Structure of CO2 Adsorbed on the KCl (100) Surface

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Structure of CO2 Adsorbed on the KCl(100) Surface Franziska Traeger,† Milica Hadnadjev,‡ Jochen Vogt,*,‡ and Helmut Weiss‡ † ‡

CvO Universit€at Oldenburg Fakult€at 5 - IRAC, Physikalische Chemie 1, 26111 Oldenburg Chemisches Institut der Otto-von-Guericke-Universit€at Magdeburg, Universit€atsplatz 2, 39106 Magdeburg, Germany ABSTRACT: The structure and dynamics of the adsorbate CO2/KCl(100) from a diluted phase to a saturated monolayer have been investigated with He atom scattering (HAS), low-energy electron diffraction (LEED), and polarization dependent infrared spectroscopy (PIRS). Two adsorbate phases with different CO2 coverage have been found. The low-coverage phase is disordered at temperatures near 80 K √and√becomes at least partially ordered at lower temperatures, characterized by a (2 2 2)R45 diffraction √ √ pattern. The saturated 2D phase has a high long-range order and exhibits (6 2 2)R45 symmetry. Its isosteric heat of adsorption is 26 ( 4 kJ mol1. According to PIRS, the molecules are oriented nearly parallel to the surface, the average tilt angle in the saturated monolayer phase is 10 with respect to the surface plane. For both phases, structure models are proposed by means of potential calculations. For the saturated monolayer phase, a striped herringbone structure with 12 inequivalent molecules is deduced. The simulation of infrared spectra based on the proposed structures and the vibrational exciton approach gives reasonable agreement between experimental and simulated infrared spectra.

’ INTRODUCTION Adsorption processes of atoms and molecules on the surfaces of solids are one of the key topics in surface chemistry.1 Physisorption, sometimes called “weak adsorption”,2 is characterized by binding energies of the adsorbing particles typically below 50 kJ mol1. Well-investigated model systems of physisorption are adsorbates of rare gases on metal surfaces.2,3 Physisorption of small molecules like CO or CO2 on ionic substrates, mostly alkali halides and oxides, has been investigated in the past decades in a considerable number of experimental and theoretical studies.423 The type of bonding in these systems is dominated by electrostatic interaction and short-range repulsion and dispersion interaction. An exchange of electronic charge density with the surface can be neglected on alkali halides, deduced, e.g., from the analysis of the IR spectra of these adsorbates.11 There is some theoretical interest in such weakly bound two-dimensional molecular adsorbates:3,17,18,24,25 compared to atom adsorption, the complexity increases due to the significance of orientational ordering. Electrostatic interaction, mainly of the dipoledipole or quadrupolequadrupole type, has the tendency to orient the molecules in domains with antiferroelectric or herringbone-like structures. Therefore, such systems serve also as model systems for studies of phase transitions between orientational order and disorder.24,25 Apart from infrared spectroscopy, which is a universal tool for the characterization of heteronuclear molecular adsorbates, diffraction techniques have proven to be indispensable for surface analysis. In the case of insulating substrates, helium atom scattering (HAS) is the diffraction method of choice, due to its extraordinary surface sensitivity and the fact that the electrically neutral helium atoms with typical primary energies of 1525 r 2011 American Chemical Society

meV neither lead to surface charging or defect generation. In recent years, low-energy electron diffraction (LEED) has been applied also to physisorbates on insulating surfaces.19,2629 CO and CO2 adsorption on the NaCl(100) surface are among the model systems of molecular physisorption, which have been studied most intensively. These were fortunate cases in the sense that the simplicity in these systems enabled researchers to gain insight not only in the adsorbate structure but also in dynamic properties like vibrational excitation and relaxation or surface phonon dispersion with exceptional completeness.6,9,14,17,23 The monolayer phase NaCl(100)/p(21)-CO2 has been called a “two-dimensional molecular crystal”,9 due to its high order and the large extension of the adsorbate islands. A well-understood feature associated with this structure is the Davydov splitting of the ν3 asymmetric stretch mode in an in-phase and an out-of-phase excitation of the two inequivalent molecules in the unit cell, mediated by dynamic dipoledipole coupling.12,13,16 However, only a little work on CO or CO2 physisorption on other alkali halide surfaces has been published so far.18 Compared to the lattice parameter of NaCl, that of KCl is increased by 11%. A more complicated adsorption behavior is thus expected on this substrate and is indeed observed in our experiments, as will become clear in this paper: apart from a lattice gas at very low coverage, an intermediate adsorbate phase is observed, which is disordered at higher temperatures, and becomes at least partially Special Issue: J. Peter Toennies Festschrift Received: December 23, 2010 Revised: April 13, 2011 Published: April 27, 2011 6986

dx.doi.org/10.1021/jp112219t | J. Phys. Chem. A 2011, 115, 6986–6996

The Journal of Physical Chemistry A

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ordered √ √at low temperatures. A high-order dense phase with (6 2 2)R45 translational symmetry is observed at saturation coverage, which, judged from the surface area of this unit cell, is large enough to contain 12 inequivalent molecules. It is obvious that the vibrational excitation patterns of such a structure are more complicated than in the case of the above-mentioned Davydov doublet in NaCl(100)/p(21)-CO2. Our attempt is to apply the same mechanism of the above-mentioned dipole dipole coupling to understand the relationship between adsorbate structure and infrared absorption in this more complicated case. Therefore, structure models are proposed which are based on cohesive energy minimizations and pair-potentials.30 Finally, the use of such structure models to understand how substrate induced strain influences molecular self-organization, will be discussed. This paper is organized as follows. In the Experimental Section the various experimental methods are introduced and the results of the experiments are given. Then, the theoretical methods are outlined and results from the calculations are presented. Finally, all results are discussed and summarized in the Discussion and Conclusions.

’ EXPERIMENTAL SECTION Helium Atom Scattering Experiments. Apparatus. A description of the He scattering setup has been published before.31 In short, a He atom beam is produced by expanding 99.9999% pure He gas through a 10 μm nozzle with stagnation pressures between of 40100 bar. Nearly monoenergetic (ΔE/E = 2%) beams with energies in the range of 12.021.5 meV are achieved by varying the source temperature between 55 and 100 K. After scattering off the surface, the beam passes through three differential pumping stages and is then detected by a magnetic mass spectrometer. In a fixed angle geometry (θi þ θf = 90.1), diffraction patterns (angular distributions) are measured by rotating the crystal around an axis normal to the plane of the incident and scattered beams; therefore, incident and final angle are changed simultaneously. The KCl surface was prepared by cleaving off a small slice from a KCl single crystal with 10 10 mm2 surface area at a surface temperature of 100 K under UHV. After cleavage and between measurements, the crystal was heated to 400 K to prevent possible deterioration of the surface by residual water. HAS Results. Structural phase transitions and adsorption/ desorption processes can be identified by monitoring the specular He beam intensity as a function of surface temperature. Figure 1a shows such a curve recorded upon lowering the crystal temperature (TS) from 100 to 40 K under a constant CO2 partial pressure of 7.0 109 mbar. Adsorption starts at around 94 K, and at TS = 77 K the first phase and from TS = 58 K on the second ordered phase is found, both of which correspond to maxima in intensity. In the following they are referred to as phase 1 and phase 2. The pronounced minimum at T = 80 K can be interpreted in terms of 2D adsorbate growth via statistical adsorption of immobile CO2 molecules. As expected, at TS = 46 K condensation of bulk CO2 is observed. For the desorption curve in Figure 1b, the surface has been heated from 40 to 100 K without further gas supply. Between 40 and 52 K the specular intensity decreases due to the rather large DebyeWaller attenuation of the multilayer, subsequently the multilayer desorbs. Going further up to 80 K the intensity decreases again, this time due to the DebyeWaller attenuation of the phase 2. At about 82 K it desorbs leaving phase 1, which finally desorbs starting at 87 K. The stability range of the first phase is much

Figure 1. Specular intensity during adsorption (a) and desorption (b) of CO2/KCl. For both curves the crystal was aligned along [110] and the incident wave vector was ki = 5.76 Å1. Curve a is corrected by a factor of 3.4, because the data were recorded with attenuated beam to prevent saturation of the detector.

smaller than observed in the adsorption curve of Figure 1a. Together with experiments, in which successively only small amounts of CO2 were dosed, this behavior indicates that phase 2 corresponds to higher coverage, which can only build up slowly by filling adsorption sites of the less dense phase 1, Figure 1a. Once this phase is complete, it is stable up to 82 K. He atom angular distributions for the [100], [110], [210], and [310] azimuthal directions are shown in Figure 2 for both phases. The angle scale has been converted to parallel momentum and the arrows indicate the position of substrate (KCl) diffraction peaks. The incident wave vector is 6.5 Å1 except for the angular distribution along [100] for phase 2, for which it is 4.8 Å1. Considering unit cells with √ √ all peak positions, superstructure √ √ (2 2 2)R45 symmetry and (6 2 2)R45 symmetry are found for phase 1 and 2, respectively. Both reveal glide plane symmetry along Æ100æ. Note that the He atoms interact with the topmost layer only. Therefore, there is no doubt that the observed superstructure reveals the symmetry of the adsorbate unit cell. Angular distributions of phase 2 recorded with various incident wave vectors are shown in Figure 3. The intensity of the additional diffraction peaks is always higher close to the integral order diffraction peaks. This behavior is not a general characteristic for He atom scattering and usually indicates buckling of the layer.32 LEED and PIRS Experiments. Apparatus. The LEED and the IR spectroscopy experiments were performed with a different experimental setup, which has been described extensively in previous studies.28,29 In the present experiments a KCl single crystal (20 20 mm2 cross section area) was cleaved ex situ under nitrogen 6987

dx.doi.org/10.1021/jp112219t |J. Phys. Chem. A 2011, 115, 6986–6996


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Figure 3. Anglular distributions along the [100] directions for various incident wave vectors as given in the figure. Figure 2. Angular distributions for both 2D phases of CO2/KCl. The positions of the diffraction peaks of KCl are marked by arrows.

atmosphere twice to give a slice of about 3 mm thickness with two fresh (100) cleavage planes. Afterward the sample was mounted on a sample holder and transferred into the vacuum chamber. The sample was cooled by means of a cold head refrigerator (Leybold) connected to the sample holder via a flexible copper braid. A tungsten filament at the sample holder was used to set and control the temperature in a range between 20 and 400 K. The temperature was measured with a silicon diode (LakeShore) with an absolute error of 2 K and a statistical error of 0.1 K. The background pressure under experimental conditions was better than 1 1010 mbar. The composition of the gas phase could be checked by means of a quadrupole mass spectrometer. In all experiments CO2 (Messer Griesheim, purity 99.999%) with natural abundance of isotopomers was used without further purification. The LEED apparatus mounted in the UHV chamber was a Omicron microchannelplate optics (MCPLEED) designed for LEED experiments with very low primary electron beam currents in the range of about 1 nA.19,33 Due to the use of such low primary currents charging of the insulating KCl single crystal is prevented, and electron beam induced defect generation is minimized. Infrared spectroscopy experiments in transmission geometry were performed using a Bruker IFS 120 HR infrared spectrometer of the Michelson type. A liquid nitrogen cooled InSb detector was used in combination with a silicon coated CaF2 beam splitter. A wire-grid polarizer was used to detect s- and p-polarized IR light, respectively. Spectra were recorded in a

range between 1900 and 4000 cm1. No signs of water contamination of the surface were detected during the experiments. The angle of incidence of the IR beam was β = 45. The resolution of the presented spectra is Δν~ = 0.2 cm1. LEED Experiments. Image A in Figure 4 shows a LEED pattern, which was recorded after the sample was exposed 5 min to 7 109 mbar CO2 at a crystal temperature of 78 K. Apart from the bright integral order diffraction peaks a diffuse inhomogeneous background is discernible, indicating the presence of a disordered adsorbate on the surface under these conditions. Then, the exposure was stopped and the crystal was cooled to 25 K. The LEED pattern B in Figure 4, recorded at this stage of the experiment, is characterized by an increase of diffraction spot intensity, as expected from the DebyeWaller effect. In addition, superstructure is more pronounced in the diffraction patterns: in accordance with the HAS√experiments, the additional super√ structure spots are on a (2 2 √2)R45 √ grid (phase 1). While additional spots situated on the ( 2 2)R45 grid are as sharp as integral order√peaks, √ additional superstructure spots that complete the (2 2 2)R45 grid have elliptical or even a streaked shape. This point will be further discussed in the next section. In another LEED experiment the clean KCl(100) surface was exposed continuously at 78 K to CO2 at 7 109 mbar. After 10 min of exposure, the LEED pattern change again (Image C in Figure √ 4) and √ rich superstructure becomes visible, consistent with the (6 2 2)R45 symmetry (phase 2) observed in the HAS experiments. Moreover, the 4-fold symmetry of the perfect KCl(001) surface is reflected also in the diffraction peak intensities of equivalent superstructure spots originating from adsorbate domains with different orientations. This indicates equal proportions of adsorbate islands oriented along [100] and [010] direction. 6988



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Figure 4. LEED patterns of the KCl(100) surface, covered with CO2. (A) After 5 min of exposure to 7√ 10√9 mbar CO2, sample temperature 78 K. (B) After cooling, the sample at stopped exposure to 25 K. (C) Pattern at saturation coverage and (6 2 2)R45 symmetry.

PIRS Experiments. In another series of experiments the adsorption of CO2 on KCl(100) was investigated in a wider pressure range using IR spectroscopy. Diagram A in Figure 5 shows a pair of s- and p-polarized spectra, which were recorded at a sample temperature of 78 K, when the clean sample was exposed to 6 1010 mbar CO2. A weak but sharp absorption at 2348.3 cm1 can be assigned to a lattice gas present at the surface under these conditions.10 This absorption is red-shifted by 1.1 cm1 with respect to the corresponding gas-phase value of the ν3 mode. Moreover, a second absorption at 2347.0 cm1 is a hint of the presence of dimers or small isolated clusters of carbon dioxide molecules on the surface under these conditions. In another experiment the clean surface was exposed to 7 109 mbar CO2 at the same sample temperature. After 5 min of exposure (1.6 Langmuir), a broad and asymmetric absorption R between 2340 and 2350 cm1 is observed in s- and p-polarized spectra (diagram B of Figure 5, upper part). A weaker band β at 2353 cm1 is also observed. As in the LEED experiment described above, the exposure was stopped, the crystal was cooled to 25 K, and the pair of IR spectra shown in the lower part in diagram B was recorded. It is characterized by a sharp doublet of asymmetric absorptions γ and δ, visible in s- and p-polarized light. From the comparison with the LEED experiment, the appearance √ of√this doublet can be assigned to the formation of the (2 2 2)R45 symmetry in the diffraction patterns, which was assigned to phase 1. When the KCl(100) surface was continuously exposed to 7 109 mbar CO2 at 78 K for more then 10 min, the PIRS spectra changed again (diagram C of Figure 5). They became dominated by a sharp and intense absorption γ at 2328.5 cm1, red-shifted with respect to the corresponding gas-phase reference by more

than 20 cm1. Two weaker bands R and β at 2325.0 and 2325.8 cm1 are due to small concentrations of 12C18O16O, as shown by Thomas.34 As many as four additional absorptions (δ, ε, ζ, and η) can be resolved at 2339.9, 2344.2, 2354.9, and 2356.2 cm1, respectively. The last mode, blue-shifted by 7 cm1 with respect to the gas-phase reference, only appears in p-polarized spectra, indicative of an induced net dipole-moment perpendicular to the surface plane. Due to the fact that the spectra in diagram C of Figure 5 were obtained under the same conditions, under which the LEED pattern in Figure √ 4C was √ recorded, we assign these to the adsorbate phase with (6 2 2)R45 translational symmetry. From the PIRS experiment, direct information about the predominant orientation of the dipole moments with respect to the surface plane can be obtained via the ratio of integrated absorptions in s- and p-polarization, respectively.8,15,16,28,29 Because the dipole moment involved with the ν3 mode of CO2 is parallel to its molecular axis, direct structural information is obtained in this way. The As/Ap ratio is plotted in Figure 6 as a function of the tilt angle θ of a dipole moment with respect to the surface plane. The derivation of this function is based on the electric field vectors of the infrared beam on the front and backside of the surface, calculated by means of Fresnel’s laws, a nonabsorbing substrate with index of refraction n = 1.47 for KCl in the mid-infrared range,35 and the presence of adsorbate domains with four possible orientations on the KCl(100) single crystal surface. As can be seen in Figure 6, the measured value of the average As/Ap ratio of 1.5 ( 0.1 in the spectra in Figure 5C is consistent with an average tilt angle of the molecules of 10 with respect to the surface plane. However, the presence of mode η visible only in the p-polarized spectra, is a clear indication for 6989



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Figure 5. PIRS spectra of CO2 adsorbed on KCl(100), recorded in the ν3 region. (A) Lattice gas absorption. (B) Spectra of the intermediate phase 1 at 78 K (upper pair) and at 25 K (lower pair). (C) PIRS spectra of phase 2 at saturation coverage.

Figure 6. As/Ap ratio (see text), as a function of the tilt angle θ of a dipole moment on a KCl(100) surface. Angle of incidence of the infrared light: β = 45.

nonzero tilt angles of at least some of the molecules in the adsorbate unit cell. Moreover, the determination of the As/Ap ratio in the spectra depicted in Figure 5B reveal also for phase 1 nonzero average tilt angles between 10 and 20. Unfortunately, in the case of the lattice gas (Figure 5A), no meaningful results could be obtained. This is due to the weakness of the measured infrared absorption in this case and, moreover, due to the fact that an adsorption/ desorption equilibrium at a coverage of only about 1% of a monolayer was hard to establish in the experiments. Furthermore, the pressure and temperature dependence of the IR spectra was investigated. Figure 7 shows the measured integrated IR absorption in s-polarization as a function of CO2 partial pressure at a crystal temperature of 84 K under the conditions of adsorption/desorption equilibrium. The dashed lines indicate the

Figure 7. Integrated absorption of s-polarized spectra in the ν3 region at various CO2 partial pressures and a sample temperature of 84 K.

phase boundaries, deduced from the various spectra profiles of the lattice gas, phase 1, and phase 2, respectively. The most striking feature of this adsorption isotherm is the marked increase of IR absorption within a very narrow pressure range between 6 108 and 7 108 mbars going from phase 1 to phase 2, consistent with an increase of surface coverage, as also deduced from the HAS experiments. At 82 and 80 K, this phase boundary shifts to lower pressures of (2 ( 1) 108 mbar and (9 ( 3) 109 mbar, respectively. From these data the isosteric heat of adsorption qs of phase 2 can be estimated from the ClausiusClapeyron equation, Dlnðp=pQ Þ qs ¼ 1 R D T

ð1Þ

where R is the universal gas constant and pQ is the standard pressure. A value of qs = 26 ( 4 kJ mol1 follows, which is 6990



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considerably smaller than the isosteric heat of adsorption of CO2 on the NaCl(100) surface of 35.6 ( 1.3 kJ mol1, measured by Heidberg et al. with the same method.15 A possible explanation for the lower heat of adsorption of the CO2 adsorbate on KCl(100) compared with NaCl(100) might be found in the larger lattice parameter of KCl, the resulting larger lattice mismatch, and thus a more unfavorable balancing between moleculemolecule and molecule surface interaction.

’ POTENTIAL CALCULATIONS AND SPECTRUM SIMULATIONS The structure of CO2 adsorbed on the KCl(100) surface was modeled by means of minimizing the cohesive energy V at 0 K of the adsorbed molecules in the approximation of pair-potentials, V ¼

∑A VMS;A þ 2 A;B ∑ VMM;AB 1

ð2Þ

The cohesive energy is understood here as the energy required to break the adsorbate structure into isolated molecules in infinite distance from the surface. In eq 2 VMS,A is the molecule-surface interaction energy of molecule A and VMM,AB is the molecule molecule interaction energy of two molecules A and B. The molecules are assumed to have a rigid internal structure with a CO bond length of 1.162 Å. The calculation of VMM,AB is based on an intermolecular potential derived from symmetry adapted perturbation theory by Bukowski et al.30 The model makes use of five interaction sites a ∈ A and b ∈ B, respectively, on pairs of molecules A and B. One site is located on the carbon (partial charge qC = þ1.63e), two on the oxygens (qO = þ0.24e), and two interaction sites with a partial charge of qM = 1.05e on the bonds between carbon and oxygen, 0.32 Å displaced from the oxygens. The sitesite interaction energy involving electrostatic interaction as well as repulsive and dispersive interaction terms in this model is30 qa qb VMM;AB ¼ eRab βab rab þ f1 ðδab 1 rab Þ rab a∈Ab∈B Cab Cab 6 8 f6 ðδab f8 ðδab ð3Þ 6 rab Þ 8 rab Þ 8 6 rrab rrab

∑ ∑

where x

fn ðxÞ ¼ 1 e

xk k ¼ 0 k! n

∑

Table 1. Sets of Lennard-Jones Parameters Used for the Calculation of Short-Range MoleculeSubstrate Interactionsa σ (Å)

KC

0.3613

2.5709

KO

0.6117

2.6750

ClC

0.3169

3.6209

ClO

0.5365

3.7250

a

The definition used for the Lennard-Jones potential between two heteropairs i and j is ULJ,ij = 4εij[(σij/rij)12 (σij/rij)6].

and Dent.39 The substrate was assumed to be rigid with a nearest neighbor distance of 3.14 Å. A possible rumpling of the KCl(100) surface was neglected, which is justified by experiment.33 Minimizations of the cohesive energies were performed using Powell’s conjugate directions method40 under variation of all five degrees of freedom for each inequivalent molecule in the simulation box. In all calculations, interactions with a sufficient number of neighboring image unit-cells were taken into account to converge V. Simulations of polarized infrared spectra were performed using a vibrational exciton approach. As shown by previous work on CO2 adsorbates on the NaCl(100) surface,12,13 such models describe dynamic dipoledipole coupling, which is known to give the most important contribution to shifts and splittings of the asymmetric stretch mode of carbon dioxide physisorbed on ionic substrates.11,13 At the same time, this model has only a comparatively small computational burden and allows thus the simulation of mode couplings among hundreds of molecules. Given the wavenumber ν~0 of a single molecule’s ν3-stretch mode Q, and the associated dipole derivative ∂μ/∂Q, the N vibrational exciton states of an adsorbate containing N molecules can be calculated solving the eigenvalue problem " # 2 Tj;k k 1 Dμ ð~ν0 ~νk Þδjk þ c ¼0 4πε0 DQ 8π2 ~ν0 j j

∑

k ¼ 1; 2; :::; N

ð5Þ

for the N vibrational exciton wave numbers ν~k and the respective mixing coefficients ckj for a vibrational exciton state jΦk æ ¼

ð4Þ

ab are TangToennies damping functions.36 Values for the Cab 6 , C8 ab dispersion coefficients as well as damping coefficients δn and repulsion coefficients Rab and βab can be taken from ref 30. In cohesive energy minimizations with a variable 3D unit cell, VMM reproduces the well-known Pa3 cubic crystal structure37 with a lattice constant of 5.48 Å and a molar volume of 24.77 cm3 mol1, 4% smaller than the corresponding experimental low temperature value of 25.84 cm3 mol1 at 13 K.38 The chosen moleculesurface potential VMS,A reproduces results from first principles calculations for the adsorption geometry of a single CO2 molecule bound to a (KCl)16 cluster. It considers Lennard-Jones type repulsiondispersion interactions between surface ions and the atomic sites of the molecule (Table 1) as well as electrostatic interaction between partial charges and the surface electrostatic potential. The latter was summed up in reciprocal space using the formula of Lennard-Jones

ε (kJ mol1)

∑j ckjj01æj02 æ:::j1jæ:::j0N æ

ð6Þ

|0jæ and |1jæ are the ground and first excited state of a molecule j’s ν3 mode. Higher excitations and the possibility of more than one molecule in the adsorbate being excited are neglected in this model. The factor Tj,k in eq 5 gives the well-known orientational dependence of dipoledipole coupling between two molecules j and k at distance rjk from each other: Tj;k ¼

ej ek 3ðej vjk Þðej v jk Þ 3 rj;k

ð7Þ

The unit vector ej points along the axis of molecule j, and vjk is the unit vector along the interconnection line of two molecules j and k. Once the vibrational exciton wave numbers and mixing parameters have been determined, an absorption stick spectrum is obtained on the basis of first-order timed-dependent perturbation theory for excitation of a state |Φkæ from the vibrational 6991



Figure 8. Monomer adsorption sites on the KCl(100) surface, obtained from potential calculations. Left: adsorption geometries (top view) of a molecule in the hollow site A with the lowest adsorption energy. Site B between between points 1 and 2 has a higher energy and is a transition state for migration to a neighboring unit cell. Right: adsorption energy of a molecule along the path 1 f 2 f 3. T is the transition state corresponding to geometry B.

ground state. The perturbation operator is the product of the external electric field vector E = E0ε and the dipole moments of the molecules. The result for the stick spectrum is N π ~ 1 νk Dμ 2 N j ðej εÞckj j2 δð~ νk ~ν Þ ð8Þ Að~ νÞ ¼ F cos β k c2 ~ ν0 DQ j

∑

∑

F is the area of the surface unit cell, and β is the angle of incidence of the infrared beam with respect to the surface normal. The scalar product between ε and the unit vector ej describing the orientation of the molecule j gives the polarization dependence. Note that ε is different on the front side and the back side of the crystal.41 It is calculated from Fresnel’s laws assuming a nonabsorbing substrate with index of refraction of n = 1.47.35 For a better comparison with experimental IR spectra the stick spectrum eq 8 is folded with a Lorentzian of line width 0.2 cm1, which corresponds to the experimental spectral resolution. Furthermore, the calculated absorption spectrum takes domain averaging over the four possible orientations of adsorbate domains on the KCl(100) surface into account. If not stated otherwise, dipole derivatives ∂μ/∂Q = 3.5 D Å1 (amu)0.5 were taken into account, consistent with absolute intensity data of CO2 films published by Yamada and Person.42 The singleton wave numbers for different isotopomers were ν ~0 = 2349.0 cm1 12 16 1 13 16 for C O2, 2283.3 cm for C O2, and 2331.7 cm1 for 16 18 16 C O O. Results of Cohesive Energy Minimizations. Monomers and Surface Diffusion. Monomer and dimer adsorption was investigated in the first stage of the simulations. The calculated optimum adsorption site of an isolated CO2 molecule on the KCl(100) substrate surface is very similar to the adsorption geometry found on the NaCl(100) surface:7,8 The molecular center of mass is located 2.90 Å over the surface in the hollow site between two neighboring Cl anions, as shown in Figure 8 (molecule A, site 3). The molecule is oriented parallel to the surface plane with the oxygens pointing toward the Kþ cations. The resulting potential energy of the molecule is 17.8 kJ mol1. Furthermore, the potential energy surface (PES) of a monomer was determined on the basis of our potential model along the lines connecting point 1 (on top Kþ), 2 (on top Cl), and 3 (hollow site) in Figure 8. According to these calculations, there is a transition state T for surface diffusion to a neighboring hollow site between point 1 and 2. The orientation of the CO2 molecule

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Figure 9. Periodic structures with a coverage of 0.5 monolayers from cohesive energy optimizations √ √ in top view (top) and side view (bottom). (A) Structure with √ (√2 2)R45 symmetry and one molecule per unit cell. (B) (2 2 2)R45 structure with two energetically equivalent but translationally inequivalent molecules and glide-plane symmetry. The glide-plane is marked as a dotted √ line, √the angle φ is the azimuthal orientation. (C) Structure with (2 2 2)R45 symmetry and two energetically inequivalent molecules.

at this site is shown as molecule B in Figure 8. The molecule is tilted and its center of mass is located 3.36 Å above the surface. From the PES an activation energy for surface diffusion of 4.3 kJ mol1 results, a value which is close to measured and modeled activation energies on the NaCl(100) surface.10 Periodic Structures. Several ordered adsorbate structures with a coverage of 0.5 and one monolayer and various translational symmetries were considered for comparison with the experimental data. The simplest √ √ structure with a coverage of half a monolayer has a ( 2 2)R45 unit cell and contains one molecule. It is the periodic continuation of the monomer geometry, with a cohesive energy of 18.72 kJ mol1. The structure in diagram A of Figure 9. A second structure √ is shown √ with (2 2 2)R45 symmetry and two molecules per unit cell is shown in diagram B of Figure 9. In this geometry the two molecules occupy energetically equivalent sites but are translationally inequivalent: the herringbone-like structure has a glide plane along the long axis of the unit cell and has the same cohesive 1 energy √ of √18.72 kJ mol . We have also located a structure with (2 2 2)R45 symmetry in which two molecules occupy energetically inequivalent sites (Figure 9C): one molecule occupies a hollow site with optimized molecule-surface interaction, and the second molecule occupies the transition state T described above with less favorable moleculesubstrate interaction, but a larger contribution from moleculemolecule interaction. Among the investigated periodic structures with a coverage of one monolayer was a (11) structure with a cohesive energy of 20.8 kJ mol1 and tilted molecules. Such a geometry can be ruled out by the present experiments. An optimized monolayer √ √ structure with ( 2 2)R45 translational symmetry is depicted in Figure 10A. It has a cohesive energy of 21.0 kJ mol1 with two energetically equivalent but translationally inequivalent molecules, oriented in a herringbone fashion with glide-plane symmetry, similar to that observed in the monolayer CO2 on NaCl(100).19 The molecules are also tilted and the adsorption sites are again the site T between Kþ and Cl. However, this structure is not stable, if it is relaxed in a simulation box comprising more than one unit cell. The periodic structure with √ the highest cohesive energy √ identified in our model was a (6 2 2)R45 geometry with 6992



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Figure 10. Periodic structures with a coverage of one monolayer from cohesive √ energy √ optimizations in top view (top) and side view (bottom). (A) ( √2√2)R45 structure with two inequivalent molecules. (B) (6 2 2)R45 structure with 12 inequivalent molecules arranged in a distorted herringbone geometry that is laterally interrupted due to the lattice mismatch with the substrate.

12 inequivalent molecules. The structure with an energy of 21.4 kJ mol1 is shown in Figure 10B. In our potential model, it is stable also in optimizations with a simulation box containing several unit cells. Although the structure has no exact glide-plane symmetry as observed in the HAS experiments, the molecules are oriented in a herringbone-like fashion with approximate glideplane symmetry. The herringbone structure is discontinued between molecules 6 and 7, and 1 and 12, respectively, forming thus striped adsorbate islands. Such stripe patterns have been observed also in other two-dimensional systems and are a characteristic feature in systems with competing interactions between adatoms or molecules and the substrate surface.29,43,44 Four inequivalent molecules in the structure in Figure 10B are oriented parallel to the surface plane, the other molecules are tilted. The average tilt angle of the molecules is 18, which is larger than an angle of 10 deduced from the PIRS spectra shown in Figure 5. The molecules 6 and 7 in Figure 10B occupy hollow sites with optimum moleculesurface interaction. Molecules 3 and 10, in contrast, are located on top of Cl. They are stabilized by moleculemolecule interaction, and are bound most strongly with a total potential energy of 33.8 kJ mol1. Results of Spectra Simulations. Simulated infrared spectra of structures obtained from energy minimizations in comparison with experimental spectra give a first idea of the reliability of these proposed structures. In the following we provide two different types of simulated spectra, one with a coverage of a half monolayer (phase 1), and one of an extended adsorbate with monolayer coverage and the above-described striped herringbone structure (phase 2). Both sets of spectra were obtained in Monte Carlo (MC) simulations at finite temperature to model disorder in the adlayer, which is especially important in the lowcoverage phase 1, where disorder has a marked effect on the infrared spectra, as shown above in the Experimental Section. In these simulations adlayer structures of 100300 molecules were considered. In the first part the structure was equilibrated at a given temperature for 50100 kilo cycles. Then, in the second part, IR spectra were calculated on the basis of vibrational exciton theory (eq 8) every 100 cycles. The spectra shown in Figures 11 and 12 are averages over 100 kilo cycles. Figure 11A shows a set of two spectra from structures with a coverage of 0.5 monolayers. The first spectrum (full line) was

Figure 11. Calculated IR spectra from Monte Carlo simulations. (A) Spectra of phase 1 at a coverage of 0.5 monolayers. The√first √ spectrum (full line) was obtained from a distorted structure with (2 2 2)R45 symmetry at a simulation temperature of 25 K. The second spectrum (dashed line) was obtained from a distorted structure of clusters, dimers, and monomers at a simulation temperature of 80 K. (B) Peak wave numbers of the in-phase mode Φþ and the out-of-phase mode Φ calculated for the structure model in Figure 9B and different azimuthal orientations φ and tilt angles θ. The arrows indicate the optimum geometry deduced from the Monte Carlo simulation. The curves indicated by symbols are calculated with a dipole derivative of ∂μ/∂Q = 3.5 D Å1 (amu)0.5. The curve with full line was calculated with ∂μ/ ∂Q = 3.8 D Å1 (amu)0.5 deduced from gas-phase CO2;42 the dashed line was calculated with ∂μ/∂Q = 3.3 D Å1 (amu)0.5 for CO2 ice.42

√ √ obtained from a (2 2 2)R45 structure according to Figure 9B, which was extended in a simulation box with an extension of 50 50 Å2. The simulation temperature was 25 K. The spectrum is characterized by a doublet at 2341.8 and 2349.0 cm1, respectively, which can be assigned to a collective in-phase excitation |Φþæ and an out-of-phase excitation |Φæ of the ν3 mode of the two inequivalent molecules 1 and 2 in the surface unit cell, very similar to that found in the monolayer CO2 p(21) on NaCl(100). The two vibrational exciton states involved with these bands (compare eq 6) are 1 jΦ( æ ¼ pffiffiffiðj11 æj02 æ ( j01 æj12 æÞ 2

ð9Þ

In accordance with the parallel orientation of the molecules in the structure model in Figure 9B, the As/Ap ratio of this PIRS spectrum is 1.55 (compare also Figure 6). The band positions of the doublet agree within 1 cm1 with those of absorptions γ and 6993



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Figure 12. (A) (top view) of a disordered adsorbate with a coverage of 0.5 monolayers. (B) Simulated spectra of the monolayer phase 2 with √ Structure √ distorted (6 2 2)R45 symmetry (T = 80 K) in comparison with experimental spectra.

δ in the experimental spectrum, Figure 5B. This clearly supports the assignment of the low-temperature √ √ structure of phase 1 to a herringbone structure with (2 2 2)R45 translational symmetry as shown in Figure 9B. However, the total absorption of the simulated spectrum exceeds the fraction of absorptions γ and δ in Figure 5B by a factor of 5. This suggests that only a minor portion of the surface area is covered by an adsorbate with √ √ (2 2 2)R45 symmetry even at 25 K. This is also supported by the weak and elliptically shaped additional diffraction spots in the LEED pattern in Figure 4B. In Figure 11B the sensitivity of the simulated infrared spectra to variations of the azimuthal orientation φ (see Figure 9B) and the tilt angle θ of the molecules is shown. Depending on the values for φ and θ, the splitting of the doublet takes values between 0 and 15 cm1. Moreover, the splitting is influenced by the value of the dipole derivative ∂μ/∂Q. Our supported value of 0.35 D Å1 (amu)0.5 is close to the value for CO2 ice (dashed line in Figure 11B). If the somewhat larger gas-phase value for ∂μ/∂Q is chosen, the splitting increases by at most 5 cm1. The second set of spectra in Figure 11A (dashed line) was obtained from a MC simulation of a structure of 100 inequivalent molecules with a coverage of 0.5 monolayers at T = 80 K. The structure depicted in Figure 12A was an arrangement of monomers, dimers, and small clusters of 35 molecules, without longrange order. Despite disorder, the cohesive energy of this structure of 18.5 kJ mol1 was very similar to those of the periodic structures shown in Figure 9. The corresponding averaged IR spectrum is characterized by a broad and asymmetric absorption with a peak wavenumber at 2346 cm1, similar in profile to the measured spectra of phase 1 at 80 K. The fact that under these conditions the LEED experiment gave no hint for an ordered adsorbate further supports the notion of phase 1 at 80 K being disordered. Figure 12B shows a pair of simulated PIRS spectra of the monolayer structure in Figure 10B in comparison with the measured monolayer spectra. The MC simulation was done at a temperature of 80 K for a simulation box with 288 inequivalent molecules covering a surface area of 75 75 Å2. According to the natural ambundance of isotopomers, 284 molecules were of type 12 16 C O2, three molecules of type 13C16O2, and one of type 16 18 16 C O O. The simulated and the measured spectra are both dominated by an intense absorption denoted as g and γ,

respectively. A deeper analysis shows that absorption g at 2332 cm1 stems from a collective in-phase excitation of all 12 molecules in the unit cell, which explains the large absorption. Another common feature is that the modes at highest wavenumber, h and η, are only visible in p-polarization, thus having an induced net dipole moment perpendicular to the surface plane. The vibrational excitation pattern connected with mode h is more complicated: the excitation is predominantly on molecules 1, 2, 11, and 12 (see Figure 10B) with nearly equal occupancies. However, molecules 1 and 2 are vibrating in-phase, but they are out-of-phase with molecules 11 and 12, and this cancels the component of the dipole moment parallel to the surface in this case. Compared to the measured band η, mode h has a too strong absorption. Moreover, the total As/Ap ratio of the simulated spectrum is 1.25, consistent with an average tilt angle of the molecules of 18, while the measured As/Ap of 1.5 points to an average tilt angle of 10. Our interpretation √ √of these results is that the underlying structure of the (6 2 2)R45 structure in Figure 10B gives a meaningful model of the adsorbate structure of the monolayer CO2/KCl(100). However, there are discrepancies: The applied potential model seems to predict too large tilt angles. Dipoledipole coupling in a similar structure with smaller tilt-angles would shift band g more to the red and would increase the overall agreement between measured and calculated spectra. Similarly, this has been discussed in the related system CO2/NaCl(100).13,16

’ DISCUSSION AND CONCLUSIONS Compared to the well-understood physisorption system CO2/NaCl(100), the adsorption of carbon dioxide on the KCl(100) surface is complicated due to a lattice mismatch of 11% between adsorbate and substrate. This is reflected by the presence of disorder in phase 1 and by the larger extension of the 2D unit cell of the saturated monolayer. According to our structure model in Figure 10B, the latter contains 12 inequivalent molecules, while the monolayer unit cell CO2/NaCl(100) contains only 2 molecules.13,19 The apparent similarities of the experimental and the simulated IR spectra (Figure 12B) are encouraging and give a first idea how close this proposed structure is to the experiment. As discussed above, the potential model predicts too large tilt angles of the molecules with respect 6994


The Journal of Physical Chemistry A to the surface, and the glide-plane symmetry, which has been unambiguously detected in the HAS experiment, is only approximately reproduced. Further tests and refinements of this structure model are thus necessary and could involve a complete LEED structure analysis based on diffraction peak intensities as a function of electron energy (I(V) analysis).19,28 Another similar technique based on the HAS experiments would be a fitting of the surface corrugation of the monolayer CO2/KCl(100) to the diffraction peak intensities as a function of incident wave vector. The variation of the peak intensities in Figure 3, which indicate a considerable amount of buckling in the topmost surface layer, are promising. Another difference to the system CO2/NaCl(100) is the existence of intermediate phase 1 with lower coverage than the saturated monolayer phase 2. This latter point is evidenced independently by means of HAS and PIRS experiments. The proposed √ √structure for the low-temperature ordered phase 2 with (2 2 2)R45 translational symmetry is characterized by a herringbone structure with two inequivalent molecules per unit cell and a coverage of 0.5 monolayers (Figure 9B). The structure exhibits glide-plane symmetry, which was also detected in the HAS angular distributions for phase 1, recorded at 60 K (Figure 2). Further support for such a structure comes from the sharp doublet of infrared absorptions γ and δ in Figure 5B, which was assigned to a Davydov splitting of an in-phase and an out-of-phase mode of the two molecules in the unit cell. However, the absolute strength of this doublet and the presence of a broad underground in Figure 5B (lower pair of spectra) suggests that at least in the PIRS/LEED experiments only a fraction of the adsorbed √ √ CO2 molecules were arranged in domains with (2 2 2)R45 symmetry. The broad underground in this spectra and also the shape of superstructure peaks in the LEED pattern Figure 4B reveal a considerable amount of disorder in the adsorbate, even at low temperature. In contrast, there are only weak signs of disorder in the HAS angular distributions in Figure 2. This difference could be explained by different surface preparation in the experiments but needs further investigations. An influence of surface steps on the presence of adsorbate domains with a preferred orientation, as discussed earlier in the case of CO2/NaCl(100),21 can be ruled out by our LEED experiments. However, √ the√possibility of the coexistence of√ domains with (2 2 2)R45 symmetry and √ ( 2 2)R45 cannot be strictly ruled out, as discussed above in the Experimental Section. In our potential model, the corresponding optimized structures (Figure 9A,B) have the same cohesive energy and the two structures differ only in the molecular orientation. At higher temperatures near 80 K, the intermediate phase 1 is disordered, evidenced by missing super structure spots in the LEED pattern Figure 4A, and the different spectra profile (upper pair of spectra in Figure 5B). Such broad spectral profiles can be reproduced by a disordered adsorbate of isolated monomers, dimers, and small clusters (dashed spectrum of Figure 11A), which have nearly the same cohesive energy than an ordered adsorbate. In view of the results for the physisorbate CO2/NaCl(100) and the present study of CO2/KCl(100), other systems with an even larger lattice misfit might be interesting, e.g., CO2/KBr(100) (misfit 16%). First experiments with this system provide no indications for a 2D adsorbate with long-range order. Moreover, further investigations on the system CO2/KCl(100) could involve both the measurement of external vibrational modes

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using inelastic helium atom scattering and the temperature dependence of line widths and positions of infrared bands. In addition, refined models especially for the simulation of infrared spectra should be envisaged. These should take the coupling of internal and external vibrational modes into account, as well as higher order effects recently introduced in the simulation of infrared spectra of SF6 and CO2 clusters.45

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This article is dedicated to Prof. Toennies on the occasion of his 80th birthday. The authors would like to thank Prof. Toennies for his encouragement to perform the He atom scattering experiments in his lab after M. Hustedt had discussed his first intriguing LEED data with us. The authors thank Michael Hustedt and Michael Thomas for bringing this interesting system to our knowledge and for their participation in the early stages of this project. ’ REFERENCES (1) Butt, H.-J.; Graf, K.; Kappl, M. Physics and Chemistry of Interfaces; Wiley-VCH: Weinheim, Germany, 2003. (2) Bruch, L. Surf. Sci. 1983, 125, 194–217. (3) Bruch, L. W.; Diehl, R. D.; Venables, J. A. Rev. Mod. Phys. 2007, 79, 1381–1454. (4) Chen, W.; Schaich, W. L. Surf. Sci. 1989, 220, L733–L739. (5) Heidberg, J.; Cabigon, L.; Kampshoff, E.; Kandel, M.; K€uhnemuth, R.; Meind, D.; Redlich, B.; Sch€onek€as, O.; Suhren, M.; Weiss, H.; Wetter, D. In Adsorption on Ordered Surfaces of Ionic Solids and Thin Films; Umbach, E., Freund, H.-J., Eds.; Springer-Verlag: Berlin, 1993. (6) Picaud, S.; Hoang, P. N. M.; Girardet, C. Surf. Sci. 1995, 322, 381–390. (7) Jug, K.; Geudtner, G. J. Mol. Catal. A: Chem. 1997, 119, 143–153. (8) Heidberg, J.; Kampshoff, E.; Sch€onek€as, O.; Stein, H.; Weiss, H. Ber. Bunsen-Ges. Phys. Chem. 1990, 94, 127. (9) Heidberg, J.; Kampshoff, E.; K€uhnemuth, R.; Sch€ onek€as, O.; Lange, G.; Schmicker, D.; Toennies, J.; Vollmer, R.; Weiss, H. J. Electron. Spectrosc. Relat. Phenom. 1993, 6465, 341–350. (10) Heidberg, J.; Kampshoff, E.; K€uhnemuth, R.; Sch€onek€as, O. J. Electron. Spectrosc. Relat. Phenom. 1993, 64/65, 803–812. (11) Ewing, G. E. Int. Rev. Phys. Chem. 1991, 10, 391–426. (12) Vigiani, A.; Cardini, G.; Schettino, V. J. Chem. Phys. 1996, 106, 5693–5705. (13) Berg, O.; Disselkamp, R.; Ewing, G. E. Surf. Sci. 1992, 277, 8. (14) Lange, G.; Toennies, J. P.; Vollmer, R.; Weiss, H. J. Chem. Phys. 1993, 98, 10096–10099. (15) Heidberg, J.; Kampshoff, E.; K€uhnemuth, R.; Sch€onek€as, O. Surf. Sci. 1992, 272, 306–312. (16) Heidberg, J.; Kampshoff, E.; K€uhnemuth, R.; Sch€onek€as, O. Surf. Sci. 1992, 269270, 120–127. (17) Vu, N.-T.; Jakalian, A.; Jack, D. B. J. Chem. Phys. 1997, 106, 2551–2554. (18) Vu, N.-T.; Jack, D. B. J. Chem. Phys. 1998, 108, 5653–5656. (19) Vogt, J.; Weiss, H. J. Chem. Phys. 2003, 1105. (20) C. Girardet, S. P.; Hoang, P. N. M. Europhys. Lett. 1994, 25, 131–136. (21) S. Picaud, A. L.; Briquez, S.; Girardet, C. J. Chem. Phys. 1995, 102, 7229. 6995



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Structure of CO2 Adsorbed on the KCl (100) Surface

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