The Brønsted-Lowry strength of an acid in a homogeneous gas or solution is defined by how readily it donates a proton. In a heterogeneous environment, however, where the separation between a donated proton and its conjugate base is determined by the chemical asymmetry of the interface, hydrogen bonding, and molecular ordering, characterizing acidity becomes nebulous. The gas-solid interface complicates the picture of acidity through the adsorption of molecules to specific sites that can tune proton transfer via specific molecule-surface interactions.
In this scenario, molecular acidity is not determined by the properties of the molecule or the surface independently, but rather by adsorption and interfacial proton dissociation. This complexity motivates us to develop a paradigm of gas-solid interfacial acidity that advances the fundamental description of acid strength beyond that found in homogeneous gaseous or solution environments. Such a paradigm can be then be used to elucidate acid-base reactivity at a range of interfaces.
Perovskites, a broad class of oxide materials, have shown promise in the synthesis of materials ranging from biofuels to pharmaceuticals via heterogeneous acid-base catalysis. To date, several studies have pursued a fundamental understanding of the acid-base character of the surface in catalytic reaction mechanisms, [1][2][3][4][5][6][7][8][9] wherein the acidic or basic nature of metal-oxide surface sites was investigated by monitoring the products of a small alcohol probe molecule, such as isopropanol, reacting at the surface of strontium titanate (SrTiO 3 , henceforth abbreviated as STO): at an acidic site, a single isopropanol molecule can undergo dehydration to form propylene and water, while at a basic site, acetone and H 2 are formed via dehydrogenation. 5,[10][11][12][13][14][15][16] However, an opposite trend was found for ethanol; Foo et al. recently found that the rate of ethanol dehydrogenation increases with the ratio of acidic sites on multifaceted STO nanocubes. 3 This apparent contradiction emphasizes the need to understand the acidity of alkanols at an oxide surface and clarify the mechanisms that control it at the molecular level.
We elucidate the scaling of interfacial acidity of a family of small alkanols with structural and chemical variations when adsorbed to a well-defined and atomically flat STO(100) surface using a combination of density functional theory (DFT) and vibrational sum-frequency generation (SFG) methods. SFG experiments selectively probe interfacial molecular species [17][18][19][20] by providing vibrational spectra that are compared with DFT results. 15,21 Using this combined DFT+SFG approach, we describe the mechanisms of adsorption and proton transfer in terms of the interactions of aliphatic alcohols with the oxide surface, with a focus on the structure of the alkanol. To this end, we are able to bridge previous theoretical investigations of alkanol adsorption on STO(100), 5 revealing the essential role of hydrogen bonding on the adsorption equilibria. Finally, we describe the interfacial acidity of the series of aliphatic alcohols from methanol to butanol on STO(100) using partition functions constructed from DFT calculations, and compare the structure-acidity relationships to the known, corresponding relationships in the gas phase and in aqueous solution. While the current study focuses on an oxide surface, the proposed paradigm of interfacial acidity might provide mechanistic insight into bond dissociation, radical formation, and radical dissociation involving proton transfer at other complex interfaces. 22,23 Our investigation commences with a study of the adsorption of isopropanol on the TiO 2 -terminated surface of STO(100). In the first section, we compute the pathway for isopropanol adsorption, leading to a description of a two-state equilibrium on the surface. We then implement SFG not only to experimentally verify the presence of this two-state chemisorption equilibrium for isopropanol, but also to reveal similar equilibria for other alkanols on STO(100), with characteristic spectral shifts related to hydrogen-bonding interactions. We ultimately apply these two-state equilibria to calculate the interfacial Brønsted-Lowry acid strengths of alkanols and determine the structural and chemical factors that control the acidity.
DFT calculations were performed using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional 24,25 and Grimme's D3 method of dispersion correction 26,27 within the Vienna ab initio Simulation Package (VASP). [28][29][30] For all atoms, projector-augmented-wave potentials (PAW) were used to describe electron-core interactions. 31,32 To allow for electron localization on the STO(100) surface, a Hubbard-U correction of 11.0 eV was applied to the 3d orbitals of Ti atoms, using the approach introduced by Dudarev et al. 33 This correction was chosen as it resulted in a calculated band gap of 3.24 eV for bulk STO, similar to that found experimentally (3.25 eV). 34 An energy cutoff of 400 eV was used for the planewave basis set, and partial orbital occupancies were described using Gaussian smearing with a width of 0.05 eV. The bulk lattice constant was calculated to be 4.02 Å, in comparison to an experimental value of 3.91 Å. 35 The TiO 2 -terminated STO(100) surface was modeled by a 3 Â 3 Â 3 supercell with an additional layer of TiO 2 along the z-direction to allow for TiO 2 termination on both sides.
A vacuum layer of 24 Å was added above the top surface layer. The total number of atoms in the supercell was 162, and adsorption of one isopropanol molecule created an adsorbate coverage of 1/9 of a monolayer (ML). The Brillouin zone of the cell was sampled using a 3 Â 3 Â 1 Monkhorst-Pack k-point grid. 36 Geometry optimizations were performed using the quasi-Newton algorithm, 37 allowing the adsorbate species and the top-most layer of STO (57 atoms) to relax until the force on each atom was less than 0.01 eV Å À1 . Transition states were calculated using the climbing-image nudged elastic band method. 38
Sample preparation and characterization followed previous work; 15 characterization results are shown in Section II of the ESI. ‡ Similarly, a comprehensive description of the SFG spectrometer used in this experiment can be found elsewhere. 39,40 Briefly, the output of a Spectra Physics Spitfire Pro Ti:Sapphire amplifier (output: 6 W, 1 kHz repetition rate, 45 fs pulses, centered near 800 nm) was split into two paths. The first path was directed into an optical parametric amplifier with difference-frequency mixer to generate broadband mid-infrared (IR) pulses tuned to excite the -OH stretching region. Approximately 2.4 W of the remaining laser output was directed into a pulse shaper to produce time-symmetric narrowband nearinfrared (NIR) pulses 39,40 used for up-conversion. The polarizations of both arms were passed through polarizers and subsequently rotated with half waveplates before being collinearly combined with a dichroic optic. The beams were focused onto the STO(100) surface at an angle of 601 relative to the surface normal. An achromatic doublet collected the radiated SFG light before being polarization-resolved, filtered, spectrally resolved and detected with a CCD camera. SFG spectra were background-subtracted and scaled by the nonresonant response obtained from the bare STO(100) sample in the PPP polarization combination. The IR beam path and sampleenvironment enclosures were continuously purged with dry nitrogen to limit IR attenuation from atmospheric water and to limit adsorption of water to the STO(100) interface during measurements. 41,42 The measured SFG intensity is proportional to the modulussquare of second-order susceptibility, w (2) eff , and the incident driving laser fields, E IR and E NIR :
The effective second-order susceptibility, w (2) eff , is the sum of resonant and non-resonant, w (2) NR , contributions:
where o IR is the frequency of incident IR laser light, o q is the resonance-transition frequency, A q is the mode-specific amplitude, and G q is related to the linewidth. Eqn (2) shows that when the incident broadband IR light has spectral components that are resonant with molecular vibrations, there is an
This journal is © the Owner Societies 2021 enhancement in the radiated signal. This enhancement serves to map the vibrational spectrum in an analogous way to conventional IR or Raman spectroscopies but, owing to the even-order field interaction (see eqn (1)), in a surface specific manner. 43 Measured SFG intensity data was fit to eqn (1) and
(2) and used in subsequent analysis.
3 Results and discussion weakened (E ads = 0.42 eV). Notably, the adsorption of isopropanol in any of the four orientations does not cause significant distortion of the surface structure.
DFT results for dissociative adsorption of isopropanol following transfer of the hydroxyl proton from adsorbed isopropanol to the neighboring surface oxygen for the ''a-H close'', ''CH 3 away'', and ''a-H away'' orientations are shown in Fig. 2. Because the ''OH away'' orientation is comparatively weakly bound and unlikely to undergo proton transfer due to its orientation, it was not included in the remainder of our study. Our computations reveal that proton transfer results in the formation of two adsorption states: one in which the proton is still hydrogen-bonded to the alkoxy oxygen (Fig. 2a), and another in which the hydrogen bond has broken to fully dissociate the proton from the isopropoxide (Fig. 2b). The adsorption energies of the hydrogen-bonded forms are E ads (''a-H close'') = 1.40 eV, E ads (''CH 3 away'') = 1.34 eV, and E ads (''a-H away'') = 1.38 eV, whereas the adsorption energies of the non-hydrogen-bonded forms are E ads (''a-H close'') = 1.43 eV, E ads (''CH 3 away'') = 1.48 eV, and E ads (''a-H away'') = 1.48 eV.
A comparison of adsorption energies in Fig. 1 and2 shows that dissociative chemisorption of isopropanol is more favorable than non-dissociative, molecular physisorption of isopropanol for all molecular orientations. Similarly, the second chemisorbed form possessing no hydrogen bond is adsorbed more strongly than the hydrogen-bonded form. Section I.C of the ESI ‡ shows the bond lengths and angles involving the Ti, surface oxygen, alkoxy oxygen, and transferred proton in the physisorbed and chemisorbed forms of isopropanol. Notably, when the hydrogen bond breaks, the proton moves closer to the TiO 2 -surface plane to increase interactions with other nearby surface oxygens. As a result, the angle between the proton-oxygen surface bond and the surface normal changes from 14-171 in Fig. 2a to 64-661 in Fig. 2b. This large change in the orientation of the bond might have important effects on the subsequent reaction pathways of isopropanol.
Table 1 shows the calculated activation energies for dissociative chemisorption and subsequent hydrogen-bond breakage of isopropanol on STO(100). The calculated value of 0.24 eV for proton transfer in the ''a-H away'' orientation is similar to that found in the literature. 5 Zero-point corrections reduce the activation energy for proton transfer to 0.12 AE 0.05 eV and negligibly change the activation energy for hydrogen-bond dissociation. The low values of activation energies suggest that adsorbed isopropanol exists in a thermal equilibrium between the molecular and dissociated forms. A Boltzmann population analysis shows that at 298 K, 0.01% of the adsorbed isopropanol exists in the molecular form, 3.00% exists in the deprotonated and hydrogen-bonded form and 96.98% exists in the deprotonated and hydrogen-bond-broken form. Predictably, an increase in temperature increases the relative population of the hydrogen-bonded form. At 500 K, relevant to the catalytic transformations of isopropanol, 5,15,16 0.46% of the adsorbed isopropanol exists in the molecular form, 10.98% exists in the deprotonated and hydrogen-bonded form and 88.57% exists in the deprotonated and non-hydrogen-bonded form. Fig. S6 in the ESI ‡ shows the energy pathways and Boltzmann populations of all orientations for each adsorbate species at 298 K.
To test the robustness of the computed qualitative differences between the energy pathways of the three orientations, we performed single-point calculations on PBE-optimized geometries and transition states using the RPBE functional, 44 as described in Section I.D. of the ESI. ‡ Tables S4-S6 in the ESI ‡ show that while the absolute energy of each species is lowered upon change from PBE to RPBE, the energy differences between species are similar between PBE and RPBE. Further, Fig. S7 and S8 in the ESI ‡ show energy scans for rotations of the hydrogenbonded and hydrogen-bond-broken forms of the chemisorbed isopropoxide among their three orientations. The scans show two noteworthy qualitative results. First, the rotational energy barriers are much lower for the hydrogen-bonded than the hydrogen-bond-broken form, suggesting that it is kinetically far more likely for the hydrogen-bonded form to rotate between the three orientations compared to the hydrogen-bond-broken form. Second, the energy barrier to rotate out of the ''a-H away'' orientation is the highest of the three orientations for both the hydrogen-bonded and hydrogen-bond-broken forms, showing that this orientation is not only thermodynamically, but also kinetically the most stable among the three orientations of the chemisorbed species.
Previous work examined the C-H stretching region of isopropanol adsorbed on STO(100) at 298 K and mapped the absolute orientation of adsorbed isopropanol using SFG methods. One of the key orientational angles was defined as the bisector of the CH 3 -C-CH 3 moiety in isopropanol to form an angle, y (CH3)2 , of 29 AE 71 with respect to the surface normal, and another, along the aC-H bond, formed an angle, y CH , of 51 AE 81. 15 These measured angles strongly agree with the corresponding calculated angles of the deprotonated forms of isopropanol in the ''a-H close'' orientation (Fig. 2). This result also corroborates our theoretical results using Boltzmann population analysis (vide supra) that the adsorption equilibrium largely favors the chemisorbed over the physisorbed form of isopropanol.
To search for the existence of our DFT-predicted chemisorbed forms of alcohols on STO(100), we measured the SFG spectra in the O-H stretching region for methanol, ethanol, isopropanol, and sec-butanol in the SSP polarization combination, with data and fits plotted in Fig. 3. The spectrum of each alcohol adsorbed on STO(100) shows a narrow, intense band at around 3640 cm À1 and a broad, lower-intensity band at around 3550-3600 cm À1 . Based on a normal-mode analysis of the dissociatively chemisorbed forms of the four alcohols, as shown in Table 2, the broad, lower-frequency band is assigned to the O surface -proton stretch when the proton is hydrogenbonded to the adsorbed alkoxide, and the narrow, higherfrequency band is assigned to the ''free'' O surface -proton stretch wherein the hydrogen bond is disrupted. This experimental result with computationally aided assignment directly supports a two-state chemisorption equilibrium. Due to the low Boltzmann population of the physisorbed form of the alcohol, the O alkoxy -proton stretch does not appear in the spectrum. Both DFT and SFG results show very little variation in the O surface -proton stretching frequency for the broken-hydrogenbond species across the four alcohols. In the SFG spectra, these frequencies for ethanol, isopropanol, and sec-butanol were nearly identical, and DFT finds a range of only 12 cm À1 over corresponding values. This is expected based on the typical ''free'' OH stretching vibrations that do not interact with neighboring species. However, the O surface -proton stretching frequencies for the hydrogen-bonded species in the SFG spectra vary over the four alcohols and parallel the frequencies predicted by DFT, with sec-butanol 4 methanol 4 isopropanol 4 ethanol. The change in the stretching frequency arises from the increase in the strength of the hydrogen bond, as corroborated by a calculated variation in the lengths of the hydrogen bond (i.e., O alkoxy -proton distance): 1.95 Å (sec-butanol) 4 1.91 Å (methanol) 4 1.90 Å (isopropanol) 4 1.88 Å (ethanol). This agreement between DFT and SFG reinforces our assignment of the broad band in this region to the O surface -proton stretch in the hydrogen-bonded state and suggests that trace amounts of water are not responsible for the measured spectral features. The strength of the hydrogen bond is determined by the competition between the amount of electron density on the alkoxide oxygen and the extent of weakening of alkoxidesurface interactions due to geometric strain from the hydrogen bond. A similar trend is seen for the frequency of the O surface -proton wagging mode (see ESI, ‡ Table S7), which redshifts with decreasing strengths of the associated hydrogen bond.
Along with frequencies, ranges for O surface -proton stretching frequencies derived from DFT results are provided in Table 2. Spectral widths also show agreement between DFT and SFG values. For DFT results, the quoted widths are reported as average absolute deviations from the mean of three frequencies, corresponding to the three orientations shown for each of the two states in Fig. 2 (see ESI, ‡ Table S8). Both DFT and SFG affirm that the hydrogen-bonded state results in a broader spectral feature in comparison to the broken-hydrogen-bond state. Notably, a larger sampling of out-of-plane orientations is afforded in the more freely rotating hydrogen-bonded alkoxide compared to the broken-hydrogen-bond state due to a closer O alkoxy -Ti distance in the latter form (vide infra). This enhanced orientational freedom results in a broader O surface -proton stretch in the spectral feature for the hydrogen-bonded species.
The Brønsted-Lowry acidity (HA " H + + A À ) of an aliphatic alcohol is dictated by the polarizability of the alkyl moiety in the gas phase and solvation of the alcohol in the solution phase. In the gas phase, alkyl substituents on the a-carbon and longer alkyl chains help to polarize the electron cloud on the alkyl moiety in a direction that stabilizes the negative charge on the alkoxide conjugate base. Consequently, the gas-phase acidity increases as: methanol o ethanol o n-propanol o n-butanol o isopropanol o tert-butanol. [45][46][47][48][49] However, in aqueous solution, alkyl substituents on the a-carbon and longer alkyl chains weaken solvation of the conjugate base and increase the entropic penalty to the structure of water. Smaller alcohols and their conjugate bases are more soluble in water, with methoxide showing a greater solvation energy than tert-butoxide, for example. Consequently, in small alkanols, the solvation energy overcomes polarization effects, reversing, in solution, the acid-strength trend revealed for the gas phase. 45,46 The question is, how does this dichotomy change at the gas-solid interface? Table 2 Unscaled O surface -proton stretching frequencies for hydrogenbonded and broken-hydrogen-bond species of selected alkanols on STO(100), obtained from SFG and DFT. For isopropanol DFT frequencies, the mean frequency and average absolute deviation from the mean computed over three orientations (Fig. 2 Based on the two-state chemisorption equilibrium of alkanols on STO(100) described above, we define the interfacial Brønsted-Lowry acidity as: (H-A) ads " H ads + + A ads
, where the hydrogen-bonded species ((H-A) ads ) serves as the ''acid'' that donates its proton to the surface as the hydrogen bond is broken, resulting in the broken-hydrogen-bond ''conjugate base'' species (A ads À ). The interfacial acid (ia) dissociation constant, K ia , is defined as the ratio of temperaturedependent canonical partition functions of the products to the reactant (see ESI, ‡ Section I.H.). A stronger acid has a larger K ia , or lower pK ia (= Àlog(K ia )) resulting from the lower free energy associated with the broken-hydrogen-bond species compared to the hydrogen-bonded-species. We note that variations in K ia are dominated by changes in the ratio of electronic partition functions resulting from adsorption energies of the two chemisorbed forms for different alcohols (see ESI, ‡ Section I.H).
Fig. 4 shows the pK ia of the series of alkanols from methanol to butanol at 298 K, calculated using the most stable orientation for each alkanol. The values of pK ia are presented in Table S16 of the ESI. ‡ For each alcohol, the most stable orientation of the chemisorbed species is the one that brings the alkyl substituent(s) close to the surface, such as the ''a-H away'' orientations of isopropanol and sec-butanol. In the case of linear alcohols, the ''a-H away'' orientation is equivalent to the ''a-H close'' orientation, whereas in the case of tert-butanol, all three orientations are equivalent to each other. The optimized structures and adsorption energies for all alkanols are provided in Section I.F of the ESI. ‡ The relationships between the structure of the alkanol and its interfacial acidity on STO(100) are revealed by the plots of pK ia as a function of the number of carbons atoms, n carbons , (Fig. 4a), and as a function of the number of alkyl substituents on the a carbon, n branches , (Fig. 4b) in the alkanol. The linear fits of pK ia values of different groups of alkanols were created to highlight qualitative trends.
While the gas-phase acidity of alcohols increases with n carbons and n branches from methanol to butanol, and the corresponding aqueous acidity decreases with n carbons and n branches , the interfacial acidity increases with n carbons but decreases with n branches . On STO(100), longer alkyl chains stabilize the conjugate base by enhancing van der Waals interactions between the base and the surface, resulting in a decrease in pK ia with increase in n carbons as chain lengths are increased at constant a-C substitution (red lines in Fig. 4, see ESI, ‡ Section I.H). These interactions increase as the alkoxide approaches closer to the surface in the broken-hydrogen-bond form (O alkoxy -Ti = 1.91-1.93 Å in the broken-hydrogen-bond form compared to 1.95-1.96 Å in the hydrogen-bonded form across different alcohols). Furthermore, the strain in the O alkoxy -Ti-O surface angle is released, changing from 78-791 in the hydrogen-bonded species to 86-881 as the O alkoxy -Ti bond is nearly perpendicular to the surface in the broken-hydrogenbond species. In contrast, greater alkyl substitution on the a-carbon compromises these alkyl-surface interactions in the broken-hydrogen-bond form and linearly increases pK ia when the total number of carbons remains constant (green lines in Fig. 4), mainly by decreasing the number of a-hydrogen atoms that interact strongly with surface oxygen atoms. Increasing n carbons and n branches each by one (i.e., increasing chain length and a-C substitution simultaneously) increases pK ia (blue lines in Fig. 4), revealing the dominant role of substitution over chain length in dictating interfacial acidity. Simply put, interfacial acidity of the alcohol is controlled more by its van der Waals interactions with the surface than the polarizability of its alkyl chain, similar to the way aqueous acidity of the alcohol is controlled more by alcohol-water interactions than polarizability effects.
To examine the effect of increasing surface temperature on interfacial acidity, we calculated K ia and pK ia at 500 K. As shown in Table S17 and Fig. S14 of the ESI, ‡ K ia (pK ia ) of each alcohol is lower (greater) at 500 K than at 298 K, primarily due to a decrease in the ratio of the electronic partition functions with temperature. The weaker acidity of the alcohols ultimately signifies the greater relative population of the hydrogenbonded species at higher temperature, suggesting that this intermediate might play an important role in surface-promoted transformations of the alcohol at catalytically relevant temperatures. While the pK ia of each studied alcohol on STO(100) increases with temperature, the variations in pK ia with n carbons and n branches remain unchanged between 298 K and 500 K (see Fig. S14 of the ESI ‡), thereby demonstrating that the relationships between the interfacial alcohol-STO geometries and the resulting K ia are preserved over a wide range of temperature.
In summary, we determined the driving forces governing the interfacial Brønsted-Lowry acidity of small alkanols adsorbed on STO(100) using a combination of SFG and DFT methods. Our work shows that the structure-acidity relationships in the alkanols are overall qualitatively different at the gas-oxide interface as compared to homogeneous gas and aqueous phases. The similarities with chain-length dependence in gasphase acidity and alkyl-substituent dependence in aqueous acidity demonstrate that interfacial acidity produces a unique combination of contrary chemical trends observed in the two homogeneous phases. Our results show the critical and oftoverlooked role played by hydrogen bonding in controlling acidity at gas-solid interfaces and indicate its importance in acid-base transformations of alcohols on oxide surfaces at higher surface temperatures. Notably, the increase in relative population of the hydrogen-bonded chemisorbed intermediate with temperature, predicted computationally for all studied alcohols, strongly suggests that this intermediate is present for various small alcohols on STO(100) at catalytically relevant surface temperatures. Therefore, the equilibrium between the hydrogen-bonded and hydrogen-bond-broken chemisorbed species revealed by our computational and experimental results could play an important role in chemical transformations of alcohols on oxide surfaces. The conceptualization of interfacial acidity is generalizable to other interfaces and protic acids, permitting a comparison of acidity of different molecules on a given surface, and, ultimately, broadening the description of a fundamentally important chemical property central to understanding chemical transformations at a range of heterogeneous environments.
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