Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 148 (2015) 271–279

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Effect of resonance dipole–dipole interaction on spectra of adsorbed SF6 molecules Anna N. Dobrotvorskaia a,⇑, Tatiana D. Kolomiitsova a, Sergey N. Petrov a, Dmitriy N. Shchepkin a, Konstantin S. Smirnov b, Alexey A. Tsyganenko a a b

Department of Physics, St. Petersburg State University, St. Petersburg 198504, Russia Universite des Sciences et Technologies de Lille, Villeneuve d’Ascq Cedex, 59655, France

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

 Spectra of adsorbed SF6 depend on

the mutual arrangement of interacting molecules.  Adsorbed molecules form an onedimensional (1D) and twodimensional (2D) systems.  The dynamic interaction (RDDI) is manifested as the doublet spectral band structure.  Components correspond to transversal and longitudinal vibrations of dipole moment.  Maximal RDD splitting between components for 1D chains is smaller than for 2D flat.

a r t i c l e

i n f o

Article history: Received 12 January 2015 Received in revised form 1 April 2015 Accepted 5 April 2015 Available online 11 April 2015 Keywords: Dipole–dipole interaction Dynamic interaction SF6 Adsorption ZnO Silicalite

a b s t r a c t Adsorption of SF6 on zinc oxide and on silicalite-1 was investigated by a combination of IR spectroscopy with the calculations of spectra by means of a modernized model, developed previously for liquids. Comparison of the experimental spectra and the results of modeling shows that the complex band shapes in spectra of adsorbed molecules with extremely high absorbance are due to the strong resonance dipole– dipole interaction (RDDI) rather that the surface heterogeneity or the presence of specific surface sites. Perfect agreement between calculated and observed spectra was found for ZnO, while some dissimilarity in band intensities for silicalite-1 was attributed to complicated geometry of molecular arrangement in the channels. Ó 2015 Elsevier B.V. All rights reserved.

Introduction Lateral interactions, studied in detail by IR spectroscopy for CO adsorbed on metals [1,2] and oxides [3–5], affect greatly the adsorption and catalytic properties of solid surfaces. The method ⇑ Corresponding author. E-mail address: [email protected] (A.N. Dobrotvorskaia). http://dx.doi.org/10.1016/j.saa.2015.04.002 1386-1425/Ó 2015 Elsevier B.V. All rights reserved.

of isotopic dilution enables us to distinguish two kinds of interactions: static effect and the dynamic interaction, referred also as resonance dipole–dipole interaction (RDDI) or dipole coupling. The former influences the energy of adsorption and the observed strength of surface sites and often determines the geometry of adsorbed layer. It can be attractive and lead to 2D islands formation [2], or repulsive, then it prevents occupation of the nearest neighboring sites and promotes the formation of domains with

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ordered structures on the low-index faces of crystals [6]. The latter kind of interaction, the RDDI, does not change chemical or most of physical characteristics of the adsorbed layer, but it modifies the positions, shapes and widths of absorption bands in the spectra of surface species. If the frequencies of adsorbed probe molecules are used as a measure of the strength of surface sites, whose concentration is reflected in the band intensities, RDDI distorts this information. It accounts also for the vibrational energy exchange in the adsorbed layers and cannot be neglected when considering the dynamics of resonance excitation or the energy dissipation processes. The theory of RDDI in adsorbed layers was first developed by Hammaker et al. [7] to explain the spectra of CO adsorbed on Pt. They considered a layer of regularly arranged dipoles, included the energy of interaction into the Hamiltonian and obtained the solution of vibrational problem, which explained the frequency shift to higher wavenumbers. But to achieve the quantitative agreement the model had to be modified by taking into account the image dipoles induced by the surrounding molecules under the metal surface [8] and interaction of the molecule with its own image [9], as well as the increase of vibrational polarizability of adsorbed molecules [10]. For oxides the observed dynamic shift was also greater than that one predicted by the model [11], despite the decrease of av corresponding to lowered integrated adsorption coefficient [12]. This means that the role of the surface is not restricted to fixation of mutual arrangement of molecules at the surface, but the solid itself participates in the interaction, enhancing it. Up to now, the dynamic interaction has been observed mostly for CO molecules somehow oriented with respect to the flat surface of crystals. It was shown, however, that complex band shapes in the spectra of such symmetric molecules as SF6 and CF4 in liquid or dissolved state can be explained by RDDI [13–16]. These molecules have extremely high integrated absorption coefficient of the asymmetric stretching vibration m3, and one could anticipate the manifestations of RDDI in adsorbed state. Adsorption of SF6 on graphite was investigated by Hess et al. [17] at 80–170 K. In their model molecules were considered as dipoles oriented normally to the surface. Only one band was observed in the spectrum, shifted from band position in gas phase to higher wavenumbers, the frequency shift being enhanced due to the conductivity of graphite. The aim of this work was to find out the manifestations of the RDDI in the spectra of SF6 adsorbed on the surface of oxide adsorbents with different geometry of the surface and to provide a new insight into the structural aspects of studied systems, comparing the observed spectra with those calculated by means of a model previously developed for liquids and modernized here for molecules adsorbed at interfaces. Two systems were chosen in this study: zinc oxide and silicalite-1. ZnO has a wurtzite-type structure with predominating flat plots of (1 0 1 0) faces, where the cations and anions are arranged in a rectangular 2D lattice. Unlike it, the surface of silicalite silica modification with ZSM-5 structure is presented by a framework of channels with maximal diameter of 6.3 Å. As far as the size of SF6 molecule is 5.13 Å [18], the adsorbed molecules can fill the silicalite channels forming a sort of 1D chains. Thus, two variants of mutual arrangement of SF6 molecules depending on the kind of adsorbent will be considered: (i) 2D structure of adsorbed layer on the flat surface, and (ii) 1D chain-like structure that had to reproduce the filling of silicalite channels with the adsorbed molecules. For comparison, spectra of solid films of SF6 on cell windows were also obtained. The latter can be considered as three-dimensional (3D) system of interacting molecules.

Experimental and calculation procedures Experimental measurements Batches of ZnO or SiO2 (silicalite-1) powders for spectral studies were pressed into thin pellets (17–30 and 2–10 mg cm2, respectively). The samples were preliminarily heated in vacuum (residual pressure < 104 Torr) for 1 h inside the IR cell, described elsewhere [19], at 723 or 773 K for ZnO and at 773 K for SiO2. After thermal activation of the samples the cell was cooled by liquid nitrogen and 0.2–0.3 Torr of He gas was let into the sample compartment to improve thermal contact between the pellet and the coolable part of the cell. After recording the initial spectrum of the cold sample a dose of SF6 was introduced into the cell and was frozen upon the cold walls of it. Then liquid nitrogen was removed and the temperature of the inner part was raised until the bands of adsorbed SF6 arose and grew, and the pressure increase indicated that the excess of adsorbate appeared in the gas phase. The cell was then cooled again and a series of IR spectra was recorded at different coverage of the samples at 77 K. For that, the sample was moved upwards to the warmer part of the cell for progressively increasing time and temperature. The desorbing molecules were trapped upon the cold walls and spectra of samples placed back between the windows showed the changes following the desorption. For the quantitative estimations of surface coverages the amount of gas brought into contact with the sample was preliminarily measured in a special calibrated small volume. Alternatively, the pressure increase caused by desorption on moving the sample from the cold inner part of the cell to the quartz tube kept at ambient temperature was measured. Unfortunately, both the methods, successively applied for CO, were found not good enough for SF6. In fact, after the bands of adsorbed SF6 reached their maximum intensity on temperature increase up to about 130–140 K, further heating led to their decrease due to desorption evidenced by the appearance of the bands of gaseous adsorbate. Attempts to cool the cell quickly so that to fix the maximum coverage also resulted in the substantial decrease of the bands of adsorbed SF6. Apparently, certain part of adsorbed molecules became trapped again on the cold walls of the cell. So, when using the former method we have to suppose that at certain temperature most of molecules are adsorbed, and cannot be sure that some part of them does not remain still trapped somewhere. Thus the coverage, measured in such a way, should be considered as the upper estimate of it. The latter method is not much better, since as soon as the temperature in the cell is high enough, so that the pressure of desorbed gas is less than the saturating vapor pressure of SF6, a great deal of adsorbate is already desorbed and the band of the remaining adsorbed species is superimposed with the strong absorption of gaseous molecules. These difficulties are the consequence of the low adsorption energy that in the case of SF6 does not differ much from the heat of condensation. During the experiments equilibrium gas pressure inside the cell was measured with Edwards Barocel 600 pressure gauges. One, for pressure range 0–10 Torr with the accuracy of 0.001 Torr was connected directly with the sample-containing central part of the cell. Another one for pressures up to 1000 Torr and accuracy 0.1 torr was placed in a separate dosing volume. For temperature measurements a thermocouple inserted into the coolant compartment close to the sample holder was used. FTIR spectra were recorded typically with 2 cm1 resolution for ZnO and 1 cm1 for silicalite, using a Nicolet 710 spectrometer with a coolable MCT detector. 128 scans were accumulated for each spectrum.

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Materials

distance, determines the strength of RDDI. The upper states for a system of two molecules are denoted by a subscript L. E is unity

Two kinds of commercial adsorbates were used in this study. One was SF6 with the natural isotopic content (95.06% 32S, 0.74% 33 S, 4.18% 34S, 0.016% 36S), referred here as 32SF6, and another, referred as 34SF6 had 99.56% of 34S, 0.25% 36S, 0.13% 33S and 0.06% 32S. Commercial ZnO (Kadox, specific surface area  50 m2/ g) and silicalite-1 synthesized at the chemical faculty of Moscow University.

matrix and H (and its conjugate Hy ) is a matrix composed from

Theoretical background

The total intensity of bands is defined by the square of the transition moment from a ground state to the zero order approximation state with allowance for the mixing coefficients of the eigenfunctions. According to the directions of the interacting molecular dipole moments, the perturbation operator (3) applied to the Eq. (4) splits it into three independent secular equations of the second order:

The theory of the RDDI effects on the band shape of the fundamental (m3) transition and the model to simulate the band shapes have been detailed in previous publications [15]. Below we give an abridged account of the RDDI theory and model for highly symmetrical molecules. To describe the interaction we use the experience of the calculations of the molecular system spectra within the approach of isotropic oscillator pair interactions. The spectrum in all cases is calculated as a sum of all transitions, taking into account the equality of transition moments in the zero approximation. Consider first the system of two identical, highly symmetrical molecules, whose centers of mass are separated by the distance R ¼ Re . The axes x, y, z of the molecular frame are arbitrarily oriented relative to the laboratory frame X, Y, Z. The RDDI energy (in cm1) corresponds to the intermolecular dipole coupling:



Pð1Þ P ð2Þ 3

hcR

½ðeð1Þ ; eð2Þ Þ  3ðeð1Þ ; eÞðeð2Þ ; eÞ 

P ð1Þ Pð2Þ hcR

3

Hð12Þ

ð1Þ

Here the relative molecular orientations are defined by the function Hð12Þ , whose range value is [20]. eðkÞ (k = 1, 2) are the unit dipole moment vectors for the two molecules in the laboratory frame; PðkÞ (k = 1, 2) denotes the norms of the dipole-moment vectors of the molecules, depending on the vibrational coordinates: ðkÞ

0 PðkÞ a ¼ P 3 q3a

ð2Þ

where q3a are the dimensionless coordinates; a = x, y, z. Other derivatives of the dipole moment are irrelevant to this problem and can be dropped after solving the secular equation. As the highly symmetrical molecules are isotropic spherical oscillators in the zero approximation, the mutual molecular orientation is unimportant, because the molecular frame can always be oriented along the laboratory frame. In this case, P0x ¼ P0y ¼ P0z and the RDDI operator is:



ðP03 Þ

2

3

hcR

ð1Þ ð2Þ ð1Þ ð2Þ ðqxð1Þ qð2Þ x þ qy qy  2qz qz Þ

ð3Þ

where the intramolecular axes (x, y, z) are superposed with those of laboratory frame (X, Y, Z) in such a way that the mass centers of identical molecules lie on the axis Z. To simulate the band shape, the secular equation should be solved by using the stationary perturbation theory. The solution gives a set of eigenvalues and eigenfunctions for an arbitrary configuration and determines the RDDI-splitted bar spectrum with the intensities calculated from the perturbed eigenfunctions. Assuming the energy eigenvalues k is calculated relative to that ð0Þ

of the unperturbed state m3 , the secular equation to be solved can be written in terms of the 3  3 matrices E and H:

kE y W LL0

W LL0 ¼0 kE

ð4Þ

Here, W LL0 is the off-diagonal matrix element of RDDI: 2

ðP 0 Þ

1 3 W LL0 ¼ aHLL0 ; a ¼ 2hcR ). This important parameter, propor3 (in cm

tional to the absorbance and depending on the intermolecular

the values of Hð12Þ corresponding to combinations of the differently directed vibrating molecular dipole moments:

Hxð1Þ xð2Þ H ¼ Hyð1Þ xð2Þ Hzð1Þ xð2Þ

Hxð1Þ yð2Þ Hyð1Þ yð2Þ Hzð1Þ yð2Þ



Hxð1Þ zð2Þ Hyð1Þ zð2Þ Hzð1Þ zð2Þ

ð5Þ

h1; 0jxðyÞ k a ¼0 h0; 1jxðyÞ a k

ð6Þ

and

h1; 0jz k 2a ¼0 h0; 1jz 2a k

ð7Þ

The secular Eq. (6) describes the interaction of doubly-degenerated UL(x), UL(y) eigenfunctions of the system and the Eq. (7) represents the interaction of nondegenerate UL(z) system eigenfunctions. The solution of these secular equations results in four bands, but in IR spectra only two bands are active: the band corresponding to the doubly degenerate vibration of X(Y)-component of the dipole moment with H = 1, WX(Y) = a and that corresponding to Z-component with H = 2, WZ = 2a. Intensity of the former is twice that of the latter. Thus, in the dimer spectrum the dipole transition matrix element is a sum of matrix elements of transitions unperturbed by the considered interaction multiplied by mixing coefficients of corresponding eigenfunctions. Consider next the system of N identical molecules (i, j = 1, 2, . . ., N). Assume that the Z axis is the preferential direction. Two possible variants of the molecular arrangement are displayed in Fig. 1. In the first case shown in Fig. 1(a) the molecules are arranged in a chain along the Z axis at equal interval R ¼ Re . The secular equation has the 3  N order and can be written in the following form:

kE Rnn 3 21 aðR21 Þ H R 3 31 að nn Þ H R31 ::: R 3 N1 að nn Þ H RN1

3

3

nn aðRR12 Þ H12

aðRRnn Þ H13 13

kE

aðRRnn Þ H23 23

3

nn aðRR32 Þ H32

::: 3

nn aðRRN2 Þ HN2

3

kE ::: 3

nn aðRRN3 Þ HN3

3 nn ::: aðRR1N Þ H1N 3 nn ::: aðRR2N Þ H2N ¼0 3 nn ::: aðRR3N Þ H3N ::: ::: ::: kE

ð8Þ

2

ðP0 Þ

3 Here a ¼ 2hcR 3 ; Rnn is the distance between nearest neighbour

molecules. In all considered cases of arrangement the system of N identical molecules one can mark out one of equivalent directions of the 3D oscillator. As the Z axis is the direction in the laboratory frame, the vibration parallel to Z axis is distinguished, irrespective of the real orientation of bonds in the molecules. For the chain of interacting molecule the spectrum is analogous to that of a dimer. It is noteworthy that here, as in the case of two molecules, the Eq. (8) splits into three independent secular equations of N order. Two identical blocks are independent on one another, and correspond to UL(x) and UL(y) eigenfunctions, while one more block corresponds to UL(z) eigenfunctions. In the second case illustrated in Fig. 1(b), the molecular system form a flat layer at the surface. Assume that N identical molecules are arranged in the X, Y plane, while the Z axis is perpendicular to

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Fig. 1. Arrangement of molecules in: (a) the chain-like (1D) system and (b) the flat (2D) system. The axes of molecular frame are oriented along those of the laboratory frame X, Y, Z. Z axis is the preferential direction.

it. The starting point is the hexagonal close packing. The secular Eq. (8) splits into two independent equations of N order for UL(z) eigenfunctions and 2  N order for UL(x) and UL(y) eigenfunctions. Z component of dipole moment component of each molecule interacts only with Z components of other molecules and does not interact with X(Y) components. The behavior of thus calculated spectra with the increasing number of interacting molecules (N) is demonstrated by Fig. 2(a) and (b). The diagrams on Fig. 2(a) exhibit frequencies and relative intensities of the band calculated for N = 31 molecules and a = 1 cm1. As can be seen, the two components appear in the spectrum as in the case of the dimer and with the same intensity ratio. The bands corresponding to doubly degenerate (X, Y) and nondegenerate Z components of the dipole moment are shifted towards the high and low frequencies, respectively. The splitting between the two components in the spectrum increases with the growing number of interacting molecules. As can be seen from the curve in the inset (a), the shift with respect to the center of mass of the simulated absorption for the band corresponding to the X(Y) component of the dipole is 2.4a cm1, while for the Z component it is 4.8a cm1. The total value of splitting reaches its saturation of about 7a, when 7 molecules are taken into account, and is insignificantly affected by further refinements. Hence, when only the RDDI is taken into account, the maximum value of the splitting in the spectrum should be 7a. Fig. 2(b) demonstrates the behavior of spectra calculated for systems of N = 91 molecules. As can be seen, the solutions of

secular equations also lead to the doublet band structure. However, the band corresponding to Z component is blueshifted now (the upper plot) and the doubly degenerate X(Y) component is redshifted (the middle plot) with respect to the center of mass. Since the intensity ratio of these components remains unchanged, the high frequency component is twice less intense as compared with another one. With the growth of N the shift values for Z and X(Y) components also increases and reach their maximum of 8.5a cm1 and 4.5a cm1, respectively. The splitting value becomes now about 13a cm1 when 91 molecules are taken into account, and further enhancement of the molecule number has no effect on this value (plots in the inset b). Thus, if only the RDDI is considered, the maximum splitting observed in the spectrum can be up to 13a cm1. The outlined theory of the RDDI effect on the fundamental band shapes can also be applied to other molecules with a relatively large value of the dipole moment first derivative by the normal coordinate ðP0i > 0:3DÞ. Thus, for one-dimensional oscillators, such as CO or CO2, placed normally to the surface only one spectral band should be seen, which corresponds to the Z dipole moment component. For two-dimensional oscillators, such as NF3 or CHF3, when their C3 axes are parallel to Z axis of the system, only one band corresponding to the X(Y) component will be observed in the IR absorption spectra. Band shape modeling The modified model developed in the previous study [15] was used to simulate the spectral band shapes. Let’s remind briefly the main points of this approach. Assume that the RDDI only is taken into account. The basis of the model is a regular chain or a flat layer whose structure is then destroyed by adopting arbitrary molecular orientations, and by introducing random displacements of particles obeyed the Gauss distribution with the dimensionless parameter (r), as well as a varied number of randomly distributed vacancies (M), which defines the effective coordination number neff. The relation between M and neff is described by the equation:

neff ¼ nin ð1  M=NÞ

ð9Þ

where nin is the number of the nearest particles in the ideal system. Thus, the model has three input parameters (a, r and M) required to simulate band shapes. The equation for the parameter 2

ðP0 Þ

3 a now is a ¼ 2hcR 3 with two variables: first derivative of the dipole

Fig. 2. Frequencies and relative intensities of fundamental bands for 1D (a) and 2D (b) systems calculated at a = 1 cm1. The shifts are reckoned from the centers-ofmass of the simulated bands. In the insets, variations of the shifts value (in terms of a parameter) vs. relative increased number of interacting molecules (N) for 1D (lefthand side) and 2D (right-hand side) systems are shown.

moment ðP 03 Þ and the nearest-neighbor distance (Rnn). Due to the vacancies, the matrix block of the secular equation to be solved has now the 3  (N  M)2 dimension. The procedure of the secular equation solution and finding of eigenvalues and eigenfunctions was realized using the MATLAB software package and the Monte Carlo simulations [15]. The band shape transformation with the input parameters (r and n) is demonstrated by Fig. 3 for 1D (a) and 2D (b) systems.

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interactions with parameters of Ref. [24]. Values of the parameters for atoms of different kinds were obtained using the Lorentz– Berthelot combination rules. The cut-off radius for the interatomic interactions in the MD simulations was equal to 15 Å.

Results and discussion ZnO: the 2D system

Fig. 3. Simulated fundamental band shapes averaged over 1000 random realizations (a = 5 cm1) as functions of r and n for 1D (a), N = 31 and 2D (b), N = 91 systems. Shits are reckoned from the centers-of-mass of the simulated bands.

The following calculations are performed for a = 5 cm1, Rnn = 5.3 Å, P 03 ¼ 0:55D [21] and N = 31 (1D) and 91 (2D). Used values of the model parameters are taken close to those optimized for liquid [15] to estimate the value of the RDDI splitting. Plots on the two upper rows (M = 0) illustrate how the fine spectral structure of the initial system (r = 0) is progressively lost at r = 0.1, meanwhile the parameter r does not affect the splitting value. The plots on the third row (r = 0) show how the splitting value diminishes and the bandwidth grows with the decrease of neff. As seen from Fig. 3(a), additional components fill the gap between the peaks of the doublet as the vacancy number increases. It might be supposed that when the RDDI with an infinite number of molecules is considered (N = 1), the doublet band structure remains only. The plots on the bottom of Fig. 3 display the band shapes obtained with the parameters r and neff optimized for the liquid SF6.

MD simulation The molecular dynamics (MD) calculations were performed with the simulation box constructed from 2  2  3 of silicalite unit cells (3456 atoms) taken along the a, b, and c crystallographic axes, respectively. The Si and O atoms were fixed at the positions corresponding to the orthorhombic silicalite modification [22]. The SF6 molecules were treated as rigid bodies with the S–F bond length equal to 1.565 Å. The initial coordinates of atoms of SF6 molecules in the zeolite channel system were taken from the output of the grand-canonical Monte Carlo simulations. The equations of motion for the rotational and center-of-mass translational degrees of freedom of the molecules were integrated using the 5th value Gear predictor–corrector and velocity Verlet algorithms, respectively, with the integration time-step equal to 5 fs. The calculations were carried out for the temperature 298 K in the canonical NVT ensemble by using Nosé–Hoover chains of thermostats coupled to the rotational and translational degrees of freedom. The MD trajectories were computed for 1.2 ns with the first 200 ps as equilibration stage. The interaction energy between atoms was described by the Lennard-Jones (12-6) potential function. The intermolecular interactions were computed by considering only interactions between the fluorine atoms. The F–F Lennard-Jones parameters were taken from Ref. [23], where they were fitted to reproduce vapor pressure, saturated liquid density, surface tension, and shear viscosity of SF6. The host–guest interaction energy was described as the O–F

Surface properties of zinc oxide depend essentially on the pretreatment conditions. In the spectrum of samples evacuated at 723 K and cooled in oxygen to avoid the reduction, in accordance with the earlier published results [25], one can see the bands of surface hydroxyls at about 3675 and 3622 cm1, and CO adsorption at 77 K leads to a sharp band at 2168 cm1 that moves on coverage decrease to higher wavenumbers [26], demonstrating strong dependence of band position on lateral interactions. Adsorption of SF6 on such samples results in too intense bands, that is why to follow the coverage dependence we have used samples preliminarily treated in vacuum and oxygen at 773 K. Apparently, during such a treatment some sintering takes place and surface properties are changed dramatically. Bands of surface OH groups are not visible anymore and in the spectrum of adsorbed CO only a broad absorption between 2160 and 2140 cm1 with a maximum near 2156 cm1 is present. The spectrum of SF6 adsorbed on a thin (17 mg/cm2) ZnO sample pretreated at 773 K is shown in Fig. 4. After inserting a small doze (0.2 lmol) of SF6 into the cell at 139 K, a band at 944 cm1 appears (curve 1). If the cell is cooled down to 77 K and then warmed up to 117 K, the total intensity of absorption becomes much higher and two satellite bands arise near 970 and 920 cm1 (curve 2). Further cooling to 108 K (curve 3) and then to 88 K (curve 4) the side bands disappear and only the central band almost at the same position as in spectrum 1 remains still visible. To achieve higher coverage a greater doze (0.9 lmol) of SF6 was introduced into the frozen cell, which was then heated to about 135 K (curve 5). Now the central maximum is almost gone and two strong bands at 977 and 915 cm1 as well as a less intense one at 989 cm1 are observed in the region of m3 vibration of adsorbed SF6. Our attempts to fix the coverage by freezing the sample to 77 K were not successful. Apparently, on lowering the temperature some part of the adsorbate always condensed upon the

Fig. 4. FTIR spectrum of ZnO pretreated at 773 K after addition of 0.2 lmol of SF6 at 139 K (1), cooling to 77 K and warming up to 117 K (2), further cooling to 108 K (3) and to 88 K (4), and after addition 0.9 lmol more of SF6 at 135 K (5). Background spectrum of the sample before adsorption is subtracted.

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cell walls leaving the sample, which was slightly heated by the IR beam or thermal radiation through the windows. For this reason the quantitative estimates of surface coverage based on the doze of molecules inserted into the cell should be regarded as an upper limit of the real coverage value. Spectrum of SF6 adsorbed on ZnO sample pretreated at 723 K (Fig. 5) is slightly different from that one calcined at 773 K. Adsorption of the excess of adsorbate and subsequent cooling to 77 K leads to a pair of narrow bands at 981 and 921 cm1, a weaker one at 903 cm1, a shoulder at 990 and a poorly pronounced maximum near 950 cm1. The latter becomes better visible when the coverage decreases and other peaks become less intense. Thus, two main peaks are shifted to higher wavenumbers by about 5 cm1 and an extra maximum arises at lower frequencies. Such a spectrum is used below for the analysis of intensity distribution between the components of the structure. Fig. 5a and b demonstrates the experimental spectrum of SF6 adsorbed on ZnO (pretreated at 723 K) at two different surface coverages measured at 77 K. To analyze the band shapes of the spectra we have applied the least-squares fitting using Gaussian sum functions. As can be seen from the figure, the structure of two main maxima near 981 and 921 cm1 with weaker bands at 903, 990 and 950 cm1 remains at lower coverage, when the integrating intensity of whole band is about 16% of its maximum value. In fact, the first spectral moments M(1) (the centers of weight of the bands) for the three main constituents are 976, 953, 921 cm1 and 977, 947, 922 cm1 for the high and low coverages, respectively. Meanwhile, serious changes occur on desorption in the areas of the constituents that are the shares of them in the total integrated absorption. For the two coverages these values are, respectively, 0.25, 0.1, 0.5 and 0.15, 0.23, 0.35. Thus, the relative intensity of the middle band grows on desorption and the intensity of the low-frequency constituent near 920 cm1 is twice that of the high-frequency one. This result is in perfect agreement with the theory and supports our assignment of the central band to the isolated SF6 molecules remaining at the surface after partial desorption of the adsorbate, and, hence, weakly interacting between each other. The doublet structure of the strongest bands is well reproduced in the calculated spectrum with two maxima at 980 and 918 cm1, shown in Fig. 5c together with the experimental spectrum obtained at maximum surface coverage of the sample

Fig. 5. Experimental spectrum in the m3 region of SF6 adsorbed on ZnO pretreated at 723 K (solid lines) at high (a) and low surface coverage (b); band shape calculated at a = 5.4 cm1, r = 0.1 and M = 42, n = 4 (dash line) compared with the measured profile at maximum surface coverage (c). Peaks shown by bottom curves in panels a and b indicate deconvoluted components which are reproduced by Gaussian function. Calculated profile is normalized to the area of the more intense lowfrequency component of the experimental spectrum.

pretreated at 723 K. Such a double peak-structure is characteristic of the RDDI. The high-frequency band corresponds to Z-component with the dipole moment vibration perpendicular to the surface, while the low-frequency one corresponds to the X(Y) component with dipole moment vibration parallel to the surface. If we neglect the conductivity or polarizability of the solid, the intensity of X(Y) component should be about 2 times greater than that of Z component. The band shape calculation was performed at a = 5.4 cm1 and Rnn = 5.2 Å, as in the dimension of ZnO unit cell along c axis.[27]. The value of the dipole moment first derivative was taken as for a free molecule ðP 03 ¼ 0:55DÞ. Then, with the following model parameters: r = 0.1 and M = 42, n = 4 the spectral width of the computed curve components qualitatively reproduces the observed in the experiment. Peaks at 903 and 907 cm1 from Fig. 5a and b could be assigned to polymolecular layers of physisorbed SF6. Alternatively, this relatively intense band can be considered as a component of the split X(Y) component. In fact, the (1 0 1 0) face of prismatic ZnO microcrystals with hexagonal wurtzite structure has two inequivalent directions, along or perpendicular to c crystal axis, and this could account for the splitting of the band in question. The peak near 990 cm1 belongs to the m2 + m6 combination mode of SF6 molecule [28]. The surface of ZnO is rather homogeneous and is represented mostly by the same regular (1 0 1 0) face [5,6]. CO adsorption on such samples at saturating conditions results in one sharp predominating band at 2168 cm1, and manifests comparatively strong dynamic interaction (Dmdyn = 6 cm1) in the adsorbed layer enhanced by the solid [11]. It was supposed that the adsorbed CO molecules at saturating condition form an ordered structure occupying each second surface Zn cation. The distance between the rows of adsorbed molecules is 5.2 Å, but due to the repulsive interaction between CO molecules they do not occupy the opposite sites in the neighboring rows, but form a sort of chessboard structure where each molecule is surrounded by 6 others, 4 at 6.1 Å and 2 more at 6.5 Å. As a result a slightly distorted hexagonal net of occupied sites with the density of 2.95 molecules/nm2. We do not know, if the interaction between the SF6 molecules in the neighboring rows is attractive enough to occupy the sites at 5.2 Å and to form a rectangular structure, or the adsorbed molecules would prefer to arrange in the quasihexagonal structure as carbon monoxide. In both cases the RDDI in such a layer should be slightly weaker than in the close packed layer with Rnn = 5.2 Å used in our model, but as in the case of CO we could anticipate that it should be somehow enhanced by the adsorbent. At any case, a good accordance between the theory and experiment for ZnO is not unexpected. Here we supposed that adsorbed SF6 forms at the surface a commensurate layer with the structure imposed by the surface of the crystal. This could be not a rule, but a result of occasional nearness of the lattice parameters of ZnO to the diameter of SF6 molecule. To verify this point experiments with SF6 adsorption on CaO and MgF2 have been carried out. Preliminary results have shown that in both cases the band is split, and the value of the splitting is not the same as for ZnO, about 44 cm1 for CaO and 52 cm1 for MgF2. To our mind, different values of the splitting support the hypothesis on the commensurate layer of the adsorbate. Thus, the adsorbed molecules do not form the same close packed layer on any surface, but form certain structure, which depends on the geometry of the surface. However, it seems that the RDDI in the layer results in much greater frequency shifts of adsorbed SF6 molecules as compared with the shifts caused by specific interaction with certain surface sites. Single molecules that account for the bands observed at low coverages and higher temperatures absorb near 940 cm1 not depending on the presence of Lewis sites on ZnO surface, or

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strong basic sites of CaO, where the band of such lone molecules appeared at 943 cm1. Silicalite as a 1D system When SF6 is adsorbed on silicalite-1 at 200 K a strong band in the region of the m3 vibration appears at 937 cm1 with a weak shoulder near 920 cm1. Cooling by liquid nitrogen and further down to 55 K results in the intensity decrease of this band accompanied by the growth of bands at 949 and 928 cm1. Spectra registered with better resolution (1 cm1) reveal the structure of the 928 cm1 band, which consists of a close pair of sharp peaks centered at 929.2 and 926.9 cm1. The bands are extremely narrow, their estimated FWMH (Dm1/2) is about 0.4 cm1 at 77 K. Besides the above bands, on temperature lowering much weaker peaks grow at 913 and 910 cm1, while the shoulder at 920 cm1 disappears. The observed changes with temperature, illustrated in Fig. 6, are completely reversible. It is not easy to follow the coverage dependence of the spectrum in the region of the asymmetric stretching vibration m3, as it could be done for ZnO, since even for thinnest pellets the band is too intense to be observed near the saturating conditions. We only can mention higher relative intensity of the 937 cm1 band at low coverages in the spectra recorded at 77 K. Temperature dependence of the SF6 spectrum in silicalite-1, illustrated in Fig. 6, supports the assignment of the 949 and 929– 927 cm1 group of bands to the collective vibrations of molecules forming chains along the channels of zeolite. Intensity increase of these bands on lowering the temperature can be explained as the result of 1D condensation i.e. the growing of molecular chains at the expense of ‘‘1D gas’’ of single molecules not interacting between each other. The latter can be associated with the 937 cm1 band, more intense at comparatively high temperatures and lower coverages. In accordance with our model, the high-frequency band at 949 cm1 should be assigned to vibrations in X and Y directions, that are perpendicular to the chain, while the low-frequency component – to those in Z direction, along the channels. The reason of splitting of the latter band in two peaks at 929 and 927 cm1 is not clear yet. Bandwidth less than 1 cm1 is very rare for the adsorbed species where the bands are usually broadened due to surface heterogeneity. Ewing [29] reported the extremely low FWMH (0.17 cm1 at 4 K) for CO adsorbed on NaCl (1 0 0) face of a single crystal. Bands

Fig. 6. Spectrum of SF6 adsorbed on silicalite-1 in the region of the m3 band, registered with the resolution of 1 cm1 at 190 (1), 150 (2), 100 (3), 77 (4) and 55 K (5).

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with the estimated FWMH of about 0.3 and 0.5 cm1 at 4 and 77 K, respectively, were observed for saturating CO layers on ZnO pressed powder samples [26]. In both these cases the reason of band narrowing was the RDD (dynamic) interaction, as it was shown by computer modeling [30]. For CO adsorbed on flat surfaces RDDI leads to the stretching band splitting in two components, only the high-frequency one to be active in IR absorption. For SF6 adsorbed on silicalite-1 both the components are active and, apparently, narrowed due to the interaction. When any sample with adsorbed SF6 was removed from the beam, a weak band could be seen at about 910 cm1 with a tailing from the high frequency side (Fig. 7 curve 2). It becomes much stronger if we leave a sample in the beam and pump off helium from the cell cooled with liquid nitrogen. The band apparently belongs to SF6 film condensed on the cold inner windows. Absorption of 3D phase could contribute to the spectrum of adsorbed SF6 at highest coverages when polymolecular layers of physisorbed molecules are formed. In accordance with that, at saturating conditions incredible growth of absorption occurs for both the adsorbents at this very region, around 910 cm1. To simulate the band shape of SF6 molecules arranged in a 1D chain we have taken the following model parameter: a = 5 cm1 (Rnn = 5.3 Å, P 03 ¼ 0:55D [21]), r and M = 0. The resulting spectrum consists of two lines shifted from the position of non-interacting molecules (939.3 cm1) to 951 (X, Y) and 915 cm1 (Z), which are shown by dash lines in Fig 7. The calculated intensity of XY component is twice that of Z band, and the band shape modeling shows that the FWMH values drastically depend on the judgmentally chosen parameters, however, with certain relation between those of two components. So, if Z band has D m1/2 = 4.0 cm1, that of XY component is smaller, Dm1/2 = 2.5 cm1. Comparing these results with the observed spectra we can find that the model well reproduces the doublet structure of the m3 band, however, as can be clearly seen in Fig. 7, the calculation overestimates the frequency difference of the components (36 cm1 against the observed 20–22 cm1). This could mean that the intermolecular distance is greater, imposed by the geometry of zeolite pores, or, maybe, the zigzag arrangement of molecules weakens the interaction. Unlike the predictions of the model, the total intensity of the 929–927 cm1 doublet is noticeably higher than that of

Fig. 7. The region of m3 vibration in FTIR spectra of SF6 adsorbed on ZnO (1), a solid film of SF6 on the cell windows (2) and adsorbed on silicalite-1 (3). The arrows show the position of the m3 band of SF6 dissolved in liquid Ar at 939.3 cm1. The vertical dash lines represent the band positions in the calculated spectra at a = 5 cm1, r and M = 0 for 2D (the left-hand side) and 1D (silicalite, the right-hand side) model systems.

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the 949 cm1 band, and the frequency shift of the doublet from the band position of a free molecule is smaller as compared with the shift of the high-frequency component. Such manifestations of the RDDI are rather characteristic of the 2D systems or other arrangement of molecules in the space.

Comparison between ZnO and Silicalite The comparison of band positions of the split band of the m3 vibration for ZnO and silicalite-1 shown in Fig. 7 demonstrates not a bad accordance with the predictions of our theory. For different pretreatment conditions, not depending on the presence of strong Lewis sites evidenced by the bands of coordinately bonded CO at 2190–2160 cm1, the spectrum of SF6 adsorbed on ZnO exhibits in the region of asymmetric stretching vibration m3 a structure of two main components, about 60 cm1 apart. One can see from Fig. 7a that the distance between the components of splitting calculated for 2D layer of interacting SF6 molecules with the parameters a = 5 cm1, r and M = 0 is in a fair agreement with the experimental spectrum. The predicted splitting for 1D chains (Fig. 7b), calculated with the same parameters, is substantially smaller, about 35 cm1. The observed frequency difference between the two components in the spectrum of SF6 in silicalite is even smaller, 20–22 cm1. At low coverages and higher temperatures a single band near 940 cm1 predominates. Its position is close to that of SF6 molecules dissolved in liquid Ar at 93 K (939.3 cm1) [21] or to the frequency of gaseous 32SF6 (949 cm1) [31].

More realistic data on SF6 distribution within the channels of silicalite-1 can be obtained by molecular dynamics. Fig. 8 shows the result of MD modeling of SF6 arrangement in silicalite with ZCM-5 structure carried out for 298 K and 53% of maximum loading of the zeolite structure with the adsorbate (12 mol/u.c.). One can see that, as anticipated, the adsorbed molecules form straight chains along the c axis (vertical direction). There are at least three chains like that, one goes through the whole picture, two others are not completed. The molecules occupy the cavities of the channel and do not occupy the windows between them, thus the distance between the molecules is greater than in the close chain (5.3 Å). This can explain the observed smaller splitting value as compared with the model. What was not taken into account in the model, is that a great deal of molecules penetrate into the narrower zigzag (sinusoidal) channels and are either separately distributed there or form chains like that one, which runs through the picture along the horizontal x axis. Thus, straight chains of molecules is too rough approximation for modeling SF6 arrangement in silicalite. Further work using MD for modeling adsorption dynamics and spectra of SF6 in zeolites is in progress, but this is already far beyond the scope of this paper. The above data persuade us that this is in fact the RDDI that accounts for the observed splitting of the m3 band in the spectra of SF6 adsorbed on ZnO and silicalite-1. Smaller value of splitting for the latter as compared with ZnO, in accordance with our model, we explain by different geometry of surfaces: flat 2D layers of adsorbate on the surfaces of ZnO and 1D chain-like arrangement of adsorbed molecules in silicalite-1 channels.

Fig. 8. Arrangement of SF6 molecules in the channels of silicalite-1 simulated by MD modeling at 53% of the maximum content for the temperature 298 K. The straight channels are oriented along x axis (vertical), zigzag channels run in x direction (horizontal).

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Conclusions Adsorption of sulfur hexafluoride on ZnO and on silicalite-1 was investigated by a combination of IR spectroscopy and theoretical spectra calculations including a modernized model combined with a refined Monte-Carlo procedure, applied earlier to molecular liquids [15]. Comparison of the experimental spectra and the results of computational modeling demonstrates a good agreement between the theory and experiment and shows that this is a strong RDDI between the adsorbed molecules with extremely high absorbance which accounts for complex spectra of this compound in the region of the m3 vibration. The spectra depend crucially on the mutual arrangement of interacting molecules, which can form (i) an one-dimensional (1D) systems, such as chains in the channels of silicalite-1; (ii) two-dimensional (2D) adsorbed layers on the plane faces of crystalline adsorbents such as ZnO, CaO, or others, and (iii) three-dimensional (3D) in solid film, earlier studied liquid SF6 [15], or solutions in rare gases [21]. The RDDI manifests itself in the spectra of 1D and 2D systems as the doublet band structure, whose components correspond to the transversal and longitudinal vibrations of the molecular dipole moment. According to the calculations, the maximal RDD splitting between the two components for 1D chains is smaller than for flat 2D systems, 36 cm1 against 65 cm1 at a = 5 cm1, Rnn = 5.3 Å. The experiment gives even more significant difference, 20–22 cm1 for molecules confined in the channels of silicalite-1 as compared with 60–78 cm1 for ZnO. While for ZnO the calculated spectra are in a fair agreement with those measured experimentally, spectra of SF6 in silicalite channels differ from those calculated for 1D chain in splitting value, intensity ratio and reveal splitting of the low-frequency component, not explained by the model. Arrangement of SF6 molecules in the pores of the zeolite studied by MD modeling was shown to be more complicated. Further studies of molecule distribution, dynamics and spectra of SF6 in zeolites by means of MD modeling are in progress. Spectra of adsorbed SF6 are not too sensitive to the properties of surface sites. Adsorption on ZnO samples pretreated at different conditions, where the sites of CO coordination are abundant or almost absent gives almost identical pair of m3 vibration bands split by about 60 cm1 differing in the positions of maxima by 3– 6 cm1. The splitting is not the same for other adsorbents, apparently, depending on the intermolecular distance in the layer imposed by the geometry of the surface. Presented data infer that the spectra of adsorbed highly symmetric molecules can be dramatically affected by strong RDD interaction, more, than by the presence of specific surface sites. Manifestations of RDDI studied above are less pronounced in the spectra of test molecules used for surface characterization, since the absorption coefficients of vibrations, sensitive to specific interactions with certain surface sites is usually not so high. E.g., in the spectra of CO molecules interacting with cationic centers (Lewis acid sites) of oxide catalysts the shift caused by RDD (dynamic) interaction does not exceed 6–8 cm1 for ZnO [11,26] or La2O3 [32]. However, at high coverages such shifts distort the data on the strength of the most abundant sites and have to be taken into account. Splitting of the bands of adsorbed molecules caused by RDDI can be interpreted as a measure of the rate of vibrational energy exchange between the adsorbed molecules. Knowledge of the rate of this process is important for understanding the mechanism of

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Effect of resonance dipole-dipole interaction on spectra of adsorbed SF6 molecules.

Adsorption of SF6 on zinc oxide and on silicalite-1 was investigated by a combination of IR spectroscopy with the calculations of spectra by means of ...
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