Tetrachloromethane

Article pubs.acs.org/JPCA

Structure of Self-Assembled Free Methanol/Tetrachloromethane Clusters M. Winkler, J. Harnes, and K. J. Børve* Department of Chemistry, University of Bergen, Allégaten 41, NO-5007 Bergen, Norway S Supporting Information *

ABSTRACT: The structure of molecular clusters of diameters at or below a nanometer is important both in nucleation phenomena and potentially for the preparation and application of nanoparticles. Little is known about the relationship between the structure and composition of the cluster and about the interplay between cluster composition, size, and temperature. The present project explores how the structure of mixed CH3OH/CCl4 clusters vary with composition and size; implicitly by changing the amount of noncondensing backing gas and thus the capacity to remove heat during cluster condensation, and explicitly through theoretical models. Experimentally, molecular clusters were produced by coexpansion of helium and a vapor of azeotropic methanol/ tetrachloromethane composition in a supersonic nozzle flow. The clusters were subsequently characterized by means of carbon 1s photoelectron spectroscopy. Additional information was obtained by molecular-dynamics simulations of clusters at 3 different sizes, 4 different compositions and several temperatures, and using polarizable force fields. Mixed clusters were indeed obtained in the coexpansion experiments. The clusters show an increasing degree of surface coverage by methanol as the backing pressure is lowered, and at the lowest helium pressure the cluster signal from tetrachloromethane has almost vanished. The MD simulations show a gradual change in cluster structure with increasing methanol contents, from that of isolated rings of methanol at the surface of a tetrachloromethane core, to a contiguous methanol cap covering more than half of the cluster surface, to that of subclusters of tetrachloromethane submerged in a methanol environment. Both experimental and computational results support a thermodynamical driving force for methanol to dominate the surface structure of the mixed clusters. At high helium pressure, the growing clusters may cool efficiently, possibly impeding the diffusion of methanol to the surface. At low helium pressure, methanol is completely dominating the outermost few layers of the clusters, possibly in parts caused by preferential loss of tetrachloromethane through evaporative cooling.

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INTRODUCTION Heterogeneous clusters of molecules, i.e., clusters consisting of two or more molecular species, are of interest both from an applied point of view and for their role in natural processes. To exemplify, such clusters are utilized for surface processing and film deposition in gas-cluster ion beam technology,1 and aqueous nanodroplets are known to play important roles in atmospheric chemistry.2,3 In order to predict and understand chemio-physical properties of clusters, one needs information about their structure and even better; how the structure depends on a number of factors such as the molecular composition, properties of the molecular constituents, cluster size, and temperature. Furthermore, it is important to understand how the cluster structure is influenced by the growth process, i.e., kinetic as well as thermodynamical aspects of cluster structure. Predictive models for cluster structure have been proposed both on a macroscopic and a molecular basis. An example of the former approach is provided by Kwamena et al.,4 who set out to predict the morphology of heterogeneous aerosols from macroscopic gas−liquid surface tensions for the two purecomponent phases as well as the interphase tension between these. The advantage of such an approach is that it requires © 2013 American Chemical Society

information for macroscopic systems only, which is often easily accessible. However, it may apply only to the largest particles as the physical properties of nanosized objects may be quite distinct from those of bulk systems made up from the same components. For example, the surface tension appearing as a parameter in the model of ref 4 may vary with the curvature of the particle surface.5 More to the point, it is perfectly conceivable that two components appear phase separated when in a nanosized binary cluster, while macroscopically, the compounds may be miscible. In such a case, the interphase tension is not a well-defined property. An early effort to predict the structure of heterogeneous clusters from the nature of the interaction between their constituents was made by Clarke et al.6 They constructed phase diagrams for clusters composed of van der Waals particles A and B in 1:1 ratio, differing in relative strengths of A−A, A−B, and B−B interactions as well as in size. However insightful, this scheme gives little guidance to real clusters, where by necessity the constituents differ not only in size and shape, but often also Received: September 30, 2013 Revised: November 13, 2013 Published: November 18, 2013 13127

dx.doi.org/10.1021/jp4097088 | J. Phys. Chem. A 2013, 117, 13127−13137

The Journal of Physical Chemistry A

Article

changing the helium backing pressure allows for a gradual change in the capacity to remove heat from embryonic clusters, which in turn may affect cluster size, structure, and composition. A first approach to helium backing may be sought in the gasdynamical model developed by Hagena and co-workers in the early days of cluster science,24 a simplified derivation of which is included in the Supporting Information for later reference. In general, helium backing increases the expansion rate as a result of lower mean atomic mass, giving less time for vapor−cluster collisions and hence cluster growth. In the case of molecular vapors, this effect is somewhat counteracted by the increased mean adiabatic index and thus more efficient cooling that is afforded by adding helium. The gas-dynamical model is primarily useful up to the onset of strong clustering, at which point the energy of condensation implied by the formation of clusters leads to considerable increase in temperature.25 In this phase, helium enhances cluster formation through collisional cooling of the warming-up clusters (thereby reducing evaporation) and by absorbing the heat of condensation. The importance of helium cooling may be illustrated by the observed strong increase in number and size of argon clusters with increasing helium pressure, in direct opposition to predictions from the gas-dynamical model.24,26 Once the vapor density has dropped sufficiently to halt further cluster growth by monomer addition, the helium density is also strongly reduced, and the final cluster temperature is believed to be determined by monomer evaporation rather than helium cooling.27 Our technique for probing the clusters, XPS, provides insight to the structure of molecular clusters in several ways. First, as core electrons are localized to individual atoms, core-level binding energies provide information about the local electric potential at the site of ionization, which indirectly reflects the distribution of charges and point polarizabilities near the molecule, i.e., the molecular surrounding. It is frequently found that the change in core-level ionization energy from that of the isolated molecule is dominated by polarization screening throughout the cluster, and when this is the case, the energy shift provides information about cluster size. Second, the escape depth of electrons with kinetic energy in the range used here is typically in the order of 1 nm, granting surface sensitivity to XPS. Complementing the experimental part of this study, a second approach to the structure of mixed methanol/ tetrachloromethane clusters is provided in the way of extensive and systematic use of molecular dynamics (MD) simulations. In addition to providing independent information on cluster structure, the MD models are used to prepare synthetic photoelectron spectra, assisting in the interpretation of the experimental data.

in the nature of their intermolecular interaction. Still, Clarke’s approach suggests that important insight may be gained from experiments and modeling of heterogeneous clusters constituted by simple species like rare-gas atoms and small organic molecules. With this in mind, researchers have endeavored to explore the structure of two-component model cluster systems with respect to the influence from size, shape, and the nature as well as strength of interaction between the constituents. Systems in mind include binary rare-gas clusters7−12 and molecular clusters that differ in interaction mechanisms from almost exclusively van der Waals bonding (O2/isoprene,13 CF4/CH4,14 and Ar/ N215), to SO2/CO216 and to hydrogen-bonded water−alcohol clusters.17−19 Very recently,20 we used inner-shell photoelectron spectroscopy to study the structure of binary chloroform/methanol clusters. Both molecules possess significant dipole moments (CHCl3, 1.04 D; CH3OH, 1.69 D),21,22 and in a polar environment, the dipoles are further enhanced by induction. Moreover, methanol forms strong hydrogen bonds among themselves, making the binary system rather complex in terms of interaction mechanisms. Evidence was presented20 for chloroform and methanol differing with respect to the relative population of bulk and surface sites, i.e., that the clusters display a radial concentration gradient. More specifically, methanol was shown to prefer surface sites, as can be rationalized by reference to its lower surface tension compared to chloroform. One may note that macroscopically, these compounds are miscible at all concentrations, preventing the use of the model by ref 4. In order to isolate the influence of specific bonding mechanisms in a system where the components may interact in a number of ways, it is useful to contrast similar but different cluster systems. In the present contribution, we study binary tetrachloromethane/methanol clusters, which are related to the system in ref 20 through the replacement of chloroform by tetrachloromethane. This change removes the possibility of permanent-dipole−permanent-dipole interaction between the two constituents of the cluster, leaving van der Waals interactions as the primary cohesive forces between the two cluster components. The severity of this change may be illustrated by the dimer binding energies: whereas the binding energy of the chloroform−methanol dimer is slightly higher than the mean binding energy of the corresponding homomolecular dimers, the binding energy of the CCl4− CH3OH pair is less than half of the mean pure-dimer energies. This is reflected in properties of the corresponding macroscopic systems: While both chloroform and tetrachloromethane show nonideal mixing behavior23 with methanol, the enthalpy of mixing is negative over a much wider range of mixing ratios for chloroform/methanol than for tetrachloromethane/methanol, consistent with the stronger intercompound interactions in the former system. The interesting question that arises is whether tetrachloromethane and methanol will form mixed clusters at all, and if so, how the structure compares to that of chloroform/methanol. To shed light on this, we have formed cluster beams by expanding a mixture of methanol, tetrachloromethane, and helium into vacuum under quasi-adiabatic conditions and subsequently probed the clusters by carbon 1s X-ray photoelectron spectroscopy (XPS). In these experiments, the helium (and total) pressure has been varied systematically while keeping the vapor composition or, more specifically, the partial pressures of CH3OH and CCl4 constant. To be explained next,

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EXPERIMENTAL DETAILS Clusters were produced in a supersonic beam expansion setup,28 using a conical nozzle with opening diameter of 150 μm and a half-opening angle of 10°. In this setup a reservoir of the liquid substance can be heated in an oven and the vapor above the liquid is expanded through the nozzle. 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. Carbon 1s (C1s) photoelectron spectra were recorded at the soft-X-ray undulator beamline I411 at MAXLab in Lund, Sweden, using a photon energy of 350 eV. The 13128



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Table 1. Overview over MD Simulations with Propagation Times in Nanosecond for Each Combination of Size, Composition, and Temperaturea simulation temperature [K] N

NCCl4

NCH3OH

χCCl4

100 104 103 99 212 203 201 201 346 362 350 348

16 30 53 63 33 64 98 125 50 114 172 221

84 74 50 36 179 139 103 76 296 248 178 127

0.16 0.29 0.51 0.64 0.16 0.32 0.49 0.62 0.14 0.31 0.49 0.64

120 1

130

140

150

160

170

180

190

200

2

1 2

1 2

1 2 1

1 1 1

1 1 1

1 1 1

2 2

2 2

2 2 1 1

2 2

2 2

2 2

1 1 1 1 2 2 1 1 1 1 1 1

210

220

230

1 1

1 1

1 1

2 2

2 2

2 2 1 1

a

Size and composition are given as total number of molecules (N), number of methanol molecules (NCH3OH), number of tetrachloromethane molecules (NCCl4), and mole fraction of CCl4 (χCCl4).

resolution was represented by a Gaussian distribution with a full width at half-maximum (fwhm) of Γinstr = 125 and 180 meV for experiments on pure CCl4 and the CH3OH/CCl4 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.

beamline is equipped with a modified SX-700 monochromator. For the detection of photoelectrons, a Scienta R4000 electron analyzer has been used. All spectra were recorded with an angle of 54.7° between the spectrometer axis and the horizontal polarization plane of the synchrotron light. In order to ensure constant composition of the vapor in the stagnation chamber, we used an azeotropic mixture of methanol and tetrachloromethane, maintained at a constant reservoir temperature (305 K). At this temperature the vapor pressure is 250 mbar and has the composition of the azeotrope, which is 55.5 mol % methanol and 44.5 mol % tetrachloromethane.29 Three experiments, which will be denoted II−IV, were conducted with different pressures of helium backing and hence total gas pressures: II 850 mbar He (1100 mbar total), III 550 (800) mbar, and IV 250 (500) mbar. The temperature of the nozzle was kept at room temperature in all experiments. In addition to this series, another spectrum, I, was recorded at somewhat higher temperature of the liquid reservoir (310 K) but with quite similar nozzle temperature (300 K). This higher oven temperature leads to higher vapor pressure of the CCl4/ CH3OH mixture. Consequently, the count rate is increased, which permits better statistics. The total pressure in this experiment was 1200 mbar. Using the same setup, single-component CCl4 clusters were produced from the pure vapor mixed with helium for backing. Two different expansion conditions were used, denoted A and B. In A, the nozzle temperature was 323 K and the reservoir of liquid CCl4 was heated to 313−314 K. At this temperature, adding the vapor pressure of 0.29 bar and a helium pressure of 1.11 bar gives a total pressure of 1.40 bar. In experiment B, the nozzle and reservoir temperatures were 341−342 and 351−353 K, respectively, while the backing gas pressure was 0.32 bar and the vapor pressure of CCl4 was 1.08 bar. Theoretical line shape models were fitted by least-squares techniques to the experimental C1s spectra as detailed in the following. The vibrational Franck−Condon envelope for gasphase methanol was adopted from ref 30, and for gas-phase tetrachloromethane from Sundin et al.31 These were subsequently convoluted by the line shape functions given by eq 12 in ref 32 to account for the natural line widths (CH3OH, 100 meV; CCl4, 62.5 meV33) and postcollision interaction during Auger decay of the core hole.32 Finally, the finite experimental

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COMPUTATIONAL DETAILS Our group has developed and validated an approach to the modeling of core-level photoelectron spectra of molecular clusters based on classical molecular dynamics (MD), details of which are published elsewhere.30,34 Briefly, the computational approach exploits the fact that in photoelectron spectra of clusters produced by adiabatic expansion, free (uncondensed) molecules are always present beside the clusters in the supersonic beam. Thus, rather than calculating absolute coreionization energies, it is sufficient to obtain ionization energies relative to those of a free molecules, i.e., shifts in ionization energies (ΔIEs). This ΔIE can be rephrased as the difference between the neutral molecule and the corresponding coreionized molecule with respect to interaction energy with the remaining part of the cluster. For most molecules, this interaction energy is dominated by contributions from electrostatics and polarization and can be reproduced by polarizible forcefields with good accuracy. Distribution of ionization energies can be obtained from MD simulations of a cluster at a finite temperature and calculating the ΔIE for each molecule in the cluster at different snaphots of the MD trajectory. Molecular dynamics simulations have been carried out with the TINKER suite of programs (version 5.1) using the framework of the AMOEBA force field.35,36 Force-field parameters for methanol were adopted from ref 30, whereas for tetrachloromethane, the force-field parameters were obtained in the course of this work as detailed in the Supporting Information. Molecular dynamics simulations were carried out for pure CCl4 clusters with N = 50, 100, 200, and 400 molecules, 13129



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Figure 1. Carbon 1s X-ray photoelectron spectra of beams formed by either expansion of pure CCl4 sample (A (top) and B (middle)) or by expansion of a CCl4/CH3OH mixture (I (bottom)). The experimental settings are given in Table 2. The spectra are aligned on the peak position corresponding to uncondensed CCl4.

we first present evidence on the nature of the produced clusters: Are they indeed mixed, or do we in addition, or exclusively, form single-component clusters? With this issue settled, we go on to extract experimental evidence for the composition and structure of the clusters and how they are influenced by the expansion conditions. From the experimental data it will soon become clear that the clusters that we produce in the laboratory are much larger than what is feasible to include in molecular dynamics simulations using accurate force fields. Nonetheless, an extensive series of MD simulations were carried out for binary clusters consisting of up to 400 molecules, providing structural information, which, with some caution, may be held against conclusions for the much larger clusters investigated experimentally. Moreover, these simulations establish how size, composition, and cluster temperature influence core photoelectron spectra for the present mixed clusters, which is helpful in the analysis of the experimental spectra. Mixed vs Pure Clusters. While it is reasonable to expect mixed clusters to form from adiabatic expansion of a mixture, it was argued in the Introduction that for the present system this is not self-evident. Hence, to explore whether binary clusters have indeed been formed, it is useful to turn first to X-ray photoelectron spectra of clusters formed from the pure components and then to compare these to spectra recorded for the mixed expansion. In this respect, the carbon 1s signal of CCl4 is a promising source of information as the molecular line is narrow and, more importantly, so is the cluster peak for a pure tetrachloromethane cluster, consistent with weak electrostatic interactions between CCl4 molecules. In Figure 1, C1s spectra from two expansion experiments A (top) and B (middle) for pure CCl4 are shown, corresponding to different stagnation conditions and different mean cluster sizes in the two cases. As both CCl4 clusters and uncondensed CCl4 molecules are present in the beam, spectra from adiabatic expansion of pure CCl4 have two easily distinguishable peaks, corresponding to CCl4 (uncondensed) monomers at an ionization energy of 296.32 eV and CCl4 molecules in clusters,

respectively. Initial structures were constructed from spherical cuts from an fcc crystal structure. During the simulations, the molecules were treated as rigid bodies and the time step was 5 fs. Pure CH3OH clusters were simulated with N = 6, 20, 55, 100, 147, and 200 fully flexible molecules and a time step of 1 fs. MD simulations were conducted for binary CH3OH/CCl4 clusters with approximately 100, 200, and 350 molecules, and for each size, CCl4 mole fractions of about χCCl4 ≈ 0.15, 0.31, 0.50, and 0.63. For each combination of size and composition, the clusters were propagated using the canonical (NVT) ensemble and a temperature of 200 K. In addition, for the two compositions χCCl4 ≈ 0.15 and 0.31, clusters with around 100 and 200 molecules were simulated at temperatures of T = 160, 180, 190, 210, 220, and 230 K. An overview over the simulations is given in Table 1. All molecules retained full flexibility, and the time step was therefore reduced to 1 fs. Initial structures were cut from short (10 ps) periodic simulations of liquid CH3OH/CCl4 mixtures with similar composition as the cluster in question, using a repeating unit of 600 molecules. For each system, the equilibration and production phases of the simulation lasted at least 0.5 ns each. The cluster-monomer shift in C1s ionization energy depends on the density of the material through the polarizability per unit volume, and to leading order, the polarization contribution to the shift scales with the density to the power of four-third.37 While the molecular polarizability in our forcefield deviates from the experiment by less than 2%, simulations of lowtemperature crystal structures give densities that are too low, translating into polarization contributions to the cluster− monomer shifts that are underestimated by 10% and 6% for CCl 4 (s) and CH 3 OH(s), respectively. See Supporting Information for details.

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RESULTS AND DISCUSSION On the basis of a detailed analysis of carbon 1s photoelectron spectra of clusters produced by coexpanding CCl4 and CH3OH, 13130



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altogether dominating part of the spectrum receives contributions from both noninterfacial and interfacial CCl4 molecules. Having established that binary cluster are present in the cluster beam, it is useful to investigate whether they are accompanied by pure clusters or are formed exclusively. From a statistical point of view, the direct formation of pure clusters of either methanol or tetrachloromethane may be thought unlikely as both components exist in roughly equal number in the azeotropic mixture (CH3OH/CCl4 = 55:45). However, methanol reaches supersaturation earlier in the expansion than does CCl4, cf., Figure 3, and only well below the solid−

shifted toward lower ionization energy, respectively. Experiment A produces smaller clusters than does B, as is demonstrated by the lesser magnitude of the cluster-tomonomer C1s shift, cf., −0.50 vs −0.75 eV. The shift toward lower energy is essentially a result of screening of the core hole by the polarizable surrounding and becomes larger in magnitude with increasing cluster size.38 The cluster signal in experiment A is well represented by a single Gaussian peak convoluted with the monomer CCl4 spectrum, only shifted down in energy by about 0.50 eV. In spectrum B, one observes a shoulder on the low-energy side of the cluster part, necessitating a second Gaussian component for an appropriate fit. The reason for this bimodal distribution is well-known and signifies the observable populations of molecules at the surface and in the bulk, respectively, which differ in their number of nearest neighbors.37,39,40 As the first coordination sphere of the ionized molecule contributes the major part of the core-hole screening, molecules in the bulk are shifted toward lower C1s binding energy compared to those at the surface. At this point it is instructive to comparing the spectral features of pure CCl4 clusters to the signal from CCl4 in mixedexpansion experiment I, which is included at the bottom of Figure 1. Evidently, the latter exhibits yet an additional feature compared to spectrum B, shifted to even lower binding energy than the bulk feature already described. Since this third structural imprint is native to clusters formed in the mixed expansion only, it is attributed to tetrachloromethane molecules in contact with methanol molecules. This assignment was further tested in molecular dynamics simulations of mixed clusters, to be detailed in a later section. Here, it suffices to consider Figure 2, where the computed C1s cluster-to-

Figure 3. Supersaturation (S) of CCl4 and CH3OH as a function of distance from the nozzle opening (in units of nozzle diameter). The arrows indicate conditions that would allow onset of homogeneous nucleation of each component, cf., Supporting Information for details. The kink in the CCl4 curve is associated with a solid−solid phase transition, see the text.

solid phase transition temperature of tetrachloromethane (near 225 K,41 after which point the equilibrium vapor pressure p0,CCl4 drops exponentially with the inverse temperature) does the supersaturation of tetrachloromethane equalize that of methanol. Although the onset of homogeneous nucleation depends on both supersaturation and temperature, methanol probably nucleates homogeneously just outside the nozzle throat. Homogeneous nucleation of tetrachloromethane is not feasible until almost a nozzle diameter downstream, but it seems probable that monomolecular nucleation of tetrachloromethane may take place much earlier on methanol clusters. After that point, cluster compositions may change by monomer addition of either kind, subject to their respective sticking coefficients, as well as by preferential evaporation of one of the species from the early, hot clusters. The observed cluster-to-monomer shifts in ionization energy contain information about the possible contribution from single-component clusters to the beam. To facilitate a discussion of the shift data for clusters, an estimate of the effective attenuation length (EAL) of the escaping photoelectron is mandatory. At around 50 eV kinetic energy of the electron, the EAL is estimated to be 4−5 Å for CCl4.42 For a kinetic energy of 60 eV, we estimate the EAL in CH3OH to be 7 ± 2 Å based on Monte Carlo simulations of the electron scattering process using cross-section data for the free molecule, cf., ref 20. The EAL values may be used in combination with MD simulations of pure clusters to prepare size-vs-shift relationships for pure CCl4 and pure CH3OH clusters as shown in Figure 4. The size-vs-shift relationships are also computed using EAL values that span the uncertainty interval

Figure 2. Distribution of shifts in ionization energies (ΔIE) of CCl4 molecules in a binary CCl4/CH3OH cluster relative to CCl4 monomer. The cluster consists of 70 methanol and 34 tetrachloromethane molecules. The ΔIE distributions stemming from CCl4 molecules that have CH3OH neighbors (interface) and those having no neighboring CH3OH (noninterface) are shown as dotted line and solid line, respectively.

monomer shifts for CCl4 are shown separately for those molecules that have only tetrachloromethane nearest neighbors and those that have at least one neighboring methanol molecule (dubbed “interfacial CCl4”). Clearly, a fraction of the interfacial CCl4 molecules give rise to lower C1s energies than what is attainable by their noninterfacial counterparts. Thus, we can be quite confident about the previous assignment. For completeness, the calculations also show that the higher-energy and 13131



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presence of mixed clusters. It is worth pointing out that in the subsequent mixed experiments, II−IV, the cluster−monomer shift for CCl4 is significantly more negative than in I, making it clear that tetrachloromethane appears exclusively in mixed clusters. In turn, this implies that a large portion of the clustered methanol molecules must appear in mixed clusters with tetrachloromethane. For methanol, however, the observed shift in experiment I is consistent with pure CH3OH clusters consisting only of a few hundred to one thousand molecules. Hence, on the basis of the shift data alone, we can not exclude the possibility of pure methanol clusters coexisting with the mixed clusters. Impact of Stagnation Conditions on Cluster Structure and Size. More than forty years ago, Hagena and Obert formulated scaling laws that relate stagnation conditions to the mean cluster size in beams produced by adiabatic expansions.43,44 While these have mainly been tested for onecomponent systems,24,38,45 the theoretical framework is applicable also to mixtures of constant composition.24 According to these laws one would expect larger mean cluster size with decreasing backing gas pressure, leaving all other parameters unchanged. However, this requires that there is an excess of backing gas that can provide sufficient cooling capacity. This assumption may become invalid as the helium pressure is sufficiently lowered. In order to analyze the impact of helium backing on the cluster formation process, it is useful to start out from a gasdynamical model. A simplified and concise presentation of the state of a vapor−helium mixture undergoing adiabatic expansion through a converging−diverging nozzle into near vacuum is provided as Supporting Information. Both the expansion rate and temperature drop are governed by mean parameters for the gas + vapor mixture. Increasing the amount of helium speeds up the flow (through the reduced mean mass) and leads to faster and stronger temperature drop (through a larger value for γ; the mean ratio of heat capacities at constant pressure and volume). These two contributions work in opposite directions with respect to cluster formation, such that a faster expansion leaves less time for collisions while a lower temperature promotes higher supersaturation and earlier nucleation. However, the number of collisions within a temperature interval (T + dT,T) is also influenced by the spread in velocity around the common, unidirectional flow velocity. Within the simple gas-dynamical model, the number of collisions taking place between a forming cluster of collisional cross-section ON and molecules of vapor component i

Figure 4. Calculated mean cluster-to-monomer shift vs cluster size for pure CCl4 (green) and pure CH 3OH (red) using different assumptions for the effective attenuation length (EAL) and T = 200 K. In each case, four data points are used to fix the free parameters in the expression ΔIE = b + cN−1/3 by a least-squares approach. For CCl4, EAL values of 5 Å (solid line, circles), 4 Å (dotted), and 7 Å (dashed) were used, and for CH3OH, EAL is 7 Å (solid line, triangle), 5 Å (dotted), and 10 Å (dashed). In each case, the intermediate EAL is considered the best estimate, with the other values providing an interval of uncertainty. The vertical black line denotes the cluster-tomonomer shift as observed for CCl4 in experiment I.

for this quantity. The figure clearly shows that for 1-component clusters consisting of the same number of molecules, the cluster-to-monomer shift is considerably larger in magnitude for pure methanol clusters than for pure tetrachloromethane clusters. More to the point, in experiment I we observe mean clusterto-monomer shifts of −0.91 eV for methanol and −0.82 eV for tetrachloromethane, cf., Table 2. In Figure 4, the latter value is compared to and found to be more negative than theoretical estimates even for the largest pure clusters of CCl4. Allowing for extra uncertainty associated with extrapolation of computed shifts from medium to larger cluster sizes as well as taking into account a tendency to underestimate the cluster density (cf., the Computational Details section), one may still conclude that for experiment I to show pure CCl4 clusters, these would have to be very large, on the order of tens of thousands of molecules. For a low number of large clusters, the cluster signal is expected to be weak, on account of most of the molecules being hidden in the interior of the cluster. Contrary to this assertion, the cluster signal from tetrachloromethane is strong and taken together with the large negative shift value; this implies a strong

Table 2. Experimental Settings (Nozzle and Oven Temperatures, Tn and To, Total Stagnation Pressure p0) and Observed C1s XPS Parameters (Cluster-to-Monomer Energy Shift ΔIE, and Gaussian Full Width at Half-Maximum of the Cluster Signal, ΓG, and the Cluster Intensity Ratioa of CH3OH/CCl4) ΔIE (eV) exptl

vapor + He

Tn (K)

To (K)

p0 (bar)

A B I II III IV

CCl4 CCl4 CH3OH/CCl4 CH3OH/CCl4 CH3OH/CCl4 CH3OH/CCl4

323 341−342 300 298 298 298

313−314 351−353 310 305 305 305

1.40 1.40 1.20 1.10 0.80 0.50

ΓG (eV)

CH3OH

CCl4

−0.91(1) −1.03(1) −1.08(1) −1.07(1)

−0.50(1) −0.75(1) −0.82(1) −0.93(1) −0.97(2) −1.07(3)

CH3OH

CCl4

ICH3OH/ICCl4

0.86(2) 0.87(2) 0.88(2) 0.97(2)

0.36(1) 0.42(2) 0.67(2) 0.62(3) 0.77(3) 0.7(1)

2.07(6) 2.6 (1) 4.8 (2) 20 (2)

a

The intensity ratio is corrected for differences in the molecular C1s photoionization cross-sections. Separate measurements were conducted that demonstrated the cross-section of methanol to be 15 ± 2% larger than that of tetrachloromethane at the present photon energy of 350 eV. 13132



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Figure 5. Carbon 1s X-ray photoelectron spectra of expansions of CCl4/CH3OH. The top panel shows the spectra for experiments IV (triangles), III (squares), and II (circles). In the lower panel, each cluster peak is represented by a single normalized Gaussian distribution (convoluted with the monomer line shape) with parameters determined in a fit to the experimental spectra, to simplify the comparison of cluster-to-monomer shifts and peak widths. The fitting lines are represented by solid (IV), dashed (III), or dotted lines (II).

characterized by molecular mass mi and density ρi,0 at the reservoir, is given by ⎛ m ⎞1/2 −dT γ /2γ − 2 τ dZi − N = Cγ(τ )ONρi ,0 ⎜ ̅ ⎟ T ⎝ mi ⎠

with cold helium atoms and by evaporation of vapor molecules. One may expect efficient cooling to favor a kinetically determined cluster structure, as opposed to an equilibrium structure that presumably would be favored by high initial temperature and correspondingly high diffusion rates within the cluster, followed by a slow approach to the terminal cluster temperature. From this perspective, it is likely that insight into cluster structure can be gained by influencing the cooling capacity during cluster nucleation and cluster growth. A practical approach to this end is to vary the pressure of helium gas in the stagnation mixture, keeping sample pressure and temperature constant. Such a series is described as experiments II−IV in Table 2, arranged in order of decreasing helium pressure, corresponding to reduced collisional cooling. We will now discuss how the stagnation conditions in experiments II−IV affect the size and structure of the produced clusters. Such an analysis is by no means trivial as several factors may compete in the observed spectra. In all three experiments, the same nozzle and oven temperatures and hence vapor pressure of the CCl4/CH3OH mixture is used, but the backing pressure of helium is varied. In the top panel of Figure 5, we present the C1s spectra obtained in experiments II−IV. Through this sequence, the total pressure is reduced, first from 1.1 to 0.8 bar and then down to 0.5 bar, by reducing the helium backing pressure. Comparing spectrum II to III, several important changes are observed. First, the cluster-to-monomer shifts increase in magnitude and go from −1.03 to −1.08 eV for methanol and from −0.93 to −0.97 eV for tetrachloromethane, i.e., quite similar changes for the two species. This clearly suggests that the mean cluster size is larger in experiment III than in II, despite the lower helium pressure. This is consistent with the

(1)

where τ = T/T0 is the temperature relative to that of the reservoir and Cγ is a slowly varying function of the temperature, cf., Supporting Information for further details. Equation 1 may be used to compare the collision frequency of the two vapor components in the same expansion. On the basis of the mass and number ratios, one would expect methanol to collide almost thrice as often with a forming cluster compared to tetrachloromethane. Moreover, methanol rapidly becomes more supersaturated than does tetrachloromethane, cf., Figure 3, and only beyond the solid−solid transition temperature does tetrachloromethane overtake methanol, at supersaturations as high as 100 or more. It is likely that nucleation takes place at lower supersaturation than that and hence that the transition point for tetrachloromethane is not of importance in the present context. In the regime in which clusters grow by the addition of cold vapor molecules, which should apply to the present study, the energy released in collisions will warm up the cluster. However, for a small molecule, tetrachloromethane has an unusually high number of low-frequency modes, which implies a large capacity to convert to internal energy the energy released in the collision. This may reduce the expected heating of and thus evaporation from the cluster, with no discrimination between components. For comparison, at 200 K, the heat capacity of methanol is about half of that of tetrachloromethane. As mentioned in the Introduction, during the growth phase, cooling of the clusters is expected to take place by collisions 13133



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Figure 6. Snapshots from MD simulations at 200 K of mixed methanol/tetracloromethane clusters with a total of approximately 350 molecules, with the CCl4 mole fraction χCCl4 changing from ∼0.63 (left) via 0.50 and 0.31, to 0.15 (right). CCl4 and CH3OH molecules are represented by spacefilling and tube models, respectively.

Table 3. Number of Evaporated Molecule (NCCl4, NCH3OH) at the End of the Simulation for the Different Combinations of Size, Composition, and Temperature simulation temperature (K) N

χCCl4

100 104 103 99 212 203 201 201 346 362 350 348

0.16 0.29 0.51 0.64 0.16 0.32 0.49 0.62 0.14 0.31 0.49 0.64

120 (0,0)

130

140

150

160

170

180

190

200

210

220

230

(0,0)

(0,0) (0,0)

(0,0) (0,0)

(0,0) (0,0) (0,0)

(0,0) (1,0) (0,0)

(1,0) (0,0) (0,0)

(1,0) (1,0) (0,0)

(5,0) (1,1)

(6,0) (0,0)

(7,0) (6,0)

(0,0) (0,0)

(0,0) (0,0)

(1,0) (0,0) (0,0) (0,0)

(0,0) (0,0)

(2,0) (0,0)

(0,0) (1,0) (0,0) (0,0) (5,0) (1,0)

(5,0) (4,0)

(11,0) (4,1)

(16,1) (9,7) (6,1) (3,1)

(3,0) (2,0) (1,0) (1,0) (2,0) (1,0) (0,0) (0,0)

picture of stronger surface presence of methanol with less helium backing, while keeping a significant component of tetrachloromethane in the clusters. Cutting the helium flow even further leads to rather dramatic changes as seen in the C1s photoelectron spectrum from experiment IV. Most notably, the CCl4 cluster signal almost vanishes and becomes about only 5% of that of the CH3OH cluster signal, which in turn is comparable to that observed in experiment III. Overall this suggests that a significant amount of cooling is provided by evaporating CCl4 from the cluster, and at these conditions one can not exclude the possibility of a fair contribution from pure methanol clusters. Quite remarkably, the same value of −1.07 eV is obtained for the cluster-tomonomer shift for both methanol and tetrachloromethane. While this value is virtually unchanged from experiment III for methanol, it represents a large change from −0.97 to −1.07 eV for CCl4. We can reconcile these observations by a combination of close-to-full surface coverage by methanol, close contact between tetrachloromethane and methanol, and still rather large clusters. This picture is corroborated by the width (ΓG) of the methanol cluster peak, which increases from 0.88 eV in experiment III to 0.97 eV in IV, indicating several layers of methanol at the surface.46 Compared to the II−IV series, experiment I is carried out at higher sample pressure (higher oven temperature) and higher nozzle temperature. The cluster-to-monomer shifts are −0.91 and −0.82 eV for CH3OH and CCl4, respectively, showing that the smallest clusters are produced in experiment I. Molecular Dynamics Simulations. MD simulations have been carried out for 12 clusters differing in size (N ≈ 100, 200,

gas dynamics as laid out above, combined with a helium pressure that is still sufficiently high to provide adequate collisional cooling of clusters. Second, the difference in cluster-to-monomer shift between the two molecules, ΔIECCl4 − ΔIECH3OH, is only about 0.10 eV in experiments II and III. From Figure 4, this is much less than the difference between pure clusters with comparable numbers of CH3OH and CCl4 and excludes the possibility of phaseseparated mixed clusters with only a very small interface. Moreover, keeping in mind that the effective attenuation length is in the order of 5−7 Å and we thus observe only a few molecular layers of the cluster, the small shift difference of 0.10 eV probably requires that the tetrachloromethane shift is boosted by a strong presence below the outer surface of the clusters and/or in contact with methanol, while the methanol shift is probably reduced by a high surface fraction. It is informative to hold these preliminary conclusions against observation for the relative intensity of the two cluster peaks and also the widths of these peaks. First, the observed methanol-to-tetrachloromethane intensity ratio between the two cluster peaks almost doubles from II to III, which is consistent with less CCl4 in the cluster but also with a higher surface coverage for methanol. Second, the full width at half-maximum (fwhm, ΓG) does not change noticeably for the cluster peak of methanol (0.87−0.88 eV), while for CCl4, a significant increase from 0.62 to 0.77 eV is observed from II to III, suggesting that the main change from II to III is an extension of a partial outer-surface coverage of methanol. We note that all observables provide a consistent 13134



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350) and composition (CCl4 mole fraction χCCl4 ≈ 0.15, 0.31, 0.50, and 0.63), at a constant temperature of 200 K. Representative structures obtained for the largest clusters (N ≈ 350) are presented in Figure 6. The structural pattern that appears is one of hydrogen-bonded cycles of methanol, most of which are found in a single domain that spreads over the surface of a rather compact CCl4 domain. Ring-opening is not observed at this low temperature, consistent with the high energy cost of breaking a hydrogen bond, but larger rings occasionally break up into two smaller ones as this does not lead to loss of hydrogen bonds. For the two clusters with the highest CCl4 contents (χCCl4 ≈ 0.50 and 0.63), a part of methanol is found as smaller rings diffusing over the surface of a tetrachloromethane core. At low mole fractions of CCl4 (χCCl4 ≈ 0.15 and 0.31), a single 3-dimensional CH3OH domain forms, and the average size of the methanol rings grows with methanol concentration. Upon lowering the temperature to 160 K, the methanol domain flattens out also at these compositions, a few smaller rings diffuse over the surface of the tetrachloromethane domain, and the number of CCl4− CH3OH contacts increases. During the simulations, individual molecules evaporate from the clusters. For CCl4, this takes place even at temperatures as low as 160 K, while no methanol molecules are lost below 210 K; see Table 3 for a detailed account. Surprisingly, the largest number of evaporated tetrachloromethane molecules is found for the clusters with the smallest mole fraction of CCl4. While the implied positive feedback would accelerate evaporation of CCl4, one needs to take into account also the drop in temperature accompanying evaporation, which is believed to determine the terminal temperature of the clusters. From this perspective, evaporation of methanol is only able to cool the cluster to 210 K, while continued loss of tetrachloromethane from clusters with 100−200 molecules reduces the temperature by another 50 K. For clusters with around 350 molecules, evaporation does not take place below 200 K. Irrespective of composition, the rate of evaporation is always higher for CCl4 than for CH3OH. However, the cooling that is accompanying evaporation may in fact make pure methanol clusters rare except for at expansion conditions that are very dilute in tetrachloromethane. To prepare a basis for reassessing the experimental carbon 1s ionization energies for clusters, theoretical model spectra were prepared from the MD trajectories for each cluster model as laid out in the Computational Details section. The theoretical spectra were subsequently analyzed by the same procedure as used for the experimental photoelectron spectra, to ensure that the resulting mean energies and peak widths may be compared between theory and experiment. The computational cluster-tomonomer shifts in C1s energy are listed in Table 4. For methanol, this shift increases almost monotonously in magnitude with increasing mole fraction of CH3OH as well as with increasing cluster size. The differences in shift from the clusters poorest in CH3OH (χCH3OH ≈ 0.37) to those richest (χCH3OH ≈ 0.84) are −0.05, −0.12, and −0.07 eV for N ≈ 100, 200, and 350 molecules, respectively. The magnitude of the CCl4 shift increases more rapidly with size than for methanol, and it is less influenced by and actually decreases slightly with increasing methanol contents. Irrespective of size and composition, the cluster-to-monomer shift of CH3OH is always larger in magnitude than that of CCl4,

Table 4. Calculated Cluster-to-Monomer Shifts (in eV) of Mixed CCl4/CH3OH Clusters of Different Compositions and Sizes at T = 200 K and Using EAL = 5 Å ∼N

χCCl4

ΔIE(CCl4)

ΔIE(CH3OH)

ΔIE(CCl4) − ΔIE(CH3OH)

100 200 350 100 200 350 100 200 350 100 200 350

0.64 0.64 0.64 0.51 0.51 0.51 0.29 0.29 0.29 0.15 0.15 0.15

−0.53 −0.61 −0.64 −0.54 −0.62 −0.64 −0.50 −0.63 −0.65 −0.48 −0.61 −0.57

−0.72 −0.69 −0.77 −0.72 −0.76 −0.79 −0.75 −0.77 −0.77 −0.77 −0.81 −0.84

0.19 0.08 0.13 0.18 0.14 0.15 0.25 0.14 0.12 0.29 0.20 0.27

with differences ΔIE(CCl4) − ΔIE(CH3OH) varying from 0.08 to 0.29 eV. For a given cluster size, the shift difference is larger for the smallest CCl4 mole fraction and leveling off with increasing CCl4 contents. The dependency on size is more complicated but in most cases the shift difference is larger at N ≈ 100 and 350 than for the intermediate size (200). A wider temperature range has been explored for the clusters with around 100 and 200 molecules and mole fractions χCCl4 ≈ 0.15 and 0.31. The magnitude of the cluster-to-monomer shifts of both CCl4 and CH3OH increases with decreasing temperature, yet in such a way that the shift difference, ΔIE(CCl4) − ΔIE(CH3OH), decreases. This temperature dependence is explored further in the Supporting Information. Finally, we shall comment briefly on the widths of the theoretical cluster spectra, summarizing a more detailed account to be found in the Supporting Information. For all mixed CCl4/CH3OH clusters, the calculated width of the CCl4 signal is larger than that of pure CCl4 clusters, in agreement with the observations reported in Table 2. For methanol, the widths are in most cases very similar between pure and mixed clusters containing the same number of methanol molecules.

■

CONCLUDING DISCUSSION At this point we will compare and contrast information obtained from molecular modeling and experiment, respectively. First, C1s spectra of tetrachloromethane show that expansion of an azeotropic mixture of methanol and tetrachloromethane does lead to mixed clusters. In the MD simulations, the mixed cluster structures appear rather stable even at elevated temperatures, although constant-T trajectories of 1 ns duration show evaporation of monomers at temperatures down to 210 K for methanol and 160 K for tetrachloromethane. Clearly, cooling by evaporation is rather efficient, allowing the observation of mixed clusters on a time horizon of milliseconds. Next, on the important issue of the qualitative structure of mixed clusters, both core photoelectron spectra and MD simulations show that methanol resides preferentially on the surface of the clusters. However, starting with the computational results, in no instance of the different temperatures, composition, or sizes does one observe complete surface coverage by CH3OH molecules around a CCl4 core, although in some cases (low temperature and high CH3OH mole fraction) CH3OH occupied the overwhelming part of the 13135



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helium. Moreover, gradually reducing the partial pressure and thus the cooling capacity from helium, at some point evaporation of tetrachloromethane may become the dominant cooling mechanism through the whole cluster formation process. Observations suggest that this happens when the helium mole fraction is down to 50%, as this is consistent with a very weak cluster signal from tetrachloromethane while maintaining a strong methanol cluster signal.

surface. In the experiments, absence of CCl4 from the surface is only evident in experiment IV and likely facilitated by evaporation of CCl4 from the surface. Complementing this observation, the simulations provide evidence for preferential evaporation of CCl4. The difference in cluster-to-monomer shift between the two components, ΔIE(CCl4) − ΔIE(CH3OH), is in general larger in the theoretical models than experiment. However, the trend from the modeling shows that this difference becomes smaller with increasing cluster size. From the observed cluster-tomonomer shift in the experiments, it is clear that the mean sizes in all the experiments are larger than those used in the simulations, by a substantial amount. Unfortunately, the rapidly increasing cost with cluster size prevents us from simulating clusters of significantly larger size than presented here. As in the experiment, the simulated cluster spectra of CCl4 show significantly larger widths in the case of mixed CCl4/ CH3OH clusters than those of pure CCl4 clusters. For CH3OH, the diversity in widths among the simulated spectra is much smaller than one would expect comparing the widths in experiments III and IV. As the exact size and composition in the experiment remain unknown, it is difficult to draw firm conclusions from this fact, but it may indicate that our cluster models underestimate the extent of surface preference of CH3OH. Using the cluster-to-monomer shift of CH3OH in the mixed expansion and comparing it to the shifts that have been calculated for pure clusters (cf., Figure 4), one can prepare a lower bound not only for the cluster size but likely also the number of methanol molecules in the cluster. The smallest shift, magnitude-wise, is observed in experiment I, at −0.91 eV, which for a pure CH3OH cluster would correspond to about 200 molecules. The actual number of molecules in the mixed cluster is in all likelihood substantially larger. In experiments II and III, we estimate lower bounds for the number of methanol molecules in the mixed cluster to 500 and 1000 molecules, respectively. In our previous study20 of mixed clusters from chloroform and methanol, we found evidence for a radial concentration gradient and with CH3OH residing preferably at the surface. In that study, we speculated that the surface preference may be rationalized by differences in surface tension between the pure components as caused by their different intermolecular binding mechanisms. Tetrachloromethane and chloroform have rather similar values for the surface tension, both being significantly larger than that of methanol, which leads one to expect rather similar mixed cluster structures. The molecular interaction between CHCl3 and CH3OH is stronger than that between CCl4 and CH3OH. In terms of cluster structure, the two mixed systems appear qualitatively similar; both being consistent with a concentration gradient and methanol enriched at the surface rather than full segregation. While our experimental technique does not allow for a quantitative comparison between the two systems, surface accumulation of methanol seems to be more complete in the CCl4/CH3OH system and certainly at the lowest helium pressure. The present study shows increasing surface preference of CH3OH with lower partial pressure of the nonclustering backing gas (helium), while keeping a strong cluster signal from tetrachloromethane. Gas-dynamical considerations suggest that methanol nucleates first, making it likely that the early forming clusters have a methanol-rich core. One may speculate that outward diffusion of methanol is enhanced by less cooling from

■

ASSOCIATED CONTENT

S Supporting Information *

Details about the AMOEBA polarizable force field for neutral and C1s-ionized tetrachloromethane are provided along with results from test calculations. Extended results are provided from the MD simulations, exploring how the C1s levels and line widths in methanol and tetrachloromethane change with temperature. A simple derivation of a one-dimensional gasdynamical model of adiabatic expansion of a helium-diluted binary vapor of fixed composition is given. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*(K.J.B.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We are pleased to thank Maxim Tchaplyguine at Beamline I411 and the MAX-lab staff for their assistance during beamtime and the Nordic Research Board (NORDFORSK), the Norwegian High Performance Computing Consortium NOTUR, and the EC Transnational Access to Research Infrastructure Program (TARI) for support.

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REFERENCES

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