Bernhard
Schläppi
,
Jessica H.
Litman
,
Jorge J.
Ferreiro
,
David
Stapfer
and
Ruth
Signorell
*
ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, CH-8093, Zürich, Switzerland. E-mail: rsignorell@ethz.ch
First published on 16th March 2015
We report on a new instrument that allows for the investigation of weakly-bound molecular aggregates under equilibrium conditions (constant temperature and pressure). The aggregates are formed in a Laval nozzle and probed with time-of-flight mass spectrometry in the uniform postnozzle flow; i.e. in the equilibrium region of the flow. Aggregates over a very broad size range from the monomer to particle sizes of 10–20 nm can be generated and studied with this setup. Soft ionization of the aggregates is performed with single photons from a homemade vacuum ultraviolet laser. The mass spectrometric detection provides molecular-level information on the size and chemical composition of the aggregates. This new instrument is useful for a broad range of cluster studies that require well-defined conditions.
In laboratory studies, weakly-bound molecular aggregates are typically generated by expanding molecular and atomic gases through a small nozzle into vacuum (referred to as “free supersonic jets”).1 Even though free jets have been extensively used for cluster formation and successfully combined with various characterization methods they suffer from an intrinsic limitation. Free expansions are non-uniform inevitably resulting in strong anisotropies in temperature, pressure (number density), and velocity in the flow.2 Cluster studies under well-defined (equilibrium) conditions are therefore not possible using free jets. As demonstrated earlier, uniform flows generated by Laval nozzles are an interesting alternative to overcome this limitation.3 The convergent–divergent shape of the Laval nozzle produces a flow with constant Mach number at the nozzle exit. By properly matching the static pressure in the expansion chamber this uniform flow can be maintained after the nozzle over an extended distance. The temperature, pressure (number density), and velocity in this postnozzle flow are constant, which in principle allows for studies under equilibrium conditions.
Continuous and pulsed Laval nozzles have been used to study reaction kinetics of molecules at low temperatures exploiting the thermally equilibrated conditions in the uniform postnozzle flow.3–10 To the best of our knowledge, Leone and co-workers were the first who probed the postnozzle flow using mass spectrometry.6 With respect to the formation of weakly-bound molecular aggregates, Laval nozzles have been combined with various characterization methods. Bartell and co-workers probed the kinetics of freezing clusters formed in a pulsed Laval nozzle with electron diffraction after the nozzle exit.11–15 However, they did not match the static pressure in the expansion chamber so that their postnozzle flow was not uniform. They essentially used the Laval nozzle simply to form large clusters. Wyslouzil and coworkers studied nucleation rates of various substances inside two-dimensional Laval nozzles using neutron scattering,16 X-ray scattering and Fourier transform infrared spectroscopy17 (FTIR). They exploited the characteristic temperature drop inside a Laval nozzle. Similarly, the clustering of UF6 inside a Laval nozzle was probed with FTIR spectroscopy by Takeuchi and coworkers in the mid-90s.18
In this contribution we report on an instrument that allows the characterization of weakly-bound molecular aggregates in the uniform postnozzle flow of a Laval expansion with soft single photon vacuum ultraviolet ionization and mass spectrometric detection. This instrument can be used for aggregate sizes that cover the whole size range from the monomer up to particle sizes of 10–20 nm (several hundred thousand mass units). The uniform postnozzle flow ensures that equilibrium conditions are maintained over an extended distance after the nozzle exit. Single photon vacuum ultraviolet (VUV) ionization close to the ionization threshold ensures that the fragmentation of the weakly-bound aggregates is minimized for a broad range of substances.19–24 Finally, the mass spectrometric detection allows not only to cover an extended cluster size range but it also provides molecular-level information (number of monomers and chemical composition) on smaller and medium-sized clusters through mass resolution.
Fig. 1 Scheme of the experimental setup. The zoomed-in section shows the cube-shaped Laval nozzle mount. |
The convergent–divergent shape of the Laval nozzle produces a uniform flow at a constant Mach number at the nozzle exit, which can be extended into the postnozzle region if the pressure in the expansion chamber pexp is matched properly (see below and Fig. 4a). As a result, gradients in temperature, pressure, and velocity are absent in the postnozzle flow and local equilibrium is established. The expansion chamber is a stainless steel chamber (80 cm length and 25 cm diameter) that is pumped by a roots blower (Pfeiffer Octa 2000) which is backed by a rotary piston vacuum pump (Leybold E250) (typical pump speed of 1900 m3 h−1 at 0.1 mbar). Typical chamber pressures during experiments range from pexp = 0.1 to 1 mbar (monitored with a MKS Instruments Baratron 626). The pressures and flow conditions have to be optimized to realize flow uniformity in the postnozzle region. In particular, the pressure in the expansion chamber pexp is required to be approximately equal to the flow pressure pF, which is the static pressure felt in the flow frame. This is achieved by adjusting the carrier gas flow rate, by supplying an additional slip gas into the expansion chamber, and by adjusting the pumping speed using a PID controlled exhaust throttle valve (MKS Instruments 653B), which is located at the entrance of the exhaust line. The slip gas (He or N2) is supplied by a manual leak valve. The pressure in the expansion chamber can be controlled to within better than 0.005 mbar, which allows us to collimate the postnozzle flow over a distance that corresponds to several nozzle diameters (typically over 10–20 cm). Fine control of pexp is of uttermost importance as the uniformity of the postnozzle flow depends sensitively on the chamber pressure.
The pressure transducer (Omega PX170 series) that is mounted on a linear manipulator and located in the postnozzle region serves to measure the impact (or dynamic) pressure pI. By shifting this pressure transducer radially (perpendicular to the flow direction) and moving the nozzle mount axially (in flow direction) one can map pI in the postnozzle region. The Mach number M of the expansion can be determined from pI and from the stagnation pressure p0 with the Rayleigh–Pitot formula:
(1) |
(2) |
(3) |
Flow temperatures TF determined as described above have been compared with spectroscopic studies on rotational temperatures of OH radicals by Spangenberg et al.8 Good agreement between the two methods was found in this study. Similar good agreement (less than 10% deviation) was obtained from relative line intensities in LIF spectra of CN radicals.5 Based on these results, we assume that the above described way to determine the relevant expansion characteristics is reasonable.
The Laval nozzles are manufactured in the ETH in-house mechanical workshop: Either the nozzle is produced from a single piece of aluminum or stainless steel using a CNC lathe or the nozzle is printed on a 3D printer (3DSystem Projet 3500 HD) using Visijet X as print material. We estimate the accuracy of the lathed nozzles to be on the order of 50 μm. The 3D printed nozzles are manufactured at a layer resolution of 16 μm. The choice of the nozzle material depends on the properties of the condensable gas in the sample gas mixture used (resistance against corrosives etc.). So far, both ways of nozzle manufacturing have proved equally suitable for our purpose.
For the sodium-doping experiments described in Section 3.3, a sodium pick-up cell was installed in the differential pumping chamber. The cell has an entrance and an exit aperture to allow passage of the molecular beam. Doping of the molecular aggregates with a single or a few Na-atoms happens in this pick-up cell (Na, Sigma-Aldrich, 99.0%). By controlling the temperature of the pick-up cell (typically between 433 and 523 K), the vapor pressure of the Na and thereby the degree of doping can be varied. For more details concerning the Na-doping method, we refer the reader to earlier work (Yoder et al.,22 Schläppi et al.25).
One of the important features of this setup is the possibility to record cluster ion signals over a very broad mass range (up to several hundred thousand mass units). It is known, that the detection efficiency for large masses (mass to charge ratios) is strongly reduced compared to low masses because it depends on the impact velocity of the ions on the MCPs. This dependence arises from the velocity-dependence of the secondary electron yield,26 which initiates the electron amplification in the ion detection process. We have modified our ion optical assembly and the electrical connections using homebuilt feedthroughs such that we can increase the impact energy up to 30 keV e−1 (e: ion charge). This is essential to detect large masses (typically above a few thousand amu e−1).
With the linear TOF tube, the mass resolution is typically m/Δm = 320 at 2000 amu e−1. This is sufficient to obtain mass resolution and thus molecular-level information on small aggregates (typically < 10000 amu e−1, depending on substance). If higher mass resolution is required, the linear TOF tube can be replaced with a commercially available high resolution reflectron (Tofwerk, HTOF, m/Δm = 3000 up to 5000 amu e−1). This is useful for the investigation of multicomponent molecular aggregates, where mass spectra are much more congested.
To overcome this limitation, we have built a pulsed, tunable VUV laser light source for SPI that provides energies between 6 and 18 eV.27,28 In contrast to REMPI, SPI with tunable VUV light is a broadly applicable ionization method. Furthermore, it is in general a soft ionization method even for weakly-bound aggregates.19–24 The VUV photons are generated by resonance enhanced 2-color-4-wave mixing in a pulsed supersonic expansion of krypton (Kr) or xenon (Xe) gas generated by a small nozzle (Parker-Hannifin, General Valve series 9). The nozzle is mounted on a 3D movable flange in the four-wave-mixing chamber (Fig. 1). The 2-photon resonances of the noble gases are pumped by the frequency doubled or tripled output of a dye laser (Radiant Dyes Narrow Scan). A second dye laser (Radiant Dyes Narrow Scan) is used to produce the third (tunable from 220–800 nm) pump photon. Both dye laser outputs are tightly focused on the noble gas jet. The two dye lasers are pumped with higher harmonic outputs (532 nm, 355 nm) of a Nd:YAG laser (Continuum Powerlite PR 9020) with a pulse duration of approximately 8 ns (FWHM). The grating chamber (Fig. 1) serves to separate the desired VUV frequency from other frequencies using a stepper-motor driven, toroidal diffraction grating (Horiba Jobin Yvon). A photo-electron multiplier (Hamamatsu R5150-10) with 50 mm2 active area is installed in the ionization/detection chamber in the line of sight of the VUV beam to monitor the light intensity (Fig. 1). The photon flux is estimated to be approximately 1010 photons per pulse.27 Typical pressures in the four-wave-mixing chamber and the grating chamber are 1 × 10−4 mbar and 2 × 10−7 mbar, respectively. Turbomolecular pumps (Pfeiffer TPH 521, 440 l s−1 for the four-wave-mixing chamber and Pfeiffer HiPace 300, 260 l s−1 for the grating chamber) backed by a single scroll pump (Leybold Vacuum SC30D) are used to evacuate these chambers.
Fig. 3 shows the results from systematic impact pressure measurements along the radial and axial directions for a Mach 4.4 nozzle and an argon–toluene mixture with 1.5% toluene. The average Mach number of 4.4 is determined from the experimental data as described below. The pulse repetition rate was 5 Hz and the expansion chamber pressure was pexp = 0.56 mbar. Fig. 3a shows radial profiles of pI for different axial distances. Except for the larger axial distances, the radial profiles are nicely uniform across the region where uniform flow is expected (radius smaller than 7 mm). The slight perturbation at larger axial distance indicates the expected loss in flow quality with increasing distance from the nozzle exit. The conversion of the measured impact pressures along the central axis (i.e. radial distance 0 mm) yields the flow temperature TF as a function of axial distance from the nozzle exit. Fig. 3b shows that reasonable uniformity of TF over axial distances of more than 8 cm (corresponding to about 4 nozzle diameters) is found. The Mach number of 4.4 ± 0.1 is determined from the experimental results for the argon–toluene mixture as an average of measurements from 0–80 mm axial distance (eqn (1)). The flow temperature TF over the same distance amounts to 40.1 ± 1.9 K (eqn (2)), which corresponds to fluctuations in the impact pressures in the centre of the expansion of approximately 85 Pa or 7.3%. The quality of our Laval expansion is comparable to the best expansions reported in the literature for pulsed Laval nozzles.6,8 Temperature fluctuations in continuously operated Laval expansions are also of comparable magnitude.5 The experimental measurements yield an average flow temperature of 40.1 K, an average number density of nF = 7.5 × 1016 cm−3 (from eqn (3)), and an average flow velocity of approximately 520 ms−1. The uniform flow in Fig. 3 is the result of an experimental optimization during which the fluctuations of is minimized over the greatest possible axial distance. The repetition rate, the flow rate, the amount of slip gas, and the pumping speed (using the throttle valve) are varied to optimize the conditions. The whole optimization is first carried out with pure carrier gas and then with the desired amount of condensable sample. In most cases, a slight re-optimization after the addition of condensable gases is sufficient to regain uniform postnozzle flows. Note that the expansion chamber pressure pexp is typically slightly higher than the flow pressure pF, in agreement with the results observed and discussed by others (see e.g. Lee et al.6).
The results of a CFD simulation (Section 2.2) for the same Laval nozzle but with pure argon gas are summarized in Fig. 4. Fig. 4a shows a contour plot of the flow temperature TF inside the nozzle (axial distance < 0 mm) and in the postnozzle region. A uniform postnozzle flow is maintained over several nozzle exit diameters. This is also evident from the corresponding simulated flow temperature which is plotted as a function of axial distance in Fig. 4b. The CFD simulation predicts over an axial distances from 0–100 mm a Mach number of 4.1 ± 0.2, a postnozzle flow temperature of TF = 47.0 ± 4.1 K, and a number density of nF = (1.1 ± 0.2) × 1017 cm−3. The corresponding design values from the interactive software (compare Section 2.2) at the nozzle exit are M = 4.0, TF = 46.6 K, and nF = 1 × 1017 cm−3 for pure argon. As mentioned above, corresponding experimentally determined values lie around M ∼ 4.4, TF ∼ 41.0 K and nF ∼ 7.5 × 1016 cm−3 under the same operating conditions. (Note that the experimental values for pure argon and an argon–toluene mixture of 1.5% are virtually identical.) Such deviations between design, simulation, and experiment are typical for Laval expansions. For completeness, Fig. 4c shows the simulated impact pressure profiles at various axial distances. The trends are very similar to the experimental ones in Fig. 3a.
Fig. 6 and 7 demonstrate how the cluster size distribution can be tuned by varying the expansion conditions. This can either be achieved by changing the Laval nozzle or the operating conditions of a Laval nozzle (carrier gas) or by changing the amount of the condensable gas in the sample gas mixture. As an example, Fig. 6 shows how the cluster size distribution can be tuned by changing the toluene content in an argon/toluene expansion. Similar to Fig. 5, bimodal distributions of toluene aggregates are observed. The most abundant cluster sizes of the two bands of the bimodal distributions (asterisk and circles, respectively), the total average cluster size (mavg), and the maximum cluster size (mmax) clearly increase with increasing toluene content.
Fig. 7 Mass spectra of small aggregates generated in a mixed argon–propane flow (M = 4.0 ± 0.1, TF = 47.1 ± 1.2 K and nF = 6.3 × 1016 cm−3) using different relative propane concentrations recorded after SPI. The labels are the same as in Fig. 6. The strong mass peak at very low mass is monomer. The inset shows that all cluster mass peaks are resolved. |
Fig. 7 provides example mass spectra of propane clusters recorded under conditions where growth processes such as coagulation of clusters do not yet take place. These cluster distributions do not show bimodal features as observed in Fig. 5 and 6. The size distribution clearly changes with changing concentration of the condensable gas. Note that for the three spectra in Fig. 7 only the concentration of the propane changes but not the temperature or the density in the flow. The observed growth in cluster size originates only from a change in saturation at constant temperature. We find a similar sensitive behaviour by changing the carrier gas composition under otherwise identical conditions, i.e. for the same propane concentration and the same total density (data not shown). In this case the change in cluster sizes originates from a change in saturation at constant pressure. Small temperature differences down to about 1 K can be realized for example by adding a few percent of N2 to the Ar carrier gas. As expected, colder expansions produce larger clusters. The very small temperature changes allow us to modify the cluster size distributions very sensitively. Note that the minor change in the carrier gas composition only changes the temperature and not the type of collisions since the large majority of collisions are still with Ar atoms. We have performed a series of systematic studies in which we demonstrate how the cluster size can be tuned systematically by tuning the flow temperature (results will be provided in a forthcoming publication). The results in Fig. 5 to 7 demonstrate that clusters over a very broad size range can be formed in Laval expansions and can be detected with mass spectrometry. The variation of the expansion conditions allows us to tune the size from monomer only, to small oligomers, and even to very large clusters very sensitively. To the best of our knowledge this is the first time such cluster studies have been demonstrated in Laval nozzles.
Finally, Fig. 8 illustrates the broad applicability of Laval nozzles combined with SPI and mass spectrometric detection for the formation of molecular aggregates of various chemical compositions for the example of dimethylether (CH3OCH3), ethane (C2H6), carbon dioxide (CO2) and krypton (Kr). All mass spectra were recorded after VUV ionization with photons of 13.3 eV energy. For the first three compounds, argon was used as a carrier gas, while pure krypton was expanded to form krypton aggregates. These examples demonstrate that in principle chemical information on the cluster composition can be obtained from the mass spectra. To determine the composition of mixed clusters, a higher mass resolution than the one in Fig. 8 might be required.
In a second series of experiments we have investigated the change in cluster size distribution as a function of the axial distance of the skimmer from the nozzle exit in the postnozzle flow region. Clusters detected at larger axial distances have spent a longer time in the postnozzle flow region; i.e. under equilibrium conditions. If equilibrium for clusters were not reached after the nozzle one would expect to record different cluster size distributions with varying axial distance. For this purpose, mass spectra of a cluster distribution were recorded as a function of the axial distance after the nozzle. The relative intensities of clusters with 5 and 50 (In=5/In=50) and 10 and 50 (In=10/In=50) toluene molecules, respectively, and absolute intensity of the cluster that corresponds to the maximum of the distribution (referred to as “mode intensity”) were extracted from these mass spectra and plotted in Fig. 10. In addition to these intensities the mass of the maximum of the cluster size distribution (referred to as “mode mass”) is displayed as a function of the axial position. (Note that all values are normalized to their respective average between 20 and 80 mm.) All values are nearly constant (less than 10% variation) over a fairly large distance between 20 and 80 mm, i.e. over the region where the postnozzle flow is uniform (see Fig. 3b). Again, the fact that the cluster size distribution is stable in the uniform flow region clearly hints at stable cluster conditions over this region. The slight deviations at short axial distances agree with deviations found in the flow temperature profile in Fig. 3b. Either a minor disturbance caused by the nozzle exit or a minor disturbance resulting from the close proximity of nozzle exit and skimmer flange could be potential explanations for this observation. At large distances, the mass distribution changes because the expansion begins to disintegrate slowly (Fig. 3b). Obviously, the cluster size distribution seems to be very sensitive to the prevailing conditions. Stable cluster size distributions are thus a strong indication that thermal equilibrium is indeed reached in the uniform postnozzle flow right after the nozzle exit.
Fig. 10 Characteristic quantities extracted from mass spectra of toluene clusters recorded as a function of the axial distance from the nozzle exit (see Fig. 4a). Same experimental conditions as in Fig. 3. The mass spectra were recorded after REMPI. |
Further clear evidence for thermal equilibrium of clusters comes from an estimate of the number of collisions a molecular aggregate experiences. A simple estimate of the collision rate in the region where the flow temperature strongly decreases in the Laval nozzle (from −100 to −50 mm in Fig. 4b) is difficult. However, it is clear that most of the collisions and cooling already happen in this region inside the Laval nozzle (see Fig. 4b). Even if we neglect the large number of collisions in this region and only include estimates for the number of collisions in the region where the flow temperature is approximately constant (above −50 mm in Fig. 4b), we end up with collision numbers that are at least equal to collision numbers in ion traps, for which thermal equilibrium for larger systems has been spectroscopically proven.32–34 This can be seen by the following example. For a single toluene molecule we estimate a collision frequency of roughly 2.5 × 107 s−1 in the region above −50 mm (Fig. 4b). Combining this with the flow speed (520 ms−1 for the M = 4.4 nozzle, see Section 3.1) and the distance over which the flow temperature is approximately constant before the nozzle exit (from −50 mm to 0 mm, see Fig. 4b), we determine the number of collisions for a single toluene molecule to be on the order of 2 × 103 in the region where the final temperature has almost been reached (above −50 mm). Note that collisions with the carrier gas dominate over collisions between toluene molecules. For a molecular cluster with a diameter of 2.5 nm (corresponding to ∼48 molecules), this number scales accordingly and amounts to more than 3 × 104 collisions (more than many hundred collisions per molecule). Results from ion traps show that it requires approximately 2 × 103 collisions with He bath gas atoms to cool and thermalize a (H2O)−48 anion cluster to 120 K; i.e. several ten collisions per molecule.32 For a molecular aggregate of about 200 molecules (diameter ∼ 4 nm) the number of collisions exceeds 105 in our Laval nozzle, which again corresponds to more than several hundred collisions per molecule. Once more, the total number of collisions in the Laval nozzle is much higher (by several orders of magnitude) because the large number of collisions at the beginning of the nozzle (between −100 and −50 mm in Fig. 4b) are not even considered in this estimate. In addition, the collisions after the nozzle exit, i.e. in the postnozzle flow, are also not yet considered in our simple estimation. We would like to note that spectroscopic studies to prove equilibrium as (rarely) performed in ion traps32–34 cannot be performed for our broad cluster distributions. The cluster spectra are congested with many bands from all cluster sizes which cannot be assigned and which make it impossible to identify hot bands. Equilibrium conditions for monomers in Laval expansions have already been proven experimentally.5,8 Together with the experimental observations described above, these estimates and comparisons with ion trap results provide clear evidence that the aggregates in the uniform postnozzle flow are indeed in thermal equilibrium with the surrounding gas.
Fig. 11 illustrates the difference with respect to collisions with the carrier gas between a free supersonic expansion and a uniform Laval expansion. For this purpose, the Na-doping cell was installed in the differential pumping chamber (Section 2.3) and heated to temperatures between 373 and 523 K and the same measurements were performed once with a Laval nozzle and once with a simple free jet nozzle attached to the expansion chamber. Temperatures of the Na-doping cell between 373 and 523 K correspond to a variation in the Na vapor pressure between 1.8 × 10−7 to 2.7 × 10−3 mbar. Molecular aggregates that pass the Na-doping cell pick up many more Na atoms per cluster at higher Na vapor pressures than at lower pressures. In a free jet, the collision frequency with the carrier gas is negligible after a few nozzle diameters (typically a few mm), i.e. at the position where the Na-doping cell is located.22,23,25 As a consequence, all Na atoms that are picked up by a cluster formed in a free jet will stay attached to the cluster until they are ionized and can thus be detected in the mass spectrum. In the Laval expansion, by contrast, the many collisions with the carrier gas that occur in the region between the Na-doping cell and the ionization remove a large fraction of the Na atoms that were originally picked up by the clusters in the Na-doping cell. Under the same experimental conditions (cell temperature), clusters with fewer Na atoms should thus be detected in the mass spectrum of the Laval expansion compared with the mass spectrum of the free jet expansion. This is illustrated in Fig. 11 for toluene clusters that were ionized with the 266 nm Quantel laser. The mass peaks labelled with asterisks are REMPI peaks of undoped clusters (no Na attached). The mass peaks at 23 mass units higher that are visible in the free jet mass spectrum (top trace) are clusters that have picked-up a single Na atom. As can be seen, single Na pick up is efficient in the free jet expansion at a cell temperature of about 433 K (Na vapor pressure of about 1.3 × 10−5 mbar). At higher temperatures, mass peak that correspond to multiple Na pick-up become increasingly dominant (spectra not shown). In the Laval nozzle, by contrast, only bare clusters with no Na atom attached are detected up to a cell temperature of about 503 K (Na pressure of about 1.0 × 10−3 mbar) as a consequence of the many collisions with the carrier gas (middle trace in Fig. 11). Temperatures around 523 K are required to detect any Na-doped clusters in the Laval expansion. The bottom trace shows an example for which multiple Na-doping is visible. The comparison of the top spectrum with the middle and the bottom spectrum nicely visualizes the fundamentally different environment in a free supersonic jet expansion (non-equilibrium) compared with a Laval expansion (equilibrium).
This journal is © the Owner Societies 2015 |