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Efficient cooling in supersonic jet expansions of supercritical fluids: CO and

Wolfgang Christen, Klaus Rademann, and Uzi Even

Citation: The Journal of Chemical Physics 125, 174307 (2006); View online: https://doi.org/10.1063/1.2364505 View Table of Contents: http://aip.scitation.org/toc/jcp/125/17 Published by the American Institute of Physics

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Efficient cooling in supersonic jet expansions of supercritical fluids: CO and CO2

Wolfgang Christena� and Klaus Rademann Institut für Chemie, Humboldt-Universität zu Berlin, Brook-Taylor-Strasse 2, 12489 Berlin, Germany

Uzi Even Sackler School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel

�Received 8 September 2006; accepted 25 September 2006; published online 7 November 2006�

Pulsed, supersonic beams of pure carbon monoxide and carbon dioxide at stagnation conditions above their critical point have been investigated by time-of-flight measurements as a function of pressure and temperature. Although both molecules form clusters readily in adiabatic expansions, surprisingly large speed ratios �above 100� indicative of very low translational temperatures �below 0.1 K� have been achieved. In particular, the supersonic expansion of CO2 at stagnation temperatures slightly above the phase transition to the supercritical state results in unprecedented cold beams. This efficient cooling is attributed to the large values of the heat capacity ratio of supercritical fluids in close vicinity of their critical point. © 2006 American Institute of Physics. �DOI: 10.1063/1.2364505�

I. INTRODUCTION

Supersonic molecular beams constitute a very powerful and versatile technique in modern physical chemistry, allow- ing strong adiabatic cooling of gaseous substances during expansion. Besides manifold applications in optical spectros- copy, in particular, biological systems such as amino acids,1–3 DNA bases,4 and peptides,5,6 supersonic jets are uti- lized in a multitude of current research topics. Prominent examples are the study of quantum effects7 and the investi- gation of physical processes at ultralow temperatures using superfluid helium clusters.8,9 In parallel, the generation of cold molecules has developed into a hot topic with a large variety of experimental approaches.10–27 Without doubt, these applications would benefit a lot if they could employ precooled molecules with minimum velocity dispersion. It is thus worthwhile to investigate the factors affecting the monochromaticity or minimum translational temperature of supersonic beams.

It is well known that the cooling efficiency in supersonic jets can be enhanced by increasing the number of collisions taking place during expansion. This can be realized in a straightforward way by increasing the stagnation pressure p0. Indeed earlier studies28,29 report very low translational tem- peratures of helium atoms expanded at high-pressure condi- tions. For molecules, however, a comparable increase in stagnation pressure might lead to quite different effects due to the presence of phase transitions. While supersonic beams of supercritical fluids have been successfully employed to transfer nonvolatile molecules into the gas phase,30 as yet the translational cooling under such high-pressure conditions has not been investigated.

This contribution presents first experimental results on

the supersonic expansion of supercritical carbon monoxide and carbon dioxide. For these molecules, the transition to the supercritical state occurs at the critical pressure pc=35 bars for CO and pc=73.77 bars for CO2, and at the critical tem- perature Tc=134.45 K for CO and Tc=304.13 K for CO2. A suitable measure for the translational cooling of a supersonic jet is the speed ratio S=v0 /�v�. Hence the emphasis of this study is on the accurate determination of the velocity distri- bution, characterized by the flow velocity v0 and the velocity spread �v� of the expanded beam. In our approach, it can be directly obtained from time-of-flight measurements. The main idea is to select a very narrow particle pulse and wait: In the course of time the initially confined molecules will spread out in space according to their velocity distribution f�v��dv�, which is determined by their translational tempera- ture T�. After a sufficiently long flight path particles are de- tected with high time resolution. This procedure directly yields the experimental arrival time distribution f�tF�dtF, al- lowing the straightforward computation of the speed ratio. For the pulsed supersonic high-pressure expansion of pure CO �32 bars� p0�70 bars, stagnation temperature T0 =323 K� surprisingly large values S�100 are derived. These numbers are comparable with results achieved for helium under similar experimental conditions29 and are significantly larger than obtained for the rare gases argon and krypton. For beams of pure CO2 �p0=74 bars,262�T0�422 K�, speed ratios S�80 �at T0=322 K� have been obtained. This is of particular relevance because supercritical carbon dioxide pre- sents an efficient solvent for nonvolatile and thermally sen- sitive molecules. It can even be used to transfer macroscopic amounts of dissolved solids into the gas phase employing pulsed supersonic expansions.30 The high speed ratios are thus quite promising for spectroscopic studies of biologically relevant molecules.

a�Author to whom correspondence should be addressed. Electronic mail: [email protected]; URL: http://wolfgang-christen.net/ home.php

THE JOURNAL OF CHEMICAL PHYSICS 125, 174307 �2006�

0021-9606/2006/125�17�/174307/5/$23.00 © 2006 American Institute of Physics125, 174307-1

II. EXPERIMENTAL SETUP

Figure 1 schematically depicts the experimental setup. It consists of an ultrahigh vacuum �UHV� chamber with a pulsed supersonic jet source and a pulsed electron gun for ionization of the beam.31 A second, differentially pumped UHV chamber �base pressure p�5�10−9 mbars� provides a fast ion detector with subnanosecond time resolution and postacceleration capabilities.

Basis of our jet source is the miniaturized pulsed valve by Even et al.32 with a conical nozzle �diameter of 0.3 mm�, which permits high stagnation pressures up to 130 bars. Due to its short opening time ��20 �s� the gas load is signifi- cantly reduced compared to other beam sources. Despite the high-pressure expansion excellent vacuum conditions of p �4�10−6 mbars can be maintained already in the first chamber �and p�1�10−8 mbars in the second chamber�. Thus collisions with the background gas, serving to reheat the cooled jet, are minimized. Two other features, resulting from the negligible gas consumption, are relevant for this experiment as well. First, the stagnation pressure can be kept constant with high precision ��p0�0.03 bars�. Second, the residence time of molecules within the valve head is long enough for achieving thermal equilibrium. Temperature is measured using a NiCr/Ni thermocouple spot-welded di- rectly to the valve body31 and is computer-controlled for ac- curately defined expansion conditions. This guarantees ex- cellent thermal stability ��T0�0.03 K� in the operation range T0=225–425 K. The jet source is mounted on a xyz-translator stage to align it to the axis defined by two conical skimmers �diameters of 3 and 2 mm, cone angle of �21°�. Furthermore, it allows adjusting the distance between valve and first skimmer. For high-pressure expansions this ability turned out to be of utmost importance with respect to skimmer interference effects, causing increased beam tem- peratures. In the present experiment, a nozzle-skimmer dis- tance of �145 mm was used.

A spatially confined group of particles can be generated

by electron impact ionization of the pulsed jet. For this pur- pose a compact, pulsed, electrically shielded electron gun is mounted on the valve body, ionizing a small part of the ex- panding gas very close ��2 mm� to the nozzle exit. Operat- ing the output electrode with pulse durations between a few hundred nanoseconds and a few microseconds ionizes a short segment of the molecular beam. In order to obtain the true thermal broadening of the ionized beam fraction, great care was taken to exclude space charge repulsion effects by gen- erating only few ions ��103� per pulse. In fact, no influence of the duration of the electron pulse on the spread of arrival times could be observed under these experimental condi- tions. The length of the field-free flight path between the ionization region and the ion detector l=1050±2 mm results in a flight time tF that is much longer than the electron pulse tE and permits to achieve tF�1000tE. Simultaneously, the focal spot of the electron beam is much smaller than the flight distance. Thus the assumption of a delta-function like section of particles is well justified. After electron impact, generated ions, together with neutrals, move toward a multi- channel plate �MCP� detector with a grounded entrance mesh. Because the mean flow velocity of the expanding jet �CO: v0�820 ms−1 and CO2: v0�726 ms−1� is not suffi- cient to generate secondary electrons at the detector surface, ions are accelerated directly in front of the MCP by floating it at a voltage of −4 kV with respect to the grounded mesh. The acceleration time is much shorter than the total flight time tF and can be neglected.

III. RESULTS AND DISCUSSION

For a three-dimensional supersonic expansion the distri- bution function of the axial beam velocity v� has the form

f�v��dv� = cv�2 exp�− �v� − v0 �v�

2 dv� . It corresponds to a Maxwellian velocity distribution at some reduced temperature T�, superimposed on the flow velocity v0. c denotes a scale factor related to the centerline beam intensity. Transformation to the experimentally more conve- nient time domain and conversion for a flux sensitive detec- tion yields the distribution of flight times,

f�tF�dtF = c l3

tF 4 exp�− � l/tF − v0�v�

2 dtF, �1� l is the total flight distance. Figure 2 depicts a representative time-of-flight measurement of CO �p0=45 bars,T0=323 K�, together with a numerical fit of the arrival time distribution according to Eq. �1�. The fit yields values of v0 =820±16 ms−1 and �v� =8.12±0.15 ms−1, corresponding to a speed ratio S=101.2±0.2. It is worth mentioning that the uncertainty in the total flight distance �2 mm� influences only the accuracy of the flow velocity v0 and the velocity spread �v�, as indicated above, while the speed ratio S is unaffected.

These results may be compared to values of the terminal flow velocity v0, which for an ideal gas can be calculated as

FIG. 1. Sketch of the experimental setup, to scale. 1: Pulsed, temperature- controlled high-pressure jet source mounted on a xyz-translator stage. 2: Variable-energy electron gun with pulsed output electrode for ionization of the expanding supersonic beam. 3 and 4: Conical skimmers with differential pumping stage. 5: High-speed detector with postacceleration for time- resolved single ion counting.

174307-2 Christen, Rademann, and Even J. Chem. Phys. 125, 174307 �2006�

v0 =�2kBT0m �� − 1 . �2� Here kB is Boltzmann’s constant, m the molecular mass, and �=CP /CV the ratio of the heat capacities at constant pressure CP and constant volume CV. For an “ideal” diatomic gas without vibrations CV=5R /2 and with CP=CV+R follows �=7/5, while the inclusion of vibrational excitations results in �=9/7; R is the gas constant. As can be seen from tabu- lated values of the heat capacities,33 at room temperature and below the vibrational mode of CO is essentially unexcited. At T0=298 K and p0=1 bars, the isothermal data yield � =1.402. Certainly, despite this agreement the assumption of an ideal gas behavior may not a priori deem justified. For this reason Fig. 3�A� depicts values of the specific heat ratio � in the experimentally accessible pressure and temperature range, as calculated from thermophysical properties.33 Figure 3�B� displays the corresponding terminal flow velocity v0 according to Eq. �2�. For the stagnation conditions of Fig. 2 �p0=45 bars and T0=323 K�, a ratio of the heat capacities �=1.472 is derived, which yields v0=772.9 ms−1. In com- parison, the flow velocity of an ‘‘ideal’’ carbon monoxide gas with �=1.4 amounts to v0=818.8 ms−1. The computation of Fig. 3�B� yields two other observations. First, the flow ve- locity decreases remarkably with increasing stagnation pres- sure. Second, in the parameter space accessible to this ex- periment the phase transition between gaseous and supercritical carbon monoxide, indicated by the dashed lines in Fig. 3, apparently does not affect the terminal flow veloc- ity v0.

For the adiabatic, isentropic expansion of an ideal gas the conservation of energy yields the relation between the

final parallel temperature T�, the stagnation temperature T0, and the local Mach number M �see, e.g., Ref. 34�,

T� = T0�1 + � − 12 M2 −1

.

Using

S =�� 2

M ,

the translational temperature T� can be phrased as

T� = T0�1 + � − 1 �

S2 −1. �3� Although the same result can be obtained from the well- known relation

�v� =�2kBT� m

, �4�

Eq. �3� avoids the experimental uncertainty with respect to �v�.

For the high-pressure expansion of CO at a stagnation temperature T0=323 K, Eq. �3� yields values of T� =110 mK ��=1.4� and T� =98.4 mK ��=1.472�, whereas T� =111±4 mK follows from Eq. �4�. Compared to the trans- lational temperatures of rare gases,29 CO molecules are as cold as helium and colder than argon and krypton by one order of magnitude. This is quite unexpected because it is well known that CO forms clusters readily,31,35 which is commonly supposed to limit the minimum temperature.

For CO2, the isothermal data 33 yield �=1.294 at T0

=298 K and p0=1 bars, very close to the “ideal gas” value of 9 /7. However, approaching the critical point the situation changes dramatically. As visualized in Fig. 3�C�, the infinite heat capacity CP at the critical point leads to a nonmonoto- nous progression of the heat capacity ratio �. Accordingly, in Fig. 3�D� the calculated flow velocities suggest a valley of minimum values v0. Experimentally, this prediction could not be verified. Probably, at these extreme conditions the model leading to Eq. �2� is oversimplified.

For a supersonic beam of carbon dioxide at stagnation conditions of p0=74 bars and T0=322 K values of v0 =686±13 ms−1 and �v� =8.59±0.16 ms−1 are obtained, cor- responding to a speed ratio S=80.2±2. According to Eq. �3� this correlates with a translational temperature of T� =225 mK ��=9/7� and T� =84 mK ��=2.46�. For compari- son, Eq. �4� yields T� =195 mK. Probing the velocity distri- bution of the beam at shorter delay times of the pulsed elec- tron beam ionization, equivalent to earlier and faster parts of the molecular beam, even lower velocity spreads �v� =7.14±0.14 ms−1 with significantly higher speed ratios S =97.5±0.5 can be obtained. At stagnation temperatures closer to the critical point, values of S=103.8±0.5 were achieved at T0=317 K and S=119±3 at T0=312 K. The lat- ter corresponds to a translational temperature of T� =99 mK ��=9/7� and T� =37 mK ��=2.46�. Obviously the super- sonic expansion of carbon dioxide at stagnation temperatures slightly above the phase transition to the supercritical state results in unprecedented cold beams.

FIG. 2. �Color online� Normalized, time-dependent intensity of the ionized section of the supersonic CO beam at the MCP detector. Stagnation condi- tions are p0=45 bars and T0=323 K. Experimental data points �dots� have been fitted �solid line� to the intensity distribution f�tF�dtF given in Eq. �1�. The length of the field-free flight path amounts to l=1050±2 mm.

174307-3 Supersonic jet expansions of supercritical fluids J. Chem. Phys. 125, 174307 �2006�

At first glance this result is quite surprising, because a significant energy release is expected to occur on condensa- tion to clusters. On the other hand, at or near the critical point unusual behavior might be conceivable due to large density fluctuations.36 Indeed, in earlier supersonic molecular beam studies of helium �pc=2.27 bars and Tc=5.2 K� the properties of He clusters were found to depend on the loca- tion of the isentropic expansion path in the phase diagram.37–39 Terminal temperatures were found to be lowest for expansions along isentropes to the liquid-phase side of the isentrope passing through the critical point. Similarly, for free-jet expansions of H2 �pc=13 bars and Tc=33.2 K�, the lowest terminal enthalpies were achieved in expansions start- ing from supercritical stagnation conditions.40 At stagnation temperatures T0�15 K, beam temperatures between 4 and 9 K have been obtained. Both for helium and hydrogen the suggested explanation was the formation of “cold” clusters by the fragmentation of a superheated liquid, whereas sub- critical expansions produce a supercooled vapor, and clusters

form by condensation. Thus in these two cases no energy would be released due to condensation, which would se- verely limit the cooling during the supersonic expansion. It remains unclear, however, if collective quantum effects pre- dominate over the more familiar classical interactions and contribute to the reported anomalies in the mass spectra. Moreover, the cooling of a liquid beam during expansion is quite limited.

We therefore suggest a somewhat different explanation involving the large heat capacity of supercritical fluids in the close vicinity of their critical point. This approach is able to explain why the minimum beam temperature occurs for stag- nation temperatures T0 slightly above the critical temperature Tc. During expansion into vacuum, the fluid density rapidly decreases, while simultaneously the system cools; if the local gas temperature approaches the critical temperature within the first few collisions, while the particle density in the beam still is sufficiently close to the critical density, the anomalous large heat capacity comes into play. At the critical point the

FIG. 3. �Color online� �A� Calculated values of the heat capacity ratio �=CP /CV using the thermophysical properties of carbon monoxide �Ref. 33�. �B� Terminal flow velocity v0 of carbon monoxide as obtained from Eq. �2�. �C� Calculated values of the heat capacity ratio �=CP /CV using the thermophysical properties of carbon dioxide �Ref. 33�. �D� Terminal flow velocity v0 of carbon dioxide as obtained from Eq. �2�. The phase transition to the supercritical state is indicated with dashed lines.

174307-4 Christen, Rademann, and Even J. Chem. Phys. 125, 174307 �2006�

heat capacity at constant pressure CP is infinite with the con- sequence that condensation to clusters does not increase tem- perature. Hence, if the expansion isentrope passes the region close to the critical point where the heat capacity ratio � is strongly enhanced �see Fig. 3�C��, molecular clusters are formed efficiently, but this process will cause a significantly reduced increase of the translational beam temperature only.

In summary, pulsed supersonic beams of molecules above their critical point have been expanded into vacuum and investigated with respect to their velocity distribution and translational temperature. For the two molecules CO and CO2 under investigation, the phase transition to the super- critical state has no apparent influence on the flow velocity v0. It does, however, lead to extremely small velocity spreads �v�. Although at high stagnation pressures the condensation to molecular clusters is very efficient, the resulting transla- tional temperatures are very small. This leads us to propose pulsed high-pressure supersonic expansions of supercritical fluids as a suitable technique for the efficient generation of very cold and extremely monochromatic molecular beams. Besides apparent applications in the chemistry and physics at ultralow temperatures this result revolves on the fundamental question of the number of two- and three-body collisions occurring in supersonic jet expansions, and their impact on condensation and cooling.

Further experiments are in progress investigating the translational temperature as a function of cluster size, and the detailed influence of the phase transition on the velocity dis- tribution.

ACKNOWLEDGMENTS

One of the authors �U.E.� acknowledges the James Franck Minerva Foundation. Chemicals have been provided by the Fonds der Chemischen Industrie. This work has been supported by the Deutsche Forschungsgemeinschaft �Grant Nos. CH262/2-1 and CH262/5-1�.

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174307-5 Supersonic jet expansions of supercritical fluids J. Chem. Phys. 125, 174307 �2006�