J. Phys. Chem. C 2009, 113, 12293–12300
12293
Adsorption of Low-Molecular-Weight Molecules on a Dry Clay Surface: An Ab Initio Study Pascal Clausen,†,‡ Wanda Andreoni,*,§ Alessandro Curioni,§ Eric Hughes,‡ and Christopher J. G. Plummer† Laboratoire de Technologie des Composites et Polyme`res (LTC), Ecole Polytechnique Fe´de´rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland, Nestle´ Research Center, Vers-Chez-Les-Blanc, 1000 Lausanne 26, Switzerland, and Zurich Research Laboratory, IBM Research GmbH, 8803 Ru¨schlikon, Switzerland ReceiVed: December 24, 2008; ReVised Manuscript ReceiVed: May 3, 2009
We present a study of the adsorption of single molecules of volatiles, such as water, ethanol, ethyl acetate, pyridine, toluene, and n-octane, on the dry surface of a smectite clay using a series of calculations based on density functional theory. Our clay model contains both tetrahedral and octahedral substitutions, and sodium as the counterion. After establishing the accuracy of our calculations for predicting the structural features of known clays, we determine the structural features of our model clay and then characterize the changes induced by molecular adsorption and the dependence of binding on the adsorption site. In all cases, binding energies are higher in configurations bound to cations located above rings with tetrahedral substitution than for those above rings with octahedral substitutions. For molecules containing an electronegative atom, binding energies inversely correlate well with their ionization potential. Our results allow an interpretation of the trend of measured vaporization rates at low coverage and reveal that they correlate inversely with the binding energies of the molecules. 1. Introduction Clay minerals are among the most common components of the Earth’s crust, and natural, modified, or artificial clays are found in a very wide range of applications, ranging from construction materials to catalysts to waste disposal to drug and agrochemical delivery agents to cat litter.1 The reason for this is their special structural and surface properties, and the large variety of chemical compositions (see, e.g., refs 2 and 3). Intense investigation has been carried out for decades with the aim of understanding how the physical and chemical behavior of these materials depends on their specific composition and structure and how it is influenced by the presence of water, guest atoms or molecules, and the environment. In this effort, studies based on computational methods have been playing an increasingly significant role, by providing otherwise inaccessible information about how water and guest molecules likely distribute themselves in the interlayer regions and insights into the basic mechanisms that lead to swelling or govern the chemical reactivity. (We refer to a recent comprehensive review4 of the most commonly employed approaches.) In particular, clays, and especially phyllosilicates, have the ability to adsorb a large variety of volatiles in the interlayer regions as well as on external and internal surfaces. This explains, for example, the use of clay-based materials as pet litter trays or efficient adsorbents in the effort to remediate soils and groundwater contaminated with petroleum hydrocarbons or as carriers for insecticides.1,5 As a consequence, there is widespread interest in the retention and evolution of volatiles in/from clays also with regard to impact on the environment (see, e.g., refs 6-16). Little is known, however, on specific mechanisms that characterize volatile-clay interactions. Recently, desorption * Corresponding author. † Ecole Polytechnique Fe´de´rale de Lausanne. ‡ Nestle´ Research Center. § IBM Research GmbH.
isotherms were measured for water, ethanol, ethyl acetate, and toluene from a sodium smectite clay,17 which revealed an unexpected trend in the volatile activities in the low-coverage regime. The order of the vaporization rates was in full contrast with the one measured in the high-coverage regime, in which they were found to be consistent with the relative values of the enthalpies of vaporization of the corresponding bulk liquids. These results have triggered the present computational study. While classical molecular dynamics and Montecarlo simulations are the methods of choice when studying processes such as the diffusion of water and water-solutions (see, e.g., refs 18-21) in clay materials, the study of molecular adsorption at clay surfaces requires a quantum-chemical approach. Surprisingly, there is still a paucity of such calculations in the literature. They are based on methods of various degrees of sophistication, ranging from semiempirical to Hartree-Fock to various implementations of density functional theory (DFT)22 but generally use oversimplified cluster models for the surface (see, e.g., refs 23-26). Adsorption of proteins on clay minerals, on the other hand, has been investigated using a more realistic supercell representation of the clay surface but had to rely on classical force-fields.27 Only rarely have (ultrashort) ab initio (DFT) molecular dynamics simulations been used, especially to investigate clay interaction with either water28,29 or small peptides30 or pesticides such as 2,4-dichlotophenoxyacetic acid.31 In the present paper, we investigate the binding of single molecules of volatiles, namely, water, ethanol, ethyl acetate, pyridine, toluene, and n-octane, to the dry surface a smectite clay model. The choice of the systems was determined by the recent experimental studies mentioned above,17 but the significance of our investigation is expected to go beyond it because of the widespread interest in the volatile-clay interaction here documented and the surprisingly missing accurate characterization of adsorption configurations and binding energies also for these simple but prototypical chemical species.
10.1021/jp811383y CCC: $40.75 2009 American Chemical Society Published on Web 06/22/2009
12294
J. Phys. Chem. C, Vol. 113, No. 28, 2009
Clausen et al.
Figure 1. Structure of pyrophillite. (a) Side and (b,c) top views of the hexagonal ring in the tetrahedral layer, showing basal oxygen (Ob), silicon (Si), apical oxygen (Oa), aluminum (Al), hydroxyl oxygen (Oh), and hydrogen atoms. Oxygen, hydrogen, silicon, and aluminum atoms are represented by red, white, orange, and blue spheres, respectively.
The atomistic model we consider here to study the adsorption is a slab, generated from a periodically repeated supercell of relatively large size (164 atoms). This choice avoids the problems inherent in a cluster approach and allows accounting for the structural relaxation induced by molecular adsorption. We apply DFT22 in the gradient-corrected approximation of the exchange-correlation functional in the pseudopotential-plane wave scheme. After recalling the basic structural features of a smectite clay in Section 2, the method is described in detail in Section 3, accompanied by a number of tests in Appendices A, B and C. The results are presented and discussed in Section 4, and conclusions are drawn in Section 5. 2. Smectite Clays: Basic Structural Properties Smectite clay minerals belong to the family of phyllosilicates. They are often referred to as 2:1 phyllosilcates, because their structure consists of bidimensional layers, in which a central octahedral sheet (Os) of alumina or magnesia is sandwiched between two silica tetrahedral sheets (Ts); in this way, apical oxygens (Oa) are shared by octahedral and tetrahedral sheets. An example, pyrophillite, is shown in Figure 1. Smectite clay minerals are ionic because isomorphic substitution is always present within the sheets with ions of lower valency (e.g., Si4+ replaced by Al3+ or Fe3+, Al3+ by Mg2+ or Fe2+, Mg2+ by Li+), thus generating a net negative charge. This charge is in turn counterbalanced by alkali or alkaline-earth guest ions located in the interlayer galleries. Therefore, smectites can be found with a large variety of properties, depending on the nature and location of both the ionic substitutions and the counterions. 3. Method Our calculations are based on DFT22 as implemented in the plane-wave pseudopotential scheme, and use the Carr-Parrinello Molecular Dynamics (CPMD)32 software. For the exchangecorrelation functional, the generalized gradient approximation (GGA) was used and, in particular, the Perdew-Burke-Ernzer-
TABLE 1: Chemical Formulas and Charges of the Clay Minerals smectite clay
chemical formula
charge per formula unit
pyrophillite Kunipia-F our model
Si4O10(OH)2Al2 (Si3.9Al0.1)O10(OH)2Mg0.34Al1.53Fe0.11 (Si3.875Al0.125)O10(OH)2Mg0.375Al1.625
0 -0.5 -0.5
hof33 (PBE) parametrization, which has been demonstrated to describe rather accurately heterogeneous systems, and also the physical properties of water34 and other hydrogen-bonded systems.35 Spin-polarization was accounted for in all open-shell systems. Atomic norm-conserving pseudopotentials were derived with the Martins-Trouiller (MT) procedure36 and applied using the Kleinman-Bylander scheme37 to treat the nonlocal terms. A relevant test is reported in Appendix B. In all calculations discussed here, the clay (either pyrophillite or its derivative) was represented by a periodically repeated slab supercell, and an appropriate distance between the slabs was chosen to minimize artifacts due to their interaction. For the electron wavefunctions, only the k ) 0 Bloch functions were considered and expanded in plane waves up to a certain energy cutoff Ec. The lattice parameters were fixed, whereas all internal atomic coordinates were optimized within 10-4 a.u. for the largest off-diagonal component of the energy gradient. To determine the appropriate size of the supercell and Ec, the dependence of calculated structural features was studied on pyrophillite. These tests are reported in Appendix A, where comparison with experimental data and previous calculations is also made. In the absence of further experimental knowledge, we did not consider it wise to reoptimize the lattice parameters of the supercell after either substitution or adsorption. This could have introduced fictitious distortions caused by artificial long-range forces. 4. Results and Discussion A. Kunipia-F Clay Model. Our initial model for the clay was based on the chemical formula of a Kunipia-F montmo-
Adsorption of Volatiles on a Dry Clay Surface
J. Phys. Chem. C, Vol. 113, No. 28, 2009 12295
Figure 2. Our clay model with Na counterions, with the substitutional atoms explicitly indicated. (a) Side and (b) top views of all types of hexagonal rings are shown from A to F; A, B, and C refer to the T-layer; D, E, and F refer to the O-layer. (c-f) Detailed top view of the rings with a Na counterion. In the tetrahedral sheet, one of the Si atoms in the ring is substituted by Al (AlT); in the octahedral site, three Al atoms are substituted by Mg. Colors are as in Figure 1.
rillonite clay,38 namely the system investigated in ref 17 with all Fe atoms replaced by Al (Table 1). It was generated from the pyrophillite 221 supercell (Appendix A), with lattice parameters a ) 10.32 Å, b ) 17.932 Å, and c ) 25 Å, by substitutions of aluminum with magnesium in the octahedral sheet and of silicon with aluminum in the tetrahedral sheet. The replacing cations were distributed randomly under the only constraint that they were not located in neighboring positions. The chemical formula thus obtained is shown in Table 1. Note that the ratio of AlT:Mg is 1:3, so that an octahedral sheet is more negatively charged than a tetrahedral one. In the initial configuration, the sodium counterions were positioned taking into account the location of the basal oxygen atoms with higher negative Mulliken charges and according to homogeneity considerations. This has led to the model shown in Figure 2, in which no counterion is present on domains C and D (see Figure 2b). Detailed results of the optimization are given in Table 2A,B, where the structural characteristics are compared with those calculated in Appendix A for pyrophillite. As expected, the most noticeable change is the increase of the thickness of both the T and O sheets. Note that the corrugation ∆Z is calculated as the standard deviation about an average Ob plane, along the [110] crystallographic direction. B. Molecular Adsorption. The clay surface in Figure 2 offers a number of nonequivalent sites for the adsorption of single molecules. Starting from several initial configurations and
relaxing all atomic coordinates in the slab, we determine a set of adsorption geometries, which include the changes induced in the clay structure, and the pattern of binding energies. In particular, for each case, we obtain information on the thermodynamically most probable adsorption sites. Prior to this, we apply the same calculations to investigate the adsorption of a single sodium atom on a bare surface. Note also, from the chemical formula of the Kunipia-F clay, that about 1 in 30 surface silicon atoms is replaced by an aluminum atom. As a result, less than one-fifth of the surface hexagonal rings are affected by the aluminum replacement. This is the case for domains A and B. Therefore, domains E and F can be considered as better representatives of the clay surface. To simplify the notation, we will indicate also the corresponding sodium sites as A-F. a. Sodium Counterion Adsorption. We positioned one sodium atom in A, B, E and F, in the absence of the other cations, and relaxed all atomic positions. When the cation is in either A or B, its nearest environment contains one aluminum substitution, whereas E and F are above the magnesium substitutions in the octahedral sheet. Thus, the latter offer more favorable sites to the cation, resulting in an energy difference of about 15 kJ/mol. Minor additional differences can be detected in the optimized geometries also after adsorption, which contribute to differentiate A from B and E from F in the binding strength of the cation. The close environment of A differs from
12296
J. Phys. Chem. C, Vol. 113, No. 28, 2009
Clausen et al.
TABLE 2: Calculated Structural Features of Our Model Clay Compared with Those of Pyrophillite
TABLE 3: Na Adsorption: Binding Energies and Sodium to the Tetrahedral (T) Plane Distances
(A)a pyrophillite
position
B.E. (kJ/mol)
Na-T plane distance (Å)
A B E F
731.6 734.0 747.6 751.2
1.299 1.263 0.927 0.891
our model (Na counterions)
parameter
(App. A)
A
B
E
F
T.th. O.th. ∆Z Ψ d(Si-Ob) d(AlT-Ob) d(Si-Oa) d(AlT-Oa) d(AlO-Oa) d(Mg-Oa) d(AlO-Oh) d(Mg-Oh) d(Oh-H) d(Na-Tplane) d(Na-Ob)
2.171 2.143 0.261 56 1.625
2.260 2.177 0.292 56 1.639 1.755 1.649 1.745 1.949
2.241 2.213 0.161 57 1.647
2.231 2.232 0.125 57 1.648
TABLE 4: Single Water Molecule Adsorption
1.605
1.600
position
configuration
B. E. (kJ/mol)
Na-Ow (Å)
Hw-Ob (Å)
EL (kJ/mol)
1.932
2.269 2.166 0.180 56 1.636 1.761 1.630 1.745 1.960 1.939
1.948
0.964
0.973 1.295 2.322 2.946
0.971 1.287 2.335 2.945
1.937 2.154 1.984 2.180 0.972 0.924 2.393 2.755
A
1.896
1.969 2.137 1.951 2.188 0.973 0.923 2.406 2.737
a b c d a b c a b a b
54.3 52.7 51.2 46.2 60.2 52.0 48.6 45.6 44.7 44.7 44.3
2.301 2.269 2.293 2.259 2.266 2.275 2.299 2.284 2.303 2.281 2.298
2.123 2.495 2.444 2.006 1.900 3.351 2.422 3.419 2.474 3.099 2.532
5.9 3.2 4.1 5.7 7.4 2.5 6.0 3.0 5.1 2.8 4.2
1.644
∠(Ob-Si-Ob) ∠(Ob-AlT-Ob) ∠(Si-Ob-Si) ∠(AlT-Ob-Si) ∠(Ob-Si-Oa) ∠(Ob-AlT-Oa) ∠(AlO-Si-Oa) ∠(AlO-AlT-Oa) ∠(Oa-AlO-Oa) ∠(Oa-Mg-Oa) ∠(AlO-Oa-AlO) ∠(Mg-Oa-AlO) ∠(Oh-AlO-Oa) ∠(Oh-Mg-Oa) ∠(AlO-Oh-AlO) ∠(Mg-Oh-AlO) ∠(AlO-Oh-H) ∠(Mg-Oh-H)
A
B
E
F
109
105 102 125 138 124
103
103
129 138
131 136
113
113
124 128
126 125
92
104 102 127 138 124 131 112 112 125 129 122 130 91
102
99
99
94 92
93 91
94 91
91 91 97 94 88 85 97 93
90 94 96 96 87 86 96 91
103
99
99 92 108 97
90 104 100
109 124 128
121
E
our model (Na counterions)
(App. A)
130 142
B
F
(B)b pyrophillite
(A)a
111
112 111 125 128 122 130 91
110
(B)b position configuration Na-T plane(Å) A
B E F
a T.th. and O.th. are the thicknesses of the tetrahedral and octahedral sheets respectively, ∆Z is the corrugation of the basal oxygen atoms, and d(X-Y) is the average distance between X and Y atoms. Distances are in Å. Other symbols are as in Figure 2. b ∠XYZ is the average angle between X and Z centered in Y. Angles are in degrees. Symbols are as in part A.
that of B in the direction of the structural hydroxyl, namely, only in the former does the structural hydroxyl point in the direction of an Ob linked to the aluminum. Also E and F differ in the configuration of the Mg atoms around the hydroxyl group. Moreover, we notice an inverse relation between the binding energy of the adsorbate and its distance from the silicon plane (Table 3), which reflects the dominance of Coulomb interaction. b. One Water Molecule. Chemical intuition suggests that there are two dominant modes of adsorption of water on the surface, either through its nucleophilic oxygen bonded to a surface cation or via a hydrogen bond to one of the underlying surface oxygens, of which the former is expected to provide
a b c d a b c a b a b
1.583 [0.287] 1.524 [0.229] 1.558 [0.262] 1.536 [0.241] 1.568 [0.282] 1.498 [0.212] 1.626 [0.340] 1.166 [0.242] 1.240 [0.317] 1.136 [0.211] 1.185 [0.261]
Na-Ob (Å) 2.416 [0.094] 2.399 [0.078] 2.410 [0.088] 2.399 [0.077] 2.412 [0.077] 2.397 [0.062] 2.475 [0.140] 2.452 [0.046] 2.463 [0.057] 2.441 [0.048] 2.447 [0.054]
3.033 [0.088] 3.018 [0.072] 3.026 [0.080] 3.013 [0.067] 3.045 [0.100] 3.016 [0.071] 3.046 [0.100] 2.776 [0.040] 2.797 [0.060] 2.787 [0.032] 2.797 [0.043]
a Binding energies (B.E.), “deformation” energy EL, and sodium-to-water distances as well as closest water to basal oxygen Ob. b Sodium to T-plane and closest sodium to basal oxygen distances. Values in parentheses denote the change (increment) with respect to the geometry optimized in the absence of water.
a stronger interaction. For this reason, in most of the initial configurations of our search we positioned the molecule with oxygen close to a sodium ion; full structural relaxation was then allowed. Table 4A lists the binding energies of one water molecule above structures A, B, E, and F as well as the characteristics of several adsorption configurations that we have found in each one, which differ in the orientation of the molecule. Note, however, that energy differences of e4 kJ/mol (∼1 kcal/mol) are beyond the accuracy of the calculations. Table 4 quotes the structural characteristics of the adsorbent clay and, in particular, the changes induced by the adsorption. Several factors determine the strength of the binding. The main results can be summarized as follows: (i) The cations in A and B and their environment are stronger attraction centers than those in E and F. This can easily be understood as a consequence of the larger negative charge present in the octahedral layer. (ii) Ob atoms are active in the binding and help stabilize the water molecule via the formation of hydrogen bonds. This is especially true in the case of the B-a configuration, which is the most stable one. Here the molecule forms a relatively strong H-bond (1.9 Å) with an Ob bound to an AlT atom (Figure 3a).
Adsorption of Volatiles on a Dry Clay Surface
J. Phys. Chem. C, Vol. 113, No. 28, 2009 12297
Figure 3. Adsorption configurations of one water molecule. (a) Configuration B-a. (b) Configuration F-a. (c) Configuration F-b. Colors are as in Figure 1. The yellow dashed lines denote hydrogen bonds.
TABLE 5: Volatile Molecules Adsorption
(iii) In the E and F domains, the binding energy is independent of the orientation of the water molecule. For example, it does not change appreciably from F-a, where it is on top of the cation (Figure 3b), to F-b, where it forms a hydrogen bond with a basal oxygen atom (Figure 3c). Table 4B shows the main changes induced in the structure, which are confined to the closest neighborhood of sodium that moves away from the surface by a non-negligible distance (∼0.3 Å). The corresponding energy loss EL is never significant, and does not correlate with the binding energy. We also explored the potential energy surface of the C and D domains, where no counterion is present. By constraining the molecule to some fixed positions and letting the other positions relax, we were able to estimate binding energies of ∼10 to ∼20 kJ/mol. However, when full structural relaxation was allowed, the molecule moved away, converging in particular to either the B-a or the A-a configuration. Still, the estimate above provides one for the energy barriers to diffusion. We can conclude that at room temperature, a water molecule on this clay surface is easily trapped by a sodium ion in any position. c. Ethanol, Ethyl Acetate, Toluene, Pyridine, n-Octane. Calculations of the properties of the isolated molecules are reported in Appendix C. Here we considered adsorption in the A and F domains. The calculated characteristics are in Table 5A. In the initial configurations, following chemical intuition, the molecules were given specific orientations that changed only slightly after optimization. In ethanol (Figure 4a), ethyl acetate (Figures 4b,c) and pyridine (Figure 4d), the lone-pairs at the electronegative elements (O or N) are pointed toward sodium. As a consequence, the aromatic ring of pyridine is almost perpendicular to the clay surface (Figure 4d) (Note that this geometry was also the result of an optimization starting with this ring parallel to the clay surface). In the case of toluene, the dominant interaction is between the cation and the π-electronic system of the molecule; consequently the aromatic ring is almost parallel to the clay surface (Figure 4e). n-Octane (Figure 4f) has axes parallel to the clay surface and perpendicular to either the A-B or the E-F direction. The differences in binding energies between ethanol, ethyl acetate, and pyridine correlate inversely with the ionization potentials of the molecules (see Table 5B), which can in turn be related to the nucleophilicity of the electronegative atom. Water is a special case because it also forms a hydrogen bond with a basal oxygen atom, which is stronger in A than in F (see Table 4A). In the case of ethyl acetate, the oxygen on the resonant bond is more nucleophilic than the one in the alkoxyl
(A) Binding Energies (B.E.), Distances between Sodium Cation and the Electronegative Element of the Volatile and between Sodium and the Silicon T-Plane B.E. volatile water ethanol ethyl acetate pyridine toluene n-octane
Na-O or Na-N
A (kJ/mol) F (kJ/mol) 54.3 53.9 59.5 72.0 34.7 15.5
44.7 47.9 51.6 63.5 24.6 9.2
Na-T plane
A (Å)
F (Å)
A (Å) F (Å)
2.301 2.283 2.212 2.366
2.281 2.274 2.220 2.394
1.580 1.555 1.579 1.520 1.619 1.462
1.135 1.153 1.233 1.179 1.320 0.980
(B) A and F domains: Binding energies (BE) compared with the ionization potentials (IP) of the moleculesa properties BE (kJ/mol) A F IP (eV) adiabatic vertical exp (ref 39) a
pyridine ethyl acetate ethanol 72.0 63.5 8.80 9.25 9.25
59.0 51.6 9.55 9.83 10.01
53.9 47.9 9.87 10.12 10.47
water 54.3 44.7 12.53 12.53 12.612
The latter are also compared with experiment.
group. Correspondingly, we calculated a much lower binding energy (23.2 kJ/mol) for the configuration in Figure 4c. The larger binding energy of ethyl acetate than of ethanol, on the other hand, can be explained by the presence of an excess electron on the carboxylate moiety. In line with the nature of the adsorption, the binding energy of toluene is on the order of the binding energy of a hydrogen bond. The much lower binding energy of n-octane is also consistent with the nature of its interaction with the substrate, which is dominated by the ioninduced dipole component. Note also that the binding energies (and the sodium to silicon plane distances) are systematically higher in A than in F, in analogy with the case of water. V. Conclusions In this paper, we have considered the low-coverage adsorption of several low-weight molecules on the surface of a smectite clay with sodium counterions. The case of water was studied more in detail given the paramount importance of the interaction of water with clay surfaces. This study will be continued in a subsequent paper. We find that, at room temperature, a water molecule can easily be trapped by any sodium ion on the surface (estimated energy barrier for diffusion is at least 10 kJ/mol), but that the strength of the binding depends on the specific location of the counterion, the net charge on the underlying
12298
J. Phys. Chem. C, Vol. 113, No. 28, 2009
Clausen et al.
Figure 4. Volatile molecules at the F site: (a) ethanol, (b) ethyl acetate (i), (c) ethyl acetate (ii), (d) pyridine, (e) toluene, (f) n-octane. The yellow dashed lines denote bonds between the electronegative atoms and the sodium cation (a-d), and the bond between the cation and the aromatic electron cloud of toluene (e).
sheet, and the possibility of forming hydrogen bonds with basal oxygen atoms. The latter play an important adjuvant stabilizing role for the adsorbate, which emerges clearly especially when water is compared with other molecules such as ethanol, ethyl acetate, toluene, and pyridine, whose binding to the clay surface is also dominated by the attractive interaction with the counterion but does not form hydrogen bonds. The difference in the binding energies of the molecules considered here can be well explained in terms of their chemical nature. These results allow us also to interpret very recent experiments reported in ref 17 where volatiles were ranked on the basis of their observed desorption trends from the smectite clay considered here. In the low-coverage regime, the order of the ranking was ethyl acetate, ethanol, water, and toluene. The calculations we have presented here reveal that this order is inversely related to that of the binding strength of the single molecules, especially when taking into account the fact that F-like domains are more
frequent than A-like ones and thus more representative of the system behavior. The present study was aimed to understand laboratory experiments made on a specific clay material with volatiles at low coverage. This is only a first step in the attempt to understand the interaction of volatiles with clay minerals and clay-based materials. To become useful for the understanding of the fate of volatiles when interacting with soil components, simulations will have to be able to include the effects of the chemical environment, including water, and of external physical conditions (temperature, light). Acknowledgment. This study was supported financially by the Nestle´ Research Center (NESTEC, Switzerland). P.C. acknowledges hospitality at the IBM Zurich Research Laboratory where all the calculations reported here were performed.
Adsorption of Volatiles on a Dry Clay Surface
J. Phys. Chem. C, Vol. 113, No. 28, 2009 12299
Appendix A: Tests on the Pyrophillite Structure Table A1 shows the convergence of the calculated values for structural features with the energy cutoff Ec used in the planewave expansion of the electronic wave functions. For this test calculation, we considered the unit cell of pyrophillite. This establishes 100 Ry as cutoff. Table A2 shows convergence of the same parameters as considered in Table A1 in terms of the size of the supercell, calculated with Ec ) 100 Ry. On this basis we selected the 211 supercell as a suitable model for our studies of molecular adsorption. Indeed, with this choice, the bondlength differences relative to experiment are within expected deviations, namely, analogous to those found between experimental data from different sources.40,41 TABLE A1: Calculated Average Structural Parameters of Pyrophillite for Increasing Eca
TABLE A2: Structural Characteristics of Pyrophillite Calculated Using Supercells of Progressively Larger Sizea Ts.th. Os.th. ∆Z Ψ d(Si-Ob) d(Si-Oa) d(Al-Oa) d(Al-Oh) d(Oh-H) ∠(Ob-Si-Ob) ∠(Si-Ob-Si) ∠(Ob-Si-Oa) (τ) ∠(Al-Si-Oa) ∠(Oa-Al-Oa) ∠(Al-Oa-Al) ∠(Oh-Al-Oa)
70
100
180
Ts.th. Os.th. ∆Z
2.147 2.163 0.320
2.144 2.157 0.316
2.143 2.158 0.320
Ψ
56
56
56
d(Si-Ob) d(Si-Oa) d(Al-Oa) d(Al-Oh) d(Oh-H)
1.643 1.643 1.947 1.889 0.972
1.640 1.642 1.941 1.887 0.966
1.639 1.641 1.941 1.888 0.966
TABLE A3
∠(Ob-Si-Ob) ∠(Si-Ob-Si)
110 127 138 108 124 128 92 101 96 92 103 123
111 128 139 108 124 128 92 101 96 92 103 123
111 128 139 108 124 128 92 101 96 92 103 123
a b c R β γ
∠(Ob-Si-Oa) (τ) ∠(Al-Si-Oa) ∠(Oa-Al-Oa) ∠(Al-Oa-Al) ∠(Oh-Al-Oa) ∠(Al-Oh-Al) ∠(Al-Oh-H) a
Calculations refer to a 111 cell. Ts.th. is the thickness of the tetrahedral sheet, Os.th. is the thickness of the octahedral sheet, ∆Z is calculated as the standard deviation around the average plane formed by basal oxygens along [110] and is an indication of their corrugation, Ψ, where cos(Ψ) ) Os.th./2(Al-O) is the octahedral flattening angle. d(A-B) is the average distance between atoms X and Y, ∠XYZ is the average angle between atoms X and Z, with vertex in Y. Lengths are in Å, angles are in degrees. ‘a’ and ‘b’ subscripts stand for the apical (or inner) oxygen atoms and the basal (or surface) oxygen atoms, respectively.
In Table A3 we compare our results (211 cell; 100 Ry) to experiment and to those of previous theoretical studies obtained with other computational schemes, also based on DFT. In particular, Larentzos et al.42 used a 212 supercell, the projectoraugmented wave (PAW) approach43 with plane-wave expansion for the k ) 0 valence wavefunctions and the Perdew-Wang44 exchange-correlation functional. Both Refson et al.45 and SainzDiaz et al.46 performed calculations on a 111 cell in the pseudopotential framework. A plane-wave expansion of the valence wave functions sampled over the Brillouin Zone was considered in ref 45, whereas only the Γ point was taken into account in ref 46, which used localized functions as basis set. In all cases the lattice parameters were optimized (Table A3). Appendix B: Tests of the Sodium Pseudopotential Here we compare calculated and experimental values for the characteristics of molecules containing sodium cations. This is
∠(Al-Oh-Al) ∠(Al-Oh-H) a
111
211
221
222
333
2.144 2.157 0.316 56 1.640 1.642 1.941 1.887 0.966 111 128 139 108 124 128 92 101 96 92 103 123
2.170 2.146 0.266 56 1.625 1.643 1.931 1.895 0.964 109 130 142 109 124 128 92 102 94 92 103 122
2.171 2.143 0.261 56 1.625 1.644 1.932 1.896 0.964 109 130 142 109 124 128 92 102 94 92 103 121
2.172 2.144 0.261 56 1.626 1.644 1.932 1.896 0.966 109 130 142 109 124 128 92 102 94 92 103 121
2.172 2.143 0.259 56 1.625 1.644 1.932 1.896 0.965 109 130 142 109 124 128 92 102 94 92 103 121
Symbols are as in Table A1.
(A) Experimental and calculated lattice parameters of pyrophillite from previous work. exp40
exp41
th.42
th.45
th.46
5.16 8.966 9.347 91.18 100.46 89.64
5.161 8.957 9.351 91.03 100.37 89.75
5.119 8.911 9.065 90.77 100.96 89.91
5.239 9.024 9.964 89.732 101.419 98.558
5.15 8.98 9.21 88.96 99.8 90
(B) Experimental and Calculated Internal Structural Parameters of Pyrophillitea exp40
exp41
this work
th.42
th.45
th.46
Ts.th. Os.th. ∆Z
2.153 2.155 2.126 2.079 0.248 0.161
2.171 2.143 0.261
2.180 2.170 2.130 2.130 0.210 0.310
Ψ
56
58
56
57
d(Si-Ob) d(Si-Oa) d(Al-Oa) d(Al-Oh) d(Oh-H)
1.612 1.633 1.922 1.888
1.615 1.623 1.953 1.938
1.625 1.644 1.932 1.896 0.964
1.620 1.630 1.920 1.890 0.970
1.635 1.670 1.660 1.950 1.940 1.910 1.900 0.977
110 132 141 109 122 126 94 100 94 94 100
109 130 142 109 124 128 92 102 94 92 103 121
109 130 144 109 126
109.5 110.1
92 102 94
94.8
∠(Ob-Si-Ob) ∠(Si-Ob-Si)
110 132 145 ∠(Ob-Si-Oa) (τ) 109 123 ∠(Al-Si-Oa) 128 ∠(Oa-Al-Oa) 93 102 ∠(Al-Oa-Al) ∠(Oh-Al-Oa) 94 93 ∠(Al-Oh-Al) 104 ∠(Al-Oh-H)
57
108.6
103
a Symbols are as in Table A1. Note that the unit-cell parameters used in “this work” are those given in ref 17 (see part A).
meant as a test of our scheme (PBE, pseudopotential) to describe the interaction of sodium with oxygen and water. Note that sodium is treated as a one-electron system, but the pseudopotential includes nonlinear core corrections to the exchange-correlation functional
12300
J. Phys. Chem. C, Vol. 113, No. 28, 2009
Clausen et al.
to account for the non-negligible overlap of valence and core shells.47 The limited accuracy of the pseudopotential emerges only in the value of the binding energy of NaH as expected in view of the small size of hydrogen. TABLE B1: Experimental and Calculated Properties of NaH, NaO, and NaOHa molecule
properties
this work
exp
NaH
bond length binding energy
1.888 177
NaO
bond length ionization potential
2.065
1.8873 0 K 181.97 ( 0.25 ZPE 7.0 2.052 7.41
adiabatic vertical
7.77 7.99 266
Na-O O-H
1.94 0.965 179
adiabatic vertical
7.82 8.04
binding energy NaOH
bond length bond angle ionization potential
0 K 252.4 ( 16.7 ZPE 2.9 1.93 0.97 179 7.89
a Bond lengths in Å, angles in degrees, ionization potentials in eV, and cohesive energies in kJ/mol. Experimental data are from ref 39, except for the ionization potentials of NaO and NaOH, which are from ref 48.
TABLE B2: Na Interaction with One Water Molecule B.E. (kcal/mol) Na-O (Å)
exp.49
this work
th28
24.0
24.3 2.197
24.1 2.215
Appendix C: Tests on the Volatile Molecules Here we compare calculated and experimental values for the characteristics of the molecules we have considered beyond water. Regarding the structure, in Table C1 we report the standard deviation from experimental data. The discrepancy found in the case of the largest-size molecule, n-octane, could be attributed to the fact that the experimental data refer to the solid phase in which the intermolecular interactions cannot be neglected. TABLE C1: Low-Weight Molecules: Standard Deviation of Calculated Values from Experimenta molecule
distances (rmsd, Å)
angles (rmsd, deg)
water ethanol ethyl acetate pyridine toluene n-octane
0.017 0.005 0.008 0.006 0.008 0.052
0.8 1.2 0.9 0.1 --3.7
a Experimental data are from ref 39 except for ethyl acetate50 and n-octane.51
TABLE C2: Low-Weight Molecules: Calculated and Experimental Values of Dipole Moment (D.M.) and Polarizability (χ) property
pyridine ethyl acetate ethanol water toluene n-octane
χ (Å3) exp39
9.63 9.5 2.23
9.22 9.7 2.03
5.27 5.41 1.53
1.60 1.45 1.79
exp39
2.215
1.78
1.69
1.854
D.M. (Debye)
References and Notes (1) Murray, H. H. Appl. Clay Sci. 2000, 17, 207.
12.51 12.28 0.43 0.375
15.98 15.9 0.00 ---
(2) >Hubbard, A. T. Encyclopedia of Surface and Colloid Science; CRC Press: Boca Raton, FL, 2002. (3) Sposito, G.; Skipper, N. T.; Sutton, L. E.; Park, H.-M.; Soper, A. K.; Greathouse, J. A. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 3358. (4) Greenwell, H. C.; Jones, W.; Coveney, P. V.; Stackhouse, S. J. Mater. Chem. 2006, 16, 708. (5) Odom, I. E. Phil. Trans. R. Soc. London A 1984, 311 (14), 391–409. (6) Heller-Kallai, L. J. Therm. Anal. Calorim. 1997, 50, 145. (7) Morrissey, F. A.; Grismer, M. E. J. Contam. Hydrol. 1999, 36, 291. (8) Steinberg, S.; Fairley, J. P.; Kreamer, D. K. J. Soil. Contam. 1994, 3, 249. (9) Li, Y.; Gupta, G. J. Soil Contam. 1994, 3, 127. (10) Ovadyahu, D.; Yariv, S.; Lapides, I. J. Therm. Anal. Calorim. 1998, 51, 415. (11) Chang, M. L.; Wu, S. C.; Chen, P. J.; Cheng, S. C. EnViron. Toxicol. Chem. 2003, 22, 1956. (12) Shih, Y.-S.; Wu, S.-C. EnViron. Toxicol. Chem. 2004, 23, 2061. (13) Cosultchi, A.; Bosch, P.; Lara, V. H. Colloids Surf. 2004, A243, 53. (14) Zhu, D.; Herbert, B. E.; Schlautman, M. A.; Carraway, E. R.; Hur, J. J. EnViron. Qual. 2004, 33, 1322. (15) Aggaewal, V.; Li, H.; Boyd, S. A.; Teppen, B. EnViron. Sci. Technol. 2006, 40, 894. (16) Rana, K.; Boyd, S. A.; Teppen, B. J.; Li, H.; Liu, C.; Johnston, C. T. Phys. Chem. Chem. Phys. 2009, 11, 2976. (17) Clausen, P.; Signorelli, M.; Schreiber, A.; Hughes, E.; Plummer, J. G. C.; Hubbard, A. T.; Fessas, D.; Schiraldi, A.; Månson, E. J. A. J. Therm. Anal. Calorim. (in press). (18) Tambach, T. J.; Bolhuis, P. G.; Hensen, J. M.; Smit, B. Langmuir 2006, 22, 1223. (19) Lock, P. A.; Skipper, N. T. Eur. J. Soil Sci. 2007, 58, 958. (20) Kosakowski, G.; Churakov, S. V.; Thoenen, T. Clays Clay Miner. 2008, 56, 190. (21) Marry, V.; Rotenberg, B.; Turq, P. Chem. Chem. Phys. 2008, 10, 4802. (22) Kohn, W.; Sham, L. J. Phys. ReV. 1965, 137, A1697. (23) Chatterjee, A.; Ebina, T.; Iwasaki, T.; Mizukami, F. J. Chem. Phys. 2003, 118, 10212. (24) Castro, E. A. S.; Martins, J. B. L. J. Comp.-Aided Mater. Des. 2005, 12, 121. (25) Alzate, L. F.; Ramos, C. M.; Hernandez, N. M.; Hernandez, S. P.; Mina, N. Vib. Spectrosc. 2006, 42, 357. (26) Briones-Jurado, C.; Agacino-Valdes, E. Int. J. Quantum Chem. 2008, 108, 1802. (27) Yu, C. H.; Norman, M. A.; Newton, S. Q.; Miller, D. M.; Teppen, B. J.; Schaefer, L. J. Mol. Struct. 2000, 556, 95. (28) Boek, E. S.; Sprik, M. J. Phys. Chem. B 2003, 107, 3251. (29) Suter, J. L.; Boek, E. S.; Sprik, M. J. Phys. Chem. C 2008, 112, 18832. (30) Tunega, D.; Gerzabek, M. H.; Haberhauer, G.; Lischka, H. J. Soil Sci. 2007, 58, 680. (31) Yu, C. H.; Newton, S. Q.; Miller, D. M.; Teppen, B. J.; Schaefer, L. Struct. Chem. 2001, 12, 393. (32) CPMD Copyright IBM Corp 1990-2008; Copyright MPI fu¨r Festko¨rperforschung Stuttgart 1997-2001; see www.cpmd.org. (33) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (34) Grossman, J. C.; Schwegler, E.; Draeger, E. W.; Gygi, F.; Galli, G. J. Chem. Phys. 2004, 120, 300. (35) Ireta, J.; Neugebauer, J.; Scheffler, M. J. Phys. Chem. A 2004, 108, 5692. (36) Trouiller, N.; Martins, J. L. Phys. ReV. B 1991, 43, 1993. (37) Kleinman, L.; Bylander, D. M. Phys. ReV. Lett. 1982, 48, 1425. (38) Clausen, P.; Watzke, B.; Hughes, E.; Hughes, E.; Plummer, J. G. C.; Hubbard, A. T.; Fessas, D.; Schiraldi, A.; Månson, E. J. A. Int. J. Eng. Sci. (submitted for publication). (39) Lide, D. R. Handbook of Chemistry and Physics; CRC Press: Boca Raton, FL, 1994. (40) Lee, J. H.; Guggenheim, S. Am. Mineral. 1981, 66, 350. (41) Wardle, R.; Brindley, G. W. Am. Mineral. 1972, 57, 732. (42) Larentzos, J. P.; Greathouse, J. A.; Cygan, R. T. J. Phys. Chem. C 2007, 111, 12752. (43) Kresse, G.; Joubert, D. D. Phys. ReV. B 1999, 59, 1758. (44) Perdew, J. P.; Wang, Y. Phys. ReV. B 1992, 45, 13244. (45) Refson, K.; Park, S.-H.; Sposito, G. J. Phys. Chem. B 2003, 107, 13383. (46) Sainz-Diaz, I.; Timon, V.; Botella, V.; Artacho, E.; HernandezLaguna, A. Am. Mineral. 2002, 87, 965. (47) Louie, S. G.; Froyen, S.; Cohen, M. L. Phys. ReV. B 1982, 26, 1738. (48) Huang, J.; Furukawa, K.; Aoto, K.; Yamawaki, M. J. J. Mass Spectrom. Soc. Jpn. 2002, 50, 296. (49) Dzidic, I.; Kebarle, P. J. Phys. Chem. 1970, 74, 1466. (50) Sugino, M.; Takeuchi, H.; Egawa, T.; Konaka, S. J. Mol. Struct. 1991, 245, 357. (51) Mathisen, H.; Norman, N.; Pedersen, P. Acta Chem. Scand. 1967, 21, 127.
JP811383Y
