Toluene Cluster Formation in Laval Expansions - ACS Publications

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Toluene Cluster Formation in Laval Expansions: Nucleation and Growth Published as part of The Journal of Physical Chemistry virtual special issue “Veronica Vaida Festschrift”. Satrajit Chakrabarty, Jorge J. Ferreiro, Martina Lippe, and Ruth Signorell* Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog Weg 2, CH-8093 Zürich, Switzerland ABSTRACT: Toluene cluster formation has been investigated in the postnozzle flows of Laval expansions at flow temperatures between ∼48 and 73 K, toluene number concentrations between ∼1013 and 1015 cm−3, and for growth times of up to ∼170 μs. The clusters were detected by soft ionization mass spectrometry to ensure minimum cluster fragmentation upon ionization. The optimum conditions were achieved with single-photon ionization using vacuum ultraviolet (VUV) photons of 13.3 eV energy and low fluences. The nature of the onset of toluene cluster formation hints at barrierless nucleation, which seems a likely scenario for the high supersaturations (>1019) of the present experiments. This contrasts with the onset behavior observed for propane in earlier studies, which suggested nucleation in the presence of a barrier. Subsequent cluster growth has been studied as a function of the growth time for various toluene partial pressures. Size-resolved growth data have been recorded for all cluster sizes from the dimer to aggregates composed of ∼2400 monomers (∼4.4 nm in size), revealing general trends in the growth behavior. The current experiments provide systematic size- and time-resolved data on cluster formation at high supersaturations as a possible benchmark for the understanding of cluster formation under such conditions. This approach probes the postnozzle flow of a Laval expansion with soft, single-photon VUV ionization mass spectrometry.12 S is well-defined in the uniform postnozzle flow of a Laval expansion and can be changed in a controlled way by changing the flow conditions, which allows us to directly record cluster size distributions as a function of S. The partial pressure of the condensable p, the flow temperature TF, and the growth time t can be varied. The latter is achieved by probing the postnozzle flow at different distances from the exit of the Laval nozzle. Cluster sizes of up to several nm can be detected, which allows us to study not only nucleation but also cluster growth. However, the condition that S must exceed 1 is not the only requirement for the observation of nucleation. Nucleation must also happen within a time window that is accessible by the experiment. In our experiment, the time window is determined by the velocity of the molecular beam and the length of the stable postnozzle flow. Conditions for which S > 1 but nucleation is not observed in our experiments are referred to as subcritical, whereas supercritical refers to conditions for which nucleation has already taken place. We typically operate under conditions where S exceeds 1019, that is, in a regime where nucleation could take place without a barrier (spinodal region).3,13,14

1. INTRODUCTION Gas-phase nucleation occurs when the supersaturation, S(T) = p/peq(T) exceeds unity, where p is the partial pressure of the condensable and peq is its equilibrium vapor pressure at temperature T. The cluster size nc (number of molecules per cluster) that corresponds to the maximum of the Gibbs free energy ΔGc of condensation is referred to as the critical cluster. The formation of nc is the rate-determining step. ΔGn progressively decreases for clusters with n > nc, resulting in spontaneous growth and eventual formation of aerosol particles. Instead of a single critical nucleus, nucleation is more accurately described by a critical region of cluster sizes characterized by ΔGc − ΔGn ≤ kBT.3 The experimental characterization of the nucleation process has mainly relied on measurement of the aerosol number concentrations dependent on S after nucleation and partial growth [refs 3−10 and references therein]. Nucleation rates were then calculated using either classical nucleation theory (CNT) or variants thereof. These methods, however, cannot capture the molecular-level details of the initial condensation process (refs 3 and 11 and references therein). Furthermore, in some cases, calculated and experimental nucleation rates were found to deviate by many orders of magnitude, with the reasons for the deviations being unclear.4−6 In our previous publications,1,2 we have introduced a new approach that allows the direct experimental detection of the onset of nucleation without relying on any theoretical model. © XXXX American Chemical Society

Received: April 4, 2017 Revised: May 2, 2017 Published: May 8, 2017 A

DOI: 10.1021/acs.jpca.7b03162 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

5.5) through toluene at a set total flow rate. The bubbler was held inside a temperature-controlled bath (Lauda Proline RP 870). The vapor pressure of toluene (condensable) and hence its concentration in the resultant flow could be tuned by adjusting the bath temperature. The gas mixture was allowed to settle in a large reservoir that was connected to two pulsed solenoid valves (Parker Series 9). The reservoir and subsequent delivery tubes were heated to approximately 60 °C to avoid condensation of toluene. The stagnation volume in front of the Laval nozzle (stagnation temperature T0, stagnation pressure p0) was fed by the valves with typical opening times of 6 ms. The convergent−divergent profile of the Laval nozzles ensured that the gas expansion had a uniform Mach number at the nozzle exit. This uniformity was extended from the nozzle exit into the vacuum chamber over a maximum axial distance of lmax = 100−150 mm by matching the background pressure pexp in the chamber to the flow pressure pF. The pressure in the stagnation volume p0 and the impact pressure pI were measured with pressure transducers (Omega PX170 series). The ratio pI/ p0 was then used to determine the experimental Mach numbers M in the expansion from the Rayleigh−Pitot relation.1,2,28 The uniformity of the postnozzle flow was experimentally verified by measuring pI/p0 as a function of the axial (l) and radial (r) distances. The flow temperature TF, the flow pressure pF, and the number concentrations of toluene monomers Ntol were then determined assuming isentropic conditions and ideal gas behavior.1,12,28 The Laval nozzles employed in the current study and their respective expansion characteristics are summarized in Table 1.

A long-term goal of our studies is to provide experimental details on nucleation and growth for different types of substances with different intermolecular interactions. Here, we present results of nucleation and growth measurements on toluene at three different flow temperatures between ∼48 and 73 K. Previous experimental data on homogeneous nucleation of toluene is limited.15,16 Schmitt et al. measured the rate of homogeneous nucleation in a fast expansion chamber in the temperature range of 215−267 K. At supersaturations of 10− 55, which are many orders of magnitude lower than those in our experiments, typical nucleation rates ranged from 102 to 105 drops/(cm3 s). The experimentally measured rates were compared to those calculated using the Reiss, Katz, and Cohen theory,17 which was found to provide the correct dependence on temperature and supersaturation and to predict the measured nucleation rates well. However, these studies could not provide any molecular-level information about the onset of nucleation. Another motivation for the choice of toluene is the possibility to investigate the influence of different photoionization methods on the recorded cluster size distribution. It is well-known in cluster mass spectrometry that most ionization methods lead to substantial cluster fragmentation and thus severely modify the actual cluster size distribution. Electron ionization has been shown to be particularly unsuitable for the detection of weakly bound clusters.18−20 For nucleation and growth studies, however, it is crucial that the ionization process does not falsify the actual cluster size distribution. Our group and other groups have shown that single-photon vacuum ultraviolet (VUV) threshold ionization at low laser fluence is a soft ionization method for clusters, provided that these clusters are not prone to extensive intracluster chemistry.21−24 Here, we directly compare two-photon ionization (TPI) using ultraviolet (UV) light with single-photon VUV ionization of toluene clusters and carry out fluence-dependent studies. A comparison with previous photoionization studies on toluene clusters is not possible because of the different conditions (fluences, wavelengths) used (refs 25 and 26 and references therein).

Table 1. Laval Nozzles Referred to by Their Nominal Mach Numbers (Mach 4.0, 3.0, and 2.5) According to the Designa s/ mm dt/mm de/mm pF/Pa lmax/mm M̅ TF/K TF/K

2. EXPERIMENTAL SECTION 2.1. Experimental Setup. A detailed description of the experimental apparatus can be found in previous publications.1,12 Figure 1 shows a simplified schematic of the experiment. Mass flow controllers were used to bubble Ar carrier gas (PanGas, 5.0) and CH4 carrier gas (Messer Schweiz,

Mach 4.0

Mach 3.0

Mach 2.5

105.0 8.1 27.1 40 150 3.98 ± 0.06 47.5 ± 1.2 48.5 ± 0.3

59.0 7.4 18.0 70 100 3.36 ± 0.09 62.1 ± 2.7 63.1 ± 0.5

46.5 9.2 16.9 102 100 2.99 ± 0.05 72.9 ± 2.9 69.8 ± 0.7

a

The length of the nozzle, the throat diameter, and the exit diameter are given by s, dt, and de, respectively. pF is the flow pressure for the optimum postnozzle flow conditions. The maximum axial distance lmax is the length over which the postnozzle flow is stable. M̅ and TF are the axially averaged Mach number and flow temperature, respectively. TF is the flow temperature and the standard deviation at fixed axial distances where the nucleation measurements were performed (60, 60, and 50 mm, respectively). The data correspond to the respective data for pCH4 = 0 Pa in Table 2.

M̅ and TF are the axially averaged Mach number and flow temperature, respectively, with the uncertainty quoted as one standard deviation (1σ). The nozzles were chosen to study toluene cluster formation at three different TF values of 47.5 ± 1.2, 62.1 ± 2.7, and 72.9 ± 2.9 K. The standard deviation of TF is an indicator of the quality of the postnozzle flow. Table 1 shows that there was a slight degradation of the flow uniformity for the two warmer nozzles. The maximum axial distance lmax over which flow uniformity was maintained is also shorter for the warmer nozzles. TF in Table 1 is the flow temperature at r = 0 and fixed axial positions of l = 60, 60, and 50 mm for the M 4.0, M 3.0, and M 2.5 nozzles, respectively, obtained from a

Figure 1. Schematic of the experimental setup. dt and de are the throat and exit diameters of the Laval nozzle, respectively, and s is the length of the nozzle. T0 and p0 are the stagnation temperature and pressure, respectively. The gray rectangle represents the uniform postnozzle flow characterized by the flow temperature TF and the flow pressure pF. The axial distance l is the distance between the nozzle exit and the skimmer. r is the radial distance. The central part of the molecular beam is sampled by a skimmer before it interacts with the UV/VUV laser. The cluster ions are then detected by time-of-flight mass spectrometry. B


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sometimes less precise. As suggested in our previous paper on propane,2 we thus use here a calibration curve to obtain precise TF values (Tables 1 and 2).

calibration curve (sections 2.2 and 3.2). The standard deviation of TF was determined from more than 40 individual measurements. The central part of the molecular beam was sampled by a skimmer (0.5 mm diameter; Figure 1). The neutral clusters were then ionized by single-photon ionization with a VUV laser or two-photon ionization (TPI) with a UV laser and detected by a home-built time-of-flight mass spectrometer. The VUV photons were generated by resonance-enhanced two-color four-wave mixing in a krypton molecular beam at a repetition rate of 20 Hz.12,29 The photon energy was 13.3 eV (93.2 nm) with a pulse fluence on the order of ∼1011−1012 photons/(cm2 pulse).29 TPI was performed with 4.66 eV (266.0 nm) or 5.83 eV (212.6 nm) light at 20 Hz. Typical pulse fluences were in the range of ∼1015−1017 photons/(cm2 pulse). High extraction voltages of up to 30 kV were used to efficiently detect heavy clusters with mass to charge ratios m/z up to several hundred thousand mass units.27 Often, the monomer abundance is much higher than the cluster abundance so that the monomer signal causes saturation effects in the mass spectrum. To avoid these effects, the monomer was selectively deflected from the expansion by a deflector plate in front of the detector.1,2 2.2. Nucleation and Growth Measurements. The nucleation experiments were performed at a fixed axial distance (60, 60, and 50 mm for the M 4.0, M 3.0, and M 2.5 nozzles, respectively; see Table 1). The flow conditions were systematically tuned in fine steps to explore the range from subcritical to supercritical conditions. These fine steps in S were achieved by either altering the partial pressure ptol of the condensable at constant TF (method 1) or by changing TF at constant ptol (method 2).1,2 The latter was achieved by adding small amounts of CH4 to the Ar seed gas, resulting in a small increase in TF. At each S, the largest cluster size nmax in the size distribution was monitored and used as a measure of the extent of cluster formation. Note that the average or a mean cluster size could also be used for the same purpose because they show the same trends as nmax.1 For propane, we observed a sudden change in the extent of cluster formation for small changes in pprop or TF at a specific Scrit (critical supersaturation), which we attributed to the onset of nucleation.1,2 We defined the critical cluster size range [nmax, nM] to be bounded by the largest cluster nmax in the last subcritical mass spectrum recorded at the highest S just before nucleation sets in and the average cluster nM (=(nmin + nmax)/2) of the first supercritical mass spectrum recorded at the lowest S for which enhanced cluster formation was observed. Scrit lies in between these two supersaturations. This allowed us to determine a critical cluster size range directly from the experimental mass spectra. For the case of propane, an increase in the propane partial pressure pprop by 0.04 Pa (method 1)1 or a decrease of TF by 0.4 K (method 2)2 was sufficient to induce nucleation. These narrow concentration and temperature ranges over which appreciable changes in cluster size distribution were observed demonstrate the sensitivity of our approach. We mixed small amounts of N2 into the main carrier gas (Ar) to warm the flow in the propane work. For the present study, we replaced N2 with CH4 because of its higher heat capacity. This allowed us to change TF over a wider temperature range using smaller amounts of additional carrier gas while still preserving uniform postnozzle flow conditions. Note that large amounts of additional CH4 (N2) gas can modify the expansion conditions. The composition of the carrier gas (Ar with CH4) can be measured precisely in our experiment, whereas the temperature TF derived from pI is

Table 2. Summary of the Toluene Nucleation Experiments for the Three Laval Nozzlesa nozzle

pCH4/Pa (% CH4)

TF ± σ/K

nmax

nM

n

CNT c

Mach 4.0 ptol = 0.044 Pa pF = 40 Pa 0.00 0.40 1.20 1.60 2.00 3.00 4.00

(0.00%) (1.00%) (3.00%) (4.00%) (5.00%) (7.50%) (10.00%)

48.5 49.2 50.6 51.3 52.0 53.8 55.5

± ± ± ± ± ± ±

0.3 0.3 0.4 0.4 0.4 0.4 0.3

25 19 13 5 7 5 3

13 10 7 5 4 3 2

0.00 0.70 1.20 1.75 2.10 2.80 3.50 7.00

(0.00%) (1.00%) (2.00%) (2.50%) (3.00%) (4.00%) (5.00%) (10.00%)

63.1 63.9 64.7 65.1 65.5 66.3 67.1 71.1

± ± ± ± ± ± ± ±

0.5 0.3 0.6 0.4 0.5 0.4 0.3 0.4

20 16 14 14 10 8 7 2

11 9 8 8 6 5 4 2

69.8 70.5 73.3 74.0 74.7 75.1 76.1 76.8

± ± ± ± ± ± ± ±

0.7 0.5 0.5 0.6 1.0 0.5 0.4 0.5

29 26 14 9 9 7 2 2

15 14 8 5 5 4 2 2

1

Mach 3.0 ptol = 0.062 Pa pF = 70 Pa

1

Mach 2.5 ptol = 0.16 Pa pF = 102 Pa 0.00 (0.00%) 1.02 (1.00%) 5.10 (5.00%) 6.12 (6.00%) 7.14 (7.00%) 7.65 (7.50%) 9.18 (9.00%) 10.2 (10.00%)

1

a

Column 1: Nominal Mach number of the nozzle, partial pressure of toluene ptol, and total flow pressure pF. Column 2: Partial pressure of methane pCH4 and corresponding percentage of methane % CH4. Column 3: Flow temperature TF. The largest cluster size in each mass spectrum is nmax, and the average cluster size is nM = (nmin + nmax)/2. is determined from classical nucleation The critical cluster size nCNT c theory.

For the cluster growth measurements, we systematically increased the axial distance l from l = 0 to 100 mm. This corresponds to an increase in the growth time t of up to ∼170 μs. We also varied the toluene partial pressure ptol. This provides a broad map of cluster size distributions as a function of growth time and concentration of the condensable.

3. RESULTS AND DISCUSSION 3.1. Influence of the Ionization Method. For mass spectrometric detection, the neutral clusters in the molecular beam have to be ionized gently to minimize cluster fragmentation. This ensures that the recorded cluster size distribution represents the original cluster size distribution as closely as possible, which is a prerequisite for reliable nucleation and growth studies. The ionization of weakly bound clusters C


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photon fluence was varied. The cluster size distributions after single-photon ionization with 13.3 eV photons do not depend on the pulse fluence (Figure 2a). Only the absolute cluster signals, and thus the signal-to-noise ratio, increase with increasing pulse fluence. DiPalma et al. reported toluene cluster measurements at three different ionization energies of 8.8, 10.4, and 11.5 eV, respectively, for clusters up to n = 13.26 They observed an increase of the relative abundances of the monomer and smallest clusters with increasing photon energy. This behavior is expected at these photon energies, which all lie within 2.7 eV of the monomer ionization threshold. It is a consequence of the strongly varying and system-size-dependent photoionization cross section in this threshold region. Not surprisingly, the strongest effect was found by DiPalma et al. for the relative abundance of the monomer because its ionization energy is higher than those of the clusters, and thus, the threshold effect in the photoionization cross sections has the biggest effect. At a photon energy of 13.3 eV, such energydependent threshold effects in the photoionization cross section no longer occur and cluster size distributions were thus generally found to be independent of the photon energy in the range up to 17.5 eV.21,22 The fact that single-photon VUV ionization is a soft ionization method for clusters21,22 and the fact that the corresponding cluster size distributions depend neither on the pulse fluence (Figure 2a) nor on the photon energy21,22 make single-photon ionization ideal for nucleation and cluster studies, in contrast to other ionization methods, such as electron ionization or multiphoton ionization (see below). It also allows us to retrieve quantitative information on the relative abundances of the different cluster sizes from the experimental mass spectra in a very simple way. At the low pulse fluences employed here, no other competing ionization processes can occur, such as, for example, multiphoton VUV ionization or the formation of multiply charged clusters. The only process that needs to be considered is single-photon VUV ionization resulting in singly charged cluster ions. To a good approximation, the photoionization cross section of a cluster with n molecules is nσ, where σ is the monomer photoionization cross section. This assumes size-independent detection efficiencies, which we ensure by applying a high extraction voltage. The probability to ionize a cluster of size n and form a singly charged cluster ion is thus

has been investigated in detail for various ionization methods.18−24,27 Single-photon VUV ionization has been shown to be a soft approach for many compounds (see the discussion in ref 22). In our previous studies, propane clusters of up to 5600 monomers (∼5.00 nm) were detected after single-photon ionization with VUV photons of 13.3 eV energy,1,2 illustrating the performance of this method. Here, we compare single-photon ionization and TPI of toluene clusters and investigate the fluence dependence of the cluster size distributions. Photons of 13.3 eV were used for the singlephoton ionization experiments. TPI experiments were performed with 4.66 and 5.83 eV photons to obtain information about the photon energy dependence. The ionization energy of the toluene monomer is 8.8276 ± 0.0006 eV.30 Cluster ionization energies typically lie up to ∼1 eV below the monomer value. Figure 2 shows cluster mass spectra measured after singlephoton (trace a) and multiphoton (traces b and c) ionization. Three mass spectra recorded at three different pulse fluences are shown for each photon energy. For a given photon energy, the Laval expansion conditions were kept constant and only the

p(n) ∝ nσ

(1)

The photoionization probability scales only with the cluster size. This allows us to retrieve the original cluster size distribution (before ionization) from the measured mass spectra simply by dividing the mass signal of cluster size n by a factor n. Such a simple correction for the cluster-sizedependent photoionization efficiency is not possible for multiphoton ionization. Knowledge of the original cluster size distribution is particularly important for proper determination of rate constants from cluster growth data. The disadvantage of single-photon VUV ionization is the need for a VUV photon source. The commercial availability of VUV laser sources is very limited, and typically, home-built lasers are used.12,29 For this reason, we investigated whether multiphoton ionization with lasers in the UV region would be an option for substances with strong UV absorptions, such as toluene. To perform the multiphoton ionization as gently as possible, we used unfocused UV laser beams and the lowest pulse fluences that still allowed us to obtain a decent signal. The results for photon energies of 4.66 and 5.83 eV are shown

Figure 2. Dependence of toluene cluster size distributions on the ionization method and the photon pulse fluence. (a) Single-photon ionization with VUV light at a 13.3 eV photon energy. TPI with UV light at (b) 4.66 and (c) 5.83 eV photon energies. The photon fluences are indicated in the figure. Left: mass spectra at n = 2−40. Doubly charged toluene clusters are indicated by asterisks in (c) in the mass spectrum in the left panel measured with a fluence of 2.6 × 1017 photons/(cm2 pulse). Right: mass spectra at n = 2−2100. D


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and thus S, in fine steps with high precision, which is a prerequisite for nucleation studies. Figure 3 shows the mass spectra of toluene recorded as a function of TF (ln S) for nucleation in the postnozzle flow of

in Figure 2b and c, respectively. The most striking result is the strong dependence of the cluster size distributions on the pulse fluence. Pronounced cluster fragmentation occurs at all fluences that provide a useful signal-to-noise ratio. Cluster fragmentation is evidenced in the mass spectra by the loss of the signal intensity of larger clusters and the increase of the intensity of the small clusters. The fragmentation of clusters at higher fluences is even more pronounced at 5.83 eV than that at 4.66 eV. At the highest fluence in panel (c), for example, there is barely any ion signal visible above n = 50, and only the smallest clusters have high signals. Doubly charged clusters (indicated by asterisks) are observed at this fluence, with n = 23 (appears at n = 11.5 in Figure 2c) being the smallest cluster that is able to accommodate two positive charges. This mass spectrum resembles closely the one reported by Hahn et al. for benzene clusters, which was measured at a comparable photon energy and pulse fluence.31 The strong cluster fragmentation upon multiphoton ionization is a result of energy deposition in the clusters. Compared with single-photon ionization, much higher fluences are required for TPI to form singly charged ions simply because the probability of absorption of two photons by the same molecule in a cluster is low.32 Assuming that the absorption cross section σ is the same for the first (absorption) and the second (ionization) step, the probability of forming a singly charged cluster of size n by direct TPI at fluence f is p+1,TPI(n,f) = nσ2f 2 exp(−nσ2f 2). For TPI to occur in a detectable amount, many more single-photon excitations occur (probability: p0(n,f) = nσf exp(−nσf)) that do not lead to ionization. The absorbed photon energy of these single-excitation events is converted into heat, which eventually leads to cluster evaporation and fragmentation. The more pronounced fragmentation observed at 5.83 eV compared with that at a 4.66 eV photon energy is likely the result of the higher absorption cross section at the higher photon energy.33 As shown by Hahn et al., TPI is not the only process that leads to singly charged cluster ions. The other important process is exciton annihilation (EA) following single-photon excitation of two different molecules in the cluster, which take place with a probability p+1,EA(n,f) = 1 2 2 2 n σ f exp(−nσf) + 1 n3σ3f 3 exp(−nσf).31 EA of more than 2

Figure 3. Toluene mass spectra measured for nucleation in the postnozzle flow of the M 3.0 nozzle. The values of TF and ln S are provided in the figure. The arrows indicate the largest cluster size nmax in each mass spectrum. nmax as a function of ln S is shown in Figure 4 for all three nozzles.

6

three single excitations is also responsible for the formation of the doubly charged cluster ions observed in Figure 2c. In contrast to single-photon VUV ionization (eq 1), multiphoton ionization offers no straightforward way to correct the measured mass spectrum for the various cluster-size-dependent ionization processes. In general, multiphoton ionization is not a reliable method for nucleation and growth studies because of cluster fragmentation and the difficulties quantifying the influence of the various competing processes on the cluster size distributions. 3.2. Nucleation Studies. Methods 1 and 2 were both used to investigate the onset of nucleation of toluene. Experimentally, method 1 proved less convenient as changing the partial pressure of toluene required long equilibration times for the gas flow. For method 2, no more than 10% of CH4 was added to warm up the flow in order to ensure that the uniformity of the flow was maintained. Typical TF values are listed with their standard deviations in Table 2 for three measurement series using method 2. The flow temperatures were recorded at the same axial position for a given nozzle l (section 2.2 and Table 1). The data demonstrate that method 2 allows us to tune TF,

the M 3.0 nozzle. The value of ln S decreases with increasing TF (increasing percentage of CH4). The arrows indicate the largest cluster size nmax recorded in each spectrum. At the lowest supersaturation, only the monomer and a very small amount of the dimer are observed. No larger clusters are visible in this mass spectrum. The extent of cluster formation increases gradually with increasing ln S. At the highest ln S, nmax is about 20 (Table 2). An interesting aspect in the toluene mass spectra is the relatively high abundance of the toluene dimer compared to the other cluster sizes. DiPalma et al. determined the photoionization efficiencies of toluene clusters up to n = 4 in the photon energy range of 8.2−10.0 eV from measurements in a free supersonic jet expansion and investigated their structures using DFT calculations.34 They concluded that toluene nucleation in their free jet starts from the antiparallel stacked toluene dimer and proceeds through nonstacked trimer and tetramer structures and not through the most stable trimer and tetramer structures, which are stacked.34,35 Note also that another theoretical study found the most preferred geometry of the toluene dimer to be a crossed antiparallel stacked E


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The Journal of Physical Chemistry A arrangement.36 In contrast to the results of ref 34, recent data from electronic spectroscopy of small toluene clusters also formed in free expansions show that the binding motif of the toluene dimer is also repeated in cluster sizes up to n = 8.37 The differences in the two studies could arise from different expansion conditions under which the clusters were formed. That the dimer is the critical cluster was suggested for other molecules.38 However, as pointed out in ref 2 and below, such statements on critical cluster sizes are probably no longer valid under conditions of very high supersaturations. Even though cluster formation in free supersonic expansions does not happen under controlled conditions as in a Laval expansion, both have in common that high supersaturations are reached. For our toluene Laval expansions, the supersaturation spans the range from 1.1 × 1019 to 4.3 × 1038. Under these conditions, barrierless cluster formation may occur (spinodal decomposition) instead of surmounting a free energy barrier.3 CNT cannot provide further insight for such barrierless processes because in the framework of CNT the barrier never vanishes, which is unphysical.3,39,40 Nevertheless, we provide in Table 2 estimated from CNT (see eq 2 in ref critical cluster sizes nCNT c = 1 for all conditions studied here, a 2). CNT predicts nCNT c result that would at least be consistent with a barrierless nucleation process. The values of nmax from Table 2 are plotted as a function of ln S in Figure 4. As pointed out previously,1,2 in the presence of a nucleation barrier, a sudden, stepwise increase of nmax is expected at the critical supersaturation ln Scrit. This behavior,

however, is not observed for toluene in Figure 4. Instead, the data show a gradual increase of nmax with increasing ln S. Such a gradual change in nmax seems consistent with a barrierless process. Nucleation studies were also carried out in the M 4.0 nozzle by changing ptol in small steps at constant TF (method 1; data not shown). The observed increase in nmax as a function of ptol did not reveal any sudden change, consistent with our observations for method 2 in Figure 4. For a barrierless process, Figure 4 would actually show the very first steps of cluster growth as a function of ln S. The figure also reveals that the values of nmax are higher for the M 2.5 than those for the M 3.0 at similar supersaturations (e.g., in the region of ln S ≈ 48−52), that is, cluster formation is more efficient in the M 2.5 nozzles. This is likely a consequence of the higher toluene partial pressures used in the measurements with the M 2.5 nozzle (Table 2). Figure 4 compares the nucleation behavior of toluene (left) with that of propane (right) reported in ref 2. The critical supersaturations in the propane case were in the range of 1011− 1013, that is, many orders of magnitude lower than the toluene supersaturations (1.1 × 1019−4.3 × 1038). The existence of a nucleation barrier, and thus a sudden, steplike increase of nmax in the region of the critical supersaturation, seems thus more likely in the propane case. In contrast to toluene, propane shows indeed a sudden, steplike increase of nmax at ln Scrit ≈ 28.7 (Scrit ≈ 2.9 × 1012), hinting at the existence of a nucleation barrier. However, as we discussed in more detail in ref 2, this steplike behavior is only an indication but not final proof of the presence of a nucleation barrier. Similarly, the present toluene data in Table 2 hint at a barrierless process but also do not provide direct proof for the absence of a barrier. A deeper understanding of our current experimental observations could be gained through modeling, for example, using dynamic nucleation theory (DNT)39,40 or extensions of CNT that are applicable to the spinodal region.41,42 3.3. Growth Studies. 3.3.1. Growth Trends. The growth of toluene clusters was investigated in the postnozzle flow of the Laval expansions for different toluene monomer concentrations Ntol. Ntol was varied by adjusting the temperature of the chiller in which the toluene container was placed. The growth time t was varied by changing the distance l between the nozzle exit and the skimmer (Figure 1). As the postnozzle uniformity can be extended over several nozzle diameters, generally, growth times of several hundred microseconds can be accessed. The temporal resolution of 3−4 μs is determined by the molecular beam velocity and the beam size of the VUV light (∼1 mm29). At the toluene concentrations used for growth studies, nucleation occurred already inside of the nozzle. Therefore, it was not possible to accurately specify the time when nucleation set in. We thus arbitrarily defined t = 0 to be the time corresponding to the shortest nozzle-to-skimmer distance (l = 20 mm). All other growth times t are specified with respect to this arbitrary zero point. A summary of the toluene growth results is provided in Table 3. To capture “snapshots” of the cluster growth process, mass spectra were recorded for several growth times and concentrations. Ntol was varied between 7.6 × 1013 and 1.5 × 1015 cm−3, and the cluster growth was monitored for growth times of up to ∼170 μs. The values of nmax listed in Table 3 are used to characterize the extent of growth. The extent of condensation (given by nmax at a given t) increases with increasing Ntol. A closer inspection of the values of the axially averaged temperature TF indicates a systematic cooling of the

Figure 4. nmax as a function of ln S. Left: Toluene. Right: Propane from ref 2. The toluene measurements were performed with M 2.5, 3.0, and 4.0 nozzles. For the propane measurements, an M 4.0 nozzle was used. The shaded rectangle in the propane data where the sudden steplike increase in nmax occurs indicates the critical cluster range of [3, 24] that was found for propane in ref 2. F


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The Journal of Physical Chemistry A Table 3. Summary of Toluene Growth Dataa Mach 4.0 ptol/Pa

Ntol/cm−3

TF/K

t/μs =

0

39

78

118

157

20 85 208 604 1443

34 105 256 745 1675

37 145 375 834 1930

47 176 429 971 2208

41

81

122

162

79 145 352 738 1792

100 163 435 916 1988

133 186 461 1041 2407

83

125

167

97 222 305 624 1110

146 321 441 689 1493

181 363 495 783 1769

nmax 0.05 0.11 0.21 0.38 0.66 ptol/Pa

7.6 1.6 3.1 5.7 9.9

× × × × ×

1013 1014 1014 1014 1014

Ntol/cm−3

49.5 48.0 47.6 47.5 47.7

± ± ± ± ±

0.9 1.3 1.5 1.9 2.5

TF/K

8 51 180 500 1075 Mach 3.0 t/μs =

0

nmax 0.12 0.16 0.30 0.57 0.97 ptol/Pa

1.3 1.9 3.6 6.8 1.2

× × × × ×

1014 1014 1014 1014 1015

Ntol/cm−3

64.3 62.1 60.2 60.7 59.5

± ± ± ± ±

2.1 1.9 2.4 2.8 4.1

TF/K

35 65 225 434 1165 Mach 2.5 t/μs =

0

54 108 272 586 1523 42 nmax

0.24 0.47 0.65 0.84 1.40

2.4 4.7 6.5 8.6 1.5

× × × × ×

1014 1014 1014 1014 1015

74.2 72.0 73.0 70.3 68.4

± ± ± ± ±

3.3 3.2 3.0 3.4 4.5

20 86 127 273 604

51 164 233 410 864

a The concentration of toluene monomer in the uniform expansion is given as the partial pressure ptol (first column) and the number concentration (second column) Ntol. TF is the axially averaged flow temperature (Table 1). nmax is the number of molecules in the largest cluster in the mass spectrum recorded at growth time t.

flow with increasing Ntol for all three nozzles. This is just the opposite behavior of what one would expect to observe. Substantial cluster formation should rather result in a warming of the flow due to the release of latent heat, as reported by Wyslouzil and co-workers.43 However, the measurements by Wyslouzil and co-workers were performed inside of the Laval nozzles where the flow is confined by the nozzle wall and heat can be exchanged between the flow and the nozzle wall. In our setup, by contrast, the flow is probed in the postnozzle region where confinement is only provided by the surrounding gas (pexp). Considering that this confinement is very delicate, substantial cluster formation and resulting heating could change the flow conditions and thus TF. Currently, we interpret the observed decrease of TF with increasing cluster formation to be the result of slightly changing flow conditions. This explanation is supported by the fact that the change in flow conditions could be compensated for by adjusting pexp. Important for the present growth studies is the observation that even without adjustment of pexp the variation in TF had actually no detectable influence on the cluster size distributions and growth trends. As expected, nmax increases with increasing Ntol and increasing t for all three nozzles (Table 3). The values of nmax for t = 0 at the lowest concentrations clearly indicate that nucleation has already occurred inside of the nozzles (see in Table 2). Although the growth times for estimates for nCNT c the three nozzles are not identicalowing to the differences in the flow velocitiesthey are sufficiently close to compare the dependence of nmax on the average temperature ⟨TF⟩ across the three nozzles. ⟨TF⟩ is ∼48 K for the M 4.0, 61 K for the M 3.0, and 72 K for the M 2.5 nozzle. For similar Ntol, the values of nmax are systematically higher for the M 3.0 nozzle compared to

those for the M 2.5 nozzle. In a simple picture, one could expect that at approximately the same toluene concentrations cluster growth is more pronounced in the colder nozzles where S is higher. This trend is indeed observed for the M 2.5 and M 3.0 nozzles, which differ in ⟨TF⟩ by 11 K (72 and 61 K, respectively). However, the value of S also influences the number concentration of the initially formed clusters, which is typically higher at higher S. Also, for the same total amount of monomer, more initial clusters also mean that within the same time interval each initial cluster grows less compared to the situation where fewer initial clusters are present. Transferred to our situation, this would result in smaller clusters at lower ⟨TF⟩. The same trend would also be expected for diffusion, which is slower at lower temperatures. The fact that the coldest nozzle (M 4.0) with ⟨TF⟩ ≈ 48 K does not clearly follow the simple picture mentioned above might be a result of diffusion and number concentration of the initially formed clusters. A more detailed understanding of the influence of the different processes can only be obtained from a combination with modeling, for example, from combined molecular dynamics− master equation approaches or transition-state-based master equation approaches.38,39 Figure 5 shows the time-dependent growth for the three different cluster sizes n = 10, 240, and 700. These three sizes are chosen to illustrate the different nature of time dependences that are observed in the growth measurements. The abundance of the smallest clusters (n = 10) decreases with increasing t because they continuously grow to larger clusters. This growth happens either by condensation of gas-phase monomers or by coagulation of smaller clusters. For intermediate sizes, here represented by n = 240, the cluster abundance first increases G


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Figure 5. Time evolution of three different cluster sizes, n = (i) 10, (ii) 240, and (iii) 700. The normalized ion signals are extracted from the mass spectra recorded with the M 3.0 nozzle for Ntol = 1.2 × 1015 cm−3.

Figure 6. (a) Time-evolution of cluster size n = 50 for different toluene concentrations Ntol in the M 2.5 nozzle. (b) False color image of the abundance of the n = 50 cluster as a function of Ntol and t. Red is high, green is medium, and blue is low abundance. All cluster signals from panel (a) were normalized to the signal recorded at t = 0 and Ntol = 1.5 × 1015 cm−3. The four quadrants have the following meaning: Q1 = short t and low Ntol, Q2 = long t and low Ntol, Q3 = short t and high Ntol, and Q4 = long t and high Ntol.

and then decreases at longer times. At early times, these clusters are formed by growth of smaller clusters, leading to an increase in the abundance of the n = 240 clusters. At longer times, their abundance decreases again because they grow themselves to even larger clusters. Again, this can take place by growth through the gas phase or coagulation. The abundance of the largest clusters (n = 700) increases almost linearly over the time scale of our experiment, during which more and more clusters of this size are formed by growth of smaller clusters. Figure 6a shows as an example of the time evolution for one cluster size (n = 50) for five different Ntol. At the lowest concentration, 2.4 × 1014 cm−3, the cluster abundance increases with time. The growth behavior is similar to the one for n = 700 in Figure 5. The same trend is maintained for the initial times at the next higher concentration (4.7 × 1014 cm−3), but beyond 120 μs, the cluster abundance decreases slightly. Similarly, at the next higher concentration of 6.5 × 1014 cm−3, the abundance increases first and then decreases. This behavior resembles that of the cluster n = 240 in Figure 5. For the two highest concentrations, the cluster abundance decreases over time, with the rate of decrease being higher at higher Ntol. This decrease in cluster abundance is comparable to the behavior of the n = 10 in Figure 5. The comparison of Figures 6a and 5 reveals similar trends for the growth of a fixed cluster size as a function of the monomer concentration and the growth of different cluster sizes at a fixed monomer concentration, respectively. A closer inspection of Figure 6a reveals that roughly four different cluster growth regimes can be distinguished, which we refer to as quadrants Q1, Q2, Q3, and Q4 with the following meaning: Q1 = short t and low Ntol, Q2 = long t and low Ntol, Q3 = short t and high Ntol, and Q4 = long t and high Ntol. Figure 6b shows the abundance for cluster size n = 50 from panel (a) as a false color image. Red means high, green medium, and blue low cluster abundance. For the color image, all cluster signals from

panel (a) were normalized to the signal recorded at t = 0 and Ntol = 1.5 × 1015 cm−3. The lowest abundance for n = 50 is observed in Q1 because the conditions to form this size are unfavorable at short t and low Ntol. A higher abundance is observed for Q2 than for Q1, indicating that the formation of this cluster size becomes more probable at longer growth times. The highest abundance is found in Q3, that is, for short t and high Ntol, because substantial growth to clusters larger than n = 50 has not set in yet at short t. Q4 shows that the latter process leads to pronounced depletion of n = 50 at long t. Analogous false color images can be retrieved from the original data for any other cluster size observed in the mass spectra. The classification into quadrants allows us to compare general trends between different cluster sizes and between the three different nozzles in a compact way. For this purpose, we normalized the sum of the signals of cluster size n in quadrant i (i = 1−4) to the sum over all different cluster sizes in all four quadrants. These normalized abundances are referred to as QN1, QN2, QN3, and QN4 and are shown in Figure 7 as a function of n for the three nozzles. The higher the value of QNi, the more favorable it is to form a certain cluster size under the conditions corresponding to this quadrant All three nozzles show similar systematic trends. Large clusters with n ≥ 500 are most favorably formed at high Ntol and long t (QN4), with the exception of the M 4.0 nozzle for which a substantial amount of large clusters is already formed at short t for high Ntol (QN3). At high Ntol, clusters in the intermediate size range (100 ≤ n ≤ 500) dominate the size distributions at all t (QN3 and QN4), while low Ntol results in the formation of only smaller clusters H


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Figure 7. Normalized abundances QN1, QN2, QN3, and QN4 as a function of cluster size n. QNi(n) (i = 1−4) is the ratio of the sum of the signals of cluster size n in quadrant i (i = 1−4) to the sum of over all different cluster sizes (n = 2−1200) in all four quadrants. Panels (a)−(c) contain data for the three different nozzles. See also Figure 6b. Figure 8. Mass spectra of toluene and propane measured in the M 4.0 nozzle during growth at the same flow temperature and comparable monomer number concentrations. The cluster radii in nm are also shown.

(≤100) almost independently of the growth time (QN1 and QN2). The latter is mainly a consequence of the limited amount of substance. The exception here is the M 2.5 nozzle, in which clusters in the intermediate size range (100 ≤ n ≤ 500) can also be formed at long t for low Ntol or (QN2). 3.3.2. Comparison between Toluene and Propane. Figure 8 shows a comparison of toluene and propane mass spectra recorded in the M 4.0 nozzle at the same flow temperatures TF = 47.5 K and for comparable monomer number concentrations of 5.7 × 1014 and 5.5 × 1014 cm−3, respectively, and a growth time of 78 μs. Further propane growth data were reported in our recent publication.2 At the same conditions, a higher fraction of larger clusters was observed for toluene compared to propane. This is visible in Figure 8 by the higher relative abundance of clusters with n ≥ 150 for toluene. In addition, the propane distribution is narrower and unimodal, while the toluene distribution appears broader and bimodal. For propane, we found that narrow unimodal distributions appear at an earlier stage in the growth than broader bimodal distributions (see Figure 6 in ref 2). The higher abundance of larger clusters and the bimodal feature indicate that toluene has already reached a later stage in the growth process compared to propane, implying faster growth for toluene, likely because of the higher supersaturation of toluene under the same conditions. Overall, we found similar trends in the size distributions as a function of t for both substances (see Figure 6 in ref 2): (i) narrow, unimodal distributions at early growth times, which seem mainly governed by growth from the vapor phase; (ii) broader, multimodal distributions at intermediate t resulting from competing growth processes, such as growth of smaller

clusters from the vapor phase and coagulation of smaller clusters; and finally, (iii) at very long t again unimodal distributions that are very broad. However, a narrowing of the size distribution at long t due to the Kelvin effect was not observed in either case,44 which indicates that in both cases we did not observe the final stage in the growth process.

4. SUMMARY Nucleation and growth of toluene clusters were investigated in the postnozzle flow of Laval expansions at high supersaturations between ∼1019 and 1038 and flow temperatures between ∼48 and 73 K. Cluster size distributions were recorded as a function of supersaturation with mass spectrometry. We observed a gradual increase of the cluster size with increasing supersaturation in the region where cluster formation starts, which hints at barrierless nucleation. This onset behavior is different from the one of propane,2 which showed a sudden stepwise increase in the cluster size at a specific supersaturation, a behavior that resembles more closely what is expected for nucleation in the presence of a barrier. The subsequent timeresolved growth of toluene clusters was studied for growth times of up to ∼170 μs. Size-resolved growth data were recorded for clusters ranging from the dimer to aggregates composed of ∼2400 monomers. Compared with the previous propane growth study,2 the data hint at faster growth of toluene clusters at the same total monomer concentrations and flow I


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(5) Sinha, S.; Laksmono, H.; Wyslouzil, B. E. A Cryogenic Supersonic Nozzle Apparatus to Study Homogeneous Nucleation of Ar and Other Simple Molecules. Rev. Sci. Instrum. 2008, 79, 114101. (6) Sinha, S.; Bhabhe, A.; Laksmono, H.; Wölk, J.; Strey, R.; Wyslouzil, B. E. Argon Nucleation in a Cryogenic Supersonic Nozzle. J. Chem. Phys. 2010, 132, 064304. (7) Feldmar, L. M.; Wölk, J.; Strey, R. New Measurements of Argon and Nitrogen Nucleation in the Cryogenic Nucleation Pulse Chamber. AIP Conf. Proc. 2013, 1527, 15−18. (8) Ghosh, D.; Bergmann, D.; Schwering, R.; Wölk, J.; Strey, R.; Tanimura, S.; Wyslouzil, B. E. Homogeneous Nucleation of a Homologous Series of n-Alkanes (CiH2i+2, i = 7−10) in a Supersonic Nozzle. J. Chem. Phys. 2010, 132, 024307. (9) Mullick, K.; Bhabhe, A.; Manka, A.; Wölk, J.; Strey, R.; Wyslouzil, B. E. Isothermal Nucleation Rates of n-Propanol, n-Butanol, and nPentanol in Supersonic Nozzles: Critical Cluster Sizes and the Role of Coagulation. J. Phys. Chem. B 2015, 119, 9009−9019. (10) Wölk, J.; Wedekind, J.; Strey, R.; Wyslouzil, B. E. In Nucleation and Atmospheric Aerosols; Smolík, J., O’Dowd, C., Eds.; Institute of Chemical Process Fundamentals ASCR and Czech Aerosol Society: Prague, 2009; p 589. (11) Wyslouzil, B. E.; Wölk, J. Overview: Homogeneous Nucleation from the Vapor Phase - The Experimental Science. J. Chem. Phys. 2016, 145, 211702. (12) Schläppi, B.; Litman, J. H.; Ferreiro, J. J.; Stapfer, D.; Signorell, R. A Pulsed Uniform Laval Expansion Coupled with Single Photon Ionization and Mass Spectrometric Detection for the study of Large Molecular Aggregates. Phys. Chem. Chem. Phys. 2015, 17, 25761− 25771. (13) Wedekind, J.; Chkonia, G.; Wölk, J.; Strey, R.; Reguera, D. Crossover from Nucleation to Spinodal Decomposition in a Condensing Vapor. J. Chem. Phys. 2009, 131, 114506−114506. (14) Savel’ev, A. M.; Starik, A. M. An Improved Model of Homogeneous Nucleation for High Supersaturation Conditions: Aluminum Vapor. Phys. Chem. Chem. Phys. 2017, 19, 523−538. (15) Schmitt, J. L.; Zalabsky, R. A.; Adams, G. W. Homogeneous Nucleation of Toluene. J. Chem. Phys. 1983, 79, 4496−4501. (16) Schmitt, J. L. Precision Expansion Cloud Chamber for Homogeneous Nucleation Studies. Rev. Sci. Instrum. 1981, 52, 1749−1754. (17) Reiss, H.; Katz, J. L.; Cohen, E. R. Translation-Rotation Paradox in the Theory of Nucleation. J. Chem. Phys. 1968, 48, 5553−5560. (18) Bobbert, C.; Schütte, S.; Steinbach, C.; Buck, U. Fragmentation and Reliable Size Distributions of Large Ammonia and Water Clusters. Eur. Phys. J. D 2002, 19, 183−192. (19) Schütte, S.; Buck, U. Strong Fragmentation of Large Rare Gas Clusters by High Energy Electron Impact. Int. J. Mass Spectrom. 2002, 220, 183−192. (20) Lengyel, J.; Pysanenko, A.; Poterya, V.; Kočišek, J.; Fárník, M. Extensive Water Cluster Fragmentation after Low Energy Electron Ionization. Chem. Phys. Lett. 2014, 612, 256−261. (21) Yoder, B. L.; Litman, J. H.; Forysinski, P. W.; Corbett, J. L.; Signorell, R. Sizer for Neutral Weakly Bound Ultrafine Aerosol Particles based on Sodium-Doping and Mass Spectrometric Detection. J. Phys. Chem. Lett. 2011, 2, 2623−2628. (22) Litman, J. H.; Yoder, B. L.; Schläppi, B.; Signorell, R. SodiumDoping as a Reference to Study the Influence of Intracluster Chemistry on the Fragmentation of Weakly-Bound Clusters upon Vacuum Ultraviolet Photoionization. Phys. Chem. Chem. Phys. 2013, 15, 940−949. (23) Dong, F.; Heinbuch, S.; Rocca, J. J.; Bernstein, E. R. Dynamics and Fragmentation of van der Waals Clusters: (H2O)n, (CH3OH)n, and (NH3)n upon Ionization by a 26.5eV Soft X-Ray Laser. J. Chem. Phys. 2006, 124, 224319. (24) Belau, L.; Wilson, K. R.; Leone, S. R.; Ahmed, M. Vacuum Ultraviolet (VUV) Photoionization of Small Water Clusters. J. Phys. Chem. A 2007, 111, 10075−10083.

temperatures, likely as a result of the higher supersaturation of toluene. Nevertheless, toluene and propane show similar qualitative growth trends as a function of monomer concentration and growth time. Pronounced temporal changes in the overall shape of the size distributions (width; monomodal vs multimodal) are observed, which indicate the presence of different growth mechanisms (growth from the vapor phase, growth by coagulation of clusters). The temporal behavior of individual cluster sizes can be divided into three classes: smaller clusters that disappear over time, medium-sized clusters that in an initial period become more abundant and in a later phase also disappear, and large clusters the abundance of which continuously increases over time. Soft ionization was crucial for the present molecular-level nucleation and growth studies. Our group and other groups had previously shown that single-photon VUV ionization is indeed soft for many types of weakly bound molecular clusters.21−24 In the present study, we compared single-photon VUV ionization with multiphoton UV ionization at comparatively low photon fluences. The comparison reveals that multiphoton ionization is not a useful alternative for two reasons. First, pronounced cluster fragmentation is observed, which depends sensitively and in an unpredictable way on the photon fluence. Second, the retrieval of quantitative data on the relative abundance of different cluster sizes from the experimental mass spectra is impractical because of unknown contributions from competing processes (single excitation, EA). A long-term goal of our work is to provide experimental data at the molecular level for nucleation and cluster growth for a variety of different compounds and conditions. In combination with modeling approaches,3,39−42,45,46 such comprehensive studies will contribute to a deeper molecular-level understanding of some of the many open questions in vapor nucleation and cluster growth. Our propane and toluene cluster work in Laval expansions is the very first step toward this goal.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +41 44 633 46 21. Fax: +41 44 633 13 16. ORCID

Ruth Signorell: 0000-0003-1111-9261 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank David Stapfer and Markus Steger from the LPC shops for their assistance in developing and maintaining the experimental setup. Financial support was provided by the ETH Zürich and the Swiss National Science Foundation (SNF Projects No. 200020-159205 and 200020-172472).

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REFERENCES

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