Langmuir 2005, 21, 10219-10225
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Does Water Condense in Carbon Pores?† J.-C. Liu and P. A. Monson* Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003 Received April 4, 2005. In Final Form: July 6, 2005
Using grand canonical Monte Carlo (GCMC) simulations of molecular models, we investigate the nature of water adsorption and desorption in slit pores with graphitelike surfaces. Special emphasis is placed on the question of whether water exhibits capillary condensation (i.e., condensation when the external pressure is below the bulk vapor pressure). Three models of water have been considered. These are the SPC and SPC/E models and a model where the hydrogen bonding is described by tetrahedrally coordinated squarewell association sites. The water-carbon interaction was described by the Steele 10-4-3 potential. In addition to determining adsorption/desorption isotherms, we also locate the states where vapor-liquid equilibrium occurs for both the bulk and confined states of the models. We find that for wider pores (widths >1 nm), condensation does not occur in the GCMC simulations until the pressure is higher than the bulk vapor pressure, P0. This is consistent with a physical picture where a lack of hydrogen bonding with the graphite surface destabilizes dense water phases relative to the bulk. For narrow pores where the slit width is comparable to the molecular diameter, strong dispersion interactions with both carbon surfaces can stabilize dense water phases relative to the bulk so that pore condensation can occur for P < P0 in some cases. For the narrowest pores studiedsa pore width of 0.6 nmspore condensation is again shifted to P > P0. The phase-equilibrium calculations indicate vapor-liquid coexistence in the slit pores for P < P0 for all but the narrowest pores. We discuss the implications of our results for interpreting water adsorption/ desorption isotherms in porous carbons.
I. Introduction Activated carbon continues to be one of the most important adsorbents for the removal of organic compounds because of its high surface area and large adsorption capacity as well as low cost. The presence of water vapor greatly reduces the adsorption capacity of organics1-3 and limits the effectiveness of activated carbon as a filter material in high-humidity environments. With the development of more ordered porous carbons, such as carbon nanotubes, the question of water permeation of such materials is also of interest. One of the central questions in understanding water adsorption in carbon materials is assessing the importance of electrostatic interactions (hydrogen bonding) between water molecules and the polar functional groups present in most porous carbons relative to the dispersion forces between a water molecule and a carbon surface. In an interesting recent study, Easton and Machin4 measured water adsorption in a graphitized carbon black. This study illustrates nicely the expected hydrophobicity of a graphitized carbon surface. In this case, the amount of water in the material remains very low until the pressure is higher than P0, corresponding to supersaturated states of the bulk vapor. Graphitized carbon black is a low-surface-area material, and the pore sizes are in the mesopore to macropore range. Because there is no hydrogen bonding with the graphite surface, water molecules near the surface experience a weaker interaction potential energy than in the bulk liquid state. This leads †
Part of the Bob Rowell Festschrift special issue. * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Rudisill, E. N.; Hacskaylo, J. J.; LeVan, M. D. Ind. Eng. Chem. Res. 1992, 31, 1122. (2) Eissmann, R. N.; LeVan, M. D. Ind. Eng. Chem. Res. 1993, 32, 2752. (3) Russell, B. P.; LeVan, M. D. Ind. Eng. Chem. Res. 1997, 36, 2380. (4) Easton, E. B.; Machin, W. D. J. Coll. Interface Sci. 2000, 231, 204.
to low adsorption and the delay of condensation in the system until the bulk pressure is beyond the saturated vapor pressure. There have been many experimental studies of water adsorption in various kinds of microporous and nanoporous carbons.1,5-16 In general, it is found that water adsorbs only slightly at low relative pressure, P/P0. The adsorption increases steeply at moderate relative pressure, and the system approaches saturation for relative pressures less than P/P0 ) 1. The most straightforward explanation for the difference between the behavior seen in these studies and that for the graphitized carbon black study is that the microporous and nanoporous carbons feature at least some local functionalization of the pore surfaces (active sites) that can give rise to strong electrostatic interactions with water molecules and hence help stabilize hydrogen bond networks in the pores. Of course, it is possible that the differences in pore size also play a role in the observed behavior. (5) Barton, S. S.; Evans, M. J. B.; MacDonald, J. A. F. Carbon 1991, 29, 1099. (6) Rubel, G. O. Carbon 1992, 30, 1007. (7) Salame, I. I.; Bandosz, T. J. Langmuir 1999, 15, 587. (8) Cossarutto, L.; Zimny, T.; Kaczmarczyk, J.; Siemieniewska, T.; Bimer, J.; Weber, J. V. Carbon 2001, 39, 2339. (9) Iiyama, T.; Nishikawa, K.; Otowa, T.; Kaneko, K. J. Phys. Chem. 1995, 99, 10075. (10) Hanzawa, Y.; Kaneko, K. Langmuir 1997, 13, 5802. (11) Kaneko, K.; Hanzawa, Y.; Iiyama, T.; Kanda, T.; Suzuki, T. Adsorption 1999, 5, 7. (12) Iiyama, T.; Ruike, M.; Kaneko, K. Chem. Phys. Lett. 2000, 331, 359. (13) Bekyarova, E.; Hanzawa, Y.; Kaneko, K.; Silvestre-Albero, J.; Sepulveda-Escribano, A.; Rodriguez-Reinoso, F.; Kasuya, D.; Yudasaka, M.; Iijima, S. Chem. Phys. Lett. 2002, 366, 463. (14) Ohba, T.; Kanoh, H.; Kaneko, K. J. Am. Chem. Soc. 2004, 126, 1560. (15) Alcaniz-Monge, J.; Linares-Solano, A.; Rand, B. J. Phys. Chem. B 2001, 105, 7998. (16) Alcaniz-Monge, J.; Linares-Solano, A.; Rand, B. J. Phys. Chem. B 2002, 106, 3209.
10.1021/la0508902 CCC: $30.25 © 2005 American Chemical Society Published on Web 08/19/2005
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Although full resolution of this issue from the experimental perspective awaits the development of microporous and nanoporous carbons that are essentially free of active sites, it is nevertheless worthwhile to investigate these issues using molecular models. There has been much recent work on developing molecular models of porous carbons,17-29 ranging from slit-pore models to models of disordered porous carbons. The slit-pore model, although not the most realistic model of a porous carbon, is certainly useful for isolating the effects of confinement on water properties, and in this article, we describe a study of the adsorption of water in slit pores aimed at addressing the question posed in our title. As we shall see, however, even in such an apparently simple model as this there are subtleties that must be addressed in interpreting the observed behavior. Our work on this problem was stimulated by some recent Monte Carlo simulation studies of water adsorption in carbon slit pores.24-28 In these studies, grand canonical Monte Carlo (GCMC) simulations were carried out for the SPC/E30 model of water adsorbed in slit pores in which the walls were modeled as atomistic graphene layers or with the Steele 10-4-3 potential for the water-carbon interaction. Various pore widths were considered in the range of 0.6-2 nm. An interesting feature of this work is that the calculated adsorption isotherms in all cases indicated that the pores are essentially filled with water for P/P0 < 1, in common with the experimental studies for microporous carbons discussed above. Although the authors did not comment in any detail on the issue, this result could be regarded as somewhat surprising. In the carbon slit-pore model considered, the water forms no hydrogen bonds with the pore walls, and in this respect, the model should behave like a graphitized carbon black rather than like the other porous carbons for which water adsorption has been studied experimentally. Of course, it is possible that we can understand this behavior in terms of the impact of confinement on the stability of dense states of water in the model. Striolo et al.24 point out that for narrow slit pores of an appropriate width a dense state of water can be stabilized by the strong attractive dispersion interactions with both pore walls. However, it is not clear whether this mechanism is still relevant for larger pore widths (e.g., 2 nm). We also mention another recent study29 of a model of water adsorption in cylindrical pores for which phase equilibrium within the pores was calculated. In that work, it was noted that for stronger solid-fluid attractions (17) Bandosz, T. J.; Biggs, M. J.; Gubbins, K. E.; Hattori, Y.; Iiyama, T.; Kaneko, K.; Pikunic, J.; Thomson, K. T. In Chemistry and Physics of Carbon 2003; Radovic, L. R., Eds.; Marcel Dekker: New York, 2003; Vol. 28, pp 41-228. (18) Segarra, E. I.; Glandt, E. D. Chem. Eng. Sci. 1994, 49, 2953. (19) Thomson, K. T.; Gubbins, K. E. Langmuir 2000, 16, 5761. (20) Acharya, M.; Strano, M. S.; Mathews, J. P.; Billinge, J. L.; Petkov, V.; Subramoney, S.; Foley, H. C. Philos. Mag. B 1999, 79, 1499. (21) Liu, J.-C.; Monson, P. A. Adsorption (in press). (22) Ulberg, D. E.; Gubbins, K. E. Mol. Phys. 1995, 84, 1139. (23) Muller, E. A.; Rull, L. F.; Vega, L. F.; Gubbins, K. E. J. Phys. Chem. 1996, 100, 1189. (24) Striolo, A.; Chialvo, A. A.; Cummings, P. T.; Gubbins, K. E. Langmuir 2003, 19, 8583. (25) Striolo, A.; Gubbins, K. E.; Chialvo, A. A.; Cummings, P. T. Mol. Phys. 2004, 102, 243. (26) Slasli, A. M.; Jorge, M.; Stoeckli, F.; Seaton, N. A. Carbon 2003, 41, 479. (27) Jorge, M.; Seaton, N. A. AIChE J. 2003, 49, 2059. (28) Slasli, A. M.; Jorge, M.; Stoeckli, F.; Seaton, N. A. Carbon 2004, 42, 1947. (29) Brovchenko, I. B.; Geiger, A.; Oleinikova, A. J. Chem. Phys. 2004, 120, 1958. (30) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269.
Liu and Monson
condensation occurred for P/P0 < 1 whereas for weaker solid-fluid attractions condensation occurred for P/P0 > 1, although the phase diagrams were presented only in terms of temperature versus density. A feature of the study was the use of the 9-3 solid-fluid potential in cylindrical geometry. The 9-3 potential is obtained from the 10-4 potential by integrating over layers of the solid and is strictly applicable only to a planar solid surface.31 Analytic expressions for integrated potentials corresponding to the 9-3 and 10-4 forms for use in cylindrical geometry have been presented by a number of authors.32-34 One effect of using a potential appropriate for a planar surface in the context of a cylindrical pore is that for a given set of potential parameters the solid-fluid attraction will be somewhat weaker than if the cylindrical geometry was incorporated into the formulation of the potential. However, the detailed effects of this will be quite complicated, and a useful comparison of the results from this particular cylindrical pore model with those for slit pores would be difficult to make. To establish whether in a model system water condenses in pores for P < P0, it is important to have an accurate estimate of P0 for the model of water being used. In the studies of the slit-pore model to which we have been referring,24-28 various methods were used to estimate P0. Striolo et al.24,25 carried out GCMC simulations for the bulk vapor and determined the chemical potential at which condensation occurred, using an equation of state to estimate the pressure from this chemical potential. Without using special sampling techniques that permit the crossing of large free-energy barriers, GCMC simulations tend to exhibit metastable states near vapor-liquid phase transitions. The point at which condensation is observed in a GCMC simulation will be a metastable vapor state at a higher pressure than the actual vapor pressure for the model system under study. Thus, the method used by Striolo et al.24,25 will tend to overestimate P0. Seaton and co-workers26-28 used two methods for estimating P0. In one study,27 they used the experimental vapor pressure rather than the value for the SPC/E model. In other studies,26,28 they used a similar approach to that of Striolo et al.24,25 except that they used a pore of width 10 nm and assumed that this would have similar behavior to that of a bulk system. Thus, the uncertainty in the location of P0 in all of these studies makes conclusions about whether water condenses for P/P0 < 1 somewhat tenuous. In this article, we describe a series of simulations for models of water adsorption in carbon slit pores of various widths. In addition to the GCMC calculations for adsorption and desorption, we make estimates of the bulk saturation conditions for the water models considered via a separate study of the bulk vapor-liquid equilibrium using the Gibbs ensemble Monte Carlo (GEMC) method.35 In some cases, we also use GEMC to estimate the vaporliquid coexistence conditions inside the pores. We find that the condensation observed in GCMC simulations may occur for states above and below the bulk vapor pressure depending on the pore width. For wider pores, we find that the condensation occurs for P/P0 > 1 whereas for a range of narrower slits condensation occurs for P/P0 < 1. In contrast to these results, we find that the equilibrium vapor-liquid transition occurs for P/P0 < 1 in all cases (31) Steele, W. A. Surf. Sci. 1973, 36, 317. (32) Peterson, B. K.; Walton, J. P. R. B.; Gubbins, K. E. J. Chem. Soc., Faraday Trans. 2 1986, 82, 1789. (33) Tjatjopoulos, G. I.; Feke, D. L.; Mann, J. A. J. Phys. Chem. 1988, 92, 4006. (34) Stan, G.; Cole, M. W. Surf. Sci. 1998, 395, 280. (35) Panagiotopoulos, A. Z. Mol. Phys. 1987, 61, 813.
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except for the very narrowest pore studied with a width of 0.6 nm. We discuss the question of which of these two pictures is most relevent to understanding experimental results for water adsorption in porous carbons. The remainder of our article is organized as follows. In the next section, we describe the models used in our work and some details of our computations. In section III, we describe our results for water adsorption isotherms, hysteresis behavior, and phase equilibrium in slit pores. Last, section IV gives a summary of our results and conclusions. II. Molecular Models and Simulation Methods A. Molecular Models for Water. We used two types of models for water in this work. The first type is fixed point-charge models: SPC/E30 and SPC.36 The second type is based on one originally developed by Nezbeda and coworkers37-40 and extended by Muller and Gubbins.41 It consists of a Lennard-Jones 12-6 potential together with four tetrahedrally coordinated square-well association sites. These sites lead to association interactions that model the hydrogen bonding between the water molecules without the explicit inclusion of electrostatic interactions. We refer to this model as the LJ4SQW model. The parameters provided by McCallum et al.42 were used for this purpose. For both types of models, the fluid-fluid intermolecular potentials were truncated at 4.5σff, where σff is the Lennard-Jones 12-6 collision diameter. For the SPC and SPC/E, we did not include the long-ranged electrostatic contributions. This follows the study by Striolo et al.,24,25 which was the study we most wanted to compare with. Moreover, these contributions would not be expected to change the qualitative adsorption/desorption behavior observed. Indeed, our estimates of the bulk vapor-liquid coexistence for the models are in very good agreement with earlier work using Ewald sums.43 B. Slit-Pore Model. The slit-pore model we used is composed of two parallel walls, and the 10-4-3 potential proposed by Steele31 was used to calculate the fluid-pore interaction. For the solid-fluid potential, with each surface we have
usf(z) )
[( ) ( )
2πFssfσsf2∆
2 σsf 5 z
10
-
σsf z
4
-
(
σsf4
)]
3∆(z + 0.61∆)3
(1)
where Fs is the number density of carbon atoms in the solid and ∆ is the layer spacing in graphite. sf and σsf are the well depth and collision diameter, respectively, of the Lennard-Jones potential acting between the water molecules and the carbon atoms. The parameters for this potential were those used by Striolo et al.24,25 The pore wall dimensions were set to 3 nm in the x and y directions, and periodic boundary conditions were applied in those directions. The pore width, H, is defined as the distance, (36) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; Hermans, J.; In Intermolecular Forces 1981; Pullman, B., Eds.; Reidel: Dordrecht, Holland, 1981; p 331. (37) Kolafa, J.; Nezbeda, I. Mol. Phys. 1987, 61, 161. (38) Nezbeda, I.; Kolafa, J.; Kalyuzhnyi, Y. V. Mol. Phys. 1989, 68, 143. (39) Nezbeda, I.; Iglesias-Silva, G. A. Mol. Phys. 1990, 69, 767. (40) Nezbeda, I.; Kolafa, J.; Pavlicek, J.; Smith, W. R. J. Chem. Phys. 1995, 102, 9638. (41) Muller, E. A.; Gubbins, K. E. Ind. Eng. Chem. Res. 1995, 34, 3662. (42) McCallum, C. L.; Bandosz, T. J.; McGrother, S. C.; Muller, E. A.; Gubbins, K. E. Langmuir 1999, 15, 533. (43) Errington, J. R.; Panagiotopoulos, A. Z. J. Phys. Chem. 1998, 102, 7470.
Figure 1. Fluid-wall interaction energy for the point-charge models of water in carbon slit pores. Results are shown for pore widths, H, of 0.6, 0.65, 0.8, 0.88, 1.0, 1.6, and 2.0 nm. The outermost curve corresponds to the widest pore, and the innermost curve, to the narrowest pore. z ) 0 is the center of the pore Table 1. Potental Parameters Used in This Work model
σff, nm
ff/k, K
rsw, nm
σsw, nm
sw/k, rOH, K nm
qO, e
q H, e
SPC 0.3166 78.2 0.1 -0.82 +0.41 SPC/E 0.3166 78.2 0.1 -0.8476 +0.4238 LJ4SQW 0.306 90.0 0.12852 0.0612 3800
in the z direction, between the centers of the surface carbon layers of the walls. We have studied the adsorption behavior of water in slit pores with several pore widths, specifically, 0.6, 0.65, 0.8, 0.88, 1.0, 1.6, and 2.0 nm. The fluid-wall interaction potentials for different pore widths are shown in Figure 1. This plot, which is similar to one given by Striolo et al.,24 shows the solid-fluid potential as a function of the z coordinate. For larger pore widths, the potential has a minimum near each pore surface. For the narrowest pores, these two minima merge into a single minimum. In the case of the pore width of 0.65 nm, a molecule at the center of the pore exhibits a very strong attraction with both of the walls. Striolo et al.24 have noted that this strong attraction can partially compensate for the loss of hydrogen bonds on confinement and help stabilize high-density states of water. The values of all of the potential parameters used in this work are given in Table 1. C. Monte Carlo Simulations. To study the adsorption behavior of water in carbon slit pores, we have used the GCMC simulation technique.44 For the vapor-liquid equilibrium for water in carbon slit pores as well as in bulk systems, the GEMC method29,35,45 was used. An orientational bias technique46 was used in both the GCMC and GEMC simulations to improve the sampling of the molecular orientations. For the calculation of the adsorption isotherms, we started from an empty slit pore for each pore width and then performed a series of simulations at successively increasing values of the activity, λ ) eµ/kT. For the desorption isotherm, we started from the final configurations from simulations at the highest activity on the adsorption branch and then performed a series of simulations at successively decreasing values of the activity. For (44) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, 1987. (45) Panagiotopoulos, A. Z. Mol. Phys. 1987, 62, 701. (46) Frenkel, D.; Smit, B. Understanding Molecular Simulations: from Algorithms to Applications; Academic Press: San Diego, 1996.
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Table 2. Saturation Activities and Densities for the SPC, SPC/E, and LJ4SQW Models of Water at 298.15 K Calculated in Our GEMC Simulations model
λ0aσ3
Fvapσ3
Fliqσ3
LJ4SQW SPC/E SPC
1.7(2) × 10-5 5.9(3) × 10-6 2.5(1) × 10-5
1.7(2) × 10-5 5.9(3) × 10-6 2.4(1) × 10-5
0.963 1.073 1.047
a
λ0 ) eβµ0conf.
both branches, each subsequent simulation was started from the final configuration of the previous run. The run lengths depended on the model and state considered. For low-density states of the systems, there are very few molecules present, and to obtain good statistics, we used run lengths of 2 × 109 configurations. For denser states of the SPC and SPC/E models, we used run lengths of 4 × 107 to 6 × 107 configurations. For denser states of the LJ4SQW model, we used run lengths of 4 × 108 to 2 × 109 configurations. The LJ4SQW potential takes much less computation time to evaluate than the point-charge potentials, but the singular nature and strength of the square-well association interaction makes it more difficult to sample configuration space efficiently so that longer runs are required. In all cases, half of the configurations were used to relax the state of the system. A configuration consists of an attempt to make a translation, rotation, creation, or destruction of a molecule. For each configuration, these moves were chosen with equal probability. In the case of the GEMC simulations, the total volume and number of molecules were chosen so that after equilibration the volume of the liquid phase would be larger than required for the given potential truncation distance and the number of molecules in the gas phase would be 50-100. To satisfy the above conditions, the total number of molecules used was 1125 for the bulk GEMC simulations and in the range of 208-576 for the GEMC simulations in the pores depending on the pore width. Simulations were run for 8 × 107 to 2 × 108 configurations for the point-charge models and for 2 × 109 to 5 × 109 configurations for the LJ4SQW model, again with half of the configurations used for equilibration. For the GEMC simulations, a configuration consists of an attempt to make a translation, rotation, or transfer of a molecule between phases or a change in the volume of the subsystems. The relative probabilities for attempting these moves were chosen to optimize the rate of equilibration. The Widom test particle method46,47 was used to obtain the equilibrium activity for each phase. For the case of water confined in slit pores, the water desorption isotherms were also used to locate the equilibrium activities by matching the liquid density from the GEMC simulation with that on the desorption isotherm. Very good agreement was obtained between these estimates. The activities at bulk vapor-liquid equilibrium for the models we used are summarized in Table 2. Our estimates of the bulk coexistence properties are in very good agreement with earlier estimates.43 III. Results and Discussion The adsorption/desorption isotherms for T ) 298.15 K calculated in this work are given in Figures 2-6. In each case, the amount adsorbed is expressed as F* ) Nσff3/V, where N is the number of molecules adsorbed in the pore, σ is the diameter of the adsorbate, and V ) Lx × Ly × H is the volume of the pore. This is plotted versus the relative activity, λ/λ0. The relative activity is approximately equal (47) Widom, B. J. Chem. Phys. 1963, 39, 2808.
Figure 2. Adsorption/desorption isotherms at 298.15 K for the LJ4SQW model of water adsorption in model carbon slit pores of different widths: H ) (a) 0.6, (b) 0.65, and (c) 0.8 nm. Filled symbols denote adsorption, and open symbols denote desorption. Lines are drawn as a guide to the eye.
to the relative pressure, P/P0, because of the small nonideality of water vapor at this temperature. We see that in each case the isotherms exhibit hysteresis between the adsorption and desorption branches. For the condensation behavior, we find overall consistency between the qualitative behaviors calculated for LJ4SQW, SPC/E, and SPC models, especially for the SPC and LJ4SQW models. Water condenses in the wider pores (H > 1 nm) at λ > λ0, consistent with the experiments on graphitized carbon black.4 However, for narrower pores there may also be condensation for λ < λ0. This can be understood from the fluid-wall interaction potential shown in Figure 1. In the narrower pores, the water molecules occupy one or two layers in the slit and interact strongly with both pore walls. This interaction with both walls stabilizes the adsorbed water even though the environment for hydrogen bonding is unfavorable relative to the bulk liquid state as suggested by Striolo et al.24 Such behavior is seen in the isotherms for pore widths of 0.65, 0.8, and 0.88 nm for the LJ4SQW model, for a pore width of 0.65 nm in the case of the SPC/E model, and for pore widths of 0.65 and 0.8 nm for the SPC model. It is notable that for the pore of width 0.88 nm for all models the liquid phase is more compressible as shown in Figures 3a, 5a, and 6c. For this pore width, the water molecules form two dense layers at higher relative activities, but at lower relative activities, the molecules form two less compact layers that facilitate hydrogen bonding. The results for the LJ4SQW (Figure 3a) indicate additional hysteresis in this region suggesting the possibility of an order-disorder transition for that model, although we have not investigated this issue further. Another feature of the LJ4SQW model results is that for wider pores (Figure 3) desorption from the pores tends to happen at lower relative pressures than for the SPC and SPC/E models. We believe that this is a reflection of the strength of the hydrogen bond network for dense states of this model and the impact that this has on the relaxation processes in the model. Similar behavior was found by McGrother and Gubbins48 in their study of LJ4SQW model water adsorption in slit pores. (48) McGrother, S. C.; Gubbins, K. E. Mol. Phys. 1999, 97, 955.
Does Water Condense in Carbon Pores?
Figure 3. Adsorption/desorption isotherms at 298.15 K for the LJ4SQW model of water adsorption in model carbon slit pores of different widths: H ) (a) 0.88, (b) 1.0, (c) 1.6, and (d) 2.0 nm. Filled symbols denote adsorption, and open symbols denote desorption. Lines are drawn as a guide to the eye.
Figure 4. Adsorption/desorption isotherms at 298.15 K for the SPC/E model of water adsorption in model carbon slit pores of different widths: H ) (a) 0.6, (b) 0.65, and (c) 0.8 nm. Filled symbols denote adsorption, and open symbols denote desorption. Lines are drawn as a guide to the eye.
Our results for the SPC/E model indicate that condensation occurs for λ > λ0 in most cases. In this respect, our results differ from earlier work.24-28 That difference is a result of our using a reliable value of λ0 from GEMC simulations. What is more curious perhaps is the large difference between our results for the SPC/E and SPC models. A clue to understanding this difference is the fact that the saturation activity and density for the SPC/E model are very much lower than those of the other two models. Low values of vapor pressure and vapor density for the SPC/E model are well documented in the literature.43 The very low density of vapor states of the SPC/E model should make it more difficult to nucleate the liquid phase, thus extending vapor-phase metastability in the GCMC simulations.
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Figure 5. Adsorption/desorption isotherms at 298.15 K for the SPC/E model of water adsorption in model carbon slit pores of different widths: H ) (a) 0.88, (b) 1.0, (c) 1.6, and (d) 2.0 nm. Filled symbols denote adsorption, and open symbols denote desorption. Lines are drawn as a guide to the eye.
So far, we have presented results for adsorption/ desorption isotherms calculated in GCMC simulations, and significant parts of these isotherms in the hysteresis region represent metastable rather than equilibrium states of the system. The persistence of such states arises from the fact that transitions between states of very different density are rare events in ordinary GCMC simulations using the Metropolis sampling method. Sarkisov and Monson49 have argued that this feature of the GCMC method can correctly capture the hysteresis encountered in experimental studies, especially if realistic model pore structures are considered. Subsequent work on Vycor glass50 and other disordered porous materials51 illustrates the utility of this perspective. Of course, the slit pore is not an especially realistic model of any actual porous material, and calculations with periodic boundaries do not address the effect of the external surface on the hysteresis, especially on desorption.52,53 Nevertheless, it remains of interest to establish the effect of confinement in well-defined pore geometries upon the properties of water. Of course, we might still ask whether the conclusions about condensation in pores that we have drawn would be the same if we were to determine the true equilibrium states of the system. With this in mind, we have used the GEMC method to locate the vapor-liquid coexistence conditions for the SPC and SPC/E models in the slit pores. Once this is done, we can replot the isotherms with the metastable states removed and with a tie line connecting the confined vapor and liquid states in equilibrium. This is shown in Figure 7 for the SPC model and in Figures 8 and 9 for the SPC/E model. Two features of these results are particularly striking. The first is the overall similarity between the results for the SPC and SPC/E models when presented in this way. Evidently, the equilibrium states (49) Sarkisov, L.; Monson, P. A. Langmuir 2000, 16, 9857. (50) Woo, H.-J.; Monson, P. A. Phys. Rev. E 2003, 67, 041207. (51) Kierlik, E.; Monson, P. A.; Rosinberg, M. L.; Sarkisov, L.; Tarjus, G. Phys. Rev. Lett. 2001, 87, 055701. (52) Rosinberg, M. L.; Kierlik, E.; Tarjus, G. Europhys. Lett. 2003, 62, 377. (53) Woo, H. J.; Porcheron, F.; Monson, P. A. Langmuir 2004, 20, 4743.
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Figure 6. Adsorption/desorption isotherms at 298.15 K for the SPC model of water adsorption in model carbon slit pores of different widths: H ) (a) 0.65, (b) 0.8, (c) 0.88, and (d) 2.0 nm. Filled symbols denote adsorption, and open symbols denote desorption. Lines are drawn as a guide to the eye.
Figure 7. Equilibrium isotherms at 298.15 K for the SPC model of water in model carbon slit pores of different widths: H ) 0.65 nm (O), 0.8 nm (0), 0.88 nm ()), and 2.0 nm (4). The vertical solid lines show the tie line between the liquid and vapor states in the pore. The dashed lines are drawn as a guide to the eye. Notice that in each case the vapor branch of the isotherms corresponds to a density close to zero on the scale of the plot.
of the two models are quite similar once an allowance for the difference in the bulk saturation activities (or vapor pressures) is taken into account. However, the difference in the hysteresis noted above remains striking. The second feature is that the vapor-liquid transition lies at λ < λ0 in all but one case considered, H ) 0.6 nm for the SPC/E model. The condensed state is thus an equilibrium state for these systems for λ < λ0. Now we have two answers to the question posed in our title. On the basis of the GCMC hysteresis loops, we conclude that for the widest and narrowest pores condensation in our model of water in a carbon slit pore does not occur until λ > λ0. However, phase-equilibrium calculations for the SPC and SPC/E models indicate that the liquid state becomes thermodynamically stable for values of λ < λ0 for all but the smallest pore size. Which of these results is most relevant to the behavior of real water in real porous carbons? It is evident from the
Liu and Monson
Figure 8. Equilibrium isotherms at 298.15 K for the SPC/E model of water in model carbon slit pores of different widths: H ) 0.65 nm (O), 0.8 nm (0); 0.88 nm ()), and 2.0 nm (4). The vertical solid lines show the tie line between the liquid and vapor states in the pore. The dashed lines are drawn as a guide to the eye. Notice that in each case the vapor branch of the isotherms corresponds to a density close to zero on the scale of the plot.
Figure 9. Equilibrium isotherms at 298.15 K for the SPC/E model of water in model carbon slit pores of different widths: H ) 0.6 nm (O), 1.0 nm (0), and 1.6 nm ()). The vertical solid lines show the tie line between the liquid and vapor states in the pore. The dashed lines are drawn as a guide to the eye. Notice that in each case the vapor branch of the isotherms corresponds to a density close to zero on the scale of the plot.
presence of hysteresis in most experimental results for water adsorption porous carbons at 298 K that a true vapor-liquid equilibrium is not seen in these systems. This would suggest that the results based on the GCMC simulations showing condensation from metastable vapor in pores are the most relevant. IV. Summary and Conclusions In this article, we have presented a Monte Carlo simulation study of three models of water (LJ4SQW, SPC/ E, and SPC) confined in carbon slit pores. Our goal has been to ascertain the extent to which water might condense in carbon pores for P < P0 in the absence of active sites on the pore walls. We have emphasized the importance of a good estimate of the bulk saturation conditions for the model, and we have determined these using GEMC simulations. We have calculated adsorption and desorption isotherms using GCMC simulations and have also determined vapor-liquid equilibrium in the pores using GEMC simulations.
Does Water Condense in Carbon Pores?
The GCMC simulations present a picture in which for the widest pores we have behavior similar to that seen experimentally for graphitized carbon black4 with condensation occurring for P > P0. For a range of narrower pores, the strong solid-fluid attractions can lead to pore condensation for P < P0 as noted by Striolo et al.24 The phase-equilibrium calculations, however, point to a stable liquid phase for P < P0 for all but the very narrowest pore sizes considered. We have argued that the results based on the GCMC simulations showing condensation from metastable vapor in the pores are probably the most relevant because in adsorption/desorption experiments on porous carbons the occurrence of hysteresis indicates that true equilibrium is not observed. We believe that resolving the question posed in this work is an important issue in developing a more complete understanding of water adsorption in porous carbons.
Langmuir, Vol. 21, No. 22, 2005 10225
Although we have studied three models of water and several pore widths, our results are far from comprehensive. For example, other temperatures could be considered as well as variations in the solid-fluid potential, including the possibility of a more sophisticated treatment of the water-carbon interaction. A similar analysis for cylindrical pores would also be worthwhile. In addition to modeling studies such as the present one, we hope that it will soon be possible to study water adsorption experimentally in porous carbons that are essentially free of active sites. Acknowledgment. This work was supported by a grant from the U.S. Army Research Office (grant no. DAAD19-02-1-0384). LA0508902
