5506
J. Phys. Chem. C 2007, 111, 5506-5513
Possible Dual-Charge-Carrier Mechanism of Surface Conduction on γ-Alumina Shuhui Cai,†,‡ Monica Caldararu,¶ Viorel Chihaia,¶ Cornel Munteanu,¶ Cristian Hornoiu,¶ and Karl Sohlberg*,‡ Department of Physics, State Key Laboratory of Physical Chemistry of Solid Surface, Xiamen UniVersity, Xiamen 361005, Peoples Republic of China, Department of Chemistry, Drexel UniVersity, Philadelphia, PennsylVania 19104, and Ilie Murgulescu Institute of Physical Chemistry of the Romanian Academy, Spl. Independentei 202, 060021 Bucharest, Romania ReceiVed: December 21, 2006; In Final Form: February 11, 2007
We cast a dual-charge-carrier model of surface conductance on γ-alumina in mathematical form. We then carry out first-principles calculations for various possible atomic-scale structures of the low- and hightemperature charge-carrier interactions with the γ-alumina surface to estimate the values of the energy parameters in the dual-charge-carrier model. By comparing the values of these energy parameters as determined by first-principles calculations to those obtained by fitting the mathematical form of the dual-charge-carrier model to experimental data, new insight is gained into the nature of the charge-carrier species. The results support the hypothesis that the intrinsic hydrogen content and surface moisture of γ-alumina provide a possible explanation of the observed thermal dependence of surface conductance.
I. Introduction Aluminum oxide, Al2O3, is a material of considerable technological and industrial importance as a result of its unusual catalytic and adsorption properties, high surface area, resistance to abrasion and corrosion, hardness, and electrical properties.1 It exists in a variety of metastable transition phases, among which the most well-known are γ, η, θ, and R, the latter being the terminus of a dehydration series starting with aluminum oxyhydroxide (boehmite). γ-Alumina is one of the quintessential materials of heterogeneous catalysis. It may be used as a catalyst in its own right, but more commonly, it serves as a support for another oxide and/or a finely dispersed metal that is added to impart properties such as improved durability or to tailor the catalytic chemistry. In order to guide tailoring and engineering of improved catalysts, it is necessary to have a clear understanding of the dynamics of this structure during catalyst operation and of its role as a support in relation to the catalytic activity of the supported phase. For many years, γ-alumina was viewed as stoichiometric Al2O3 in a defect spinel structure. There were, however, persistent reports of hydrogen in the bulk material, with no emerging consensus.2-6 A reinterpretation of published experimental data based on the results of quantum mechanical calculations showed that γ-alumina is, in fact, a sequence of hydrogen-containing compounds of the form H3mAl2-mO3. The terminus of the sequence is the widely promoted defect spinel structure.7 A natural consequence of the variable stoichiometry of γ-alumina is that it has the property that it can store and subsequently evolve water, but in an unusual, reactive way.7 This property may lie at the root of many of the mysteries associated with this material in catalytic processes, such as * To whom correspondence should be addressed. E-mail: sohlbergk@ drexel.edu. † Xiamen University. ‡ Drexel University. ¶ Ilie Murgulescu Institute of Physical Chemistry of the Romanian Academy.
hydrogen spillover.8,9 This is extremely important in terms of the acidic properties of the surface of alumina-containing catalysts. Indeed, normally at low temperature, the acidity of oxide surfaces must be dominated by Bronsted acidity, while at high temperature, due to the partial dehydration, the oxide surface will show mostly Lewis-type acidic sites. In the case of alumina, this process will be controlled by the hydrogen migration from/to the surface. In this work, we combine mathematical modeling, firstprinciples calculations, and experimental results to gain new information about the role of interactions of hydrogen and water with γ-alumina through their possible role in charge transport. We show that the intrinsic hydrogen content and surface moisture of γ-alumina provide a possible explanation of the observed thermal dependence of surface conductance. 1. An Observation. Conductance measurements of γ-alumina between concentric cylinder electrodes have revealed interesting temperature dependence.10 As shown in Figure 1, upon heating from room temperature (RT) to 673 K (solid points), it is found that the surface conductance displays two distinct regimes. After a brief initial rise (we denote this regime as 0), the surface conductance falls with increasing temperature (regime I), but after reaching a minimum at some intermediate temperature (ca. 450 K), the surface conductance rises again (regime II). Upon cooling (open points), the temperature dependence in the hightemperature (HT) regime II is fully reversible, but the low temperature (LT) regime I displays a significant hysteresis, recovering most of the original surface conductance only after an extended time (denoted by the large arrow in Figure 1). 2. Hypothesis. A dual-charge-carrier model has been advanced to explain the observed nonlinear thermal dependence of surface conductance.10 In this model, charge is carried across the surface by two independent types of atomic or molecular charge carriers. (For example, at low temperatures this might be water carrying charge as H3O+, and at high temperatures, charge might be carried by proton hopping.) Starting at RT, the brief initial rise in conductance in regime 0 is presumed to
10.1021/jp068817n CCC: $37.00 © 2007 American Chemical Society Published on Web 03/20/2007
Mechanism of Surface Conduction on γ-Alumina
J. Phys. Chem. C, Vol. 111, No. 14, 2007 5507 to hopping; ∆ ) internal energy barrier to hopping; ∆ξ ) entropic contribution to hopping barrier. Experimentally, G is measured. This is, by definition, the reciprocal of surface resistance
G ) 1/R
(1)
We make the substitutions F ) 2π(ln ro/ri)R (we consider a section through concentric cylinder electrodes) and σ ) 1/F to obtain
G ) σ2π(ln ro/ri)
(2)
Figure 1. Thermal dependence of surface conductance of γ-alumina.10 One full heating-cooling cycle is shown. Solid points, heating; open points, cooling; solid curve, best-fit model.
We then make the substitution σ ) µnq (mobility may be thought of as a proportionality factor between conductivity and the concentration of charge carriers11), which yields
be due to enhanced molecular vehicle mobility with temperature, but upon further increase in temperature, this vehicle is lost from the surface, leading to decreasing surface conductance in regime I. The conductance only increases again when hightemperature charge carriers in the material (possibly H carrying charge as H+) become mobile in regime II. The migration of protons is assumed to occur through a hopping mechanism, as described in the discussion accompanying a 1952 paper by de Boer and Houben.2 Upon cooling, the proton mobility decreases with temperature, decreasing the conductance. One might expect the conductance to remain at its lowest value upon return to RT because the low-temperature charge-carrier vehicles were lost from the surface during the excursion to high temperatures, but in fact, the LT conductance very slowly recovers. Presumably the slow recovery of the LT surface conductance is due to re-forming of the charge-carrier water molecules on the surface. The reactive sponge process of γ-alumina7 is an obvious route to the re-formation of water at the surface. Herein, to test the above hypothesis, we cast the dual-chargecarrier model in mathematical form. We then consider different possible atomic-scale structures for interaction of the charge carriers with the γ-alumina surface. Next, we compute adsorption energies, hopping distances, hopping barriers, and hopping frequencies for these structures using first-principles methods. By comparing the values of the energy parameters obtained with first-principles calculations to those obtained by fitting the mathematical form of the dual-charge-carrier model to the experimentally observed thermal dependence of surface conductance, we obtain new insight into the identity of the charge carriers.
G ) µnq2π(ln ro/ri)
II. Theory 1. Derivation of the Thermal Dependence of Surface Conductance for the Dual-Charge-Carrier Model. To derive the thermal dependence of surface conductance between concentric cylinder electrodes, we start with the following definitions: R ) surface resistance; G ) surface conductance; F ) surface resistivity; σ ) surface conductivity; ri ) outer radius of the center electrode; ro ) inner radius of the outer electrode; q ) charge on charge carrier, assumed to be +1e for both carriers; d ) hopping distance; m ) charge-carrier mass; n ) concentration of charge carriers (per unit area); N ) concentration of charge-carrier binding sites (per unit area); E ) electric field; µ ) mobility ) ratio of drift velocity to applied field ) V/E; V ) drift velocity ) µE; ∆F ) free-energy change on adsorption (∆F′ ) molar-free-energy change on adsorption; see also eq 10); ∆E ) change in internal energy upon adsorption; ∆S ) entropy change upon adsorption; ∆f ) free-energy barrier
(3)
showing that conductance is directly proportional to mobility and directly proportional to charge-carrier concentration. If we assume two independent and noninteracting types of charge carriers, we may write
G ) [q2π(ln ro/ri)]‚(µ1n1 + µ2n2)
(4)
We now use the fact that mobility is a constant of proportionality between drift velocity and electric field to write
G ) [q2π(ln ro/ri)E]‚(V1n1 + V2n2)
(5)
The quantities ri, ro, q, and E are merely constants for a given system; therefore, we can write
G ) B‚(V1n1 + V2n2)
(6)
where B is a constant. Because unknown external factors such as contact resistance govern the overall magnitude of conductance, in this study, the constant B in eq 6 is taken to be an adjustable parameter. We will next consider each of the factors V and n in turn. First we consider the velocity, V. In the surface hopping model, a charge carrier rests temporarily in a potential well on the alumina surface where it undergoes vibrations about the classical minimum of the potential with a frequency ν, denoted ν1 for the first charge carrier and ν2 for the second charge carrier. In other words, a charge carrier of type j attacks the potential barrier between rest sites with a frequency νj. (This is the “attempt frequency”.12) The probability p that the charge carrier surmounts the barrier depends on the height of the free-energy barrier to hopping for that type of carrier ∆fj and the carrier’s kinetic energy, which for a thermal distribution, may be taken to be kT,13 where k is the Boltzmann constant, so that
( kT∆f)
p ) exp -
(7)
When the charge carrier does successfully traverse the energy barrier, it travels a distance d before coming to temporary rest in the adjacent site. Its average velocity is given by the rate at which the carrier attacks the barrier times the probability that it will surmount the barrier times the distance it travels if it does cross the barrier. For hopping parallel to an applied electric field, the barrier to hopping in the forward direction will be lowered by Eqd/2, and the barrier in the reverse direction will be increased by Eqd/2. This difference in barrier heights leads to an overall drift of charge carriers, the velocity of which is given
5508 J. Phys. Chem. C, Vol. 111, No. 14, 2007
Cai et al.
by the difference between the forward and reverse velocities
Vj ) νjpE>(∆fj-Eqjdj/2)dj - νjpE>(∆fj+Eqjdj/2)dj
TABLE 1: Computed Values Relevant to the Dual-Charge-Carrier Model of Surface Conductance
(8)
proposed charge carrier
∆E (eV)
∆ (eV)
ν (cm-1)
chemisorbed water chemisorbed -OH H-bonded water HA
-1.43 1.09 0.2a 0.78 (0.46b) >0.84 >2
284c 284d 413
Substituting eq 7 into 8 yields
(
Vj ) νjdj exp -
)
(
)
∆fj - Eqjdj/2 ∆fj + Eqjdj/2 - νjdj exp kT kT (9)
-3.5 -6.4
HB HC
428 -
Next, we consider the charge-carrier concentration, n. In the experimental setup the conductance measurement is carried out under a flow of gas, a nonequilibrium condition. For simplicity, we assume the surface and the surrounding gas to be in quasiequilibrium. Upon heating, the charge-carrier vehicles will partition themselves between the surface and the gas phase according to the difference in free energy between the adsorbed and desorbed states. We may analyze this partitioning by referencing the process
coverage. Conversely, weak binding (∆F ≈ 0), very low gas partial pressure (P ≈ 0), and/or high temperature will yield low surface coverage. For Nj total charge-carrier sites of type j, the number of carriers on the surface nj is given by
A + V f As
nj ) Nj‚θj
a Typical hydrogen-bond strength.28 b Experimental value from ref 33. c Local mode frequency for O atom. d Value for chemisorbed water used.
(10)
(17)
where A is a gas-phase molecule, V is a vacant surface site, and As is a surface-adsorbed molecule. The equilibrium constant K for this reaction 10 is given by
Substituting the expression for carrier velocity (9) and the expression for carrier density (17) into the expression for conductance in the dual-charge-carrier model (6) yields
K ) [AS]/([V]PA)
G)B×
(11)
Here, [AS] is the mole fraction of surface-adsorbed species, [V] the mole fraction of surface vacancies [V], and PA is a unitless quantity, the ratio of the pressure of gas-phase A species (P′A) to standard pressure, PA ) P′A/(1 atm). The equilibrium constant may also be expressed in terms of the molar free energy of the adsorption process (∆F′)
(
K ) exp -
∆F′ RT
)
K ) θ/[(1 - θ)P]
(13)
Expression 13 can be rearranged to yield the well-known Langmuir model
θ ) KP/(1 + KP)
(14)
By substitution of eq 12 into 14, we have
∆F′ RT θ) ∆F′ 1 + P exp RT
(
)
(
)
(15)
In terms of the per-molecule free energy of adsorption (∆F), the surface fractional occupation is
∆F kT θ) ∆F 1 + P exp kT
(
P exp -
(
(
ν1d1‚exp -
)
)
(16)
Note that very strong binding of the molecule to the surface (∆F , 0), very large partial pressure of the adsorbate species above the surface, and/or low temperature will favor high surface
)
∆f1 - Eq1d1/2 - ν1d1‚ kT ∆f1 + Eq1d1/2 exp kT
( (
[
(
ν2d2‚exp -
)
)]
∆F1 kT + N1 × ∆F1 1 + P1‚exp kT P1‚exp -
(12)
Note that, while ∆F′, R, and T are dimensional quantities, the exponent and K itself are unitless. If we denote the fraction of occupied surface sites as θ and drop the subscript “A” from PA, expression 11 becomes
P exp -
{[
(18a)
)
(
)
(18c)
∆f2 - Eq2d2/2 - ν2d2‚ kT ∆f2 + Eq2d2/2 exp kT
( (
)
∆F2 kT N2 × ∆F2 1 + P2‚exp kT P2‚exp -
(
}
)
× (18b)
)]
× (18d)
(18e)
Expression 18 is consistent with the typical expression for surface conductance in that it has a factor with the hopping barrier in the exponent14 and a factor dependent on the partial pressure, but in the present case, there are terms for each of two charge carriers. Both the free energy of adsorption (∆Fj) and the hopping barrier (∆fj) will, in general, have energetic and entropic components. Assuming negligible PV work during the adsorption and hopping processes, we may write
∆Fj ) ∆Ej - T‚∆Sj
(19a)
∆fj ) ∆j - T‚∆ξj
(19b)
Here, ∆Ej is the energy change during adsorption, ∆Sj is the entropy change during adsorption, ∆j is the energy barrier to hopping, and ∆ξj is the entropy change between the classical minimum of the potential and the top of the hopping barrier.
Mechanism of Surface Conduction on γ-Alumina
J. Phys. Chem. C, Vol. 111, No. 14, 2007 5509
Substitution of eq 19 into 18 yields
{[
G)B×
( ) ( ) ( ) ( ( ) ( ( ) ( ( ) ( ) ( ) ( ( ) ( ( ) (
ν1d1‚exp
∆1 - Eq1d1/2 ∆ξ1 ‚exp - ν1d1‚ k kT ∆1 + Eq1d1/2 ∆ξ1 ‚exp exp k kT
ν2d2‚exp
)
)]
∆E1 ∆S1 ‚exp k kT + N1 × ∆E1 ∆S1 1 + P1‚exp ‚exp k kT P1‚exp
[
(20a)
)
∆2 - Eq2d2/2 ∆ξ2 ‚exp - ν2d2‚ k kT ∆2 + Eq2d2/2 ∆ξ2 exp ‚exp k kT
)
∆E2 ∆S2 ‚exp k kT N2 × ∆E2 ∆S2 1 + P2‚exp ‚exp k kT P2‚exp
}
)
)]
× (20b)
(20c)
× (20d)
Chemisorption of water and OH occurs at Lewis acid sites (exposed Al), which appear in abundance only on the Al-O termination. We consider water and OH migration in the direction of closest Al-Al spacing. Since water will chemisorb to the Al-O termination before hydrogen bonding, it is only necessary to consider the oxygen termination for hydrogenbonding interactions of water with γ-alumina. On the basis of the assumption that the low-temperature (first) charge carrier is water and the high-temperature (second) charge carrier is H, we use the subscripts 1 ) w and 2 ) H in expression 20. We note that the energy cost of removing a H atom from an oxide surface is typically quite large16 (ca. several eV/atom, as confirmed by the first-principles calculations reported here, see Table 1); therefore, we expect the H atoms to remain bound to the alumina throughout the experimentally sampled temperature range of 300 < T < 673 K. This means that the number of H atoms on the surface nH ≈ NH and does not vary appreciably with T because the surface fractional occupation is always θH ≈ 1. With the above subscript designations and simplification, the dual-charge-carrier model of surface conductance, applied to the present system, is
(20e)
Expression 20 is the fully expanded form of the dual-chargecarrier model for surface conductance. It gives the thermal dependence of the macroscopic surface conductance in terms of the microscopic energy, entropy, and positional changes involved in the charge transport. 2. Linking the Dual-Charge-Carrier Model to Alumina Surface Microstructure. We have considered several possible candidate structures for interactions of the charge carriers with the alumina surface. These are shown in Figure 2. At low temperature, water is assumed to act as a chargecarrier vehicle based on experimental observation of the evolution of water from γ-alumina upon heating.3,7,10 An alternative is that OH serves as a charge carrier. Selected interaction geometries include: (1) H2O chemisorption to the Al-O-terminated γ-alumina surface through coordinate covalent bonding by donation of a free electron pair on the oxygen atom of H2O into empty orbitals of the valance-unsaturated surface Al atoms forming a bridging Al-O-Al structure (see Figure 2a); (2) -OH on the Al-O-terminated γ-alumina surface through an interaction analogous to that described for chemisorbed H2O above (imagine the water structure in Figure 2a with one of the H atoms deleted); and (3) H2O hydrogen-bonded to the terminating row of oxygen atoms on the oxygenterminated γ-alumina surface (see Figure 2b). The high-temperature charge carrier is assumed to be H based on experimental observation of mobile protons in alumina.7,15 We considered three interaction geometries: (1) HA, hydrogen atoms attached to the exposed corner row of oxygen atoms on the γ-alumina surface; (2) HB, hydrogen atoms attached to the row of oxygen atoms at the bottom of the “trench” on the γ-alumina surface; and (3) HC, hydrogen atoms attached to the terminating row of oxygen atoms on the oxygen-terminated γ-alumina surface. The specific migration paths for H were selected to follow surface oxygen atoms because hopping from oxygen to oxygen is a known H-transport mechanism in alumina.2,13 The general direction of these hopping paths was chosen because the oxygen-oxygen separation is shortest in this direction. Hopping in the perpendicular direction would involve longer hops with presumably larger energy barriers.
G)B×
{[
( ) ( ) ( ) ( )] ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )]
νwdw exp
(21a)
∆w - Eqwdw/2 ∆ξw ‚exp - νwdw‚ k kT ∆w + Eqwdw/2 ∆ξw exp ‚exp × (21b) k kT
∆Ew ∆Sw ‚exp k kT + Nw × ∆Ew ∆Sw 1 + Pw‚exp ‚exp k kT Pw‚exp
[
νHdH exp
(21c)
∆H - EqHdH/2 ∆ξH ‚exp - ν H dH ‚ k kT ∆H + EqHdH/2 ∆ξH exp ‚exp × (21d) k kT N H}
(21e)
In this case, the terms have the following physical interpretations. Term 21b leads to an increase in G with T due to the increase in mobility of water as increasing thermal energy increases the probability that it will cross its hopping barrier. Term 21c leads to a decrease in G with T due to loss of water from the surface. Term 21d leads to an increase in G with T due to the increase in mobility of H as increasing thermal energy increases the probability that it will cross its hopping barrier. On the basis of the above interpretations, expression 21 would appear to be capable of reproducing the general form of the experimentally observed G(T), given appropriate values of the parameters. In assessing potential charge-carrier surface structures, it is useful to take note of some other facts. We expect νw < νH because mw > mH. Chemisorbed water molecules occupy Al-O-Al bridging sites on the γ-alumina (110C) surface, and H is assumed to be from surface OH. These sites are shown in Figure 2. It is observed experimentally that, as T increases, the low-temperature charge carrier is desorbed before the onset of mobility of the high-temperature charge carrier. Given the above constraints, for eq 21 to produce an overall thermal dependence consistent with the observed G(T) shown in Figure 1, the following condition must hold
∆fw < |∆Fw| < ∆fH < |∆FH|
(22)
5510 J. Phys. Chem. C, Vol. 111, No. 14, 2007
Cai et al.
Figure 3. Computed potential energy curve for movement of HA between two surface-bonded sites on the γ-alumina surface. Adjacent points are connected with line segments as a visual aid.
Figure 2. (a) Al-O-terminated surface (top of structure) for γ-alumina (110C). Two possible migration paths for H are shown. HA atoms move along an exposed edge of oxygen atoms. HB atoms move along a row of oxygen atoms at the bottom of the “trench.” Chemisorbed water may hop such that the oxygen moves between bridging Al-O-Al positions. Red ) oxygen, purple ) aluminum, yellow ) hydrogen. (b) Oxygen-terminated surface (top of structure) for γ-alumina (110C). Hydrogen-bonded water is attached to the terminating row of oxygen atoms. HC atoms hop along the terminating row of oxygen atoms.
The conditions ∆fw < |∆Fw| and ∆fH < |∆FH| are a natural consequence of the fact that the carriers may hop without being desorbed from the surface. The overall relationship follows from the experimental observation that, as T increases, the lowtemperature charge carrier is desorbed before the onset of mobility of the high-temperature charge carrier. Mathematically, as T increases, term 21c decreases the conductance due to loss of the low-temperature charge carrier (and, therefore, decreases the overall G) before term 21d starts to increase the conductance due to increasing mobility of the high-temperature charge carrier (thereby increasing the overall G). A first-principles calculation of ∆Ew, ∆w, and ∆H therefore provides a means to test the identity of the charge-carrier vehicles. 3. Calculations. We estimate the adsorption energy and energy barriers to the mobility of H2O and H across a γ-alumina surface with first-principles density functional theory calculations,17 which have proven to be quite reliable for the determination of atomic-scale configurations and related total-energy properties such as the heights of energy barriers to diffusion and reaction, properties of direct relevance here. Pseudopotentials18 are used so that core electrons are treated implicitly and valence electrons are treated explicitly. The calculations employ the generalized gradient approximation to the exchange correlation energy.19 A plane-wave basis with a cutoff energy of 380 eV was used to describe the valence electronic density, and the calculations were done in supercells with periodic boundary conditions. Integrations over the Brillouin zone employed a grid of k-points with a spacing of 0.01 nm-1 chosen following the Monkhorst-Pack scheme.20 The surface was modeled by infinitely repeating slabs of γ-alumina five layers
thick with a vacuum spacing between slabs of 1.0 nm, oriented so as to expose the preferentially exposed (110C) layer.21 Two ideal slabs are used; one is constructed based on the structural relaxation of a 70 atom unit cell of fully hydrogenated γ-alumina (stoichiometry H5Al25O40, Al-O termination),22 and the other is constructed based on the structural relaxation of a similar unit cell with an “extra” terminating row of oxygen atoms bridging adjacent Oh (four-coordinated) Al atoms on the surface with Al-O-Al structures (oxygen termination).23 Previous studies of the γ-alumina surface demonstrated that, at five layers, the surface structure is converged with respect to increasing the slab thickness.22,24 During optimizations, the atoms in the bottom layer were frozen, as were the dimensions (a, b, c, R, β, γ) of the unit cell. The calculations were carried out with the Cambridge serial total energy package (CASTEP) codes.25 Details specific to particular calculations are given together with the results. Vibrational frequencies for surface H and O of surface water were estimated with cluster calculations based on the PM3 Hamiltonian using the same slab model as that shown in Figure 2a.26 All atoms were frozen during these calculations except for the inspected H or H2O, and the resulting vibrational frequencies were identified by animation of the computed normal-mode vibrational motions. Their numerical values were scaled by a factor of 0.9761, as is recommended for PM3 calculations.27 III. Results 1. H Mobility. Figure 3 shows several points on the computed potential energy curve for displacement of a H atom from one surface site to an adjacent one on the γ-alumina surface for type HA, as depicted in Figure 2a. To map out such a curve, the mobile H atom was frozen in various positions between fully optimized initial and final positions, and all other atoms were relaxed except those in the bottom layer of the slab. The unit cell parameters were also held fixed. The distance given in Figure 3 is that from a chosen surface oxygen atom, to which the H is initially bound. The curve starts from a local minimum in the potential energy curve where the H is bonded to the surface oxygen at a distance of about 0.1 nm. As the O-H distance increases, the H passes over an energy barrier before reaching an even lower local energy minimum. It can be seen that the energy decreases significantly once the H passes over the energy barrier, accompanied by a large variation in the H-O distance, indicating breaking of the old H-O bond and formation of a new H-O bond. The computed H hopping barrier
Mechanism of Surface Conduction on γ-Alumina
J. Phys. Chem. C, Vol. 111, No. 14, 2007 5511
Figure 4. Computed potential energy curve for movement of OH and H2O between adjacent bridging (Al-O-Al) sites on the γ-alumina surface. In the minimum energy chemisorbed position, the oxygen atom of OH/H2O is near a bridging site between two surface Al atoms. d||(O-Al1) indicates the projection of the O-Al1 distance to the row of Al atoms.
is ∆H ) 0.78 eV. Values of the hopping barriers for the various types of surface H atoms considered are collected in Table 1. The hopping path is not mapped for HB and HC because the energy differences between the initial and final positions were found to be much larger, ca. 2.0 eV in the latter case, which eliminates HC as a possible charge carrier. 2. H Abstraction. To estimate ∆EH for HA atoms, we compute the total energies of the reactant and product species for the adsorption reaction
slab‚V + H f slab
(23)
where slab‚V represents a periodic slab model of fully hydrogenated γ-alumina exposing the (110C) surface with a hydrogen vacancy. (In the cases of HB and HC, a H atom was added to a vacancy-free slab, slab + H f slab‚H.) As noted in the Calculations subsection, the atoms in the upper four layers of the slab were relaxed, while the atoms in the bottom layer and cell parameters were fixed in the calculations. The results for the three types of adsorbed H atoms are collected in Table 1. As anticipated, the values of ∆EH are sufficiently negative that θH ≈ 1 throughout the entire experimentally sampled temperature range (300 < T < 673 K). 3. H2O and OH Mobility. To estimate the barrier to H2O mobility (∆w), we have carried out calculations to sample the potential energy surface experienced by a water molecule moving on the γ-alumina surface. We first considered chemisorbed water on the Al-O termination of the energetically favored (110C) exposure. The molecule is first placed on the bridging site of two adjacent Oh Al atoms (e.g., Al1 and Al2 in Figure 2a) on the surface and is optimized to its minimum energy position. The oxygen atom is then systematically moved forward and backward along the direction of the Al-Al row with respect to the slab by changing the AlO(H2) bond length ((0.01 nm per step) and the displacement of the Al-O(H2) bond from normal to the surface ((10° per step). The H positions are found for each placement of the oxygen by structural optimization, while the oxygen atom and the slab are frozen. The lowest energy curve for H2O to move from one bridge site to the neighboring one was then obtained (see Figure 4). The results show that the minimum energy position for a H2O molecule chemisorbed on the γ-alumina surface places the
oxygen atom of the H2O near a bridging site between two surface Al atoms. By symmetry arguments, every other Al atom is equivalent. The energy barrier for moving the H2O molecule from one bridging site to a symmetry-equivalent adjacent one is ∆w ) 1.09 eV. To estimate the barrier to -OH mobility, a OH moiety was placed on the bridging site of two adjacent Oh Al atoms similar to that of H2O, illustrated in Figure 2a, and a structural optimization was carried out in which the atoms of the OH moiety were allowed to seek their energetically preferred positions with respect to the atoms in the alumina surface, which were held frozen. The potential energy profile along this optimization trajectory is included in Figure 4. Along this optimization pathway, the OH first relaxes toward one bridging site (note that the energy initially decreases with little variation in the projected O-Al1 distance) and then gradually translates to the adjacent bridging site (in this region, the energy decrease is accompanied by a gradual change in the projected O-Al1 distance), remaining roughly equidistant from the Al. The energy difference between the two bridging sites suggests that the OH hopping barrier is greater than that for chemisorbed water. For hydrogen-bonded water, the configuration space for movement of the H2O molecule upon the surface proved too large to allow for sufficient computational exploration of the PES to determine the hopping barrier. We note, however, that it is possible for the H2O molecule to move across the surface without ever breaking more than one hydrogen bond at a time. A typical hydrogen-bond strength, such as that in the water dimer,28 is ca. 0.2 eV; therefore, we anticipate a low barrier to hopping for hydrogen-bonded water, probably ca. 0.2 eV. It is possible that the water molecule itself does not move but merely serves as a scaffold for mobile protons. In this case, the hopping barrier would still be comparable to the strength of a hydrogen bond. We elaborate on this possibility in the Discussion section. 4. H2O Abstraction. To estimate ∆Ew, we computed total energies for the product and reactant species of the adsorption reaction
slab + H2O f slab‚H2O
(24)
where slab‚H2O represents a periodic slab model of the γ-alumina (110C) surface with an adsorbed water molecule. The atoms in the bottom layer of the slab and unit cell parameters were frozen during optimizations. The resulting absorption energies are collected in Table 1. IV. Discussion We first tested the hypothesis that the low-temperature charge carrier is chemisorbed water (which carries the charge as H3O+ or H2O+) and that the high-temperature charge carrier is H in its preferred binding site HA (which carries the charge as H+). In this case, the predicted energy barrier for H mobility is ∆H ) 0.78 eV. More importantly, however, the barrier to abstraction of chemisorbed H2O from the Al-O-terminated surface (|∆Εw| ) 1.43 eV) is greater than the barrier to H mobility. This result is not consistent with the experimental data. Since the frequency factors (νH and νw) favor mobility of H and since the surface concentration factors are comparable (NH ≈ 2Nw), the loss of conductivity at low T must arise from loss of a charge-carrier vehicle through a reaction involving an energy barrier that is lower than the barrier to mobility of the high-temperature charge carrier. In short, the first-principles calculations suggest that this choice for the charge-carrier interaction with the γ-alumina surface is incorrect.
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TABLE 2: Values Relevant to the Dual-Charge-Carrier Model of Surface Conductance from Fitting Experimental Dataa ∆Ew (eV)
∆w ∆EH ∆H ∆Sw ∆ξw ∆SH ∆ξH (eV) (eV) (eV) (J/K‚mol) (J/K‚mol) (J/K‚mol) (J/K‚mol)
-0.69 0.12 -∞b 0.35
-114
3
na
0
Electric field E ) 667 V and the hopping distance d ) 0.265 nm. Assumed to be effectively infinite within the temperature range of interest. a
b
Figure 5. The physisorbed (hydrogen-bonded) layer of water molecules may serve as a scaffold for mobile protons.
On the basis of the above results, it is reasonable to conclude that, at low temperature, chemisorbed water does not serve as the charge-carrier vehicle. By similar arguments, other choices can be eliminated as well; ∆E for -OH is too large for it to serve as the low-temperature charge carrier. It will remain on the surface throughout the entire experimentally accessed temperature range [300 < T < 673 K]. This result is consistent with temperature-dependent IR studies of OH on alumina surfaces.6,15,29 All of the types of adsorbed H can be eliminated as the low-temperature charge carriers, analogously. A more reasonable hypothesis is that the low-temperature charge-carrier vehicle is hydrogen-bonded water on the oxygenterminated surface. The HA atoms, which have the lowest hopping barrier among all types of adsorbed H investigated, will be the first to become mobile as T is increased and are a logical choice for the high-temperature charge carriers. Since the entropy parameters in expression 21 are not easily determined with first-principles computations, we have fit expression 21 to the experimental data. Since the experiments were carried out in “dry” gases, we assume 1% relative humidity at room temperature, corresponding to Pw ) 0.00026 atm. We use the calculated values of νw, νH, dw, and dH and vary the energy and entropy parameters to identify the best-fit curve. The best-fit parameters are collected in Table 2. Note that the energy parameters are in generally good agreement with those determined by first-principles calculations, if we assume that the lowtemperature charge-carrier vehicle is hydrogen-bonded water on the oxygen-terminated surface and HA is the high-temperature charge carrier. The fitted value for the adsorption entropy of water is consistent with measured adsorption entropies for other small molecules.30 We note from expression 21, however, that increasing the partial pressure of the adsorbate mimics an increase in the entropy of adsorption, exp(∆S/k). Fitted values for adsorption entropy are, therefore, no more reliable than the uncertainty in the estimate of partial pressure. If we assume the uncertainty in the first-principles total energies to be ca. (0.2 eV, the only computed value that differs significantly from its best-fit analogue is that of the H-hopping barrier, ∆H. Such a discrepancy is not unprecedented. DFT calculations of proton hopping in SiO2/Al2O3 zeolites similarly overestimated the height of the energy barrier to hopping.31 As was the case in that zeolite study, the discrepancy here could be, in part, due to the fact that our approach is not guaranteed to locate the minimum energy pathway. We did note that, in
some of our optimizations, the presence of additional H atoms along the sides of the trench in the alumina surface leads to significant changes in the H-migration path by introducing complicated concerted motions of one or more of the additional H atoms as the selected H migrates. Zero-point vibrational energy accounts for a small portion of the discrepancy. For the mobile H, there is one vibrational mode at the minimum that is not present at the top of the hopping barrier. If we take this mode to be the one corresponding to the attempt frequency (413 cm-1), the corresponding zero-point energy is 0.026 eV. This is added to the total energy of the initial state but not to the transition state so that it lowers the barrier, but insufficiently to remove the discrepancy. Proton tunneling could also lead to an apparent decrease in the hopping barrier. Previous work on H mobility in catalytic aluminas suggests that quantum tunneling is negligible at least for the ground-state vibrational level,13 but there is evidence that proton tunneling plays a role in broadening OH vibrational bands in the related material boehmite at elevated temperatures.32 Owing to the above issues, we believe that the discrepancy between the best-fit value of ∆H and the firstprinciples prediction is more likely to arise from inaccuracy in the latter. Indeed, electrochemical measurements have yielded a hopping barrier for H in alumina of 0.46 ( 0.12 eV in “amorphous alumina”.33 This value is in good agreement with our fitting. It seems plausible that, in the experiment, the alumina surface is slightly “amorphized” so that there are H-migration paths that are not present on our idealized model surface. While it is clear that the H atoms in alumina are protonic in character,7,13,15 it is less clear how hydrogen-bonded water molecules carry charge. Though the water molecules themselves could, in principle, carry charge, it seems more likely that the physisorbed (hydrogen-bonded) layer of water molecules serves as a scaffold for mobile protons.34 This case is shown schematically in Figure 5. The protons move easily among the hydrogenbonded water molecules. Effectively, H3O+ is moving along the surface, but only the proton is actually mobile. Thermal loss of the hydrogen-bonded water from the surface leads to a decrease in conductance because the scaffold supporting the movement of protons is lost. In other words, it may not be the charged species but the charge-carrier vehicle that is lost upon heating. Finally, we note that there is a subtle change in slope in the high-temperature region of the experimentally observed thermal dependence of conductance (marked with the small arrow in Figure 1). This small feature is comparable in magnitude to the experimental uncertainty, but it is reproducible. Our analysis of possible charge carriers provides a possible explanation for this feature. We note that there are several types of surface H atoms possible. Surface OH structures have been studied at length, especially by Tsyganenko6,35-37 and Liu29, as reviewed in ref 38. Of the types considered here, the HA-type surface atoms will be the first to become mobile with increasing temperature, but other types (notably HB) will become mobile at slightly higher temperatures. It is possible that the observed increase in slope of the G(T) curve with increasing T results from the onset of mobility of a second type of surface H, plausibly HB. V. Conclusion We have cast a dual-charge-carrier model of surface conductance on γ-alumina in mathematical form. We have then carried out first-principles calculations for various possible atomic-scale structures of the low- and high-temperature chargecarrier interactions with the γ-alumina surface to estimate the
Mechanism of Surface Conduction on γ-Alumina values of the energy parameters in the dual-charge-carrier model. By comparing the values of these energy parameters as determined by first-principles calculations to those obtained by fitting the mathematical form of the dual-charge-carrier model to experimental data, we have gained insight into the nature of the charge-carrier species. We are able to exclude chemisorbed water and -OH as charge carriers. Hydrogen-bonded water appears to be the most plausible charge-carrier vehicle at low temperatures, possibly serving as a scaffold to support mobile protons. Surface H atoms along the naturally appearing “trenches” on the alumina surface appear to be the most likely candidate for the charge carriers at high temperatures. Extension of the analytic form of the dual-charge-carrier model to include more charge carriers is straightforward. This model provides a new way to make direct connection between atomic-scale surface structures and macroscopic conductance measurements. Acknowledgment. This work was supported, in part, by DuPont, by the U.S. DOE under Contract Number DE-FC0201CH11085 and by NATO-PST-CLG-980354. Computations were partially supported by the National Center for Supercomputing Applications (NCSA) and utilized the SGI Origin2000 at NCSA, University of Illinois at Urbana-Champaign. References and Notes (1) Wefers, K.; Misra, C. Oxides and Hydroxides of Aluminum; Alcoa Technical Paper No. 19; Alcoa Laboratories: Pittsburgh, PA, 1987. (2) de Boer, J. H.; Houben, G. M. M. Proc. Int. Symp. React. Solids 1952, I, 237. (3) Soled, S. J. Catal. 1983, 81, 252. (4) Ushakov, V. A.; Moroz, E. M. React. Kinet. Catal. Lett. 1984, 24, 113. (5) Zhou, R.-S.; Snyder, R. L. Acta Crystallogr., Sect. B 1991, 47, 617. (6) Tsyganenko, A. A.; Mardilovich, P. P. J. Chem. Soc., Faraday Trans. 1996, 92, 4843. (7) Sohlberg, K.; Pennycook, S. J.; Pantelides, S. T. J. Am. Chem. Soc. 1999, 121, 7493. (8) Stoica, M.; Caldararu, M.; Rusu, F.; Ionescu, N. I. Appl. Catal., A 1999, 183, 287.
J. Phys. Chem. C, Vol. 111, No. 14, 2007 5513 (9) Stoica, M.; Caldararu, M.; Ionescu, N. I.; Auroux, A. Appl. Surf. Sci. 2000, 153, 218. (10) Caldararu, M.; Postole, G.; Hornoiu, C.; Bratan, V.; Dragan, M.; Ionescu, N. I. Appl. Surf. Sci. 2001, 181, 255. (11) Ruzyllo, J. Semiconductor Glossary; Prosto: State College, PA, 2005. (12) Munch, W.; Seifert, G.; Kreuer, K. D.; Maier, J. Solid State Ionics 1996, 86-88, 647. (13) Sohlberg, K.; Pennycook, S. J.; Pantelides, S. T. Recent Res. DeV. Phys. Chem. 2000, 4, 41. (14) Sberveglieri, G. Sens. Actuators, B 1995, 23, 103. (15) Tsyganenko, A. A.; Smirnov, K. S.; Rzhevskij, A. M.; Mardilovich, P. P. Mater. Chem. Phys. 1990, 26, 35. (16) Rashkeev, S. N.; Sohlberg, K.; Galzoff, M. V.; Novak, J.; Pennycook, S. J.; Pantelides, S. T. Phys. ReV. B 2003, 67, 115414. (17) Kohn, W.; Sham, L. J. Phys. ReV. A 1965, 140, 1133. (18) Kleinman, L.; Bylander, D. M. Phys. ReV. Lett. 1982, 48, 1425. (19) Perdew, J. P. Phys. ReV. B 1986, 33, 8822. (20) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (21) Knozinger, H.; Ratnasamy, P. Catal. ReV.EmDashsSci. Eng. 1978, 17, 31. (22) Sohlberg, K.; Pennycook, S. J.; Pantelides, S. T. J. Am. Chem. Soc. 2001, 123, 26. (23) Sohlberg, K.; Rashkeev, S.; Borisevich, A. Y.; Pennycook, S. J.; Pantelides, S. T. ChemPhysChem 2004, 5, 1893. (24) Sohlberg, K.; Pantelides, S. T.; Pennycook, S. J. Surf. Sci. Lett. 2000, 470, L88. (25) Payne, M. C.; Teter, M. P.; Allan, D. C.; Arias, T. A.; Joannopoulos, J. D. ReV. Mod. Phys. 1992, 64, 1045. (26) Cai, S.-H.; Sohlberg, K. J. Mol. Catal. A: Chem. 2006, 248, 76. (27) Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502. (28) Szalewicz, K.; Cole, S. J.; Kolos, W.; Bartlett, R. J. J. Chem. Phys. 1988, 89, 3662. (29) Liu, X. S.; Truitt, R. E. J. Am. Chem. Soc. 1997, 119, 9856. (30) Bartels-Rausch, T.; Eichler, B.; Zimmermann, P.; Gaggeler, H. W.; Ammann, M. Atmos. Chem. Phys. 2002, 2, 235. (31) Franke, M. E.; Sierka, M.; Simon, U.; Sauer, J. Phys. Chem. Chem. Phys. 2002, 4, 5207. (32) Fripiat, J. J.; Bosmans, H.; Rouxhet, P. G. J. Phys. Chem. 1967, 71, 1097. (33) Seo, J. H.; Lee, D. N. J. Electrochem. Soc. 2003, 150, B329. (34) Kavasoglu, N.; Bayhan, M. Turk. J. Phys. 2005, 29, 249. (35) Smirnov, E. P.; Tsyganenko, A. A. React. Kinet. Catal. Lett. 1977, 7, 425. (36) Smirnov, E. P.; Tsyganenko, A. A. React. Kinet. Catal. Lett. 1984, 26, 405. (37) Tsyganenko, A. A.; Filimonov, V. N. J. Mol. Struct. 1973, 19, 579. (38) Sohlberg, K.; Pennycook, S. J.; Pantelides, S. T. Chem. Eng. Commun. 2000, 181, 107.
