J. Phys. Chem. C 2007, 111, 5735-5742
5735
Simulation Study of Water Adsorption on Carbon Black: The Effect of Graphite Water Interaction Strength G. R. Birkett and D. D. Do* Department of Chemical Engineering, UniVersity of Queensland, St Lucia, QLD 4072, Australia ReceiVed: December 10, 2006; In Final Form: January 25, 2007
The adsorption of water on carbon black has been calculated on several model graphitized carbon blacks using Monte Carlo simulation. The surface is modeled using different interaction strengths for a Steele type potential and the placement of various functional groups on the surface. The results for the various surface configurations are compared with the few experimental results available in the literature. Traditionally used parameters for the Steele potential provide isotherms with no similarity to those seen in experiment. Increased interaction well depths with the surface lead to more realistic isotherms but still require strongly attractive functional groups for qualitative agreement. The well depth used to achieve this falls within the realm of interaction strengths proposed in the literature by various methods. Full agreement with experiment isotherms is not achieved apparently because of a lack of large clusters formed in the simulations.
2. Potential Models
1. Introduction Molecular simulation has become the preferred theoretical method for the study of adsorption. With a sufficiently accurate potential model for adsorbate-adsorbate interactions and adsorbate-adsorbent interactions, all adsorption properties can be calculated. Potential models need to not only be accurate but also computationally efficient such that simulations of a reasonable number of particles can be computed within a reasonable time frame. For carbon adsorbents, the adsorption behavior is generally dominated by the dispersion force between an adsorbate molecule and the carbon surface or pore. This is certainly true of adsorbates such as argon, nitrogen, and methane where most adsorption behavior can be accurately reproduced with Lennard-Jones (LJ) type potentials for both the adsorbate and the carbon surface. Where the carbon adsorbent is modeled as a flat surface or slit pore, the preference is to use an estimate of the sum of interaction of the adsorbate with the semi-infinite graphite surface commonly referred to as the Steele1 potential. This potential has been used in a range of molecular simulation studies of water in carbon slit pores2-7 without consideration of the difference between the interaction of a polar molecule with a graphite surface compared with a nonpolar molecule for which the Steele potential is well suited. The nature of interactions with a surface is hard to elicit from experiments on porous materials and simulations dealing with pores because of the myriad of factors which affect the adsorption including functional group concentration and topology,4 finite extent of pores,7 and pore connectivity.8,9 To this end, the comparably simple system of adsorption of water on carbon black seems more suitable to separate the various factors which affect the adsorption on a carbon surface. This study presents the effect of water-carbon interaction strength on the adsorption of water on a model carbon black and compares with some of the limited experimental data available in the literature.
2.1. Fluid Potential Models. Two rigid polyatomic models have been used to model water in this study, the SPCE10 model and the TIP4P11 model. These are what may now be considered traditional potential models of water with a single LJ site located at the center of the oxygen atom and three fixed point charges representing the charge distribution of the molecule. Two positive charges (q+) are located along the oxygen hydrogen bond, at a distance ROH, and a single negative charge (q-) is located along the bisector of the oxygen-hydrogen bonds, at distance ROM. The parameters of these two models are given in Table 1. The vapor-liquid equilibrium properties of the two models have been calculated using GEMC.12,13 The GEMC simulations were performed without long-range corrections to more closely mimic the GCMC simulations which were also performed without long-range corrections. The use of long-range corrections in the GEMC was also tested, and it was found to make a minimal difference to the vapor pressure of the models. The properties of the two models from GEMC are given in Table 2. The saturated liquid densities of the models are in good agreement with experiment because of this being a major concern in the parametrization of these potentials. The vapor pressures are in poor agreement, with the SPC/E model giving a much lower vapor pressure and the TIP4P model giving a much greater vapor pressure. However, the large difference in the vapor pressure of the two models serves the purpose of revealing the effect this has on the adsorption isotherms. 2.2. Surface Model. The simulation cell is bound in the z-direction by the walls of a slit pore. Only one of the walls of the pore has an attractive interaction with the fluid molecules. This pore wall interacts with a fluid molecule according to the Steele 10-4-3 potential1 given by
[( ) ( )
uisurf ) 2πFsos(σos)2 ∆
2 σos 5 zi
10
-
* To whom correspondence should be addressed. Phone: +61 7 3365 4154. Fax: +61 7 3365 2789. E-mail:
[email protected].
10.1021/jp068479q CCC: $37.00 © 2007 American Chemical Society Published on Web 03/27/2007
σos 4 zi
(
)]
σos4
3∆(zi + 0.61∆)3
(1)
5736 J. Phys. Chem. C, Vol. 111, No. 15, 2007
Birkett and Do
TABLE 1: Water Model Parameters parameter
SPCE
TIP4P
OO/kb (K) σOO (nm) ROH (nm) ROM (nm) ∠HOH (deg) q- (e) q+ (e)
78.23 0.3166 0.1 0.0 109.47 0.8476 0.4238
78.02 0.3154 0.09572 0.015 104.52 1.04 0.52
TABLE 2: Saturation Properties of SPCE and TIP4P Water Models and Experimental Values at 300 Ka parameter VAP
P (kPa) FV (mol/m3) FL (kmol/ m3) ∆HV (kJ/ mol) a
SPCE
TIP4P
exp
0.938 0.373 56.43 50.02
4.76 1.92 55.55 44.12
3.54 1.42 55.3 43.9
Subscripts denote uncertainty in the final digit (e.g., 0.93 ( 0.08).
where uisurf is the interaction between a water molecule, i, and the carbon surface, Fs is the graphite’s carbon density (114 nm-3), ∆ is the separation distance between graphite layers (0.3354 nm), zi is the separation of the water’s LJ site and the surface, and os and σos are the LJ well depth and collision diameter between the water’s LJ site and the surface calculated using the Lorentz-Berthelot mixing rule.14 The carbon’s LJ collision diameter, σss, was always set as being equal to 0.34 nm but the LJ well depth is varied from the standard value of ss/kB ) 28 K up to a value of 128 K. Using the LorentzBerthelot mixing rule, this corresponds to a range of interaction well depths from os/kB ) 46.8-100 K. So, the interaction energy is increased up to a value almost double that traditionally used in this type of study. The basis of using ss/kB ) 28 K is a result of a study by Crowell15 matching the interaction energy of basal planes of graphite to the compressibility of graphite in the direction perpendicular to the basal plane. This gives a minimum in the interaction energy between water and graphite of -6.82 kJ/mol. Now, the interaction of water with the graphite surface is expected to differ from this because of the dipole of water producing induction effects on the surface and interacting with the quadrupole of carbon atoms in the graphene layers. How much the dipole changes the interaction of a water molecule with a graphite surface is open to debate. Methods for quantifying this range vary considerably in their complexity and their estimation of the interaction between a water monomer and the graphite surface. A summary of several estimations of the minimum in the interaction of a single water molecule with a graphite surface is presented in Table 3. The selection of estimations presented in Table 3 shows the large variation in the estimate between different methods and research groups.
The methods of Kiselev16 and Zhao and Johnson22 are functions of distance from the surface only and use an angle-averaged approach to the dipole-induced dipole (both) and dipolequadrupole (Zhao and Johnson only). This makes these methods easy and fast to use in simulations but are still reliant upon several assumptions, including the fixed polarizability and quadrupole of the graphite sheet. Ab initio methods should provide a better estimate of the interaction between water molecule and a graphite sheet. Clearly, this is impossible to directly use in a Monte Carlo simulation and can provide only an indication of the accuracy of empirical potentials used. Also, there is as yet no agreement between ab initio studies with the majority providing an estimate within several kJ/mol of each other but studies like Feller and Jordan21 provide estimates vastly different from the rest. Seemingly, one of the major issues with ab initio calculations is that there is no clear consensus as to whether a graphite sheet’s induction effects become greater or smaller as the sheet becomes larger. All this indicates the difficulty in choosing a water-graphite potential model for molecular simulation. Without any clear benefit of one model over another, it seems as reasonable to use an effective Steele type potential as any other. The range of water-graphite interaction potentials used in this study give minimum interaction energies from -6.82 kJ/mol to -14.58 kJ/mol which is well within the range presented in Table 3. The opposing wall has no attractive term and has only an effectively infinite repulsion for molecules that cross the pore wall. The simulation cell is repeated periodically in the x and y directions to approximate an infinite surface. The model pore has a width of 3.0 nm and a length in the simulation cell of 7.5 nm. A pore width of 3.0 nm allows a good approximation of carbon black with the opposite hard wall having no observable effect on the adsorption at the Steele potential surface until many layers are formed at pressures very close to the vapor pressure of the fluid. Since all adsorption behavior discussed occurs at submonolayer coverage, the noninteracting wall has no affect on the adsorption. 2.3. Functional Groups. Several types of functional groups are used in the simulations. For the majority of simulations, the functional groups used are fixed water molecules. The water molecule is fixed parallel to the carbon surface at a distance of 0.32 nm from the surface. This distance was chosen because it is where the energy minimum exists in the surface’s Steele potential. Such an arrangement is an idealized representation of the heterogeneity of the surface. It allows for very good bonding with adsorbing water molecules and should be a good way of promoting adsorption without resorting to unrealistically attractive functional centers. If adsorption cannot be promoted
TABLE 3: Different Interaction Potential Minimums between Water and Graphite from the Literature author Kiselev16 Zhao and Johnson17 Werder et al.18 Liu and Monson9 Lin et al.19 Sudiarta and Geldart20 Feller and Jordan21
method
value (kJ/mol)
sum of dispersion and dipole-induction interactions. sum of dispersion, dipole-induction, and dipole quadrupole interactions with a water dipole of 1.85 D matching experimental water-graphite contact angle of 82° using molecular dynamics and LJ interactions only matching activated carbon adsorption to GCMC simulations using a platelet model of activated carbon. density functional tight binding calculations of water on a single sheet of graphite modeled as fused benzene rings ab initio calculations using Møller-Plesset perturbation theory applied to a single water molecule and six fused benzene rings ab initio calculations using Møller-Plesset perturbation theory applied to a water molecule and 16 fused benzene rings
-15.5 -10.98 -6.33 -9.66 -12.14 -10.26 -24.3
Simulation of Water Adsorption on Carbon Black
J. Phys. Chem. C, Vol. 111, No. 15, 2007 5737
Figure 1. Side projection of functional groups used in simulations.
TABLE 4: Interaction Parameters of Functional Groups group
site
carbonyl
Ca O Ca O H Ca C O O H
hydroxyl carboxyl
a
σ(nm)
/kb (K)
0.296
105.8
0.307
78.2
0.375 0.296 0.3
52.0 105.7 85.6
q (e) 0.5 -0.5 0.2 -0.64 0.44 0.08 0.55 -0.5 -0.58 0.45
Carbon located in plane of graphene sheet.
TABLE 5: Carboxyl and Hydroxyl Site Separations and Angles group
bond
R (nm)
carboxyl
Ca-C C-OH CdO O-H Ca-O O-H
0.152 0.1214 0.1364 0.097 0.1364 0.096
hydroxyl a
