2186
J. Phys. Chem. 1995, 99, 2186-2193
Infrared Spectra and Structure of Ethene on NaCl(100) Kyle R. Willian and George E. Ewing* Department of Chemistry, Indiana University, Bloomington, Indiana 47405 Received: July 20, 1994; In Final Form: November 11, 1994@
Polarized infrared spectra and isotherms of monolayer ethene, C2H4, at 70 and 77 K on NaC1( 100) are reported. Epitaxial growth of bulk ethene adlayers at 55 K on the NaCl(100) is also explored. The isotherms show that the ethene monolayer forms in constant density islands. The heat of adsorption is -20 f 2 kJ/mol, while the pairwise interaction energy between neighboring ethene molecules is -0.8 f 0.1 kJ/mol. The orientation of the ethene molecules in the monolayer is determined by polarized infrared spectroscopy. Using this orientation and making comparisons to the bulk, an ethene monolayer structure is proposed. Each unit cell in the monolayer contains two ethene molecules lying in a configuration similar to the solid with perturbations, however, due to the influence of the NaC1( 100) surface. The surface density is one ethene for each sodium chloride ion pair. This proposed monolayer structure is further investigated by diperiodic group symmetry analysis and by a transition dipole-transition dipole exciton splitting calculation.
Introduction In this paper we explore the thermodynamics and structure of ethene adlayers on NaCl(100). Adsorption of small molecules on alkali halide surfaces is ideal for adsorbate studies for a variety of reasons. In the first place, since the substrate ions have closed-shell configurations, they are isoelectronic with corresponding rare-gas atoms and as a consequence the smooth surface reveals a chemical inertness to many adsorbates. The molecule to surface bonding is thus mostly due to van der Waals forces (classical electrostatic forces, hydrogen bonding, dispersion, etc.) and the molecular properties of adsorbed species are found to be similar to those in the gas phase. Further, the alkali halides are transparent throughout the infrared and most of the UV spectrum. While theoretical modeling,Ip4 helium diffract i ~ n ,electron ~ , ~ diffra~tion,~ and several spectroscopies8-10have been applied to the study of small molecules on these substrates, well and others9,l2have shown polarized infrared spectroscopy to be a particularly effective tool for the determination of adsorbate geometries and thermodynamic properties. In the past several years thermodynamic and structural studies of small molecules on the NaCl( 100) surface of single crystals have drawn considerable attention. The monolayer structures of C0,l1-l6 C02,17-20CH4,21-23and C2H224have been determined by infrared spectroscopy. An interesting finding from these studies is that monolayer structures are often similar to their respective bulk solid structure. Hence, the intermolecular interactions responsible for the packing and orientation of molecules in the (three dimensional) crystalline solid are present in the (two dimensional) adlayers as well. For CO on NaCl(100) extensive studies have mapped the flow of vibrational energy in the m ~ n o l a y e r . ~ In ~ - a~ ~future paper we shall describe the photochemistry of ethene on NaC1( 100). This paper will serve as a preamble to our photochemistry study. Here the results of ethene, C2H4, physisorbed to single crystal NaC1( 100) are discussed. Examination of the adsorption isotherms provides information on the thermodynamics of the adsorbate-surface and adsorbate-adsorbate interactions. Polarized infrared spectroscopy is used to determine the orientation of the adsorbate. Both ethene monolayer and epitaxial growth on NaCl( 100) are investigated. By making small modifications @
Abstract published in Advance ACS Abstracts, January 1, 1995.
0022-365419512099-2186$09.0010
to the structure of solid ethene, we propose a monolayer structure which resembles the solid.
Experimental Section Details of the single-crystal experiment can be found elsewhere.11J7.21s24 Only a brief description of the apparatus with the specific spectroscopic conditions of this study will be given here. The adsorption substrates were single-crystal boules of sodium chloride (Optovac) cleaved along (100) planes resulting in two 25 x 25 x 3 mm3 slabs. These two slabs were mounted on a copper sample holder and placed onto the work surface of an open-cycle liquid helium cryostat (Janis Research). The salt sample holder assembly is contained in an ultrahigh-vacuum chamber (UHV) in which a base pressure of 8 x 10-lo mbar was maintained with an ion pump (Varian). Spectra were recorded with a Fourier transform spectrophotometer (Mattson) at resolutions of 1.0 and 0.5 cm-l. The infrared probe beam passed directly through both crystals so that four surfaces total were interrogated. Upon exiting the UHV chamber, the IR beam passed through a polarizer (Molectron) so that, E, spectra (the electric vector polarized perpendicular to the plane of incidence) and Ep spectra (polarization in the plane of incidence) were collected. These polarizations are depicted in Figure la. An MCT detector cooled to 77 K was used for most survey scans. For the weak features in the C-H stretching region of the monolayer, an InSb detector was used with a cold filter (bandpass 2800-4200 cm-l) to increase the signal-to-noise ratio. The entire optical path was isolated from the atmosphere and purged with dry nitrogen gas. The spectral range explored was 900-4200 cm-l, with 500 scans coadded for both background and sample. Resulting background and sample interferograms were then triangularly apodized and ratioed to produce absorbance spectra. Integrated absorbances of spectroscopic bands are defined by A = Jban,Jog(Idr) dP and reported with the subscript s or p on A to designate the polarization. Bandwidths, fwhm (full width at half-maximum) are indicated with the symbol r. Once the temperature of interest was attained (70 or 77 K with an accuracy of f l K17) for monolayer isotherms, the background spectrum was taken. Ethene was then admitted into the chamber through a leak valve and continuously pumped away so that a constant pressure was maintained. Sample spectra were recorded once the pressure of interest provided steady-state adsorption. Research-grade 0 1995 American Chemical Society
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J. Phys. Chem., Vol. 99, No. 7, 1995 2187
Infrared Spectra and Structure of Ethene on NaCl(100)
0 0020 -
0 0010
2
F
EP
-
00000 -
0.0030
0.0020
0 0010
0 0000
1
i
-1
4
=
1
* - -1 L
l
I
I
/
l
3150
3100
3050
3000
2950
4:
1500
1450
1400
A
1050
1000
850
Wavenumber (cm”)
Figure 1. Coordinate and angle definitions. Upper case X , Y , and Z define the laboratory-fixed coordinates. The laboratory Z axis is perpendicular to the NaCl(100) surface and the X - Y axes define the (100) plane: (a) propagation of the infrared beam, k, and the electric field components Ep and E,; (b) angle, ai, of a transition dipole, pi, from the laboratory-fixed 2 axis.
10-
--a a
1%
I I I ’OK I
06 -
06-
(51
E
04-
0
I
02-
I
I
I
bl I
,
I-
1
0.0
10’0
10’
104
10’
104
104
Pressure (mbar)
Figure 2. Adsorption isotherms of ethene on the NaCl(100) surface at 70 and 77 K. The curves are fit to the quasi-chemical adsorption model (see text for details).
ethene (Matheson, 99.99% pure) was used without further purification. Pressures were measured with an ionization gauge and corrected for the ionization cross section of ethene.28
Results Isotherms. Data for the isotherms of ethene at 70 and 77 K are displayed in Figure 2. At 70 K, no absorbance features were observed below mbar corresponding to no coverage, so 0 = 0. At a pressure of 1 x mbar, ethene absorbance in a variety of bands abruptly appears. At pressures above mbar, since the absorbances showed no further increase, a monolayer was assumed to have formed and 0 = 1. Intermediate values for 0 were determined by ratioing the integrated absorbance of a spectroscopic feature to that of its corresponding monolayer integrated absorbance. The error bars on the data points in Figure 2 reflect our estimate of the photometric accuracy; f 1 0 % on measured A values. At 77 K adsorption begins at a pressure an order of magnitude higher than for 70 K and the isotherm is not as steeply rising. The vapor pressures
Figure 3. Polarized infrared spectra of ethene adsorbed to the NaCl(100) surface at 70 K. The top panel is the Eppolarized spectra, the bottom panel is for E, polarization. Below the experimental data, in each case, is shown a computer generated dipole-dipole exciton modeled “stick” spectrum. The lower left Es spectrum of the region 3150-2950 cm-’ was taken at 77 K while all the rest are at 70 K.
of solid ethene are calculatedz9 to be approximately 3 x and 5 x lop4mbar, respectively, for 70 and 77 K, which are about 1000 times greater than for monolayer adsorption. Just as for methane*l and e t h ~ n ethe , ~ ethene ~ monolayer is formed at pressures many orders of magnitude below the solid vapor pressure. The band areas for all the absorbances were directly correlated to, and reversible with, changes in ethene pressure. Hence, equilibrium conditions were assumed. Monolayer Spectra. The polarized infrared spectra of ethene on the NaCl(100) surface at 70 K and 0 = 1 appears in three regions as shown in Figure 3. With Ep polarization there is a strong feature at 968 cm-’, but with E, polarization this feature is absent. By contrast however, the weaker features at 2981 and 3097 cm-’ have absorbance in both polarizations. A weak band at 1441 cm-’, also present in both polarizations, is somewhat obscured by background water vapor lines (as a result of unstable NZpurge conditions). All the absorptions in these three regions displayed identical pressure dependence and followed the ethene coverage isotherm of Figure 2. Other features outside the regions represented in Figure 3, were exceedingly weak and could be assigned to atmospheric gases outside the UHV chamber or to trace impurities in the interior of the NaCl crystals. The positions of the adlayer peaks did not change with 0 for submonolayer coverages. The bandwidths, peak positions, and integrated absorbances for all of the monolayer spectroscopic data are presented in Table 1. The “stick” spectra below the measured absorbance profiles are the results of a transition dipole-transition dipole coupling calculation, the significance of which will be discussed shortly. Epitaxial Growth of Ethene. To explore the solid formation and ensure that the spectra in Figure 3 were not due to the solid, ethene was condensed onto the single crystal of NaCl at 55 K and the spectrum compared to solid phase data from other investigation^.^^-^^ The vapor pressure of ethene at this temperature is estimated t o be 6 x mbar.29 Therefore, controlled growth of the solid at a pressure of 3 x lo-’ mbar was possible. (This pressure corresponds to 8 layershin if unit accommodation coefficient is assumed.) Ep polarized spectra of multilayer ethene (0 14, i.e., 14 layers) at 55 K are presented in the upper panel of Figure 4. These multilayer spectra are compared to the Epmonolayer spectra (from Figure 3), which are reproduced in the bottom panel of Figure 4. Features are seen in the multilayer spectra of Figure 4 at 3089,
2188 J. Phys. Chem., Vol. 99, No. 7, 1995 0012,
oolo
,
-
,
,
,
,
-
Willian and Ewing interaction^.^^^^^,^^ This isotherm has the form
1-
Fourteen layers
+
]
( y - 1 2 0 ) ( 1 - 0) 0 (1) (y+1-20)0 1-0
[ E
where
0004
0 002
0 000
0 oolo 00000
j m,,-, 3150
3100
3050
3000
2950
1500
1450
1400
1050
1000
950
Wavenumber (cm")
Figure 4. Ep polarized spectra of approximately 14 layers of ethene condensed onto the NaCl(100) single crystal at 55 K (upper panel) compared to the 70 K Ep monolayer spectra (bottom panel).
3066, 2973, a doublet at 1440 and 1436, and a doublet at 952 and 941 cm-l. Notice, however, that there is a small shoulder at 965 on the 952 cm-' band of the doublet. This shoulder is nearly at the same position as the corresponding monolayer feature. For the features around 1440 cm-l it is clear that the corresponding monolayer band is buried in the multilayer peaks, while in the region 2950-3150 cm-' the signal-to-noise ratio in the multilayer spectrum prevents the observation of the monolayer features. The band positions in the multilayer spectra of Figure 4 are, within experimental error, identical to the highresolution study of a polycrystalline sample at 55 K by Zhao et aL30 It is important to note, however, that their spectra and that of o t h e r ~ ~ are l - ~of~polycrystalline samples deposited on a variety of undefined surfaces, while we slowly condensed layers of ethene under controlled-pressure conditions on characterized NaCl( 100) faces. We found, however, significant differences in the relative strengths of absorbances for our multilayer ethene and the polycrystalline samples. Specifically, the relative absorbances of our multilayer bands on the single crystal (100) surface with respect to each other (for a particular polarization) remained constant from the outset of condensation and up to 4.5 h later. For example, even though each feature in the multilayer spectra in Figure 4 grew in continually, the initial relative absorbances did not change. Spectra taken at 0 % 300 (300 layers) looked nearly identical to those shown in Figure 4, and hence it was concluded that the epitaxial solid was forming. We note that in the spectra of these thick ethene multilayers we did observe other weak features, but these weak features are still consistent with solid ethene.30-35 Further, as shown clearly in Figure 4,the positions and relative absorbances of the multilayer features differed significantly from those associated with the monolayer. Discussion Theory of Adsorption Isotherms. For adsorption of molecules with small lateral energy interactions relative to kT, such as CO on NaCl(100) in its high-temperature phase, coverage increases gradually with pressure and can be represented by a Langmuir isotherm.z7 Shapes of the isotherms in Figure 2 , with sharp increases in coverage at characteristic pressures and temperatures, suggest island formation. Similar isotherms have been observed for adsorption of CH423 and C2HzZ4 on NaCl( 100) and have been successfully described by the quasichemical model which incorporates lateral adsorbate-adsorbate
y = [ l - 40(1 - 0)(1 - exp[-w/krl)l'" (2) and p o is the standard state pressure (for SI units p o = 1 Pa). The gas-phase partition function is qgas,and qads is the partition function of the adsorbed molecule. The zero-point binding energy of the molecule to the surface is DO,and w is the pairwise lateral interaction energy between nearest-neighbor adsorbates, with n the number of these neighbors. In this model, both DO and w are independent of temperature. Inspection of eqs 1 and 2 show that in the limit w 0, the quasi-chemical model reduces to the Langmuir isotherm, Le., the quasi-chemical model assumes independent and equivalent adsorption sites. When molecules in nearest-neighbor sites begin to fill, the interaction between them becomes significant. Hence, w is a measure of the tendency for the adsorbates to form islands and its value determines the slope of the isotherm. To extract DOand w ,we must first supply information on n and the partition functions. For ethene, as for methanez3and e t h ~ n e , the * ~ lattice is square (as will be justified shortly) and n = 4. To obtain the gasphase partition function, we use standard methods of statistical thermodynamics together with spectroscopic constants37to find qgas= 3.8 x 1O1Oand 5.5 x 1O1Ofor 70 and 77 K, respectively. For the adsorbed-phase partition function, we use the development of Richardson et al.38with
-
6
6
(3) where iji (in cm-l) is one of the vibrational frequencies of the six normal modes of ethene against the surface (corresponding to the three frustrated translational and three frustrated rotational degrees of freedom). Using Fi = 50 or 200 cm-I as reasonablez4,38lower or upper limits for these frequencies, we find qads = 14 or 1 and qads = 20 or 1 for 70 and 77 K, respectively. These two possibilities introduce a 5% uncertainty in DO,while simultaneous fitting of the 70 and 77 K data in Figure 2 resulted in w = -0.8 f 0.1 kJ/mol. The values DO= 20 kl/mol and w = -0.8 kJ/mol have been used to obtain the theoretical curves of Figure 2. Comment on the relatively small value for w is saved until later when the monolayer structure is resolved. The heat of adsorption, AHads,@,can now be determined by setting 0 = 0.5 in eqs 1 and 2 and applying the ClausiusClapeyron equation:
(6 In p / 6 n , = - & f a d S @ / ~ ?
(4)
The result is
AHadsads,@ = -(Do - nw/2) - 4RT
+
6
RTzqi(hcQJkT) exp(-hcqjkn
(5)
i= 1
The value obtained, AHads,@= -20 f 2 kJ/mol, using our choices of DO,w, and qds, matches within experimental error those from other investigations of ethene on NaCl crystallite film~.~~-~l Band Assignments. For reference, the normal modes of ethene are pictured in Figure 5 and gas phase frequencies listed
Infrared Spectra and Structure of Ethene on NaCl(100)
J. Phys. Chem., Vol. 99, No. 7, 1995 2189 to conclude that the shoulder at 965 cm-' in Figure 4 must be some version of v12 in the monolayer which is being perturbed by the solid multilayers growing above it. The scissoring motion, v6, in the gas is centered at 1444 cm-', and in our solid it appears as a doublet at 1440 and 1436 cm-'. The position of this doublet and its assignment are identical with other condensed phase The single monolayer peak at 1441 cm-' in Figure 3, therefore, must also be v6. Next, we consider the C-H stretching vibrations v5 and vg which appear in the gas phase at 2989 and 3106 cm-', respectively. The two bands at 2973 and 3089 cm-' that we observed in our multilayer spectrum (Figure 4) can be associated with v5 and v8 respectively, in agreement with other reported solid-phase ~ a l u e s . ~ OIn - ~the ~ monolayer at 70 K, therefore, the singlet band at 3097 cm-' must be v8, and the band at 2981 cm-' is assigned to v5. Note that v12 in the monolayer is blueshifted from the solid by 16 cm-', while the C-H stretching vibrations, vg and v5, are blue-shifted by only 8 cm-'. This emphasizes that the differences in the environment between the monolayer and the bulk as expressed by changes in vibrational frequencies is only 2% or less. Finally, there is a very weak feature at 3066 cm-' in the multilayer spectrum of Figure 4, which we assign to the combination mode v2 V6 ( B I , ) . ~ ' - ~ ~ Solid Structure. The correlation splittings in the spectrum o f multilayer ethene observed on NaCl( 100) are consistent with the high-temperature phase of solid ethene. Although there is still some speculation on whether solid ethene undergoes a phase at higher transition below 50 K,30,32.33,43 the temperatures has been established. The unit cell of the ethene crystal at 85 K51,52has the space group symmetry P21h (C2h5) with unit cell lattice constants of a = 4.626 A, b = 6.620 A, and c = 4.067 A. If we imagine ethene epitaxial growth, then any one of its three unit cell faces, the ab plane (OOl), the ac plane (OlO), or the bc plane (loo), could be parallel to the NaCl(100) surface. The ab plane is a likely choice because its lattice constant and its two-dimensional density are closest to that of the solid unit cell of NaCl with space group Fm3m and a = b = c = 5.64 A.53 The density of sodium-chloride ion pairs at the NaCl(100) surface is, SN~+CI= 6.3 x 1014 pairs cm-2. The density of the molecules in the unit cell of the ethene crystal projected into the ab plane is, &b = 6.5 x loi4 molecules cm-2 so S a b is only 3% more than SNa+cl-,while for Sa, or &,c it is 15% or 43% more. A reasonable scenario for epitaxial growth then produces a structure where every two sodiumchloride ion pairs exposed has a stack of unit cells of the ethene crystal placed with their (001) faces parallel to the plane of NaCl(100). A representative sheet of solid ethene unit cells with their (001) planes parallel is shown in Figure 6a. The dashed lines outline the unit cells in the ab plane, each containing two molecules. Note that within each cell one ethene, in addition to having a different orientation, lies slightly above its partner (Le., the center of mass of the two molecules in each unit cell are not in the same plane). Monolayer Structure. With the formation of solid-phase ethene on the NaCl surface reasonably discussed and the solid structure determined by others, we now focus on the monolayer. In earlier experiments with a film of NaCl crystallites4' we found that ethene adsorbs such that there is one molecule per NafC1- ion pair. Since it has been established that the CO adsorbed phase is commensurate with the Na+Cl- ion pairs and that it follows Langmuir adsorption behavior,38films of NaCl crystallites can be characterized for available adsorption sites.38 Using this knowledge, we adsorbed ethene to a film41 and the resulting isotherm which has a BET form,54 gave the same
+
Figure 5. The 12 normal modes of ethene with their symmetry notations and the orientation of the molecular x-y-z axes. This molecular axis system was chosen to be consistent with the Mulliken notation,'2 where the C-C bond defines the molecular z axis and x is perpendicular to the molecular plane. (Most texts and vibrational spectroscopists tend to use the coordinates where the z axis is normal to the molecular plane and the x axis is along the C-C bond, while most theoreticians and electronic spectroscopists use Mulliken notation.) TABLE 1: Vibrational Spectrgscopy of Ethene (Spectroscopic Constants V , r, A,,, and A, in Units of cm-l) adsorbed phase (monolayer 70 K) gasb mode" e e r AP As y1(Ag) 3026 1623 y3(Ag) 1342 v4(AU) 1023 0.0009 0.0018 2981 3.9 v5(Blu) 2989 0.0020 0.0036 1441 11.4 v6(Blu) 1444 Y7(B2g) 943 0.00105 0.0018 3097.4 5.5 v@zu) 3106 ~(&u) 826 YlO(B3g) 3103 YlI(B3g) 1236 ~12(B3~) 949 968.2 6.0 0.011 50.0036 a
Symmetry species are defined in Figure 5 . * Reference 42.
in Table 1. All six ungerade modes are infrared active; however two, v4 and vg, weakly absorb in the gas phase.31,37$42 We shall therefore be discussing v12, v8, v5, and v6, which have the largest infrared oscillator strengths. The band center of the out-of-plane bending mode v12 is found in the gas at 949 cm-'. It has the largest oscillator strength of all the modes. Hence, the strongly absorbing doublet in the solid at 941 and 952 cm-l in Figure 4 has been assigned by us and 0 t h e r s ~ as ~ 3v12. ~ ~ The doublet is caused by correlation field splitting since there are two molecules per unit cell in the ~ o l i d . ~ ONo - ~ ~splitting is found in the monolayer, however, but it is natural to assign the strong signal at 968 cm-' in the Ep spectrum of Figure 3 to v12. It also seems logical, therefore,
Willian and Ewing
2190 J. Phys. Chem., Vol. 99, No. 7, 1995
measured using the ratio of the integrated absorbances, A,,/&. The angles, pi, as we shall see, drop out of consideration. The integrated absorbance, A, of a vibrational transition is dependent on the integrated molecular cross section, a, of that transition. The cross section in turn, depends on how the components of the transition dipole along the laboratory fixed coordinates couple to the electric field of the infrared probe beam. These relationships have been worked out previously for the case of a single transition d i p ~ l e ' ~ and . ~are ~ presented here as follows:
L L
2NSByi
ASi=
( ~ . ~ o ~ ) ce(i os
+ q2)(i + auOl,)2
(7)
where the subscript i has been added to the original formulas to account for the three different transition dipoles px,p,,, and pz of ~ 1 2 ,Y8, and 13,respectively. The subscripts s and p designate the polarization, 8 is the angle of incidence of the infrared beam (see Figure la), N is the number of surfaces probed;and S is the density of adsorbates on the surface. Since Es light is partially reflected by the substrate, the factor 24 1 q2)appearing in eq 7 accounts for this with q = 1.52 the index of refraction for NaC1.55 The terms (1 Ct@l)* and (1 Ct@11)* correct for the effect of induced dipoles normal to and in the plane of the adlayer, respectively. The induced dipoles normal to the surface depend on @1= Here the Ewald sum of the interaction among an infinite array of these dipoles on a square lattice is S3 = 9.033656and the nearest-neighbor distance between these dipoles, a = 3.97 A, is the distance between two nearest Na+ ions (or the two nearest C1- ions) on the NaCI(l00) surface (since there is one ethene per Na+CIpair). The correction due to induced dipoles in the plane of monolayer, as shown by others,57makes use of V'll = - I / 2 V ' l . The magnitude of the induced dipoles are also dependent on the polarizability of the adsorbed species. For our analysis we simply use the average polarizability, Ct = (a, am az)/3 = 4.2 A3, calculated from the larizability along the molecular of a, M am= 3.6 f rand ax = 5.4 A3. Justification for, and the consequences of, using the average polarizability will be addressed later. Looking at eqs 6 and 7 , we see that it still remains to determine axi, Dyi, and Dzi, the components of the molecular integrated cross section, ai, of each transition dipole, pi, of the isolated molecule in the laboratory frame. As we show elsewhere for a nondegenerate vibration,I7 the molecular integrated cross section is obtained from the gas-phase integrated cross section, ag,through ai = 3agi. Transformation of the molecular frame to the laboratory frame is made through the appropriate direction cosines17 by
+
+
+
Figure 6. Proposed monolayer structure for ethene on the NaCI( 100)
surface. The top motif (a) is a sheet peeled from the (001) face of crystalline ethene at 85 K.52 The dashed lines are the unit-cell boundaries in the a, b plane. The bottom panel (b) shows our proposed monolayer structure at 70 K. The diperiodic group in this panel is No. 23 (CB).The crystallographic a-h-c axes are defined with respect to the laboratory X- Y-2 axes. The 2 and c axes are perpendicular to the page. The dashed lines define the unit cell boundaries of the monolayer. In our model the center of mass of each ethene molecule of the monolayer lies directly above a Na+ in the surface below. surface density as CO at monolayer coverage. Thus we are lead to the conclusion that since the density of ethene adsorbates is one per Na+CI- pair, the monolayer unit cells must be in registry with the NaCl( 100) square net characterized by its 5.64 A lattice constant. Using van der Waals space filling models of ethene placed onto a model of the NaCl(100) surface showed that ethene cannot lie completely flat if it is to form a commensurate monolayer. Only if the ethene molecular plane is canted slightly with respect to the surface or the molecules in the adlayer are somewhat corrugated (or both) will they be able to form a monolayer that is in registry with the NaCI( 100) lattice. We now determine the orientation of the ethene molecule in the monolayer with respect to the surface, i.e., the X, Y, 2 laboratory axis system as shown in Figure lb. The transition dipole of the v12 vibration is along the molecular x axis (see Figure 5 for the molecular coordinate system), while v8 and v5 have their transition dipoles aligned with the molecular y and z axes, respectively. Each of these vibrational modes has a transition dipole, pi, which make the angles ai and pi (where i = x, y , and z for v12, v8, and v5, respectively) with respect to the laboratory-fixed coordinate system. The ai angles can be
+ +
axi= 3ag,sin2 aicos2 pi ayi= 3agisin2 ai sin2 pi
(9)
aZi= 3agicos2 ai where the subscript i has again been added to the original formulas. The angle pi requires particular attention. On the NaCI( 100) surface there are four equivalent directions, but this may not be the case for the monolayer. The ethene layer probed by the
J. Phys. Chem., Vol. 99, No. 7, 1995 2191
Infrared Spectra and Structure of Ethene on NaCl( 100) infrared beam is likely formed of many separate yet structurally equivalent rotational domains. The spectra, therefore, represent an average over all the rotational domains and hence we can set (sin2 pi) = (cos2 pi) = l/2 in eqs 8 and 9 and get 2 sXi= 3 / 2 ~ g sin i ai
(1 1)
2 aYi= 3 / 2 ~ g sin i ai
When eqs 10-12 are inserted into eqs 6 and 7, their ratio can be solved to obtain the tilt angle:
ai= tan-'
1
6(1
+ a$,,)*/(l + B$J2
[8(Ap/A,,Y(1 +
r2>- 11
]
''2
(13)
where the ratio Add, for each band comes from the spectral data listed in Table 1. It is convenient to consider each transition dipole, pi, separately using appropriate photometric error limits for each spectroscopic feature through ddA,. We start with p,, where v12 is the only observed vibrational feature associated with this transition dipole. There appears to be no absorption around 968 cm-' in the E, spectrum suggesting that the molecular x axis is exactly perpendicular to the surface. The noise level, however, allows for the possibility that the molecular plane could be canted with weak absorption of v12 buried in the noise. An upper bound is estimatetd for the angle a, in the following way: If the absorbance noise level, 0.0006, in the E, spectrum of the v12 region is multiplied by 6 cm-' (r of v12 in the E, spectrum), we obtain A, 5 0.0036 cm-' and, together with A, from Table 1, ddd, 2 3.1. Hence, from eq 13, the maximum that the x axis could be inclined from the surface normal is a, = 23". The appropriate range is therefore 0" Ia, I23". Next we consider p, for which the only observed mode is v8. Features are seen in both E, and E, polarization with an estimated photometric error limit of f 1 0 % on A, and d, values in Table 1. The corresponding range on the y axis tilt is 5 1" I a, I69". The orientation of the transition dipole, p,, remains to be determined. We see that there are two modes, vg and v6 which need consideration. The features for v5 are clearly defined and the f 1 0 % error on integrated absorbances is again appropriate. The tilt range from v5 is 56" Ia, I90". For v6, since it is obscured by atmospheric water lines, we suggest a more generous error of f 2 0 % on the integrated absorbances. The tilt range is 45" Ia, I90". While the tilt range for a,for the v5 and v6 modes differ somewhat, they are mutually compatible. We can now specify the orientation of the monolayer ethene molecules with respect to the laboratory frame. We note first that the angles a,, a,, and az,which define the position of the molecular axis system with respect to the laboratory fixed Z axis are not independent. If two are specified, the third can be calculated. The three angles must adhere to the following trigonometric relationship: cos2 a,
+ cos2 a,+ cos2 a,= 1
(14)
as simple geometric considerations show. Upon insertion of the tilt angle ranges calculated above for a,, a,, and a,,into eq 14, only a small range of geometric arrangements are allowed. The range on the calculated angles become limited to the following possibilities, a, = 22" f lo, a, = 68" f lo,and a, = 86" f 4". Clearly errors of only f l " are unrealistic since the photometry gave errors as big as f22". What is important,
however, is that due to the constraints of eq 14 on the ranges for a,, a,, and a, (i.e., on the photometric calculations), it is fairly certain that the molecular z axis is nearly parallel to the surface. Most of the overall tilt in the molecule with respect to the NaCl surface is a result of rotation around the z axis. As a final orientation to use for a visual representation and for our dipole-dipole calculations, we choose a, = 23", a, = 67", and a, = 90". A sheet of monolayer ethene molecules with this orientation is depicted in Figure 6b. (It is important to note that changes by as much as f5" in a,, a,, and a, would not be apparent in the scale of presentation in Figure 6b. Further they affect our dipole-dipole calculations by only a few percent). Since it was shown above that epitaxial growth occurs, it is logical to assume that the monolayer resembles the solid. However, although the monolayer structure in Figure 6b resembles the bulk arrangement in Figure 6a, three important differences exist. First, the plane of each ethene molecule in the monolayer is more parallel to the surface. In the bulk, Figure 6a, the orientation of an ethene molecule with respect to the laboratory Z axis is a, = 34", a, = 58", and a,= 79". Second, the center of mass of each molecule in the unit cell now lies in the same plane, Le., the molecules in the monolayer sheet in Figure 6b are not corrugated like they are in the bulk sheet in Figure 6a. And third, the dimensions of the unit cells in Figure 6b have been adjusted from rectangular to square, a = 5.64 A and b = 5.64 A, to match the NaCl(100) surface lattice. We can imagine that each ethene is centered above a Na+ ion due to favorable electrostatic interaction of the ethene z-bond system and the positive charge on the sodium cation; hence, the ethene molecules in Figure 6b are separated by 3.97 A. We now comment on the small pairwise interaction energy, w = -0.8 f0.1 kJ/mol, between adsorbates. Recent theoretical calculations61 indicate that ethene dimers are oriented in an interlocking crossed position (i.e., the C-C bond axes of the dimers make a cross) having an interaction energy of -6.87 kJ/mol. The molecules in the monolayer, Figure 6b, form a T-shaped structure, and their molecular planes all lie nearly in the same plane. Clearly the primary factor in the packing and orientation of the ethene molecules in the monolayer is not due to optimization of adsorbate-adsorbate interactions (as it is in the solid where the dominant intermolecular interaction is hydrogen-hydrogen repulsion46,47,49,50~52), but due to the overwhelming influence of the electric field produced by the NaCl substrate. The compromises needed to form the monolayer result in lowering the painvise interaction by an order of magnitude from the isolated dimer value. Before moving on, we can compare the density of adsorbates, S = 6.3 x 1014 molecules cm-2, demanded by the monolayer structure in Figure 6b (as well as isotherm measurements on films of NaC1( 100) crystallites) to that obtained from eqs 6 and 7. Using dpfor v12 in eq 6 we find for example, S,, = 2.6 x 1014 molecules cm-2 and for v5, A,,and d, both give S,, = 1 x ioi4 molecules cm-2 and for v8, S, = 8 x molecules cm-2. Why the discrepancy? We believe the difficulty arises from the values of integrated cross sections, we have used in eqs 6 and 7. The values selected, as the transformations of eqs 10-12 shows, are those of the gas-phase Bgi. While the adsorbed-phase vibrational frequencies are within 1% of their gas-phase values, the oscillator strengths can be dramatically changed by the substrate. In an extreme case, while H2 has no infrared dipole oscillator strength in the gas phase, the electric fields from the ionic substrate allow significant absorption from the adsorbed m ~ l e c u l e . ~ *For . ~ CO ~ on NaCl( loo),the integrated oscillator strength differs by 30% from its gas-phase value. Richardson et al.14 explore some of the origins of these surface-
2192 J. Phys. Chem., Vol. 99, No. 7, 1995
Willian and Ewing
induced changes. In general one expects the biggest fractional changes to occur for the weakest oscillator strengths. Indeed for C2I& on NaCl( loo), the greatest deviations from S = 6.3 x 1014molecules cm-2 occur for calculations from the weak bands, v5 and vs, and the smallest deviation is from the strongest band, v12. In summary eqs 6 and 7 are not useful for photometric determination of adsorbate densities. Why then can we have confidence in photometric determination of adsorbate orientations? Fortunately the angles, a;,from eq 13 arrive from the ratio of eqs 6 and 7, where the absolute values of ax,, B y > ,and Bz,(Le., Bg,)cancel. The integrated cross section does not appear in eq 13. However, we do need to consider the corrections for induction effects, the terms aflil and a f l ~that , have been used. The electric field above the NaCl( 100) surface is complex.64 A large molecule, ethene, with three distinct polarizabilities has been placed into this intricate electric field. Ideally, not only should each transition dipole be considered separately (as we have done), but the component of each induced dipole along the laboratory axis frame as a result of the component of each of the three molecular polarizabilities should be considered as well. In other words, the molecular polarizabilities, a,, a,, and a, each have components along the laboratory axes, resulting in nine induced dipoles that should be considered. A calculation of this magnitude is clearly excessive for our purposes. The IR beam probes the average position of the resulting transition dipoles, the pi’s. The interrogating photons are not concerned with the origin of these transition dipoles, and ultimately our spectroscopic measurements only provide information on these average positions. Hence, even though eqs 6 and 7 are not rigorously accurate, our formula for the transition dipole angle, a;,eq 13 is still valid. The neglected factors (the true adsorbed phase-integrated cross sections and the components of the polarizab es) which influence A, and A, have been averaged out in eq 13. The term [(l (1 f Cif111)2] in eq 13 is a practical way to incorporate induction effects. Using the specific values for the polarizabilities a,, a,, and a,, instead of the isotropic polarizability, in eq 13 resulted in changes of only a few degrees in the angles a,, a,, and a,. Photometry used for calculating molecular orientations as we have done is then expected to give reasonable results. We now classify the symmetry of our proposed monolayer structure to see if it is consistent with the infrared spectra of Figure 3. We choose to use the 80 diperiodic groups for this analysis. It has been shown by many others17,22.24,65-68 that surface structures are best described as three-dimensional, although they have periodicity in only two dimensions. Thus the 17 2-Dplane groups restrict analysis since they do not allow for this third dimension. The 80 diperiodic groups not only have been applied to the analysis of surface structures but also have been used to delineate domain and phase boundarieP and surface reconstruction and surface phase transition^.^^*^^ In the present analysis of monolayer ethene, the notation from our previous paper^'^,^^ will be used. The sheet in Figure 6b has four symmetry operations: the identity (E), an inversion (i), along the b axis which is normal to and a screw operation a glide plane (4)aligned with the a axis. These operations place the monolayer into ourl7 diperiodic group no. 23 which is isomorphic to the factor group C 2 h as in the solid. Correlation of the factor group, C2h, from the isolated ethene molecule, D2h. is consistent with the ungerade modes ~ 1 2 ,VS, v5, and v.5, all remaining IR active.69 At this point we can justify the assumption that the center of mass of the ethene molecules in Figure 6b are all in the same plane. A monolayer with altemating molecules raised and lowered (corrugated) with
+
(cb)
respect to each other results in the loss of the glide plane. If the molecules in the monolayer were corrugated as in the solid, Figure 6a, the monolayer would belong to our diperiodic group no. 15 which is isomorphic to the factor group C2. Correlation of CZfrom DZh results in all 12 modes becoming IR active, and we see no evidence of any other modes in the monolayer in the temperature range 70-77 K other than those already discussed.
Dynamic Transition Dipole-Transition Dipole Coupling. We can also test our proposed monolayer structure with a theoretical calculation. Dynamic transition dipole-transition dipole coupling, which causes correlation field splitting, can be represented by the quantum mechanical exciton A detailed explanation of the model can be found elsewhere,16~18s70 and only a cursory description is given here. Consider a collection of n molecules that are coupled to each other through transition dipoles. If there were no coupling, the properties of the individual molecules would essentially be like that of an isolated molecule (Le., a gas-phase molecule). A patch of n molecules is n-fold degenerate since a photon could excite a vibration in any one of the indistinguishable molecules. The coupling among the transition dipoles removes this degeneracy and the system can be treated with n-fold degenerate perturbation theory. The perturbation Hamiltonian in this model is
where c is the speed of light, h is Planck’s constant, and EO is the vacuum permeability constant. The vector 4 is the transition dipole of thejth molecule, and lk is the transition dipole of the kth molecule. The molecules are separated by a distance R, where Rjk is the unit vector between 1, and lk. The transition dipole, ,up1,for each vibration, v12, vg, v5, and v.5. in the n molecules is calculated from
where Bgiis again the gas-phase cross section for each vibration v12, Vg, v5, and v.5,and 6; is the observed monolayer transition frequency (cm-’). Each vibration is considered separately, and the orientation of its transition dipole as obtained above is entered into the calculation. Computer-generated “stick” spectra result, which are shown in Figure 3 along with the experimental data. In these calculations, a square patch of 128 molecules (n = 128) was considered, a relatively small domain size but sufficient to explore the dynamics that cause splitting. The effect of increasing the domain size is the convergence of some minor sidebands onto main features as n m. The discussion of our resulting “stick’ spectra shown in Figure 3 begins by looking at v12 which has the strongest gasphase integrated cross section.30,31*71 Two lines (two “sticks”) at 968 and 963 cm-’, due to correlation field splitting, are in fact predicted in the E, spectrum. Further there is sideband structure at 963 cm-’ in the Ep spectrum as well. Notice, however, that all of these smaller lines are only 5-10% of the main line at 968 cm-I in the Ep spectrum. Thus, unless the signal-to-noise ratio in our experiment could be increased by at least a factor of 10, these smaller bands cannot be seen. Also, since r = 6 cm-’, and the splitting is predicted to be only 5 cm-’, we are bandwidth limited as well. For the weaker transitions v5, vg, and v.5,whose integrated cross sections are all smaller than v12 by roughly a factor of 10,30,31,71 we see that only single lines are expected. That is not to say that correlation
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J. Phys. Chem., Vol. 99, No. 7, 1995 2193
Infrared Spectra and Structure of Ethene on NaCl(100) field splitting does not exist, simply that dipole-dipole interactions cannot account for it in modes with weak transitions. As we have noted, values of Bg1 are altered by the substrate. However, changes in correlation splittings that result from these alterations do not change the qualitative conclusions we have reached.
Conclusion Spectral and isothermal data presented here show that monolayer adsorption of ethene onto the NaCl( 100) surface occurs with a density of 1 moleculehodium chloride ion pair. This adsorption does not follow a Langmuir isotherm but instead has quasi-chemical behavior at 70-77 K, indicating island formation at these temperatures. The monolayer produced resembles a sheet parallel to the (001) plane from solid ethene. The axis defined by the C-C bond in the ethene molecules in the monolayer is nearly flat with respect to the surface, while the plane of each ethene is twisted about this axis by -20". Above the vapor pressure of the solid at 55 K, ethene crystals grow with their ab(001) plane most likely parallel to the NaC1( 100) surface.
Acknowledgment. This work was supported by a grant from the National Science Foundation (CHE91-15444). K.R.W. wishes to thank Dr. Otto Berg, Dr. Laura Quattrocci, Dr. Keith Dum, Dr. David Dai, and especially Dr. Chris Purse11 for their help and advice. References and Notes (11 Gevirzman. R.: Kozirovski. Y.: Folman, M. Trans. Faraday SOC. 1969,64, 2206. (2) Polanvi. J. C.; Williams, R. J.; O'Shea, S. F. J. Chem. Phys. 1991, 94, 978. (3) Picaud, S.; Hoang, P. N. M.; Girardet, C.; Meredith, A.; Stone, A. J. Surf. Sci. 1993, 294, 149. (4) Davidson, E.; Mahmud, S. Surf. Sci., in press. ( 5 ) Liu. G. Y.: Robinson. G. N.: Scoles. G.: Heinev, P. A. Sud. Sci. 1992,262, 409. (61 Schmicker. D.: Toennies, J. P.; Voller, R.; Weiss, H. J. Chem. Phys. 1991, 95, 9412. (7) Schimmelpfennig, J.; Folsch, S.; Henzler, M. Surf. Sci. 1991, 250, 198. (8) Hardy, J. P.; Ewing, G. E.; Stables, R.; Simpson, C. J. S. M. Surf. Sci. 1985, 159, L474. (9) Blass, P. M.; Jackson, R. C.; Polanyi, I. C.; Weiss, H. J. Chem. Phys. 1991, 94, 7003. (10) Folsch, S.; Stock, A.; Henzler, M. Surf. Sei. 1992, 264, 65. (11) Richardson, H. H.; Ewing, G. E. J. Phys. Chem. 1987, 91, 5833. (12) Heidberg, J.; Kampshoff, E.; Suhren, M. J . Chem. Phys. 1991, 95, 9408 and references therein. (13) Richardson, H. H.; Ewing, G. E. J. Electron. Spectrosc. Relat. Phenom. 1987, 45, 99. (14) Richardson, H. H.; Chang, H.-C.; Noda, C.; Ewing, G. E. Suif. Sci. 1989, 216, 43. (15) Noda, C.; Richardson, H. H.; Ewing, G. E. J . Chem. Phys. 1990, 92, 2099. (16) Disselkamp, R.; Chang, H.-C.; Ewing, G. E. Sur$ Sci. 1990, 240, 193. (17) Berg, 0.; Ewing, G. E. Surf. Sci. 1989, 220, 207. (18) Berg, 0.;Disselkamp, R.; Ewing, G. E. Surf. Sci. 1992, 227, 8. (19) Heidberg, J.; Kampshoff, 0.; Schonekas, 0.;Stien, H.; Weiss, H. Ber. Bunsen-Ges. Phys. Chem. 1990, 94, 112; Ibid. 1990, 94, 118. (201 Heidbern. J.: KamDshoff, E.: Kuhnemuth, R.; Schonekas, 0. Suff Sci.~1992, 272, y06. (21) Quattrocci, L.; Ewing, G. E. J . Chem. Phys. 1992, 96, 4205.
(22) Quattrocci, L.; Ewing, G. E. Chem. Phys. Lett. 1992, 197, 308. (23) Ouattrocci. L. Doctoral Thesis, Indiana University, of . Department Chemistry, Bloomington, IN 47405, 1992. (24) Dunn, S. K.; Ewinp, G. E. J. Phys. Chem. 1992, 96, 5284. (25) Chang, H.-C.; Ewing, G. E. Chem. Phys. 1989, 139, 55. (26) Chang, H.-C.; Ewing, G. E. Phys. Rev. Lett. 1990, 65, 2125. (27) Ewing, G. E. Acc. Chem. Res. 1992, 25, 292. (28) O'Hanlon, J. F. A Users Guide to Vacuum Technology, 2nd ed.; Wiley Interscience: John Wiley & Sons, New York, 1989; p 125. (29) Stephenson, R. M.; Malahowski, S . Handbook of the Thermodynamics of Organic Compounds; Elsevier: New York, 1987; p 44. (30) Zhao, G.; Ospina, M. J.; Khanna, R. K. Spectrochim. Acta 1988, 44A, 27. (31) Dows, D. A.; Wieder, G. M. J. Chem. Phys. 1962, 37, 2990. (32) Jacox, M. E. J. Chem. Phys. 1961, 36, 140. (33) Rytter, E.; Gruen, D. M. Spectrochim. Acta 1979, 35A, 199. (34) Duncan. J. L.: McKean. D. C.: Mallinson. P. D. J . Mol. Suectrosc. 1973,45, 221. ' (351 Dows. D. A. J. Chem. Phvs. 1962, 36, 2833. (36) Hill, T. An Introduction t i Statistical Thermodynamics;AddisonWesley: Reading, MA, 1960. (37) Herzberg, G. Molecular Spectra and Molecular Structure. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand Reinhold: New York, 1945; Vol. 11. (38) Richardson, H. H.; Baumann, C.; Ewing, G. E. Surf. Sci. 1987, 185, 15. (39) Heidberg, J.; Hoge, D. J. Opt. Soc. Am. 1987, B/4, 242. (40) Schinzer, W. C. Doctoral Thesis, Indiana University, Department of Chemistry, Bloomington, IN 47405, 1985. (41) Willian, K. R.; Ewing, G. E., to be published. 142) Shimanouchi. T. Tables of Molecular Vibrational Frequencies; Part 1; NSRDS-NBS 6. (43) Enan. C. J.; KemD, J. D. J. Am. Chem. Soc. 1937, 59, 1264. (44) Brecher, C.; Halfbrd, R. S. J. Chem. Phys. 1961, 35, 1109. (45) Brith, M.; Ron, A. J . Chem. Phys. 1969, 50, 3053. (46) Elliot, G. R.; Leroi, G. E. J. Chem. Phys. 1973, 59, 1217. (47) Blumenfeld, S. M.; Reddy, S . P.; Welsh, H. L. Can. J . Phys. 1970, 48, 513. (48) Hashimoto, Ma.; Hashimoto, Mi.; Isobe, T. Bull. Chem. Soc. Jpn. 1971, 44, 3230. (49) Taddei, G.; Giglio, E. J. Chem. Phys. 1970, 53, 2768. (50) Dows, D. A. J. Chem. Phys. 1962, 36, 2836. (51) van Nes, G. J. H.; Vos, A. Acta Crystallogr. 1977, B33, 1653. (52) van Nes, G. J. H.; Vos, A. Acta Crystallogr. 1977, B35, 2593. (53) Donnay, J. D. H.; On&, H. M. Crystal Data, Determinative Tables, 3rd ed.; Inorganic Compounds; National Bureau of Standards: Washington, DC, 1973; Vol. 2. (54) Brunauer, S.; Emmett, I. H.; Teller, E. J. Am. Chem. Sac. 1938, 60, 309. ( 5 5 ) Palik, E. D., Ed. Handbook of Optical Constants of Solids; Academic Press: Orlando, FL, 1985. (56) Van Der Hoff, B. M. E.; Benson, G. C. Can. J . Phys. 1953, 31, 1087. (57) Chen, W.; Schaich, W. L. Surf. Sei. 1989, 218, 580. (58) Amos, R. D.; Williams, J. H. Chem. Phys. Lett. 1979, 66, 471. (59) Gough, K. M. J. Chem. Phys. 1989, 91, 2424. (60) Marovlis, G. J. Chem. Phys. 1992, 97, 4188. (61) Ahlrichs, R.; Brode, S.; Buck, U.; DeKreviet, M.; Lavenstein, Ch.; Rudolph, A.; Schmidt, B. Z. Phys. D 1990, 15, 341. (62) Folman, M.; Kozirovski, Y. J . Colloid Interface Sei. 1992,38, 51. (63) Dai, D. J.; Ewing, G. E. J. Chem. Phys. 1993, 98, 5050. (64) Lennard-Jones, J. E.; Dent, B. M. Trans. Faraday Soc. 1928, 24, 92. (65) Wood, A. E. Bell Syst. Tech. J . 1964, 43, 541. (66) Zielinski, P. Surf. Sci. Rep. 1990, 11, 179. (67) Ipatov, I. P.; Kitaev, Y. E. Prog. Surf. Sci. 1985, 18, 189. (68) Hatch, D. M.; Stokes, H. T. Phase Transitions 1986, 7, 87. (69) Wilson, E. B., Jr.; Decius, J. C.; Cross, P. C. Molecular Vibrations; McGraw-Hill: New York, 1955. (70) Dai, D.; Ewing, G. E. J. Electron. Spectrosc. Relat. Phenom. 1993, 64/65, 101. (71) Nakanaya, T.; Kondo, S . ; Saeki, S. J. Chem. Phys. 1979, 70,2471. (72) Mulliken, R. S. J . Chem. Phys. 1955, 23, 1997. JP941861V
