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Properties of H₂, Ar, and Ne clusters in superfluid ⁴He nanodroplets : towards a search for superfluidity… Nakahara, Hiroko 2009

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Properties of H2, Ar, and Ne clusters in superfluid 4He nanodroplets Towards a search for superfluidity in large supercooled H2 clusters by Hiroko Nakahara B.Sc., The University of British Columbia, 2006 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in The Faculty of Graduate Studies (Physics) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) December 2009 © Hiroko Nakahara 2009 Abstract The ultimate goal of this research project is to develop an experiment to probe for superfluity in large clusters of molecular hydrogen in ultra-cold helium-4 nanodroplets. Superfluidity has now been observed in a wide variety of systems and hydrogen is a good candidate to exhibit this macroscopic quantum phenomenon in a molecular system. In this thesis, two major advances were made enroute to the eventual search for superfluidity in bulk clusters of molecular hydrogen. 1. In the first advance, the fluidity of supercooled molecular H2 was investigated in helium-4 nanodroples ( i05 atoms) at 0.38 K. To clearly demonstrate that the 112 clusters are fluxional, or fluid-like, separate studies of argon and neon clusters were also made for comparison. To probe the behavior of the clusters, a single tetracene probe molecule was also inserted into the droplet and the laser induced fluorescence (LIF) from the tetracene was studied as a function of the cluster size and the pickup method. In the prior pickup method, the cluster species is added to the 4He droplet before to the probe molecule and in the post pickup method, the tetracene is added and then the cluster species is added. Due to the difference in the pickup order, the configuration of the probe molecule and the cluster species can differ. The observed spectral shift of tetracene LIF in the presence of the cluster species was studied for both pickup methods. For Ar and Ne clusters, the spectral shifts from the prior and post pickup methods show clear differences. This observation suggests that for prior pickup, the tetracene molecule attaches to the surface of the cluster and does not penetrate into the centre of the cluster and we conclude that the Ar and Ne clusters are not fluid-like in the helium droplets. For para-hydrogen and normal-hydrogen the LIF spectra of tetracene are independent of pickup order and we conclude that the supercooled H2 clusters remain fluid-like at 0.38 K. 2. The second advance made in this thesis was to configure the droplet apparatus to study the rotational states of probe molecules in 4He droplets doped with 112 clusters. The rotational states are studied by a combination of infrared and mass spectroscopy. Methane is the probe molecule used and when introduced into the 411e droplet it is surrounded by the H2 cluster. If the surrounding H2 liquid is superfluid, the methane rotates freely with a low moment of inertia. Conversely, if the 112 remains a normal fluid, the dopant molecule drags hydrogen molecules along as it rotates and has a much larger moment of inertia. Rotationally resolved infrared spectroscopy of the methane gives clear information about the state of the surrounding supercooled liquid 112. As a first step, the v3 vibrational mode of bare methane in 4He droplets was studied. The R(0) transition of the 7)3 stretching mode of methane was partially observed and found to be consistent with the R(0) peak for CH4-doped 4He droplet systems previously measured by the Miller group [1]. Hiroko Nakahara nhiroko©physics.ubc.ca 11 Table of Contents Abstract ii Table of Contents iii List of Tables v List of Figures vi 1 Introduction 1 1.1 Bose-Einstein condensation and superfluidity 1 1.2 Molecular hydrogen: ortho-Hydrogen and para-Hydrogen 1 1.2.1 BECofH2 3 1.3 Previous studies of superfluidity in hydrogen clusters 4 1.4 Free rotation of fermionic molecules 6 2 Tetracene Laser-Induced Fluorescence 10 2.1 Motivation 10 2.2 LIF 11 2.3 Experimental setup for LIF measurements 13 2.4 LIF of tetracene 16 2.4.1 LIF of tetracene in gas phase 16 2.4.2 Bare tetracene in 4He droplets 16 2.5 Size determination of the 4He droplets 20 2.6 LIF results: H2, Ne, and Ar clusters 23 2.6.1 H2, Ne, and Ar cluster sizes 23 2.6.2 Correction for the cluster size in helium droplets 25 2.6.3 Ar, Ne, nH2, and pH2 clusters 26 2.7 Discussion 30 2.7.1 Maximum cluster size 30 2.7.2 Intermediate cluster sizes of Ar, Ne, pH2, and nH2 31 2.7.3 Large cluster sizes of Ar, Ne, pH2, and nH2 34 2.7.4 Pickup order dependence for large H2 clusters 35 2.7.5 Evaporation and cooling rate of 4He droplets 37 2.8 Summary of the LIF results 43 3 Measurement of the v3 vibrational band of CH4 in Helium droplets . . 44 3.1 Motivation: A search for superfluidity in large supercooled H2 clusters . . 44 3.2 Depletion experiment techniques 48 3.3 Preparation for the depletion experiment 51 3.3.1 Installation of the CW nozzle 51 in Table of Contents 3.3.2 Performance check of the quadrupole mass spectrometer 54 3.3.3 Performance check of the CW nozzle 58 3.3.4 Sample and laser preparation 60 3.3.5 Gas Phase JR Spectrum of Methane 64 3.3.6 Depletion experiment setup 65 3.3.7 Preliminary Results 66 3.3.8 Depletion experiment summary 69 4 Conclusions and outlook 71 Bibliography 72 iv List of Tables 1.1 Condensation temperatures of 4He, H2, Ne, and Ar 3 2.1 Droplet size, max cluster size, and nozzle conditions for LIF measurements. 32 V List of Figures 1.1 Bose-Einstein condensation cartoon 2 1.2 Symmetric top and free rotation of OCS probe molecules 5 1.3 JR spectra of OCS-(oD2)N and OCS-(pH2)N clusters in helium droplets . 6 1.4 Pendular spectroscopy of the linear and polar molecule HCCCN 7 1.5 Free rotation of HCN probe molecules in Fermionic HD clusters 8 2.1 Mg-phthalocyanine and tetracene 11 2.2 Two types of laser-induced fluorescence (LIF) 12 2.3 Droplet machine chambers and the pulsed nozzle 14 2.4 The prior and post pickup methods 15 2.5 LIF spectrum of tetracene in the gas phase 17 2.6 Comparison of LIF spectra of tetracerie in the gas phase and in 4He droplets 18 2.7 LIF spectrum of single tetracene probe molecules in 4He droplets 19 2.8 Bare tetracene LIF spectrum and the phonon wing 20 2.9 Saturation check of LIF spectrum as a function of laser energy 21 2.10 Argon pressure dependence of the bare tetracene LIF signal intensity . . . 22 2.11 Prior and post cluster size determination (Ar, nH2 and Ne) 24 2.12 Tetreacene LIF spectra in droplets with prior and post Ar clusters 26 2.13 Tetreacene LIF spectra in droplets with prior and post Ne clusters 27 2.14 Tetreacene LIF spectra in droplets with prior and post nH2 and pH2 clusters 29 2.15 LIF signal spectral shift for Ar, Ne, and H2 clusters versus cluster size . . 33 2.16 Two possible tetracene configurations for prior pickup 34 2.17 Pickup order dependence of the LIF signal for large nH2 and pH2 clusters 36 2.18 Cooling rate assumptions for the prior and post pickup methods 37 2.19 Helium-4 droplet energy: bulk and surface vibration modes 38 2.20 Helium capture and emission probability and the Weisskopf formula . . 39 2.21 Numerically calculated helium droplet cooling curves 41 2.22 Heating of 4He droplets from the integrated specific heat 42 3.1 The Coriolis force as seen by a rotating observed 45 3.2 The Coriolis force for a rotating mass oscillating in the radial direction . . 45 3.3 Bending modes of a rotating triatomic molecule 46 3.4 Energy levels and selection rules for the stretching mode of CH4 47 3.5 Comparison of our experimental setup and one used by a previous group. 48 3.6 R(0), P(1), Q(1), and R(1) transitions of CH4 measured by Nauta and Miller 49 3.7 Experimental setup for the CH4 depletion experiment 50 3.8 The CW nozzle and nozzle compartment 51 3.9 The CW nozzle compartment and the closed cycle 4He fridge 52 3.10 Measurement of the flow rate of the CW nozzle 53 3.11 Thermometers and heaters of the nozzle compartment 53 vi List of Figures 3.12 The 4He droplet beam skimmer 54 3.13 The quadrupole mass filter 55 3.14 Quadrupole mass filter region of stability and resolution 56 3.15 High-q head and rf controller of the quadrupole mass analyzer 56 3.16 Filament, ion optics, and mass filter of the quadrupole mass analyzer . . . 57 3.17 Mass spectra before and after optimization 58 3.18 Bare tetracene LIF signals measured using the pulsed and CW nozzles . . 59 3.19 Helium droplet mass spectra for nozzle temperatures from 6.4 to 20 K . . 60 3.20 High resolution mass spectra for masses less than 45 amu 61 3.21 Chamber pressures as a function of nozzle temperature 62 3.22 Droplet and laser setup for the depletion experiment 63 3.23 Gas phase spectrum of the v3 vibrational band of methane using FTIR. . 65 3.24 Aculight laser measurement of the 1)3 vibrational band of gas-phase methane 66 3.25 R(0), R(1), P(1), and Q(1) branches of the 1)3 vibrational band of methane 67 3.26 Setup of all of the depletion experiment components 68 3.27 Preliminary depletion signals from CH4-doped 4He droplets 70 vii Acknowledgements First, I thank my supervisor, Dr. Momose for giving me the opportunity to work on an exciting research project in his top scientific laboratory. I also appreciate the generosity and guidance shown throughout the duration of my degree. I learned a lot from observing your perspective as an established and respected scientist. I also have to thank his wife for hosting our group in her home and providing delicious, comfortable, and relaxing dinners that healed my spirits. I would like to thank their dogs, Dave and Coo, for being extremely friendly and cheering me up. Thank you also to Dr. Walter Hardy for agreeing to read and comment on this thesis. I thank Dr. Tsubouchi, Dr. Miyamoto, and IVIs. Watanabe for answering my questions and encouraging me to form my own opinions about my research. I thank Eric to being my colleague and listening to my complaints. I thank En Watanabe for our nights out eating and drinking, for the time spent doing assignments together, but most importantly for being a close friend. Without a doubt, the person I have to thank the most is Dr. Susumu Kuma. His constant attention, kindness, openness, and extreme patience were of great value to me. I especially appreciate his efforts to educate me, not only about physics knowledge, but also how to enjoy physics and science. It is by no means an overstatement to say that without his support I would not have completed this project. I would also like to extend my appreciation to my previous supervisors: Dr. Stanley Yen, Dr. Scott Oser, Dr. Lorn Whitehead, and Dr. Michele Mossman for encouraging me to pursue physics and providing me with exciting projects. Thank you to my friend Keiko Ojima for eating out with me and helping me relax and enjoy the wide variety of food available in Vancouver. I need to send thanks to Yuna, Rika, Hide, and Kenneth for discussions regarding course work and having fun with me at my hot pot parties. I also thank Nicholas Baal for providing me with wonderful memories of life in Canada. I have also benefitted from teachers at college: Dr. Bates, Mr. Feldman, Mr. Joensen, Mr. Krauz, Dr. Perrott, Jakkie, Tamara, Philomena, Felicity, Tom, and Linda. They helped me start my education in Canada and showed great patience and kindness while I learned English. I would like to thank all of my family. My host family, Mom, Dad, Grandma, Joella, Niana, Karindi helped me start life in Canada and were always there for me. I need to thank my Mom for her love and the tremendous amount of support that she offered, more than I could have expected. To my Grandma and Grandpa and my Auntie and Uncle and family in Kobe thanks for the continued support and for providing a welcoming environment whenever I visit. I thank my Brother for helping me convince my family to let me studying in Canada and for sincere and honest discussions about my life in a manner that nobody else could. I am comforted by the cheerfulness and humor of my sister-in-law Misa. I am all the time touched by the heart-warming atmosphere of my Auntie and Uncle in Chiba. To my Dad, thank you for constantly taking care of me, even from across the Pacific Ocean. I can’t say enough about your constant encouragement and endless love. Finally, I thank my husband Jake for his continuous support and understanding. From the bottom of my heart, thank-you. viii Chapter 1 Tntro ion 1.1 Bose-Einstein condensation and superfluidity Superfluidity is a state of matter in which the consequences of microscopic quantum phe nomenon are dramatically revealed in the bulk properties of materials. Since its discovery in liquid 4He in 1937, superfluidity has continued to play a central role in contemporary condensed matter physics. Superfluidity has now been observed in a wide variety of sys tems: liquid 4He (boson), liquid 3He (fermion), liquid3He/4mixtures, electron gases of conventional (BCS) and unconventional superconductors, laser-cooled dilute alkali gases [2], and is widely believed to exist in the cores of neutron stars. While superfluidity is common to all these systems, the mechanism driving it varies considerably. Superfluidity is intimately linked to Bose-Einstein condensation (BEe), a state in which a large fraction of the bosons occupy the ground state of the system. The onset of BEC con densation occurs when the volume occupied per particle becomes equal to the temperature- dependent quantum volume given by the cube of the de Brogue wavelength. When this criterion is met, the wavefunctions of neighbouring bosons overlap and the system collapses into its ground state. Figure 1.1 shows a cartoon picture of the BEC of a gas. The focus of this thesis is the buildup to an experiment to search for superfluidity in yet another unique system - liquid hydrogen H2. Liquid H2 is a molecular system, and it is this fact that distinguishes it from the systems listed above. Because hydrogen is light, it has a large de Broglie wavelength and one expects to be able to access regimes where quantum phenomena are important. For a system of Bose particles, the BEC transition temperature T can be estimated by: = 3.31h2 (n)2!3 (1.1) mkB g where h is Planck’s constant divided by 2ir, g is the spin degeneracy of the particles, m is the particle mass, kB is Boltzmann’s constant, and n is the particle number density [3]. For example, in liquid helium-4 this equation predicts a BEC transition at T = 2.82 K (superfluidity in 4He occurs at 2.17 K). 1.2 Molecular hydrogen: ortho-Hydrogen and para-Hydrogen Before discussing the possibility of superfluidity in liquid H2, it is important to distinguish between ortho-hydrogen (oH2) and para-hydrogen (pH2). Molecular hydrogen is homonu clear since its only two nuclei are identical protons. Protons are spin-l/2 Fermions and hence the total molecular wavefunction 1bmoi must change sign under the exchange of the two protons, ‘ç/’moi(1, 2) = mot(2, 1) where 1 and 2 label the two protons. The total molec ular wavefunction can be separated into a product of four components = EVRbN where E, V, R, and N represent the electronic, vibrational, rotational, and nuclear spin 1 1.2. Molecular hydrogen: ortho-Hydrogen and para-Hydrogen BEC Vq =1 = h J2nmkT Vq = quantum volume lq = de Brogue wave length ) m = mass of particles k Boltzmann’s constant ______ ____ I 0 ITT) = (IU)+ ITT)) 4) . . •• .• Normal Gas, V/N >> vq Quantum Gas, V/N Vq ‘1 p _ ___ Figure 1.1: Left: A normal gas in which the effective volume occupied per particle is much greater than the quantum volume, the cube of the de Broglie wavelength Vq = 1. Right: When the quantum volume is of the same order as the physical volume, the wavefunctions begin to overlap. At this point the majority of the particles condense into the ground state. parts of the total wavefunction. The exchange of the two protons does not affect The symmetry of for the ground state of H2 is denoted by 1Eg. The superscript 1 indicates that the two electrons are paired in the singlet S = 0 state. The symbol is used to indicate that both electrons occupy u-orbitals so that the total orbital angular momentum around the internuclear axis is zero. Finally, the subscript denotes the overall parity of the state and g indicates even parity. Because both electrons occupy symmetric orbitals in the ‘g state their interchange leaves bE unchanged [4]. Only the rotational and nuclear spin wavefunctions need to be considered. When the proton spins are parallel they form the symmetric spin triplet state with a total nuclear spin I = 1: (1.2) whereas, when the spins align antiparallel I = 0 and the antisymmetric spin singlet state is formed: = (ITT)- ITT)). (1.3) 2 1.2. Molecular hydrogen: ortho-Hydrogen and para-Hydrogen n (x1028 m3) m (amu) g T (K) 4He 1.88 4 1 2.8 pH2 2.14 2 1 6.1 oH2 2.14 2 9 1.4 Ne 3.63 20 1 0.87 Ar 2.15 40 1 0.31 Table 1.1: Predicted Bose-Einstein condensation temperatures for 4He, oH2, pH2, Ne, and Ar. Proton exchange is equivalent to a rotation of the H2 molecule by r radians and in this case .‘ (_1)J/yR, where J is the rotational state. To preserve antisymmetry of the total wavefunction, J = 1,3,5,... must be odd when the proton spins are parallel (oH2) and J = 0, 2,4,... is even when the spins are antiparallel (pH2). At high temperatures normal- hydrogen (nH2) gas is 75% oH2 and 25% pH2 because the ratio of symmetric nuclear spin states to antisymmetric states is 3:1. 1.2.1 BECofH2 At 20 K, the mass density of liquid hydrogen is 70.99 grams/litre. The ground state of oH2 is J = 0 and I = 0 resulting in a spin degeneracy g = 1. The ground state of pH2, on the other hand, has nonzero rotational and nuclear spin states J = 1 and I = 1 resulting in a high spin degeneracy g = 9. This high spin degeneracy suppresses the Bose-Einstein condensation temperature of pH2. Table 1.1 gives the predicted T ‘s of oH2 and pH2 using Eq. 1.1. Argon and neon are also included in the table for future use. Studying superfluidity in liquid hydrogen is technically challenging because bulk liquid H2 solidifies when cooled below the triple point T3 = 13.8 K, which is well above the predicted Ta’s of both pH2 and oH2. To study superfluidity in liquid molecular hydrogen, the H2 must be supercooled well below the freezing temperature. The technique used in this thesis is to capture and rapidly cool clusters of H2 to 350 mK in superfluid 4He nanodroplets. The nanodroplet size can vary from to 108 atoms. Spectroscopy of molecules embedded in helium droplets have been studied by a number of groups [5, 6, 7]. This strategy has two main advantages. First, nucleation rates are greatly suppressed in small clusters. At low temperatures, nucleation is dominated by thermal fluctuations and for clusters of ‘-‘. atoms the characteristic nucleation time is estimated to be of the order of 1018 s [8]. Molecules at the surface of a H2 cluster are less bound than the interior molecules and are less likely to solidify. Since small clusters have a higher fraction of their molecules at the surface, the effective freezing temperature is reduced. Second, the helium nanodroplets rapidly cool the H2 clusters and provide a very clean environment free of nucleation sites [8, 9]. Molecules are inserted into the H2 clusters and are used as a probe for superfluidity on a microscopic scale [10, 11]. There have been extensive studies on doped hydrogen clusters, these include experimental, theoretical, and computational studies of H2 clusters made from free-jet expansions of pre-cooled H2 gas and clusters of H2 captured and cooled in 4He nanodroplets [8, 12, 13, 14, 15, 16, 17, 18, 19, 20]. Path integral Monte Carlo (PIMC) simulations have been used to study (pH2)N clusters with N < 22. These simulations 3 1.3. Previous studies of superfluidity in hydrogen clusters predict that these small clusters become superfluid when T < 2 K [14, 19]. It is the macroscopic properties of superfluidity that are most captivating and the focus of this thesis will be the design and construction of an experiment to search for signatures of superfluidity in large (N 1000) liquid H2 clusters. In the buildup to this experiment, several related preliminary studies were carried out. These studies are the topic of the next chapter. 1.3 Previous studies of superfluidity in hydrogen clusters Previous studies of very small H2 clusters with N = 14— 16 have claimed to have observed microscopic superfluidity [19]. To probe the supercooled liquid H2 for superfluidity, the rotational states of a dopant molecule were analyzed by infrared spectroscopy. The dopant molecule is introduced and becomes surrounded by H2. The H2 cluster-dopant molecule system is inside a 4He nanodroplet. If the surrounding H2 liquid is superfluid, the dopant can rotate freely and has a low moment of inertia. Conversely, if the H2 remains a normal fluid, the rotation of the dopant molecule is impeded by the friction it feels from the surrounding H2 and has a greatly enhanced moment of inertia. Therefore, rotationally resolved infrared spectra of the dopant molecule give clear information on the superfluidity of the surrounding H2. Perhaps the most cited evidence for superfluidity in liquid H2 comes from the helium droplet experiments of the Vilesov group [12]. The dopant molecule used in this study is the linear carbonyl sulfide (OCS) molecule. If the liquid H2 surrounding the dopant molecule is superfluid, a large decrease in the effective moment of inertia is observed and the OCS behaves as a linear molecule. Rotational excitations of the bare linear OCS molecules are governed by the selection rule LJ = ±1. If, on the other hand, the liquid hydrogen is a normal fluid the effective moment of inertia of the OCS probe molecule is significantly increased. The OCS molecule, dressed by the adjacent H2’s, adopts the rotational spectrum of a symmetric top molecule. In this case, the LJ = ±1 transitions are present and an additional /J = 0 transition is allowed. The /.S.J = —1 transitions are labeled as the P-branch, /.J = +1 the R-branch, and LJ = 0 the Q-branch. In the Grebenev et al. experiments, the absence of the Q-branch in the rotational spectrum of the OCS probe molecule is interpreted as a signature of superfluidity of the liquid H2. Figure 1.2 shows the allowed transitions for the bare and dressed linear OCS probe molecule. Grebenev et al. conducted an intensive spectroscopic study of 112 clusters in 4He droplets at 380 mK and low-temperature 150 mK droplets made from3He/4mixtures. They studied relatively small H2 clusters with the number of molecules varying from N = 14 — 17. For N < 17, the first shell of H2 molecules surrounding the OCS probe molecule is incomplete. Detailed rotational spectra were obtained from four different droplet systems: 1. OCS in pH2 and pure helium-4 nanodroplet. 2. OCS in pH2 and helium-4/helium-3 nanodroplet. 3. OCS in ortho-deuterium (oD2) and pure helium4 nanodroplet. 4. OCS in oD2 and helium-4/helium-3 nanodroplet. Superfluidity in the deuterium (2H or D) is expected to be suppressed for a number of reasons: larger mass, a mixture of nuclear spin states (1/6 I = 0 and 5/6 I = 2), and a high spin degeneracy [121. The rotational spectra obtained from these four droplet systems 4 1.3. Previous studies of superfluidity in hydrogen clusters Liquid H2 is Normal fluid Symmetric top ‘I, = ±l IQ-Branch I _____ No Q-Branch IO Figure 1.2: Left: When surrounded by normal fluid hydrogen, adjacent H2 molecules attach to the OCS resulting in a large net moment of inertia. The rotational spectrum is that of a symmetric top molecule in which the F-, Q-, and R-branches are all allowed. Right: In a superfluid 112 environment, the linear OCS molecule rotates freely with a very small moment of inertia and Q-branch (zJ = 0) transitions are forbidden. The absence of the Q-branch from the rotational spectrum is interpreted as a signature of superfluidity of the liquid H2. are shown in Fig. 1.3. In the pure 380 mK 4He droplets, only strong Q-branch peaks are resolved. The signal to noise is substantially improved in the 150 mK3He/4 droplets and the small P- and R-branches can be clearly resolved. At both temperatures, the OCS spectra from droplets with oD2 clusters show strong Q-branches consistent with spectra expected for a symmetric top molecule. The Q-branch is also observed for pH2 clusters in pure 4He droplets at 380 mK. It is only in the pH2 clusters at 150 mK that the observed OCS spectra do not reveal the zJ = 0 Q-branch. In this case, the spectra are consistent with linear molecule spectra with small moments of inertia. Grebenev et al. have interpreted these results as evidence for superfluidity in small pH2 clusters at 150 mK. There is, however, an alternative interpretation of the experimental results which does not invoke superfluidity of the liquid 112 clusters. This interpretation is the topic of the next section. r ixJ=_iWhi IIWhFJ=l Frequency of absothed radiation Superfluid 5 1.4. Free rotation of fermionic molecules C 0 C) C) > C) 2057.2 pH2 0.38 K pH2 0.15 K 2057.6 2058.0 2058.4 v (cm1) Figure 1.3: Comparison of JR spectra measured for OCS-(0D2)N and OCS-(pH2)N clusters in helium droplets. (A) oD2 in 4He droplets. The F- and R-branches are not easily resolved, however, there are strong Q-branch peaks for N =15, 16, and 17. (B) oD2 in3He/4 droplets. All three branches are easily observed. (C) pH2 in 4He droplets. Strong Q-branch peaks are observed for clusters of N =14, 15, and 16. (D) pH2 in3He/4droplets. Only for the pH2 clusters in the low-temperature droplets are the Q-branch peaks observed to vanish. An indication that the surrounding pH2 may have entered into a superfluid state [12]. 1.4 Free rotation of fermionic molecules The Vilesov study measured the rotational spectra of a probe molecule surround by bosonic pH2 and observed the absence of the Q-branch when T = 150 mK. This observation implies free rotation of the probe molecule, possibly caused by superfluidity of the surrounding hydrogen. Moore and Miller similarly studied rotation of a probe molecule, however it 0D2 0.38 K 0D2 0.15 K 2057.6 2058.0 2058.4 OCS(pH)in 4He 14 C15 16 I I n4HeflHe Qo16 14 6 1.4. Free rotation of fermionic molecules was surrounded by fermionic HD molecules. The RD molecule is a fermion and hence cannot undergo Bose-Einstein condensation into a superfluid state. They demonstrated the disappearance of the Q-branch of the probe molecule in the presence of Fermi-molecule clusters for certain values of N. They showed the probe molecule hydrogen cyanide (HCN) can undergo nearly free rotation when isotropically surrounded by RD fermions inside helium nanodroplets [21]. Moore and Miller used pendular spectroscopy which simplifies the infrared spectra by collapsing the P-, Q- and R-branch rotational lines to a single line. This simplification is achieved by the application of an external electric field. The polar probe molecule dipole moment orients along the direction of E-field such that the molecule can no longer freely rotate. As the field strength is increased, the rotational motion of the molecule is gradually transformed into vibrations about the electric field direction. Quantum mechanically, the rotational states split into pendulum states. The transformation from free rotor states to the pendulum states with increasing electric field is illustrated in Fig. 1.4. The figure also shows the JR spectra of cyanoacetylene (HCCCN) Free rotor states 0 Figure 1.4: Left: Jn zero electric field polar molecules rotate freely. The rotational states are that of a free rotor. As the electric field strength is increased, the polar molecule orients along the field direction and its rotational motion is restricted. At high field, the rotational structure of the molecule collapses to the pendulum states. Right: The infrared spectrum of HCCCN in 4He droplets in the presence of an electric field due to a voltage difference across parallel plates in the laser interaction region. The applied voltage varies from 0 to 10 kV. In zero field, the rotational structure of the HCCCN molecule is easily resolved into P and R-branches. The ZJ = 0 Q-branch is absent because the HCCCN is a linear molecule undergoing free rotation. As the field strength is increased, the P- and R-branches become weaker the Q-branch emerges. At 10 kV, the F- and R-branches completely vanish and the Q-branch is very intense [5]. in 4He droplets as a function of the strength of the applied E-field. Rotational structure of the HCCCN (P- and R-branches) collapse into a single pendulum peak near the Q-branch frequency. Miller and Moore studied the relationship between the isotropy of the HD solvent shell and the free rotation of the HCN probe molecule inside 4He droplets. Consider adding RD solvent molecules to a helium droplet doped with a single HCN probe molecule in zero 5 Pendulum states I HGCCNn He Droplets Pendular E peak 10.00 kV @—Q-branch Ema Rotational structures E 3327.0 3327.5 7 1.4. Free rotation of fermionic molecules electric field. When the number of RD molecules is small (N 1 — 5, for example), the HCN experiences an anisotropic HD-HCN pair potential and there is a preferred orientation for the HCN. As a result, the HCN cannot freely rotate. As the number of RD molecules added increases they start covering more of the angular space surrounding the the probe molecule and the interaction potentials are more evenly distributed about the HCN. At a certain point, RCN molecule starts feeling a quasi-uniform potential in all angular directions and the motion of the RCN decouples from the motion of the HD molecules. When the condition of a quasi-uniform potential is met, the HCN can undergo nearly free rotation. This decoupling transition occurs at, or near to, the point where the first shell of RD molecules encircling the RCN closes. Therefore, in zero field, the probe molecule can freely rotate only when the first solvent shell is very nearly complete. As stated above, in an applied field the HCN molecule aligns with the field direction and its rotation is impeded so that a single pendular line is expected for any number N of RD molecules. Figure 1.5 shows the measured JR spectra of HCN in HD clusters for N=8 to 14 in zero applied electric field and at high field. The high field spectrum shows pendulum peaks for all Figure 1.5: The bottom spectrum is of HCN surround by an HD cluster of size N = 8, 9,. . . , 14 in a 4He droplet in a strong external electric field. The structure of the rotational states collapse into singular pendulum states. The pendular peaks are observed for all values of N. The top spectrum is taken an the same droplet system in zero electric field. The Q-branch vanishes at N = 12 and 13, and indication of nearly free rotation of the probe molecule as the first HD shell surrounding the HCN closes [21]. values of N that fall approximately where one would expect to find the Q-branch in a zero field measurement. Indeed, the zero field measurement does reveal clear Q-branch peaks for N = 8, 9, 10, 11, and 14. What is significant is that the Q-branch peaks for N = 12 and 13 3301 3302 3303 3304 3305 Wavenumber (cm’) 8 1.4. Free rotation of fermionic molecules are absent. Moore and Miller argue that at N = 12 and 13 the first shell of HD molecules surrounding the HCN is complete and gives rise to an isotropic potential that allows the HCN to undergo nearly free rotation. A detailed zero field study of the R(O)-branch was made for N = 12 to confirm that the rotational spectrum of the HCN probe molecule agrees with that expected for a linear molecule. These results parallel those of Vilseov [12] study, however Moore and Miller have demonstrated the disappearance of the Q-branch in 4He nanodroplets doped with fermionic HD clusters which cannot Bose condense into a superfluid state. In a separate, but related, study Moore and Miller demonstrated that the probe molecule HF can also undergo nearly free rotation when isotropically surrounded HD fermions inside helium nanodroplets [22]. The two studies of Moore and Miller conclude that the disappearance of the Q-Branch implies free rotation of the probe molecule, but that free rotation does not require super fluidity of the surrounding molecules. Free rotation can be induced when the surrounding environment of the probe molecule is isotropic. These experiments show that the results of the Vilesov group can be interpreted without invoking superfluidity in the hydrogen clusters. 9 Chapter 2 Tetracene Laser-Induced Fluorescence 2.1 Motivation The Vilesov study described in §1.3 investigated microscopic superfluidity in very small (N < 20) H2 clusters [12]. The Miller study described in §1.4 examined free rotation inside Fermionic HD clusters of the same size [21, 22]. In both cases, the H2 clusters were very small, just barely completing the first layer surrounding the probe molecule. To study bulk properties of superfluidity, which are arguably the most captivating for the scientific community, our group have been working towards the search for superfluidity in large (N > 1000) liquid H2 clusters. Very large clusters are spherical and for H2 molecules, only 40% of the molecules make up the surface of the spherical cluster [23]. The bulk of the cluster is made up of the remaining 600 interior H2 molecules. Thus, when compared to the clusters discussed in sections 1.3 and 1.4, surface effects are expected to be greatly suppressed in the larger clusters studied in this thesis. In the previous work by our group, we studied the laser induced fluorescence (LIF) spectra of Mg-phthalocyanine (Mg-Pc) attached to clusters of up to 900 H2 molecules inside 4He nanodroplets. Spectra from droplets with Ar clusters were also obtained in a similar manner for comparison because the Ar clusters are expected to be rigid at 0.38 K [5, 101. Two types of droplet systems were produced by adding the cluster species before or after the Mg-Pc pickup. When the cluster species are picked up before the Mg-Pc, the cluster species forms inside the droplet and then the Mg-Pc is added to the droplet. If the formed cluster is fluid-like, then the Mg-Pc penetrates the cluster layer and sits at the center of the cluster inside of the droplet. When the cluster species are picked up after the Mg-Pc, the Mg-Pc enters the droplet first and then the cluster species start forming around Mg-Pc. If the formed cluster is fluid-like, the spectra measured by both pickup methods will be the same. The spectral shifts of the dopant molecule for both pickup methods were compared to the spectra obtained from the bare dopant molecule in helium droplets. These shifts were studied as function of cluster size. It was observed that the spectra obtained with the H2 clusters had no dependence on the pickup order of the dopant and the cluster molecules. This observation led to the key result that H2 clusters of the size studied are fluxional (liquid-like) at 0.38 K. Prior to experiments to probe for superfluidity in supercooled molecular hydrogen clus ters, the LIF pickup order experiments will be repeated to show that the results discussed above are independent of the choice of dopant molecule. In these LIF experiments the probe molecule tetracene (C18H2)will be used. Figure 2.1 shows that the tetracene molecule is smaller than the Mg-Pc molecule. Thus, for a fixed number N of cluster molecules, the tetracene molecule will be surrounded by a greater number of complete layers and allows 10 2.2. LIF for more sensitive tests of the fluid-character of the cluster species. Moreover, the pickup (a) (b) 0 0 0 0 00000 000000000 2A Figure 2.1: (a) The Mg-phtalocyanine (Mg-Pc) probe molecule. (b) The smaller tetracene probe molecule [24]. order experiments will be done using H2 and Ne clusters in addition to Ar clusters. Noble gases are used because they have completely filled electron shells and interact oniy very weakly with the probe molecule. Ne clusters were chosen because most of their relevant properties lie between that of H2 which is fluid-like in 4He droplets and Ar which is not. For example, the mass of Ne is 20 amu compared to 2 and 40 amu for H2 and Ar respectively. As shown in Table 1.1, the predicted Bose-Einstein condensation temperature of Ne falls between those of H2 and Ar. Perhaps most importantly, the depth of the intermolecular potential well of Ne is also intermediate between H2 and Ar. In temperature units, the estimated well depths for H2, Ne, and Ar are 34.8, 43.3, and 143 K respectively. For com parison the intermolecular potential well depth of helium is 11 K [5]. By measuring the LIF of tetracerie in the presence of these three cluster species, we can systematically study the cluster behavior as the cluster molecules become less quantum-like (short de Broglie wavelength due to large mass) and more strongly interacting (deep intermolecular potential wells). 2.2 LIF Laser-induced fluorescence (LIF) spectroscopy is one spectroscopic method used to study molecular structure. In our experiment, LIF spectroscopy is used to investigate the helium droplet system doped with tetracene and a cluster species. The LIF process involves re peated transitions of the tetracene probe molecule induced by laser radiation. A molecular system has electronic energy levels that split into vibrational and rotational sub-levels. Fig ure 2.2 shows vibrational energy levels labeled with quantum number v (i = 0, 1,2,...). .4 --- 2A 11 2.2. LIF In a two level system, double-prime notation refers to the (lower) ground state and the (a) (b) ------- v’=2 v2 Excited v’l ---_-__--- v’=l state - - V —o -I-— --- V —o ‘ Electronic I I I - - Ground -_-_-----V--- v”l ------ -- = State L_ V v”O L - V - Figure 2.2: (a) Transitions associated with fluorescence (disperse) spectra in a molecular system. The wavelength of a incoming laser is fixed to produce one absorption transition. Fluorescence resulting from decay processes to the lower allowed levels occur and are spec trally resolved (shown as red circles). (b) Transitions associated with excitation spectra in a molecular system. By varying the wavelength of the incoming laser, several different ab sorption transitions are produced in sequence. The total fluorescence is globally measured for each of these excitations. excited (upper) state are represented by single-primes. When a molecule at a distinct level within the lower electronic (ground) state absorbs a photon from the laser, it is excited to a new electronic state (absorption step). The energy difference between the two energy levels corresponds to the energy of the incoming photon. This state is unstable so that the species decays spontaneously to a lower energy level resulting in the emission of a photon, a process known as fluorescence (photon-emission step). The allowed emission transitions from the excited energy level to lower energy levels are determined by the quantum selection rules for the electronic dipole transitions. We can distinguish between two types of fluorescence spectra that are obtained using two basic approaches. In the first method, a species is repeatedly excited to the same state using a fixed wavelength laser. The resulting fluorescence spectrum is measured using a wavelength selective detection system and is known as fluorescence (disperse) spectrum. From this spectrllm, the allowed lower energy states are studied. In the second method, a range of excited states are sequentially accessed by tuning the wavelength of the laser. The total florescence signal over all emission wavelengths is recorded for each excited state. This type of spectrum is called the excitation spectrum and is used for studying the distinct upper states within the electronically excited state. In the droplet LIF experiments performed in this thesis work, the excitation spectra are studied [25]. 12 2.3. Experimental setup for LIF measurements 2.3 Experimental setup for LIF measurements Helium nanodroplets are created by using high pressure (Po = 20 bar) to force pre-cooled 4He atoms through a cryogenic 0.5 mm diameter nozzle into a vacuum chamber [261. The nozzle used in this experiment is a pulsed nozzle which opens and closes repeatedly and is typically run at 10 Hz. The length of each pulse of the nozzle is 40-50 ps. The nozzle contains a valve (General Valve Division of Parker Instrumentation Corp.) equipped with a poppet sealed with a copper gasket and it is controlled the commercial pulse driver IOTA ONE (General Valve). This pulsed nozzle is connected to a closed-cycle refrigerator (Sumitomo SRDK-408D) which cools the nozzle body to a temperature T0 = 8 K. The actual temperature at the tip of the nozzle where the 4He gas exits is estimated to be 15 K and is based on the measured speed of the helium droplets, Vd = 350 rn/s [27]. The supersonic beam of atoms cluster and form into nanodroplets. These droplets al most instantly cool by evaporative cooling. The temperature of the 4He droplet is predicted to level off at 0.4 K for times larger than i0 s [5]. In our experiment 0.4 K is used as the 4He droplet temperature. Then the energetic 4He atoms evaporate from the droplet as it travels through the nozzle vacuum chamber where the droplet production takes place. The size of the helium droplet used in this experiment is 6 x for measurements with pH2, nH2, and Argon cluster species. After these measurements the droplet size appeared to be diminish probably due to a worn out poppet. The old poppet was replaced with a new one, the nozzle temperature was optimized at T0 = 6 K, and nozzle pressure remained fixed at Po = 20 bar. Under these conditions, the pulsed nozzle produced helium droplets of 2.9 x atoms. This is the droplet size used for the measurements made with neon clusters. The droplet size measurement is discussed in Ref. [26]. The complete experimental apparatus along with some of the individual components are shown in Fig. 2.3. After production, the4He droplets enter a neighboring chamber called the main chamber through a skimmer which eliminates droplets with off-axis trajectories. As depicted in Fig. 2.4, the droplets pass through three 15 mm long pickup cells located at 12 cm, 17 cm, and 22 cm respectively. The centre pickup cell holds a powder of tetracene molecules (C18H2)heated to a temperature of 130°C. This temperature has been shown to generate an optimal tetracene vapour pressure for capturing an average of one tetracene molecule per helium droplet [28]. The other two pickup cells are used for the cluster molecules, either high purity Ar (99.995 %), high purity H2 (99.995 %), or Ne. There are two pickup schemes used. In one scheme the first pickup cell (the cell before the tetracene cell) is loaded with the appropriate cluster species (Ar, H2, or Ne) and the droplets pickup the cluster species before pickup of the tetracene probe molecule. This pickup method is called “prior pickup”. For prior pickup the third cell is left empty. In the other scheme, called “post pickup” the first cell is empty and the cluster species is loaded in the third cell located downstream from the tetracene cell. Both the prior and post pickup schemes are shown in Fig. 2.4. During either loading stages the 4He droplets, which act as an inert superfluid background, will absorb Ar, H2, or Ne. When introduced into the helium droplet the cluster molecules cool very rapidly to 0.4 K. The two pickup cells are connected to gas lines that can be filled with Ar, H2, or Ne and the gas line pressure is adjustable to obtain the desired cluster size. Pressure gauges are installed for each vacuum chamber and gas line. The third, and final, chamber attached adjacent to and downstream from the main chamber is called the mass chamber. This chamber is equipped with a quadrupole mass analyzer which was used to align the droplet beam for the LIF experiments. The mass 13 2.3. Experimental setup for LIF measurements Sample Pick up - cells cells U Figure 2.3: Left: A schematic representation and a digital photograph of the three UHV chambers. The nozzle chamber is responsible for the droplet production and contains the pulsed nozzle system. The main chamber contains three pickup cells where the dopant and cluster atoms/molecules are added to the 4He droplets. The droplets are analyzed in the mass chamber. Right: Closeup of the high pressure nozzle. The top frame is a digital photograph of an old used poppet along side a new poppet. A ridge is worn into the old poppet where it seals against the nozzle. analyzer is used extensively in later depletion experiments and is discussed in greater detail in chapter 3. Low vacuum in all three chambers is achieved using rotary pumps. The nozzle chamber is then pumped using a diffusion pump. Both the main chamber and the mass chamber are pumped using turbo molecular pumps. At low nozzle temperatures, the droplet production rate is increased and in this case the droplet chamber is pumped in parallel by a diffusion pump and a mechanical booster pump. As seen in Fig. 2.4, the 3 mm diameter laser beam perpendicularly intersects the droplet beam in the main chamber 25 cm from the nozzle. As eluded to above, five different droplet systems were studied in the LIF experiments: 1. 4He droplets doped with tetracene 2. 4He droplets doped with tetracene and pH2 clusters Nozzle Main Mass Chamber Chamber Chamber Nozzle with Pick up cellspoppet LJ Nozzle with poppet - 15mm 0 12 17 22cm LDYC laser Nozzle with poppet Nozzle valve 14 2.3. Experimental setup for LIF measurements Prior pickup 0.7 cm — rm ri ri LIII Li nozzle skimmer Mg-Pc 1.5 cm LASER Post pickup ÷ I I I 0 3 25cm Figure 2.4: This figure shows the path of the 4He droplet beam and the relative positions of the nozzle, skimmer, the pickup cells, and the intersection point with the laser. The probe molecules are depicted as solid circles and the cluster molecules as open circles. Top: In the prior pickup method the cluster species is picked-up before the probe molecule. Bottom: In the post pickup method the probe molecule is injected before the cluster species. 3. ‘He droplets doped with tetracene and nH2 clusters 4. He droplets doped with tetracene and Ar clusters 5. ‘THe droplets doped with tetracene and Ne clusters. For droplets containing a cluster species, the LIF measurements were done using both the prior and post pickup methods. When a droplet is hit by the laser, the tetracene in the droplet is excited and laser induced fiorescence (LIF) is produced. The emitted light is detected by a photomultiplier tube (PMT) (Hamamatsu R2066) located approximately 30 cm above the intersection point of the laser and the droplet beam. The LIF light is focused by a collimating lens system onto the PMT. The system to study the dynamics of doped helium droplet beams discussed above was developed in Kyoto. This machine was initially used at Kyoto University and is now the primary droplet apparatus at the University of British Columbia [5, 26]. In the LIF experiments with Ar and H2, a Nd:YAG laser (Coherent, Infinity) was used to pump an OPO (Optical Parametric Oscillator [29]) laser (Spectra-Physics, MOPO-SL, repetition rate: 10 Hz, pulse width: 10 ns, and nominal line width: 0.2 cm’) and in some cases the Nd:YAG laser pumped a dye laser (Lambda Physik, SCANMATE 2E, repetition rir I I I 12 17 22 15 2.4. LIF of tetracene rate: 10 Hz, pulse width: 5 ns, and line width: 0.1 cm’). In the LIF experiments on Ne clusters, a new Nd:YAG laser (Surelight) was used to pump the dye laser. The LIF signal from the PMT was recorded using a Labview program written by Susumu Kuma. The pulse driver and the pump laser were connected to a pulse generator (Standford DG535) to synchronize the laser pulses and the gas pulse. The pulse generator opens the nozzle so that the 4He droplet is generated and then travels 0.25 m to the detection site below the PMT. The measured speed of the helium droplets was vd = 350 rn/s so that the travel time is approximately 700 ps. Typically, droplets are generated only after a pulse length greater than 145 ps is applied to the nozzle. The nozzle pulse length was chosen to be in the range 185-330 ps such that the effective driving pulse length is t = 40-185 us. Thus takes helium droplet 740-885 ps to travel from the nozzle to the detection site. The total delay time for the laser pulse was adjusted to match this total travel time of the droplet from the nozzle to the detection region. The delay time between the laser pulse and the nozzle opening was optimized by maximizing the LIF signal. 2.4 LIF of tetracene This section will discuss LIF measurements of tetracene. The goal is to compare the LIF spectra of tetracene in the gas phase to that of bare tetracene in 4He droplets. 2.4.1 LIF of tetracene in gas phase Figure 2.5 shows the LIF spectra tetracene in the gas phase for wavelengths spanning 4500 — 4250 A. These measurements were made by Even et al. by studying supersonic expansions of Ar seeded with tetracene [30]. In this study, the tetracene sample was heated to 220°C and used to seed an otherwise pure Ar gas. The mixture of tetracene and Ar undergo supersonic expansion through a 150 urn diameter nozzle at a nozzle pressure of 180 Torr. After traveling 5-7 mm, the beam of the mixture intersects a dye laser beam with a bandwidth of 0.3 cm1. The LIF spectra shown in the figure are normalized to the intensity of the laser power. Spectra of tetracene seeded using different carrier (Ar, Kr, and Xe) gases were carefully compared. Most of the observed spectral features are independent of carrier gas and are attributed to the bare tetracene molecule. Comparing the spectra of tetracene expanded in different diluents reveals that the peak at 4472 A (22361 cm—’) is clearly independent of the carrier gas and is identified as the vibronic transition from the electronic singlet ground state So to the first excited singlet state S1 with accuracy of ±3 A (±13 cm1) which depends on the accuracy of the calibration of the laser wavelength [30]. The position of this peak varies considerably among the different studies [30, 31, 32, 33]. The value used in our study is 22396.53 cm and is taken from Ref. [31]. The peak at 4410 A corresponds to the totally symmetric vibrational mode in the first excited electronic state and is also independent of the type of carrier gas. Thus the study of Even et al. showed that the two peaks at 4472 A and 4410 A are spectral features of a free tetracene molecule [30]. In units of inverse centimeters, the peak positions are 22396.53 cm1 and 22707.84 cm [31]. 2.4.2 Bare tetracene in 4He droplets The LIF spectrum of single tetracene molecules inside helium nano-droplets (N 6 x 105) was measured for wavelengths spanning 4405 A — 4510 A (22702 cm — 22172 cm’). 16 2.4. LIF of tetracene I __._______.J I_____ 4250 4300 43S0 4400 4450 4500 WAVELENGTh (A) Figure 2.5: LIF spectrum of tetracene in gas phase measured by Ref. [30]. The powder sample of tetracene was heated to seed a gas of Ar. This gaseous mixture underwent supersonic expansion through a 150 urn diameter nozzle. The peak at 4472 A corresponds to the electronic origin (excitation from the v” = 0 ground state to the v’ = 0 first excited state). The 4410 A peak corresponds to the totally symmetric vibrational excitation of tetracene. The resulting spectrum is shown in the bottom part of Fig. 2.6. The stagnation, or nozzle, conditions were Po = 20 bar and T0 = 8 K and the laser output energy was 80 pJ. The top plot of Fig. 2.6 is a repeat of Fig. 2.5. The bottom of plot of Fig. 2.6 shows the electronic band origin at 4484 A (22300.5 cm’) and the totally symmetric vibrational mode of the first excited state at 4422 A (22613.0 cm—’). Both peaks show broad tails that extend to low wavelength (i.e. to the blue) and are attributed to phonon wings discussed at the end of this section [28]. Our laser has not been properly calibrated. To get an approximate calibration, the electronic band origin measured by our group (22301.5 cm1)was compared to that measured by the Vilesov group (22293.5 cm’) [34]. Our laser wavelength is off by 7 cm from the excimer pumped dye laser (20 us long pulses at a repetition rate of 71 Hz and the linewidth of 0.5 cm’) used by Vilesov [34]. The electronic band origin of a the free tetracene molecule (22396.53 cm’) is shifted by —103 cm1 to 22293.5 cm when inside the 4He droplet. Figure 2.7(a) shows a detailed LIF spectrum of the electronic band origin of single tetracene molecules in 4He droplets. The nozzle conditions for this measurement were iden tical to those used previously (Po = 20 bar, T0 = 8 K, and laser energy 1 11J). The spectrum in the figure is a zero phonon spectrum consisting of two peaks at v = 22300.5 cm1 and v = 22301.5 cm1. The two peaks correspond to an electronic transition between the lowest vibrational states, namely the S0 ground state and S1 first excited state which are assigned the labels c and /3 respectively. The splitting of the transition into a doublet is interpreted TETRACENE cco *4 17 2.4. LIF of tetracene 4500 Figure 2.6: LIF spectrum of tetracene in the gas phase compared to the LIF spectrum of tetracene in 4He droplets. Top: LIF spectrum of free tetracene molecules cooled in a supersonic expansion of Ar at 180 Torr. (same data shown in Fig. 2.5). Bottom: LIF spectrum of single tetracene molecules embedded in 4He droplets. The stagnation conditions were P0 = 20 bar and T0 = 8 K and the laser output energy was 80 iJ. as being due to two different configurations of the helium atoms in the first shell surrounding the tetracene. Each configuration is characterized by a slightly different shift [28, 34, 35]. The 1 cm1 split is not seen in spectra for free tetracene molecules. In Fig. 2.8 the c and peaks are accompanied by a broad peak shifted to the right by approximately 5 cm1. This broad peak is labeled as the phonon wing (PW). It is due to compressional volume vibrations of the helium droplets and is excited when the electronic transitions of a molecule occur [5]. This PW is attributed to the roton characteristic of the elementary excitations of the superfluid 4He droplets [36]. The PW appears strongly in Fig. 2.8, but not in Fig. 2.7(a). The difference is the laser TETRACNE ccxx I Al 4250 4300 430 4400 4450 40O 4250 4300 4350 4400 4450 wavelength (A) 18 2.4. LIF of tetracene (a) 2000 1500 1000 500 0 (b) 0.12 0.04 Bare tetracene in He droplets 22700 Figure 2.7: LIF spectrum of single tetracene probe molecules in helium droplets. (a) The bare LIF measurement with no cluster atoms in the droplet. The peaks are due to transitions between the ground S0 state and the first excited S1 state. The transition splits into a doublet due to two different configurations of the first shell of 4He atoms surrounding the tetracene probe molecule. (b) A broader spectral range that includes the electronic band origin at 22300.5 cml and the totally symmetric vibrational state at 22613.0 cm. energy used to make the measurement. The intensity of the LIF spectrum due to single tetracene molecules in helium droplets becomes saturated for high laser energies as shown in Fig 2.9. In Fig. 2.7(a), the laser energy was 1 11J (below the saturation point) and the PW is not present. In Fig. 2.8 the laser energy was 120 pJ (well above the saturation point) and there is a large PW. The LIF intensity as a function of the laser energy was measured using P0 = 20 bar, T0 = 8 K, and v = 22301.5 cm* To vary the laser energy, various neutral density filters (0.19’o, 1%, 10%, 30%, 50%) were inserted in the path of the laser beam before it enters the main chamber. A 470 nm cutoff filter (Y-47) was placed in front of 22296 22298 22300 22302 22304 wavenumber (cm’) 0.08 0.00 22200 22300 22400 22500 22600 wavenumber (cm) 19 20 10 2.5. Size determination of the 4He droplets Figure 2.8: LIF spectrum of a single tetracene probe molecule in a helium droplet. This is a bare LIF measurement with no cluster atoms in the droplet. This spectrum includes the a- and /3-peaks, as well as the phonon wing (PW). the Hamamatsu R2066 photomultiplier tube (PMT). The laser power was monitored using a photodiode (UDT SENSORS 1ODP) placed where the laser exits the main chamber. The intensity of tetracene LIF signal was measured by the PMT. The LIF signal saturates for laser energies above 1 pJ. For the remainder of this thesis, all LIF measurements were performed at laser energies of 1 pJ. 2.5 Size determination of the 4He droplets The helium droplet size is determined by a Poisson measurement which is used to obtain the capture cross-section of the droplet. Then the liquid droplet model is used to determine the size of the droplet from the measured cross-section. In the Poisson measurement, the Ar pickup pressure dependence of the LIF signal from the tetracene is monitored. For this measurement the Ar gas was added, not just from the pickup cell, but from the whole of the main chamber. This was done because the pickup cell does not have a sensitive pressure gauge to monitor the Ar pressure precisely. The main chamber, on the other hand, is equipped with a sensitive ion gauge (NELVA PP98X033). Helium droplets are produced using the usual stagnation conditions of Po = 20 bar and T0 = 8 K and with a nozzle pulse repetition of 10 Hz. The droplet picks up tetracene and then the doped droplet beam is intercepted by the laser set to a fixed frequency of 22301.8 cm1,which corresponds to the centre of /3-peak of a single tetracene molecule in a pure 4He droplet (see Fig. 2.7). A cut filter (Y-46, Y-47, or Y-48), used to block low wavelengths, is placed in front of the PMT to reduce noise and ND filters are used to limit the laser power to ‘-j-’ 1 pJ. The LIF signal 50 40 30 0 22298 22300 22302 22304 22306 wavenumber (cm) 20 2.5. Size determination of the 4He droplets Photodiode Mass - . Main Nozzle I Pick up cells H Scanmate ___j N]J filters Figure 2.9: Left: LIF intensity due to single tetracene probe molecules in helium droplets as a ftinction of laser energy. These measurements were taken at v = 22301.5 cm1. Above a laser energy of 1 11J, the intensity of the LIF signal begins to saturate. Right: Setup used to make the saturation measurements. The neutral density (ND) filters were inserted before the laser beam enters the main chamber and were used to vary the laser power. The laser energy was monitored by a photodiode and the intensity of the LIF signal was measured by the PMT located above the main chamber (not shown in the figure). intensity was measured as a function of the pressure increase in the vacuum chamber due to the added Ar molecules [37]. The probability that one droplet captures N Ar atoms is given by the Poisson distribution: PN(Z) = (2.1) where Z is average number of Ar atoms captured by a droplet. The number of captured atoms is proportional to the Ar partial pressure, Z = X13Ar where the proportionality constant x is expressed as: ucapL /(Ve)+(vr) (22)X kBTV (Vj6) where cap is the capture cross-section, L = 0.22 m is the distance between the nozzle to the LIF detection point, kB is Boltzmann’s constant, and T is the temperature of the pickup chamber which corresponds to the temperature of the Ar gas [37]. The square root factor is a correction factor for the root-mean-square velocities of the droplet beam (Vje) and Ar atoms (V3r). The probability that a droplet captures no Ar atoms (N = 0) is P0(Z) = exp(—Z) = exp(—XPAr) exp(—PAr/r). Having rewritten x as r1, the capture cross-section can be reexpressed as: , I /2 — tBT / \VHe 1 23cap — (Vie) + (‘Vjr) Figure 2.10 shows the Ar pressure dependence of the LIF signal measured at ji = 22301.8 cm1 for 4He droplets with N=0. Keeping v fixed at 22301.8 cm1 guarantees that only LIF signals from droplets with a single tetracene and N = 0 Ar atoms are detected. 0.1 1 10 100 Laser energy (iJ) 21 2.5. Size determination of the 4He droplets 0 0 Pressure (xl 06 Pa) Figure 2.10: Argon pressure dependence of the LIF signal detected by the PMT. The data are fit to an exponential decay to extract r = 9.6 x i0 Pa’. The addition of Ar atoms or a second probe molecule will shift the 3-peak position away from the laser frequency. The data in the figure are fit to an exponential to extract a value for T, which is 9.6 x i0 Pa. The x-axis of Fig. 2.10 is the Ar pressure in the pickup cell. We assume that Ar pressure in the pickup cell is proportional to the Ar pressure in the main chamber. However, to measure the Ar pressure iii the main chamber requires the use of an ionization gauge. This type of pressure gauge produces enough electrons to damage the PMT. Thus, the LIF signals and Ar chamber pressure cannot be measured simultaneously. To avoid this problem, an Ar gas line from a compressed Ar gas cylinder attached to the side of the main chamber was monitored using a pressure gauge. As Ar gas was injected into the main chamber, the Ar chamber pressure was measured as a ftmnction of the Ar gas line pressure. Next, the LIF signals were measured as a function of the Ar gas line pressure which were later converted to the Ar pressure in the main chamber. Finally, we note that the calibration of the ion gauge depends on the type gas is being measured. In the case of Ar, the pressure read from the display must to be divided by a correction factor of 1.21. The average droplet speed was estimated from time of flight (TOF) measure ments. First, the TOF for droplets to travel from the nozzle to the LIF detection region in the main chamber was measured’. The TOF from the nozzle to the mass analyzer in the mass chamber was also measured. By taking the difference of the two time of flight measurements, and knowing the distance between the LIF detection point and the mass an alyzer, the speed of the fully formed and cooled droplets can be calculated. From the TOF measurements was calculated to be 350 rn/s. The root mean square speed of the ar ‘The time for the LIF signal to travel from the droplet to the PMT can obviously be neglected. 14 12 10 8 4 2 100 200 300 400 22 2.6. LIF results: H2, Ne, and Ar clusters gon atoms in the pickup chamber was calculated to be 400 rn/s using = V3kBT/m and T = 300 K. Inserting these numbers into Eq. 2.3, the capture cross-section is found to be cTcap = 1.5 X A2. Finally, the droplet size is determined from the cross-section using the liquid drop model [38]. Assuming the capture cross-section is the same as the total droplet cross- section: 1 cap = irR, where R0 = 222Ne A, (2.4) where R0 is the droplet radius and NHe is the average number of helium atoms. The cube of the prefactor 2.22 A is essentially the effective volume occupied by each 4He atom inside the droplet. Using this expression and crcap = 1.5 X A2, the droplet is found to contain NHe 3.0 X atoms. This was the droplet size measured immediately after moving the droplet apparatus to the new laboratory. The helium droplet size was increased by an order of magnitude to 2.9 x io atoms by improved the cooling of the nozzle [37]. 2.6 LIF results: H2, Ne, and Ar clusters 2.6.1 H2, Ne, and Ar cluster sizes For the LIF measurements of tetracene in the presence of H2, Ar, and Ne clusters, the spectral shifts are compared using the two pickup methods and as a function of the cluster size. To determine the cluster size in helium droplets for a given pickup cell pressure we again use the Poisson distribution. Consider, for example, Ar clusters. At a fixed pickup cell pressure FAr the average number of cluster atoms in a droplet Z, which is proportional to the pressure, is constant and the Poisson distribution can be written as a function of N: P(N) = .je_Z. (2.5) Recall that this distribution function gives the probability that a 4He droplet captures N cluster atoms. By definition, the average value of N is given by: (N) = Z = XPAr = . (2.6) The value of T is determined using the method discussed above and then the average cluster size (N) is set simply by adjusting cluster species pressure in the pickup cell. The quantity T depends on the pickup method and the species being captured. Thus, each time the pickup method or the cluster species is changed the Poisson measurement must be repeated. The results of all the Poisson measurements are summarized in Fig. 2.11. Poisson measurements for the argon species were done for N = 0, N = 1, and N = 2 using fixed wavenumbers. of 22301.8 cm1, 22263.4 cm1, and 22239.7 cm1 respectively. In the case of H2 clusters, the LIF signal was measured as a function of H2 pressure for N = 0 and N = 1 (twice). For Ne, only the N = 0 case was measured. For each cluster species, the pickup cell pressure was converted from the Ar gas line pressure in the manner discussed in §2.5. For the Ar Poisson measurement, a global fit of N = 0, N = 1, and N = 2 data sets was performed. The three functions shown in Fig. 2.11 were used with 7 fit parameters (yo, Yl, Y2, A0, A1, A2, x). The parameter x appears in all three functions. This x is the reciprocal 23 2.6. LIF results: H2, Ne, and Ar clusters 1500 - 1000 500 1 2 3 4 5 6 “oh (x106 Pa) t Prior t Post (xlO6Pa) (xlO6Pa) 7.5±0.2 7.6±0.4 6.0±0.7 5.1±0.5 2. 1±0.4 1.8±0.4 Ratio (Prior: Post) 1:1 1: 0.9 1: 0.9 N=1 N=2 Figure 2.11: The prior and post cluster size determination for Ar, nH2, and Ne cluster species. The Poisson analysis is used to extract x = l/T from global fits to the data. of r as discussed above. For nil2 clusters a global fit to three functions is also used, but the N = 1 function is used twice. For Ne clusters only one N = 0 function is used. 20 - 10 0 5000 4000 3000 2000 1000 12 20 I I I! Priori N=0 0 N=0K> N=1 0 NI 10 0 1 2 3 4 5 6 0 1 2 3 “oh (x105 Pa) Pth (x105 Pa) 2500 lnH2PoSt’ N=0I N=1 2000 zZ 0 2 4 6 8 10 12 14 “oh (x10 Pa) “oh (x104 Pa) 160 I I I I I 8 Ne PostNe Pnor \QN0QN=0\0N=0ON=0 4 4. 2 0I•0— I 0 5 10 15 20 2 4 66 8 10 POh(x10 Pa) 0 Ar nFL Ne N =0 Fit functions y0+A0e0 y1+A1(X PCh)e pCh)e T 24 2.6. LIF results: 112, Ne, and Ar clusters The table at the bottom of Fig. 2.11 shows the results for all of the r determinations. The value of r changes for post and prior pickup methods, however the ratio of the two values should be the same for all cluster species. The prior:post -r ratios for different cluster species agree within experimental error. Using the values of r, the measured pickup cluster species pressure, and Eq. 2.6, the average cluster size (N) can be calculated. 2.6.2 Correction for the cluster size in helium droplets The cluster size determination discussed in the previous section neglects the decrease of the droplet size upon pickup of the cluster species due to evaporative loss. Suppose that in the helium droplets there is an average cluster size N, which is set by the pressure P in the pickup cell. If the average cross section of the droplets is u(P), then the average size of clusters is: N(P) = Af(P)dP, (2.7) where A is a constant assumed to be proportional to the length of the pickup region and the pickup efficiency. If the number of 4He atoms lost from the droplet due to the pickup of a single cluster atom is a constant a, then the droplet cross-section can be written as: a(P) = B(no — aN(P))2”3, (2.8) where B is proportional to the density of the helium in droplets and n0 is the average size of droplets before introduction of the cluster species. Combining Eqns 2.7 and 2.8, leads to: dN = ABdP. (2.9)(no — aN(P))2/3 With these definitions the ratio no/a represents the maximum possible cluster size that would completely evaporate the 4He droplet. The normalized droplet size can then be written as x = N(0)/(no/a). Rewritten in terms of x, Eq. 2.9 becomes: 2/32 = ABdP, (2.10) n0 (1—x)/ or: dx 2 = A(Bn3) = Au(O)dp = dy. (2.11)(1 — x) /3 no/a no/a From Eq. 2.8, Bn0 = o(0) corresponds to the average droplet cross-section in the absence of cluster atoms, or equivalently the average cross-section neglecting evaporative losses from the pickup process. The important quantity is y which represents the normalized cluster size while ignoring evaporative losses. This differential equation can be solved by making the substitution z = (1 — x)’/3 such that: 1 dx dydz=_(12=—--. (2.12) The initial conditions are set by considering an empty pickup cell. This situation corre sponds to P = 0 and requires that the average cluster size N(0) = 0, and by extension x = y = 0. By definition, z = 1 when x = 0. With the given initial conditions, Eq. 2.12 is trivial to integrate and yields: z=—y/3+1, (2.13) 25 2.6. LIF results: H2, Ne, and Ar clusters which, when rewritten in terms of x, is: (2.14) For example, suppose that the Poisson measurement for nH2 is completed such that the cluster size dependence on the pickup cell pressure is set. Next suppose that at the chosen operating pressure the cluster size is determined to be (N) = 370 molecules when evaporative losses of the droplet are neglected. The maximum cluster size will be discussed in §2.7.1, for this example assume that (Nmax) = 480. In this case, the normalized cluster size in the absence of evaporation is y = 370/480 = 0.77 and the normalized droplet size including evaporation is x = 0.59. Finally, the average cluster size with evaporative losses is (Neva) = 0.59 x 480 = 280 molecules [37]. 2.6.3 Ar, Ne, nH2, and pH2 clusters In the following discussion, the cluster sizes (N) picked up by the helium droplets were estimated using the methods outlined in the previous sections. Figure 2.12 shows LIF spectra of tetracene obtained after the capture of argon atoms using both the prior and post pickup methods. i ________ I I <N>=184JA4 = 11111 <N> = 21 <N> = 6 B&e I I 21600 21800 22000 22200 22400 22600 wavenumber (1) Figure 2.12: Tetracene LIF spectra in the presence of Ar clusters of various sizes for both prior and post pickup methods. The observed spectral shifts are different for the two pickup methods and in all cases are larger for post pickup of the cluster atoms. The cluster sizes and the pickup method are indicated in the figure. Both spectra show two peaks which are assigned to vibronic transitions between the electronic singlet ground state S0 and the first excited singlet state S1 of tetracene. For droplets containing bare 21600 21800 22000 22200 22400 22600 wavenumber (cm’) 26 2.6. LIF results: H2, Ne, and Ar clusters tetracene with (N) = 0, the peak at v = 22301.8 cm1 corresponds to the band origin of the bare tetracene, which is an electronic transition from the lowest vibrational state 5o to the first excited vibrational state S1. The peak which is shifted to higher frequency by about 300 cm is identified as an excitation of totally symmetric vibrations in the Si state [36j. The spectra measured for prior and post pickup of Ar show broad peaks with line widths of 100 — 200 cm1. The prior and post pickup peaks have different shifts with respect to the band origin for all values of (N). For (N) = 180 the prior and post pickup peaks are shifted by —200 cm1 and —600 cm respectively. The observed spectral shift increases as the Ar cluster size increases. The spectrum at (N) = 20 for post pickup shows three peaks. The third peak is not seen in the prior spectrum. Figure 2.13 shows the LIF spectra of tetracene measured for Ne clusters from (N) 0 to 300 atoms for both prior and post pickup. I ________ I I I I ieroaL1 I <N> = <N> = <N> <N> = E <N> = 7 Bare I I I 21800 22000 22200 22400 22600 22800 21800 22000 22200 22400 22600 22800 Wavenumber (cm1) wavenumber (cm’) Figure 2.13: Tetracene LIF spectra in the presence of Ne clusters of various sizes for both prior and post pickup methods. Above (N) 30, the prior pickup peak positions have a very weak dependence on the cluster size. In contrast, the post pickup peaks continue to exhibit enhanced frequency shifts as the cluster size is increased. Both pickup methods show more spectral features at intermediate cluster sizes, presumably due to different cluster configurations. For both prior and post pickup, when (N) < 10, there is slight shift to higher frequency by approximately 10 cm* For (N) > 10, all the peaks are shifted to lower frequency. For prior pickup, the maximum shift for the largest cluster is 30 cm. For comparison, the maximum shift for the post pickup is 100 cmi. For the post pick, the peaks continue to shift further as the cluster size is increased. However, in the case of prior pickup, the peak positions do not vary significantly for (N) = 30, 120, or 300. For intermediate cluster sizes, both pickup methods reveal more spectral structure. Specifically, both of the dominant 27 2.6. LIF results: H2, Ne, and Ar clusters peaks adopt nearby satellite peaks which are most likely due to different configurations of the cluster atoms. Figure 2.14 shows LIF spectra of tetracene measured for several different nH2 and pH2 cluster sizes. The nH2 spectra shifts for both the prior and post pickup methods are very similar for all cluster sizes. The maximum shift for both pickup methods is about 500 cm1. Both sets of pH2 spectra are again very similar and have maximum shifts of approximately 460 cm1. In fact, there are no significant features that distinguish between prior or post pickup orders or between nH2 and pH2. These results from H2 clusters differ from those obtained from Ar and Ne clusters and a discussion of the implications of these observations will be taken up in the next section. 28 2.6. LIF results: H2, Ne, and Ar clusters 22600 21600 21800 22000 22200 22400 22600 wavenumber (cm’) I pH2 Posti <N> = 2500 <N>=1600 <N>=770 <N> = 470 <N> = 150 <N> = 50 Aq410 <N> = bare1 I I I nH2 Priori <N> = 1900 I I lnHzPosti i I <N> = 2500 <N> 100 <‘>=o <N> =1470 <N>=170 __/tw/\q <N> = 30 bare I I 21600 21800 22000 22200 22400 wavenumebr (cm ) <N> 1500 <N> = 700 I <N>=470 <N> = 150 <N> <N> = 3 bare I 21600 21800 22000 22200 22400 22600 21600 21800 22000 22200 22400 22600 wavenumber (cni5 wavenumber (1) Figure 2.14: Top: Tetracene LIF signal in the presence of nH2 clusters of various sizes for prior and post pickup. There are no distinguishing features between the two sets of spectra. Bottom: Tetracene LIF signal in the presence of pH2 clusters of various sizes for both prior and post pickup orders. Again the two sets of spectra are essentially indistinguishable. 29 2.7. Discussion 2.7 Discussion 2.7.1 Maximum cluster size When 4He droplets pickup the tetracene probe molecule and the cluster species, the thermal energy from the foreign species are passed to the droplets causing helium atoms to evaporate from the droplet surface. The maximum cluster size is the number of cluster species needed to cause the 4He droplet to completely evaporate. To estimate the maximum cluster size of a foreign species, the incoming energy of the the tetracene probe molecule and the cluster species must be considered [37]: 1. Energy brought by tetracene 2. Energy brought by cluster species (Ar, Ne, or H2) 3. Binding energy of cluster species 4. Binding energy between tetracene and cluster species (Ar, Ne, or H2) (1) Tetracene energy When tetracene molecule is picked up by the droplet its temperature is 405 K. Generally, a nonlinear N-atom molecule has a total of 3N degrees of freedom (DOF). Of these 3N DOF, there are 3 translational degrees of freedom, 3 rotational degrees of freedom and 3N — 6 vibrational degrees of freedom [39]. Tetracene is a nonlinear 30 (NC18H2 = 30) atom molecule consisting of 18 carbon atoms and 12 hydrogen atoms. Tetracene is a nonlinear molecule and so has 3 rotational degrees of freedom and 84 vibrational degrees of freedom. (3NC1SH2 — 6 = 3(30) — 6 = 84). Each degree of freedom contributes an energy of kBT/2, so that the total internal energy is 87kBT/2 = 1.2 x i0 cm. From the time of flight (TOF) measurement, the velocity of helium droplet is calculated to be 350 m/s and from the Maxwell-Boltzmann distribution for tetracene at 405 K, its rms speed is 210 rn/s. The average relative velocity between the velocities of helium droplet and tetracene sample is 2 2 1/2given by Vrel = (‘U’He + VC18H2) and the translational energy of the tetracene is: ¶vr2ei = (Vie +V18H2)= Ve + ICBT = 1.6 X cm1, (2.15) where VHe=35Om/s, Vi8H12 = 3kBT/m, and m = 228 amu is the mass of the tetracene. The total energy brought into a helium droplet on pickup of a single tetracerie is 1.4 x i0 cm. (2) Cluster energy In a similar way one must take into account both the internal and translational energy of each cluster species (Ar, Ne, H2). Ar, Ne, and H2 are all at room temperature when introduced into the droplet. The vibrational energy of H2 is neglected because its excited vibrational levels are not occupied at room temperature. The total energy absorbed by the helium droplet upon capturing a single cluster species is 520 cm1,410 cm1, and 530 cm for Ar, Ne, and H2 respectively. 30 2.7. Discussion (3) Cluster binding energy Next suppose that multiple cluster atoms or molecules (for example, N Ar atoms) are captured by the droplet. At these low temperatures, the 4He droplet is a quantum system due to its large de Brogrelie wavelength. The interaction between the dopant molecule and the surrounding helium is very weak, so that the droplet provides the foreign species an environment that is nearly equivalent to free space. The cluster atoms interact much more strongly with themselves and neighboring Ar atoms bind together. This process releases energy into the droplet equal to the Ar-Ar binding energy. The binding energies are estimated from the evaporative energy minus the kinetic energy whose values were taken from the CRC handbook [40]. The Ar-Ar, Ne-Ne, and H2-H binding energies are 450 cm1, 110 cm1, and 50 cm1 respectively. (4) Tetracene-cluster binding energy The binding of tetracene with cluster species also has to be taken into account. Again, consider argon clusters as an example. The first layer or shell of Ar atoms around tetracene contains 20 Ar atoms and they collectively release a binding energy of 1.1 x cm1 into the 4He droplet [41, 42]. The van der Waals distances of Ar and Ne are 3.76 A and 3.09 A respectively [5]. Thus the number of Ne atoms in the first layer is expected to be (3.76/3.09)2 x 20 30. Similarly, 24 H2 molecules are needed to complete the first shell around the tetracene. The interaction between the cluster species and the helium droplet is represented by an intermolecular potential well depth, which is proportional to the polarizability. The polarizability of Ar, Ne, and H2 is 1.64 A3, 0.396 A3, and 0.803 A3 respectively [5]. The binding energy between tetracene and a single Ar is 520 cm1. The binding energy between tetracene and a single Ne is therefore estimated to be 520 cm1 x (0.396/1.64) 130 cm1 and to be 255 cm1 for H2 [41]. The total binding energy between tetracene and the first solvation shell of clusters around tetracene is 126 cm1 x 30 3800 cm1 for Ne and 6100 cm1 for H2. The total energy delivered into a helium droplet is obtained by summing contribu tions (1) to (4). To determine the maximum cluster size of each foreign species the sum (1)+(2)+(3)+(4) is equated to the total binding energy of the droplet. From LIF measure ments with Ar clusters the helium droplet size was found to be 5.55 x [37]. A crude estimate of the maximum cluster size is then obtained from: 5 cm’(5.55 x 10) = 13809 cm1 + 10740 cm1 + N(447 cm1 + 517 cm1), (2.16) where 5 cm1 is the4He-e binding energy. For Ar clusters, this equation gives 260 atoms. The helium droplet size was increased to 2.9 x i0 for the the LIF measurements with Ne and H2 clusters and the maximum cluster sizes are estimated in the same way to be N1 2700 and NX 2500. For all LIF measurements with Ar and Ne clusters, the cluster sizes studied are much smaller than the maximum size estimated here. For H2, we studied clusters that were very close to [37]. The helium droplet size, maximum cluster size, and nozzle condition described in this chapter are summarized in Table 2.1. 2.7.2 Intermediate cluster sizes of Ar, Ne, pH2, and nH2 The spectral shifts of the tetracene LIF from the band origin are plotted in Fig. 2.15 as a function of cluster size (N). The plot includes Ar, Ne, and H2 clusters for both prior and 31 2.7. Discussion Ar H2 112 Ne (N) = 0 ‘-.- 470 (N) = 700 2500 Fig. 2.12 Fig. 2.14 Fig. 2.14 Fig. 2.13 Droplet size (x104) 5.5 5.5 29 29 Max cluster size 260 470 2400 2700 Nozzle Temperature T0 (K) 8 8 6 6 Nozzle Pressure P0 (bar) 20 20 20 20 Table 2.1: Summary of the droplet size, maximum cluster size, and nozzle conditions used in the measurements of tetracene LIF spectra. Small droplets (5.5 x 104) were used to study Ar and 112 clusters. Large droplets (29 x 104) were used to study 112 and Ne clusters. post pickup methods. The general characteristics of the observed spectral shifts can be explained using the following crude arguments. The transition studied in this experiment is from the electronic singlet ground state to the first excited singlet state So —+ S. The frequency of this transition is obviously set by the difference in energy between these two states. However, in the presence of a cluster species the energies of these states can be shifted by different amounts due to van der Waals interactions between the tetracene and the cluster. This interaction can be understood by considering two isolated neutral atoms that come into close proximity. The instantaneous dipole moment of one of the atoms produces an electric field at the site of the second atom. This electric field induces a dipole moment on the second atom. Likewise, the electric field from the second atom induces a dipole moment on the first atom. The interaction energy between the two induced dipoles is called the van der Waals interaction and is given by E 0 Ci8H2Ar/R6,wherec1812 is the polarizability of tetracene, cAr is the polarizability of Ar atoms, and R is the distance separating the two atoms [23]. The depth of the potential well for this interaction is proportional to the product of the two polarizabilities. The depth of the potential for the first excited state is larger than that of the ground state because the polarizability of the excited state is larger. In the excited state, the electron clouds of the tetracene have greater spatial extent and hence the charge distribution is more easily distorted in the presence of an external electric field. Now consider a droplet containing tetracene and an Ar cluster of N atoms. Next add one Ar atom to the droplet. There will be a van der Waals interaction between the single Ar atom and the matrix of tetracene-Ar cluster. Both the ground S0 and excited S1 states of the tetracene will be shifted in energy because of this interaction. However, because of its larger polarizability the S1 state is more strongly affected and there is an overall downward shift of the S0 —* S1 transition energy relative to the band origin. The shifts observed for Ar, pH2 and nH2 increase monotonically towards lower frequency for both pickup methods as the cluster size increases as seen in Fig. 2.15. For Ar clusters there is an abrupt change in the evolution of the spectral shift at (N) 20. Above 20, the spectral shift has a considerably weaker dependence on cluster size. Similarly, for pH2 and nH2 there is a smooth dependence of the shift up to cluster sizes of (N) = 20- 45 after which there is little change of the overall spectral shift. This abrupt change in the dependence of the spectral shift on the cluster size is an indicator that the first shell 32 2.7. Discussion C) Figure 2.15: Spectral shift of the tetracene LIF signal for Ar, Ne, and 112 clusters as a function of the cluster size. The open symbols are for prior pickup and the solid symbols for post pickup. The shifts due to 112 clusters are essentially indistinguishable. This fact is interpreted as a signature of the fluid-like nature of PH2 and nH2 clusters at 0.38 K. There is a large difference in the prior and post pickup spectral shifts due to Ar clusters and a smaller, but still distinct, difference when Ne clusters are used. It is concluded that neither the Ar nor Ne clusters show fluid-like behavior. surrounding tetracene is complete. The atoms/molecules in the second and the third shells are further away from the central probe molecule and therefore have much weaker van der Wall interactions (oc R—6). The observed size of the first Ar shell nearly matches the size of 20 atoms estimated in §2.7.1 [41, 42]. Also in that section, the completion of the first shells of P112 and nH2 clusters were estimated to require approximately 24 atoms. This number is comparable to the position of the kink seen in the spectral shift data from 20-45 molecules (atoms) corresponding to the completion of the first shell of molecules (atoms). The first shell of Ne was calculated to be approximately 30 atoms and the shift of Ne in the prior pickup appears to start saturating around 30 in the plot. However, the Ne data is the least convincing because of the relatively small shift compared to the signal-to-noise ratio and because it is the data set with the fewest data points. The LIF line widths for all cluster species and all cluster sizes are observed to be broad compared to those for (N) = 0. The cluster sizes (N) quoted in Figs. 2.12-2.15 are the average cluster sizes picked up by helium droplets. Due to the Poisson pickup statistics, there is a distribution of cluster sizes whose width is ±/S1. Roughly speaking, the spectra shown in the figures contains the peaks corresponding to the cluster sizes from (N) — v’N to (N) + /iSi which cause the measured peaks to appear as a single broad line [43]. In addition, for each cluster size there are many possible configurations for the cluster atoms/molecules 10 4 5 6789 100 <N> 4 5 6789 1000 33 2.7. Discussion that surround the tetracene. Each configuration could produce slightly different S0 —f S transition frequencies which would contribute to the broadening of the peaks [43J. Finally, when tetracene is electronically excited the lower frequency vibrations are also excited which will also contribute to the broadening. 2.7.3 Large cluster sizes of Ar, Ne, pH2, and nH2 Fig. 2.15 shows that for prior pickup the largest Ar cluster of 180 atoms results in a shift of 200 cm1 and for post pickup the shift is 700 cm1. The prior and post shifts due to Ne clusters of similar sizes are 30 cm1 and 100 cm1 respectively. For both Ar and Ne clusters we observed that the LIF spectral shift is not independent of the pickup order and that the dependence on pickup order exists for all cluster sizes. The dependence of the shift on pickup order can be explained by a difference in the configuration of tetracene with Ar or Ne matrices for the different pickup orders as described in Fig. 2.16. In the case of prior pickup, the cluster species are picked up prior to the sample (a) Prior pickup 0 QorQ Cluster TetraceneHe droplet species (b) Post pickup 0 Tetracene Cluster species Figure 2.16: The the prior pickup method, there are two possible tetracene/cluster configu rations. (a) In the prior pickup method the cluster species is picked up before the tetracene probe molecule. Initially, the tetracene sits at the surface of the cluster species. If the cluster is fluid-like, the tetracene will penetrate the surface of the cluster and migrate to the centre. If the cluster is not fluid-like the tetracene remains at the surface. (b) In the post pickup method the tetracene is picked up first and will always be at the centre of the cluster. molecule. The cluster forms in the helium droplet and then the tetracene is picked up and attaches to the surface of the cluster. On the other hand, the post pickup allows the helium droplet to pickup the probe molecule first and then the cluster species. The cluster forms around the sample molecule enclosing it deep within the cluster. For these two cases the 34 2.7. Discussion van der Waals interaction between the tetracene and the cluster atoms will be different and the two sets of measured spectra are expected to differ. The pickup order dependence has been previously studied in small clusters of Ar in 4He droplet experiments using HF and tetracene probe molecules [44, 45]. In prior pickup, the surface of the Ar or Ne cluster supports tetracene. In post pickup, tetracene is located at the center of the cluster. The spectral shift is determined by the difference in energy between the ground state and the first excited state. When the energy difference is compared in both pickup methods, it is inversely related to only the average cluster species-tetracene distance (cc R6) because the polarizabilities of the ground state and first excited states are the same in both pickup methods. For a fixed cluster size, the average distance of the prior pickup is greater than that of post pickup. As a result, the overall spectral shift of the LIF frequency in the prior pickup method is smaller than that in the post pickup method. It is clearly seen in the data that for Ar and Ne clusters the prior pickup shifts are less than the post pickup shifts. From this observation we believe that for Ar and Ne prior pickup clusters the tetracene molecule attaches to the surface of the cluster and does not penetrate into the cluster. We conclude that Ar and Ne clusters are solid-like in 4He droplets at 0.38 K. As discussed in the previous section, the polarizabilities of tetracene and the cluster species sets the strength of the interaction potential and the observed frequency shift of the LIF signal is believed to be approximately proportional to these polarizabilities. The distances between H2 molecules, Ar atoms, and Ne atoms in their solid forms are 3.78 A, 3.75 A, and 2.74 A respectively [46]. The interatomic distances are fairly similar, so, for the simple argument that follows, the mean distances between tetracene and the various cluster species are assumed to be nearly the same. To compare the interaction between tetracene and each cluster species the polarizabilities of the cluster species are needed and they are H2 = 0.8 A3, cZAr = 1.64 A3, and Ne = 0.392 A3. The shift for the largest 112, Ar, and Ne clusters in post pickup are 450-500 cm1, 700 cm1, and 100 cm1 respectively. The ratios do not quite correspond to the ratios of the polarizabilities, however the order of the shift is correct. 2.7.4 Pickup order dependence for large H2 clusters For the largest nH2 clusters the shifts are about 500 cm1 for both pickup orders. For large PH2 clusters the spectra shifts are also order independent and the values are approximately 450 cm1. For post pickup of H2 clusters, as discussed above, the probe molecule initially attaches to the surface of the cluster. However, in contrast to Ne and Ar clusters the sample molecule penetrates through the layers of the H2 cluster such that it is positioned nearly at the center of the cluster. Thus, the arrangement of the tetracene and cluster species inside the helium droplet are the same for both pickup methods. In conclusion, the independence of the pickup order of the H2 clusters implies that the nH2 and pH2 clusters are fluid-like in 4He droplets at 0.38 K. An alternative possible explanation is that the H2 cluster is initially solid and then melted by the energy absorbed from the tetracene molecule upon pickup. Once melted, the tetracene places itself near the center of the cluster before it has the chance to freeze again. This possibility is examined and then eliminated by the simple argument that follows. For Ar clusters of at least 5 atoms a clear difference in the shift is observed between the prior and post pickup methods. This implies that the Ar cluster has solid-like characteristics and that the tetracene is near the surface of the cluster for prior pickup. Thus, the tetracene probe molecule does not have enough energy to melt 5 Ar atoms when it reaches the cluster. 35 2.7. Discussion This explanation is supported by the assumption that tetracene releases most of its energy (405 K —* 1.4 x cm’) into helium droplet rapidly before it reaches the cluster and causes the evaporation of 3600 helium atoms. This cooling process is discussed in further detail in the next section. Because the fusion energy of Ar is approximately ‘- 100 cm’ per atom and a cluster of 5 Ar atoms does not melt, the tetracene cannot have more than 500 cm1 of energy when it reaches the surface of the cluster. Because the fusion energy of H2 is approximately 10 cm1 per atom, the tetracene could not melt more than about 50 H2 molecules. The data clearly show that even for H2 cluster sizes (N) >> 50 the observed spectral shifts for prior and post pickup are very similar. We conclude that H2 clusters are fluid-like in 4He droplets. A small difference in the shifts for both pickup methods is observed at around (N) = 250 — 2000 for both pH2 and nH2, as highlighted in Fig. 2.17. A possible explanation Prior pick up 14ot quite at the center Figure 2.17: The plot shows a slight difference in the spectral shift of the tetracene LIF signal for large nH2 and pH2 clusters. For prior pickup, the tetracene may not sit at the exact center of the cluster. A possible explantation is that tetracene behaves like an impurity to the fluid-like clusters so that solidification of the cluster is induced. for this observation is that the tetracene molecule may be regarded as an impurity in the H2 clusters. Solidification of the H2 cluster may be initiated by tetracene in the initially fluid-like environment. If this were the case, in the prior pickup method the tetracene is not at the center of the H2 cluster. There is a small difference between the nH2 and P112 spectral shifts for large (N) > in both prior and post pickup measurements. This suggests that the interaction between nH2 cluster and tetracene might be slightly different from the interaction between pH2 cluster and tetracene. Recall that nH2 includes both pH2 and oH2 in the ratio of 1 to 3. Despite this discussion, we firmly believe that pH2 and nH2 clusters are fluid-like iii helium droplets at 0.38 K. 2 3 4 56789 100 <N’ 36 2.7. Discussion 2.7.5 Evaporation and cooling rate of 4He droplets In this section the evaporation and cooling rates of4He droplets after pickup of the tetracene dopant molecule are discussed. In the prior pickup method the helium droplet first picks up the cluster (H2, Ar, or Ne) which is initially at 300 K. Then it is assumed that the cluster/droplet system rapidly cools back to 0.38 K via evaporation before picking up the tetracene molecule. In the post pickup method the helium droplet first picks up the tetracene molecule which is initially at 405 K. It is also assumed that the droplet rapidly cools back to 0.38 K before picking up the cluster. These assumptions are shown as a cartoon in Fig. 2.18. 1st Pick up He 300K droplet •.... Ar/Ne/Hz 0.38 K 0.38K 0.38K Figure 2.18: In prior pickup the droplet first picks up the cluster species and then rapidly cools back to 380 mK before picking up the tetracene probe molecule. In post pickup the order is reversed. The droplets absorbs the tetracene, cools back to 380 mK, and then picks up the cluster species. The first step towards verifying these assumptions is to estimate the evaporation rate of the 4He droplet, which then can be related to the cooling rate. Brink and Stringari calculated the cooling rates of pure 4He droplets, mixed3He/4droplets, and pure 3He droplets [38j. They studied helium droplets of sizes ranging from 102 to iü atoms at a temperature of 1 K. For their systems, the properties of helium droplets are mainly dominated by excitations of the surface vibrational modes. The droplet size used in our LIF study was 5.5 x iü and the Brink and Stringari study seems to be applicable to our droplets. In their study the three major points are considered: (1)the surface excitation energy of the 4He droplets, (2) the Wiesskpf formula (this formula was originally developed to calculate the emission probability of neutrons or charged particles from highly excited heavy nuclei), and (3) application of the Weisskopf formula to estimate the cooling rate of helium droplets. 2nd Pick up 405 K Tetracene — Prior Post 0.38 K I 0.38 K 0.38 K 300K 405 K 4 0.38K 0.38K 37 2.7. Discussion (1) Surface excitation energy Helium droplets in the ground state can be treated using the liquid drop model, a sphere of constant density. There are two types of elementary excitations of such a sphere, bulk vibrational modes and surface vibrational modes. In the plot of Fig. 2.19, the top black line represents the lowest bulk vibrational modes and the lower black line represents the lowest surface vibrational modes. The bulk vibrational modes are not excited until the 10 - I___.J I i. — — a) — I — T=037j( I I 10-i- I a) c.1_4 I zo 10-i I 101 102 i04 106 Number of He atoms in He droplet Figure 2.19: The top solid black line shows the energy of the lowest bulk vibrational modes. The lower black line shows the energy of the lowest surface vibration modes. The dashed blue lines enclose the region studied by Brink and Stringari where only surface modes are important. The hatched line at 0.37 K is the typical temperature of a 4He droplet [38]. The droplets used in our LIF measurements lie on the hatched line, but just to the right of the blue region at (N) = 5.5 x iü atoms. droplet temperature exceeds a few degrees Kelvin or until the droplet size becomes larger. The surface vibrational modes are lower in energy by about an order of magnitude. The spacing between the surface excitations is of the order of 0.1 - 0.4 K. Thus for their system, the properties of the helium droplets are mainly controlled by excitations of the surface vibrational modes, given by: Esurf = (2.17) where Esurf is average total thermal energy of all the surface modes, is constant that includes the surface tension, /3 = (kBT)’, and N is the number of helium atoms in the droplet. Lowest bulk modes — — I I I I I I I I I • I • I U I modes 38 2.7. Discussion Figure 2.20: The ratio of the probability for a N — 1 cluster to capture a single He atom to the probability of an N cluster to emit a single helium atom is equal to the ratio of the number of states available for capture to the number of states available for emission. The desired probability is (2) and the Weisskopf formula will be used to calculate it. the probability for capture and the number of available states for capture and emission are needed. We want to obtain the probability to form a compound droplet from a (N — 1)-atom droplet and a single atom enclosed in a volume Q. The mean probability W for an atom with an energy between and e + dE to be captured by an N — 1 droplet to form a N-atom droplet with an energy between EN and EN + dr is given by: W = u(EN,e)v (2.18) where o- (EN, e) is the cross-section for collision and v is the velocity of the atom before capture. The number of states available for the capture is denoted WN (EN). The number (2) Weisskopf formula To obtain the probability that a 4He atom evaporates from the surface of the droplet two processes have to be considered. The first is the formation of a droplet of N atoms from the absorption of a single atom into a preexisting droplet of N — 1 atoms and the second is the disintegration of a droplet of N atoms into a droplet of N — 1 atoms. The two processes are treated independently. The ratio of the two processes is given by the ratio of the number of states available for capture and the number of states available for emission as sketched in Fig. 2.20. To obtain the desired emission (evaporation) probability, labeled (2) in the figure, Capture Emission —I I N-i cluster with EN-I N cluster with EN . I — - N cluster with EN N-i cluster with EN-I Probability of the formation of N cluster (Capture) 1 Probability of the disintegration of N cluster to N- 1 cluster (Emission) 2 The number of The number of — states available states available for — for the formation : the disintegration of ofN cluster N cluster to N-i (Capture) cluster - (Emission) (3’ x 2) = ç3 39 2.7. Discussion of states available for the emission is given by the product of the number of N — 1 states that the initial N-atom droplet can decay into after emitting one atom wN_1 (EN_i) and the number of states available to the atom emitted into the volume Q in the energy range to € + de. Assembling these three components as in Fig. 2.20 leads to the Weisskopf formula for 4He droplet evaporation: m WN_1(EN_1)Wde = gu—e de, where EN_i = EN — E0 — e. (2.19) 7r WJ\T(EJ\T) Wd is the probability for an N-atom droplet with energy EN to emit one atom with kinetic energy between € and + dE yielding a N — 1-atom droplet with energy EN_i. The spin degeneracy of the emitted 4He atom is g = 1. The density of states of the helium droplet is denoted by w and P20 is the binding energy of a single 4He atom to the droplet. We are interested in the emission process in which one helium atom evaporates from the N-atom droplet to form an N — 1-atom droplet. To apply the Weisskopf formula to this problem EN must be large compared to E0. Statistical analysis of the evaporation process requires that there are many states available to the N — 1 cluster with energy EN — E0 and this condition is satisfied when EN >> Eo. For a helium droplet with N = 1000 and T = 1 K, EN is 39 K which is greater than E0 which is estimated to be 6 K in Ref. [38j. In our experiments, N 5 x 10 and EN is 2200 K, which is much greater than E0, estimated to be 7 K for our droplets. To evaluate the Weisskopf formula, the cross-section o- is assumed to be classical. We also assume that every helium atom that hits the (N — 1)-atom droplet is absorbed to form an N-atom droplet. By calculating the density of states from the surface excitations, Brink and Stringari arrived at an approximation to the density of states: WN_i /WN exp(). The chemical potential p. of the emitted atom becomes -E0 for T —+ 0. Now the Wd integral can be evaluated to obtain the evaporation rate F: E—E0 — = fwdE WN_i(E-EO (2.20) F = exp [—p] , (2.21) valid for EN >> E. This evaporation rate can be used to calculate the droplet cooling rate. For each emitted 4He atom the droplet loses energy E0 (binding energy). Combining the above result with the surface vibration excitation energy Brink and Stringari finally arrive ar the 4He droplet cooling rate: = 28mE0Texp [—p] , (2.22) valid for droplet sizes N =- 102 — i0 with initial temperatures near 1 K. This differential equation can be solved numerically to give temperature of the helium droplet as a function of time. (3) Cooling rate of He droplet The 4He droplet cooling rate, as calculated by Brink and Stringari, is plotted in Fig. 2.21 for N = 10 and with an initial temperature of 1 K [38]. The temperature of 4He droplet drops rapidly during the time interval t = 10_8 to 10’ s after which the cooling rate is nearly independent of the initial conditions. Droplets of this size cool to 0.38 K in about 10 seconds. 40 2.7. Discussion T [°K] — - 1 - Log t (see) —. -6 -5 -4 -3 -2 Figure 2.21: Helium droplet cooling curves numerically calculated by Brink and Stin gari [38]. The pure 4He droplets (solid curve) are expected to cool below 400 mK in 10 us. Our case: the cooling rate of 4He clusters Equation 2.22 can be applied to the droplets in our experiments. First consider the prior pickup case. The energy delivered to the droplet includes the thermal energy of the cluster species and the cluster binding energy. For a cluster of 100 argon atoms, the total energy is 1.9 x 10—18 J. For a cluster of 200 H2 molecules, the energy absorbed by the droplet is 2.3 x 10—18 J. The initial temperature of the 4He droplet is 0.38 K [47] and we want to estimate the temperature rise of the droplet due to the pickup of the cluster species. The specific heat capacity of liquid 4He is shown in Fig. 2.22. An estimate of the temperature change of the droplet due to the absorption of the cluster species can be made by numerically integrating the specific heat data from 0.38 K up to a final temperature T such that: / CvdT = Eciuster, (2.23) JO.38 K where Eciuster equals 1.9 x 10—18 J for 100 Ar atoms and 2.3 x 108 J for 200 H2 molecules. This procedure gives T = 2.16 K for the Ar cluster and T = 2.18 K for the H2 cluster. By using Eq. 2.22, or referring to Fig. 2.21, the droplet is expected to cool back down to 0.38 K in 4.7x i0 s. The sample cell of the cluster species is separated from the tetracene pickup cell by ‘-j.’ 5 cm and the speed of 4He droplet is 350 rn/s. Thus, it takes 1.4x i0 s for 4He droplet to reach the second pickup cell. During this travel time, the droplet has ample time to cool to 0.38 K. Recall that this is the cooling rate calculated assuming only surface vibrational modes. Our droplets (N = 5.5 x 10 and T 2 K after pickup) are above the cutoff for bulk vibrational modes and the actual cooling rate may be modified. As the helium droplet cools, some helium atoms evaporate from the surface. Each atom that evaporates from the droplet takes away an energy E0 given by [38]: E0 —a —a8N’, (2.24) 41 2.7. Discussion 70 40 0 20 rdD 10 0 0.0 Figure 2.22: Heat capacity of liquid 4He as a function of temperature. The data were obtained from the website of Russel J. Donnely [48]. The shaded grey area represents the energy to heat the liquid from low temperature to 1.77 K. where a = —7.15 K and a8 = 6.95 K. For our droplets, E0 7 K and is only weakly dependent on N. To dissipate the energy added by absorption of a cluster species, roughly Eciuster/E 4He atoms must evaporate. For a cluster of 100 Ar atoms this corresponds to 1.9 x 4He atoms and 2.4 x iü atoms for a cluster of 200 H2 atoms. Now consider the second pickup stage. When entering the tetracene pickup cell, the temperature of the 4He droplet is 0.38 K and its size is reduced to 3.6 x iü (3.1 x 104) atoms for a cluster of 100 Ar atoms (200 H2 molecules). Pickup of the tetracene adds 4.9 >< i0’ J (4.9 x 1019 J) to the droplet. This energy includes the thermal energy of the tetracene and the binding energy between the tetracene and the first layer of cluster atoms (molecules). Equation 2.23 can be applied again and shows that the droplet will be heated to 2.0 K (applies to Ar and H2 clusters). The final doped-droplets are detected in a region separated by 8 cm from the tetracene pickup cell. The TOF is 2.3>< i0 s which gives the droplet plenty of time to cool back down to 0.38 K. For post pickup, the order is reversed. The 4He droplet picks up the tetracene probe molecule and the droplet must absorb the internal and kinetic energy of the tetracene EC18H2. As discussed in §2.7.1, the total energy absorbed is 2.75 x i0’ J. This pickup heats the helium droplet to 1.77 K. Before reaching the next pickup cell the droplet cools back to 0.38 K and losses 2.8 x i0 4He atoms due to evaporation. Consider picking up a cluster of 100 Ar atoms. The Ar thermal energy, the Ar-Ar binding energy, and the binding energy between the tetracene and the first layer of cluster atoms must all be taken into account. When this is done, the Ar cluster adds 2.14 x 1018 J to the droplet. A cluster of 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Temperature (K) 42 2.8. Summary of the LIF results 200 H2 atoms adds 2.5 x 10—18 J. In both cases the droplet is heated to just above 2 K and has more than enough time to cool to 0.38 K before being intercepted by the laser beam. During the cooling the droplet will evaporate 2.6 x i0 atoms. This analysis is valid provided that the droplet can be properly treated as a sphere with a constant density (the liquid drop model). Moreover, the evaporation rate is only valid when surface vibrations dominate. Our droplets are just at the point where bulk vibrations are likely to be important. 2.8 Summary of the LIF results In this experiment Ar, H2, and Ne clusters with tetracene as a probe molecule were studied in helium-4 droplets at 0.38 K to investigate their fluidity by detecting the LIF signal of tetracene. Two pickup methods were used to produce two types of droplet systems: droplets that pickup the cluster species before the probe molecule and droplets that pickup the probe molecule before the cluster species. Interaction of the tetracene with the cluster species shifts the LIF peaks with respect to the peak positions of the bare tetracene. The spectral shifts from the Ar and Ne clusters are not independent of the pickup order and this observation suggests that tetracene molecule does not penetrate Ar or Ne clusters at 0.38 K. We, therefore, conclude that the Ar and Ne clusters are not fluid-like at 0.38 K. In contrast, the spectra obtained from tetracene with nH2 and pH2 clusters are independent of the pickup order, suggesting that the tetracene can move through the layers of the H2 clusters to position itself at the cluster centre. This result indicates that the H2 clusters remain fluid-like at 0.38 K. 43 Chapter 3 Measurement of the 113 vibrational band of CH4 in Helium droplets 3.1 Motivation: A search for superfluidity in large supercooled H2 clusters The previous experiments were designed to observe if Ne/Ar/H2clusters are fluid in helium droplets at 0.38 K. The results showed that Ne/Ar do not behave like a fluid, but that H2 is fluid-like at 0.38 K. The goal of this methane depletion experiment is to try to observe su perfluidity of molecular hydrogen in 4He nanodroplets by analyzing the rotational states of a dopant molecule. Our candidate dopant is CH4. Methane is a good probe molecule because it interacts weakly with hydrogen. Before experiments with droplets containing both CH4 and H2, experiments with CH4 only are attempted to test the apparatus and to compare our results with those obtained by Nauta and Miller [1]. These authors studied the rota tional and vibrational dynamics of methane in helium nanodroplets. For LIF measurement of tetracene with Ar/Ne/H2 in helium nanodroplets, the suitable frequency range is optical and ultraviolet. The superfluidity experiment with methane uses the rotational-vibrational transitions that are in the infrared frequency range. Coriolis force and splitting When considering the vibrations and rotations of a molecule, the vibrational angular mo mentum L must be taken into account. This vibrational angular momentum is related to Coriolis forces. Before discussing the Coriolis forces for a molecule, we first consider the simpler, but analogous, system of a ball moving on a rotating disc. Suppose that a ball rolls radially outward from the center of a rotating disk. To an external observer the ball rolls along a straight path. However, in the frame of the disc the ball appears to move along a curved path as shown in Fig. 3.1 and therefore appears to be under the influence of external forces. The radial component of the force is the centrifugal force and tangential component is the Coriolis force. Both of these forces are fictitious, or inertial, forces which arise because the observer is in a non-inertial reference frame [4]. As a second example consider a mass attached to a spring rotating about an axis with the opposite end of the spring anchored at the rotation axis as in Fig. 3.2. When the mass moves radially outward (stretching the spring), the Coriolis force opposes the motion of the rotation and the mass appears to decelerate to an observer in the rotating reference frame. On the other hand, when the mass moves radially inward the Coriolis force force acts in the same direction as the rotation and the mass appears to accelerate. This cycle repeats and the mass periodically accelerates and decelerates [4]. Finally, consider a linear triatomic molecule. A linear molecule has 3N — 5 vibrational degrees of freedom (plus 3 translational degrees of freedom and 2 rotational degrees of 44 3.1. Motivation: A search for superfluidity in large supercooled H2 clusters Figure 3.1: Top: To a stationary observer, the ball follows a straight line as it rolls across the rotating surface. Bottom: To an observer in the rotating frame the ball follows a curved path as if acted upon by external forces. Figure 3.2: A mass attached to a spring is rotating and oscillating in the radial direction. To an observer in the rotating frame, when the mass experience a Coriolis force. The the mass moves outwards it is deflected in the direction that opposes the rotation. When it moves towards the centre it is accelerated in the direction of the rotation. freedom). For example, in a linear triatomic molecule (N = 3), there are four normal modes: symmetric stretch, asymmetric stretch, and a doubly degenerate pair of bending modes (perpendicular to each other) [39]. If the molecule is rotating and its antisymmetric vibrational mode is excited as in Fig. 3.3, then the Coriolis force must be taken into account. In the antisymmetric stretch mode of the triatomic molecule as the bond distance separating one pair of neighbouring atoms decreases, the distance separating the second pair increases. The atom attached to the shrinking bond moves radially inward and experiences a Coriolis force that accelerates it in the direction of the rotation. The atom attached to the expanding bond experiences a 45 3.1. Motivation: A search for superfluidity in large supercooled 112 clusters i) Figure 3.3: Top: A linear triatomic molecule is undergoing antisymmetric vibration while rotating. To an observer in the rotating frame, the atom attached by the expanding bond is deflected against the rotation. Simultaneously, the atom attached by the shrinking bond is deflected along the direction of the rotation. The net effect is that the linear molecule ap pears to bend in the direction shown. Bottom: During the second half of the antisymmetric vibration the molecule bends in the opposite direction. The mixing of the antisymmetric vibrational mode with the bending mode, due to the Coriolis effect, lifts the degeneracy between the in-plane and out-of-plane bending modes. force in the opposite direction and as a result the linear triatomic molecule appears to bend in one direction. During the second half of the asymmetric stretch, the molecule bends in the opposite direction as shown in the figure. The result is that, due to the Coriolis force, a rotating linear molecule with an excited antisymmetric stretching mode will induce one of the bending modes of the molecule. This mixing of the stretching mode with one of the degenerate bending modes causes the degeneracy of the in-plane and out-of-plane bending modes to be lifted. This effect is related to the molecule’s vibrational angular momentum 1 which is associated with rotations about the internuclear axis of the molecule [4, 23]. The Coriolis force splits the degeneracy of the bending mode and the split is expressed quantum mechanically by the vector summation of R = J + 1. The quantum number R is the sum of rotational state J and vibrational angular momentum state 1. In our experiment we will study the v3 (v = 1) stretching mode of methane. This mode of CH4 in helium droplets was first investigated by Miller’s group [1]. For this stretching mode 1 = 1, 50 that R = J + 1 (this is the vector addition, so when J = 0, R = 1 and when J = 1, R 0, 1,2, and so on). The allowed transitions are governed by the selection rules /.R 0 and /J = 0, ±1 [49]. The possible transitions for various values of J are shown in Fig. 3.4. The P, Q, and R transitions label rotational transitions for LiJ = —1, 0, 1 respectively. The 46 3.1. Motivation: A search for superfluidity in large supercooled H2 clusters R=4 J=3 F° - R=3F F R=3=2 A iR r A R=1 V F A4 R=2 3=1 F°p A l- R= 1 3=0 Selection ruleSelection rule — IJ=0,±l t — — —J = 2 L P(2) Q(2) R(2) R— 2 ::= P(1)Q(i)R(1) R(0) Figure 3.4: Energy levels and selection rules for the P, Q, and R transitions for the 1)3 stretching mode of CH4. number given in the bracket describes the initial rotational state before the transition. For example, the P(1) transition was initially in a J = 1 state. For v = 1, the J = 1,2 and 3 states have three levels: top, middle, and bottom. The R transitions go only to the bottom of each J value and are labeled by F, the P transitions go to the top and are labeled by F, and the Q transitions go to the middle and are labeled by F° [50]. Miller’s group observed the R(0), P(l), Q(1), and R(1) transitions of the triply degener ate asymmetric C-H stretching vibration of methane in helium nanodroplets. In their study an expansion of helium gas at high pressure (40 bar) is used to produce helium droplets. The pressurized helium gas passes through 5-micrometer diameter nozzle which is cooled to 21 K. Nanodroplets with an average size of 2100 atoms are formed by a clustering process. The helium droplets then enter 8 cm long cell and are doped with CH4 molecules. The CR4 pressure was optimized so that the helium droplet absorbs a single CH4 molecule. After leaving the pickup cell, the droplets are exposed to a 50 mW F-centered laser beam. The laser path was interrupted by a chopper at approximately 250 Hz. The droplet beam passes between a section of two parallel mirrors used to make many laser-droplet beam crossings. This increases the excitation efficiency by roughly an order of magnitude. When the rotational-vibrational relaxation of CH4 molecule occurs, the helium droplet partially evaporates. A bolometer was used to monitor the decrease in the droplet beam intensity due to the evaporation. A phase sensitive detection enhanced the signal to noise ratio of the signal from the bolometer. A comparison of the Miller experimental setup and the one used in thesis thesis is made in Fig. 3.5 [1] 47 3.2. Depletion experiment techniques Figure 3.5: Top: The experimental setup used for the depletion experiment in this thesis. This is the same figure as Fig. 3.7. Bottom: Experimental setup used by Nauta and Miller to study the R(0), P(1), Q(1), and R(1) transitions of CH4 in 4He nanodroplets. The stark cells were not used in during the measurement [1]. Figure 3.6 shows the R(0), P(1), Q(1), and R(1) transitions measured by Nauta and Miller. In preparation for the experiments designed to search for superfluidity in supercooled molecular hydrogen, we first reproduced these same spectra using our depletion apparatus. 3.2 Depletion experiment techniques In this depletion experiment, Helium nano-droplets are produced by expanding ultra-high purity (99.995%) 4He gas at high pressure (20 bar). The 4He gas is forced through 5 im diameter nozzle cooled to 16 K by a closed-cycle refrigerator (Sumitomo SRDK-408D) and into the main ultra-high vacuum (UHV) chamber. A continuous wave (CW) cryogenic nozzle was used in this depletion experiment, rather than the pulsed nozzle that was used in the previous LIF experiments. The beam of helium atoms cluster and form into nano droplets. Under these nozzle conditions (Po = 20 bar and T0 = 16 K), the average size of the nano-droplets was estimated to be approximately 3000 4He atoms. This estimate was based on the dependence of the mean droplet size on nozzle temperature and pressure measured by J. P. Toennis [5]. These droplets undergo evaporative cooling and cool to 0.4 K in i0’ s [5]. The measured speed of the helium droplets is Vd = 350 rn/s and the Our experiment He droplet size: 3000 atoms P0= 20 bar T12K d=5jim 4He R.E. Miller Low temp Cluster Nozzle growth Mass Spectrometer Ii I] Mirrorêu ha D I[m ________ Laser Pick up Photon absorption Ionizer beam cell and evaporation 0 He droplet size: 2100 atoms P0 40 bar 8 cmT021 K d5 tm Pick-up Cell F-centered laser ‘50mW Liquid Nitrogen x-y translation Dewar and Shield Multi-pass/ Stark Cells 48 3.2. Depletion experiment techniques I II I I R(O) Q(1) P(1) R(1) 3005 3010 3015 3020 3025 3030 3035 3040 3045 Wavenumber (cni’) Figure 3.6: R(0), P(l), Q(1), and R(1) transitions of CH4 in 4He nanodroplets measured by Nauta and Miller 3.6. distance traveled during the cooling is approximately 3.5 cm. Next, the helium droplets pass through the first pickup cell containing methane (CH4) gas and absorb, or pickup, CH4 molecules. As discussed in the first chapter, the number of methane molecules absorbed by the droplets is set by the methane pressure in the pickup cell. Unlike the pickup order dependence experiment discussed in the first chapter, there are only two pickup cells in this experiment: one for methane and the other for hydrogen. The pickup cell previously used for tetracene was removed for this experiment. In the tetracene experiments, discussed previously, the sample is a solid which is heated to 130°C to increase its vapor pressure in the pickup chamber. Methane, on the other hand, is a gaseous sample which is loaded into the pickup cell from a compressed gas cylinder. In the experiments discussed in this chapter the 1)3 vibrational stretching mode of the methane is measured using infrared spectroscopy. In later experiments, pH2 will be added in a second pickup cell to search for signatures of superfluidity in the molecular hydrogen. After absorption of the methane probe molecules, the nanodroplets are exposed to a laser beam which propagates in the direction opposite to that of the molecular beam. Absorbed photons excite the rotational and vibrational states of the probe molecule. These excited states relax and cause the evaporation of 4He atoms from the nanodroplet. As a result the droplet has a reduced 49 3.2. Depletion experiment techniques electron impact cross-section for ionization. The nanodroplets then pass through a mass spectrometer where they are simultaneously destroyed and ionized by an electron beam and the residual gas is analyzed. During the measurements the laser frequency is continuously scanned, and at frequencies which correspond to rotational-vibrational transitions of the CH4 probe molecule a depletion of the mass spectrometer signal is observed [5]. A schematic diagram of the experimental setup is shown in Fig. 3.7. Mass Spectrometer Mirror 4He Laser beam Figure 3.7: Experimental setup for the CH4 depletion experiment. 4He atoms cluster into droplets after leaving the 5 pm nozzle. The droplets pickup CR4 molecules in the pickup chamber and are then probe by an JR laser. Finally, the droplets are ionized and analyzed by a mass spectrometer. The pulsed nozzle was replaced with the CW nozzle for this infrared depletion exper iment because the helium droplets from the CW nozzle are about an order of magnitude smaller than the droplets from the pulsed nozzle. Using these smaller droplets results in an enhanced depletion signal [26]. For example, for droplets containing 30,000 4He atoms the absorption of a single incoming JR photon causes the evaporation of approximately 600 atoms and results in a depletion of the mass spectrometer signal by only 1.3%. Photon induced evaporation in smaller droplets will lead to a greater suppression of the mass spec trometer signal. Droplets containing 5000 4He atoms typically result in a 5% dip in the mass spectra. If the droplet size becomes too small, the probe molecule is not effectively cooled by the evaporative cooling mechanism. The method of infrared depletion spectroscopy is well established in the droplet research community. Nauta and Miller were the first to study the rotational and vibrational transitions in the v3 band of methane in droplets with an average size of 2100 helium atoms [5]. In this experiment, the average droplet size is 3000 4He atoms. This size estimate was based on published results from the Toennies group and from the nozzle conditions (nozzle temperature 16 K and nozzle pressure 20 bar) [5]. The energy of one JR photon is approximately 3000 cm1 and the dissociation energy of helium is 5 cm1. Therefore, the absorption of a single photon leads to the evaporation of approximately 600 Helium atoms. The ionization cross section is related to the number of atoms N by 0crn O N21’3. A decrease in Helium droplet size from 3000 to 2400 results in a decrease of the cross section, and hence, and a depletion of the mass spectrometer signal by 14%. He droplet size: 3000 atoms P0= 20 bar T12K d=5im CH4 Low temp Cluster Nozzle growth o Pick up Photon absorption Ionizer cell and evaporation 50 3.3. Preparation for the depletion experiment 3.3 Preparation for the depletion experiment 3.3.1 Installation of the CW nozzle The CW nozzle used in this depletion experiment was based on the design originally devel oped by Susumu Kuma with the support of Adrey Vilesov’s group. Helium gas is delivered from a compressed helium cylinder through a stainless tube up to the first stage of a closed- cycle refrigerator (Sumitomo SRDK-408D). The refrigerator consists of two stages, a top stage that is cooled to 40 K and a bottom stage that is cooled to 4.2 K [51]. After reaching the 40 K stage, the 4He gas line is changed to copper to promote good thermal contact between the 4He gas and the top stage of the fridge. The copper line is wrapped around the 40 K stage several times and tightly anchored in place at several locations. Before reaching the bottom cold stage the 4He line is switched back to stainless steel. Stainless steel is used because of its low thermal conductivity and avoids unwanted heating of the 4.2 K cold head of the fridge. The stainless steel 4He line terminates at the nozzle compartment which is mounted on the fridge cold head. In this way, the 4He gas is precooled before reaching the nozzle. The nozzle compartment and nozzle components are pictured in Fig. 3.8. The exit, He gas Copper hollow cylinder CW Nozzle Aperture(5 pm hole) Gasket // Gasket Figure 3.8: Top: Cartoon drawing of the nozzle compartment with a zoomed in view of the nozzle assembly. Bottom: (left) Digital photograph of the nozzle compartment and the fully assembled CW nozzle. (middle) The nozzle caps have been removed exposing the 2 mm diameter aperture with a 5 m pinhole. (right) Digital photograph of the aperture. or exhaust, end of the nozzle compartment is capped with the 2 mm diameter aperture 51 3.3. Preparation for the depletion experiment which has a 5 im diameter pinhole (TAAB A057-0005). Because this is a CW nozzle, there are no moving parts required such as those needed for the pulsed nozzle assembly discussed in the preceding chapter. The tiny aperture is tightly pinched between a 2 mm copper gasket and a copper cap. The essential parts required for the nozzle were carefully soni cated in methanol and then acetone. When the copper nozzle compartment was mounted on the 4.2 K cold head of the fridge, thermal contact was improved by applying a thin layer of Apiezon N grease between the two mating surfaces. Figure 3.9 shows the nozzle compartment mounted on the two-stage fridge. 1st stage of fridge 40 K 2r42 K He gas Stainless Copper tube hollow cylinder (nozzle compartment) Figure 3.9: Top: Cartoon drawing of the two-stage fridge and the stainless steel line deliv ering precooled high-pressure 4He gas to the CW nozzle. Bottom: Digital photograph of the nozzle compartment mounted on the cold head of the fridge. The fridge is inside the copper heat shield. Before mounting the nozzle compartment to the cold head of the fridge, the volume flow rate of helium gas from the CW nozzle was measured as shown in Fig. 3.10. The nozzle was pressurized to 20 bar with 4He gas and immersed in a beaker of methanol. The helium gas emitted from the nozzle was captured using an inverted 20 ml graduated cylinder which was initially filled with methanol. The cylinder captures helium gas, the methanol at the top end of the cylinder is replaced with the helium. The previous volume flow rate obtained using this CW nozzle obtained January 31, 2003 at Kyoto University was 0.43 ml/s (5 ml in 11.5 s). The flow rate depends on how tightly the copper cap is pressed against the aperture gasket. The copper cap is first made hand-tight and then further tightened using an adjustable wrench. Several attempts were made to match the flow obtained at Kyoto University. The best result was obtained by using the wrench to tighten the copper cap 20° further after it was hand tightened. This procedure produced a volume flow rate of 0.22 ml/s (5 ml in 22.2 s, January 6, 2009). Next, two heaters are installed to control the nozzle temperature and are shown in Fig. 3.11. The first heater is wrapped around the bottom of the 40K stage of the fridge and a 52 3.3. Preparation for the depletion experiment { He gas line Cylinder r cw I Nozzle Methanol 4 Nozzle Figure 3.10: Measurement of the flow rate of the CW nozzle. Left: The helium gas exiting the nozzle is captured by an inverted graduated cylinder immersed in methanol. Right: Digital photograph of the flow rate measurement apparatus. Heater ( 50 )Manganin wire -nd 30 cm (1.7 fl) stage CW of fndge Nozzle _-II Heater(50fl) Hegas I Temperature sensor D35664 Copper Temperature hollow cylinder sensor D35696 Figure 3.11: Left: Cartoon drawing of the heaters and thermometers for the bottom of the two-stage fridge and the nozzle compartment. Right: Digital photograph of the nozzle compartment with the heaters and thermometers installed. DC power supply is used to make rough adjustments of the nozzle temperature. The second heater is wrapped around the nozzle compartment and then extended by 30 cm of manganin wire. A Cryocon 34 temperature controller is used fine tune to nozzle temperature. Two silicon diodes are installed to monitor the temperature of the bottom and tip of the nozzle compartment. The silicon diode used for the tip of the nozzle is a Lakeshore D35664 diode and was calibrated by the manufacturer. A Lakeshore D35696 silicon diode was used at the bottom of the nozzle compartment. A custom calibration table was not provided for this diode and a standard calibration table for silicon diodes provided by Lakeshore was used. The 2 mm skimmer used for the pulsed nozzle was exchanged with a 0.8 mm skim mer. From the previous experiments by Susumu Kuma, it was determined that the 0.8 mm skimmer is the optimal size for this CW nozzle. Figure 3.12 shows the skimmer and skim mer assembly. After the installation of all parts, the base temperature of the nozzle was measured and found to be 6.24 K. The base temperature at the bottom of the nozzle compartment was 4.04 K. 53 3.3. Preparation for the depletion experiment Nozzle Main Mass chamber chamber chamber T1 L cw Mirror Nozzle 2mm skimmé Figure 3.12: Top: This image shows the locations of the nozzle compartment and skimmer within the UHV chambers. Bottom: (left) Skimmer installation. (right) Comparison of the 0.8 mm and 2 mm skimmers. 3.3.2 Performance check of the quadrupole mass spectrometer Quadrupole mass spectrometer A quadrupole mass spectrometer is used to measure the depletion signal of methane cap tured by helium droplets. A quadrupole mass spectrometer consists of four parallel, elec trically conducting round rods separated by a distance 2ro. The two opposing rods are electrically connected and the two pairs have opposite polarity as in Fig. 3.13. A superpo sition of a DC potential U and rf potential Vcoswt, /2 = U/2 + V/2coswt, is applied to one pair of electrodes and —/2 is applied to the second set. Ions traveling along the axis of the quadrupole filter experience a hyperbolic electric potential given by: 2I(x,z)=—(x —z). (3.1) The on-axis y component of the ion velocity is constant, but the x and z components oscillate at frequency w. The equations of motion for ions with charge q and mass m in this potential are given by Mathieu’s equations: mr0 — —-o(t)z = 0. mr0 (3.2a) (3.2b) View from nozzle chamber Skimmer 54 3.3. Preparation for the depletion experiment Figure 3.13: Electrode configuration of the quadrupole mass filter. The axis of the filter is aligned with the b-axis which is into the page. The x and z motion of the ion is stable for certain values of the parameters a and b which are defined as: 4qU (3.3a) mr0w b 2qV (3.3b) mr0w2 The region of stability is shown as the coloured region in Fig. 3.14. The line of operation is defined by a straight line through (a, b) = (0, 0) with slope a/b = 2U/V. Ions with q/m outside of the region of stability have large amplitude oscillations and collide with one of the electrodes and are lost. Only ions with charge to mass ratios inside the region defined by Lb will reach the detector at the opposite end of quadrupole filter. The width of Lb, or the mass resolution, can be tuned by adjusting U/V and hence the slope of the line of operation. The centre value of the mass passed by the filter can be tuned (without changing the resolution) by changing U and V while maintaining a constant U/V ratio [23, 50]. Quardrupole Mass Analyzer: Frequency matching, calibration, and ion optics optimization As seen in Fig. 3.15, the quadrupole mass analyzer contains the three major units: quadrulpole controller, radio frequency power source, and high-q head. The quadrupole controller unit controls and monitors the operation of the whole system. The rf voltage applied to the electrode pairs is produced by the rf power source. In the high-q head unit the rf voltage is tuned to the desired level for mass filtering. The tuning is achieved using a high quality tuning transformer (high-q head). The rf potential transfer system contains a circuit con sisting of the high-q head inductor and the capacitance of the quadrupole mass filter. The frequency of the radio frequency power source is adjusted such that it matches the resonant frequency of the circuit. The resonant frequency is the frequency that transfers the highest rf voltage from the high-q head to the quadrupole filter. The transferred rf potential is maximized so that a wide range of mass is accessible for a fixed b given by Eq. 3.3b. This frequency matching (or impedance matching) was done by Susumu Kuma [52]. After the frequency matching, the mass spectrum of the residual gas in the mass chamber was measured under high vacuum conditions using the quadrupole mass analyzer. A typical +,o 55 3.3. Preparation for the depletion experiment 1.0 Figure 3.14: Plot of the dimensionless quadrupole mass filter parameters a verses b. The red line defines the line of operation and has slope a/b = 2U/V. Ions with masses that fall within the shaded region of stability will pass through the filter and be detected. The resolution of the filter is determined by Lb. VACUUM WALL QUADRUPOLE FILTER IGH-Q ‘ - EAD ( GROUND -- SELO CABLEOft. CABLE IF NECESSARY 9o I RADIO FREQUENCY 1 POWER SOURCE Capacitance of quadrupole mass filter Figure 3.15: This figure shows the rf controller and high-q head units of the quadrupole mass analyzer. mass chamber pressure is 10—6 Pa and is pumped by a turbomolecular pump (PFEIFFER VACUUM) and a liquid nitrogen cold trap. Usually the mass spectra in any vacuum system has strong peaks corresponding to mass 18 amu (H20) and 28 amu (N2). Thus our calibration of the mass meter dials on the front panel of QUADRUPOLE CONTROL was done by observing the H2O and N2 mass peaks in the mass chamber spectrum. [52] In the depletion experiment, before entering the quadrupole filter, helium droplets doped 0.3 0.237 0.2 0.1 0.0 0.0 56 3.3. Preparation for the depletion experiment with methane are bombarded by electrons emitted from a filament. The fragments of the droplets are ionized and are passed through the quadrupole filters to reach the detector. The ion optics are used to accelerate and focus the ions through an aperture and into the quadrupole filter. Then the ions are filtered at a desired mass or over a desired mass range. An electron multiplier is used as a detector located at the end of the analyzer. The schematics of the location of the ion optics are shown in the Fig. 3.16. Ion optics S and N Quadrupole mass filter M - - - L R s L Fo : Filament N Figure 3.16: The quadrupole mass filter, ionizing filament F0, and ion optics elements 5, N, M, L, and R. are used to direct the ions towards and then through the quadrupole analyzer. Ion optics M, L, and R act like a ion optic lenses so that the ions are focused during their flight to the quadrupole analyzer. Below is the optimization procedure for the mass spectrum analyzer: 1. Each of the ion optics elements are optimized such that the intensity of helium dimer (m = 8 amu) was maximized. 2. The LIF of tetracene in helium droplets and mass spectra of the helium droplets were measured as discussed in the next section. 3. Further optimization of the ion optics was carried out to increase the intensity of the methane (m 16 amu) peak in the mass spectrum of methane embedded in helium droplets. 4. The alignment of ion optics was finalized by observing the depletion signal obtained from methane in helium droplets. In Fig. 3.17, the intensity of the methane peak (m = 16 amu) increased by a factor of 102 after completing the optimization procedure. 57 3.3. Preparation for the depletion experiment i03 102 rI 101 10° Before optimization After optimization S=-72V S=-72V M=-38V M=-40V L=-50V L=-1OV R=+5V N=+5V N=+5V F =-55.5V F =-55.5V Figure 3.17: The mass spectrum shown in blue is measured after optimizing the intensity of helium dimer (m = 8 amu) and the mass spectrum shown in red is measured after completing the entire optimization procedure outlined above. 3.3.3 Performance check of the CW nozzle ElF of tetracene in helium droplets and mass spectra of helium droplets After exchanging the nozzle and skimmer, the LIF spectrum of tetracene in helium droplet was measured as a crude way of checking the installations. The LIF spectrum shown in Fig. 3.18 was measured with the 0.8 mm skimmer and the CW nozzle at T0=14 K and P0=20 bar. The Scanmate dye laser describe earlier was used for this measurement with a resolution of 0.1 cm1. Both the c and 3 peaks are present at 22300.7 cm1 and 22301.8 cm1 respectively (see §2.4.2). The spectrum was not normalized by the laser power because it is nearly constant for the short 3 cm1 scans. Both peak positions are comparable to those found in the previous spectrum obtained using the 2 mm skimmer and the pulsed nozzle. Next, a large number of helium droplet mass spectra were measured as a function of 0 10 20 30 40 Mass (u) 58 3.3. Preparation for the depletion experiment Pulse nozzle - -- CW nozzle Bare tetracene in He dropiets Bare Teteacene in He droplets with CW nozzte 20 15 10 22298 22300 22302 22304 22306 wavenumber [cm4] wavenumber (cm ) To = unknown (at this time no temp sensor) To = 14.0 K Po=2Obar Po=20bar Pulse Nozzle • CW nozzle 2 mm skimmer • 0.8 mm skimmer Figure 3.18: Left: LIF spectrum averaged over 10 scans measured using the pulsed nozzle operated at P0 = 20 bar and uses the 2 mm skimmer. The spectrum is similar to that originally measured using the pulsed nozzle. Right: LIF spectrum measured with the 0.8 mm skimmer and CW nozzle at T0 = 14 K and P0 = 20 bar averaged over 5 scans. The c peak is at 22300.7 cm1 and the /3 peak is at 22301.8 cm1. the nozzle temperature. When helium droplets enter the region near the filament in the mass chamber, they are ionized at an ionizing energy of Uei = 55.5 eV with a typical ionizer electron-beam current of ‘em = 0.3 — 0.4 mA. If the helium droplet production and the mass detection system are optimized, then a series of ionized helium (for example, helium dimer, helium trimer, and so on) are detected and a wide range of mass spectra is obtained from the helium droplet beam. Our measured droplet spectra should be comparable to those published by the Toennies group [53]. We measured the mass spectra over two mass ranges, a short range and a long range. For the short range the measured mass covers 0 to 45 amu and the long range sweeps over 140 amu. The resolution of the quadrupole mass analyzer was chosen by adjusting the L.m/m dial where /Xm/m = 0.126/(0.16784 — U/V) [52]. By adjusting /.m/m, the ratio U/V is varied which determines the mass resolution equivalent to b in Fig. 3.14. The ratio /m/m = 44 was chosen for the short range measurements and = 55 for the long range measurements. The sweeping repetition rate for both ranges was 10 Hz. Under these conditions, the peaks in the mass spectra are clearly separated. Mass spectra were taken at P0 = 20 bar with nozzle temperatures spanning 6 and 20 K and are shown in the Fig. 3.19 along with the corresponding spectra obtained by the Toennies group [53]. The spectra for nozzle temperatures from T0 = 9 to 15 K show a gradual decrease in intensity for m> 8 and no strong peaks are observed for m> 56 amu. There is also a slight decrease in the peak at m = 48 as temperature is decreased. Our spectra and the spectra measured by the Toennies group are most similar at 15 K. We believe that the temperature of the helium gas exiting the nozzle is at most 5 K off of the temperature measured by the diode sensor at the tip of the nozzle compartment. The mass spectra taken at T0 = 6.4 and 20 K look very similar to the residual gas spectrum taken with no helium droplet beam as averaged over 5 ...........N.. I 59 3.3. Preparation for the depletion experiment Figure 3.19: Left: Helium droplet mass spectra measured by Buchenau et al. with a nozzle pressure P0 = 20 bar and nozzle temperatures from 5.5 K to 20 K [53]. Right: Equivalent mass spectra obtained in our measurements using the 0.8 mm skimmer and the CW nozzle. highlighted in Fig. 3.20. Peaks at m = 4 (helium monomer) and 8 amu (helium dirner) are the only significant differences. During the mass spectrum analysis of the helium droplets, the pressure in the three chambers was simultaneously monitored. Figure 3.21 shows that pressure in the mass chamber is smallest for nozzle temperatures of 6.5 and 20 K. In the high-resolution short range mass spectra for Fig. 3.19, the intensity of the helium monomer and dimer peaks are weakest at T0 = 6.5 K, suggesting that this nozzle temperature is producing the weakest helium droplet beam. 3.3.4 Sample and laser preparation Laser and pickup cell alignment The middle pickup cell used for the tetracene sample in the previous LIF experiment was removed. The other two pickup cells were left in place: one is used as the methane pickup cell and the other is used as the hydrogen pickup cell. The two cells are positioned such that they are far from mass chamber so that the interaction time of the helium droplet with the laser is long. Before the two cells are installed, the alignment of the IR laser though the chambers is optimized. The JR laser used in the depletion experiment is an Aculight Argos Model 2400 periodically-poled Lithium Niobate (PPLN) optical parametric oscillator (OPO). This is a CW source that provides wavelengths from 2.3-3.9 urn with a P0 2.0 MPa U) U) C 0 U 0 C 0) (I) 1 101 101 0 C, 0.0 11) 0 101 101 Moss (omu) 10’ 10’ 0 20 40 60 80 Mass (amu) 100 120 140 60 3.3. Preparation for the depletion experiment P0=2.OMPa 102 - T0=20.OKI - 102 - T0=hi0Ki - ;;;, , I Ifl’ —: ‘11111111111111111111111 111111 1T5=12.512i - h Otis _.lII I 1111111111111111111 to2 I=9.5KI - ; I I I I I I I I I I I I I I I I I I I I I I I I I IT0 =6.4 r; Mass (ama) P0 = 2.0 MPa T=20.0KI - IIIIIIIIIiiiiHmIImHmImi to2 - (02 - IT0=t5.OKI - I _____ to2 Vo—125dI - 2 I o I :: : 102 Ir2=9SKj 0 ITr64 JC1 - to Reaidual gaam in mona chamberl S’s Figure 3.20: Left: Helium droplet mass spectra measured up to 140 amu with a nozzle pressure P0 = 20 bar and nozzle temperatures from 6.4 K to 20 K. This is the same data shown in Fig. 3.19. The mass spectra from the residual gas in the mass chamber with no droplet beam is shown as the black spectrum. Right: High resolution short range mass spectra to 45 amu. power output> 1 Watt at all wavelengths and linewidths <1 MHz. The laser output power is approximately 3 Watts over the range of wavelengths required for our experiment (near 3 itm) [54]. However, because the JR light is not visible, the alignment is difficult. One general way to do the alignment is to adjust the laser alignment using a helium neon laser. First, it must be ensured that the He-Ne laser passes through the chamber. Then the two pickup cells are installed such that the He-Ne laser goes through the 5 mm diameter holes in the pickup cells. After the alignment of the laser was set properly with the He-Ne laser, the two irises are put into place so that the He-Ne laser passes through them. Finally, to align the JR laser relative to the chambers and pickup cells, it is only necessary to verify that the laser passes through the two irises. The chamber-laser arrangement is shown in Fig. 3.22. There is a 2 mm2 diameter mirror mounted between the nozzle tip and the skimmer inside 100 10 102 101 too To’ to2 10’ 102 2- 0 cM .5 I 100 120 I0 too to 100 too 102 to’ 100 140 0 6 -a 10 0 20 40 60 80 100 120 140 Maaa (omu) Mesa (ama) 61 3.3. Preparation for the depletion experiment 6 8 10 12 14 16 18 20 T0 [K] Figure 3.21: Chamber pressures as a function of nozzle temperature for a nozzle pressure of P0 = 20 bar. Top: Nozzle chamber. Middle: Main chamber. Bottom: Mass chamber. the nozzle chamber. The mirror position is adjustable so that it can be put into or removed from the laser path. During the laser alignment the mirror is inserted between the nozzle tip and the skimmer and directs the laser towards a window in the nozzle chamber wall. When the laser is aligned properly the laser enters mass chamber, passes through the 5 mm holes of the pickup cells in the main chamber, goes through the 0.8 mm skimmer, hits the 2 mm2 mirror in front of the nozzle and is reflected out through the window of the chamber. I 16 14 12 10 8 6 Pnozzle 6 8 10 12 14 16 18 20 T0 [K] ‘C I 6 8 10 12 14 16 18 20 T0 [K] 51 I 4 3 I I I I I Pmassl P0 = 20 atm 2 I I I I I I I 62 3.3. Preparation for the depletion experiment HNclscr Nozzle chamber Middle cell removed. Mass chamber Gold Mirror Figure 3.22: Top: Schematic diagram of the chamber, cell, and laser arrangement. Bottom: (left) Digital photograph inside the main chamber. The red circle highlights the second cell which was removed for the mass depletion experiment. (right) Digital photograph of the optics used to direct the laser into the mass chamber. When the He-Ne laser passes centred through the chambers and the pickup cells the red He-Ne laser shines brightly out of the nozzle chamber window. Three gold mirrors are used to direct the laser into the mass chamber as shown in Fig. 3.22. The gold mirror reflects nearly 100% of the IR laser. The small window mounted on the mass chamber is made of calcium-fluoride (CaF2) and transmits wavelengths in the range of 0.15-9 m with nearly 100% efficiency. The window is tapered to prevent interference of multiply reflected JR light within the window. Once the laser alignment is completed, the two pickup cells are reinstalled. Both cells are set as close to the nozzle chamber as possible. Finally, the two irises are placed as hole marks for the final JR laser alignment and the chambers are closed. Next the methane pickup cell was prepared. A methane gas line is connected to the first pickup cell. The methane pressure is controlled and optimized so that on average 4He droplets absorb a single CH4 molecule. A crude estimate of the optimal methane pressure was made using knowledge from the previous LIF experiments. In the LIF experiments using the pulsed nozzle, the average droplet size obtained from the Poisson measurements Main chamber *- CW Skimmer Nozzle // 2nd cell is moved close to 1st cell Iris CaF2 Window (0.1 5um-9um) 63 3.3. Preparation for the depletion experiment was 3 x io 4He atoms. Also, the optimized neon line pressure for helium droplets of this size to pick up single neon atoms was 0.3 Pa. For the CW nozzle at a temperature of 16 K and pressure of 20 bar the helium droplet size is estimated to be 3 x The reduction in droplet size by a factor of 100 reduces the cross-section for pickup by a factor of roughly (1/100)2/3 = 0.046. This reduced cross-section can be compensated for by increasing the pressure in the CH4 gas line by a factor of 1/0.046, which requires to a methane gas line pressure of 7 Pa. A better determination of the 4He droplet size needs to be made from a Poisson measurement. 3.3.5 Gas Phase JR Spectrum of Methane Prior to the depletion experiment, the spectrum of the 113 stretching vibrational band of methane in the gas phase was measured using a technique called Fourier transform in frared spectroscopy (FTJR). This type of spectroscopy is based on a modified Michelson interferometer. The CW infrared laser beam is split by a beam-splitter. One beam travels to a fixed mirror and the other to an adjustable mirror. Moving the adjustable mirror introduces a path length difference between the paths of the two beams and introduces a time delay. Both beams are reflected back to the beam splitter where they interfere. The interference signal is measured as a function of the time delay (path difference, or position of the adjustable mirror). Once collected, the combined signal is called an interferogram. This interferogram has encoded in it detailed information about all the wavelengths present in the JR source. The interferogram is passed through the sample of interest before being detected. Some wavelengths in the JR beam are absorbed by the sample and others are transmitted. Fourier transforming the detected time domain interferogram converts the signal into a frequency domain absorption spectrum. The FTIR technique leads to a large enhancement in the signal to noise ratio compared to classic techniques which require prisms and filters to scan frequency. A high spectral resolution can be achieved by choosing large path differences between the two mirrors. Figure 3.23 shows the spectrum of the 113 stretching vibrational band of methane gas measured by Dr. Miyamoto from our group. The P and R branches shown in the figure are assigned by following the global analysis of a high-resolution infrared absorption spectrum of methane measured Ref. [55]. Our results and the high-resolution results agree within the experimental uncertainty of our measurement ( 0.01 cm’). Next, the R and Q branches of the stretching vibrational band of gas-phase methane were measured using the Aculight JR source. The setup is shown in Fig. 3.24. The methane gas filled sample cell is exposed to JR light from the Aculight Argos 2400 and the transmitted JR light detected using a diode. Scanning the wavenumber of the IR source is achieved using a coarse adjustment and a fine adjustment. First, the coarse adjustment is done by tuning the position of a periodically-poled nonlinear (PPLN) crystal located inside the laser system. This process is used to bring the wavenumber of the beam near the desired branch (R( 1), R(0), P(1), or Q(1)). Next, the voltage of the pump source for the laser system was swept from 0 to 80 V using an Agilent 33250A function generator and a FLC A400DJ voltage amplifier to scan the wavenumber of the laser over a 2 cm1 range. The diode signal and the sweeping voltage are sent to an AD converter and recorded by a computer program. Figure 3.25 compares the spectra measured by FTIR and by the Aculight laser. Attempts were made to measure the R(0), R(1), P(1), and Q(1) branches using the Aculight laser system. Each Aculight measurement shown represents only a single scan. The P( 1) mea surement is very noisy because the amplitude of this peak is small. Multiple scans and 64 3.3. Preparation for the depletion experiment 0 3.3.6 Depletion experiment setup FTIR High resolution Experiment IR spectrum of (cm-I) CH4 (cm-1) R(0) 3028.76 3028.752900 R(1) 3038.51 3038.499200 R(2) 3048.17 3048.153317 3048.169000 R(3) 3057.71 3057.688000 3057.727000 3057.760693 P(1) 3009.02 3009.011370 P(2) 2999.01 2999.060410 2998.994010 P(3) 2988.94 2988.795286 2988.932512 2989.033465 0(1) 3018.83 3018.824480 2980 3000 3020 3040 3060 3080 3100 venumber (cm4) Figure 3.23: Left: Absorption spectrum of the v3 vibrational band of methane in gas phase measured by FTJR. The resolution of the measurement is ‘- 0.01 cm1. Right: The peaks were assigned using the published high-resolution data found in Ref. [55]. Our measured peak positions agree with the published positions within experimental uncertainty. averaging are needed to extract a meaningful signal. The Aculight spectra do not match the FTIR spectra as wavenumber increases. This discrepancy occurs because the output wavelength of the Aculight system does not change linearly when low voltages are applied to the pump source. This problem must be solved before performing the full depletion experiment. After completing the optimization of the CW nozzle, sample, and laser the detection system the depletion experiment was setup. For the depletion experiment, mass signals greater than 6 amu are considered. A strong peak is expected at each multiple of 4 amu due to the helium monomer, dimer, trimer, and so on. As mentioned previously, a strong peak is expected at m = 18 amu due to H20. The peak at m = 28 amu (a cluster of seven 4He atoms) is enhanced because it is coincident with to an N2 peak. The peak at m = 16 amu is also enhanced because there are contributions from clusters of four 4He atoms as well as CH4. All of these features are clearly present in the spectra of Figs. 3.19 and 3.20. During the depletion experiment, the depletion signal is at most 3 — 5%, sO it is important to optimize the mass spectrum analyzer. A significant increase iii signal to noise is achieved by using a phase-sensitive lock-in detection scheme. Figure 3.26 shows the experimental for the depletion experiment which makes use of an optical chopper. The chopper is metal wheel with equally space apertures. When rotating, the chopper periodically interrupts, or blocks, the JR light from entering the mass chamber. When the JR laser is blocked, all of the CH4 doped helium droplets enter directly into the mass analyzer where they are destroyed and ionized by the electron beam and the fragments then detected by the electron multiplier. The mass analyzer controller allows the user to set the span of masses to be detected starting from some minimum mass. In this experiment the mass analyzer was set to detect all masses greater than 6 amu. 65 3.3. Preparation for the depletion experiment Function Generator Agilent 33250 A —— output x20 In/out converter -- Voltage amplifier FLC A400DI This configuration excludes the very strong helium monomer peak which would otherwise dominate the total mass signal. When the chopper allows the laser beam to pass through and enter into the mass chamber, the Cl4 in the 4He nanodroplet is excited. It quickly relaxes back to the ground state and causes some 4He atoms to evaporate from the droplet before it enters the mass analyzer. Therefore a small oscillation of the nanodroplet mass signal is observed at the chopper frequency. The chopper also supplies a reference signal for the lock-in amplifier. The electric current generated by the electron multiplier of the mass analyzer is fed into a pre-amplifier where it is converted to a voltage. This voltage is detected by the lock-in amplifier. A spectrum of the depletion signal is obtained by scanning the JR laser frequency during the measurement. A Labview computer program is used to record the measured lock-in detector signal and the laser power. When constructing a spectrum of data the depletion signal is normalized by the laser power [56]. 3.3.7 Preliminary Results The R(0) depletion signal peak for methane in helium droplets was observe with its peak po sitioned at 3029.05 cm1. This data set had a limited scan range that spanned 3029 cm1 to 3029.4 cm1. Future scans will make use of new laser components that will enable scans that cover 3 cm1 at a time. Preliminary results are shown in Fig. 3.27. This spectrum was measured with a nozzle temperature of T0 = 12.5 K and laser chopping at 130 Hz. The Laptop computer “USB 6009 lab view” Sample cell for CH4 -- L J AculightArgos 2400 j Aculit Controllerji Fiber Amplifer ] L IPG Seed PZT Tune(Backside) Figure 3.24: Setup to measure the v3 vibrational band of methane in the gas phase using the Aculight laser. 66 3.3. Preparation for the depletion experiment Figure 3.25: From top to bottom: the R(0), R(l), P(1), and Q(1) branches of the v3 vibrational band of gas-phase methane. The R(0) and R(1) peak positions obtained using FTIR and Aculight laser system are in reasonable agreement 0.1 cm—’). The Aculight P(1) and Q(1) spectra are less satisfying. first measurement shown, in the top of the figure, was made before optimization of the the 3028.0 3028.5 3029.0 3029.5 3030.0 3030.5 wavenumber (cm’) 3038.0 3038.5 3039.0 wavenumber (cm’) 3039.5 3040.0 3007.5 3008.0 3008.5 3009.0 3009.5 wavenumber (cm’) 3010.0 3017.5 3018.0 3018.5 3019.0 3019.5 wavenumber (cm4) 3020.0 67 3.3. Preparation for the depletion experiment Shape of voltage applied to PZT Figure 3.26: Setup of all of the depletion experiment components. The ramp voltage is used to sweep the laser frequency. laser and alignment of the droplet and ion optics. After obtaining this initial R(0) depletion signal a series of optimizations were performed to enhance the signal size. A number of nozzle temperatures from 14 to 18 K were tested. The best signal was obtained using a nozzle temperatureT0=16.4 K. At P0=20 bar this change in temperature corresponds to a decrease in the droplet size from 20, 000 to 3000 [oj and we observed a factor of seven increase in the depletion signal. Chopper frequencies from 100 to 300 Hz were tested. The signal showed little dependence on the choice of frequency. Ultimately, 140 Hz was chosen as the optimal operating point. Finally, the laser, droplet beam, and ion optics alignments were optimized to give the largest depletion signal. In the optimization procedure the nozzle temperature was found to be the most important tuning parameter. The optimized R(0) depletion signal is shown as the bottom plot in Fig. 3.27. The R(0) peak for the CH4-doped 4He droplet system was previously measured by Miller’s group and was found to be centred at 3028.7626 cm’ [1]. This result differs from our preliminary measurements by approximately 0.3 cm1, however our wavelength meter was not properly calibrated at this early stage of the measurement. The width reported by Nauta et at. is 0.2 cm1 which seems consistent with our partial measurement of the R(0) peak. Frequency Marker \ mass L - T — Chopper controller [ZZ] I. - - - / \ / AculigtAigos ‘240Q - I Wavelength meter LBristol i / Mass chamber Oscilios9p L 1Preamp Standford L_ LZ:5R570 - Lock- X put uoutput - F -. - 001 4 2.T LL. — convener O_12O_/”\ Scan speed: 2 V/Sec Laptop computer “USB 6009 lab view” 68 3.3. Preparation for the depletion experiment 3.3.8 Depletion experiment summary In our droplet machine we achieved an average droplet size of approximately 3000 helium atoms produced with the CW nozzle at T0 = 16.5 K and P0 = 20 bar. Methane was used as the dopant probe molecule and will also be used as a probe of superfluidity in molecular hydrogen in the experiments to be completed in the very near future. Rotational and vibrational excitations and relaxation of methane in helium droplets was induced by an infrared laser and observed with a quadrupole mass analyzer. Using our limited JR scanning range, the partial R(0) peak was measured. The next step will be to expand the scan range and observe the rest of the R(0) peak as well as the other three transitions R(1), P(1), Q(1). Our scans will be compared to those measured by Miller’s group [1]. A careful measurement of the helium droplet size has to be made by a Poisson experiment. Finally H2 will be added to the CH4-doped droplet in the second pickup cell. The JR spectra will be studied as a function of the number of H2 molecules with the objective of investigating the possibility of superfluidity in molecular hydrogen. 69 3.3. Preparation for the depletion experiment Figure 3.27: Top: First CH4-doped 4He droplet depletion result. This attempt was made prior to the final laser and droplet beam alignments. Bottom: The signal to noise ratio of the R(O) peak was enhanced after optimization of nozzle temperature, chopper frequency, and ion optics (red line). The signal to noise was further enhanced by increasing the lock-in amplifier time constants (blue line). 12x103 10 Before optimization 8 6 4 2— 0— 3029.0 3029.1 3029.2 wavenumber (cm1) 3029.3 7x103 6 5 3029.4 4 3 2 1 0 3029.0 3029.1 3029.2 3029.3 wavenumber (cm1) 3029.4 70 Chapter 4 Conclusions and outlook In the first part of this thesis the fluid characteristics of Ar, Ne, and H2 clusters were studied by using two pickup methods. In the prior pickup method, the helium droplet absorbs the cluster species first and then the tetracene probe molecule. In the post pickup method the helium droplet first picks up the tetracene and then the cluster species. The spectral shift of the tetracene LIF signal was studied as a function of cluster size and pickup order for Ar, Ne, nH2 and pH2 clusters. For Ar and Ne clusters, the spectral shift was found to depend on the pickup order, implying that these clusters are rigid and not fluid-like. In contrast, the spectral shifts in the presence of 112 clusters are independent of the pickup order and we conclude that both the supercooled nH2 and pH2 clusters remain fluid-like in the 411e droplets at 0.38 K. In the second part of this thesis project, the rotational and vibrational relaxation of methane in 411e droplets was studied in a depletion experiment. Methane-doped 4He droplets were probed using an JR laser. After the absorption of a photon by the probe molecule, partial evaporation of the helium droplet occurs. These droplets are ionized and analyzed by a mass spectrometer. Four transitions: R(0), R(1), P(1), and Q(1), are expected to be observed using a combination of infrared and mass spectroscopy. In our pre liminary results, the R(0) peak was partially observed and found to be in good agreement with previous studies [1]. In the depletion experiment, the remaining three transitions R(l), P(1), and Q(1) will be measured to reproduce and confirm the results of Miller’s studies [1]. The helium droplet size for the CW nozzle has to be measured using the Poisson techniques described in the LIF chapter. The final step will be to add hydrogen clusters to the methane-doped 4He droplet. The spectral shift of JR spectra will be studied as a function of pickup order for various cluster sizes to confirm the fluid-like character of the 112 clusters. From the methane JR spectra, the rotational constant of the methane in the presence of 112 clusters will be determined. By comparing this rotational constant to that of the gas phase of methane, we will be able to search for signatures of superfluidity in the supercooled hydrogen clusters. Our group has studied both solid para-hydrogen and 4He nanodroplets extensively and is poised to resolve of the important issue of superfluidity in large clusters of molecular hydrogen. 71 Bibliography [1] K. Nauta and R. E. Miller. Rotational and vibrational dynamics of methane. Chem. Phys. Lett., 350:225, 2001. [2] Elizabeth A. Donley, Neil R. Claussen, Simon L. Cornish, Jacob L. Roberts, Eric A. Cornell, and Carl E. Wieman. Dynamics of collapsing and exploding Bose-Einstein condensates. Nature, 412:295, 2001. [3] F. London. The A-phenomenon of liquid helium and the Bose-Einstein degeneracy. Nature, 141:643, 1938. [4] P. W. Atkins and R. S. Friedman. Molecular Quantum Mechanics Thrid Edition. Oxford University Press, New York, 1997. [5] J. P. Toennies and A. F. Vilesov. 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