J. Phys. Chem. 1996, 100, 1189-1196
1189
Adsorption of Water on Activated Carbons: A Molecular Simulation Study Erich A. Mu1 ller† Departamento de Termodina´ mica y Feno´ menos de Transferencia, UniVersidad Simo´ n Bolı´Var, Caracas 1080, Venezuela
Luis F. Rull‡ Departamento de Fı´sica Ato´ mica, Molecular y Nuclear, UniVersidad de SeVilla, 41080 SeVilla, Spain
Lourdes F. Vega§ Departament d’Enginyeria Quı´mica, UniVersitat RoVira i Virgili, 43006 Tarragona, Spain
Keith E. Gubbins* School of Chemical Engineering, Cornell UniVersity, Ithaca, New York 14853 ReceiVed: August 3, 1995; In Final Form: August 18, 1995X
We report a molecular simulation study for a model of water adsorption on nonporous and porous activated carbons. The grand canonical Monte Carlo method is used, and the temperature is fixed at 300 K. Water molecules are modeled as a Lennard-Jones sphere with four square-well sites to account for the hydrogen bonding. The carbon surfaces consist of planar graphite sheets, with active chemical sites on the surface modeled as square-well sites. The effect of the density and geometric arrangement of the active sites on the surface is studied. Both macroscopic properties (particularly adsorption isotherms) and molecular configurations are obtained. The adsorption mechanism for water on such surfaces is markedly different from that of simple nonassociating molecules such as hydrocarbons or nitrogen. In contrast to the usual buildup of adsorbed layers on the surface, water adsorption is characterized by the formation of peculiar three-dimensional water clusters and networks, whose formation relies on a cooperative effect involving both fluid-fluid interactions and fluid-solid ones with suitably placed active sites. Both the density and arrangement of the sites on the surface have a pronounced effect on the adsorption. Capillary condensation is observed only for low densities of active sites; for higher densities, continuous filling occurs.
1. Introduction Adsorption isotherms for water on carbons show a distinctly different behavior to that of simple adsorbates such as nitrogen, hydrocarbons, and other organics.1 For graphitic carbons, for which surface chemical groups have been removed, there is almost no adsorption at low and moderate pressures; in the case of porous carbons, capillary condensation occurs at some higher pressure. For these same carbons, hydrocarbons or nitrogen adsorb strongly at much lower pressures. The physical reason for such behavior is clear intuitively. In order to adsorb on the surface, the water molecules must conform to the surface geometry, and this breaks hydrogen bonds (H bonds) that would be present had the molecules remained in the bulk phase. Thus, adsorption onto graphitic carbons is energetically unfavorable, and there is no strong entropic incentive to adsorption to overcome this. The underlying molecular mechanism has been studied in some detail by molecular simulation, and the simulations are in good agreement with experiments.2,3 Activated carbons, prepared by heating carbonaceous material in the presence of water, oxygen, or carbon dioxide, have a variety of surface chemical sites, such as hydroxyl, carboxyl, quinone, peroxide, aldehyde, etc., groups.4 Water adsorption * E-mail:
[email protected]. † E-mail:
[email protected]. ‡ E-mail:
[email protected]. § E-mail:
[email protected]. X Abstract published in AdVance ACS Abstracts, December 15, 1995.
0022-3654/96/20100-1189$12.00/0
on such materials shows a wide range of behavior. The ability of the water molecules to form H bonds with the surface sites helps compensate for the loss of water-water H bonds that may occur on adsorption so that adsorption is usually larger than for graphitic carbons. Some typical experimental results are shown in Figure 1. The curves shown represent successive experimental measurements in which the material is heat treated at increasingly higher temperatures, in some cases in the presence of hydrogen, to progressively remove the surfaceoxygenated sites. It is seen that the adsorption of water is greatly enhanced by the presence of an appreciable surface density of sites, whereas for the graphitic carbon with few if any sites (curve VII) the water uptake is negligible except at high pressures; i.e., the surface is hydrophobic. Walker and Janov5 carried out similar studies of a nonporous carbon, graphon, and found a direct relationship between the number of water molecules adsorbed and the number of oxygenated sites present. There have been numerous experimental studies of water adsorption on activated carbons (e.g., refs 6-14). Unfortunately, the carbons on which these measurements are made are poorly characterized in general, making comparisons with theory or simulation results difficult. Recent differential scanning calorimetry measurements,15 together with earlier results,9,16 show that the average adsorption energy of a water molecule in an activated carbon is almost the same as the vaporization energy of bulk water. This result is in contrast to similar measurements of simpler fluids (which show adsorption energies substantially larger than the vaporization energy) and © 1996 American Chemical Society
1190 J. Phys. Chem., Vol. 100, No. 4, 1996
Mu¨ller et al.
Figure 2. Sketch of the water molecule. The large open circle represents the LJ core of the molecule. The small open (H-type) and shaded (O-type) circles are the SW associating sites. O-type sites bond only to H-type sites. H-type sites also bond to sites placed on the surface.
Figure 1. Adsorption of water vapor on oxygenated carbon. (I) Heated in vacuo at 200 °C, (II) in vacuo at 950 °C, (III) in vacuo at 1000 °C, (IV) at 1100 °C in a hydrogen stream, (V) in hydrogen at 1150 °C, (VI) in hydrogen at 1700 °C, and (VII) at 3200 °C. Solid symbols denote desorption. From ref 1.
suggests that the adsorption may be dominated by water-water or water-site interactions, rather than water-carbon interactions. The molecular behavior of water adsorbed onto activated carbons is of considerable practical importance, in addition to being of scientific interest, since such carbons are widely used for separations in the chemical, petroleum, and pharmaceutical industries, as well as in the removal of pollutants from water and air. The presence of water vapor in air or gas streams containing pollutants or contaminants is known to greatly affect breakthrough curves (plots of pollutant concentration leaving an adsorption bed vs time); breakthrough occurs at much earlier times than for dry gas streams (e.g., refs 17 and 18), presumably because the water molecules adsorb strongly on the active sites and so block part of the surface. In the use of activated carbons for water treatment, the selectivity and adsorption will again depend strongly on the type and placement of active sites. The work presented here is intended to be the first step in a systematic study using molecular simulation to understand the mechanism of adsorption of water and aqueous solutions in model activated carbons and to answer several fundamental questions, including the following. What is the molecular mechanism by which adsorption occurs, and how does it differ from that of simple fluids? How is the adsorption, and selectivity in the case of mixtures, affected by the type, density, and placement of the active sites on the surface? Is there an optimum density, type, and geometric arrangement of sites that give a maximum adsorption or selectivity? How are the adsorption and selectivity affected by the pressure, temperature, pore width, and pore shape? How does the density, type, and placement of active sites affect phase transitions such as capillary condensation? Do new phase transitions occur? Such questions are very difficult to answer by direct experiment, because of the difficulty of preparing well-characterized materials. Molecular simulation offers the possibility to study these effects individually and systematically for precisely defined model materials.
In this paper, we focus on pure water and, particularly, the molecular mechanism of adsorption and the effect of density and placement of active sites. There is some controversy in the literature concerning the adsorption mechanism. Some authors9,16,19-21 have proposed, based on experimental studies, that clusters of molecules nucleate around high-energy sites on the surface; these adsorbed water molecules then act as secondary nucleating sites and eventually induce condensation. A frequently cited empirical theory by Dubinin and Serpinsky22,23 relies on this description to fit the adsorption branch of the water isotherm. Nevertheless, it is still common to theoretically describe the adsorption mechanism of water in a similar way as that of simple fluids; i.e., a monolayer is formed at low pressures, and further layers are formed only after essentially full coverage by this primary monolayer. There appears to have been little previous simulation work on water adsorption on active carbons, apparently because of the daunting CPU times involved. We are only aware of two such studies, by Segarra and Glandt24 and Maddox et al.25 Segarra and Glandt used the SPC point charge model for water and modeled the active carbon using randomly oriented platelets of graphite with a dipole distributed uniformly over the edge of the platelets to mimic the activation. However, the failure to include discrete active sites may not capture the molecular details of the adsorption mechanism in real active carbons. Maddox et al. used a somewhat different point charge model for water, TIP4P, and modeled the carbon as having well-defined slit pores whose surfaces contained a number of discrete and uniformly placed active sites, which were modeled as COOH groups using the OPLS potential model. The models used in both of these studies involve long-range Coulombic forces. In order to minimize the cut-off errors induced due to the effect of simulating a finite system, large system sizes are needed. In this work, we avoid the problem by using square-well sites to mimic the association. 2. Intermolecular Potentials The model for the repulsive-dispersion interaction between molecules studied is a 12-6 Lennard-Jones potential, φLJ,
φLJ(r) ) 4ii
[( ) ( ) ] σii r
12
-
σii r
6
(1)
which is a function of the center-to-center distance, r, and has two parameters, ii and σii, related to the size of the molecules and the energy of interaction, respectively. Water is modeled as a spherical LJ atom with four SW associating sites placed in a tetrahedral geometry, as shown in Figure 2. Two sites correspond to the hydrogen atoms (H type), the other two corresponding to the lone pair electrons in the oxygen atom (O type). The square-well (SW) interactions
Adsorption of Water on Activated Carbons
φHB )
{
-HB 0
if rAB < σHB otherwise
J. Phys. Chem., Vol. 100, No. 4, 1996 1191
(2)
are characterized by a diameter σHB and an energy well HB; rHB is the site-site distance. The site diameter is fixed at σHB ) 0.2σff, where ff refers to fluid-fluid parameters. Neutron scattering results26,27 show that at low temperatures, a hydrogen bond is formed when 2 water molecules are roughly 0.94 molecular diameters apart. This suggests the placement of the sites at 0.42σff from the center of the LJ core. No account for the long-range attraction is explicitly given. The presence of long-range forces is difficult to take into account in simulations of confined media, due to the anisotropy of the system and the difficulty that this generates when considering the long-range corrections. This can be avoided by using extremely large systems, but the computational cost is prohibitive. For example, a similar study using a point charge model of water required very long CPU times even when solved on a massively parallel computer.25 The void in the attractive tail of the potential is likely to be compensated in part by an increase in the depth of the square-well sites and of the LJ well depth, as will be apparent when the parameter values are discussed. The fluid-fluid LJ parameters and the H-bonding energy for water were adjusted to experimental properties. While several possibilities may be envisioned, the fitting of a potential directly to experiments requires a great deal of trial-and-error choices along with a large computational effort (molecular simulations) to validate the choice of parameters. Here, instead, Wertheim’s TPT1 theory28,29 is employed. The theory is known to be in good agreement with experiment for this model.30 A brief description of the theory is given in the Appendix. The theory is then used to find a set of parameters which best reproduce the vapor-liquid equilibrium properties, saturated vapor density (Fvapor), saturated liquid density (Fliquid), vaporization energy (∆Uvap), and vapor pressure (P0). The parameters obtained from such a search are σff ) 0.306 nm, ff/k ) 90 K, and HB/k ) 3600 K, where k is Boltzmann’s constant. The values of the parameters are seen to be physically reasonable. The LJ parameters are close to but slightly smaller than those which describe methane (for methane, σff ) 0.381 nm and ff/k ) 148.1 K), as is expected. The H-bonding parameter is, however, larger than expected. Spectroscopic measurements31 estimate the H-bonding strength to be roughly 50% lower. In this model, the electrostatic forces are neglected; the lack of attractive forces is taken into account by an increase in HB/k. The properties of the model thus defined are presented in Table 1. Alongside are the results obtained from molecular simulations and experiments. Close agreement is not observed, although the results are similar. The most noticeable disagreement is in the densities and activities. The lack of an explicit long-range attraction is reflected in a liquid density which is lower than expected. Reasonable agreement is observed for the fraction of monomers, X, and the vaporization energy, ∆Uvap, indicating that the model has approximately the correct bonding behavior. Most of the energy of vaporization will come from the breakage of H bonds, so it is important to have a reasonable value for this quantity if the H-bonding character is to be studied. The disagreement in activities is of importance when converting from variables used in the simulations (activities) to variables used to plot the results (pressures). As a result of that, TPT1 is not used to relate activities to pressures; instead, we use a more accurate virial expansion which is described in the next section. The commonly cited estimate for the area occupied by an adsorbed water molecule9 is 0.105 nm2. This estimate is
TABLE 1: Properties of Saturated Water at 300 Ka Fvapor, mol/dm3 Fliquid, mol/dm3 Xvapor Xliquid P0, kPa ∆Uvapor, kJ/mol ζ0, nm-3
exptl
MC
TPT1
1.42 × 10-2 55.316
(3 ( 1) × 10-2 47.4 ( 0.5 0.9 ( 0.1 0
1.433 × 10-3 54.175 0.9705 2.3 × 10-6 3.522 55.83 9.1 × 10-4
3 × 10-4 b 3.536 41.38
43 ( 1 1.67 × 10-2
a MC values are obtained from GCMC simulations at fixed temperature and activity ζ. TPT1 theory is detailed in the Appendix A. X corresponds to the fraction of water molecules not involved in a H bond. b Data extrapolated from ref 31.
Figure 3. Lateral view of the pore geometry. Periodic boundary conditions are used in the x (from left to right) and in the y (in and out of the page) directions. Open circles represent the carbon atoms forming the walls of the pore; shaded circles represent the square-well sites (activated sites). Other parameters are detailed in the text.
obtained from bulk-liquid-density data. If we consider a model of nonassociating water molecules, i.e., only LJ spheres of σff ) 0.306 nm in a closed packed hexagonal monolayer, each molecule will occupy 0.081 nm2, in poor agreement with the above-mentioned estimate. However, the tetrahedrical hydrogen bonding of water implies a much more open structure, with a coordination number of four and a corrugated monolayer. In this more realistic geometry, each molecule occupies 0.1 nm2, in close agreement with the above-mentioned estimate. It will become apparent, however, that any reference to water adsorption in terms of monolayers leads to an incorrect picture of the actual physical process. The water model used is too crude to be used as a general water potential in other applications. No long-range forces or polarizabilities are taken explicitly into account, and only the properties at a single temperature are optimized. Nevertheless, it provides a simple idealized model which bears some of the most important physical characteristics thought to be of importance for this particular study. The solid phase is modeled as a single slitlike pore having two infinite parallel walls in the x-y plane separated by a distance H in the z direction, as shown in Figure 3. Each of the two walls is taken to be the basal plane of a graphite-like surface made up of LJ atoms of diameter σss. Thus, on each plane, the atoms are organized in a hexagonal array. The solid density is Fss, and H is defined as the distance separating the planes, on each side of the pore, through the centers of the LJ atoms forming the surface of the walls. In this study, we approximate the solid surface as a continuum one, thus enabling us to locate the active sites at will. The LJ potential between one sphere of the fluid and each of the molecules of the solid is integrated over the lateral solid structure. By summing over the planes of molecules in the surface, separated by a distance ∆, the 10-4-3 potential, φwall, is obtained:32
1192 J. Phys. Chem., Vol. 100, No. 4, 1996
φwall(z) )
[( ) ( )
2πFsssf(σsf)2∆
2 σsf 5 z
10
-
Mu¨ller et al.
]
σsf4 σsf 4 (3) z 3∆(z + 0.61∆)3
where the crossed solid-fluid interaction parameters (sf, σsf) are calculated according to the Lorentz-Berthelot rules σsf ) (σss + σff)/2 and sf ) (ssff)1/2 and the subscript ss refers to the solid while ff refers to the fluid parameters. Fss, ∆, ss, and σss have been chosen to model a graphite surface:32 Fss ) 114 nm-3, ∆ ) 0.335 nm, ss/k ) 28.0 K, and σss ) 0.340 nm. The structureless pore surfaces are doped (activated) by placing association sites on the walls, as shown in Figure 3. Associating sites are placed at a distance z ) 0.5σss ) 0.17 nm from each wall, i.e. protruding from the surface, and have identical size and energy parameters to those found on the water molecules. They mimic oxygenated sites (O type) and, thus, will H bond only to one of the two sites labeled as hydrogen atoms in the water molecules. Experimental observations13 suggest that, on average, the interaction seems to be independent of the active surface group (carboxylic, carbonylic, phenolic, etc.) in which the oxygen is incorporated. The model used here, which assumes a single type of associating site, should therefore provide a rough first approximation to the H-bonding characteristics of activated carbons. For a given slit pore of width H, the external potential experienced by any LF sphere in the fluid at z is calculated as the superposition for the two walls. In summary, the total solid-fluid interaction potential, φsf, is given by
φsf(z) ) φwall(z) + φwall(H - z) + φHB
(4)
The unactivated pore model has been used previously in extensive theoretical and simulation studies of simple fluids.33,34 The extension to activated surfaces was proposed by us35 in the context of studying adsorption of associating chain molecules. This model has enough flexibility to allow a systematic study of the main variables which seem to govern the adsorption of water in activated pores, while retaining enough simplicity to be computationally tractable. 3. Simulation Details We have used grand canonical Monte Carlo simulations (GCMC), as detailed in ref 36, to obtain the properties of the inhomogeneous system. In GCMC, the temperature, T, the volume of the pore, V, and the chemical potential, µ, are kept fixed. The number of molecules is thus allowed to vary, and its average is the relevant quantity of interest. The main variable of interest is µ, which is the same for the bulk phase in thermodynamic equilibria with the pore. In simulations, the total chemical potential is sometimes replaced by the more convenient activity, ζ, defined as
ζ)
exp(µ/kT) Λ3
(5)
where Λ is the De Broglie wavelength, which includes contributions from translational rotational degrees of freedom. Assuming the ergodicity of the simulations is essential for obtaining meaningful results. In the case of associating fluids, this matter is of critical importance, since if the association bond between two molecules is too strong, once the bond is formed, it would be statistically improbable that it would ever be broken. Such a situation would violate microscopic reversibility and thus affect the ergodicity of the simulations. In these simulations,
Figure 4. Number, N, of molecules in pore of width 2 nm with 18nm2 surface area and n ) 1 site/nm2 as a function of the number of Monte Carlo cycles. Dashed lines are for a two-center LJ model for propane, at ζ ) 0.01 nm-3; solid lines are for our model of water at ζ ) 0.0014 nm-3. Temperature is 300 K.
due to the large value of the association energy, special attention was paid to these details. Even though the association SW energy is large, it is the relation to the average energy, kT, of the system which is of relevance. The ratio HB/kT ) 3600/ 300 ) 12 is within the range in which an unbiased MC simulation will be practical. For ratios HB/kT equal to or greater than 20, biased techniques37-40 are needed. Even when the correct sampling of the phase space is guaranteed, the fluctuations seen in the simulations evidence the fact that there are many energetically favored configurations in which the system will stay for many MC steps. Due to this, long simulations are needed in order to ensure that equilibrium is reached. Typical runs require 107 configurations for equilibration and 5 × 107 configurations for accumulation of averages. Systems where capillary condensation occurs require runs up to 10 times longer due to the difficulties in achieving equilibrium. Ergodicity was also checked in some simulations by monitoring the bonding states of chosen molecules. In Figure 4, an example is shown of how the simulations of water may be an order of magnitude longer than a comparative simulation for a nonassociating fluid, in this case propane. Here propane is modeled as a two-site LJ fluid (details of the potential are given in the next section). The pore dimensions are in both cases the same, and the activities are fixed so that comparative amounts of molecules are adsorbed in both cases. It is seen that for “propane”, equilibrium is achieved with 5 × 105 steps, and 107 steps are enough to produce accurate statistics. For water, on the other hand, equilibrium requires close to 4 × 107 steps, and even after 108 steps, the statistics are considerably poorer. Periodic boundary conditions36 and minimum image conventions were applied in all Cartesian directions for the bulk fluid and in the x and y directions in the pore. No long-range corrections were applied to the confined fluid, due to the computational difficulties associated with it. However, the pore length was 3 nm, roughly 10σff, so all molecular interactions up to at least a distance of 5σff in the x and y direction were explicitly taken into account. In all cases presented, T is fixed to 300 K. Experimental adsorption isotherms are usually given in terms of the amount adsorbed vs relative pressure, P/P0, of the bulk gas; here P0 is the saturation pressure of the bulk gas. In GCMC simulations, the activity ζ, rather than the pressure P, is specified, and a method is needed to relate ζ and P for the bulk gas. TPT1 is not accurate enough at low densities. Instead, we use a virial equation of state in terms of activities.41 If we require that the pressure be expressed in reduced terms, P/P0, and if we employ a known saturation state point, for example, the variables (ζ0,F0) given in Table 1, the desired relation is obtained
Adsorption of Water on Activated Carbons 2 2 P 2ζζ0 + (F0 - ζ0)ζ ) P0 (F + ζ )ζ 2 0
0
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(6)
0
where the subscript 0 refers to the bulk gas saturation properties. The corrections for the gas-phase nonideality are small, usually less that 10% in the value of P/P0. 4. Results 4.1. Adsorption on Single Surfaces (Large Pores). The adsorption behavior for a sufficiently wide pore should approximate that of two single, planar carbon surfaces. We have studied such a case by simulating a pore of width 6 nm. This pore width is approximately 20 molecular diameters, so effectively the center of the pore should not be subject to direct interactions with the wall, and the two surfaces should behave independently. The sides of the pore (in the x and y directions) were fixed at L ) 3 nm, and periodic boundary conditions were used in these directions so that the pore is effectively of infinite length. This geometry proves to be a simple and efficient way to overcome the problem of establishing boundary conditions for simulating single surfaces. The nature of the unactivated walls was studied for models of both water and propane. Propane is modeled using a twocenter LJ potential, the LJ spheres being connected tangentially, with LJ site parameters σff ) 0.3659 nm and ff/k ) 209.37 K. These parameters are obtained by fitting to the experimental values of the phase diagram of bulk propane.42 In Figure 5, the isotherms for water and propane are shown. The amount adsorbed is expressed in µmol/m2 of surface, and the pressure of each substance is reduced with respect to its own vapor pressure. Water turns out to be a very poor adsorbate, and only at higher pressures is any noticeable amount adsorbed. At high pressures, the water molecules adsorbed on the walls act as nucleation sites, and at sufficiently high pressures (not shown), capillary condensation is observed. Capillary condensation in pores will be studied in detail in the next section. The adsorption isotherm for water is concave or type III according to the Brunauer classification system.1 The experimental results of Walker and Janov5 for water on graphon (a nonporous graphite) at 20 °C are shown for comparison. The agreement is very good. We note that our model is a perfect graphitic surface, while the experimental surface has 0.2% impurities. For propane, the carbon surface is an excellent adsorbant. At low pressures, a monolayer is rapidly formed, as indicated by the steep rise in the amount adsorbed and by visual observation of the configurations produced. After this initial layer, subsequent adsorption is a weaker function of pressure, indicating a screening effect of the first layer. The isotherm is of type II and is typical of hydrocarbons adsorbing in graphite. Activation, however, changes the adsorption of water by decreasing the hydrophobic nature of the surface. Activation is obtained in this model by randomly placing spherical SW sites on the surface. Typical experimentally observed site densities range from 0.2 site/nm2 (e.g., ref 15) to 1.44 sites/ nm2 (e.g., ref 14). Figure 6 shows the isotherms for surfaces with increasing activation, n ) 0, 0.222, 0.444, and 1 site/nm2. The figure shows how a small density of sites can have a profound effect on the adsorption characteristics. For comparison purposes, the density of carbon atoms in the model surfaces is 38.177 atoms/nm2. In the low-pressure regime, the effect of the sites is to each adsorb a water molecule. This only occurs at low coverage, and it is seen that at higher pressures, some cooperative effect takes place. Water molecules
Figure 5. Adsorption isotherms for water and propane on a graphite surface at 300 K. Closed circles are simulation results for water; squares are for propane. Open circles are experimental results of water on graphon at 20 °C (ref 5). Lines are a guide to the eye.
Figure 6. Adsorption isotherms for water on an activated carbon surface at 300 K. Closed circles are for n ) 0 (unactivated surface); triangles are for n ) 0.222 site/nm2; squares are for n ) 0.444 site/ nm2; open circles are for n ) 1 site/nm2. Lines are a guide to the eye.
may now adsorb not only to sites on the wall but to other adsorbed water molecules, thus forming heterogeneous regions of high and low density on the surface. In the case of the adsorption of water, once groups of water clusters are formed around active sites, they will eventually connect, producing a large exposed surface of bonded water molecules. At sufficiently high pressures, pore filling will occur. 4.2. Adsorption in Pores. In order to examine the confinement effect, we have studied a pore of width H ) 2 nm, roughly 6.5 molecular diameters. This pore width corresponds to the borderline of a micropore and a mesopore according to the accepted IUPAC classification.43 Without placing associating sites on the walls, the pore is hydrophobic, and the adsorption of water is almost negligible until very high reduced pressures, when capillary condensation causes pore filling. In Figure 7, the adsorption isotherm is shown for the inactivated carbon. To activate the surfaces, sites are placed randomly on the surfaces, each wall having a mirror-image distribution of sites. Upon doping the surfaces with a site density of n ) 1 site/nm2, the behavior of the systems changes significantly. Pore filling is shifted toward a much lower pressure, and the sharp capillary condensation observed in the absence of sites is no longer observed; instead, there is a steep rise in the adsorption at P/P0 ≈ 0.07. This S-shaped adsorption isotherm is typical of experimental results.6-14 In Figures 8-11, some snapshots are presented of the configurations obtained from the molecular simulations corresponding to the points marked in Figure 7. Figure 8 shows the pore at a relatively low pressure, and only a few molecules are adsorbed. Figures 9-11 show increasingly higher pressures. In all these cases, it is readily apparent that water molecules
1194 J. Phys. Chem., Vol. 100, No. 4, 1996
Figure 7. Adsorption isotherms for water in carbon slit pores of H ) 2 nm at 300 K. Circles are for an activated pore, n ) 1 site/nm2; squares for an unactivated (graphitic) pore. Closed symbols are for adsorption, open for desorption. Figures 8-11 correspond to points labeled a through d, respectively. Lines are a guide to the eye.
Mu¨ller et al.
Figure 10. Snapshot of a configuration from a GCMC simulation at P/P0 ) 0.0631 (point c, Figure 7). Other conditions as in Figure 8.
Figure 11. Snapshot of a configuration from a GCMC simulation at P/P0 ) 0.0932 (point d, Figure 7). Other conditions as in Figure 8. Figure 8. Snapshot of a configuration from an equilibrated GCMC simulation of water on an activated carbon pore of H ) 2 nm at 300 K, P/P0 ) 0.0083. This corresponds to point a in Figure 7. Pore walls are at the top and bottom of the figure. Associating sites (small dark spheres) are placed on the surface, corresponding to n ) 1 site/nm2. The LJ cores of the water molecules are drawn to a smaller scale to aid in the visualization.
TABLE 2: Variation in the Number of Adsorbed Water Molecules, N, for Different Site Distributions and Site Densities, n, in sites/nm2 a N geometry
n)1
n ) 1.5
random 1 random 2 random 3 regular array dense array
30 ( 2 19 ( 2 15 ( 5 5(1 41 ( 2
39 ( 4 30 ( 3 28 ( 4 14 ( 4 52 ( 1
a Activity is fixed at ζ ) 0.001 nm-3 corresponding to P/P ) 0 0.0419; temperature is 300 K.
Figure 9. Snapshot of a configuration from a GCMC simulation at P/P0 ) 0.0419 (point b, Figure 7). Other conditions as in Figure 8.
are adsorbed onto sites on the wall or onto previously adsorbed water molecules; there is a negligible amount of adsorption directly onto inactivated portions of the surface. Molecules seem to prefer to bond to adsorbed molecules, rather than on free surfaces. This behavior is peculiar to systems in which strong adsorption occurs only at certain surface sites. Figure 10 shows the formation of a sheet or “curtain” of water molecules stretching between the two walls of the pore. A percolation limit is reached at this pressure, P/P0 ≈ 0.063, for this system. A most interesting feature is again the availability not only of free surface in the pore but of free associating sites (e.g., the site in the far right corner). It is clear that the adsorption is a cooperative effect and the position of the sites is crucial to the overall behavior of the system. Figure 11 shows
the pore after it is filled with a dense liquidlike adsorbate phase. This phase is very stable, as evidenced by the large hysterisis loop of Figure 7. The hysterisis loop is also observed for the nonactivated pore (it coincides with the desorption branch of the activated pore and thus is not shown in Figure 7) and is caused by the strong fluid-fluid interactions which allow a metastable condition. 4.3. Effect of Site Location. Adsorption of water is clearly a cooperative effect, and the placement of the sites is likely to have a strong effect on the adsorption characteristics. Adsorption will be enhanced when surface sites are located in a way that allows clusters of water molecules to easily form “bridges” between sites. In the preceding sections, the associating sites were placed randomly on the surface. (While the placements of the sites are random, the random number generator is deterministic for a given initial “seed”. In this way, the “random” placements may be easily reproduced by employing the same seed.) In Table 2, we show the effects of several different random placements of associating sites (obtained with different site distributions) and compare them with results for two cases in which each site is placed in an ordered array. In the first of these, which we term “regular array” in Table 2, the sites are placed in a equally spaced array (square
Adsorption of Water on Activated Carbons
J. Phys. Chem., Vol. 100, No. 4, 1996 1195
Figure 12. Arrangement of surface sites for n ) 1 site/nm2 for (a) random array, (b) regular array spanning the surface, and (c) dense square array over one-quarter of the surface.
Figure 14. Adsorption as a function of site density, n, in sites/nm2 for a pore of 2 nm, a temperature of 300 K, and an activity fixed at ζ ) 0.001 nm-3 corresponding to P/P0 ) 0.0419. Open circles (right ordinate) correspond to the number of molecules adsorbed, N; closed circles (left ordinate) are the number of molecules per associating site.
Figure 13. “Bridging” between two water molecules which are H bonded to sites on the surface. The water molecule in the center of the figure is H bonded to the molecules to the right and left of the figure but is not on the surface plane. This cluster was isolated from an equilibrium configuration.
array for n ) 1 site/nm2, staggered array for n ) 1.5 sites/nm2) that spans the entire surface. In the second, termed “dense array”, this regular distribution is taken only over one-fourth of the available area. In Figure 12, these distributions are shown for n ) 1 site/nm2. The differences in the results cannot be attributed solely to statistical errors but are clearly due to the different possible bonding configurations available to a water molecule by the different geometries. It is seen that in the dense array, the adsorption is maximized, while it is minimal in the regular array. An analysis of the configuration shows that given two sites to which water molecules adsorb, if the distance between them is close enough, other molecules may form bonds, i.e., bridges, between these molecules. An example of such a bridge is shown in Figure 13. It is interesting to note that the molecule forming the bridge (the center one in the figure) is not in the same z plane as the molecules bonded to sites on the surface; i.e., it is closer to the center of the pore, forming a cluster rather than a two-dimensional layer. This association cluster can itself be a nucleation site for other water molecules. Thus, it is seen that it is not the overall site density which is the relevant physical parameter but rather the local density of sites and their relative location. 4.4. Effect of Site Density. In order to study the effect of site density, n was varied keeping the pore width fixed at H ) 2 nm, the temperature at 300 K, and the activity at ζ ) 0.001 nm-3 corresponding to P/P0 ) 0.0419. For an unactivated pore, this pressure is too low to observe any appreciable adsorption. Each reported site density is obtained by randomly adding sites to an existing site distribution. This is done to minimize the effect of the site location on the results. In Figure 14, a plot of the number of water molecules as a function of the site density, n in sites/nm2, is shown. The results are shown both in terms of the total number of molecules and the number of water molecules per site. It is seen that at relatively low coverage (0 < n < 3), the number of adsorbed water molecules is proportional to the number of sites. This is expected because, at these low coverages, the sites are rather sparsely located and there is little chance of cooperative effects. Figure 9 is a
snapshot corresponding to such a case for n ) 1 site/nm2. At higher site densities (n > 7), the addition of sites has little effect. At this point, both surfaces of the pore are covered by water molecules forming a rough layer, effectively screening any attraction from the walls or the remaining unoccupied sites. The pore is only partially filled, and the pressure (activity) is not high enough to induce condensation. 5. Conclusions A model for adsorption of water in activated carbons is presented. This model is expressed in terms of simplified intermolecular potentials and its properties are readily found by means of computer simulations. The intermolecular forces which are thought to be of main importance, repulsion, dispersion, and hydrogen bonding, are explicitly taken into account. The model is in qualitative agreement with experimental results. One of the most promising features of the model is that it allows the influence of the system variables, such as site adsorption strength, site density, and placement of sites, to be studied in a systematic fashion. It is seen that, in opposition to simple nonpolar molecules which adsorb on graphite, forming effectively two-dimensional monolayers, the adsorption of water on activated surfaces is carried out by a distinctively different mechanism. Water adsorbs preferentially on activated sites on the surface. The adsorbed water molecules act as nucleation sites for further adsorption of water, forming three-dimensional clusters. Depending on the position of the associating sites on the surfaces, these clusters, consisting of several associated water molecules, may or may not become connected with each other. Large clusters of water molecules may span from one wall of the pore to the other, even when a significant amount of free surface area is still available. The experimental detection of these clusters in carbons has been recently reported by Iiyama et al.44 Two factors are seen to be important in determining the enhanced water adsorption due to activation: the site density and the site distribution. A relatively low site density is seen to significantly enhance the water uptake. On the other hand, if sites are placed at appropriate distances from each other, a secondary mechanism of water adsorption is seen in which molecules bridge between adsorbed molecules. This fluidfluid cooperative effect is unique for water and is responsible for most of the peculiar adsorption properties of water. When no sites are present on the surfaces of the pore, we observe capillary condensation at a certain pressure, as in simpler adsorbate systems. This pressure decreases as the site density increases. At even higher site densities, the phase transition is no longer observed, as it is replaced by a continuous pore filling.
1196 J. Phys. Chem., Vol. 100, No. 4, 1996
Mu¨ller et al.
Acknowledgment. We are grateful to the Department of Energy (Grant No. DE-FG02-88ER13974) for support of this research and to NATO for a grant (No. CRG.931517) to support the international collaboration. We acknowledge the use of the supercomputer facilities at the Cornell Theory Center (IBM SP2) and the Centro Informa´tico y Cientı´fico de Andalucı´a where some of the simulations were performed. The computations were supported by a NSF Metacenter grant (No. MCA93S011P). Appendix: TPT1 Theory We will outline here only the main premises and results of Wertheim’s first order thermodynamic perturbation theory (TPT1) for associating fluids, as applied to the bulk water model. For further details, the reader is referred to the original papers28,29 and to a recent review.45 In TPT1, the fluid-fluid intermolecular potential is divided into a reference potential, taken in this case to be a spherical LJ interaction, and a perturbation which accounts for short-range directional attractions, taken here to be the square-well H-bonding potentials. It may be shown that the Helmholtz free energy of the fluid, A, may be expressed as
ALJ A ) - ln Xa4 - 2Xa + 2 NkT NkT
(A.1)
where ALJ is the LJ free energy, found from a suitable equation of state,46 and Xa is the fraction of molecules not bonded at a single association site a. The fraction of nonbonded water molecules is found to be X ) Xa4. The quantity Xa is found explicitly as
Xa )
-1 + x1 + 8F∆ 4F∆
(A.2)
where F is the number density and ∆ is the association strength, defined as
∆ ) ∫gLJ(12)fHB(12) d(2)
(A.3)
The integral is taken with respect to all orientations and positions of a molecule labeled (2). gLJ is the LJ radial distribution function, and fHB is the SW Mayer f function, fHB ) exp[-φHB/ kT] - 1. Given the site geometry, the quantity ∆ may be obtained as a function of density and temperature.42 References and Notes (1) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity, 2nd ed.; Academic: New York, 1982. (2) Ulberg, D. E.; Gubbins, K. E. Mol. Simul. 1994, 13, 205. (3) Ulberg, D. E.; Gubbins, K. E. Mol. Phys. 1995, 84, 1139. (4) Bohm, H. P. Carbon 1994, 32, 759. (5) Walker, P. L.; Janov, J. J. Colloid Interface Sci. 1968, 28, 449.
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