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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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, Ar, and Ne clusters 2 Properties of H He nanodroplets in superfluid 4 Towards a search for superfluidity in large supercooled 2 clusters H 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. 2 was investigated in 1. In the first advance, the fluidity of supercooled molecular H helium-4 nanodroples ( i0 5 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 He droplet method. In the prior pickup method, the cluster species is added to the 4 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 2 clusters remain fluid-like at 0.38 K. supercooled H 2. The second advance made in this thesis was to configure the droplet apparatus to He droplets doped with 112 clusters. study the rotational states of probe molecules in 4 The rotational states are studied by a combination of infrared and mass spectroscopy. 11e droplet it is Methane is the probe molecule used and when introduced into the 4 2 cluster. If the surrounding H 2 liquid is superfluid, the methane surrounded by the H 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 3 vibrational mode of bare methane in 4 He droplets was studied. The a first step, the v R(0) transition of the 7)3 stretching mode of methane was partially observed and found -doped 4 4 He droplet systems previously to be consistent with the R(0) peak for CH the Miller group [1]. measured by 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 Bose-Einstein condensation and superfluidity 1.2 Molecular hydrogen: ortho-Hydrogen and para-Hydrogen 1.2.1 BECofH 2 1.3 Previous studies of superfluidity in hydrogen clusters 1.4 Free rotation of fermionic molecules  1 1 1 3 4 6  2  Tetracene Laser-Induced Fluorescence 2.1 Motivation 2.2 LIF 2.3 Experimental setup for LIF measurements 2.4 LIF of tetracene 2.4.1 LIF of tetracene in gas phase 2.4.2 Bare tetracene in 4 He droplets 2.5 Size determination of the 4 He droplets 2.6 LIF results: H , Ne, and Ar clusters 2 2.6.1 H , Ne, and Ar cluster sizes 2 2.6.2 Correction for the cluster size in helium droplets 2.6.3 Ar, Ne, nH , and pH 2 2 clusters 2.7 Discussion 2.7.1 Maximum cluster size 2.7.2 Intermediate cluster sizes of Ar, Ne, pH , and nH 2 2 2.7.3 Large cluster sizes of Ar, Ne, pH , and nH 2 2 2.7.4 Pickup order dependence for large H 2 clusters 2.7.5 Evaporation and cooling rate of 4 He droplets 2.8 Summary of the LIF results  10 10 11 13 16 16 16 20 23 23 25 26 30 30 31 34 35 37 43  3  Measurement of the v 3 vibrational band of CH 4 in Helium droplets 3.1 Motivation: A search for superfluidity in large supercooled H 2 clusters 3.2 Depletion experiment techniques 3.3 Preparation for the depletion experiment 3.3.1 Installation of the CW nozzle  .  .  .  .  44 44 48 51 51 in  Table of Contents 3.3.2 3.3.3 3.3.4 3.3.5 3.3.6 3.3.7 3.3.8  4  Performance check of the quadrupole mass spectrometer Performance check of the CW nozzle Sample and laser preparation Gas Phase JR Spectrum of Methane Depletion experiment setup Preliminary Results Depletion experiment summary  Conclusions and outlook  Bibliography  54 58 60 64 65 66 69 71 72  iv  List of Tables 1.1  He, H , Ne, and Ar 2 Condensation temperatures of 4  2.1  Droplet size, max cluster size, and nozzle conditions for LIF measurements.  3 32  V  List of Figures 1.1 1.2 1.3 1.4 1.5  Bose-Einstein condensation cartoon Symmetric top and free rotation of OCS probe molecules )N and OCS-(pH2)N clusters in helium droplets 2 JR spectra of OCS-(oD Pendular spectroscopy of the linear and polar molecule HCCCN Free rotation of HCN probe molecules in Fermionic HD clusters  2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22  Mg-phthalocyanine and tetracene Two types of laser-induced fluorescence (LIF) Droplet machine chambers and the pulsed nozzle The prior and post pickup methods LIF spectrum of tetracene in the gas phase Comparison of LIF spectra of tetracerie in the gas phase and in 4 He droplets LIF spectrum of single tetracene probe molecules in 4 He droplets Bare tetracene LIF spectrum and the phonon wing Saturation check of LIF spectrum as a function of laser energy Argon pressure dependence of the bare tetracene LIF signal intensity Prior and post cluster size determination (Ar, nH 2 and Ne) Tetreacene LIF spectra in droplets with prior and post Ar clusters Tetreacene LIF spectra in droplets with prior and post Ne clusters Tetreacene LIF spectra in droplets with prior and post nH 2 and pH 2 clusters LIF signal spectral shift for Ar, Ne, and H 2 clusters versus cluster size Two possible tetracene configurations for prior pickup Pickup order dependence of the LIF signal for large nH 2 and pH 2 clusters Cooling rate assumptions for the prior and post pickup methods Helium-4 droplet energy: bulk and surface vibration modes Helium capture and emission probability and the Weisskopf formula Numerically calculated helium droplet cooling curves Heating of 4 He droplets from the integrated specific heat  11 12 14 15 17 18 19 20 21 22 24 26 27 29 33 34 36 37 38 39 41 42  3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11  The Coriolis force as seen by a rotating observed The Coriolis force for a rotating mass oscillating in the radial direction Bending modes of a rotating triatomic molecule Energy levels and selection rules for the stretching mode of CH 4 Comparison of our experimental setup and one used by a previous group. R(0), P(1), Q(1), and R(1) transitions of CH 4 measured by Nauta and Miller Experimental setup for the CH 4 depletion experiment The CW nozzle and nozzle compartment The CW nozzle compartment and the closed cycle 4 He fridge Measurement of the flow rate of the CW nozzle Thermometers and heaters of the nozzle compartment  45 45 46 47 48 49 50 51 52 53 53  .  .  .  .  .  .  .  .  .  .  2 5 6 7 8  vi  List of Figures 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 3.21 3.22 3.23 3.24 3.25 3.26 3.27  The 4 He droplet beam skimmer The quadrupole mass filter Quadrupole mass filter region of stability and resolution High-q head and rf controller of the quadrupole mass analyzer Filament, ion optics, and mass filter of the quadrupole mass analyzer Mass spectra before and after optimization Bare tetracene LIF signals measured using the pulsed and CW nozzles Helium droplet mass spectra for nozzle temperatures from 6.4 to 20 K High resolution mass spectra for masses less than 45 amu Chamber pressures as a function of nozzle temperature Droplet and laser setup for the depletion experiment 3 vibrational band of methane using FTIR. Gas phase spectrum of the v Aculight laser measurement of the 1)3 vibrational band of gas-phase methane R(0), R(1), P(1), and Q(1) branches of the 1)3 vibrational band of methane Setup of all of the depletion experiment components Preliminary depletion signals from CH -doped 4 4 He droplets .  .  .  .  .  .  .  .  54 55 56 56 57 58 59 60 61 62 63 65 66 67 68 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 1.1  ion  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 4 He 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 He (fermion), liquid 4 He/ 3 H e mixtures, electron gases of tems: liquid 4 He (boson), liquid 3 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 temperaturedependent 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 H . Liquid H 2 2 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: = 3.31h 2 (n) 3 ! 2 (1.1) g mkB 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 4 He occurs at 2.17 K). -  1.2  Molecular hydrogen: ortho-Hydrogen and para- Hydrogen  Before discussing the possibility of superfluidity in liquid H , it is important to distinguish 2 ) and para-hydrogen (pH 2 ). Molecular hydrogen is homonu 2 between ortho-hydrogen (oH 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 = EVRbN ular wavefunction can be separated into a product of four components 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  Vq  h =  J2nmkT )  .  =  quantum volume  lq = de Brogue wave length m = mass of particles k Boltzmann’s constant  . •• .•  Normal Gas, V/N  >>  Quantum Gas, V/N  vq  Vq  I  ‘1  p 0  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 H 2 is denoted by 1 Eg. 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:  ITT) (IU)+ ITT))  =  (1.2)  4) whereas, when the spins align antiparallel I is formed: =  =  0 and the antisymmetric spin singlet state  (ITT)- ITT)).  (1.3)  2  1.2. Molecular hydrogen: ortho-Hydrogen and para-Hydrogen  4 H e 2 pH 2 oH Ne Ar  28 m n (x10 ) 3  m (amu)  g  T (K)  1.88 2.14 2.14 3.63 2.15  4 2 2 20 40  1 1 9 1 1  2.8 6.1 1.4 0.87 0.31  He, oH , pH 2 , Ne, and 2 Table 1.1: Predicted Bose-Einstein condensation temperatures for 4 Ar.  2 molecule by r radians and in this Proton exchange is equivalent to a rotation of the H (_1)J/yR, where J is the rotational state. To preserve antisymmetry of the total case ) and 2 wavefunction, J = 1,3,5,... must be odd when the proton spins are parallel (oH ). At high temperatures normal2 J = 0, 2,4,... is even when the spins are antiparallel (pH hydrogen (nH ) gas is 75% oH 2 2 and 25% pH 2 because the ratio of symmetric nuclear spin states to antisymmetric states is 3:1. .‘  1.2.1  2 BECofH  2 At 20 K, the mass density of liquid hydrogen is 70.99 grams/litre. The ground state of oH , on 2 is J = 0 and I = 0 resulting in a spin degeneracy g = 1. The ground state of pH 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 pH . Table 1.1 gives the predicted T ‘s of oH 2 2 and pH 2 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 H 2 solidifies when cooled below the triple point T 3 = 13.8 K, which is well above the predicted Ta’s of both pH 2 and . 2 oH 2 must be supercooled well To study superfluidity in liquid molecular hydrogen, the H below the freezing temperature. The technique used in this thesis is to capture and rapidly 2 to 350 mK in superfluid 4 He nanodroplets. The nanodroplet size can cool clusters of H 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 1018 nucleation time is estimated to be of the order of s [8]. Molecules at the surface of a 2 cluster are less bound than the interior molecules and are less likely to solidify. Since H 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 H 2 clusters and provide a very clean environment free of nucleation sites [8, 9]. Molecules are inserted into the H 2 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 H 2 clusters made from free-jet expansions of pre-cooled H 2 gas and clusters of H 2 captured and cooled in He nanodroplets [8, 12, 13, 14, 15, 16, 17, 18, 19, 20]. Path integral Monte Carlo (PIMC) 4 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 H 2 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 H 2 clusters with N = 14— 16 have claimed to have observed microscopic superfluidity [19]. To probe the supercooled liquid H 2 for superfluidity, the rotational states of a dopant molecule were analyzed by infrared spectroscopy. The dopant molecule is introduced and becomes surrounded by H . The H 2 2 cluster-dopant molecule system is inside a 4 He nanodroplet. If the surrounding H 2 liquid is superfluid, the dopant can rotate freely and has a low moment of inertia. Conversely, if the H 2 remains a normal fluid, the rotation of the dopant molecule is impeded by the friction it feels from the surrounding H 2 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 H . Perhaps the most cited evidence for superfluidity in liquid H 2 2 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 H 2 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 H ’s, adopts the 2 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 H . 2 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 4 He droplets at 380 mK and low-temperature 150 mK droplets made from 4 He/ 3 H e mixtures. They studied relatively small H 2 clusters with the number of molecules varying from N = 14 17. For N < 17, the first shell of H 2 molecules surrounding the OCS probe molecule is incomplete. Detailed rotational spectra were obtained from four different droplet systems: —  1. OCS in pH 2 and pure helium-4 nanodroplet. 2. OCS in pH 2 and helium-4/helium-3 nanodroplet. 3. OCS in ortho-deuterium (oD ) and pure helium4 nanodroplet. 2 4. OCS in oD 2 and helium-4/helium-3 nanodroplet.  Superfluidity in the deuterium ( H or D) is expected to be suppressed for a number 2 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  ixJ=_iWhi  I  r  IIWhFJ=l  Frequency of absothed radiation  No Q-Branch  IO  Superfluid  Figure 1.2: Left: When surrounded by normal fluid hydrogen, adjacent H 2 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 H . 2  are shown in Fig. 1.3. In the pure 380 mK 4 He droplets, only strong Q-branch peaks are resolved. The signal to noise is substantially improved in the 150 mK 4 He/ 3 H e droplets and the small P- and R-branches can be clearly resolved. At both temperatures, the OCS spectra from droplets with oD 2 clusters show strong Q-branches consistent with spectra expected for a symmetric top molecule. The Q-branch is also observed for pH 2 clusters in pure 4 He droplets at 380 mK. It is only in the pH 2 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 pH 2 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.  5  1.4. Free rotation of fermionic molecules  0D2 C 0  0.38 K  C) C) > C)  0D2  0.15 K 2057.6  2057.2  2058.0  OCS(pH in 4 ) 2 He 16  2058.4  14  15  C pH2  0.38 K I  I  n4 HeflHe  Qo  16  14  pH2  0.15 K 2057.6  2058.0  v  2058.4  ) 1 (cm  Figure 1.3: Comparison of JR spectra measured for OCS-(0D )N and OCS-(pH 2 )N clusters 2 in helium droplets. (A) oD 2 in 4 He droplets. The F- and R-branches are not easily resolved, however, there are strong Q-branch peaks for N =15, 16, and 17. (B) oD 2 in 4 He/ 3 H e droplets. All three branches are easily observed. (C) pH 2 in 4 He droplets. Strong Q-branch peaks are observed for clusters of N =14, 15, and 16. (D) pH 2 in 4 He/ 3 H e droplets. Only for the pH 2 clusters in the low-temperature droplets are the Q-branch peaks observed to vanish. An indication that the surrounding pH 2 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 2 and observed the absence of the Q-branch when T = 150 mK. This observation implies pH 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 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) Pendulum  Free rotor states  0  states  HGCCNn He Droplets E 10.00 kV  5  I  Pendular peak @—Q-branch  Rotational structures Ema  E  3327.0  3327.5  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 4 He 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 4 He 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 4 He droplets. Consider adding RD solvent molecules to a helium droplet doped with a single HCN probe molecule in zero  7  1.4. Free rotation of fermionic molecules 1 5, for example), the electric field. When the number of RD molecules is small (N 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 —  3301  3302  3303  3304  3305  Wavenumber (cm’) Figure 1.5: The bottom spectrum is of HCN surround by an HD cluster of size N = 8, 9,. , 14 in a 4 He 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 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 4 He 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) H 2 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 H 2 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 H 2 clusters. Very large clusters are spherical and for 2 molecules, H 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 H 2 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 H 2 molecules inside He nanodroplets. Spectra from droplets with Ar clusters were also obtained in a similar 4 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 H 2 clusters had no dependence on the pickup order of the dopant and the cluster molecules. This observation led to the key result that H 2 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 ) 12 will be used. Figure 2.1 shows that the tetracene molecule is H 18 (C 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 .4  ---  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 H 2 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 H 2 which is fluid-like in 4 He droplets and Ar which is not. For example, the mass of Ne is 20 amu compared to 2 and 40 amu for H 2 and Ar respectively. As shown in Table 1.1, the predicted Bose-Einstein condensation temperature of Ne falls between those of H 2 and Ar. Perhaps most importantly, the depth of the intermolecular potential well of Ne is also intermediate between H 2 and Ar. In temperature units, the estimated well depths for H , Ne, and Ar are 34.8, 43.3, and 143 K respectively. For com 2 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,...). 11  2.2. LIF  In a two level system, double-prime notation refers to the (lower) ground state and the (a)  (b) v’=2  Excited state  Electronic Ground State  v2  ---_-__---  v’l  —o  ‘  I  I  -_-_-----V--L_ V  v’=l -  -I-—  I  v”l v”O  ---  -  -  ------  L  -  V  —o  -  =  --  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 He atoms through a cryogenic 0.5 mm diameter nozzle into a vacuum chamber [261. The 4 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 T 0 = 8 K. The actual temperature at the tip of the nozzle where the 4 He 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 4 He 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 4 He droplet temperature. Then the energetic 4 He 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 , nH 2 pH , and Argon cluster species. After these measurements the droplet size appeared 2 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 T 0 = 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, the 4 He 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 12 heated to a temperature of 130°C. This temperature has been shown to generate H 18 (C ) 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 H 2 (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, H , or Ne) and the droplets pickup the cluster species before pickup 2 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 4 He droplets, which act as an inert superfluid background, will absorb Ar, H , or Ne. When introduced into the helium droplet the cluster molecules cool very 2 rapidly to 0.4 K. The two pickup cells are connected to gas lines that can be filled with Ar, , or Ne and the gas line pressure is adjustable to obtain the desired cluster size. Pressure 2 H 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 Nozzle Chamber  Nozzle with poppet  Mass Chamber  Main Chamber Pick up cells  Sample cells  Pick up cells  -  LJ  Nozzle with poppet  -  U  15mm  0  12 17 22cm  LDYC laser Nozzle with poppet  Nozzle valve  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 4 He 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. 4 He droplets doped with tetracene 2. 4 He droplets doped with tetracene and pH 2 clusters 14  2.3. Experimental setup for LIF measurements  Prior pickup —  0.7 cm  rm ri ri LIII  nozzle skimmer  Li  Mg-Pc 1.5 cm  LASER  Post pickup  ÷  rir  I  I  I  0  3  12  I 17  I 22  I 25cm  Figure 2.4: This figure shows the path of the 4 He 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 nH 2 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 H , a Nd:YAG laser (Coherent, Infinity) was used 2 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 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 4 He 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.  LIF of tetracene  2.4  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 4 He 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 cm . The LIF spectra shown in the figure are normalized to the 1 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 1 with accuracy of ±3 A (±13 cm S ) which depends on the accuracy of the calibration of 1 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 cm 1 and 22707.84 cm [31]. —  2.4.2  Bare tetracene in 4 He 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  TETRACENE  cco  *4  I  4250  4300  __._______.J 43S0  I_____  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 T 0 = 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 cm ) was compared 1 that measured to 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 cm 1 to 22293.5 cm when inside the 4 He droplet. Figure 2.7(a) shows a detailed LIF spectrum of the electronic band origin of single tetracene molecules in 4 He droplets. The nozzle conditions for this measurement were iden tical to those used previously (Po = 20 bar, T 0 = 8 K, and laser energy 1 11 J). The spectrum in the figure is a zero phonon spectrum consisting of two peaks at v = 22300.5 cm 1 and v = 22301.5 cm . The two peaks correspond to an electronic transition between the lowest 1 vibrational states, namely the S 0 ground state and S 1 first excited state which are assigned the labels c and /3 respectively. The splitting of the transition into a doublet is interpreted 17  2.4. LIF of tetracene TETRACNE  ccxx  I  Al  4250  4300  430  4250  4300  4350 wavelength  4400  4400  4450  40O  4450  4500  (A)  Figure 2.6: LIF spectrum of tetracene in the gas phase compared to the LIF spectrum He droplets. Top: LIF spectrum of free tetracene molecules cooled in of tetracene in 4 a supersonic expansion of Ar at 180 Torr. (same data shown in Fig. 2.5). Bottom: LIF He droplets. The stagnation conditions spectrum of single tetracene molecules embedded in 4 0 = 8 K and the laser output energy was 80 iJ. 0 = 20 bar and T were P  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]. 1 split is not seen in spectra for free tetracene molecules. The 1 cm In Fig. 2.8 the c and peaks are accompanied by a broad peak shifted to the right by approximately 5 cm . This broad peak is labeled as the phonon wing (PW). It is due to 1 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 He droplets [36]. elementary excitations of the superfluid 4 The PW appears strongly in Fig. 2.8, but not in Fig. 2.7(a). The difference is the laser 18  2.4. LIF of tetracene Bare tetracene in He droplets (a) 2000 1500  1000 500  0 22296  22298  22302  22300  22304  wavenumber (cm’)  (b)  0.12  0.08  0.04  0.00 22200  22300  22400  22500  22600  22700  wavenumber (cm)  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 1 state. The transition splits into a 0 state and the first excited S between the ground S He atoms surrounding the doublet due to two different configurations of the first shell of 4 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 J (below the saturation point) and the in Fig 2.9. In Fig. 2.7(a), the laser energy was 1 11 was 120 pJ (well above the saturation point) Fig. 2.8 the laser energy present. In PW is not and there is a large PW. The LIF intensity as a function of the laser energy was measured 0 = 8 K, and v = 22301.5 cm* To vary the laser energy, various using P 0 = 20 bar, T 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 19  2.5. Size determination of the 4 He droplets  50 40 30 20 10 0 22298  22300  22302  22304  22306  wavenumber (cm) 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 4 He 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 T 0 = 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 cm , which corresponds to the 1 centre of /3-peak of a single tetracene molecule in a pure 4 He 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 1 pJ. The LIF signal ‘-j-’  20  He droplets 2.5. Size determination of the 4  Photodiode  Mass  I  .  Nozzle  Main  -  Pick up cells H  Scanmate ___j 0.1  1  10  N]J filters  100  Laser energy (iJ)  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 cm . Above 1 a laser energy of 1 11 J, 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 = Ar 13 where the proportionality X constant x is expressed as: X  ucapL  /(Ve)+(vr)  kBTV  (22)  ) 6 (Vj  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 (Z) = exp(—Z) = exp(—XPAr) 0 P , the capture 1 exp(—PAr/r). Having rewritten x as r cross-section can be reexpressed as: —  cap  , I tBT /  /2 \VHe (Vie)  —  +  1  23  (‘Vjr)  Figure 2.10 shows the Ar pressure dependence of the LIF signal measured at ji = 22301.8 cm 1 for 4 He droplets with N=0. Keeping v fixed at 22301.8 cm 1 guarantees that only LIF signals from droplets with a single tetracene and N = 0 Ar atoms are detected. 21  2.5. Size determination of the 4 He droplets 14 12  10 8  4 2 0 0  100  200  300  400  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.  22  2.6. LIF results: H , Ne, and Ar clusters 2  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 . 2 A be cTcap = 1.5 X 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 crosssection: 1 (2.4) 0 = 222Ne A, cap = irR, where R where R 0 is the droplet radius and NHe is the average number of helium atoms. The cube He atom inside of the prefactor 2.22 A is essentially the effective volume occupied by each 4 , the droplet is found to contain 2 A the droplet. Using this expression and crcap = 1.5 X X This the droplet size measured immediately after moving the atoms. was 3.0 NHe 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 2.6.1  LIF results: H , Ne, and Ar clusters 2 , Ne, and Ar cluster sizes 2 H  , Ar, and Ne clusters, the 2 For the LIF measurements of tetracene in the presence of H 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 4 He 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 , 22263.4 cm 1 , and 22239.7 cm 1 wavenumbers. of 22301.8 cm 1 respectively. In the case 2 clusters, the LIF signal was measured as a function of H 2 pressure for N = 0 and of H 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, , A 0 , A 1 , x). The parameter x appears in all three functions. This x is the reciprocal 2 Y2, A 23  2.6. LIF results: H , 2  Ne,  and Ar clusters 20  I! Priori  I  I  N=0 N=1  K>  N=0 NI  0 0  20 10 -  10  0 0  1  2  3 “oh  4  6  5  0  1  2 5 Pa) Pth (x10  5 Pa) (x10 2500  5000 4000  2000  3000  1500  2000  -  1000  5  10 “oh  I  160  15  zZ  1000  0  20  2  4  6  (x10 Pa)  I  I  “oh  I  I  N=0 N=1  PoSt’I 2 lnH  500  0  3  8  10  12  14  4 Pa) (x10  8  Ne Pnor \0N=0ON=0  Ne Post \QN0QN=0  12  4  4. 0—  2 I 2  4  8 66 POh(x10 Pa)  t Prior  t  Post  Pa) 6 (xlO  Pa) 6 (xlO  7.5±0.2  7.6±0.4  Ar  0I• 0  10  1  2 “oh  4 3 (x10 Pa) 6  5  6  Fit functions  Ratio  (Prior: Post)  N =0  + 0 y  N=1  +A 1 y (X PCh)e 1  1:1  nFL  6.0±0.7  5.1±0.5  1: 0.9  Ne  2. 1±0.4  1.8±0.4  1: 0.9  e0 0 A  N=2  pCh)e  T Figure 2.11:  The prior and post cluster size determination for Ar, nH , and Ne cluster 2  species. The Poisson analysis is used to extract  of r as discussed above. the  N  =  x  =  l/T from global fits to the data.  For nil 2 clusters a global fit to three functions is also used, but  1 function is used twice. For Ne clusters only one  N  =  0 function is used.  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 4 He 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  —  , 3 ” 2 aN(P))  (2.8)  where B is proportional to the density of the helium in droplets and n 0 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) 3 / 2 (no aN(P)) —  With these definitions the ratio no/a represents the maximum possible cluster size that would completely evaporate the 4 He droplet. The normalized droplet size can then be written as x = N(0)/(no/a). Rewritten in terms of x, Eq. 2.9 becomes:  n2/32 0 (1—x)/  =  ABdP,  (2.10)  or: (1  dx x) 2 /3  —  =  A(Bn ) 3 no/a  =  Au(O)dp no/a  =  dy.  (2.11)  From Eq. 2.8, Bn 0 = 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 dz=_( 3 / 2 ) 1  dy =—--.  (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: H , Ne, and Ar clusters 2  which, when rewritten in terms of x, is: (2.14) For example, suppose that the Poisson measurement for nH 2 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, nH , and pH 2 2 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  21600  21800  22000  I 22200  wavenumber  (1)  I 22400  22600  21600  21800  22000  22200  wavenumber (cm’)  22400  22600  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 S 0 and the first excited singlet state S 1 of tetracene. For droplets containing bare  26  2.6. LIF results: H , Ne, and Ar clusters 2 tetracene with (N) = 0, the peak at v = 22301.8 cm 1 corresponds to the band origin of the bare tetracene, which is an electronic transition from the lowest vibrational state . The peak which is shifted to higher frequency 1 o to the first excited vibrational state S 5 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 cm . The prior and post pickup peaks have different shifts with 1 respect to the band origin for all values of (N). For (N) = 180 the prior and post pickup peaks are shifted by —200 cm 1 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  1 ieroaL  I  <N> =  <N> =  <N>  <N> =  E  <N>  Bare  21800  22000  22200  I 22400  Wavenumber (cm ) 1  22600  22800  =  21800  7  I 22000  22200  I 22400  22600  22800  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  , Ne, and Ar clusters 2 2.6. LIF results: H peaks adopt nearby satellite peaks which are most likely due to different configurations of the cluster atoms. 2 and pH 2 Figure 2.14 shows LIF spectra of tetracene measured for several different nH are very 2 spectra shifts for both the prior and post pickup methods cluster sizes. The nH . 1 similar for all cluster sizes. The maximum shift for both pickup methods is about 500 cm Both sets of pH 2 spectra are again very similar and have maximum shifts of approximately 460 cm . In fact, there are no significant features that distinguish between prior or post 1 2 and pH . These results from H 2 2 clusters differ from those pickup orders or between nH 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: H , Ne, and Ar clusters 2 2 Priori nH  I  lnHzPosti  I  i  <N> = 1900  <N>  100  <N>  <‘>=o <N>  I <N> = 2500  1500  <N> = 700  <N>=470 =1470 I <N> = 150  <N>=170  __/tw/\q  <N> = 30  <N>  <N> = 3  21600  I  bare  bare 21800  I 22000 22200 wavenumebr (cm  )  I 22400  22600  21600  21800  22000 22200 wavenumber (cm’)  22400  22600  2 Posti I pH <N> = 2500  <N>=1600  <N>=770  <N> = 470  <N> = 150  <N> = 50  Aq410  <N> =  1 bare 21600  21800  22000  22200  wavenumber (cni5  22400  22600  21600  21800  I 22000  I 22200 (1) wavenumber  I 22400  22600  Figure 2.14: Top: Tetracene LIF signal in the presence of nH 2 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 pH 2 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 2.7.1  Discussion Maximum cluster size  When 4 He 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 4 He 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 2. Energy brought by cluster species (Ar, Ne, or H 3. Binding energy of cluster species 4. Binding energy between tetracene and cluster species (Ar, Ne, or H ) 2 (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 (NC 12 = 30) atom H 18 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. 6 = 3(30) 6 = 84). Each degree of freedom contributes an energy of kBT/2, SH 1 (3NC 12 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 1/2 2 2 given by Vrel = (‘U’He and the translational energy of the tetracene is: +) 12 H 18 VC —  —  —  ¶vr2ei  =  (Vie  +  V 1 H ) 8 2  =  Ve  + ICBT  =  1.6  X  , 1 cm  (2.15)  where VHe= O m/s, Vi 35 12 = 3kBT/m, and m = 228 amu is the mass of the tetracene. The H 8 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, H ). Ar, Ne, and H 2 2 are all at room temperature when introduced into the droplet. The vibrational energy of H 2 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 cm , 410 cm 1 , and 530 cm 1 for Ar, Ne, and H 2 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 4 He 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 2 -H binding energies are 450 cm H , 1 110 cm , and 50 cm 1 1 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 1 cm into the 4 He 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 2 molecules are needed to complete the first 30. Similarly, 24 H 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 H 2 is 1.64 A , 0.396 A 3 , and 0.803 A 3 3 respectively [5]. The binding energy between tetracene and a single Ar is 520 cm . The 1 binding energy between tetracene and a single Ne is therefore estimated to be 520 cm 1 x (0.396/1.64) 130 cm 1 and to be 255 cm 1 for H 2 [41]. The total binding energy between tetracene and the first solvation shell of clusters around tetracene is 126 cm 1 x 30 3800 cm 1 for Ne and 6100 cm 1 for H . 2 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 cm 1 + 10740 cm 1 + N(447 cm 1 + 517 cm ), 1  (2.16)  where 5 cm 1 is the 4 HeH 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 H 2 clusters and the maximum cluster sizes are estimated in the same way to be N 1 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 H , 2 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, pH , and nH 2 2  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 H 2 clusters for both prior and 31  2.7. Discussion  Fig. 2.12  H 2 (N) = 0 470 Fig. 2.14  112 (N) = 700 2500 Fig. 2.14  Fig. 2.13  5.5 260 8 20  5.5 470 8 20  29 2400 6 20  29 2700 6 20  Ar  ‘-.-  ) 4 Droplet size (x10 Max cluster size Nozzle Temperature T 0 (K) Nozzle Pressure P 0 (bar)  Ne  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 6 H 8 Ci A 2 , r/R i where c 1812 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 S 0 and excited S 1 states of the tetracene will be shifted in energy because of this interaction. However, because of its larger polarizability the S 1 state is more strongly affected and there is an overall downward shift of the S 0 —* S 1 transition energy relative to the band origin. The shifts observed for Ar, pH , and nH2 increase monotonically towards lower frequency 2 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 2 and nH pH 2 there is a smooth dependence of the shift up to cluster sizes of (N) = 2045 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)  4  10  5  6789  100  4  5  6789  1000  <N>  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 nH 2 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— ). The observed size of the first Ar shell nearly matches the size of 6 20 atoms estimated in §2.7.1 [41, 42]. Also in that section, the completion of the first shells of 2 11 and nH2 clusters were estimated to require approximately 24 atoms. This number is P 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 —  33  2.7. Discussion that surround the tetracene. Each configuration could produce slightly different S 0 —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, pH , and nH 2 2  Fig. 2.15 shows that for prior pickup the largest Ar cluster of 180 atoms results in a shift of 200 cm 1 and for post pickup the shift is 700 cm . The prior and post shifts due to 1 Ne clusters of similar sizes are 30 cm 1 and 100 cm 1 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 He droplet  Cluster species  QorQ Tetracene  (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 He droplet experiments using HF and been previously studied in small clusters of Ar in 4 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 R ) because 6 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 4 He 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 H 2 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 , cZAr = 1.64 A 3 , and Ne = 0.392 A 3 . The shift for the largest 112, Ar, and 3 2 = 0.8 A H Ne clusters in post pickup are 450-500 cm , 700 cm 1 , and 100 cm 1 1 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 H 2 clusters  For the largest nH 2 clusters the shifts are about 500 cm 1 for both pickup orders. For large clusters the spectra shifts also order independent are and the values are approximately PH2 450 cm . For post pickup of H 1 2 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 H 2 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 H 2 clusters implies that the nH2 and pH 2 clusters are fluid-like in 4 He droplets at 0.38 K. An alternative possible explanation is that the H 2 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 cm’) into helium droplet rapidly before it reaches the cluster and (405 K —* 1.4 x causes the evaporation of 3600 helium atoms. This cooling process is discussed in further 100 cm’ detail in the next section. Because the fusion energy of Ar is approximately per atom and a cluster of 5 Ar atoms does not melt, the tetracene cannot have more than 1 of energy when it reaches the surface of the cluster. Because the fusion energy 500 cm of H 2 is approximately 10 cm 1 per atom, the tetracene could not melt more than about 50 2 cluster sizes (N) >> 50 the observed 2 molecules. The data clearly show that even for H H 2 clusters are spectral shifts for prior and post pickup are very similar. We conclude that H fluid-like in 4 He droplets. A small difference in the shifts for both pickup methods is observed at around (N) = 2 and nH , as highlighted in Fig. 2.17. A possible explanation 2 250 2000 for both pH ‘-  —  Prior pick up  1 4 ot quite at the center  2  3  4  56789  100 <N’  Figure 2.17: The plot shows a slight difference in the spectral shift of the tetracene LIF signal for large nH 2 and pH 2 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 2 clusters. Solidification of the H H 2 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 H 2 cluster. There is a small difference between the nH 2 and 2 11 P spectral shifts for large (N) > in both prior and post pickup measurements. This suggests 2 cluster and tetracene might be slightly different from the that the interaction between nH interaction between pH 2 cluster and tetracene. Recall that nH 2 includes both pH 2 and oH 2 in the ratio of 1 to 3. Despite this discussion, we firmly believe that pH 2 and nH 2 clusters are fluid-like iii helium droplets at 0.38 K.  36  2.7. Discussion  2.7.5  He droplets Evaporation and cooling rate of 4  He droplets after pickup of the tetracene In this section the evaporation and cooling rates of 4 dopant molecule are discussed. In the prior pickup method the helium droplet first picks , Ar, or Ne) which is initially at 300 K. Then it is assumed that the 2 up the cluster (H 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  •....  2nd  Ar/Ne/Hz  Tetracene  Pick up  405 K —  Prior  0.38 K  0.38 K  300K  405 K Post  I 0.38K  0.38 K  0.38 K  4 0.38K  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 4 He droplet, which then can be related to the cooling rate. Brink and Stringari He He/ 3 H e droplets, and pure 3 He droplets, mixed 4 calculated the cooling rates of pure 4 102 to iü atoms at droplets [38j. They studied helium droplets of sizes ranging from 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 He droplets, (2) the Wiesskpf formula (this formula was originally developed to of the 4 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.  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  -  Lowest bulk modes I___.J  I  i.  a)  —  — —  — —  I —  T=037j( I I  -i10  a) 4 _ 1 c.  I I I I I I • •  zo  10-i  I  U  101  102  modes  I I I I I I I  I  106  4 i0  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 He droplet [38]. important. The hatched line at 0.37 K is the typical temperature of a 4 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: (2.17) Esurf = -  is constant that where Esurf is average total thermal energy of all the surface modes, includes the surface tension, /3 = (kBT)’, and N is the number of helium atoms in the droplet. 38  2.7. Discussion  (2) Weisskopf formula He atom evaporates from the surface of the droplet two To obtain the probability that a 4 The first is the formation of a droplet of N atoms from the considered. processes have to be 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, —  —  Emission  Capture  I  —I  I —  Probability of the disintegration of N cluster to N- 1 cluster (Emission)  Probability of the formation of N cluster (Capture)  -  N cluster with EN  N cluster with EN  N-i cluster with EN-I  .  —  —  The number of states available for the formation of N cluster (Capture)  N-i cluster with EN-I  The number of states available for disintegration of the : N cluster to N-i cluster (Emission)  -  2  1  (3’  x 2)  =  ç3 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 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 4 He droplet evaporation: Wde  =  m WN_1(EN_1) gu—e de, where EN_i 7r  =  WJ\T(EJ\T)  EN  —  0 E  —  e.  (2.19)  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 4 He atom is g = 1. The density of states of the helium droplet 0 is the binding energy of a single 4 He atom to the droplet. is denoted by w and P2 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 E . Statistical analysis of the evaporation process 0 requires that there are many states available to the N — 1 cluster with energy EN — E 0 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 E 0 which is estimated to be 6 K in Ref. [38j. x In our experiments, N 10 and is 2200 K, which is much greater than E , 0 5 EN 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 -E 0 for T —+ 0. Now the Wd integral can be evaluated to obtain the evaporation rate F: 0 E—E =  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 4 He atom the droplet loses energy E 0 (binding energy). Combining the above result with the surface vibration excitation energy Brink and Stringari finally arrive ar the 4 He droplet cooling rate: =  T exp 0 mE 28  [—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 4 He 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 4 He droplet = 10_8 drops rapidly during the time interval t 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 4 He droplets (solid curve) are expected to cool below 400 mK in 10 us.  Our case: the cooling rate of 4 He 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 H 2 molecules, the energy absorbed by the droplet is 2.3 x 10—18 J. The initial temperature of the 4 He 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 4 He 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 H 2 molecules. This procedure gives T = 2.16 K for the Ar cluster and T = 2.18 K for the H 2 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 5 cm and the speed of 4 He droplet is 350 rn/s. Thus, it takes 1.4x i0 s for 4 He 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 E 0 given by [38]: ‘-j.’  0 E  —a  —  N’, 8 a  (2.24)  41  2.7.  Discussion  70  40  0  20  rdD 10 0 0.0  0.5  1.0  1.5  2.0  2.5  3.0  3.5  4.0  Temperature (K) Figure 2.22: Heat capacity of liquid 4 He 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 a 8 = 6.95 K. For our droplets, E 0 7 K and is only weakly dependent on N. To dissipate the energy added by absorption of a cluster species, roughly He atoms must evaporate. For a cluster of 100 Ar atoms this corresponds to Eciuster/E 4 1.9 x He atoms and 2.4 x iü atoms for a cluster of 200 H 4 2 atoms. Now consider the second pickup stage. When entering the tetracene pickup cell, the temperature of the 4 He 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 H 2 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 H 2 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 4 He droplet picks up the tetracene probe molecule and the droplet must absorb the internal and kinetic energy of the tetracene 12 As discussed in §2.7.1, the total energy absorbed is 2.75 x i0’ J. This pickup H 18 EC . 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 4 He 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 42  2.8. Summary of the LIF results  200 H 2 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, H , and Ne clusters with tetracene as a probe molecule were studied 2 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 pH 2 clusters are independent of the pickup order, suggesting that the tetracene can move through the layers of the H 2 clusters to position itself at the cluster centre. This result indicates that the H 2 clusters remain fluid-like at 0.38 K.  43  Chapter 3  Measurement of the 113 vibrational band of CH 4 in Helium droplets 3.1  Motivation: A search for superfluidity in large supercooled H 2 clusters  The previous experiments were designed to observe if Ne/Ar/H 2 clusters are fluid in helium droplets at 0.38 K. The results showed that Ne/Ar do not behave like a fluid, but that H 2 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 4 He nanodroplets by analyzing the rotational states of a dopant molecule. Our candidate dopant is CH . Methane is a good probe molecule because 4 it interacts weakly with hydrogen. Before experiments with droplets containing both CH 4 and H , experiments with CH 2 4 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/H 2 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  2 clusters 3.1. Motivation: A search for superfluidity in large supercooled H  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 3 (v = 1) stretching mode of methane. This mode of CH we will study the v 4 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 H 2 clusters  J=3 F° 3=2  -  F F  R=  A iR  r  A  F 3=1 F°p  A  3=0  =  2  ::=  V  R=1 A R=2 4 lR= 1  Selection rule  Selection rule IJ=0,±l J  R=4 R=3  —  t  P(2) Q(2) R(2) R— 2 P(1)Q(i)R(1) R(0) —  —  —  L  Figure 3.4: Energy levels and selection rules for the P, stretching mode of CH . 4  Q,  and R transitions for the  1)3  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 CH 4 molecules. The 4 pressure was optimized so that the helium droplet absorbs a single CH CR 4 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 CH 4 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  Our experiment P 20 bar = 0 12K d=5jim 0 T  He droplet size:  Ii  I]  He 4 Low temp Nozzle  R.E. Miller  Mirror  êu  ha Cluster growth  Mass Spectrometer  3000 atoms  D  0  I[m  Pick up Photon absorption Ionizer and cell evaporation He droplet size:  P 40 bar 0 8 cm 21 K 0 T Pick-up Cell d5 tm  Laser beam  2100 atoms F-centered laser ‘50mW  Multi-pass/ Stark Cells x-y translation  Liquid Nitrogen Dewar and Shield  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 4 in 4 He nanodroplets. The stark to study the R(0), P(1), Q(1), and R(1) transitions of CH 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%) 4 He gas at high pressure (20 bar). The 4 He 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 T 0 = 16 K), the average size of the nano-droplets was estimated to be approximately 3000 4 He 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 48  3.2. Depletion experiment techniques  I  I  I  I  R(O) Q(1)  P(1)  3005  3010  R(1)  3015  3020  3025  3030  3035  3040  3045  Wavenumber (cni’) Figure 3.6: R(0), P(l), Q(1), and R(1) transitions of CH 4 in 4 He nanodroplets measured by Nauta and Miller 3.6.  distance traveled during the cooling is approximately 3.5 cm. ) 4 Next, the helium droplets pass through the first pickup cell containing methane (CH gas and absorb, or pickup, CH 4 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, pH 2 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 He atoms from the nanodroplet. As a result the droplet has a reduced the evaporation of 4 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 4 probe molecule a depletion of the mass spectrometer signal is observed [5]. A schematic CH diagram of the experimental setup is shown in Fig. 3.7.  P 20 bar = 0 12K d=5im 0 T  He droplet size:  3000 atoms  Mass Spectrometer  4 CH Mirror  He 4 o  Low temp Nozzle  Cluster growth  Pick up Photon absorption Ionizer and cell evaporation  Laser beam  Figure 3.7: Experimental setup for the CH 4 depletion experiment. 4 He atoms cluster into droplets after leaving the 5 pm nozzle. The droplets pickup CR 4 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 4 He 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 4 He 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 v 3 band of methane in droplets with an average size of 2100 helium atoms [5]. In this experiment, the average droplet size is 3000 4 He 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 cm 1 and the dissociation energy of helium is 5 cm . Therefore, 1 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 0 1’ A 2 N . crn O 3 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%.  50  3.3. Preparation for the depletion experiment  3.3 3.3.1  Preparation for the depletion experiment 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 closedcycle 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 He gas line is changed to copper to promote good thermal contact the 40 K stage, the 4 between the 4 He 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 4 He 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 4 He line terminates at the nozzle compartment which is mounted on the fridge cold head. In this way, the 4 He gas is precooled before reaching the nozzle. The nozzle compartment and nozzle components are pictured in Fig. 3.8. The exit,  CW Nozzle  Aperture (5 pm hole) Gasket  He gas Copper hollow cylinder  //  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. st 1  stage  of fridge 40 K 2r42 K He gas Stainless tube  Copper 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 4 He 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 4 He 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  { r  Cylinder  He gas line  cw  I  Methanol  Nozzle  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.  Manganin wire 30 cm (1.7 fl)  Heater ( 50 ) -nd  stage of fndge  CW Nozzle  _-II  Heater(50fl) Hegas  I  Temperature sensor D35664  Temperature Copper 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  1 T cw Nozzle View from nozzle chamber  Mass chamber  Main chamber  Nozzle chamber  L  Mirror  Skimmer  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: ). 2 I(x,z)=—(x 2 —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:  (3.2a)  0 mr —  —-o(t)z  0 mr  =  0.  (3.2b)  54  3.3. Preparation for the depletion experiment  +,o  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:  b  4qU mr w 0 2qV 2 w 0 mr  (3.3a)  (3.3b)  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 55  3.3. Preparation for the depletion experiment  0.3  0.237 0.2  0.1  0.0 0.0  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  Oft. CABLE  9o  --  I 1  Capacitance of quadrupole mass filter  SELO CABLE IF NECESSARY  RADIO FREQUENCY POWER SOURCE  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 (H 0) and 28 amu (N 2 ). Thus our 2 calibration of the mass meter dials on the front panel of QUADRUPOLE CONTROL was done by observing the H O and N 2 2 mass peaks in the mass chamber spectrum. [52] In the depletion experiment, before entering the quadrupole filter, helium droplets doped 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  -  -  -  s  M L R  L  Fo  N  : Filament  Figure 3.16: The quadrupole mass filter, ionizing filament F , and ion optics elements 5, 0 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 after completing the optimization procedure.  =  16 amu) increased by a factor of 102  57  3.3. Preparation for the depletion experiment  3 i0  102  rI  101  10°  0  10  30  20  40  Mass (u)  Before optimization  After optimization  S=-72V M=-38V L=-50V N=+5V F =-55.5V  S=-72V M=-40V L=-1OV R=+5V N=+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 =14 K 0 in Fig. 3.18 was measured with the 0.8 mm skimmer and the CW nozzle at T =20 bar. The Scanmate dye laser describe earlier was used for this measurement 0 and P 1 and . Both the c and 3 peaks are present at 22300.7 cm 1 with a resolution of 0.1 cm normalized by the laser 22301.8 cm 1 respectively (see §2.4.2). The spectrum was not 1 scans. Both peak positions are power because it is nearly constant for the short 3 cm 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 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  averaged over 5  10  22298 wavenumber (cm  )  To = unknown (at this time no temp sensor) Po=2Obar Pulse Nozzle 2 mm skimmer  ...........N..  22300 22302 wavenumber [cm ] 4  22304  I  22306  To = 14.0 K Po=20bar • CW nozzle • 0.8 mm skimmer  Figure 3.18: Left: LIF spectrum averaged over 10 scans measured using the pulsed nozzle 0 = 20 bar and uses the 2 mm skimmer. The spectrum is similar to that operated at P originally measured using the pulsed nozzle. Right: LIF spectrum measured with the 0 = 20 bar averaged over 5 scans. The 0 = 14 K and P 0.8 mm skimmer and CW nozzle at T . 1 c peak is at 22300.7 cm 1 and the /3 peak is at 22301.8 cm  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 P 0 = 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 T 0 = 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 T 0 = 6.4 and 20 K look very similar to the residual gas spectrum taken with no helium droplet beam as —  —  59  3.3. Preparation for the depletion experiment  0 P  2.0 MPa  1 101  101 0 U)  C,  U)  0.0 0  C 0 U  11)  101  0 C 0)  (I)  101  10’ 10’  Moss (omu)  0  20  40  60  80  100  120  140  Mass (amu)  Figure 3.19: Left: Helium droplet mass spectra measured by Buchenau et al. with a nozzle pressure P 0 = 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 T 0 = 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 60  3.3. Preparation for the depletion experiment  0 = 2.0 MPa P  =2.OMPa 0 P 100  10  102  =20.OKI 0 T  -  T=20.0KI  102  -  -  101 too  IIIIIIIIIiiiiHmIImHmImi  2 to 102  =hi0Ki 0 T  -  ;;;, Ifl’  To’ 20  10’  cM  Otis  -  h  102  2  _.lII  I  -  I  111111  =12.512i 5 1T  to2  =t5.OKI 0 IT  -  I  ,  ‘11111111111111111111111  —:  -  (02  -  2 to  I  I::  1111111111111111111  Vo—125dI  o  -  I0  I=9.5KI  2 to  ; I  I  I  I  to  I I  I  I  =9SKj 2 Ir  too  -  I  I  I  I  I  I  I  I  I  I  I  I  I  I  I  I  100  I  too  r;  102  IT =6.4 0  ITr64 JC1  to’ 100  100  120  140  -  0  0  to  Mass (ama)  102 .5  6  Reaidual gaam in mona chamberl  10  -a  I  S’s 0  20  40  60  80  Maaa (omu)  100  120  140  Mesa (ama)  Figure 3.20: Left: Helium droplet mass spectra measured up to 140 amu with a nozzle pressure P 0 = 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 mm 2 diameter mirror mounted between the nozzle tip and the skimmer inside 61  3.3. Preparation for the depletion experiment  16 Pnozzle 14  I  12 10 8 6 6  8  10  12  14  16  18  20  14  16  18  20  I  I  0 [K] T  ‘C  I 6  8  10  12  0 [K] T 51  I  I  I  I Pmassl  4  0 = 20 atm P 3 2  6  I  I  I  I  I  I  I  8  10  12  14  16  18  20  0 [K] T  Figure 3.21: Chamber pressures as a function of nozzle temperature for a nozzle pressure of P 0 = 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 mm 2 mirror in front of the nozzle and is reflected out through the window of the chamber. 62  3.3. Preparation for the depletion experiment  HNclscr Nozzle chamber  Main chamber  Mass chamber Iris Gold Mirror  *nd 2 Skimmer // CW cell is moved st 1 Nozzle Middle cell close to cell removed.  CaF 2 Window (0.1 5um-9um)  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 (CaF ) and transmits wavelengths in the range of 0.15-9 m with nearly 2 100% 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 4 He droplets absorb a single CH 4 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 63  3.3. Preparation for the depletion experiment He atoms. Also, the optimized neon line pressure for helium droplets of this was 3 x io 4  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 CH 4 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 4 He 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 cm 1 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  2980  3000  3020  3040  3060  3080  3100  R(0) R(1) R(2)  FTIR Experiment (cm-I) 3028.76 3038.51 3048.17  R(3)  3057.71  P(1) P(2)  3009.02 2999.01  P(3)  2988.94  0(1)  3018.83  High resolution IR spectrum of ) 1 4 (cmCH 3028.752900 3038.499200 3048.153317 3048.169000 3057.688000 3057.727000 3057.760693 3009.011370 2999.060410 2998.994010 2988.795286 2988.932512 2989.033465 3018.824480  venumber (cm ) 4 3 vibrational band of methane in gas phase Figure 3.23: Left: Absorption spectrum of the v measured by FTJR. The resolution of the measurement is 0.01 cm . Right: The peaks 1 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.  3.3.6  Depletion experiment setup  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 H 0. The peak at m = 28 amu (a cluster of seven 4 2 He atoms) is enhanced because it is coincident with to an N 2 peak. The peak at m = 16 amu is also enhanced because there are contributions from clusters of four 4 He atoms as well as CH . 4 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 CH 4 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 Laptop computer “USB 6009 lab view”  Function Generator Agilent 33250 A output  ——  x20  converter  In/out  -  Voltage amplifier FLC A400DI 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 v 3 vibrational band of methane in the gas phase using the Aculight laser.  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 Cl 4 in the 4 He nanodroplet is excited. It quickly relaxes back to the ground state and causes some 4 He 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 cm . This data set had a limited scan range that spanned 3029 cm 1 1 to 3029.4 cm . Future scans will make use of new laser components that will enable scans 1 that cover 3 cm 1 at a time. Preliminary results are shown in Fig. 3.27. This spectrum was measured with a nozzle temperature of T 0 = 12.5 K and laser chopping at 130 Hz. The 66  3.3. Preparation for the depletion experiment  3028.0  3028.5  3029.0  3029.5  3030.0  3030.5  wavenumber (cm’)  3038.0  3038.5  3039.0  3039.5  3040.0  wavenumber (cm’)  3007.5  3008.0  3008.5  3009.0  3009.5  3010.0  3019.0  3019.5  3020.0  wavenumber (cm’)  3017.5  3018.0  3018.5 wavenumber (cm ) 4  Figure 3.25: From top to bottom: the R(0), R(l), P(1), and Q(1) branches of the v 3 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 67  3.3. Preparation for the depletion experiment  /  Frequency Marker  —  \  \ /  Chopper controller  AculigtAigos ‘240Q  -  [ZZ]  mass L  I.  Wavelength meter LBristol i  /  -  T  -  -  I  Shape of voltage applied to PZT  -  O_12O_/”\ Mass  Scan speed: 2 V/Sec  chamber  p 9 Oscilios  LL_ 1  Preamp Standford  Laptop computer “USB 6009 lab view”  LZ:5R570 -  Lock-  X  put  uoutput  F L.  -  -.  001  -  2.T —  4L convener  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 temperature T =16.4 K. At P 0 =20 bar this change in temperature corresponds to a 0 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 CH -doped 4 4 He 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 cm , however our wavelength meter 1 was not properly calibrated at this early stage of the measurement. The width reported by Nauta et at. is 0.2 cm 1 which seems consistent with our partial measurement of the R(0) peak.  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 T 0 = 16.5 K and P 0 = 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 2 will be added to the CH H -doped droplet in the second pickup cell. The JR spectra will 4 be studied as a function of the number of H 2 molecules with the objective of investigating the possibility of superfluidity in molecular hydrogen.  69  3.3. Preparation for the depletion experiment  Before optimization  3 12x10 10 8 6 4 2— 0— 3029.0  3029.1  3029.2  3029.3  3029.4  3029.3  3029.4  wavenumber (cm ) 1  3 7x10 6  5 4 3 2 1  0 3029.0  3029.1  3029.2 wavenumber (cm ) 1  Figure 3.27: Top: First CH -doped 4 4 He 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).  70  Chapter 4  Conclusions and outlook In the first part of this thesis the fluid characteristics of Ar, Ne, and H 2 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, 2 and pH 2 clusters. For Ar and Ne clusters, the spectral shift was found to depend Ne, nH 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 pH 2 clusters remain fluid-like in the 4 11e droplets at 0.38 K. In the second part of this thesis project, the rotational and vibrational relaxation of methane in 4 11e droplets was studied in a depletion experiment. Methane-doped 4 He 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 4 He 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 4 He 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. Superfluid Helium Droplets: A Uniquely Cold Nanomatrix for Molecules and Molecular Complexes. Angew. Chern., mt. Ed., 43:2622, 2004. [6] G. Scoles and K. K. Lehmann. Nanomatrices are cool. Science, 287:2429, 2000. [7] M. Y. Choi, G. E. Douberly, T. M. Falconer, W. K. Lewis, C. M. Lindsay, J. M. Merritt, P. L. Stiles, and R. E. Miller. Infrared spectroscopy of helium nanodroplets: novel methods for physics and chemistry. mt. Rev. Phys. Chem., 25:15, 2006. [8] E. L. Knuth, F. Schflnemann, and J. P. Toennies. Superfliud Helium Drolets: A Uniquely Cold Nanomatrix for Moleucles and Molecular Complexes. Angew. Chem. mt. Ed., 43:2622, 2004. 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