Surface Thermodynamics and Kinetics of MgO(100) Terrace Site

Article pubs.acs.org/JPCC

Surface Thermodynamics and Kinetics of MgO(100) Terrace Site Hydroxylation John T. Newberg* Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716, United States ABSTRACT: Surface thermodynamic and kinetic models are applied to MgO hydroxylation data obtained under adsorption−desorption water vapor conditions using ambient pressure X-ray photoelectron spectroscopy. Experimental conditions range from 0.67−67 Pa and 270−600 K (10−5 to 20% relative humidity). The resulting standard state enthalpy (ΔH°) and entropy (ΔS°) for terrace site hydroxylation are −40 ± 1 kJ mol−1 and −50 ± 3 J mol−1 K−1, respectively, and independent of OH coverage. At 298 K, this gives a Gibbs free energy of ΔG° = −25 kJ mol−1. The bulk reaction of water vapor with MgO to form Mg(OH)2 (brucite) is ΔG° = −36 kJ mol−1, suggesting that the hydroxylation of the top layer of MgO is a metastable state. Hydroxylation (adsorption) follows zero order kinetics with respect to surface site concentrations, suggesting water is a precursor prior to dissociative adsorption. Dehydroxylation (desorption) kinetics are first order, with a frequency factor of ν = 1.4 (±1.2) × 1011 s−1, suggesting that recombinative desorption occurs through a pair of hydrogen-bonded OH groups.

1. INTRODUCTION The chemistry of metal oxide surfaces is important in a wide array of applications.1 The adsorption and reaction of water on magnesium oxide (MgO) plays an important role in technological and environmental processes and is one of the most heavily studied water-surface reactions, as evidenced from review papers.2−10 The surface chemistry of water on MgO has been studied extensively using traditional X-ray photoelectron spectroscopy (XPS),11−29 examining the MgO interface under postexposure conditions in order to elucidate the extent to which water dissociates on the surface and hydroxyl (OH) groups remain under ultrahigh vacuum (UHV) conditions. This chemistry was also examined recently using ambient pressure XPS (APXPS), quantitatively assessing the extent to which water dissociates at MgO(100) terrace sites in the presence of water vapor under adsorption−desorption conditions.30,31 Scrutinizing the APXPS results with published experimental and computer simulation literature lead to the conclusion that water autocatalytically dissociates at MgO(100) terrace sites, reversibly forming a hydroxyl overlayer at the interface with a saturated thickness similar to vertical lattice constant of bulk Mg(OH)2 (brucite).31 The precise hydroxyl overlayer structure has yet to be elucidated under adsorption−desorption conditions. APXPS has also been used to examine the interaction of water vapor with other oxides, including FeO,32 α-Fe2O3(0001),33 Fe3O4(001),34 BaCeY-oxide,35 GeO2,36 Cu2O,37 Al2O3,37 TiO2(110),38 and SiO2.39 The extent to which hydroxylation occurs on metal oxide is driven by both interfacial structure and composition of the surface. The use of APXPS to investigate gas−solid interfaces has led to an exponential rise in the number of publications since 2005.40 However, only a handful of these studies have reported © 2014 American Chemical Society

the surface energetics under adsorption−desorption conditions. For example, Starr et al.41 examined the adsorption of acetone on ice and extracted an adsorption enthalpy (ΔH) of −45 kJ mol−1 using first-order Langmuir kinetics. Ketteler et al.38 reported a coverage-dependent ΔH for molecular water adsorption onto TiO2(110), which converged to the bulk water heat of condensation for coverages above 0.5 monolayers. Although scarce in the APXPS literature, extracting surface energetics from careful studies of gas−solid systems under vacuum conditions is a well-established science.42,43 To date, the most extensively used method to determine surface energetic and kinetic parameters is thermal desorption spectroscopy (TDS).42,44 Conditions for desorption experiments are such that the adsorption process is negligible while desorption of the adsorbate from surface sites predominates the kinetics, and the rate of desorption (rd) is given by the WignerPolanyi equation. At constant heating rates (β = dT/dt) TDS peaks (Tmax) change with desorption energy barrier (Ed), desorption frequency factor (νd), and desorption reaction order (n).42,43 TDS has been used extensively to examine molecular water desorption and dehydroxylation from metal oxide surfaces.10 Values of Ed and νd vary widely, with observations of zero, first, or second order desorption kinetics (n = 0, 1, 2) depending on the metal oxide. While TDS provides valuable molecular level details, the desorption kinetics are decoupled from adsorption kinetics and generally require initial cryogenic Special Issue: John C. Hemminger Festschrift Received: May 28, 2014 Revised: July 29, 2014 Published: July 29, 2014 29187

dx.doi.org/10.1021/jp5052613 | J. Phys. Chem. C 2014, 118, 29187−29195

The Journal of Physical Chemistry C

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temperatures and vacuum pressures to study water on metal oxides. Catalytic and environmental processes involving gas−surface interactions operate under conditions where adsorption and desorption occur concomitantly. In order to elucidate surface energetics under such conditions, careful studies are needed that can probe surfaces under near ambient conditions. Here we conduct surface thermodynamic and kinetic analyses on MgO(100) terrace site hydroxylation data observed under adsorption−desorption conditions using APXPS. We report the standard state thermodynamics (ΔH°, ΔS°, ΔG°), vibrational frequency factor for dehydroxylation, and reaction orders of hydroxylation (forward dissociation reaction) and dehydroxylation (reverse recombination reaction). The results of this analysis give rise to hydroxylation energetics that heretofore have not been reported under adsorption−desorption conditions in the Torr pressure range.

2. DATA OVERVIEW The experimental details and results for surface hydroxylation of MgO(100), as well as the XPS quantification method have been described in detail previously.30,31 MgO(100) films were prepared by vapor deposition on an Ag(100) single crystal. The surfaces were probed in the presence of water vapor using synchrotron-based APXPS at beamline 11.0.2 at Lawrence Berkeley National Laboratory.45−47 Under ambient water vapor conditions, O 1s spectra revealed four distinct species corresponding to the MgO oxide (Ox), hydroxyl (OH), molecularly bound surface water, and gas phase water (see ref 30, Figure 3a). From integration of XPS O 1s and Ag 3d intensities, Ox, OH, and H 2 O film thicknesses were calculated.30 The freshly prepared films were exposed to increasing relative humidities by exposure to room temperature water vapor at constant pressures (6.7−0.67 Pa) and decreasing the sample temperature. The overall temperature range for experiments was from 263 to 600 K. Under these conditions a quasi-equilibrium state was rapidly obtained and surface hydroxyl coverages did not change as a function of time. Figure 1 shows APXPS results of total hydroxyl coverage versus sample temperature (Figure 1a) and relative humidity (RH; Figure 1b) for four different isobar experiments at 67 (red), 20 (green), 2.7 (blue), and 0.67 Pa (black). Each uptake curve was conducted on separate, fresh MgO(100)/Ag(100) films with initial dry oxide coverages of 5.3, 4.1, 4.5, and 5.5 ML, respectively. In order to show similar uptake profiles, Figure 1a was plotted as a function of decreasing temperature on a linear scale, while Figure 1b was plotted as a function increasing RH on a log scale. As seen from Figure 1b, when converting into RH units the isobar data overlap, indicating that the hydroxyls are under adsorption (hydroxylation) and desorption (dehydroxylation) quasi-equilibrium conditions. This is also evidence that the room temperature water vapor thermally accommodates with the sample interface upon adsorption, and the relative humidity (RH) is accurately reflected by the pressure (p) of the water vapor in the chamber and the sample surface temperature (Ts). The relative humidity here is defined as RH = 100(p/p0), where p0 is the water vapor pressure above liquid water48 at Ts. The total observed OH coverages (ΘOH) is a combination of hydroxyl coverage at defect sites (ΘD; 0.97. Such linearity is evidence that under our experimental conditions, the enthalpy of hydroxylation is independent of temperature. Figure 3b shows results of calculated ΔH° values from the slopes of Figure 3a (eq 11) as a function of terrace site OH coverage. The error bars in ΔH° are 1.96 σ (90th percentile) in Aexp. As seen from the data, all five ΔH° values are statistically indifferent, indicating that from Θ ≈ 0.1 ML all the way up to saturation ΔH° remains independent of coverage. Thus, to within experimental uncertainty the enthalpy of hydroxylation at terrace sites is independent of both temperature and coverage and has an average (±1.96 σ) from all five measurements of ΔH° = −40 ± 2 kJ mol−1 (dashed line in Figure 3b).

where the standard state pressure is p° = 1 atm = 101325 Pa and the surface standard state is referenced to m = n = 1 at a coverage of Θ° = 0.5 ML, which gives a convenient value of Θ °/(1 − Θ °) = 1.50 The simplest and most widely used Langmuir equation is the first order equation (m = n = 1), which from eq 6, gives

Θ=

KLp 1 + KLp

(8)

where the Langmuir constant (KL) is given by

KL = K °Keq

(9)

Rather than assume values of m and n a priori for the evaluation of isobaric curves, we instead use a more general formalism by keeping m and n as variable parameters. It will be shown later that the stoichiometric coefficients m and n can be determined empirically by fitting to isobar uptake curves. 29189



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no longer interacting with bare Mg2+ and O2− ions at the interface, but instead with a saturated hydroxyl layer. Thus, the observed ΔH° values are to be understood as arising from H2O−OH interactions at the interface and not merely H2O− MgO interactions. It should be emphasized that the ΔH° for molecular water adsorption observed from Foster et al. is determined for data collected up through 95% RH, whereas the ΔH° extracted from the study herein is for water dissociation (hydroxylation) in a very small RH window from 0.01 to 0.1% RH (see Figure 2). The Clausius−Clapeyron analysis presented herein can be extended to the study of hydroxylation enthalpies of other water−metal oxide systems using APXPS. Similar to TDS studies used to extract surface energetics, we emphasize here that the ability to extract energetics using APXPS requires very diligent surface science experiments. Carefully prepared sample interfaces need to react under well-controlled temperature and pressure conditions. Moreover, the potential for X-ray induced damage and sample contamination from adventitious carbon need to be explicitly examined and minimized. 3.1.3. Isobar Analysis to Determine m, n, and ΔS°. In this section we will derive a general expression to model the shape of isobar curves (Θ vs T and RH). With m and n as variables, there is no analytical solution to eq 6 for Θ as a function of T. In order to analyze an isobar uptake curve, we instead solve eq 6 for T as a function of Θ to get

The temperature independence is not unusual for gas-surface studies, which often yield linear Clausius−Clapeyron fits. However, the coverage independence is quite surprising. Enthalpies of adsorption are often strongly dependent on surface coverage.42 For example, an increase in ΔH° (i.e., larger negative value) with coverage is indicative of attractive lateral interactions of the adsorbate, whereas a decrease in ΔH° (i.e., smaller negative value) with coverage suggests there are repulsive interactions of the adsorbate. Other mechanisms, such as step edge and island growth, can also lead to coverage dependent ΔH° values. The results herein suggest that there are no adsorbate−adsorbate interactions occurring as a function of increasing coverage. This could suggest that hydroxylation− dehydroxylation events under ambient conditions are quite facile, occurring at isolated terrace sites where the hydroxyl pairs do not interact laterally with other hydroxyl pairs during their lifetime at the interface. To our knowledge these are the first reported results extracting the enthalpy of hydroxylation (i.e., heat of dissociative water uptake) for any water−surface interaction under our experimental adsorption−desorption conditions. However, the enthalpy of water adsorption (i.e., heat of molecular water uptake) under adsorption−desorption conditions has been heavily studied for many systems. As mentioned in the Introduction, APXPS was used to determine the enthalpy of water adsorption on TiO2(110).38 Ferry et al.51 conducted isothermal studies under adsorption−desorption conditions in the presence of high-vacuum pressures (1 × 10−9 to 5 × 10−7 Torr) and temperatures from 210 to 221 K. Assuming water coverage was proportional to the change in intensity of the MgO(100) LEED spots, a Clausius−Clapeyron analysis of the isotherms gave a value of ΔH° = −85 kJ mol−1. Such a large enthalpy of adsorption was suggested to be attributed to the large attractive force between water and the Mg 2+ and O 2− ions at the interface. However, this interpretation contradicts UHV XPS water experiments under similar temperature conditions,12,28 which show that both molecular water adsorption and hydroxylation occurs on MgO(100). Thus, the observed decrease in LEED (100) spot intensity by Ferry et al.51 upon increasing water vapor pressure was likely not solely due to molecular adsorption as the authors interpreted, but a combination of both molecular water adsorption and hydroxylation and is therefore difficult to interpret. The molecular adsorption of water on bulk MgO(100) crystals was investigated by Foster et al.52−54 using FTIR to monitor the OH stretch of adsorbed water in the 3400 cm−1 region under ambient water vapor, isothermal conditions from −10 to 40 °C. While there was evidence of Mg(OH)2 formation in the 3700 cm−1 region on aged samples, it was suggested this was due to a minor amount of hydroxyls at defect sites. ΔH° values were reported as a function of coverage and converged to a value of −44 kJ mol−1 for the enthalpy of condensation for bulk water at coverages above 3 ML.54 In the region of low water coverage ( 0.1%, the interface of MgO(100) is fully saturated with a monolayer of hydroxyl groups (Figure 1b). Under the ambient RH conditions used by Foster et al., water is

T=

ΔH o ΔS o − R ln{Θn /[K op(1 − Θ)m ]}

(12)

With K° (eq 7) and p constant for isobaric studies, and ΔH° = −40 kJ mol−1, as determined from the Clausius−Clapeyron analysis, this leaves ΔS°, m, and n as variable fitting parameters. Such an analysis assumes that ΔH° and ΔS° are independent of both temperature and coverage within the range of experimental conditions. We have already shown this to be the case for ΔH° (Figure 3), and as we will show later this is also the case for ΔS°. Equation 12 allows for the analysis of isobar curves as a function of temperature. In order to assess Θ as a function of RH (data in Figure 2), we use the definition of RH: RH =

100p p0 (T )

(13)

where p0(T) is given by the temperature-dependent function of Wagner and Pruss.48 By substituting calculated values of T from eq 12 into p0(T) in eq 13, RH values are calculated as a function of coverage Θ and then plotted as Θ versus RH. The goal of this section is to optimize values of ΔS°, m, and n by fitting to isobar data (Figure 2) using eq 13. However, it will first be instructive to see how varying these parameters gives rise to distinct changes in the shape and shift of an isobar curve. First we shall examine how the stoichiometric coefficients m and n affect the shape. Using the experimentally determined average value of ΔH° = −40 kJ mol−1 (Figure 3b), K°, as defined in eq 7, and a constant value of ΔS° = −50 J mol−1 K−1, Figure 4a shows 0.67 Pa isobar curves for values of m = n = 2 (black line), 1 (green line), and 0.1 (blue line). As seen from Figure 4a, as m and n decrease, the isobar curve becomes sharper, where ultimately in the limit of m = n = 0 it becomes a step function. Figure 4b shows results for constant m = 1, while varying n = 2 (black), 1 (green), and 0.1 (blue). There is little variation in 29190



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Figure 4. Isobar curves as a function of RH (eq 13) showing the sensitivities of m and n on the shape in (a)−(c) and the sensitivity of ΔS° on the shift in the isobar curve in (d). Figure 5. Isobar fits to the data using (a) eq 12 and (b) eq 13, resulting in optimized values of ΔS° = −50 J mol−1 K−1, m = 0, and n = 1.

the upper region of the isobar near saturation, whereas in the lower coverage regime, a smaller n generates a sharper rise. Thus, variations in the adsorbate stoichiometry n (see eq 3) greatly influence the curvature in the lower coverage regime (n is related to the desorption reaction order). For constant n = 1 (Figure 4c), with m = 2 (black), 1 (green), and 0.1 (blue), there is little variation between the isobar curves in the lower coverage regime, whereas in the upper coverage regime, a smaller m generates a sharper rise. Thus, variations in the surface site stoichiometry m (see eq 3) greatly influence the curvature near saturation (m is related to the adsorption reaction order with respect to surface sites). Because m and n sensitively affect the curvature of an isobar curve in distinctly different regions (high vs low coverage regimes, respectively), they are sensitive parameters that can be determined by fitting to the data. Next we will examine how ΔS° influences an isobar for constant m and n. Using m = n = 1, Figure 4d plots values of ΔS° = −40 (black line), −50 (green line), and −60 J mol−1 K−1 (blue line). Unlike m and n, ΔS° has little effect on the shape of the isobar curve and instead leads to a shift to higher RH when going from −40 to −60 J mol−1 K−1. In summary, Figure 4 shows that m, n, and ΔS° affect an isobar shape and shift in characteristically different ways and, therefore, allow us to confidently extract values from these parameters by fitting to the data. Figure 5 shows results for the best fits to the data as a function of temperature (Figure 5a) and RH (Figure 5b). The best fits correspond to values of ΔS° = −50 J mol−1 K−1, m = 0, and n = 1. Note, from eq 6 we can see that for m = 0 and n = 1, Θ ∝ pe−ΔH°/RT. Thus, for constant pressure conditions, coverage increases exponentially with decreasing temperature, which is what is observed experimentally (Figure 5a). In the next section we will compare the value of ΔS° = −50 J mol−1 K−1 extracted here to a ΔS° value extracted from the intercepts of Clausius−Clapeyron fits. 3.1.4. ΔS° as a Function of Coverage. From the experimental intercepts (bexp) extracted from the Clausius− Clapeyron fits (Figure 3a), the adsorption entropy as a function of coverage is calculated (see eq 10) by ⎡ ⎛ ⎤ ⎞ Θn ⎥ ΔS o = R ⎢ln⎜ o m ⎟ − bexp ⎣ ⎝ K (1 − Θ) ⎠ ⎦

As seen from eq 14, calculating ΔS° as a function of coverage depends on the stoichiometry coefficients, which we have determined from the isobar analysis to be m = 0 and n = 1. Figure 6a shows results of ΔS° as a function of coverage using eq 14 and K° defined by eq 7. The error bars in ΔS° are

Figure 6. (a) Entropy of hydroxylation (ΔS°) determined from the intercepts (bexp) of the Clausius−Clapeyron fits from Figure 3a and using eq 14. Error bars correspond to 1.96 σ in bexp. Dashed line corresponds to the average value of all five data points (−50 ± 7 J mol−1 K−1). (b) Gibbs free energy (ΔG°) at 298.15 K. Error bars correspond to propagated errors in ΔH° and ΔS°. Dashed line corresponds to average of all five data points (−25 ± 1 kJ mol−1).

1.96 σ in bexp. As seen from Figure 6a, the values of ΔS° in the low coverage regime are statistically indifferent from those in the high coverage regime. Thus, within experimental uncertainty, ΔS° is constant with coverage. The average (±1.96 σ) of all five measurements is −50 ± 7 J mol−1 K−1 and is shown by the dashed line in Figure 6a. This value is consistent with the value obtained in the previous section via isobar curve analysis. Similar to ΔH°, an observed coverage independent ΔS° was surprising. If island growth were occurring, for example, then

(14) 29191



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where s0 is the initial sticking probability at zero coverage and Ea is the energy barrier for adsorption. Assuming thermal accommodation of the adsorbate, Ea is predominantly overcome by the sample temperature Ts.56 f(Θ) is a probability function of surface coverage which represents the probability that a collision will take place at an unoccupied site. There are a number of functional forms for f(Θ) in the literature which consider the elementary interaction statistics of the adsorbate with vacant and filled sites, and terminates at monolayer coverage.57 Here we consider eq 3 as an overall reaction rather than an elementary reaction step and use the Langmuirian formalism f (Θ) = (1 − Θ)m, where m is the adsorption reaction order defined previously. The flux F of Ag to the surface is given by F = p/ (2πMkTg)1/2, where p is in Pascals, M is the molar mass of the impinging molecule (kg mol−1), k is the Boltzmann constant (1.38 × 10−23 J K−1 molecule−1), and Tg is the gas phase temperature in Kelvin. This gives rise to units of molecules (or atoms) m−2 s−1 for F. The rate of adsorption (ra) is the product of F and s (eq 17), which gives

the degrees of freedom of the adsorbate would change as a function of coverage. The OH groups in the center of the island would be laterally interacting with adjacent OH groups in all directions, whereas OH groups on the edge of the islands would not be surrounded by OH groups in all directions. Such differences in lateral interactions would lead to variations in vibrational and rotational degrees of freedom and, thus, changes in the entropy of the adsorbate. A coverage independent ΔS° suggests that under low and high coverage conditions hydroxylation−dehydroxylation events at terrace sites have similar degrees of freedom, which may suggest a mechanism of dissociation-recombination events occurring via isolated hydrogen-bonded hydroxyl pairs at terrace sites that do not interact laterally with other hydroxyl pairs. Figure 6b shows the Gibbs free energy (ΔG°) calculated at 298.15 K as a function of coverage. The average (±1.96 σ) of all five measurements is −25 ± 1 kJ mol−1. The stoichiometry of the surface reaction is consistent with forming a surface Mg(OH)2 species,30 although the exact structure has yet to be determined experimentally under ambient conditions. The bulk reaction of water with MgO leading to Mg(OH)2 (brucite) is calculated from Gibbs free energy of formation values55 to be ΔG°(298.15 K) = −35.6 kJ mol−1. This suggests that the surface reaction leads to a hydroxylated Mg(OH)2 interface that is metastable, with an as yet undetermined kinetic barrier leading to the bulk formation of Mg(OH)2. From the APXPS experiments it was observed that this metastable hydroxylated interface remains stable at least on the order of several hours, which was the time duration of the synchrotron experiments to capture individual isobars. This stability is evidenced in the results of Figure 1 which lead to a saturation of OH coverage at one monolayer. If the metastable interfacial hydroxylation reacted significantly into the bulk, then the saturation effect observed in Figure 1 for all isobars would not be present. Instead, there would be a continual rise in the coverage of OH as it reacted beyond one monolayer and into the bulk. 3.2. Surface Kinetics. Next, we will consider a kinetic approach to understand hydroxylation and dehydroxylation under adsorption−desorption equilibrium conditions similar to the work of Weiss and Ranke.56 In so doing, one can extract the desorption frequency factor (ν) for dehydroxylation of the metal oxide surface, which is the goal of this section. 3.2.1. Kinetic Derivation for Keq. The rate expression for Aad in eq 3 in units of coverage and pressure is given by m

rate = ra − rd = kap(1 − Θ) − kd Θ

n

ra = kap(1 − Θ)m

where ka is given by s0 ka = e−Ea / RTs 2πMkTg

ka Θn = kd p(1 − Θ)m

rd = kdg(Θ)

(20)

where kd is given by kd = (NT)n νne−Ed / RTs

(21)

where νn is the desorption frequency factor, n is the desorption reaction order, NT is the total surface site density (sites m−2), and Ed is the desorption energy barrier. g(Θ) is the probability function for desorption from an occupied site. For Langmuirian-type desorption g(Θ) = Θn. Substituting this into eq 20, the rate of desorption becomes rd = kd Θn

(22)

Setting ra = rd, from eqs 16, 18, 19, 21, and 22, we get

(15)

Keq =

s0 Θn e−q / RTs m = n p(1 − Θ) (NT) νn 2πMkTg

(23)

where q is the isosteric heat of adsorption given by

q = Ea − Ed

(24)

This convention is chosen such that q values for an exothermic process will be negative, similar to ΔH°. Equation 23 gives the equilibrium constant for adsorbate Aad as a function of elementary kinetic parameters s0, νn, and q. Note, ra = rd is a quasi-equilibrium since eq 23 allows for Tg ≠ Ts, whereas true equilibrium has Tg = Ts.42 3.2.2. νn as a Function of Coverage. Solving eq 23 for ln p gives

(16)

Next we use adsorption−desorption kinetic theory42 in order to obtain equations for ka and kd (and, therefore, Keq) as a function of elementary kinetic parameters. For an activated process, the sticking probability (s) as a function of Θ is given by s = s0e−Ea / RTsf (Θ)

(19)

and has units of molecules (or atoms) m−2 s−1 Pa−1. The rate of desorption (rd) is given by

where ra and rd are the rates of adsorption and desorption, and ka and kd are the adsorption and desorption rate constants, respectively. Here we again emphasize that eq 3 is an overall reaction, which from a kinetics perspective contains, heretofore, undefined reaction orders m and n. Under quasi-equilibrium conditions, ra = rd, and the equilibrium constant is defined by Keq =

(18)

⎡ (NT)n νn 2πMkTg q Θn ⎢ ln p = + ln ⎢ (1 − Θ)m RTs s0 ⎣

(17) 29192

⎤ ⎥ ⎥ ⎦

(25)



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negligible. Under such conditions, molecularly bound water desorbs at lower temperatures, followed by driving off the more strongly bound OH groups at higher temperatures. The experiments performed in this study were under adsorption− desorption conditions, where molecularly bound waters are present at the interface during the dehydroxylation process. More specifically, between 0.01 to 0.1% RH, where the hydroxyl coverage rapidly raises to saturation (Figure 2), the molecular water coverage increases to about one-third of a monolayer at 0.1% RH.31 Thus, in comparison to TDS, where desorption via hydroxyl recombination predominates the kinetics, both hydroxylation and dehydroxylation are occurring concomitantly under the APXPS experimental conditions. The desorption frequency factor is a pre-exponential term for the desorption process (eq 21), here modeled under adsorption− desorption conditions. Assuming the first order kinetics are due to hydroxyl recombination,10 the relatively small value of ν = 1.4 × 1011 s−1 could indicate that there are less degrees of freedom in the recombinative transition state compared to the adsorbed OsH and MgsOH states. The effect, if any, that adsorbed water has on the recombinative desorption mechanism remains unclear. 3.2.3. Zero Order Hydroxylation Kinetics. While dehydroxylation kinetics have been studied relatively extensively under UHV conditions,10 little is known about the adsorption kinetics for hydroxylation. The results herein give rise to a zero order adsorption kinetic (m = 0). More specifically, from eq 14 we see that a value of m = 0 corresponds to a zero order kinetic with respect to terrace site surface concentrations given by (1 − Θ) m . Zero order kinetics with respect to gas phase concentrations is not uncommon in heterogeneous catalysis, for example, with bimolecular surface reactions in the limit of high pressures.58 Zero order adsorption kinetics with respect to surface sites have been reported, for example, with N2 on Ir(110) under cryogenic conditions.59 This was observed by integrating TDS peak areas to determine coverage, which was monitored as a function of adsorption temperature. The resulting uptake curve shape was interpreted to be zero order adsorption, indicative of precursor kinetics. To our knowledge, the results presented herein are the first report of zero order surface kinetics with respect to surface site concentrations for a gas-surface reaction under ambient adsorption−desorption conditions. Reiterating that the observed zero order kinetic is for the overall reaction in the adsorption direction of eq 3, it is apparent that there must be other as yet unknown fundamental reaction steps leading to an observed m = 0. Such zero order kinetics suggest that terrace site hydroxylation may follow a precursor mechanism involving molecularly bound mobile waters.

where a Clausius−Clapeyron analysis allows for the determination of q from the slope. A similar expression to eq 25 was derived by Weiss and Ranke,56 showing that the intercept of a Clausius−Clapeyron fit should be sensitive to desorption kinetics (i.e., νn). As we will show, for terrace site hydroxylation νn is independent of coverage within experimental error. From a Clausius−Clapeyron analysis of ln p versus 1/Ts the desorption frequency factor can be calculated as a function of coverage from the experimental intercept (bexp) given by νn =

s0 (1 − Θ)m ebexp n n (Θ) (NT) 2πMkTg

(26)

The MgO(100) terrace site surface density is defined from the cubic lattice constant (a = 2.1 × 10 −10 m) and a unit cell of 2MgO (2a)−2, or NT = 1.13 × 1019 MgO sites m−2, where the Mg2+ and O2− ion pair is defined as a single site for the heterolytic dissociation of water. Figure 7 shows νn as a function of coverage using eq 26 assuming s0 = 1 and using the experimentally determined values

Figure 7. Desorption frequency factor (νn) as a function of coverage using eq 26. Error bars correspond to 1.96 σ in bexp. Dashed line corresponds to the average value of all five data points (1.4 × 1011 s−1).

of m = 0 and n = 1. The error bars in νn are 1.96 σ in bexp. With n = 1, νn is a first order desorption frequency factor. Similar to ΔH° and ΔS°, νn is seen to be statistically indifferent from low to high coverages and is, therefore, independent of coverage within experimental error, all the way up to saturation. The average (±1.96 σ) for all five measurements is 1.4 (±1.2) × 1011 s−1. There have been an extensive number of studies looking at the dehydroxylation of metal oxides using TDS, with observed desorption kinetics ranging from zero, to first, to second order.10 Thus, our observation of a first order dehydroxylation kinetic (n = 1) under ambient conditions is not surprising. Using the example of dehydroxylation from α-Cr2O3 (0001), Henderson10 proposed that a first order dehydroxylation kinetic is due to the recombination of paired hydroxyls at the interface, that is, first order with respect to the coverage of the paired hydrogen-bonded OH groups. For a water monomer on MgO(100) terrace sites, it is energetically unfavorable to exist in the dissociated state unless stabilized by adjacent molecularly bound waters.31 Thus, the observed first order desorption kinetics could be due to recombination of a hydroxyl pair composed of a hydrogen at a surface oxygen site (OsH) hydrogen bonded to a hydroxyl group atop an adjacent Mg surface site (MgsOH), both of which are stabilized by molecularly bound water. During the first order desorption process, this hydrogen-bonded hydroxyl pair is suggested to recombine and desorb from the surface. TDS experiments are conducted under high vacuum where desorption into the vacuum predominates and readsorption is

4. CONCLUSIONS Traditionally, TDS has been the most heavily used technique to extract molecular level coverage dependent surface energetic parameters. The results presented herein represent a step forward in narrowing the pressure gap on molecular level surface energetic analyses. The surface energetics presented in this study for the hydroxylation-dehydroxylation at MgO(100) terrace sites were extracted by conducting thermodynamic and kinetic analyses of ambient pressure XPS experimental data30,31 under adsorption−desorption conditions. Results were assessed as a function of coverage (isosteric conditions). First order desorption kinetics due to hydroxyl recombination gave a frequency factor for desorption of 1.4 × 1011 s−1. The 29193



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adsorption kinetics were zero order, suggesting that molecularly bound water is a mobile precursor prior to dissociation at terrace sites. The standard state enthalpy and entropy for hydroxylation were found to be independent of surface coverage up through saturation, an unusual behavior, suggesting that the hydroxylation−dehydroxylation mechanism does not occur via island formation or through lateral interactions. Such coverage independence suggests that once dissociated, the hydroxyl pairs at individual MgO sites do not interact laterally as the hydroxyl coverage increases with increasing relative humidity up through surface saturation. The room temperature Gibbs free energy for terrace site hydroxylation was found to be less stable than that for the bulk reaction of water with MgO to form bulk Mg(OH)2 (brucite), suggesting that the complex kinetics lead to a metastable hydroxyl structure at the interface. The results presented herein represent the first comprehensive surface energetic analyses for XPS studies under ambient conditions and help set the stage for future APXPS thermodynamic and kinetic analyses under adsorption− desorption conditions relevant to chemical systems in energy and environmental sciences.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by NSF ANT-1019347 and startup funding from the University of Delaware. The author wishes to thank Hendrik Bluhm, Gordon Brown, David Starr, Tom Kendelewicz, Susumu Yamamoto, and Soeren Porsgaard for fruitful discussions during the initial stages of development.

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Surface Thermodynamics and Kinetics of MgO(100) Terrace Site

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