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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Insight into the Bonding of Silanols to Oxidized Aluminum Surfaces Matic Poberznik, Dominique Costa, Anne Hemeryck, and Anton Kokalj J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12552 • Publication Date (Web): 10 Apr 2018 Downloaded from http://pubs.acs.org on April 10, 2018

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The Journal of Physical Chemistry

Insight into the Bonding of Silanols to Oxidized Aluminum Surfaces Matic Poberˇznik,a,b,1 Dominique Costa,c,2 Anne Hemeryckd,3 , Anton Kokalja,4 * a b c

Department of Physical and Organic Chemistry, Joˇzef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia

University of Ljubljana, Faculty of Chemistry and Chemical Technology, Veˇcna pot 113, SI-1000 Ljubljana, Slovenia

Ecole Nationale Supérieure de Chimie de Paris, Chimie-ParisTech, 11 Rue Pierre et Marie Curie, 75005 Paris, France d

LAAS CNRS, Université de Toulouse, CNRS, Toulouse, France April 4, 2018

Abstract In the context of elucidating the mechanism by which siloxane based sol-gel coatings adhere to the surface, the adsorption of a model silanol molecule, CH3 Si(OH)3 , and its oligomers (up to the trimer) on oxidized and fullyhydroxylated aluminum substrates is described using density-functional-theory (DFT). To link our calculations with the synthesis of siloxane based sol-gel coatings, the focus is given on a condensation mechanism. We find that the formation of a monodentate bonding mode with the hydroxylated surface via the condensation mechanism is exothermic by ≥ 0.5 eV in all considered cases. In contrast, the formation of a bidentate bonding mode is exothermic only for the trimer. However, taking entropic contributions into account we find that the formation of the bidentate bonding mode is exergonic already for the dimer, due to favorable entropic effects of a liberated water molecule during the reaction. In contrast, the reaction entropy is unfavorable for the monodentate formation, because the effects of the immobilized silanol molecule counteract and surpass those of the liberated water molecule. The monodentate to bidentate transformation is therefore determined by the interplay between entropy and energy, and we find that the longer the oligomer chain the more likely is the bidentate formation due to increasingly favorable reaction energies. These results further reveal that for the silanol monomer additional molecule–surface chemical bonds do not form via the condensation mechanism, due to the strained configurations it has to adopt in the bidentate bonding mode.

1

ORCID ID: 0000-0002-4866-4346 2 ORCID ID: 0000-0002-3781-9867 3 ORCID ID: 0000-0002-0201-1171 4 ORCID ID: 0000-0001-7237-0041 * Corresponding Author: Anton Kokalj, Tel: +386-1-477-3523; Fax: +386 1 251 93 85, E-mail: [email protected], URL: http://www.ijs.si/ijsw/K3-en/Kokalj

1

Introduction Aluminum, together with its alloys, is one of the most widely used materials today, mainly due to its corrosion resistance, low density and relatively low cost. It is well known that its excellent corrosion resistance is a consequence of a spontaneously formed thin oxide film, which protects the metal from deterioration in many environments, especially in the pH range from 4 to 8. To achieve corrosion resistance under even harsher conditions chromate conversion coatings were historically used but due to their carcinogenicity alternatives are sought. 1,2 One of

the most promising alternatives are hybrid sol-gel coatings which, apart from ensuring corrosion protection, also provide the possibility of imbuing the surface with other desired properties, such as hydrophobicity. 3,4 The sol-gel process involves the formation of an amorphous oxide structure through progressive hydrolysis/condensation reactions from molecular precursors. Typical precursors are metalloid alkoxides, designated as M(OR)n , where M is Si, Ti, Zr, Al or some other element and R represents an alkyl group. In the context of corrosion inhibition alkoxysilanes are the most commonly used and studied precursors, mainly due to their relatively low reactivity towards hydrolysis. The sol-gel process generally involves 4 steps; (i) the hydrolysis of the metalloid alkoxide, (ii) the condensation and polymerization of monomers to form longer chains, (iii) growth of the particles and (iv) the agglomeration of the polymer structure which results in the formation of a gel structure. 5–9 The focus of this work is on the second step, the condensation and polymerization of monomers, with specific emphasis on the formation of bonds with the surface. After the first step, the hydrolysis of alkoxysilanes, molecules

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The Journal of Physical Chemistry with the silanol functional group (silanols) are present in the solution. These silanols then react via a condensation mechanism either with other standalone silanols forming larger polymer chains or with surface hydroxyl groups forming bonds with surface metal atoms. The polymerization condensation reaction between standalone silanol monomers has been thoroughly studied both experimentally and theoretically. 10–14 The reaction with the metal surface is however more difficult to characterize and a scheme first proposed by Arkles et al. 15 is typically used to explain the adhesion of these films to the metal surface. Though there exists some experimental evidence to confirm the formation of such bonds, 16,17 theoretical studies on the subject are scarce. Torras et al. 18 studied silane deposition onto the aluminum surface in the presence of organophosphonic acid as an adhesion promoter utilizing a combination of experimental and theoretical techniques. They found a stable monodentate binding mode for standalone Si(OH)4 on the 4×4 supercell of the γ−AlOOH(010) surface, while the same mode was found to be unstable at higher coverage, on the 2 × 2 supercell. In both cases however the monodentate binding mode was preferential to the bidentate binding mode by about 1 eV. 19 A similar conclusion was reached by Hardin et al. 20 who performed a spectroscopic analysis of the interactions between alkylated silanes and alumina nanoporous membranes. On the basis of the amount of methanol side product formed they reasoned that a single covalent bond is formed between the standalone silane and the surface. Motta et al. 21 modelled the adsorption of fluoroalkyl silanes on the γ−AlOOH(010) surface and found the formation of a bidentate bonding mode unfavorable for a single monomer unit, but they identified a stable bidentate bonding mode for the dimer. The aim of this work is to provide an atomistic insight into the initial steps of the formation of siloxane based sol-gel coatings on oxidized aluminum surfaces. Specifically the monodentate and bidentate bonding modes of both standalone and polymerized model silanol molecules are analyzed using DFT calculations. First the computational method is presented, followed by the description of our model of the aluminum surface. In this context the issue of hydroxylation of the oxidized Al surface is also addressed. 2

Computational Method and Technical Details DFT calculations were performed with the PWscf code from the Quantum ESPRESSO distribution 22,23 using the generalized gradient approximation (GGA) of PerdewBurke-Ernzerhof (PBE). 24 We used the pseudo-potential method with ultra-soft pseudo-potentials. 25,26 Kohn-Sham orbitals were expanded in a plane wave basis set up to a kinetic energy cutoff of 35 Ry (280 Ry for the charge-density cutoff). Brillouin zone (BZ) integrations were performed with the special point technique 27 using a MethfesselPaxton smearing 28 of 0.03 Ry. Molecular graphics were produced by the XCRYSDEN graphical package. 29

2ML O @ Al(111)

Al(111)

topview

topview

Aloct

(4×4)

(4×4)

sideview Aloct

sideview + 2ML of O

Altet

Altet

}

~5Å

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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Figure 1. Topview and sideview of the Al(111) before (left) and after oxidation (right) with 2 ML of atomic oxygen as proposed by Lanthony et al., 30 where 1 ML corresponds to one O atom per surface Al atom of Al(111). The (4 × 4) supercell is indicated on both topview snapshots. Note that oxidation affects only the two topmost Al layers and below them the Al slab remains visually unaffected (indicated by a dashed line). Tetrahedrally (Altet ) and octahedrally (Aloct ) coordinated Al ions in the topmost layer of the oxide film are also indicated.

2.1

A Model of the Oxidized Aluminum Surface

Aluminum is an fcc metal and our calculated bulk lattice parameter of 4.04 ˚ A 31 is in accordance with the experimental value of 4.05 ˚ A. 32 However, a metallic Al surface is not a realistic model of the aluminum surface, because it is well known that in the atmosphere or an aqueous environment, the Al surface is covered by a thin oxide film, which presumably has an amorphous structure with a limiting thickness that depends on the conditions (pressure, temperature) of oxidation. 33–36 At ambient conditions the limiting thickness is about 2 nm, but it was shown that the potential gradient resulting from the formation of a thin oxide film is limited to a relatively thin ≈ 7 ˚ A region within the film. 37 In light of the above statements, we utilized a model consisting of an ultrathin oxide film supported on an Al(111) slab; the Al(111) surface was chosen, because it has the lowest surface energy among pristine Al surfaces. 38 The model was built by oxidizing the Al(111) surface along the lines followed by Lanthony et al. 30 In particular, we started with a 9 layer Al(111) slab model and a (4 × 4) supercell, with the bottom three layers constrained to the bulk positions and the in-plane lattice spacing fixed to the calculated equilibrium bulk Al lattice parameter of 4.04 ˚ A. The ultrathin oxide film was then formed in two steps: first (i) one monolayer (ML) of oxygen atoms was adsorbed onto fcc sites on the top-side of the Al(111) slab (coverage in ML


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units is defined as the number of O atoms per surface Al atoms) and then (ii) additional oxygen atoms were placed above it. During the relaxation the Al ions from the first metallic layer diffused through the chemisorbed O layer via a barrierless mechanism. The oxidation proceeds in this manner until an equivalent of 2 ML of oxygen is reached and one metallic layer diffuses through the chemisorbed layer. Above this coverage the diffusion of Al ions through the ultrathin oxide film is no longer barrierless. 30 Hence, our ultrathin oxide film supported on Al(111) contains an equivalent of 2 ML of oxygen atoms; its structure is shown in Figure 1 together with the structure of pristine Al(111). The resulting ultrathin film contains both 4-fold (tetrahedral) and 6-fold (octahedral) coordinated Al ions, which commonly appear in crystalline structures of aluminum oxides. The oxygen atoms form a regular hexagonal network with an O–O distance of about 3 ˚ A. The thickness of the film is about 5 ˚ A which is comparable to the thickness associated with the oxidation induced potential gradient and in line with the limiting thickness obtained in UHV experiments. 34 A film of comparable thickness, though based on the structure of γ−Al2 O3 , was also utilized by one of us in previous studied as a plausible model in the early stages of passivation. 39–41 Adsorbates were adsorbed on the top-side of the slab model, i.e., on the ultrathin oxide film. The bottom three layers of Al(111) underneath the oxide film were kept fixed, whereas all other degrees of freedom were relaxed. The thickness of the vacuum region was set to at least 15 ˚ A and a dipole correction of Bengtsson 42 was applied to cancel an artificial electric field that develops along the direction normal to the surface due to periodic boundary conditions imposed on the electrostatic potential. The BZ integrations of the oxidized Al(111)–(4 × 4) model were performed using a uniformly shifted 3 × 3 × 1 k-mesh. In the present work many molecular configurations were considered, but typically only the most stable identified configurations are presented and discussed. 2.2

A Model Silanol

For the sake of definiteness the interactions between the silanols themselves and the oxidized metal surface were studied with the CH3 Si(OH)3 molecule, although a few specific calculations were performed with the (CH3 )3 SiOH molecule. To simplify the denotation the methyl group will be designated by Me, CH3 ≡ Me, and therefore: CH3 Si(OH)3 ≡ MeSi(OH)3 , (CH3 )3 SiOH ≡ Me3 SiOH. Often an even simpler denotation will be used to designate the MeSi(OH)3 molecule, i.e., R3 SiOH and occasionally R2 Si(OH)2 . The structure and different representations of MeSi(OH)3 molecule are shown in Figure 2; the molecule has three OH groups and a methyl group bonded to an Si atom. Me3 SiOH on the other hand only has a single

OH group and is thus suitable for the analysis of various possible molecule–surface interactions; it was therefore used only to estimate the strength of individual adsorption bonds and it will be specifically indicated when results refer to it.

Me HO

Si

SiR3

OH

=

= H

HO

O

Figure 2. Three different representations of the chosen model silanol molecule, MeSi(OH)3 , where Me stands for methyl. From left to right: skeletal chemical formula, 3D space-filling model, and a simplified representation.

Standalone molecular species were modeled in large boxes with at least 15 ˚ A of vacuum between periodic replicas. The Martyna Tuckerman correction 43 was applied to better approximate an isolated system. Molecular calculations were also performed in the aqueous phase using the self-consistent continuum solvation model of Andreussi et al., 44 where default parameters for water were applied. 2.3

Energy Equations

We will rely on a few energy quantities that are defined below. The reaction energy change (∆E) is calculated as the difference between the sum of the total energies of products and the sum of total energies of the reactants: ∆E = Eproducts − Ereactants =

products X i

Ei −

reactants X

Ej .

(1)

j

Unless stated otherwise, the reactions considered are not necessarily elementary and can involve one or more intermediate steps. The strength of a particular bond is evaluated by the binding energy (Eb ) or the bond-strength (D). The Eb of the bond between fragments A and B is calculated as: Eb = EAB − EA − EB , (2) where AB designates either a standalone molecule or a molecule/surface adsorption system and Ei designates the total energy of a species i, where i = A, B, or AB. Depending on the type of bonding, fragments A and B can either be radicals or intact molecular species (for radicals spinpolarization was taken into account). By convention the bond-strength D is positive and hence opposite to binding energy, D = −Eb . Note that in the case of non-dissociative molecular adsorption the molecule–surface binding energy is synonymous with adsorption energy. Other energy quantities will be defined when used. It should be noted that energy quantities reported in this work, such as ∆E and Eb defined above, are calculated at


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zero temperature without the zero-point correction, unless explicitly indicated otherwise. 2.3.1

In contrast, for standalone silanols (momomers and oligomers) and water molecules the contributions from translational and rotational modes were considered—these modes were treated using the ideal-gas approximation and the rigid rotor model—and the pV term was taken into account, i.e.:

Enthalpies and Gibbs Free Energies

In this study only the thermodynamic feasibility of reactions is considered without any kinetic aspects. To better describe thermodynamic aspects of the polymerization of standalone silanols and their adhesion to hydroxylated aluminum surfaces via the condensation mechanism, we also calculated reaction enthalpies (∆H) and reaction Gibbs free energies (∆G) at temperature T = 298.15 K and for gaseous species at partial pressure p = 1 atm. To this end, computationally the most intensive task is the calculation of vibrational partition function. To make the vibrational calculations of surface structures feasible with our available computational resources, we had to reduce the thickness of the slab models and the k-point sampling. In particular, the thickness of the Al support below the oxide film was reduced to two Al(111) layers, whereas the BZ integrations were performed only with the Γ k-point. For these calculations all degrees of freedom were relaxed and vibrational frequencies were evaluated at the Γ q-point using the PHonon code 45 from the Quantum ESPRESSO distribution. 23 Thermal energies (including zero-point energies) and entropies were calculated by coding the respective statistical mechanics equations into the dynmat.x code of the PHonon package (see Section S1 in the Supporting Information). Vibrational contributions to thermal energy and entropy were calculated using a quasi harmonic approximation of Cramer-Truhlar 46 within which the vibrational frequencies below 100 cm−1 are raised to 100 cm−1 in order to approximately correct for the breakdown of the harmonic oscillator model for low-frequency vibrational modes (note that at room temperature 100 cm−1 corresponds to about 12 RT , where R is the gas constant). For surfaces and adsorbates thereon, only the vibrational contribution to thermal energy and entropy was taken into account, whereas the pV term was neglected for enthalpy and Gibbs free energy (dimensional analysis reveals that for solids this term is negligible at ambient pressures); also the configurational entropy of adsorbates was neglected. Enthalpy and Gibbs free energy are calculated by superposing vibrational contributions to thermal energy and entropy of the computationally-reduced slab model, with the KohnSham total energy obtained with the full slab model (E0full ) at zero temperature without zero-point energy, i.e.: red H(T ) = E0full + Evib (T ) + pV red ≈ E0full + Evib (T )

(3)

and red G(T ) = H(T ) − T Svib (T ),

(4)

red where Evib (T ) and S(T )red vib are vibrational thermal energy (including the zero-point energy) and entropy of the computationally-reduced slab model, respectively.

Page 4 of 18

H(T ) = E0 + E(T ) + pV = E0 + Etrv (T ) + kT,

(5)

G(T ) = H(T ) − T Strv (T ),

(6)

and

where Etrv (T ) and Strv (T ) are translational–rotational– vibrational thermal energies and entropies, respectively, while k is the Boltzmann constant. Our treatment is therefore analogous to that followed in ref 47. Once the enthalpies and Gibbs free energies of all the species involved in a given reaction are calculated, the reaction enthalpies ∆H and reaction Gibbs free energies ∆G are obtained analogously to eq (1). 3

Results and Discussion This section consists of three subsections. The first subsection addresses the oligomerization of standalone MeSi(OH)3 monomers. In the second subsection we demonstrate that even in the presence of low-pressure water vapor the oxidized Al surface is hydroxylated. Finally, in the last subsection we characterize the adsorption of silanols on anhydrous and hydroxylated oxidized Al surfaces.

3.1

Polymerization of Standalone MeSi(OH)3

Condensation polymerization reactions between standalone silanol molecules have been extensively studied, both theoretically and experimentally, 10,12–14 thus we first compare our corresponding results to those available in the literature. For the formation of dimer and trimer the respective reactions are: 2R3 SiOH → R3 Si–O–SiR3 + H2 O, 3R3 SiOH → R3 Si(OSiR2 )2 R + 2H2 O.

(7) (8)

These two reactions were modeled with MeSi(OH)3 monomers both in vacuo and in the aqueous phase; for the latter the solvent was described implicitly. 44 The corresponding results and the reaction schemes are shown in Figure 3. The reaction energy (∆E) for the formation of the dimer via the condensation mechanism is exothermic. The in vacuo ∆E value is −0.22 eV (−0.11 eV/monomer), which is in line with the value of −0.21 eV obtained by Catlow et al. 48 for an analogous reaction of Si(OH)4 . In the aqueous phase the ∆E is −0.18 eV (−0.09 eV/monomer). The in vacuo ∆G is −0.03 eV and its magnitude is smaller in comparison to ∆E. This is almost exclusively a consequence of the decrease in roto-translational entropy


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(a) +

Me Si

HO

+

OH

HO

+

∆E=−0.22 eV (−0.18 eV)aq

HO

Me

Me

Si

Si

OH OH

HO

∆G=−0.03 eV

HO

Me O

Si

OH +

H 2O

OH

(b)

∆E=−0.07 eV ∆G=−0.09 eV

(c)

3×

+ 2×

∆E=−0.59 eV (−0.43 eV)aq

Me

Si

Me

3×

HO

Si

OH OH

OH

O ∆G=−0.17 eV

Me

HO HO O Si Si

HO

Me

+ 2H2O

HO

Figure 3. Skeletal and 3D space-filling representations of the condensation reactions between (a,b) two and (c) three MeSi(OH)3 monomers. In (a) and (c) the reported ∆E and ∆G values are calculated with respect to completely separated noninteracting components; in vacuo values are written in black and aqueous phase values are written in parentheses and colored blue. (b) 3D space-filling representation of H-bonded reactant and product complexes (H-bonds are indicated by thin black dotted lines) involved in the dimer formation along with the corresponding in vacuo ∆E and ∆G.

when two free standalone R3 SiOH molecules form a dimer and a water molecule, 49 whereas vibrational contributions largely cancel out. In most of the literature the ∆E with respect to interacting reaction complexes is typically calculated and to provide an additional comparison to the results of other groups we calculated it as well (see Figure 3b). The respective ∆E for the dimer formation is −0.07 eV which coincides with the value obtained by Schaffer et al. 14 for the dimerization of Si(OH)4 . The corresponding ∆G = −0.09 eV, which is very similar to the ∆E value. This corroborates the above analysis, i.e., the roto-translational entropies of the two complexes are very similar, because they have the same molecular mass. Note that both reactant and product complexes in Figure 3b have three hydrogen bonds, hence contributions stemming from H-bonds largely cancel in the ∆E; consequently this ∆E reflects the net gain only due to “pure” condensation,

that is, Si–OH and SiO–H bond-breaking and SiO–Si and HO–H bond-making. On the other hand, the formation of the dimer from standalone components (Figure 3a) additionally involves the formation of an H-bond. From these two considered cases it can be therefore inferred that a single H-bond and a “pure” condensation step contribute −0.15 and −0.07 eV to the ∆E, respectively. As for the trimer, the in vacuo ∆E for the most stable identified configuration is −0.59 eV (−0.20 eV/monomer), while the respective ∆G is −0.17 eV. The ∆E value can be remarkably well explained by the above decomposition analysis, in particular, the formation of the trimer (cf. Figure 3c) involves two “pure” condensation steps and three H-bonds, hence ∆E = 2 × (−0.07) + 3 × (−0.15) = −0.59 eV. Thus the greater exothermicity (per monomer) exhibited by the trimer formation in comparison with the dimer formation is a consequence of the extra intramolecular H-bonds that form within the trimer. In the aqueous phase the ∆E is −0.43 eV (0.14 eV/monomer), but the most stable identified configuration (not shown) has only two intramolecular H-bonds (one less than in the gasphase). Notice that 2 × (−0.07) + 2 × (−0.15) = −0.44 eV, which is very close to −0.43 eV. Another way to look at this result is that the preference of the trimer over the dimer is diminished in the aqueous phase, because the oligomers can form either intramolecular H-bonds within themselves or intermolecular H-bonds with solvent water molecules. 3.2

Hydroxylation of the Oxide Film

In the presence of water vapor, water molecules can adsorb, at least in principle, either dissociatively (forming hydroxyl groups on the surface) or non-dissociatively. 50,51 Both modes of adsorption were considered on our model of the oxidized surface, as to ascertain which of the two is more stable. In all considered cases the tetrahedral Al site was found to be the preferred adsorption site, whereas on the octahedrally coordinated Al ions no stable bonding mode was found. Molecular non-dissociative adsorption of water was described as: H2 O + ∗ → H2 O∗, (9) whereas dissociative adsorption of water was considered by the following reaction: 1 H2 O + ∗ → OH∗ + H2 , 2

(10)

where standalone ∗ designates a free adsorption site, while A∗ denotes an adsorbed species A. H2 is used here and later on as a convenient reference. This choice is physically sound not only because hydrogen evolution is known to occur on aluminum 52 but moreover because, according to our calculations, reaction 10 is preferred over the H2 O + O∗ + ∗ → 2OH∗ alternative on the current model. The respective average change in energy per water molecule



for reactions (9) and (10) is: ¯mol = ∆E

1 (EnH2 O/slab − Eslab − nEH2 O ) n

(11)

and ¯diss = ∆E

i 1h n EnOH/slab + EH2 − Eslab − nEH2 O , (12) n 2

where n is the number of water molecules per supercell and Eslab is the total energy per supercell of the anhydrous clean slab. EnH2 O/slab and EnOH/slab are the corresponding total energies of slabs with n adsorbed water molecules and n adsorbed OH groups per supercell, respectively. EH2 O and EH2 are the total energies of isolated H2 O and H2 molecules, respectively. TABLE 1: Average reaction energy change per water molecule ¯mol ) and dissociative (∆E ¯diss ) adsorption of for molecular (∆E water on the oxidized Al(111) surface. n denotes the number of water molecules (or hydroxyls) per (4 × 4) supercell. Coverage (Θ) is given in ML and % units; 1 ML corresponds to one O atom per surface Al atom of Al(111), whereas 100 % corresponds to all occupied tetrahedral Al ions on the surface (recall that octahedral Al ions do not bind adsorbates). n 1 2 4 8

Θ (ML) 1/16 1/8 1/4 1/2

Θ (%) 12.5 25 50 100

¯mol ∆E (eV/H2 O) −0.61 −0.56 −0.50 −0.55

¯diss ∆E (eV/H2 O) −1.40 −1.41 −1.64 −1.63

The calculated values for the change in energy for both adsorption modes at various coverages are summarized in Table 1. Note that there are 8 tetrahedrally and 8 octahedrally coordinated surface Al ions per supercell (cf. Figure 1), hence we considered up to 8 water molecules per supercell, which corresponds to a relative coverage of 100 %, because—as already stated above—the octahedrally coordinated Al ions do not bind adsorbates. The non-dissociative molecular adsorption energy of wa¯mol ) is about −0.6 eV irrespective of the surface ter (∆E coverage, whereas dissociative adsorption of water is considerably more exothermic. At low coverage the respective ¯diss is about −1.4 eV, while at high coverage the value ∆E reaches about −1.6 eV. Our calculations therefore clearly indicate that water molecules favor dissociative adsorption on the supported ultrathin oxide film, which results in a hydroxylated surface. At low coverage the standalone OH∗ prefers to bond to the top site (middle panel of Figure 4a), but at high coverage the bridge sites become competitive. Even more so, a stronger OH∗ bonding at higher coverage stems from a stable configuration in which all bridge sites in a single row are occupied. On the (4 × 4) supercell such a configuration is possible only for coverages equal to or greater than 50 %. It is interesting to note that if all bridge sites in one row are occupied then an even more stable configuration can

Page 6 of 18

form with OH∗ at top sites on the second row; these topbonded OH∗ are interconnected with H-bonds and form a zig-zag pattern. The combination of these two adsorption sites is found to be the stablest at full hydroxylation and is shown in the right panel of Figure 4a. To determine the optimal coverage of OH∗ groups on the surface at given conditions (temperature T and partial pressure p), the stability of surfaces with varying degrees of hydroxylation is considered in the framework of atomistic thermodynamics. 53 The change of Gibbs free energy for dissociative adsorption of n water molecules per supercell according to reaction (10) can be written as: ∆Gdiss = GnOH/slab +

n GH2 − Gslab − nGH2 O , 2

(13)

where various G terms have analogous meaning to respective E terms used above. In this equation the G terms representing solids can be approximated with the DFT calculated total energies, i.e. GnOH/slab −Gslab ≈ EnOH/slab − Eslab (for these calculations the vibrational contributions to thermal energy and entropy were neglected), whereas the free energies of H2 O and H2 can be expressed with respective chemical potentials. Within the ideal-gas approximation, the chemical potential of molecular species i can be written as µi (T, pi ) = µi (T, p0 ) + kT ln(pi /p0 ), where p0 stands for a given standard pressure and i = H2 O or H2 . As for the reference state of µi (T, p) the DFT calculated total energy of molecular species is taken, i.e., µi (0K, p0 ) ≡ µ0i = Ei . By defining the ∆µi as: ∆µi = µi − µ0i = µi − Ei ,

(14)

the ∆Gdiss can be written after some simple algebraic manipulation as: ¯diss + 1 ∆µH − ∆µH O ), ∆Gdiss ≈ n(∆E 2 2 2

(15)

where we consider the ∆µH2 and ∆µH2 O as independent; the atmosphere in contact with the surface acts as a ther¯diss modynamic reservoir of H2 and H2 O. Note that ∆E is normalized to a single water molecule, whereas ∆Gdiss is normalized to the supercell, hence the factor n. It is convenient to renormalize the ∆Gdiss to the unit-area as to obtain the quantity that can be termed as dissociativeadsorption surface free energy, i.e., γdiss =

∆Gdiss , A

(16)

where A is the area of the supercell. Utilizing eq (16) the stability of surfaces with varying degrees of hydroxylation was investigated by calculating the dependence of γdiss on water and hydrogen chemical potentials, γdiss ≡ γdiss (∆µH2 , ∆µH2 O ). The results are summarized in Figure 4, from which it is clearly seen that irrespective of the two chemical potentials the fully hydroxylated surface with 8OH∗ groups per supercell is the most stable, unless the chemical potential of water (hydrogen) is


Page 7 of 18

clean surface

OH*/supercell OH/supercell

8OH*/supercell

(a)

top

(10−15 atm, 300 K)

−1.2

10

−20

−1.6 −25

−1.8 −2.0 −2.0 −1.8 −1.6 −1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −0.2 ΔµH2O (eV) (b) 10−25

10−20

800

1 10−15 10−10 10−5 Preasure (atm) @ 300 K 600 400 Temperature (K) @ 1 atm

0.0

0

OH*/supercell 2OH*/sup

−10

ace

8OH*/supercell

−1.0

10

−20 −30

4OH*

8O

ur f

−0.8

H*

ns

4OH*/supercell

−1.4 10

1200

ΔµH2 (eV)

10−15

−0.6

cle a

1000

Pressure (atm) @ 300 K

800

10−5 10−10

(1 atm, 300 K)

−0.4

400

Adsorption surface free energy [meV/Å2]

−0.2 1

an

0.0

105

200

600

✔

most stable surface

bridge

cle

0

Temperature (K) @ 1 atm

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


4OH*/supercell

ercell

/supe rcell

/su pe

rce l

l

−40 −2.0 −1.8 −1.6 −1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 ∆µH O [eV/molecule] (c) 2

105

200

0

Figure 4. (a) Topviews of the oxidized surface with different degrees of hydroxylation; two possible sites (top and bridge) for OH∗ binding to the surface are shown on the far left. At lower OH∗ coverage the top site is preferred, but at high coverage the bridge site becomes competitive. (b) A two-dimensional phase diagram for the hydroxylation of the ultrathin oxide film on the Al(111) substrate as a function of water and hydrogen chemical potentials. The phase diagram was constructed by considering reaction (10) and eq (16); molecular adsorption of water is not considered because it is always inferior to dissociative adsorption (cf. Table 1). Using the ideal gas approximation, the dependence of each chemical potential was also recast into a temperature scale at partial pressure p = 1 atm and into a pressure scale at T = 300 K (shown by two additional axes for each chemical potential). (c) Excerpt of dissociative-adsorption surface free energy, γdiss of eq (16), as a function of ∆µH2 O at ∆µH2 = 0 for various OH∗ coverages. Phase diagrams of (b,c) clearly show that the fully hydroxylated surface (8OH∗/supercell) is the most stable surface, except when the water (hydrogen) chemical potential is so low (high) that the clean anhydrous surface becomes the stablest. The water pressure axis in (b) reveals that at room temperature even traces of water vapor are sufficient to make the 8OH∗ phase the stablest. In between the domain of the clean and fully hydroxylated surfaces there is a tiny region where the half-hydroxylated surface (4OH∗/supercell) is the stablest (e.g. at ∆µH2 O ∈ [−1.62, −1.64] eV for ∆µH2 = 0). For illustrative purposes, the two crosses shown in the domain of the 8OH∗ phase indicate (p, T ) points for standard 1 atm and super ultra-high-vacuum 10−15 atm pressures at T = 300 K and pH2 O = pH2 (note that the vapour pressure of water at room temperature is 0.0313 atm).

so low (high) as to make the clean anhydrous surface the stablest. There is only a very tiny region in between the domains of fully hydroxylated and clean surfaces, where the half-hydroxylated surface with 4OH∗ groups per supercell is the stablest. In Figure 4b the dependence of each chemical potential was also recast into a temperature scale at partial pressure p = 1 atm and into a pressure scale at

T = 300 K. The water pressure axis reveals that at room temperature even traces of water vapor are sufficient to make the surface fully hydroxylated. This observation is not specific to our model of the film, because similar conclusions were also reached for pristine and metal supported surfaces of γ-Al2 O3 , although the absolute coverage corresponding to full hydroxylation depends on the model of the



surface. 39,40,54,55 Weak H

Si(CH3)3

O

1.89 Å

H

O

Strong

Si(CH3)3

O H

O

H

1.95 Å

Si(CH3)3

O

Al

Si(CH3)3

O

2.06 Å

Al

oxide film

oxide film

oxide film

oxide film

aluminum

aluminum

aluminum

aluminum

O···HO*

OH···Osurf

O→Alsurf

1.69 Å

O−Alsurf

Figure 5. Schemes of different possible molecule/surface interactions, the corresponding binding energies and molecule– surface bond lengths for Me3 SiOH. Below each scheme the respective bond designation is stated. The missing hydrogen atom in the strong bonding mode is indicated with a dashed green circle.

3.3

Adsorption Bonding modes of Silanoles

3.3.1

Individual Molecule–Surface Interactions

A typical adsorption mode of the MeSi(OH)3 molecule with the hydroxylated surface involves several different concomitant interactions, hence it would be convenient to decompose this integral molecule–surface bonding into individual components as to understand how each of them contributes to the overall bonding. To model only one interaction at a time, we consider the bonding of an alternative silanol molecule, Me3 SiOH, which contains only a single OH group, with either the anhydrous clean surface or the surface with a single standalone OH∗ per supercell (these two surfaces are shown in the left and middle panel of Figure 4a). Four different interactions were considered and the bond strength of each was calculated with eq (2); these interactions are depicted schematically in Figure 5. The first three modes involve the bonding of the intact Me3 SiOH molecule with the surface, i.e., (i,ii) H-bonding to an OH∗ group or to a surface O ion and (iii) dative bonding to a surface Al ion, whereas the last mode involves (iv) the interaction of a dissociated Me3 SiO species with a surface Al ion. The bonding modes from (i) to (iv) are designated as O· · · HO∗, OH· · · Osurf , O→Alsurf , and O–Alsurf , respectively, where Osurf and Alsurf designates the O and Al ions on the surface of the oxide film (occasionally the subscript “surf” will be omitted for brevity). From the calculated binding energies and bond lengths, reported in Figure 5, it can be seen that the first three interactions are weak: bond strengths of the two H-bonds are about 0.2 eV, whereas that of the dative O→Al bond is about 0.6 eV. In contrast, the last interaction is very strong, the bond strength is about 4.5 eV. Notice also that the molecule–surface bond length is considerably shorter for the strong O–Al bonding mode (1.7 ˚ A) compared to the weak dative O→Al bond (2.1 ˚ A), whereas the two H-bond lengths are between 1.9 and 2.0 ˚ A. The difference in binding energies for the inves-

Page 8 of 18

tigated modes is also reflected in charge density difference plots (Figure 6), which clearly show that the charge accumulation resulting from bond formation is the greatest for the strong O–Al bonding mode, while for the other modes it is notably diminished and follows the order: O→Alsurf > O· · · HO∗ ≈ OH· · · Osurf . 3.3.2

Adsorption Bonding of MeSi(OH)3 with Anhydrous Surface

Next we turn to our model molecule, MeSi(OH)3 , which has three OH groups with which it can form up to three bonds with the surface. To aid in scrutinizing individual interactions involved in the molecule–surface bonding, we first analyze the adsorption on the anhydrous surface. Both non-dissociative and dissociative adsorption modes are considered, which are described by the following reactions: R3 SiOH + ∗ → R3 SiOH∗ (17) and

1 (18) H2 2 the respective changes in energy are calculated analogously to eqs (11) and (12); here we model only one molecule per supercell (n = 1). Dissociative adsorption involves the breaking of a silanol O–H bond, hence the remaining H atom has to bond elsewhere or leave the surface. Similarly as in the analysis of water dissociation the H2 molecule was chosen as the hydrogen sink. The most stable identified non-dissociative and dissociative adsorption modes are shown in Figure 7 along with respective energy changes. In the non-dissociative adsorption mode the molecule forms three weak bonds with the surface: two OH· · · Osurf hydrogen bonds and a dative O→Alsurf bond. The respective adsorption energy is about −1 eV, which corresponds to the sum of individual interactions as estimated in Figure 5, i.e., 2 × (−0.2) + (−0.6) = −1.0 eV. In the dissociative adsorption mode the molecule also forms three bonds with the surface: one strong O– Alsurf bond and two weak bonds: one OH· · · Osurf hydrogen bond and one dative O→Alsurf bond. This corresponds to the gross molecule–surface binding energy of Eb ≈ −4.5+−0.2+−0.6 = −5.3 eV, where the values from Figure 5 were used as estimates of individual involved interactions (it will be shown below that these estimates are reasonable). The respective change in energy is −2.31 eV. Therefore the dissociative mode of adsorption is thermodynamically preferred, because it is by 1.3 eV lower in energy than the non-dissociative mode (∆E of −2.3 vs −1.0 eV, cf. Figure 7) even when bond-breaking is accounted for. Note that in addition to the molecule–surface bonding, reaction (18) also involves the silanol O–H bond-breaking and half of the H–H bond-making. Similarly as in the case of non-dissociative adsorption, the ∆E is also reasonably described by the sum of calculated individual involved contributions, i.e. ∆Ediss ≈ Eb + D(O–H)R3 SiOH − 0.5D(H–H) = −5.3 + 5.2 − 0.5×4.5 = −2.35 eV, where R3 SiOH + ∗ → R3 SiO∗ +


Page 9 of 18 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

The Journal of Physical Chemistry Δρmin= −0.006 e/a03

Δρmax= +0.006 e/a03

O···HO*

Δρmin= −0.012 e/a03

OH···Osurf

Δρmax=+0.012 e/a30

O−Al

O→Alsurf

Figure 6. Charge density difference, ∆ρ(r) = ρmol/slab (r) − ρmol (r) − ρslab (r), plotted along the bonding plane for different molecule/surface interaction modes shown schematically in Figure 5. Note that the ∆ρ(r) is plotted with two different scales to more clearly reflect the bonding, in particular a lower density scale is used for the two H-bonding modes (seven contours from −0.006 to +0.006 e/a30 ) and a higher density scale is used for O→Alsurf and O–Al bonding modes (seven contours from −0.012 to +0.012 e/a30 ). Red (blue) color represents electron charge excess (deficit) regions, i.e., electrons flow from blue to red regions.

SiR3

H

O

SiR3

H

2 eV −1.0

O

+

oxide film

−2.3 1

aluminum

oxide film

eV

O oxide film

SiR3

+ ½H2

aluminum

aluminum

sideview

sideview

topview

topview

Figure 7. Schematic representation of adsorption of MeSi(OH)3 silanol on the anhydrous oxidized Al surface. The left reaction path shows non-dissociative molecular adsorption, whereas the right reaction path shows dissociative adsorption. For each reaction path only the most stable identified structure is shown (top- and side-view) along with the respective reaction energy. Note that dissociative adsorption involves the breaking of a silanol O–H bond and the remaining H is assumed to form H2 .

Eb is the gross molecule–surface binding energy (estimated above), D(O–H)R3 SiOH is the O–H bond-strength of R3 SiOH and D(H–H) is the bond-strength of H2 . 3.4

Adsorption of Silanols on Hydroxylated Surfaces

As demonstrated in section 3.2, the oxidized surface of aluminum is fully covered by hydroxyl groups even when only traces of water are present in the environment. In the

case of the fully hydroxylated surface the non-dissociative adsorption of MeSi(OH)3 would involve up to three Hbonds between the molecule and the surface OH∗ groups. From Figure 5 we can estimate that the corresponding binding energy should be about −0.6 eV. As for the dissociative adsorption on the fully hydroxylated surface, it can proceed via a condensation mechanism, which is similar to the one that occurs between two R3 SiOH monomers [cf. reaction (7)] and is commonly proposed for the formation


The Journal of Physical Chemistry SiR3 O

O

H

+

H

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

O

∆E=−0.91 eV

oxide film

oxide film

aluminum

aluminum

SiR3

+ H 2O

of the silanol bond with the surface, i.e.: R3 SiOH + OH∗ → R3 SiO∗ + H2 O.

(19)

(20)

where R2 SiO∗O∗ designates a bidentate species, that is, a species that bonds with two O atoms thus forming two strong O–Alsurf bonds. However, the reaction (20) and the respective energy change is not very convenient for the evaluation of the thermodynamic feasibility and stability of bidentate formation. Instead it is considered as a further condensation step of the parent monodentate, i.e., we utilize the following two sequential reactions and respective energy (enthalpy) changes to describe the formation of monodentate and bidentate modes:

Substitution of a Standalone OH∗ Group

We analyze the condensation reaction (19) in a reductionist manner and therefore first consider it on a simplified surface model that consists of a standalone OH∗ (i.e. the model shown in the middle panel of Figure 4a). The corresponding schematic representation of the reaction is shown in Figure 8. The resulting configuration of R3 SiO∗ is the same as the one described above for the dissociative adsorption on the anhydrous surface (Figure 7 right) with the molecule–surface binding energy of Eb = −5.3 eV. However, the current ∆E of −0.9 eV is smaller in magnitude if compared to the −2.3 eV of the anhydrous surface, which is mainly due to the cost of breaking the OH– surface bond. Again the ∆E is well described by the sum of the calculated individual contributions involved in bond-breaking and bond-making. In particular, ∆E = Eb − D(OH–surface) + D(O–H)R3 SiOH − D(O–H)H2 O = −5.3 + 4.4 + 5.2 − 5.2 = −0.9 eV, where the value of 4.4 eV was used for the OH–surface bond and 5.2 eV for the O–H bond of H2 O, while other values were already used above. If the ∆E of −0.9 eV is compared to −0.2 eV obtained for the MeSi(OH)3 dimerization (cf. Figure 3a), it is possible to conclude that the reaction with the surface is favored in comparison to the reaction with another R3 SiOH molecule. Further analysis reveals that the reaction with the surface is favored, because it is easier to break the OH–surface bond (4.4 eV) than the Si–OH bond (5.7 eV). 3.4.2

stituted OH∗ groups and the number of water molecules formed per adsorbed species. Monodentate bonding therefore stems from reaction (19), whereas bidentate bonding results from the following reaction: R2 Si(OH)2 + 2OH∗ → R2 SiO∗O∗ + 2H2 O,

Figure 8. Reaction scheme for the condensation reaction between a silanol and a standalone OH∗ group on the oxidized Al surface (the respective surface model is shown in the middle panel of Figure 4a). The structure of the product R3 SiO∗ is the same as that shown on the right of Figure 7.

3.4.1

Page 10 of 18

Condensation Reactions on the Fully Hydroxylated Surface

Next the condensation reaction on the fully hydroxylated surface for the MeSi(OH)3 monomer, its dimer and trimer is considered. In this context we consider the monodentate and bidentate bonding modes. Defining Monodentate and Bidentate Bonding The two bonding modes are defined by the number of strong O–Alsurf bonds the adsorbate forms with the surface; this number is also equivalent to the number of sub-

R2 Si(OH)2 + OH∗ → R2 Si(OH)O∗ + H2 O,

∆X1 (21)

R2 Si(OH)O∗ + OH∗ → R2 SiO∗O∗ + H2 O,

∆X2 , (22)

where ∆X1 and ∆X2 (X ≡ E, H, or G) are used as criteria for evaluating the thermodynamic aspects of the two bonding modes. Note that ∆E values reported below are calculated at T = 0 K without the zero-point energy corrections, whereas ∆H and ∆G are calculated (with zeropoint energies included) at a temperature of 298.15 K and for gaseous species at a partial pressures of 1 atm. For adsorption structures the configurational entropy is neglected and the coverage is one silanol molecule per (4×4) supercell (except in one case the coverage is two silanol monomers per supercell). Monodentate Bonding The most stable identified monodentate bonding configurations for the monomer, dimer, and trimer along with the respective reaction schemes and changes in thermodynamic potentials are presented in Figure 9. Note that for each considered case the reported ∆E1 and ∆H1 values are very similar, whereas the respective ∆G1 values are by about 0.4 eV more positive. The reason for more positive values of ∆G1 compared to ∆H1 can be traced to the loss of freedom upon the adsorption of the silanol (i.e. the silanol is immobilized), even though a water molecule is liberated during the reaction. However, a water molecule is less massive than the silanols (note that roto-translational entropy contributions are proportional to the logarithm of the molecular mass) and also has a rotational symmetry number of 2, which further reduces its rotational entropy. The reaction enthalpy for the monodentate bonding of the monomer is exothermic, ∆H1 = −0.84 eV (Figure 9a). The ∆E1 value of −0.87 eV is similar to the one observed for the substitution of a standalone OH∗ group and indicates that the interaction is equally strong on both considered surfaces. Similar values in the two cases can be understood by considering the involved interactions. In both cases the molecule forms one strong O–Alsurf bond and


Page 11 of 18 (a) monomer H

O

H

O O H

+

oxide film

O

H

∆E1=−0.87 eV ∆H1=−0.84 eV ∆G1=−0.50 eV

aluminum

H

O

O

O

SiR3

SiR3

∆E ≡ ∆E(T=0 K) w/o ZPE

H

∆H ≡ ∆H (T=298.15 K, p=1 atm) + H 2O

oxide film aluminum

sideview

topview

sideview

topview

O SiR 3 i H R 2S O O O

(b) dimer O O H

+

H

O

SiR 3

O

H

O

H

R 2Si

∆G ≡ ∆G (T=298.15 K, p=1 atm)

∆E1=−0.73 eV ∆H1=−0.71 eV ∆G1=−0.26 eV


H

+ H 2O


sideview

topview

topview

(d) O SiR 3 O i S i R2 R 2S H O O O

(c) trimer


−0.1

∆E1=−0.49 eV ∆H1=−0.48 eV ∆G1=−0.08 eV

oxide film

∆G 1

−0.2

+ H 2O

aluminum

sideview

∆X1 (eV), X ≡ E, G, H

O O H

+

H

H

O

SiR 3

O

R 2S

O

H

O i 2S i R

0.0

H

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


−0.3 −0.4

trimer

−0.5

∆H 1

−0.6 −0.7 dimer

−0.8 −0.9

topview

sideview

∆E 1

monomer 0

1 2 3 Number of intramolecular H−bonds

Figure 9. Monodentate formation on the fully hydroxylated surface via a condensation mechanism for the silanol (a) monomer, (b) dimer, and (c) trimer. The topview and sideview of the hydroxylated surface are shown only in (a), because they are the same in all three cases. Only the most stable identified structure for each monodentate species is shown, along with the respective reaction change in thermodynamic potentials (for more detailed snapshots of these structures see Figure S1 in the Supporting Information). The conditions at which ∆E1 , ∆H1 , and ∆G1 were calculated are indicated by the legend at the top-right. (d) The reduction of the magnitude of ∆E1 , ∆H1 and ∆G1 as going from monomer to trimer correlates with the number of intramolecular H-bonds that are broken upon adsorption of the standalone silanol. The number of such H-bonds is 0, 1, and 3 for the monomer, dimer and trimer, respectively (cf. Figure 3). The H-bond strength, calculated from the slope of the ∆E1 line in (d), is 0.12 eV, thus being in reasonable agreement with 0.15 eV as inferred in section 3.1 from the dimer alone.


The Journal of Physical Chemistry H

O O H

O

oxide film

∆H1=−0.84 eV ∆G1=−0.50 eV

aluminum

SiR3

∆H=−0.19 eV ∆G=−0.03 eV

∆H=−0.05 eV ∆G=+0.21 eV H

O O H

H

O

H

aluminum

SiR 3

O

O


SiR3

O

∆H=−0.11 eV ∆G=+0.05 eV O

H

O O H

H

O

O

SiR 3

aluminum

O Si i R2 R 2S

O

O

O SiR 3

O

H

H

O i 2S i R R 2S

H

O

H

∆H=−0.34 eV ∆G=−0.14 eV

oxide film

2H2O +

O SiR 3

i R 2S O O

+ 2H2O ∆H1=−0.71 eV ∆G1=−0.26 eV

SiR3 H

O

H

O

oxide film

Si H 2O + R 2

SiR3 H

H

H

O

O

+ H 2O

O

H

H

aluminum

SiR3

SiR3 O

H

oxide film

H

O

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

+ 3H2O ∆H1=−0.48 eV ∆G1=−0.08 eV


Figure 10. Reaction scheme of possible paths leading to monodentate bonded trimer on the fully hydroxylated surface via a condensation mechanism.

several weak interactions. In the current case there are two OH· · · Osurf and two O· · · HO∗ hydrogen bonds (see the respective topview snapshot in Figure 9a), which contribute about 4 × 0.2 = 0.8 eV to the bonding, whereas in the case of the substitution of a standalone OH∗ group (cf. Figure 8) there is one OH· · · Osurf hydrogen bond (0.2 eV) and one dative O→Alsurf bond (0.6 eV), contributing again about 0.8 eV to the bonding. It is interesting to note that on the hydroxyl free surface the bonding O atom of the silanol adsorbs on the top site, while on the fully hydroxylated surface it bonds to the bridge site for all considered cases; a similar trend was discussed above for the OH∗ group (i.e. at low coverage OH∗ bonds to the top site, but at high coverage the bridge sites also become populated). For the silanol dimer the formation of monodentate molecule–surface bonding is also exothermic, ∆H1 = −0.71 eV. (Figure 9b). Although this value is slightly smaller in magnitude than that for the monomer–surface bonding, it is still by about 0.4 eV more exothermic than for the dimer bonding with the standalone monomer (cf. Figure 10). Finally, the ∆H1 for the monodentate adsorption mode of the trimer is −0.48 eV (Figure 9c). This value is lower in magnitude than those obtained for the monomer and dimer, but this is a consequence of the extra intramolecular H-bonds within the standalone trimer that are broken upon adsorption. Indeed, we find that the reduction in the magnitude of ∆E1 and ∆H1 as going from the monomer to the trimer correlates with the number of intramolecu-

Page 12 of 18

lar H-bonds within the respective standalone silanol that are broken upon adsorption (Figure 9d); the number of such H-bonds is 0, 1, and 3 for the monomer, dimer and trimer, respectively (cf. Figure 3). ∆G1 values also display a similar trend, although the correlation with respect to the number of broken H-bonds is not as good as for ∆E1 and ∆H1 . The results presented in Figure 9 therefore lead to the conclusion that, regardless of the length of the silanol chain, the formation of the monodentate bonding with the surface is both exothermic and exergonic. If ∆H1 and ∆G1 values are compared to those obtained for the formation of the standalone dimer and trimer, it can be concluded that the formation of a bond with the surface is preferential to the formation of a bond with another silanol monomer unit—this is clearly evident from Figure 10, which schematically depicts various possible reaction paths as going from standalone monomers to monodentate adsorbed trimer—i.e., the adsorption of the monomer is preferential to the formation of a bond with another standalone monomer and the adsorption of the dimer is preferential to its condensation with another monomer to form a standalone trimer.

Bidentate Bonding For the successful adhesion of a siloxane layer on the aluminum surface, the formation of multiple strong O–Alsurf bonds with the surface is required. Thus the possibility of the formation of additional strong bonds with the surface for the monomer, dimer and trimer was also investigated. In particular we modeled the formation of the bidentate as a further condensation step of the parent monodentate via reaction (22). In this context the consideration of distances between nearby OH∗ groups is relevant. For our model the distance between them is about 3 ˚ A within the row, whereas the distance between OH∗ groups in adjacent rows is between 4 and 5 ˚ A. An O–O distance of about 3 ˚ A is typical in aluminum oxide and hydroxide polymorphs and similar distances in our model further validate its use. For the bidentate bonding mode the substitution of both nearest and more distant OH∗ groups (i.e., OH∗ in the same row and in adjacent row) was considered and only the most stable identified monomer, dimer, and trimer configurations are presented in Figure 11 along with the respective reaction schemes and accompanying changes in thermodynamic potentials. In contrast to the monodentate formation described above, here the Gibbs free energies are more negative than the enthalpies, by about 0.5 eV. This larger exergonicity of ∆G2 compared to ∆H2 can be largely attributed to the liberation of a water molecule during the reaction, i.e., the rototranslational contribution of a gas-phase water molecule to the free energy at T = 298 K and p = 1 atm is about −0.5 eV. For the monomer the formation of an additional strong O–Alsurf bond with the surface is considerably endothermic, ∆H2 = 1.13 eV (Figure 11a). This value is so large


H

O

R2Si

O

H

O

O

H

(a) monomer

O ∆E2=+1.24 eV ∆H2=+1.13 eV ∆G2=+0.49 eV


O

SiR2

O

+ H 2O


sideview

sideview

topview

topview

(b) dimer

H

O Si i R2

R 2S O

O

O H

O

H

H ∆E2=+0.08 eV ∆H2=+0.04 eV ∆G2=−0.47 eV


O

R2Si

O

O

SiR2 O

+ H 2O


sideview

sideview

topview

(c) trimer

topview

O Si i R2

O R 2S i S 2 H R O O oxide film aluminum

O

O H

SiR2 R2Si

H

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


H

Page 13 of 18

O ΔE2=−0.14 eV ΔH2=−0.19 eV ΔG2=−0.65 eV

H

O

oxide film

SiR2 O

+ H 2O

aluminum

sideview

sideview

topview

O

O

topview

Figure 11. Reaction schemes for the bidentate formation considered as a further condensation step of the parent monodentate for the silanol (a) monomer, (b) dimer, and (c) trimer. Only the most stable identified structure for each monodentate and bidentate species is shown (for more detailed snapshots of these structures see Figures S1 and S2 in the Supporting Information). The arrows on the zoom-up snapshots (shown on the right for each species) indicate strong Si–O–Al bonds.



O

R2Si O

O

H

H

OH

+ oxide film

SiR3 H

O

aluminum

∆H=−0.21 eV ∆G=+0.14 eV

H

O

H H O O R2Si R2Si O

H

O Si i R2

R 2S O

O

aluminum

+ H 2O

aluminum

∆H=+0.04 eV ∆G=−0.47 eV

∆H ∆G =− =− 0.0 0. 3 e 26 V eV H

O

R2Si O

+ H 2O oxide film

O

oxide film

∆H=−0.07 eV ∆G=+0.21 eV

O

O H

H

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

O

SiR2 O

+ 2H2O ∆H=+0.18 eV ∆G=−0.40 eV


Figure 12. Reaction scheme for the bidentate formation of the dimer. Two possible reaction paths are considered and both consist of two elementary steps. The starting point of the two paths is the same: a monodentate bonded monomer. In the upper path this monomer first reacts with a standalone monomer thus forming a monodentate dimer, which in the second step transforms into bidentate dimer (this elementary step is depicted in Figure 11b). In the bottom path the standalone monomer instead first adsorbs adjacent to a preadsorbed monodentate bonded monomer and then in the second step these two adjacent monomers transform into a bidentate bonded dimer. Note that each elementary step releases a water molecule. Although the overall reaction (indicated by the diagonal arrow) is both marginally-exothermic and exergonic, the first elementary step is endergonic and the second step is endothermic, regardless of the pathway taken.

that the reaction is endergonic even when the favorable entropy contributions are taken into account, ∆G2 = 0.49 eV. This implies that the bidentate bonding mode is improbable for the monomer and reactions with other monomer units are preferential. For the dimer the ∆E2 is 0.08 eV and ∆H2 is 0.04 eV (Figure 11b). Both values are considerably smaller than those obtained for the monomer, though still marginally endothermic. On the other hand ∆G2 with a value of −0.47 eV is exergonic, due to favorable entropic effects of liberated water molecule. It should be noted that the reaction path considered by Figure 11b is not the only way that leads to a bidentate bonded dimer. Alternatively, such a configuration can also form via the condensation of two adjacent monodentate monomers; these two possibilities are schematically depicted in Figure 12. This alternative reaction, though slightly less favorable (∆H = +0.18 eV and ∆G = −0.40 eV) than the one considered in Figure 11b, is also thermodynamically feasible. It is interesting to note from Figure 12 that if one considers the formation of a bidentate dimer as a net reaction starting from standalone and monodentate bonded monomers than the

Page 14 of 18

reaction is exergonic and also marginally exothermic with a ∆G of −0.26 eV and ∆H of −0.03 eV. Such a net reaction was considered by Motta et al. 21 in the case of fluoroalkyl silanes on the boehmite surface and they found the reaction thermodynamically favorable. However, breaking the reaction into elementary steps we find that, regardless of the path taken, the first step is always endergonic and the second step is always endothermic (Figure 12). Finally for the trimer the formation of the second strong O–Alsurf bond is found to be both exothermic, ∆H2 = −0.19 eV, and exergonic, ∆G2 = −0.65 eV (Figure 11c). In this case the bidentate formation is more thermodynamically favorable than any considered condensation between standalone silanols (cf. Figure 10) and is the preferred pathway. Current calculations therefore reveal a clear trend concerning the bidentate formation, i.e., the longer the silanol chain in terms of monomer units the more likely the bidentate bonding to the surface. The reason for the high endothermicity of ∆H2 for the monomer can be attributed to the strained configuration the monomer has to adopt to form two O–Alsurf bonds. Consequently, the longer is the chain the more flexible is the oligomer and the easier it adopts to the bidentate bonding. This is evident from the trend of ∆H2 as going from the monomer to the trimer (Figure 11). Bidentate formation in aqueous phase Due to obvious modeling reasons, all the surface reactions presented above were modeled at the solid/gas interface, although experimentally the solid/liquid interface is the relevant one. A way to obtain the reaction Gibbs free energies in the aqueous-phase is via a thermodynamic cycle, 56 which in addition to the quantities reported above, requires the hydration free energies of the involved species. To this end, the reaction Gibbs free energies for the bidentate formation can be roughly estimated by first observing from the snapshots of Figure 11 that the structure of a given monodentate and its associated bidentate is to some extent similar. We thus infer that the respective hydration energies should largely cancel out in ∆G2 calculation. As for the free energy of liquid water, it can be obtained by utilizing the equilibrium between liquid water and its vapor, H2 O(l) H2 O(g). At T = 298.15 K the water vapor pressure is 0.0313 atm, hence the Gibbs free energy of liquid water is: p (23) GH2 O(l) = G0 + kT ln 0 = G0 − 0.09 eV, p where G0 is the Gibbs free energy of gas-phase water at T = 298.15 K and partial pressure of 1 atm. This implies that the so approximated aqueous-phase ∆G2 values are by −0.09 eV more exergonic than those reported in Figure 11. The respective aqueous-phase ∆G2 values are therefore estimated to 0.40, −0.56, and −0.74 eV for the monomer, dimer, and trimer, respectively, and the physical picture described above still holds.


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4


Conclusions

Supporting Information

By means of DFT calculations we investigated the feasibility of the commonly used hypothesis that the adhesion of the sol-gel network to the aluminum surface is achieved by forming Si–O–Al chemical bonds via the condensation mechanism. According to our calculations the formation of a monodentate bonding mode on the hydroxylated surface via the condensation mechanism is exothermic and exergonic for all considered oligomers. However, for the strong adhesion of a siloxane layer on the aluminum surface, the formation of multiple strong O–Al bonds with the surface is required. In this context, we found that the formation of a bidentate bonding mode as the subsequent condensation step is appreciably endothermic, roughly athermic, and exothermic for the monomer, dimer, and trimer, respectively. However, when entropic effects are taken into account the bidentate formation becomes exergonic already for the dimer. The monodentate to bidentate transformation is therefore determined by the interplay between entropy and energy. Although the oligomer size at which the bidentate formation becomes feasible may depend on the model of the surface, the trend that the longer the oligomer chain the more likely the formation of the bidentate bonding mode with the surface is clearly established. Moreover, due to the similar distributions of OH groups on the model used in the present paper and on other alumina polymorphs we are rather confident that this result is extendable to other models as well as to realistic passive films, which are amorphous but retain some short range order. Our results therefore imply that each siloxane unit in the molecular layer above the alumina surface can form at most one strong Si–O–Al bond. Moreover, some units likely act as molecular spacers between the units that bind to the surface via the Si–O–Al bond as to reduce the strain. Finally, we observed all along this paper that the overall reactions energies can be well described by the sum of individual interactions involved in bond-breaking and bondmaking, which we attribute to the local character of the bonding among and within the species considered in this work.

Acknowledgments

The authors thank Prof. Ingrid Miloˇsev and Peter Rodiˇc for valuable discussions. This work is a part of the MEra.Net project COR ID: Design of corrosion resistant coatings targeted for versatile applications, co-financed by the Slovenian Ministry of Education, Science, and Sport (Grant No. 3330-16-500040) and by the French National Research Agency (Grant No. ANR-15-MERA-0004). MP and AK also acknowledge the financial support from the Slovenian Research Agency (Grant No. P2-0393).

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Table of Contents (TOC) Image

endothermic endergonic O

Si

O

O

Si

Si

O

O Si

Si

exothermic exergonic

athermic exergonic

Si

Si O

O

O

Si

Si

O

Si O

O

O

Si

Si

O

O O

Si

O

O Si

Si

O

O

Si

O

O

O

O

O

O

O

O

O

OH

O

OH

Al

Al

Al

Al

Al

Al

Al

Al

Al

Al

Al

Al

strain is reduced


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Insight into the Bonding of Silanols to Oxidized ... - ACS Publications

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