical mechanics considerations to be
K)
JS ∆E - zb/2 σ exp ν02πmkT JG kT
(7)
(29) Yang, C.-h. J. Colloid. Interface Sci. 1998, 208, 379. (30) Wang, Q.; Challa, S. R.; Sholl, D. S.; Johnson, J. K. Phys. ReV. Lett. 1999, 82, 956. (31) Challa, S. R.; Sholl, D. S.; Johnson, J. K. Phys. ReV. B 2001, 63, 245419.
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Figure 8. Pore size dependence of AC coverage by phenol adsorption in cylindrical nanopores from water solutions (with 10-100 ppm) at 298 K expressed as the monolayer coverage (a) and the corresponding adsorption isotherms for AC with surface area S ) 1000 m2/g and pores of various diameters with Cmax ) 0.323 g/g AC (b). Values on the right axis in the left panel correspond to the adsorption on flat graphite surface (pore diameter D tends to infinity).
where σ is the molecule cross section, JS and JG are the internal partition functions of gaseous and adsorbed molecule and the exponent n ) zb/2kT, where b is a contribution to energy due to lateral interaction (ν is the vibration frequency, which in ref 29 is assumed to be coverage-dependent as well). Our results indicate that the change of energy with occupancy is not coherent (Figure 4) and we cannot pursue this approach. Using the thermodynamic approach (eqs 1 and 6), we calculated the coverage for activated carbons comprising of homogeneous cylindrical pores with various diameters (Figure 8a) and the adsorption weight isotherms (Figure 8b) showing that only the narrow pores contribute to adsorption and the maximal weight loading can reach 0.323 g/g AC for AC with surface area of 1000 m2/g; for more common AC with, say 400 m2/g, the maximal adsorption (0.1 g/g AC) is slightly above experimental values of about 0.05 g/g AC.11,12 Actual AC solids incorporate a range of pore-sizes, of which only the narrow ones contribute to adsorption; that explain the disagreement above.
7. Conclusions Thermodynamic parameters for phenol adsorption from the gas phase and from water media in various sites on the AC surface (functional groups, nanopores, and flat graphite surfaces) are calculated using density functional theory and molecular mechanics methods. We found three distinguishing features characterizing phenol adsorption on AC:
(i) Phenol interaction with surface functional groups is characterized by low interaction energy and for most groups is thermodynamically unstable at room temperature. In the case of adsorption from aqueous solution, this kind of interaction is negligible due to competitive and much stronger interactions of water molecules with polar adsorption sites. (ii) Contrary, phenol exhibits a high affinity to hydrophobic adsorption sites on AC surface, whereas the adsorption of water molecules from aqueous solution is energetically unfavorable. Therefore, water and phenol molecules are adsorbed on different sites of AC surface. (iii) Nanopores of 1-2 nm in diameter present the best adsorption position for phenol. Application of the obtained geometric and thermodynamic parameters for estimation of the phenol storage capacity of AC leads to the conclusion that only narrow pores contribute to the adsorption. In future work, we will extend this approach to other organics pollutants. Acknowledgment. This work was supported by the Grand Water Research Institute. I.E. gratefully acknowledges the partial financial support of the Center for Adsorption in Science, Ministry of Immigrant Absorption, State of Israel. LA052100U
