Structure of Neutral Nanosized Clusters Produced by Coexpansion of

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Structure of Neutral Nanosized Clusters Produced by Coexpansion of CF4 and CH4 M. Winkler, J. Harnes, and K. J. Børve* Department of Chemistry, University of Bergen, NO-5007 Bergen, Norway ABSTRACT: Mixed CH4/CF4 clusters as well as pure clusters of CF4 were produced by adiabatic expansion and studied by carbon 1s (C1s) X-ray photoelectron spectroscopy. Evidence is presented that CH4 and CF4 do indeed form binary clusters in CH4/CF4 coexpansion experiments and that these clusters exhibit radial structure; i.e., CF4 is primarily found in the bulk. The interpretation of the photoelectron spectra is supported by calculations of C1s ionization energies based on theoretical clusters models.

’ INTRODUCTION Molecular clusters, i.e., clusters consisting of discrete molecules and held together by intermolecular forces, are of interest for a number of reasons. They offer insight into nucleation and growth processes with application to crystal formation (growth) and condensation.1 Many reactions in atmospheric chemistry take place in or at the surface of molecular clusters. Within gas cluster ion-beam technology, clusters of rare gases and molecules are utilized for surface processing and to assist thin-film deposition.2 The physical and chemical properties of clusters vary with size. Therefore, controlling the size is an important aim in cluster research. A further degree of freedom can be introduced by changing the cluster composition to consist of more than one species. Clearly, it is desirable to explore the potential of tuning the properties of these systems. Clarke et al.3 presented simulations of mixed clusters of two rare-gas-like particles A and B of the same size but with distinct two-body interaction potentials. Depending on the relative strength of the interactions A
A, A
B, and B
B, the particles form clusters of different structures, such as homogeneously mixed clusters or clusters where one particle type prefers bulk sites while the other makes up the surface.3 In reality, cluster components may differ not only in interaction strength but also in shape and size, introducing further parameters. Indeed, mixed rare-gas clusters have been studied both theoretically3,4 and experimentally.5
13 Cluster systems consisting of two different rare gases, namely, (Ar/Xe),11,12,14 (Ar/Kr),5,6 and (Ne/Ar), 9 have been produced by coexpansion of a gas mixture and studied by inner-shell X-ray photoelectron spectroscopy (XPS). These studies suggest that two-component rare-gas clusters have radial structure with the heavier and more polarizable rare gas preferring the interior sites. For the use of XPS in cluster studies, see the recent review by Bj€orneholm et al.15 In the cases of self-assembled Ne/Ar clusters and Ar/Xe clusters, a layered core
shell structure has been proposed.5,9,10 However, for the latter system a recent study11 suggests that the structure may be less well-defined. Moving to molecular constituents rather than rare gases introduces further degrees of r 2011 American Chemical Society

freedom in terms of shape as well as different types of molecular interaction. While there are numerous studies of small oligomers formed by two molecular species, investigations into the structural organization of binary medium-sized (from about 100 to several thousand molecules) clusters are few.16
19 In this study we extend the knowledge about mixed clusters to such species that are formed from two molecular components by adiabatic coexpansion. Both methane and tetrafluoromethane have tetrahedral symmetry, and their first nonzero electrostatic moment is the octopole. Thus, the electrostatic interactions between these molecules are weak, and they are primarily bound by van-der-Waals forces. Hence, CH4 and CF4 are similar to rare gases on account of both high symmetry and the nature of their interaction and thus make a useful stepping stone to the molecular case. Here, we aim to assess whether binary clusters are formed in a coexpansion of CH4 and CF4, and if so, to explore the radial cluster structure. The investigation is based on carbon 1s (C1s) photoelectron spectroscopy of cluster beams and supported by molecular dynamics (MD) simulations of well-defined cluster models. Noteworthy, the computational models allow us to explore how the ionization energy changes with size and structure, thus providing a firm basis for interpreting our experimental observations. We will first present and analyze C1s spectra of pure tetrafluoromethane clusters and relate the mean ionization energy to cluster size. While methane clusters have been studied by XPS,20 neutral clusters of CF4 have not been examined earlier and are of interest in their own right. Next, by comparing spectral data from the coexpansion experiments of CH4 and CF4 to those for the single-component clusters, we show that the produced clusters are indeed mixed and that they show a fairly ordered radial structure with methane preferring the surface sites. Received: July 5, 2011 Revised: September 19, 2011 Published: September 21, 2011 13259

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’ COMPUTATIONAL DETAILS The purpose of computational modeling in this study is twofold. First and foremost, it is used to calculate ionization energies to assist the analysis of the photoelectron spectra. Second, we use computational models to obtain information about the stability and structure of mixed clusters. Calculation of ionization energies requires a reasonably accurate description of the electrostatic field of the molecule, the molecular polarizability, and intermolecular distances. As the typical size of the clusters produced experimentally makes a quantum mechanical description too demanding, we resort to a force-field (FF) approach as described earlier.21,22 Molecular dynamics (MD) simulations are performed employing the AMOEBA force field23,24 as implemented in the molecular-modeling package TINKER 4.2. AMOEBA includes a polarizable atomic multipole description of electrostatic interactions. The details of the force-field parametrization and comparison to quantum mechanical calculations are given in the Appendix. Important to notice, our force field reproduces the shifts in ionization energy of dimers of CH4 and CF4 as calculated at the MP2 level within 0.01 eV. The relative stability of the CH4
CH4, CF4
CF4, and mixed CH4
CF4 dimers as obtained by MP2 is well reproduced by the force field. The dimer binding energies are overestimated by 0.10
0.14 kcal/mol (16
23%) compared to values obtained at the MP2 level of theory. Molecular Dynamics Simulation of Clusters. MD simulations have been carried out within the canonical ensemble at a temperature of 50 K. The molecules were treated as rigid bodies. As polarization contributes very little to the intermolecular interactions, it was turned off during the propagation of the neutral clusters. The equilibration and production phases of the clusters lasted at least 500 ps each using 5 fs time steps. Clusters of sizes 50, 100, 150, 200, 300, and 400 were simulated in the single-component cases. Initial structures for mixed clusters were derived from spherical cuts from the CF4 crystal structure,25 and the desired number of CF4 molecules were replaced randomly with CH4. In addition to these randomly mixed structures, we propagated two core
shell structures. Calculation of Ionization Energies. Our approach has been described in detail elsewhere,21 and we shall thus give only a general outline. The distribution of ionization energies (IE) in a cluster is obtained by calculating the ionization energy (relative to the monomer) for each molecule in the cluster for a large number of cluster geometries. This is achieved by substituting one neutral molecule at the time in the cluster with one that resembles the core-ionized species and calculating the difference in intermolecular interaction energy. The geometries are obtained by taking snapshots from the MD simulations of the clusters as described above. The distribution of IE is subsequently convoluted with the line shape associated with the monomer and a Gaussian function to account for various contributions to broadening (see below). ’ EXPERIMENTAL DETAILS Clusters were produced in a supersonic beam expansion setup described in ref 26, using a conical nozzle with opening diameter of 150 μm and a half-opening angle of 10°. The cluster beam is led through a 300 μm skimmer to remove most of the uncondensed gas before interacting with the synchrotron light. Helium was used as backing gas to increase the degree of condensation. The gas-mixtures have been prepared and equilibrized before use. Carbon 1s (C1s) photoelectron spectra were recorded at the soft-X-

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Table 1. Conditions and Results for the Cluster Experiments for Pure Tetrafluoromethanea experiment

Tn (K)

p0 (bar)b pCF4 (bar) ΔIE (eV)c Δfwhm (eV)d

a

268
271

2.2

0.6


0.49

0.48

b c

214
216 171
175

2.1 2.1

0.7 0.4


0.55
0.52

0.49 0.46

d

175
177

1.5

0.2


0.43

0.42

a

The expansion conditions are given in terms of temperature of the nozzle (Tn), stagnation pressure (p0), partial pressure of tetrafluoromethane (pCF4), cluster-to-monomer shift in carbon 1s ionization energy (IEcluster
IEmonomer = ΔIE), and the Gaussian full-width-athalf-maximum of the cluster peak (Δfwhm). b Fluctuations in pressure have been 0.05 bar or less. c Fitting of subsets of the complete data set results in deviation of up to 0.01 eV for ΔIE and Δfwhm. Overall an uncertainty of 0.02 eV would be a conservative estimate. d Contribution from finite instrumental resolution to the Gaussian distribution has been subtracted in squares.

ray undulator beamline I41127 at MAX-Lab in Lund, Sweden, using a photon energy of 350 eV. The beamline is equipped with a modified SX-700 monochromator. For the detection of photoelectrons, a Scienta R4000 electron analyzer has been used. All spectra have been recorded with an angle of 54.7° between the spectrometer axis and the horizontal polarization plane of the synchrotron light. In the case of pure tetrafluoromethane clusters, C1s spectra were recorded for four different combinations of pressure, temperature, and mixing ratio with the backing gas, as detailed in Table 1. Experimental conditions for the experiment of coexpanding CF4 and CH4 are given in Table 2. Theoretical line shape models were fitted by least-squares techniques to the experimental spectra detailed in the following. The vibrational Franck
Condon envelope for methane was adopted from ref 28 and for gas-phase tetrafluoromethane from ref 29. These were subsequently convoluted by the line shape functions given by eq 12 in ref 30 to account for the natural line width (100 meV for C1s) and postcollision interaction during Auger decay of the core hole. Finally, the finite experimental resolution was represented by a Gaussian distribution with a fullwidth at half-maximum (fwhm) of Γinstr = 113 and 179 meV for experiments on pure tetrafluoromethane and the CF4/CH4 mixture, respectively. The cluster peaks were treated similarly, except that we allow for a free Gaussian width to account for broadening caused by the size and possible temperature distribution of clusters in the beam. The intensity and energy position of each model spectrum as well as a linear background were determined in a least-squares fit to the experimental spectrum.

’ RESULTS AND DISCUSSION This section is organized as follows. Initially, single-component CF4 clusters are investigated with respect to their carbon 1s (C1s) photoelectron properties, and a quantitative relationship is established between the mean C1s ionization energy and cluster size. C1s photoelectron spectra of methane clusters have been reported earlier,20 and here we reanalyze the published data by drawing on information from theoretical modeling, thereby exploring the size dependency of the cluster
monomer shift also for CH4 clusters. Next, by comparing spectral data obtained for the single-component clusters to data obtained from two experiments where CH4 and CF4 are coexpanded, we show that the observed clusters are indeed mixed. We then turn to 13260

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Table 2. Conditions and Results for the Methane
Tetrafluoromethane Coexpansion Experimentsa ΔIE (eV)c

pX (bar) experiment

Tn (K)

p0 (bar)b

CF4

CH4

Δfwhm (eV)d

CF4

CH4

CF4

CH4

ACH4/ACF4e

I

139
140

1.4

0.1

0.1


0.76


0.74

0.38

0.51

8.6

II

147
148

2.2

0.1

0.2


0.57


0.54

0.51

0.49

2.9

a The expansion conditions are given in terms of temperature of the nozzle (Tn), stagnation pressure (p0), partial pressure of two molecular species (pX), cluster-to-monomer shift in carbon 1s ionization (IEcluster
IEmonomer = ΔIE), full-width-at-half-maximum of the cluster peak (Δfwhm), and the ratio of the cluster peak signals of CH4 to CF4 (ACH4/ACF4). b Fluctuations in pressure have been 0.05 bar or less. c Fitting of subsets of the complete data set result in deviation of up to 0.01 eV for ΔIE and Δfwhm. Overall an uncertainty of 0.02 eV would be a conservative estimate. d Contribution from finite instrumental resolution to the Gaussian distribution has been subtracted in squares. e Ratio of the cluster peak area. In the same manner as uncertainties for ΔIE, the relative error of the ratio can be estimated to be 20%.

Figure 1. Carbon 1s spectra of a beam of clustered and uncondensed CF4 molecules (monomers) recorded for experimental settings c (black circles) and d (gray squares), as detailed in Table 1. The fitted curve and the underlying cluster (solid) and monomer (dashed) peaks are shown for experiments c (black) and d (gray), respectively. The two spectra are normalized on the monomer peak and aligned at the adiabatic threshold of 301.898 eV.

molecular dynamics models of mixed clusters and compute the associated shifts in C1s ionization energies. This facilitates the interpretation of spectra from the coexpansion experiments and allows us to draw conclusions with respect to radial structure. Single-Component Clusters of CF4. Carbon 1s photoelectron spectra were recorded for pure clusters of tetrafluoromethane as produced under four different stagnation conditions (a
d) that are detailed in the Experimental section and in Table 1. Experiments a and b were conducted under similar total and partial pressures but different temperatures of 268
271 and 214
216 K, respectively. Conversely, experiments c and d were run under different pressure conditions but with similar nozzle temperatures of around 175 K. The C1s photoelectron spectra corresponding to experiments c and d are shown in Figure 1. In adiabatic expansion experiments uncondensed molecules (monomers) are always present beside the clusters. Thus the spectra contain signals from both kinds of molecules, a fairly broad and structureless cluster peak with a high-energy shoulder at about 301.9 eV representing the monomers. The cluster peak is well represented by a single Gaussian peak convoluted with the monomer line shape. This is different from the previously studied case of pure methane clusters,20 which display distinct surface and bulk features in their XPS spectra. However, this bimodal distribution is not resolved here for the pure tetrafluoromethane clusters. The main difference

Figure 2. Dependence of the calculated mean cluster-to-monomer shift on the size of clusters for CF4 (black squares) and CH4 (gray circles). The solid curves represent fits of the function ΔIE = b + c 3 N
1/3 to the data. The dotted lines represent the asymptotes of the functions. The arrows indicate mean cluster-to-monomer shifts observed in the present experiments a
d and in experiments A and B of ref 20.

between the two spectra in Figure 1 is the energy position of the cluster peak, i.e., the mean cluster
to
monomer shift in ionization energy, ΔIE. This parameter and also the width (fwhm) of the cluster peak are included in Table 1 for each experiment. For experiments c and d, the observed values for ΔIE are
0.52 and
0.43 eV, respectively. Assuming the cluster
monomer shift to get increasingly negative with increasing cluster size, we conclude that the mean cluster size decreases when lowering the total stagnation pressure and the partial pressure of tetrafluoromethane when the temperature is kept constant. For conditions a and b, we find ΔIE of
0.49 and
0.55 eV, respectively, implying that the cluster size increases when the nozzle temperature is lowered from around 270 K to approximately 215 K. In general, the observed dependence of the mean cluster-tomonomer shift (ΔIE) and hence that of the average cluster size on the stagnation conditions is as expected. Experiments b and c show similar shifts, although larger shift (in magnitude) in b than c. Going from conditions b to c, the decrease in partial pressure by 0.3 bar therefore seems to outweigh the effect of reducing the temperature by about 40 K. The Gaussian line widths of the cluster peaks in spectra a and b are almost the same and about 0.5 eV while those of c and especially d are somewhat narrower. Recently, the mean cluster-to-monomer shift in an atomic core line (ΔIE) has been demonstrated to provide quantitative estimates of the mean cluster size for a beam of single-component molecular clusters of carbon dioxide.31 Establishing such a 13261

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Figure 3. Carbon 1s photoelectron spectra of clusters produced by expanding a mixture of CH4 and CF4 into vacuum. The spectra recorded with the settings of experiment I and II are shown in the upper and lower panel, respectively. Experimental data shown as gray circles. The signals corresponding to uncondensed monomers are represented by light gray shaded area. The signals from molecules in clusters are represented by thin black lines. In the case of CH4, the cluster contribution can be divided into a bulk part (dark gray area) and surface part (white area). The linear background is denoted by the black dotted line. Contribution from CH4 shakeup is shown as a dashed gray line in the inset, which shows an enlargement of the CF4 part of the spectrum.

relationship between mean size and ΔIE for the present singlecomponent clusters is useful for the subsequent analysis of spectra from the coexpansion experiments. This will be achieved by preparing theoretical models of clusters with different number of monomers, N, and in each case computing the mean cluster
monomer shift in C1s energy as outlined in the Computational Details section. A complication in this respect is the essential dependence on the attenuation length of photoelectrons in the cluster material. The attenuation length affects the effective observed surface-tobulk ratio in the spectra and hence the observed mean cluster-tomonomer shift. A database32 is available for predicting effective attenuation lengths (EALs) by taking into account both the inelastic and elastic scattering of the photoelectron. The practical EALs predicted by this database are around 5 Å for tetrafluoromethane and 7 Å for methane. These values are in good agreement with cross section data for total and elastic scattering of the free molecules33,34 and will be used here. A further important parameter for estimating cluster size based on the C1s shift is the density of the material, since ΔIE depends on the polarizability per unit volume. While the molecular polarizabilities in our force field deviate from the experimental values by less than 3%, the densities predicted by the MD simulations are less accurate. The computed densities are 2.30 and 0.56 g/cm3 for tetrafluoromethane and methane respectively, which are to be compared to experimental values of 2.160 g/cm3 (49 K)25 and 0.507 g/cm3 (50 K),35 respectively. Thus the MD-based densities are overestimated by 6.5% and 10.4%. Based on our cluster models, we calculated ΔIEs for six different cluster sizes (N = 50, 100, 150, 200, 300, 400) as described above. To leading order, the polarization contribution to the shift scales with density to the power of four-thirds.36 Hence, in order to correct for the difference between the calculated and experimental density, we scale the contributions to ΔIEs that are due to polarization by constant factors of 0.919 and 0.876 for CF4 and CH4, respectively.

For spherical clusters one expects the ionization energy and hence ΔIE to change with cluster size N as ΔIE ¼ b þ c 3 N
1=3

ð1Þ

where b and c are constants. In Figure 2 we show fits of such a function to our calculated values for single-component tetrafluoromethane (black squares) and methane clusters (gray circles), respectively, in both cases taking into account the effect of photoelectron attenuation and a correction factor for the density. From Figure 2 it can be seen that the mean size of the clusters ranges from a few hundreds in experiments a and d to a few thousands in experiment b. Our estimates for methane clusters produced in experiments A and B of ref 20 are about 1000 (B) and 10 000 (A) molecules. These numbers are significantly larger than originally suggested in ref 20. We believe that this discrepancy is caused by ref 20 employing a too high value for the electronic attenuation length (10 Å compared to 7 Å used here) as well as their use of an idealized cluster structures that is biased toward a too small surface-tobulk ratio. Mixed Clusters of Methane and Tetrafluoromethane. Here, we first present the results from the coexpansion experiment of methane and tetrafluoromethane, before discussing computational model structures. The theoretical calculations provide insight into factors that influence the cluster-to-monomer shift of the two components in the case of a mixed cluster. This information will be used to make conclusions about the structure of the clusters produced experimentally. The coexpansion experiments were conducted using the same experimental setup as in the single-component cluster experiments, expanding a gaseous mixture of methane and tetrafluoromethane and in addition helium for backing pressure. Carbon 1s spectra were recorded at two different stagnation conditions. The conditions and results are summarized in Table 2. 13262

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The Journal of Physical Chemistry A The C1s spectra recorded in experiments I and II are shown in Figure 3. Methane and tetrafluoromethane are easily distinguished in the spectrum with the methane signal at around 290 eV and the one corresponding to tetrafluoromethane at around 301.5 eV. The ionization energies of gaseous methane and tetrafluoromethane have been measured to be 290.686 ( 0.030 eV and 301.898 ( 0.030 eV, respectively.37 These values were used as constraints in the fitting procedure. The two main peaks can be analyzed in terms of cluster and monomer contributions. While surface and bulk features are not visible to the naked eye, we found that the cluster part of methane is considerably better fitted using two lines, corresponding to surface and bulk parts, rather than only one. Apart from monomer and cluster signals from the two compounds, the onset of a broad feature near the CF4 region was apparent in the spectrum of experiment I. By curve fitting one finds that it is centered at an ionization energy that is about 13 eV above the methane gas-phase line, and only the tail of this feature is visible in the inset of Figure 3 as a dashed curve. The feature can be attributed to shake up of methane and possibly receives contributions from inelastic scattering satellites. In C1s spectra of gaseous methane, the lowest-lying shake-up peaks have been located 15
16.6 eV above the main line,38
40 and a shift of the feature consistent with its present location is expected as it most likely stems mainly from methane molecules in clusters. A most important observation in experiment I is that the CF4 cluster-to-monomer shift is very substantial, at
0.76 eV according to Table 2, which is in fact about 0.2 eV larger in magnitude than the largest shift observed in our single-component tetrafluoromethane experiments. The observed shift is even more negative than what we predict for an infinitely large CF4 cluster, which is indicated by a vertical dotted line in Figure 2 at a ΔIE value of
0.64 eV. Even if the electronic attenuation length in tetrafluoromethane were twice as large as currently estimated, i. e., 10 rather than 5 Å, the observed cluster-to-monomer C1s shift would exceed the large
N asymptotic value for pure CF4 clusters. It therefore seems that we are observing tetrafluoromethane molecules in a more polarizable environment than the pure compound can provide. At this point it may be noted that the other component present in the gas mixture, methane, has a larger polarizability per unit volume than does tetrafluoromethane, on account of its smaller molecular size and thus higher number density more than compensating for its lower molecular polarizability. Thus, the highly negative value of ΔIE observed for CF4 constitutes clear evidence that the tetrafluoromethane molecules are in a methane-rich environment, i.e., the presence of mixed clusters. In contrast to the large shift, the width of the CF4 peak in experiment I, 0.38 eV as given in Table 2, is actually smaller than the peak width observed in any of the pure CF4 cluster experiments. This suggests that the structural diversity of CF4 sites is less in the mixed case than in the pure-cluster case. In the pure cluster, the structural diversity is probably dominated by the difference between surface and bulk sites, i.e., diversity in the coordination number. A second striking observation in the mixed experiments is the difference in intensity between the methane and tetrafluoromethane peaks as evident from Figure 3 in the case of experiment I. Even though in that experiment an equimolar mixture of the two compounds undergoes adiabatic expansion, the peak area corresponding to methane in clusters is larger by a factor of 8.6 compared to that corresponding to tetrafluoromethane in clusters. In addition to the molar ratio in the cluster, the observed

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Figure 4. Radial distribution of methane and tetrafluoromethane molecules relative to the cluster center of mass (CM). Cluster size N = 300 with a 1:1 ratio of CH4:CF4 molecules. The data shown are averaged over the last nanosecond of the MD simulation. The number of molecules are summed into shells with a thickness of 0.25 Å.

intensity ratio depends on both the electronic effective attenuation length (EAL) and the individual photoionization cross sections of the molecules. Computed cross section data41 and our own measurements42 suggest that one methane molecule gives a signal that is about 1.5 times more intense than that from one tetrafluoromethane molecule. Incorporating this factor would reduce the observed methane-to-tetrafluoromethane ratio to 5.8 for experiment I. Due to attenuation of the photoelectron signal, this ratio should be understood as the composition only in the outer layers of the clusters, and the overall compositions may well differ. We shall return to discuss the structure and size of the mixed cluster after presenting our results from a computational model of the mixed clusters. A final observation to report from the experimental part of the mixed-cluster study is the close agreement between tetrafluoromethane and methane with respect to cluster
to
monomer shift in the C1s ionization energy. These values are reported in Table 2 to be
0.76 and
0.74 eV, respectively, in experiment I and
0.57 vs
0.54 eV in experiment II. This shift is actually marginally less negative for methane than for the tetrafluoromethane, which stands in contrast to expectations formed on the basis of shift values in the pure-component clusters, cf. Figure 2. We will see below that this observation constitutes a strong criterion with respect to identifying possible structures of the mixed clusters. Computational Model Structures. Molecular dynamics (MD) simulations of mixed clusters can give valuable information toward a correct interpretation of experiments, in addition to providing independent information. In this section we will first examine the stabilities of different cluster structures by means of MD simulations. Second, we will present computed cluster-tomonomer shifts and relate them to the experimental data. One should note that the simulated structures are not believed to be at thermodynamical equilibrium but are models to understand possible driving forces that determine the cluster structures. Two clusters of sizes of 150 and 300 molecules, respectively, were propagated for 3 ns. For each size, different compositions with CF4:CH4 mixing ratios of 1:1, 1:2, and 1:5 were explored, making up a total of six cluster models. The initial cluster structures were derived from spherical cuts from the CF4 crystal structure, and the desired number of CH4 molecules were introduced by randomly replacing CF4 with CH4. In addition to these homogeneously mixed structures, we propagated two 13263

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Figure 5. ΔIEs of mixed and pure clusters assuming an effective electron attenuation length of 6 Å. Left panel: cluster-to-monomer shifts (ΔIE) for homogeneous (randomly) mixed clusters and pure single-component clusters of size N = 300. Right panel: Layered mixed cluster consisting of 49 CF4 molecules (interior) and 250 CH4 molecules (outer shell).

core
shell structures. These latter structures contained 49 molecules of one species making up the interior of the cluster, surrounded by 250 molecules of the other kind. Each of these structures were propagated for 1 ns at 50 K. In both cases molecules from the 49-molecule core started to diffuse into the surface layer suggesting that a well-defined core
shell structure is neither thermodynamically nor kinetically stable at this temperature. However, the randomly mixed clusters exhibit a tendency for surface segregation of CH4 molecules for all mixing ratios and sizes simulated. The surface segregation can be seen in Figure 4 for the radial distribution of molecules relative to the center of mass in the clusters. In the outer region from about 14 Å onward to the outer border of the cluster the ratio of methane-totetrafluoromethane rises monotonously. In order to compare our model structures to the experiment, MD trajectories of the mixed clusters were used to calculate cluster-to-monomer shifts (ΔIEs). Snapshots of the structures have been taken every picosecond, and the ΔIEs are averaged over 500 ps, i.e., 500 cluster structures. These results are summarized in Figure 5. Since the radial position of a molecule, i.e., whether it is located at the surface or in the bulk, has a strong influence on its corelevel ionization energy, we decompose the mean ΔIEs into contributions from surface and bulk molecules. Here we distinguish between surface and bulk molecules in a fashion that resembles the distinction in the experiment: the distributions of ΔIE is bimodal, and we take the minimum in between to distinguish these two types of sites. The attenuation length of the photoelectron depends on the composition of the cluster. Here, we present ΔIEs assuming an attenuation length of 6 Å which is simply the mean value of the attenuation length of the pure components. However, our conclusions in the following remain valid under any reasonably chosen value. In the left panel of Figure 5, the bulk, surface, and mean ΔIEs for both molecular species are displayed for randomly mixed clusters of different compositions. The shifts are consistently more negative for CH4 than for CF4. Since it applies to both surface and bulk regions, this finding cannot result from the evolution of asymmetric populations of surface and bulk sites in the cluster.

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Figure 6. Radial distribution function in a homogeneously mixed cluster consisting of 150 CF4 and 150 CH4 molecules as obtained by molecular dynamics. The radial distribution function is normalized by the total number of pairs per volume of the cluster, where the cluster volume is determined by the Connolly surface.

Rather, the more negative CH4 shifts can be rationalized by considering the radial pair distribution function for each of the species (see Figure 6). Methane molecules have on average shorter nearest-neighbor distances than do tetrafluoromethane molecules—a consequence of the smaller size of methane. Since the contribution of the first surrounding shell is the most important to the polarization energy, it follows that even for a homogeneously mixed cluster we should expect the shift for methane to be more negative than that for tetrafluoromethane. From the left panel of Figure 5, it is evident that decreasing the CF4 molar fraction in the cluster leads to larger magnitude of ΔIE values, consistent with the lower polarization per unit volume of CF4 compared to CH4. However, the change with composition is quite similar for the two molecular species as well as for both surface and bulk regions. The difference in ΔIEs between CF4 and CH4 is larger in the bulk than in the surface as is to be expected due to the lower coordination number in the surface. Depending on the size, the average coordination number of surface atoms in rare-gas clusters is between 6 and 9 while the coordination number of bulk atoms is ideally 12. Thus, one should expect the difference in the surface shift to be roughly between one-half and two-thirds of the bulk shift. In our model we observe somewhat less, which can be attributed to the tendency of CH4 to segregate to the outer surface in our MD simulation of the homogeneously mixed clusters. In the right panel of Figure 5, ΔIE values are compared for two structures, each corresponding to a CF4 molar fraction just below 0.2: (i) a homogeneously mixed structure and (ii) a core
shell structure with 49 CF4 molecules residing primarily in the center and 250 CH4 molecules making up the outer shell. Of the 49 CF4 molecules, only two are found at the surface during the simulation time of 1 ns. It is seen that for CF4 molecules in the bulk the magnitude of ΔIE is smaller than for CH4 molecules in the bulk. Likewise is the magnitude of the shift for CF4 molecules at the surface smaller than for CH4 molecules at the surface. Still, the magnitude of the overall mean ΔIE is slightly larger for CF4 than for CH4 as a consequence of these molecules residing nearly exclusively in the bulk. This strongly suggests that the magnitude of the mean ΔIE shift for CF4 can only be larger than that for CH4 as a result of significantly different populations of bulk and surface sites between these two species, and then only if CF4 is more abundant in the bulk. 13264

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The Journal of Physical Chemistry A Comparison of Computational and Experimental Results. From the previous section, we expect a decrease in the magnitude of the shift for methane and an increase for tetrafluoromethane upon going from pure to homogeneously mixed clusters. Noteworthy, in a homogeneously mixed cluster, the shift for methane is predicted to be quite a bit lower, i.e., more negative, than that of tetrafluoromethane molecules for all mixing ratios. Thus, our experimental observation of approximately equal shifts for tetrafluoromethane and methane suggests a structure where the tetrafluoromethane-to-methane ratio is different and then higher in the bulk than in the surface. The shift differences (ΔIE(CH4)
ΔIE(CF4)) observed are 0.02 and 0.03 eV for experiments I and II, respectively. A conservative estimate for the error in this difference is 0.04 eV. Hence, the lower bounds for the shift differences are
0.02 and
0.01 for experiments I and II, respectively. These rather pessimistic values are still slightly larger than the one for the homogeneously mixed model cluster, which are found to be between
0.03 and
0.05 eV. Thus we conclude that the nature of surface segregation found in the experiments is more pronounced than the one found in the homogeneously mixed model clusters. This finding is supported by the observed ratio of methane and tetrafluoromethane cluster signals in experiment I. Starting from a tetrafluoromethane-to-methane ratio of 1:1 at the start of the expansion, one should expect to find an even higher ratio in the cluster. The reason is that the more weakly bonded methane will evaporate at a higher rate than tetrafluoromethane. However, what is observed is the opposite: a decrease in the tetrafluoromethaneto-methane ratio. It is thus likely that the larger part of tetrafluoromethane is hidden in the interior of the cluster and that methane is enriched at the surface. In experiment II the observed ratio of methane and tetrafluoromethane cluster signals is essentially the same as the molar ratio of the two molecules in the gas mixture, again consistent with surface enrichment of methane. The difference between experiments I and II is probably caused by the different mean cluster sizes. The clusters in experiment II are considerably smaller than those in I as they show a less negative ΔIE, and hence the observed CH4/CF4 ratio in the cluster signal of experiment II can be expected to be much closer to the actual ratio in the whole cluster. Another significant difference between the two experiments is the width of the CF4 cluster signal which is 0.38 eV in experiment I and 0.51 eV in II. This is consistent with the absence of CF4 at the exposed surface of clusters produced in experiment I. The fact that the effective attenuation length (EAL) of the photoelectron varies with its kinetic energy may be used to probe the radial structure of a cluster. By increasing the photon energy in an XPS experiment, photoelectrons generated deeper inside the cluster may reach the detector, thus providing a mechanism for depth profiling. We attempted this approach at the conditions of experiment I subject to increasing the photon energy from 350 to 450 eV. This led to an increase in the ratio of the CF4 cluster signal relative to that of CH4, ACF4/ACH4, by about one-third. However, taking into account the photon-energy dependency of the molecular cross section, the increase in ACF4/ACH4 due to the longer EAL of the electron was clearly less than the uncertainty of the experiment and thus inconclusive. In order to obtain the required accuracy, one would need to use a considerably higher photon energy than 450 eV, which unfortunately was not available at a useful flux at MAX-Lab. Regarding the size of the clusters one may compare shifts for methane in the mixed expansion to those of pure methane

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clusters. As a mixed cluster of methane and tetrafluoromethane will have a smaller polarizability per unit volume than a pure methane cluster with the same number of molecules, the mixed methane
tetrafluoromethane cluster will have a less negative shift. In the mixed experiment we observe shifts for methane of
0.74 and
0.54 eV. The corresponding size estimate for these shifts for pure methane clusters are 900 and 70 molecules. Thus these numbers can be considered as lower bounds to the actual cluster sizes in the experiments I and II, respectively. As CH4 and CF4 have high symmetry and interact mainly through van-der-Waals forces, they are quite similar to rare gases. In particular, CH4 and CF4 may be compared to Ar/Kr or Kr/Xe which have similar ratios of atomic (or molecular) size (Ar/Kr = 0.94, Kr/Xe = 0.91, CH4/CF4 = 0.91).25,35,43
45 For the Ar/Kr system it is suggested that krypton dominates the bulk and argon favors the surface,5 while the radial structure of medium sized Kr/Xe clusters has—to our knowledge—so far not been studied. A possibly important difference to these binary rare-gas systems is the nonideal behavior of CH4/CF4 mixtures. CF4 and CH4 show large positive mixing enthalpies for all mixing ratios with a maximum of around 0.5 kJ/mol (at 98 K)46 occurring close to the equimolar composition. By contrast the deviation from ideal mixing behavior for argon and krypton is small with mixing enthalpies smaller than 0.05 kJ/mol (at 117 K) for any composition.47 In the analogous system of binary alloys, surface segregation is a well-known phenomenon, and a macroscopic model of phase separation for nanoparticles of alloys is described in the literature for particles with a radius R g 2 nm.48 In this thermodynamical model the driving forces for surface segregation and phase separation are the differences in surface tension between the two components and the enthalpy of mixing that depends on the composition of the inner and outer phase in the cluster. Thus, in case of CF4/CH4 the large positive enthalpy of mixing presents an additional driving force for phase separation, and one may expect to find a higher propensity for surface segregation for a mixture of CF4/CH4 than for Kr/Ar. Indeed, Kr/Ar clusters show a significant portion of krypton at the surface even at very low concentrations of Kr in the initial mixture,5 whereas in experiment I of this study the small width of the CF4 cluster peak suggests that CF4 is largely absent from the surface.

’ CONCLUSION We have studied pure clusters of tetrafluoromethane and mixed clusters of tetrafluoromethane and methane produced by adiabatic coexpansion. For pure tetrafluoromethane clusters, we find no distinct surface or bulk features and fairly broad cluster peaks. For both CF4 and CH4, a relationship between cluster size and C1s shift in ionization energy (ΔIE) is established. We produced clusters from a gaseous mixture of tetrafluoromethane and methane using two different sets of stagnation conditions. For CF4 molecules, more negative ΔIEs are observed in coexpansion with methane than in the expansion of pure CF4. This large shift is very likely a result of the presence of CH4 which has a larger polarizability per unit volume than does CF4 and thus provides strong evidence that mixed clusters are indeed produced. Furthermore, theoretical cluster models show that for a homogeneously mixed cluster, ΔIE is smaller in magnitude for CF4 than for CH4. This can be qualitatively rationalized by the fact that in such a configuration, CH4 molecules have on average shorter distances to their neighbors and more neighbors with larger molecular polarizability, which leads to a stronger stabilization of core-ionized methane due to polarization. However, 13265

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The Journal of Physical Chemistry A in our experiments we find the ΔIE for CF4 to be very similar to that of CH4. This is explained by different populations of surface and bulk sites between these two species, with CF4 being more abundant in the bulk and CH4 enriched in the surface. We attempted depth profiling to further investigate the radial structure, but the data from this experiment remained inconclusive. Such an investigation remains as an interesting task for future studies at a different facility.

’ APPENDIX: DETAILS OF THE FORCE FIELD Force-Field Parametrization. In order to obtain parameters for the electrostatic interaction, a distributed multipole analysis (DMA) of the electron densities from MP2 calculations was carried out according to Stone.49 This provides multipole moments for each atomic site of the molecule. The polarization model is parametrized in terms of atomic polarizabilities. The atomic polarizabilities of hydrogen and fluorine were adopted from Duijnen,50 with the polarizability of fluorine reduced by 1% to achieve better agreement with the experimental molecular polarizability of tetrafluoromethane. With the resulting set of parameters the experimental molecular polarizabilities of methane and tetrafluoromethane are reproduced with an error of less than 3%. The AMOEBA force field does not provide van-der-Waals (vdW) parameters for fluorine. We found that vdW parameters provided for fluorine by Halgren51 led to largely overestimated binding energies compared to ab initio calculations (see below). More satisfying results could be obtained by reducing the vdW well depth by 25% and choosing the vdW radius according to equation 27 in ref 51 by Halgren which relates the vdW radius to the atomic polarizability. The final parameters are listed in Table A.1. Quantum Mechanical Benchmark Calculations. The geometry of neutral monomers, dimers, and trimers of methane and tetrafluoromethane were optimized in the framework of the MP2 method and aug-cc-pVTZ53 basis sets. The geometries were constrained to Td symmetry for monomers, D3d symmetry for dimers, and C3v symmetry for trimers. Intramolecular bond distances optimized for the monomers were kept frozen in the optimizations of the oligomers. Despite the use of a fairly large basis, the counterpoise estimate of the basis set superposition error (BSSE) amounts to 24
44% of the uncorrected dimer binding energy and hence between 31 and 80% of the corrected energies. The corrected binding energies Eb are
0.46,
0.60, and
0.64 kcal/mol for the methane dimer, tetrafluoromethane dimer, and the mixed dimer respectively. The binding energy of the complex AB is here defined as Eb(AB) = Etot(AB)
Etot(A)
Etot(B). As calculations of higher oligomers are very time consuming with this basis set, a more compact basis set by Tsuzuki et al.54 was used. In their study54 they found this basis set to provide comparable energies and intermolecular distances for the dimers of methane and tetrafluoromethane. However, it should be noted that the counterpoise corrections for the Tsuzuki basis set are as large as 46
78% of the uncorrected Eb and 85
353% of the corrected energy. Therefore the reliability of this basis set may be in doubt. Comparing oligomer geometries computed by these two basis sets, we find in fact good agreement for the C
C distance of the various dimers with deviations less than 0.03 Å, while the deviation for the methane trimer is 0.14 Å. In Table A.2 we summarize the binding energies obtained by MP2 and FF calculations. The FF overestimates the binding energy in each case by 0.10
0.14 kcal/mol (16
23%) compared

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Table A.1. Electrostatic Moments, Atomic Polarizabilities, and vdW Parameters for Neutral and C1s-Ionized Methane and Tetrafluoromethanea CH4 parameter

CF4

C

H

C

F C

z-axis

H

C

F

x-axis

H

H

F

F

α

1.334

0.5189

1.334

0.495

R*

3.82

2.98

3.82

3.26

ε

0.106

0.024

0.106

0.060

0.6736


0.1684

Neutral Molecules q


0.0833

0.3332

μz

0.0647

0.2270

θxx


0.1435


0.3389

θyy θzz


0.1435 0.2870


0.3389 0.6778

C1s-Ionized Molecules
0.0531

q μz

0.2633
0.0008

0.7639

0.0590 0.0776

θxx


0.0853


0.3228

θyy


0.0853


0.3228

θzz

0.1706

0.6456

a

The atomic dipoles and quadrupoles are defined with respect to a local reference frame defined by neighboring atoms (z-then-x).52 Electrostatic moments are given in atomic units, polarizabilities (α) in Å3, vdW radii (R*) in Å, and well depths (ε) in units of kcal/mol. q, μ, and Θ refer to the atomic charge, dipole, and quadrupole. Additionally, for hydrogen, a reduction factor of 0.94 is used. This means that for hydrogen, the vdW site is shifted by a factor of 0.06 of the carbon
hydrogen bond length toward the carbon atom compared to the corresponding atomic sites. Only nonzero electrostatic moments are listed.

Table A.2. Binding Energies (kcal/mol) for Dimers of CH4 and CF4 As Calculated with MP2 in Conjunction with Two Different Basis Sets Compared to Binding Energies Obtained with the Force Field (FF)a system

aug-cc-pVTZ

Tsuzuki

FF
0.56

CH4 dimer


0.46


0.46

CF4 dimer


0.60


0.69


0.74

CH4
CF4


0.64


0.60


0.74

a

The aug-cc-pVTZ basis set from Dunning53 and an alternative set suggested by Tsuzuki et al. for these particular systems54 were used. The energies are corrected for the basis set superposition error.

Table A.3. Shifts in C 1s Ionization Energy (eV) Relative to the Monomer Calculated at the MP2 Level Using the aug-ccpVTZ Basis and Compared to Values Obtained with the Force Field (FF)a system

a

MP2

FF

CH4 dimer


0.09


0.09

CH4
CF4


0.05


0.05

CF4 dimer


0.05


0.04

CH4
CF4


0.09


0.08

The underlined atom is the site of ionization.

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The Journal of Physical Chemistry A to MP2 calculations using the aug-cc-pVTZ basis set. Optimized dimer C
C distances are computed for MP2 (FF) to 4.03 (3.94) Å, 3.69 (3.66) Å, and 3.79 (3.75) Å for CF4, CH4, and CF4
CH4 dimers, respectively. Shifts in carbon 1s ionization energies of pure and mixed dimers predicted at MP2 level are reproduced by the force field to the accuracy of 0.01 eV and are given in Table A.3.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We thank Henrik Bergersen and Andreas Lindblad for help during the experiments and helpful discussion of the experimental data. We thank Leif J. Sæthre for providing important resources for the project. The Norwegian Research Council is gratefully acknowledged for grants of computer time through the Norwegian High Performance Computing Consortium (NOTUR). The University of Bergen is thanked for support through the NanoUiB initiative. Support from NORDFORSK—Nordic Research Board and the European Community—Research Infrastructure Action under the FP6 “Structuring the European Research Area” Programme (through the Integrated Infrastructure Initiative “Integrating Activity on Synchrotron and Free Electron Laser Science”) is also highly appreciated. The authors acknowledge the help of MAX-lab beamline manager Maxim Tchaplyguine. ’ REFERENCES (1) Johnston, R. L. Atomic and Molecular Clusters; Master Series in Physics and Astronomy; Taylor & Francis: London, 2002; p 56. (2) Yamada, I.; Toyoda, N. Surf. Coat. Technol. 2007, 201, 8579–8587. (3) Clarke, A. S.; Kapral, A.; Patey, G. N. J. Chem. Phys. 1994, 101, 2432–2445. (4) Vach, H. J. Chem. Phys. 2000, 113, 1097–1103. € (5) Lundwall, M.; Tchaplyguine, M.; Ohrwall, G.; Feifel, R.; Lindblad, A.; Lindgren, A.; Sorensen, S.; Svensson, S.; Bj€orneholm, O. Chem. Phys. Lett. 2004, 392, 433–438. € (6) Lundwall, M.; Bergersen, H.; Lindblad, A.; Ohrwall, G.; Tchaplyguine, M.; Svensson, S.; Bj€orneholm, O. Phys. Rev. A. 2006, 74, 043206. (7) Danylchenko, O. G.; Kovalenko, S. I.; Samovarov, V. N. Low Temp. Phys. 2006, 32, 1182–1188. (8) von Pietrowski, R.; von Haeften, K.; Laarmann, T.; M€oller, T.; Museur, L.; Kanaev, A. V. Eur. Phys. J. D 2006, 38, 323–336. (9) Lundwall, M.; Pokapanich, W.; Bergersen, H.; Lindblad, A.; € Rander, T.; Ohrwall, G.; Tchaplyguine, M.; Barth, S.; Hergenhahn, U.; Svensson, S.; Bj€orneholm, O. J. Chem. Phys. 2007, 126, 214706. (10) Doronin, Y.; Samovarov, V. Opt. Spectrosc. 2007, 102, 906–909. (11) Hoener, M.; Rolles, D.; Aguilar, A.; Bilodeau, R. C.; Esteves, D.; Velasco, P. O.; Pe sic, Z. D.; Red, E.; Berrah, N. Phys. Rev. A 2010, 81, 021201. € (12) Lindblad, A.; Rander, T.; Bradeanu, I.; Ohrwall, G.; Bj€orneholm, O.; Mucke, M.; Ulrich, V.; Lischke, T.; Hergenhahn, U. Phys. Rev. B 2011, 83, 125414. (13) Arion, T.; Mucke, M.; F€orstel, M.; Bradshaw, A. M.; Hergenhahn, U. J. Chem. Phys. 2011, 134, 074306. € (14) Tchaplyguine, M.; Lundwall, M.; Gisselbrecht, M.; Ohrwall, G.;  Feifel, R.; Sorensen, S.; Svensson, S.; Martensson, N.; Bj€orneholm, O. Phys. Rev. A 2004, 69, 031201.

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