Anharmonicity and Confinement in Zeolites: Structure, Spectroscopy

Article pubs.acs.org/JPCC

Anharmonicity and Confinement in Zeolites: Structure, Spectroscopy, and Adsorption Free Energy of Ethanol in H‑ZSM‑5 Konstantinos Alexopoulos,† Mal-Soon Lee,‡ Yue Liu,§ Yuchun Zhi,§ Yuanshuai Liu,§ Marie-Françoise Reyniers,*,† Guy B. Marin,† Vassiliki-Alexandra Glezakou,‡ Roger Rousseau,*,‡ and Johannes A. Lercher*,‡,§ †

Laboratory for Chemical Technology, Ghent University, 9000 Gent, Belgium Institute for Integrated Catalysis, Pacific Northwest National Laboratory, Richland, Washington 99352, United States § Department of Chemistry and Catalysis Research Institute, TU München, Lichtenbergstrasse 4, 85748 Garching, Germany ‡

S Supporting Information *

ABSTRACT: To account for thermal and entropic effects caused by the dynamics of the motion of the reaction intermediates, ethanol adsorption on the Brønsted acid site of the H-ZSM-5 catalyst has been studied at different temperatures and ethanol loadings using ab initio molecular dynamics (AIMD) simulations, infrared (IR) spectroscopy, and calorimetric measurements. At low temperatures (T ≤ 400 K) and ethanol loading, a single ethanol molecule adsorbed in H-ZSM-5 forms a Zundel-like structure where the proton is equally shared between the oxygen of the zeolite and the oxygen of the alcohol. At higher ethanol loading, a second ethanol molecule helps to stabilize the protonated ethanol at all temperatures by acting as a solvating agent. The vibrational density of states (VDOS), as calculated from the AIMD simulations, are in excellent agreement with measured IR spectra for C2H5OH, C2H5OD, and C2D5OH isotopomers and support the existence of both monomers and dimers. A quasi-harmonic approximation (QHA), applied to the VDOS obtained from the AIMD simulations, provides estimates of adsorption free energy within ∼10 kJ/mol of the experimentally determined quantities, whereas the traditional approach, employing harmonic frequencies from a single ground state minimum, strongly overestimates the adsorption free energy by at least 20∼50 kJ/mol. This discrepancy is traced back to the inability of the harmonic approximation to represent the contributions to the vibrational motions of the ethanol molecule upon confinement in the zeolite.

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studies on adsorption of alcohols in zeolites,10−18 which makes it an ideal candidate for studying and benchmarking alternative theoretical methodologies. In particular, we are concerned by the role of anharmonicity on the potential energy surface and its impact on the entropy and enthalpy of adsorption. Recently, it has been shown that these contributions to the free energy are critical for a quantitative understanding of adsorption and confinement of alkanes in zeolites.19,20 Given the very flat potential energy surface for the proton transfer between the alcohol and the zeolite, finite temperature and dynamical effects must be considered to better understand the nature of adsorbed alcohols in zeolites.21 Moreover, for loosely bound complexes in zeolites with many soft degrees of freedom, entropy losses calculated based on the harmonic oscillator approximation can be greatly overestimated.22 Although ab initio molecular dynamics (AIMD) based schemes are the natural choice for

INTRODUCTION Zeolitic materials, such as H-ZSM-5, offer promising perspectives for the catalytic conversion of renewable biomass-derived alcohols into fuels and chemicals. Compared to metal oxides with diverse surface and acid properties, zeolites have relatively well-defined and uniform Brønsted acid site (BAS) structures, which lend themselves to rigorous kinetic and theoretical investigations on the requirement of acid strength and the effect of solvation environment and confinement on the reaction free energetics. Of particular interest for the current study is the role of confinement on the reaction entropy and enthalpy.1−9 Specifically, the present study addresses the critical role of anharmonic contributions to the vibrational partition function and ultimately the adsorption free energy of ethanol in H-ZSM-5. In acid-catalyzed reactions, adsorption is the first step leading to the protonation of the alcohol molecule, which weakens the strength of the C−O bond and makes the protonated alcohol more susceptible to elimination and substitution reactions.1 There have been a multitude of theoretical and experimental © 2016 American Chemical Society

Received: January 27, 2016 Revised: March 8, 2016 Published: March 21, 2016 7172

DOI: 10.1021/acs.jpcc.6b00923 J. Phys. Chem. C 2016, 120, 7172−7182

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The Journal of Physical Chemistry C sampling anharmonic and reactive systems, decomposition of the resulting free energetics into an entropic and an enthalpic term is highly challenging in light of the high computation cost of a single trajectory. The nature of the flat potential energy profile of the adsorbed alcohol has long been a matter of debate in the literature. Whether the alcohol becomes protonated or not upon adsorption on the Brønsted acid site still remains unclear based on experimental data.23,24 Molecular dynamics simulations of methanol in various zeolites have shown that the zeolitic proton fluctuates between the active site and the alcohol molecule, while the protonation of the alcohol becomes more significant with decreasing zeolite pore size.21 Upon adsorption of an alcohol molecule, the acid proton can be shared equally and symmetrically between the alcohol and the oxygen atoms of the zeolite cage (here denoted as a Zundel-like cation) or the alcohol can be directly protonated and hydrogen bonded to the walls of the zeolite cage (here denoted as an Eigen-like cation). Alternatively, the proton can be shared between two alcohol molecules when the alcohol loading is increased. The formation of such protonated ethanol dimers has already been reported both in the gas phase25 and in several zeolites.26 Here, we probe this issue in the context of ethanol adsorption by means of ab initio molecular dynamics and quasi-harmonic estimates of free energy.18−21 Computed free energy and vibrational density of states (VDOS) are compared with calorimetric and infrared (IR) measurements on carefully prepared H-ZSM-5 samples to validate our findings. Specifically, this work addresses the effect of temperature, loading, and deuteration on the structural, thermochemical, and spectroscopic properties of ethanol adsorption in H-ZSM-5. It is shown that the current AIMD simulations quantitatively account for the observed IR spectroscopic changes upon ethanol (and selected deuterated variants) adsorption in HZSM-5 as well as account for the measured adsorption enthalpy and entropy. Moreover, it is illustrated that the critical component for achieving this agreement is an accurate estimate in the changes to the VDOS associated with the low-frequency modes in ethanol upon adsorption and its impact on both zeropoint vibrational energy (ZPVE) and vibrational entropy, which can only be accounted for by acknowledging the anharmonic nature of the potential energy surface.

influence on the adsorption energy is included in section S1 of the Supporting Information. First, the cell parameters and atomic positions of the bare zeolite (H-ZSM-5 with Si/Al = 95) are optimized. Al12O24H, located at the intersection of these channels, is chosen as the acid site because of its accessibility for bulky reactants. Brändle and Sauer also proposed this location for the acid site.34 The optimized unit cell parameters, a = 20.47 Å, b = 20.11 Å, c = 13.58 Å, α = β = γ = 90°, are in very good agreement with experimental data (a = 20.1 Å, b = 19.9 Å, c = 13.4 Å, α = β = γ = 90°).35 Using the optimized zeolite unit cell, we further optimized monomeric and dimeric structures of ethanol adsorbed on the Brønsted acid site of H-ZSM-5. Both nondeuterated and deuterated ethanol variants were used (C2H5OH, C2D5OH, C2H5OD). We also optimized the structure of gas-phase ethanol with/without deuterium using a cubic box size of 20 Å. Molecular Dynamics Simulations. To determine the local structure and various thermodynamic properties, DFT-based ab initio molecular dynamics (AIMD) simulations are performed within the canonical NVT ensemble at various temperatures (T = 100, 300, 400, 500, 700 K) using a 0.5 fs time step and a Nosé−Hoover chain thermostat with a frequency of 1500 cm−1 to control the temperature. Three types of simulations were performed: bare zeolite, gas-phase ethanol, and ethanol adsorbed in zeolite. For each simulation, well-equilibrated trajectories of at least 50−100 ps were collected to obtain reliable statistical properties. Statistical averages were typically collected from the last 40 ps of the simulation, and statistical error bars were compiled by examining the convergence of the statistics with different time intervals. As discussed below, there is a transformation in the nature of the adsorbed intermediate at temperatures between 300 and 400 K. In this temperature range, we (i) verified the statistics using data with simulation time beyond 100 ps and (ii) conducted additional simulations at 300/400 K with the most equilibrated configuration from the 400/300 K run to confirm that the result was not strongly influenced by hysteresis. Spectroscopic properties were obtained from the vibrational density of states (VDOS) using the Fourier transform of the velocity−velocity time-correlation function

METHODS Computational Details. Electronic Energy Calculations. Periodic density functional theory (DFT) calculations are performed within the generalized gradient approximation (GGA) with the exchange correlation functional of Perdew, Burke, and Ernzerhoff (PBE)27 as implemented in the CP2K package.28 Grimme’s second-generation corrections (DFT-D2) are used to take into account dispersion forces or van der Waals interactions to describe energies more precisely.29 For the core electrons, norm-conserving pseudopotentials are used,30,31 while the valence wave functions are expanded in terms of double-ζ quality basis sets optimized for condensed systems to minimize linear dependencies and superposition errors.32 Electrostatic terms are calculated using an additional auxiliary plane-wave basis set with a 300 Ry cutoff.33 The Γ-point approximation is employed for the Brillouin zone integration because of the significant size of the supercell. An evaluation of alternate basis sets and van der Waals corrections and their

where v is the velocity and the angular brackets indicate the statistical average over time. Associated decompositions by projecting atom types out of the total VDOS (p-VDOS) enabled the assignment of the contribution from different species to the peaks in the vibrational spectra. IR spectra were also calculated from the Fourier transform of the autocorrelation of the total dipole moment. The harmonic approximation was used to extract the quantum correction factor that satisfies the fluctuation−dissipation theorem.36 The total dipole moment at each time step was evaluated using the Berry-phase approach,37 as implemented in CP2K. Quasi-Harmonic Statistical Thermodynamics. Although sampling of the configuration space of the nuclei is performed with a classical mechanics description of molecular dynamics, accounting for the quantum nature of the partition function is mandatory for a reliable representation of the statistical thermodynamics of the system. This is achieved by utilizing the obtained VDOS, which include classical descriptions of the anharmonicity of the system, in harmonic quantum partition

D(ω) =

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7173

∫0

∞

e−iωt ⟨ν(τ ) ·ν(τ + t )⟩dt

(1)


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The Journal of Physical Chemistry C functions for vibrations.18−21 We denote this method as a quasi-harmonic approximation (QHA), whereas we denote the traditional approach, based on static structures and harmonic vibrational modes often used in most quantum chemistry codes, as the harmonic approximation (HA). Free energetics as a function of temperature were studied by calculating the changes of entropy and enthalpy upon adsorption by deconvoluting the translational, rotational, and vibrational contributions. The translational and rotational entropies of the gas-phase ethanol molecule were calculated using the formulas38 ⎤ ⎡⎛ 24πemk T ⎞3/2 B ⎥ ⎟ Strans = R ln⎢⎜ σ σ σ ⎠ x y z ⎥⎦ ⎢⎣⎝ h2 Srot

⎡⎛ 8π 2 I I I A BC = R ln⎢⎜⎜ ⎢⎣⎝ σs

⎞⎛ 2πek T ⎞3/2 ⎤ B ⎟⎟⎜ ⎟ ⎥ 2 ⎠⎝ h ⎠ ⎥⎦

It should also be noted that all 3N degrees of freedom were treated as vibrational for the surface species (i.e., bare zeolite and ethanol adsorbed in zeolite). The standard adsorption entropies (ΔS°ads) and enthalpies (ΔH°ads) were calculated as

∫0

ωmax

(2)

3N − 6 Uvib = 2

3 kBT 2

∫0

ωmax

(3)

(4)

(5)

⎛ ℏω ⎞ ℏωcoth⎜ ⎟D(ω)dω ⎝ 2kBT ⎠

(8)

(9)

Applying this approach to an ensemble of structures obtained from AIMD provides both local anharmonicity, i.e., deviations in the computed vibrational frequencies associated with nonparabolic descriptions of local minima on the potential energy surface, and global anharmonicity arising from configurationally sampling of multiple minima and points on the potential energy surface that are far away from each other. A detailed comparison of the absolute entropy for gas-phase ethanol can be found in the Supporting Information (section S2), showing that our computed entropies are within 2% of those reported using the NASA polynomials, whereas the HA consistently underestimates entropy by as much as 4%. Experimental Details. Catalyst Postsynthesis Treatment. To reduce the effect of extra-framework Al on the local environment and the adsorption activity of Brønsted acid sites, a commercial H-ZSM-5 sample with a Si/Al ratio of 15 (CBV3024E, Zeolyst International) was treated with (NH4)2SiF6 (denoted as AHFS) according to the following procedure (see section S3 of the Supporting Information for IR spectra before and after this treatment). A 2 g amount of NH4ZSM-5 sample was added to 80 mLof deionized water, stirred in a 100 mL PTFE liner, followed by addition of 1.42 g (8.0 mmol) of AHFS to the solution and then stirring vigorously at 353 K for 5 h. The resulting product was centrifuged, rinsed six times with hot deionized water (353 K), and dried overnight at 393 K. The final calcination was done at 823 K for 5 h in 100 mL min−1 synthetic air with a heating rate of 10 K min−1. The concentration of Brønsted acid sites in the calcined sample was found to be 707 μmol/g based on pyridine titration. Gravimetric and Calorimetric Measurements. Gravimetric and calorimetric measurements were carried out with a Setaram TG-DSC 111 thermoanalyzer with a Baratron pressure transducer. The sample was pressed into thin wafers and subsequently broken into small platelets. Then, 10−15 mg of the platelet was placed into a quartz crucible of the balance and activated at 823 K for 1 h with a heating increment of 10 K min−1 under vacuum (p < 10−4 mbar). After activation, ethanol was added in pulses at 313 K. The weight increase and heat flux were measured during pressure equilibration with the adsorbate. As will be apparent below, to extract thermochemical data from the isotherm measurements, a two-step equilibrium where ethanol can adsorb either as a monomer (eq 10) or as a dimer (eq 11) was solved

where ℏ = h/2π and N is the number of atoms in a system. Note that the VDOS, D(ω), is calculated from the velocities, v, where the translational and rotational contributions have been projected out. In a similar manner, translational, rotational, and vibrational enthalpies were calculated using the formulas Utrans = Urot =

ΔH °ads = ΔET = 0K + ΔUtrans + ΔUrot + ΔUvib − RT

ΔG°ads = ΔH °ads − T ΔS°ads

⎡ ⎛ ⎞ ⎢ ℏω coth⎜ ℏω ⎟ ⎢⎣ 2kBT ⎝ 2kBT ⎠

⎛ ⎛ ℏω ⎞⎞⎤ − ln⎜⎜2sinh⎜ ⎟⎟⎟⎥D(ω)dω ⎝ 2kBT ⎠⎠⎥⎦ ⎝

(7)

where ΔET=0K is obtained from the optimized structures of ethanol adsorbed in zeolite, bare zeolite, and gas-phase ethanol. The standard state for gas-phase ethanol is taken as p° = 1 bar. Finally, the standard Gibbs free energies of adsorption (ΔG°ads) as a function of temperature were calculated as

where R is the universal gas constant, e = exp(1) is the Euler number, m is the molecular mass, kB is the Boltzmann constant, T is the temperature, h is the Planck constant, σx, σy, and σz are the principal root-mean-square (rms) fluctuations of the center of molecular mass as obtained from an AIMD trajectory, IA, IB, and IC are the average principal moments of inertia, and σs is the symmetry number (σs = 1). Note that the formula for the translational partition function takes into account the wobbling of the center of mass of the nonrigid gas-phase molecule as it undergoes vibrations and rotations. This representation has been shown to give a more accurate account of translational partition functions of nonrigid bodies than the standard formula which depends only on the reduced mass.38 The rotational motion for the gas-phase ethanol is decoupled from vibrations by first rotating the molecule into a unique reference at each MD time step and projecting out the component of the velocities associated with rotations. The moments of inertia, I, are calculated at each time step, and their average values ⟨IA⟩, ⟨IB⟩, and ⟨IC⟩ are used in eq 3 instead of the T = 0 K quantities based on static optimized geometries. This approach allows us to capture the impact of molecular deformations upon rotational and translational degrees of freedom and their contributions to the free energy. The vibrational entropy was obtained by a quasi-harmonic approximation employing the computed VDOS39−42 Svib = R(3N − 6)

ΔS°ads = ΔStrans + ΔSrot + ΔSvib

(6) 7174

* + EtOH(g) ↔ EtOH*

(10)

EtOH* + EtOH(g) ↔ (2EtOH)*

(11)


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The Journal of Physical Chemistry C

Figure 1. Radial distribution functions around Hα and Hβ of the adsorbed ethanol monomer on the BAS of H-ZSM-5 at different temperatures together with the color code used for the neighboring atoms.

Finally, the corresponding standard adsorption entropy (ΔS°i) is calculated for each adsorption step by using the following equation

where the asterisk (*) denotes a surface BAS (Brønsted acid site). The equilibrium constants, K1 and K2 for eqs 10 and 11, respectively, are associated with adsorption of monomeric species and addition of a second ethanol molecule to form dimers. Solving the coupled equilibrium between these adsorbed species and the gas-phase ethanol provides us with the fitting expression for the isotherm C EtOH = C BAS·

ΔSi° =

(12)

where pEtOH is the partial pressure of ethanol and CEtOH and CBAS are the concentrations of adsorbed ethanol and Brønsted acid sites, respectively: see section S3 of the Supporting Information for details on this derivation. This analysis allows the estimation of the equilibrium adsorption coefficients K1 and K2. Additionally, the standard adsorption enthalpy for monomer (ΔH°1) and dimer (ΔH°2) formation on the Brønsted acid site is found by fitting the calorimetric measurements to the following expression qdiff =

(14)

Infrared Measurements. IR spectra of adsorbed ethanol were measured on a Bruker IFS 88 spectrometer. The catalyst sample was pressed into self-supporting wafers and activated in vacuum for 1 h at 723 K. Ethanol was adsorbed at a pressure range from 0.001 to 1 mbar at 313 K. After reaching equilibration, spectra were recorded with a resolution of 4 cm−1 in the region between 400 and 4000 cm−1. Difference spectra were obtained by subtracting the spectrum of the bare catalyst.

2 K1pEtOH + 2K1K 2pEtOH 2 1 + K1pEtOH + K1K 2pEtOH

ΔHi° + R ·ln(K i) T

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RESULTS AND DISCUSSION First, the structural models obtained from our AIMD simulations are presented. Then comparisons with measured IR spectra of C2H5OH, C2D5OH, and C2H5OD in H-ZSM-5 are used to validate these models and to corroborate the ability of the theoretical simulations to reproduce the vibrational modes of these systems. Finally, a detailed analysis of the enthalpic and entropic contributions to adsorption is presented together with a discussion of the ramifications for modeling reactions in zeolites.

δCMo δC Di ( −ΔH1°) + ( −ΔH1° − ΔH2°) δC EtOH δC EtOH (13)

diff

where q is the differential heat of adsorption and CMo and CDi are the concentrations of adsorbed ethanol monomer and dimer, respectively. 7175


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Figure 2. Radial distribution functions around Hα, Hβ, and Hγ of the adsorbed ethanol dimer on the BAS of H-ZSM-5 at different temperatures together with the color code used for the neighboring atoms.

Figure 3. Most stable structures (at 0 K) of the adsorbed ethanol monomer of (a) a Zundel-like configuration, (b) a higher energy Eigen-like configuration, and (c) dimer on the Brønsted acid site of H-ZSM-5. Color code: Si (blue), Al (green), O (red), C (gray), H (white), H bonds (dashed blue).

Adsorbed Structures. The nature of the adsorbed species is described based on AIMD simulations performed to study the monomolecular and bimolecular adsorption of ethanol on the Brønsted acid site located at the intersection of the straight and zigzag channel of H-ZSM-5. Radial distribution functions, g(R), together with atom labeling are presented for monomers and dimers in Figures 1 and 2, respectively, and used to determine an average adsorbed structure at different temperatures and ethanol loadings. A histogram of distance difference between Hx−Oe and Hx−Oα or Hx−Oβ (x = α, β) (Figure S5), the fluctuations in the distances between H and O as a function of time (Figure S6), and the g(R) between the Al3+ site and Oe (Figure S7) are used to further explore the structural changes. In Figure 1, the g(R) for Hα of the adsorbed monomer at T = 100 K shows two overlapping peaks at ∼1.2 Å due to a Zundellike structure where the proton (Hα) is equally shared by the oxygen of the zeolite (Oα) and the oxygen of the ethanol (Oe). This is seen in Figure S5 as a strong peak at ∼0 Å. We also

notice a bonding interaction at 1.8 Å indicating a hydrogenbond formation between Hβ and one of the oxygen on the zeolite surface (Oz) that is not immediately adjacent to the acid site (Figures 1 and S6). We observe that complete proton transfer from the zeolite surface to ethanol can occur at T > 400 K, leading to an equilibrium mixture of both Eigen-like and Zundel-like species. This can more clearly be seen in Figure 1 for T = 500−700 K, where both Hα and Hβ interact with oxygens at the Brønsted acid site whereas the H bond with one oxygen on the zeolite surface (Oz) disappears and the g(R) shows a new peak at ∼1 Å indicating the transfer of Hα to the ethanol, i.e., forming protonated ethanol at these temperatures. However, both hydrogen atoms fluctuate between Zundel-like and Eigen-like ethanol structures as can be seen from the lower and broader intensity of the peak at ∼0 Å and the small peak at ∼1.5 Å in Figure S5 of the Supporting Information. Our AIMD simulations show that at low temperatures and ethanol loadings Zundel-like species are the dominant structural form for 7176


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Figure 4. Simulated difference VDOS at 300 K and experimental IR difference spectra at 313 K of nondeuterated and deuterated ethanol adsorbed in H-ZSM-5 at different ethanol loadings/pressures. (a−c) Difference VDOS obtained from AIMD. (d−f) Difference IR spectra at low (0.001 mbar) and higher pressures (1 mbar) where the dominant adsorbed species are assumed to be mostly monomers and dimers, respectively.

Vibrational Spectra. The structural models obtained from AIMD are validated by direct comparison with experimental IR difference spectra. Figures 4 and S4 show a compilation of pressure-dependent IR adsorption difference spectra for C 2 H 5 OH, C 2 D5 OH, and C 2 H 5OD, which are directly compared to calculations with the same isotopic substitutions for both monomeric and dimeric species. On the outset, we note that identification of surface species after ethanol adsorption on H-ZSM-5 is nontrivial due to the presence of a mixture of both monomeric and dimer species, which change in population with increasing ethanol loading. To facilitate comparison with experiment, the difference VDOS are presented by subtracting the VDOS of the pure H-ZSM-5 from that of the total system at the same temperature. Figure 4 shows a comparison between the vibrational density of states of ethanol adsorbed in H-ZSM-5 and the experimental IR difference spectra at low (pEtOH = 10−3 mbar) and high (pEtOH = 1 mbar) ethanol loadings for the three isotopomers. Overall, the agreement between the simulated and the measured spectra reported in Figure 4 is striking, indicating that the current models reproduce well all the salient features of the experimental data. Upon ethanol adsorption, the peak at 3610 cm−1 corresponding to the BAS disappears. As expected, a C− H stretching region appears at 2800−3100 cm−1 in the case of adsorbed C2H5OH and C2H5OD, while a C−D stretching region appears at 2000−2300 cm−1 in the case of adsorbed C2D5OH. Upon C2H5OH or C2D5OH adsorption, there is a new peak at 3550 cm−1, which is sharper at low ethanol loading and is attributed to the O−H stretch of nonprotonated ethanol that is H bonded to zeolite oxygen. The peak at 3550 cm−1 is also observed for the monomer species upon C2H5OD adsorption, but it is not observed for the dimer species upon C2H5OD adsorption. Apart from the intensity difference of this peak between low and high ethanol loading, another characteristic difference between the adsorbed monomer and dimer

monomeric adsorption of ethanol on H-ZSM-5 and that full deprotonation of the zeolite framework occurs from 400 K onward. To the best of our knowledge, this is the first study to report such a Zundel-like structure for the adsorbed ethanol monomer at ambient temperatures along with its transformation to the Eigen-like structure at higher temperatures. On the other hand, regardless of the temperature, increasing the ethanol loading to two molecules per acid site, the proton is completely transferred to the ethanol molecules which are in turn H bonded to the oxygen atoms surrounding the zeolite acid site (see, for example, the two right panels of Figure 2 at 300 K). The Hβ proton fluctuates between being bound to either molecule preferentially or being equally shared in a dynamic equilibrium. As such we denote this structure as an adsorbed protonated dimer. Figure 2 shows also that at T ≥ 400 K one ethanol moves away from the acid site, leading to a structure which is best described as a protonated ethanol stabilized by hydrogen bonding to an additional ethanol, i.e., the second ethanol molecule acts as a solvating agent stabilizing the protonated ethanol by H bonding. It is worth noting that Chiang and Bhan26 already reported the presence of such protonated ethanol dimers during ethanol dehydration over several zeolites. To obtain representative structures of the adsorbed ethanol monomer and dimer species that are needed for the calculation of adsorption energies at 0 K (see eq 8), several structures from the AIMD trajectories were slowly annealed to 0 K and further optimized at 0 K to remove any residual forces. The most stable structures at 0 K are shown in Figure 3. Although a single ethanol molecule in a Zundel-like ground state is the most stable at 0 K, the fully protonated ethanol is the most stable in the presence of a second ethanol molecule. These low-energy minima provide reasonable approximations to the adsorbed structures at finite temperature and are used as a basis to compute free energy, which will be discussed below. 7177


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Figure 5. (a) Simulated IR spectrum of monomeric and dimeric ethanol in H-ZSM-5 at 300 K. Partial VDOS at 300 K for Hα (red), Hβ (blue), and Hγ (green) of adsorbed C2H5OH (b) and C2D5OH (c) and for Dα (red), Hβ (blue), and Dγ (green) of adsorbed C2H5OD (d). See Figures 1 and 2 for atom labeling.

species is the appearance of a broad band around 3200 cm−1 in the case of adsorbed C2H5OH or C2D5OH dimer and around 2400 cm−1 in the case of adsorbed C2H5OD dimer. Finally, the band around 1600/1400 cm−1 related to the O−H/O−D bending mode of corresponding isotopomers is also well reproduced. Although the effect of ethanol loading is less pronounced and there is little to distinguish between monomer and dimer species, the characteristic nature of the H-bonding structure (i.e., Eigen-like or Zundel-like species) can be directly assessed by AIMD simulations.43−47 For this purpose, we computed the IR intensities for the C2H5OH adsorbed system as shown in Figure 5a. The computed IR intensities are dominated by the mobile protons and readily show that the Zundel-like monomer has an intense band between 3300 and 3800 cm−1 while the protonated dimer exhibits a broader continuum between 2300 and 3800 cm−1. These continua are consistent with those observed for high and low ethanol loading in Figure 4d, further strengthening our structural assignment. In addition, as seen from Figure 5b−d, the analysis of p-VDOS on relevant H atoms explains well the appearance of the sharp peak at 3550 cm−1 for all monomers (Hβ) and the broad band around 3200 or 2400 cm−1 for the dimers (Hα or Dα, respectively) along with the disappearance of the peak at 3550 cm−1 for the C2H5OD dimer (no Oe2−Hγ stretch). In general, our analysis of the available spectroscopic data shows that the protonation patterns as found in the current AIMD simulations are in good accord with the available spectroscopic data for the mobile protons in these systems, further strengthening our confidence in the current structural models. This in turn justifies the use of the simulated VDOS for the calculation of adsorption thermodynamics, which will be the focus of the following section. Finally, it is worth mentioning that the interpretation of the available spectroscopic data of this study is found to be sufficient without the need of invoking an interpretation based on Fermi resonance phenomena between stretching and bending modes frequently used in the literature.48 Adsorption Thermodynamics. The adsorption isotherm and differential adsorption heat are shown in Figure 6. The differential heat decreases with the increase of adsorbed ethanol, indicating a gradual change of surface species from monomers to dimers. Although a similar trend for adsorption heat was observed as well in the literature,40 the value was reported without distinguishing the contribution from monomer and dimer. To obtain the thermodynamic parameters for ethanol adsorption on H-ZSM-5, especially to identify the

Figure 6. (a) Adsorption isotherm of C2H5OH (triangles) and C2D5OH (circles) on H-ZSM-5 at 313 K. Full line is obtained from eq 12 using the estimates of Table 1. (b) Adsorption heat of C2H5OH (triangles) and C2D5OH (circles) on H-ZSM-5 as a function of adsorbed ethanol amount at 313 K. Full line is obtained from eq 13 using the estimates of Table 1.

individual value for monomer and dimer, we solved a coupled equilibrium between gas-phase ethanol and adsorbed monomers and dimers and obtained an expression for the isotherm given in eq 12, which was used to fit the experimental adsorption isotherm data. The experimental standard enthalpies for both adsorption steps (i.e., ΔH°1 and ΔH°2) were determined by fitting eq 13 to the measured heats of adsorption versus ethanol uptake. To the best of our knowledge, this is the first study where the analysis of the gravimetric and calorimetric data is based on a two-step adsorption equilibrium accounting for the existence of both monomers and dimers, which is also supported by our analysis of the available spectroscopic data. Since the isotopic exchange of H with D in the ethyl groups does not influence the adsorption isotherm and heats of adsorption as seen in Figure 6, a single fit was used on the experimental data reported for both C2H5OH and C2D5OH adsorption. The estimated values of the equilibrium coefficient 7178


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The Journal of Physical Chemistry C and the adsorption heat for each adsorption step are reported in Table 1. Table 1. Adsorption Parameters Determined for Each Adsorption Step (1 = eq 10 and 2 = eq 11) by Fitting Eq 12 to the Experimentally Obtained Isotherms and Eq 13 to the Experimentally Obtained Heats of Adsorption Together with Their 95% Confidence Intervals adsorption step

1

2

Ki (−) ΔH°i (kJ/mol)

(4.5 ± 0.3) × 104 −89 ± 1

(2.9 ± 0.2) × 104 −67 ± 1

Figure 7. Gibbs free energy profile at 300 K for ethanol adsorption on the Brønsted acid site (*) of H-ZSM-5 (HA, harmonic approximation; QHA, quasi-harmonic approximation; EXP, experiment).

The quasi-harmonic (QHA) adsorption enthalpies and entropies for both adsorption steps are presented in Table 2 Table 2. Standard Adsorption Enthalpies, Entropies, and Free Energy (T = 300 K) for Each Adsorption Step (1 = eq 10 and 2 = eq 11) Determined with Different Methodsa adsorption step ΔH°ads (kJ/mol)

HA QHA Exp HA QHA Exp HA QHA Exp

ΔS°ads (J/mol/K)

ΔG°ads (kJ/mol)

1

2

−126 −107 ± 0.5 −89 ± 1 −173 −210 ± 17 −208 ± 3 −74 −44 ± 6 −27 ± 0.1

−98 −83 ± 0.5 −67 ± 1 −175 −184 ± 13 −138 ± 3 −46 −28 ± 4 −26 ± 0.1

results from the ZPVE correction, see Table 3. Previous studies18 have reported a similar adsorption enthalpy for the ethanol monomer using HA as those reported here but have invariably claimed good agreement with experimental numbers from Lee et al.40 of 130 ± 5 kJ/mol. This value is appreciably higher than the experimental value reported here because it is obtained at higher temperature (400 K) where exothermic etherification substantially occurs.26 Nonetheless, there are several sources of error on this energy term from the theoretical perspective that need clarification. First, the concentration of acid sites is estimated to be 0.71 mol/kg by pyridine titration but is only 0.17 mol/kg in our theoretical model. Second, the calculated adsorption enthalpy is dominated by ΔE0, the DFT binding energy difference at T = 0 K. Basis set errors (see section S1) and cutoff parameters for the Grimme description of dispersion interactions are well converged in our current set of calculations and provide only a slight overestimation of binding by at most 3 kJ/mol. Although we cannot rule out a DFT functional error, it is noticeable that both GGA and hybrid functionals perform similarly with an indeterminacy on the order of 10 kJ/mol.18 Focusing on the computed entropy for ethanol adsorption, we find that QHA reproduces very well the experimental value for monomer formation and captures partially the experimental adsorption entropy difference between the two adsorption steps. The smaller loss of entropy upon adsorption of a second ethanol molecule is to be expected from a compensation effect on the basis of its smaller adsorption enthalpy as compared to the adsorption of the first ethanol molecule. On the other hand, HA underestimates significantly the entropy losses for the first adsorption step and overestimates the entropy losses for the second adsorption step, without showing a significant shift in the adsorption entropy between the two adsorption steps. Therefore, HA approximation fails to follow the expected compensation effect between adsorption enthalpy and entropy, while QHA does. In terms of relative Gibbs free energies at 300 K, it is clear from Figure 7 that QHA lies closer to the experimental free energy profile as compared to HA. Thus, it is clear that the inclusion of anharmonic effects occurring at finite temperatures is very important for accurate estimation of Gibbs free energies. This is in good agreement with a recent study by Piccini et al.,22 which shows that anharmonic effects need to be included in order to obtain accurate thermodynamics for the adsorption of small alkanes on the Brønsted acid site of chabazite. We now reflect on where this difference in energetics stems from by considering the difference induced by adsorption in the

a

HA, harmonic approximation; QHA, quasi-harmonic approximation with 95% confidence intervals; Exp, experimental with 95% confidence intervals.

and compared to both experimental results (Exp) and calculated results using the standard treatment for rotations and translations and harmonic approximation (HA) for vibrations.49 A breakdown of the different terms used in the calculation is presented in Table 3, while Gibbs free energy profiles for the monomolecular and bimolecular adsorption of ethanol at 300 K are shown in Figure 7. As seen in Table 2, the QHA enthalpy estimates are less than 18 kJ/mol than the current experimental measurement for monomer and dimer, while the HA even further overestimates adsorption enthalpies by 30−40 kJ/mol for both monomer and dimer. The primary difference between the two estimates Table 3. Decomposition of Standard Adsorption Enthalpies (kJ/mol) and Entropies (J/mol/K) for Each Adsorption Step (1 = eq 10 and 2 = eq 11) at 300 Ka 1 HA ΔET=0K ΔZPVE ΔUtrans ΔUrot ΔUvib ΔStrans ΔSrot ΔSvib a

−127 3 −4 −4 12 −157 −95 78

2 QHA −127 29 −4 −4 32 −118 −98 5

HA −105 6 −4 −4 18 −157 −94 76

QHA −105 29 −4 −4 33 −117 −97 29

HA, harmonic approximation; QHA, quasi-harmonic approximation. 7179


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enthalpic and entropic components of the free energetics, which arise due to confinement of organic molecules. Specifically, we examined the spectroscopic and thermochemical properties of the prototypical reaction of ethanol adsorption on the Brønsted acid site of H-ZSM-5. By comparison with IR spectroscopy, we have shown that ethanol adsorbs at low ethanol loading as a single monomer on BAS, with the acid proton being shared between the oxygen of the alcohol and the oxygen atoms of the zeolite cage adjacent to the Al site, in a Zundel-like configuration. This species is dominant for T ≤ 400 K and in equilibrium with an Eigen-like protonated ethanol at T > 400 K. At higher ethanol loading, one obtains dimeric species, where a protonated ethanol is stabilized by an additional alcohol molecule. Computed and measured IR spectra confirm these structural models. More importantly, these structural models can account for the measured enthalpy and free energy of ethanol adsorption as a function of ethanol loading. Employing a QHA analysis of the AIMD trajectories, the adsorption free energy is captured within chemical accuracy (∼10 kJ/mol). More critically, the traditional approach for describing thermochemistry through a harmonic representation of the nuclear motion overestimates the adsorption free energy by as much as 20−50 kJ/mol. The implication of this observation is that the confinement effect on ethanol hinders many of its vibrational modes, most particularly those at low frequency, and that one needs to capture the anharmonic parts of the potential energy surface to recover its influence upon the adsorption free energy.

p-VDOS for two different subsystems: ethanol and zeolite. For illustrative purposes, these differences in p-VDOS are plotted in Figure 8 for monomer and dimer formation at 300 K for

Figure 8. Difference in p-VDOS before and after adsorption at 300 K for the ethanol (blue), zeolite (green), and total system (red) in the low-frequency regime for the first (a, eq 10) and second (b, eq 11) adsorption step. Curves are defined such that positive values are associated with an increase in p-VDOS upon adsorption.

frequencies below 1000 cm−1 (i.e., the modes most responsible for entropy). While the p-VDOS differences are oscillatory for the zeolite framework, they are consistently positive for ethanol, indicating an overall increase in the low-frequency vibrational modes of the molecule upon confinement. By performing QHA analysis on the p-VDOS before/after adsorption, we are able to systematically assign energy and entropy terms to different parts of the structure that most accounts for the observed free energetics, see Table 4. This analysis indicates that ΔUvib (most

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b00923. Influence of basis set and van der Waals correction on binding energy; computed absolute entropy of gas-phase ethanol compared with NASA polynomial data; additional details on experimental data; additional structure data from AIMD; temperature dependence of the VDOS; temperature dependence of the adsorption thermodynamics (PDF)

Table 4. Decomposed ZPVE, Energy (kJ/mol), and Entropy (J/mol/K) Change Due to Vibrational Motion for Each Adsorption Step (1 = eq 10 and 2 = eq 11) at 300 K 1 EtOH H-ZSM-5 total

2

ΔZPVE

ΔUvib

ΔSvib

ΔZPVE

ΔUvib

ΔSvib

23 6 29

28 4 32

29 −24 5

34 −5 29

38 −5 33

31 −2 29

ASSOCIATED CONTENT

S Supporting Information *

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from ΔZPVE) originates predominantly from the ethanol part of the system, which is critical for obtaining lower adsorption enthalpies for both adsorption steps, while ΔSvib is less than 10 J/(mol·K) for monomer formation due to compensation between the contribution from ethanol and zeolite. On the other hand, the contribution from the zeolite to ΔSvib for the second adsorption step leading to dimer formation is almost insignificant due to the very similar vibrational behavior of the zeolitic proton in the adsorbed monomer and dimer (see Figure 5b, Hα for monomer and Hβ for dimer). These changes are not accounted for by the HA, which only attributes 12−18 kJ/mol to the ΔUvib and overestimates the contribution to ΔSvib by over 45 J/(mol·K) (see Table 3). Overall, an accurate representation of the role of confinement on ethanol adsorption free energetics requires accounting for the anharmonic parts of the potential energy surface.

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Phone: +32-09264-5677. *E-mail: [email protected]. Phone: 509-372-6092. *E-mail: [email protected]. Phone: 509-375-2725. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This article is dedicated to our colleague Dr. Bruce Garrett on the occasion of his 65th birthday. He has achieved significant impact in his career with his contributions to our understanding of how dynamical processes and anharmonicity contribute to rate theories as well as served as a dedicated steward of PNNL’s fundamental science programs over the past decade. K.A., M.F.R., and G.B.M. were supported by the Long Term Structural Methusalem Funding by the Flemish Government, grant no. BOF09/01M00409. M.S.L., V.A.G., R.R., and J.A.L. were supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical

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CONCLUSIONS In this article we addressed one of the most daunting challenges in modern catalysis, namely, the proper description of the 7180


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Sciences, Geosciences & Biosciences. PNNL is a multiprogram national laboratory operated for DOE by Battelle. Computational resources were provided at W. R. Wiley Environmental Molecular Science Laboratory (EMSL), a national scientific user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research located at PNNL, the National Energy Research Scientific Computing Center (NERSC) at Lawrence Berkeley National Laboratory and the Stevin Supercomputer Infrastructure at Ghent University.

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Anharmonicity and Confinement in Zeolites: Structure, Spectroscopy

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