Calculation of Entropy of Adsorption for Small Molecules on Mineral

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Calculation of Entropy of Adsorption for Small Molecules on Mineral Surfaces Akin Budi, Susan Louise Svane Stipp, and Martin Peter Andersson J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11860 • Publication Date (Web): 21 Mar 2018 Downloaded from http://pubs.acs.org on March 21, 2018

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The Journal of Physical Chemistry

Calculation of Entropy of Adsorption for Small Molecules on Mineral Surfaces A. Budi,∗ S.L.S. Stipp, and M.P. Andersson Nano-Science Center, Department of Chemistry University of Copenhagen, DK-2100 Copenhagen OE, Denmark E-mail: [email protected]

Abstract

terial in an aqueous environment. Interactions between the constituent minerals and organic matter play an important role in determining the recovery rate of crude oil from reservoirs, as well as the quality of drinking water in aquifers where organic contaminants are present. The interactions between mineral surfaces and organic molecules also play a central role in biomineralisation, where organisms engineer mineral growth for protection and support. Both calcite and quartz are common biominerals in marine environments. 1–3 Theoretical calculations make a useful contribution to efforts to elucidate the fundamental mechanisms behind the interactions between an organic molecule and a surface. 4–21 Techniques such as density functional theory (DFT) are often used because they allow accurate adsorption energy and geometry to be determined without the need of developing accurate force fields, as are needed for classical molecular dynamics simulations. On the other hand, with DFT, the size of the model system is somewhat limited compared to classical force field studies. DFT calculations are generally limited to zero temperature, providing only energies and trends, not temperature dependent free energies. To enable comparison between calculations and experiments at finite temperature, entropy should to be taken into account in the calculations. Some of the translational entropy of a free molecule is lost when it adsorbs on a surface and indeed at high temperatures, a molecule might not bind at all, when

We performed density functional theory calculations for small organic molecules adsorbed on calcite, quartz and kaolinite mineral surfaces and calculated the entropy change as a result of adsorption. Our results demonstrate that the entropy contribution to the free energy is mainly independent of the mechanism of binding but it is affected by surface coverage, molecule size, character and degrees of freedom. Compared with experimental results for weakly bonded molecules, density functional theory calculations predict a higher loss of entropy as a result of adsorption, which can be used as the upper limit for estimating the entropy contribution for adsorption to a mineral surface. The study has demonstrated a linear relationship between the entropy of the adsorbed molecule and the gas phase entropy, which can be used to estimate the entropy contribution to the free energy of adsorption on minerals, without explicit density functional theory calculations, an important step forward in predicting the behaviour of contaminants and other organic compounds in porous media such as soils, aquifers and oil reservoirs.

Introduction Calcite, quartz and kaolinite are major minerals in soil and groundwater aquifers as well as in limestone and sandstone oil reservoirs, where pore surfaces interact with organic ma-

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the gain in entropy from being free outweighs the enthalpy gained from adsorption. Recently, McKenzie et al. investigated the adsorption of organic molecules on silica surfaces and observed the importance of hydrogen bonds in mediating nonbonded interactions and the role of surface composition to the binding mechanism of organic molecules. 20 They also observed that the rigidity of the organic subunit enhanced adhesive contact by decreasing the conformational degrees of freedom, which in turn offered additional stability with respect to the surface interactions. Approximations for entropy change as a result of binding can be made using a force field based potential of mean force technique. 22 Gaberle et al. used this method along with adsorption energy and geometry obtained using DFT to estimate the entropy contribution to the free energy of adsorption. 23 They found that the contribution from entropy could match the contribution from enthalpy, even at relatively low temperatures. The accuracy of such force field based techniques depends on how well the force fields are parameterised. In general, force field parameters are not transferrable to systems beyond what they were originally parameterised for, thus somewhat limiting their applicability. In contrast, determination of entropy through vibrational partition function, using calculations based on quantum mechanics, gives a transferrable means to estimate the entropy contribution to the free energy of adsorption on any surface. 24 Experimentally, the entropy of adsorption can be determined from measurements of heat capacity, from adsorption behaviour in equilibrium experiments and temperature programmed desorption, which assumes that the rate of adsorption is equal to that of desorption. Campbell and Sellers used these techniques and attempted to formulate a general expression for predicting the entropy of an adsorbed molecule based on the entropy of the same molecule in the gas phase. 25 They did this by analysing the extent of adsorption for a range of molecules (mostly alkanes) on mineral surfaces and deriving the empirical relationship between the entropy of the two states. They found remark-

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able agreement for solid surfaces such as MgO, TiO2 , PdO, ZnO, Pt and graphite. In this study, we aimed to assess how the bonding mechanism and surface composition and properties affect the entropy of adsorption of small organic molecules on three minerals that are common at the Earth’s surface – calcite, quartz and kaolinite. We calculated the entropy change of these molecules explicitly using a DFT based, small displacement technique and we compared the results with those obtained using Campbell and Sellers’s empirical formula. 25 Furthermore, the effect of surface coverage on both adsorption energy and entropy was investigated.

Methods Initial structures Following the procedure described in Ataman et al., 18,19 we used QuantumESPRESSO 26 to optimise the bulk lattice parameters for calcite, quartz and kaolinite. Kaolinite has two basal planes available for binding, a gibbsite like Al face and a quartz like Si face. All the computational parameters were identical to those outlined in Ataman et al., 18,19 including the use of modified DFT-D2 C6 parameters for ionic solids. 27 The only change in the procedure was to use a 3 × 3 × 3 Monkhorst–Pack grid 28 for lattice parameter optimisation for bulk quartz instead of 3 × 3 × 1. This is because, unlike calcite and kaolinite, the cell lengths in quartz are similar to each other. The symmetric 6 layer calcite slab was adopted from our previous work, which used a [2 × 1] supercell for the {10¯14} surface. 21 The bulk quartz structure was adopted from Levien et al. 29 and the bulk kaolinite structure, from Bish. 30 After optimisation, a symmetric 5 layer [2 × 2] supercell of a {10¯10} slab of quartz was created. This was then hydrogen passivated to neutralise the dangling bonds. For kaolinite, we created a [2 × 1] supercell consisting of 2 layers for our starting structure. Table 1 shows the optimised lattice parameters for these slabs. At least 20 Å of vacuum was


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added as a spacer to ensure that the periodic images did not interact.

was the Perdew, Burke and Erzenhof (PBE) type, 33 within the generalised gradient approximation (GGA). 34 A double numerical basis set with polarisation was used, which in DMol3 exhibits negligible basis set superposition error. 35,36 The slab structures were reoptimised while keeping the lattice parameters constant before the vibrational partition function was calculated, to ensure that they were minimised with respect to the functional and basis set combination that we used. The electronic convergence criterion was set to 2.7 × 10−4 eV, geometries convergence to 10−4 Å and force convergence to 2.7 × 10−2 eV/Å. A semiclassical Grimme dispersion correction of D2 form was used to account for weak dispersion interactions. 37 All the geometry optimisation calculations were performed at the Gamma point, while the harmonic frequency calculations were performed on 2 × 2 × 1 Monkhorst–Pack grid 28 to achieve a more stringent accuracy criterion necessary to calculate the vibrational partition function that gives the entropy. No imaginary frequencies were found for any structure, which confirmed that they were true minima on the potential energy surface. The change of entropy can be calculated explicitly using the following formula:

Table 1: Lattice parameters for the slab calculation. Lattice parameter [Å] a b

Calcite 8.20 10.12

Quartz Kaolinite 10.02 11.00

10.43 9.05

The molecules chosen for this work were water, carbon dioxide, benzene, methane, ethane, methanol, ethanol, formic acid and acetic acid because they contain some of the most common functional groups found in nature. We included longer variants of the molecules, with the same functional groups, to investigate the influence of the length of the alkyl group on binding strength and entropy of adsorption. Two coverages were studied: low coverage, which refers to a single molecule in the surface unit cell, and high coverage, which refers to 4 molecules in the surface unit cell. The surface unit cells for all three minerals were of similar area so we could use the same number of molecules for the high coverage study.

Computational parameters ∆S(T ) = Ssurf+mol (T ) − (Ssurf (T ) + Smol (T )) , (2) where ∆S(T ) represents the change in entropy as a result of adsorption, Ssurf+mol (T ) represents the entropy of the combined system of a molecule adsorbed on a surface, Ssurf (T ), the entropy of the clean surface and Smol (T ), the entropy of the molecule in gas phase. By collecting data from equilibrium adsorption experiments and temperature programmed desorption of alkanes and other small molecules from mineral and metal surfaces, Campbell and Sellers found that the entropy of a molecule adsorbed on a surface still retains most of the gas phase entropy. 25 This is because the molecule is trapped in a potential well, which is steep in the direction perpendicular to the surface and thus it restricts motion in that direction. They proposed the empirical formula:

The adsorption energies were obtained using QuantumESPRESSO, following the procedure outlined in Ataman et al. 18,19 and calculated using the following formula: Eads = Esurf+mol − (Esurf + Emol ) ,

(1)

where Eads represents the adsorption energy, Esurf+mol represents the total energy of a molecule adsorbed on a surface, Esurf , the total energy of the clean surface and Emol , the total energy of a single molecule. The adsorption energies obtained using the parameters specified in Ataman et al. 18,19 gave very good agreement with experimental data for desorption temperature on calcite. The entropy calculations were performed in DMol3 31,32 using the small displacement method to obtain the vibrational partition function. The exchange-correlation functional used


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Sads (T ) = 0.70Sgas (T ) − 3.3R,

from the gas phase to adsorbed state (i.e. the adsorption energy, Eads ) and T ∆S is the entropy contribution to the free energy arising from a change of entropy, ∆S, at temperature, T.

(3)

where Sads represents the entropy of the molecule in the adsorbed state, Sgas , the entropy in gas phase and R, the gas constant. This in turn gives the change in entropy as a result of adsorption, ∆S: ∆S(T ) = Sads (T ) − Sgas (T ) = −0.30Sgas (T ) − 3.3R.

Results and discussion Adsorption energy

(4)

The motion of a molecule, that is initially free to move in three dimensions, is restricted when it adsorbs, to movement in two dimensions. It loses roughly one third of its gas phase entropy when it adsorbs, which corresponds to losing translational entropy in the direction of the surface normal. This two dimensional movement can be thought of as either an ideal 2D gas or an ideal 2D lattice gas, depending on whether or not the adsorbed molecule can overcome the translation and rotation energy barrier. 38 If kT is smaller than the energy barrier, then the harmonic approximation applies, with errors in the order of 0.25 R (approximately 6 meV at 298.15 K). If kT is greater than the energy barrier, then the hindered translator/rotor model applies. 38 Furthermore, Campbell et al. shows that there exists a concentration dependent configurational entropy, 39 which for an ideal 2D gas is given by: (e) (5) , S1 = R ln θ where R represents the gas constant and θ represents surface concentration. For an ideal 2D lattice gas, this term becomes:

Sconfig

[ ( ) ] 1−θ ln (1 − θ) = R ln − . θ θ

(a)

(b)

(c)

(d)

Figure 1: Side view of the mineral surfaces used in this study: (a) calcite, (b) quartz, (c) kaolinite (Al) and (d) kaolinite (Si). The periodic boundaries are shown as vertical lines. Table 2 presents the adsorption energies for the series of molecules on the mineral surfaces. The adsorption energy of a water molecule at low coverage is consistent with the results of Juhl et al., who reported −0.83 eV for the calcite {10¯14} surface, −0.51 eV for hydroxylated quartz {10¯10} and −0.43 eV for muscovite {001}. 40 The surface composition and structure

(6)

Finally, the free energy of adsorption, ∆G, can be found using the formula: ∆G = ∆H − T ∆S,

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(7)

where ∆H represents the change in enthalpy,


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Table 2: Adsorption energy per molecule (in eV) at low and high coverages. Binding mechanism Water H-bond/e.s.† Methanol H-bond/e.s.† Ethanol H-bond/e.s.† Formic acid H-bond/e.s.† H-bond/e.s.† Acetic acid Methane Dispersion Dispersion Ethane Dispersion Benzene Carbon dioxide Dispersion Molecule

†

Calcite Low High 18 −0.83 −0.84 18 −0.80 −0.89 −0.83 18 −1.06 −0.98 18 −1.06 −0.99 18 −1.23 −0.13 −0.21 −0.18 18 −0.38 −0.32 18 −0.67 −0.31 18 −0.32

Quartz Low High −0.55 −0.52 −0.63 −0.62 −0.67 −0.69 −0.60 −0.63 −0.63 −0.67 −0.07 −0.08 −0.13 −0.18 −0.35 −0.49 −0.07 −0.17

Kaolinite (Al) Low High −0.58 −0.56 −0.64 −0.64 −0.67 −0.71 −0.82 −0.76 −0.85 −0.84 −0.17 −0.18 −0.23 −0.27 −0.39 −0.51 −0.30 −0.26

Kaolinite (Si) Low High −0.22 −0.15 −0.22 −0.22 −0.24 −0.30 −0.22 −0.27 −0.22 −0.32 −0.08 −0.09 −0.12 −0.17 −0.19 −0.30 −0.10 −0.11

electrostatic

calcite > quartz ≥ kaolinite (Si). This can be understood by examining the mineral surface structure (Figure 1). There is an abundance of hydrogen donor and acceptor species on calcite, hydroxylated quartz and kaolinite (Al). Kaolinite (Si) does not have these species at the surface and therefore, interactions are dominated by dispersion. Within the same functional group, longer alkyl chains tend to increase binding strength, which is consistent with results presented by Ataman et al. 18 The adsorption energy per molecule at high coverage is generally higher than for a single molecule (Table 2). This is more pronounced in larger molecules such as benzene, where the molecules can interact with each other and enhance binding with the surface. The order of stability for the molecules interacting by hydrogen bonding is maintained for the small molecules (calcite > kaolinite (Al) ≥ quartz > kaolinite (Si)). For the molecules that interact mainly through dispersion forces, the order of stability was calcite > kaolinite (Al) > quartz ≥ kaolinite (Si). In terms of functional groups, the order of stability on calcite and kaolinite (Al) was carboxylic acid > alcohol > water > benzene > carbon dioxide > alkane, irrespective of coverage. For quartz, the order was carboxylic acid ≃ alcohol > water > benzene > alkane ≥ carbon dioxide. For kaolinite (Si), all of the molecules have nearly the same adsorption energy at low coverage, with only 0.15 eV sepa-

for muscovite are similar to the Si kaolinite surface. The adsorption energy of benzene on hydroxylated {10¯10} quartz obtained in our study is higher than that of McKenzie et al., who reported −0.03 eV. 20 The cause for this difference could be the different strength of the dispersion contribution from the modified D2 C6 parameter compared with the original formulation. Sølling et al. performed cluster calculations using a hybrid functional at the B3LYP level 41–43 of water and carbon dioxide adsorbing on calcite, quartz and clay. They found adsorption energies of −1.00, −0.69 and −1.02 eV for water and −0.42, −0.28 and −0.52 eV for carbon dioxide on calcite, quartz and clay. 44 The stronger adsorption energies could be caused by some edge effects that are unavoidable in nonperiodic calculations. Nonetheless, there is good agreement in terms of order of stability, despite the difference in level of theory. De Leeuw et al. used a force field based technique to calculate the adsorption energy of water on hydroxylated quartz {10¯10} and obtained a higher value, i.e. −0.89 eV. 5 We attribute this difference to the different computational technique used in that work. At low coverage, the general order of stability for the molecules that interact through hydrogen bonding for the four surfaces is: calcite > kaolinite (Al) ≥ quartz > kaolinite (Si). However, for the molecules that interact through dispersion forces, the general order of stability on the four surfaces is: kaolinite (Al) >


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rating the strongest bound molecule (ethanol) and the weakest (methane). At high coverage, the order of stability is carboxylic acid ≃ benzene > alcohol > water ≃ alkane > carbon dioxide. The reason for the very different behaviour on kaolinite (Si) could be the arrangement of closely coordinated Si and O atoms, which forces adsorbed molecules to interact mainly through dispersion forces. Intermolecular interactions at high coverage can help stabilise the molecules, as is evident in the case of the largest molecules in this study: acetic acid, ethanol and benzene, where adsorption energies increased from −0.2 to −0.3 eV.

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entropy. This is consistent with more degrees of freedom for larger molecules. Also, T ∆S is positively correlated with temperature, as expected. An increase in temperature from 298.15 K to 350 K increases T ∆S by 0.05–0.10 eV. The empirical formula 25 yields smaller values than the explicit calculation of entropy change. The prediction for T ∆S for carbon dioxide is the closest to that found using the empirical formula. This close agreement probably results from the limited degrees of freedom. For other molecules that interact through dispersion forces, there is also closer agreement between T ∆S and the value from the empirical formula, with an average difference of 0.11 eV at 298.15 K and 0.12 eV at 350 K. This contrasts with values for molecules that hydrogen bond, with a difference of 0.18 eV at 298.15 K and 0.21 eV at 350 K. The smaller values obtained from the empirical formula compared to our DFT calculations can be explained by the averaging of different adsorption geometries, which is inherent and expected in real experiments. In contrast, our DFT calculations use a single stable configuration, which corresponds to the minimum energy configuration in the potential energy surface. Hence, the resulting structure is in the most restricted state compared with other adsorption geometries and consequently, the change in entropy is also higher. Therefore, the entropy change obtained using explicit DFT calculation serves as an upper limit for determining entropy. This is consistent with observations from Balog et al., who used a force field technique along with normal mode analysis to interpret experimentally determined vibrational density of states for a protein. 46 They concluded that protein flexibility was directly responsible for the inhomogeneous broadening of the experimentally determined vibrational density of states.

Entropy contribution to the free energy of adsorption To determine if the adsorbed molecules considered in this work can be thought of as an ideal 2D gas or an ideal 2D lattice gas, we calculated the translational energy barrier of water, carbon dioxide (low Smol ) and acetic acid (high Smol ) using the synchronous transit method 45 from one adsorption site to two other sites in different directions. The lowest energy barriers were 0.27 eV for water on kaolinite (Si), 0.11 eV for carbon dioxide on kaolinite (Si) and 0.24 eV for acetic acid on kaolinite (Si). This indicates that these adsorbed molecules are in the ideal 2D lattice gas regime where the harmonic approximation applies. 38 We assume that high coverage corresponds to a monolayer coverage (θ = 1) and low coverage corresponds to θ = 0.25. Table 3 shows the entropy contribution to the free energy of adsorption, T ∆S, for the molecules at two different temperatures, with the entropy change, ∆S, calculated explicitly using DFT and Equation 4. The values have been corrected for the configurational entropy using Equation 6. T ∆S per molecule at low coverage is consistently lower than at high coverage by an average of 0.05 eV. This indicates that entropy is dependent on surface coverage. Unlike the adsorption energies, T ∆S for these molecules is mostly independent of the binding mechanism. However, there is a tendency for larger molecules to have a larger change in


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Table 3: Entropy contribution to the free energy of adsorption, T ∆S (in eV). Molecule

Calcite Low High

Water Methanol Ethanol Formic acid Acetic acid Methane Ethane Benzene Carbon dioxide

−0.52 −0.46 −0.51 −0.54 −0.56 −0.43 −0.50 −0.50 −0.26

−0.52 −0.57 −0.60 −0.56 −0.60 −0.47 −0.52 −0.60 −0.29


−0.61 −0.54 −0.60 −0.63 −0.65 −0.49 −0.58 −0.58 −0.31

−0.61 −0.66 −0.71 −0.65 −0.70 −0.55 −0.60 −0.69 −0.33

Quartz Kaolinite (Al) Kaolinite (Si) Empirical Low High Low High Low High formula At room temperature (298.15 K) −0.45 −0.48 −0.45 −0.49 −0.34 −0.39 −0.27 −0.51 −0.54 −0.48 −0.52 −0.38 −0.41 −0.31 −0.55 −0.58 −0.51 −0.57 −0.38 −0.49 −0.34 −0.47 −0.51 −0.50 −0.56 −0.39 −0.44 −0.32 −0.45 −0.56 −0.51 −0.58 −0.47 −0.52 −0.35 −0.35 −0.41 −0.39 −0.43 −0.35 −0.40 −0.28 −0.41 −0.45 −0.40 −0.45 −0.40 −0.45 −0.31 −0.48 −0.53 −0.47 −0.55 −0.43 −0.53 −0.35 −0.18 −0.23 −0.24 −0.30 −0.16 −0.22 −0.24 At 350 K −0.53 −0.57 −0.53 −0.57 −0.40 −0.46 −0.32 −0.60 −0.63 −0.57 −0.61 −0.44 −0.48 −0.37 −0.64 −0.68 −0.60 −0.67 −0.44 −0.57 −0.41 −0.55 −0.60 −0.59 −0.66 −0.46 −0.51 −0.38 −0.55 −0.66 −0.60 −0.68 −0.55 −0.61 −0.42 −0.41 −0.48 −0.45 −0.50 −0.41 −0.46 −0.33 −0.47 −0.52 −0.47 −0.52 −0.46 −0.53 −0.37 −0.55 −0.61 −0.55 −0.64 −0.50 −0.61 −0.43 −0.21 −0.26 −0.29 −0.35 −0.19 −0.26 −0.29

Relationship between entropy of a molecule in the adsorbed state and in gas phase

There is excellent agreement between the slope of the lines of best fit (excluding carbon dioxide) and Campbell and Seller’s empirical formula, which suggests that it is valid for DFT entropy predictions. However, there is a shift in the intercept, that depends on the mineral surface composition and structure. The largest difference is observed for calcite. Calcite has a high number of hydrogen donor and acceptor sites, which strengthens the interactions between a molecule and the surface. The difference of the intercept for calcite and the empirical formula is 5.1 R. This indicates that while the linear relationship between the entropy of a molecule in the adsorbed state and in the gas phase holds true, the absolute value of the entropy change on adsorption depends on the exact surface that the molecule adsorbs on. The maximum difference for the mineral surfaces examined in this study was ∼8 R (i.e. ∼0.20 eV at 298.15 K and ∼0.24 eV at 350 K). Our correlations (Figure 2) can be used to estimate the change in entropy resulting from adsorption on

We can further analyse the entropy contribution by following the approach of Campbell and Sellers. 25 We plotted the entropy of the adsorbed molecule (in units of R) against the entropy of the same molecule in the gas phase. Campbell and Seller’s empirical formula was derived from experimental data, which assumes a standard state that corresponds to a surface concentration of 0.01. 39 To facilitate direct comparison with this formula, we have added the configurational entropy as prescribed in Equation 6, setting θ = 0.01. Figure 2 reveals a strong linear relationship for the molecules in this study, with the exception of carbon dioxide. It is not clear why carbon dioxide behaves differently. It is possible that the potential energy surface for carbon dioxide is quite flat. Also, carbon dioxide is the only linear molecule in our study.


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Calcite 298.15 K Calcite 350 K 0.74×Sgas − 8.4

25

Empirical formula 0.7×Sgas − 3.3 Sads [R]

Sads [R]

10

15 10

CO2 20

25

30 Sgas [R]

35

5

40

CO2 20

25

(a) Kaolinite (Al) 298.15 K Kaolinite (Al) 350 K 0.68×Sgas − 5.0

25

30 Sgas [R]

35

40

(b) Empirical formula 0.7×Sgas − 3.3

Kaolinite (Si) 298.15 K Kaolinite (Si) 350 K 0.62×Sgas − 0.6

25

Empirical formula 0.7×Sgas − 3.3

20 Sads [R]

20 15 10 5

Empirical formula 0.7×Sgas − 3.3

20

15

5

Quartz 298.15 K Quartz 350 K 0.68×Sgas − 4.9

25

20

Sads [R]

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15 10

CO2 20

25

30 Sgas [R]

35

5

40

CO2 20

(c)

25

30 Sgas [R]

35

40

(d)

Figure 2: Entropy for organic molecule adsorption on (a) calcite, (b) quartz, (c) kaolinite (Al) and (d) kaolinite (Si) compared with the gas phase at 298.15 K and 350 K. Data for carbon dioxide have not been included in the lines of best fit. The empirical formula corresponds to Equation 4, from Campbell and Sellers. 25

Entropy corrected adsorption energy

minerals without performing new, resource demanding DFT calculations. For strongly polar mineral surfaces, the calcite correlation can be used to estimate the entropy loss upon adsorption. For hydroxyl terminated minerals, either the quartz or the kaolinite (Al) correlation can be used and for mostly non polar mineral surfaces, the kaolinite (Si) correlation can be used to estimate the entropy loss upon adsorption. The maximum deviation from the fitted line for each mineral surface (excluding carbon dioxide) was ∼3 R, which corresponds to ∼0.08 eV at 298.15 K and ∼0.09 eV at 350 K, and is lower than systematic DFT uncertainties of GGA functionals compared to experimental values. 47

We can now compare the effect of entropy on the free energy of adsorption for these molecules (Table 4). Some molecules, particularly on calcite are more stable at high coverage, which supports the hypothesis that intermolecular interactions help in stabilising them. Of the molecules that interact through dispersion forces, only benzene on calcite at high coverage, carbon dioxide on calcite at both coverages and carbon dioxide on kaolinite (Al) at low coverage are stable at room temperature but adsorption free energy is low. The rest of the molecules, that bind through dispersion forces, do not adsorb on any surface above room temperature (except for carbon dioxide on kaolinite (Al) at low coverage with free energy of adsorption of −0.02 eV), which is consistent with their low


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Table 4: Entropy corrected free energy of adsorption ∆G (in eV). Molecule

Calcite Low High


−0.31 −0.34 −0.32 −0.44 −0.43 0.30 0.32 0.18 −0.05

−0.32 −0.32 −0.46 −0.51 −0.63 0.26 0.14 −0.07 −0.03


−0.22 −0.26 −0.23 −0.35 −0.34 0.36 0.40 0.26 0.00

−0.23 −0.23 −0.36 −0.42 −0.53 0.34 0.22 0.02 0.01

Quartz Kaolinite (Al) Low High Low High At room temperature (298.15 K) −0.10 −0.04 −0.14 −0.08 −0.12 −0.08 −0.16 −0.12 −0.13 −0.11 −0.16 −0.14 −0.13 −0.11 −0.32 −0.19 −0.18 −0.11 −0.34 −0.26 0.28 0.33 0.22 0.25 0.28 0.17 0.27 0.18 0.13 0.04 0.08 0.04 0.03 0.05 −0.06 0.03 At 350 K −0.02 0.04 −0.06 0.01 −0.03 0.01 −0.08 −0.03 −0.03 −0.01 −0.07 −0.04 −0.06 −0.03 −0.23 −0.09 −0.08 −0.01 −0.25 −0.16 0.39 0.32 0.34 0.28 0.34 0.34 0.24 0.25 0.20 0.13 0.16 0.13 0.09 −0.02 0.08 0.06

adsorption energies in vacuum compared with the molecules that hydrogen bond. The low adsorption energy in vacuum is also the reason why none of the molecules adsorb on kaolinite (Si), i.e. their free energy of adsorption is > 0. The order of stability for the molecules that hydrogen bond follows the same order as adsorption energy, where calcite > kaolinite (Al) ≥ quartz > kaolinite (Si). Sølling et al. reported adsorption free energy of −0.61, −0.27 and −0.60 eV for water and −0.05, +0.09 and −0.20 eV for carbon dioxide on calcite, quartz and clay at room temperature. 44 There is again some overestimation that stems from the use of a nonperiodic system, in addition to a different level of theory. Nonetheless, we obtained a similar order of stability.

Kaolinite (Si) Low High 0.12 0.15 0.14 0.17 0.25 0.26 0.27 0.24 0.06

0.24 0.19 0.19 0.17 0.20 0.31 0.28 0.23 0.11

0.18 0.22 0.20 0.24 0.33 0.32 0.34 0.31 0.09

0.30 0.26 0.27 0.24 0.29 0.37 0.35 0.31 0.15

gen bond adsorb more strongly than molecules that adhere only through dispersion forces, at least for small molecules. In general, high coverage increases binding energy because of attractive intermolecular interaction between the molecules. The attractive interaction between adsorbed molecules becomes more pronounced for larger molecules. Entropy contributions to the free energy are affected by surface coverage, with low coverage yielding lower T ∆S than high coverage. However, they are minimally affected by binding mechanism. Molecule size and degrees of freedom have a much larger effect. The entropy contribution, determined using DFT, serves as an upper limit for the actual entropy contribution. For molecules bound to a mineral surface, that are not able to diffuse freely along the surface, the DFT calculations should provide good estimates for the entropy loss. When measured experimentally, there is an averaging because of different adsorption geometries, which results in a lower entropy contribution with respect to

Conclusions Our study suggests that the binding mechanism for a molecule to a mineral surface affects the strength of adsorption. Molecules that hydro-


9


explicit DFT calculations. We found surface dependent linear relationships between the entropy of a molecule adsorbed on calcite, quartz and kaolinite and the corresponding gas phase entropy, which is consistent with previous, experimentally derived scaling relationship. Our linear correlations provided reasonable upper bounds for the loss in entropy as a result of adsorption to minerals without the need for explicit DFT calculations. The only calculation needed is for the entropy of the molecule of interest in a gas phase. The change in entropy upon adsorption contributes significantly to the free energy of adsorption.

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(4) Skinner, A. J.; LaFemina, J. P.; Jansen, H. J. F. Structure and bonding of calcite: A theoretical study. American Mineralogist 1994, 79, 205–214. (5) de Leeuw, N. H.; Higgins, F. M.; Parker, S. C. Modeling the surface structure and stability of α-quartz. The Journal of Physical Chemistry B 1999, 103, 1270–1277. (6) Warne, M. R.; Allan, N. L.; Cosgrove, T. Computer simulation of water molecules at kaolinite and silica surfaces. Physical Chemistry Chemical Physics 2000, 2, 3663–3668.

Acknowledgements

(7) Kerisit, S.; Parker, S. C.; Harding, J. H. Atomistic simulation of the dissociative adsorption of water on calcite surfaces. The Journal of Physical Chemistry B 2003, 107, 7676–7682.

We acknowledge support from the Mærsk Oil Research and Technology Center, BP Exploration Operating Company Limited, under the Enhanced Oil Recovery Technology Flagship ExploRe Programme and the Minerals in Biology (MIB) Consortium, funded by the UK EPSRC Frame Grant #EP/I001514/1. The calculations were performed on the computing cluster maintained by the High Performance Computing Centre at the University of Copenhagen (HPC/UCPH).

(8) Kerisit, S.; Parker, S. C. Free energy of adsorption of water and metal ions on the {10¯14} calcite surface. Journal of the American Chemical Society 2004, 126, 10152–10161. (9) Yang, M.; Stipp, S. L. S.; Harding, J. Biological control on calcite crystallization by polysaccharides. Crystal Growth & Design 2008, 8, 4066–4074.

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Graphical TOC Entry 25 Sads [R]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Empirical formula

20

DFT

15 10 5 20

25

30 Sgas [R]


14

35

40

Calculation of Entropy of Adsorption for Small Molecules on Mineral

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