UNIMOLECULARREACTIONDYNAMICSINHELIUMNANODROPLETS by DaniilStolyarov ADissertationPresented tothe FACULTYOF THEGRADUATE SCHOOL UNIVERSITYOF SOUTHERNCALIFORNIA InPartial Fulfillmentofthe RequirementsfortheDegree DOCTOROF PHILOSOPHY (CHEMISTRY) May2005 Copyright 2005 DaniilStolyarov Contents ListofFigures iv Abstract vii Preface ix 1 Elementary excitations ofa heliumnanodroplet (Discrete spectrum) 1 1.1 Surface excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Force constant . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Mass parameter . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Compressionmodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Densityofstatesandmicrocanonicalthermodynamicfunctionsofhelium droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Evaporativecooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Reference List 17 2 Dynamic properties of liquid 4He and 4He clusters and their influence on the unimolecular reactionrate 18 2.1 Developementofconceptual frameworkofthetheoryofliquidhelium . 21 2.1.1 Early experimentson liquidhelium . . . . . . . . . . . . . . . 21 2.1.2 Conceptsofquasiparticleandelementaryexcitationenergyspec- trum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2 Feynman’smicroscopictheory ofliquidhelium . . . . . . . . . . . . . 28 2.2.1 Inelasticneutronscatteringin frames ofFeynman’stheory . . . 34 2.3 Dynamic structure factor S(q,ω) measured in the neutron scattering experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.4 Extention of the microscopic theory of liquid helium on the case of heliumnanodroplet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.4.1 StaticstructurefunctionS(q) . . . . . . . . . . . . . . . . . . 44 2.4.2 Surface excitations . . . . . . . . . . . . . . . . . . . . . . . . 50 2.4.3 DynamicstructurefunctionS(q,ω)ofheliumdroplets . . . . . 52 ii 2.5 Influenceofheliumenvironmenton unimolecularreaction rate . . . . . 56 2.6 Collisionalenergy transferfunctionforliquidheliumenvironment . . . 61 2.6.1 Phonon region . . . . . . . . . . . . . . . . . . . . . . . . . . 66 2.6.2 Independent particleregion . . . . . . . . . . . . . . . . . . . . 68 Reference List 71 3 Experimental methods and instrumentation 74 3.1 Massdepletionspectroscopy . . . . . . . . . . . . . . . . . . . . . . . 74 3.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Reference List 82 4 Mass-depletion spectroscopy ofNO in helium droplets belowits gas phase 2 dissociationthreshold 83 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.2 Experimentalresults . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.3 Theoreticalconsiderations . . . . . . . . . . . . . . . . . . . . . . . . 87 4.3.1 Spectral lineshifts . . . . . . . . . . . . . . . . . . . . . . . . 88 4.3.2 Spectral linewidths . . . . . . . . . . . . . . . . . . . . . . . . 91 4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.4.1 Originofthewidths . . . . . . . . . . . . . . . . . . . . . . . 95 4.4.2 TheHe-NO binarycomplex . . . . . . . . . . . . . . . . . . . 97 2 4.4.3 Mechanismand model . . . . . . . . . . . . . . . . . . . . . . 99 Reference List 101 5 Mass-depletion spectroscopy of NO in helium droplets above its gas phase 2 dissociationthreshold 104 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.2 Resultsand Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Reference List 115 iii List of Figures 1.1 Calculationoftheelementary surface . . . . . . . . . . . . . . . . . . 3 2.1 Specific heat of liquid 4He. The broken line shows the calculated spe- cificheat ofan idealBose gashavingthesamedensityas liquid 4He. . . 22 2.2 Liquid4Heelementaryexcitationenergyspectrummeasuredbyneutron scattering. [11] The insert shows the energy spectrum predicted by Landau. [25] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3 Pair correlation function (a) and static structure function (b) of liquid heliumobtainedin neutronscatteringexperiments[38]. . . . . . . . . . 30 2.4 ComparisonoftheenergyspectrumpredictedbyFeynman’stheorywith one obtained experimentally. The energy spectrum calculated from the equation (2.23) using the structure factor values obtained in neutron scattering experiment [38] is marked by solid circles. The energy spec- trum measured experimentallyby neutron scattering [1] is marked with open circles. The free particle energy spectrum: !2q2/2m is shown by thedashed line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.5 DynamicstructurefunctionS(Q,ω)measured in theneutron scattering experiment [1] at different values of momentum transfer Q. The mea- surementswere madeatthetemperatureT = 1.1K. . . . . . . . . . . . 40 2.6 Dynamicstructurefunction of the bulk helium measured in the neutron scatteringexperiment[1]andshowninfigure2.3,mappedontheenergy vs. momentum diagram. The hatched area showes the multiphonon scattering region. The upper and lower energy boundaries of the peak correspondingto half thepeak intensityare denoted by solid lines. The dashedlinerepresent thefree particledispersioncurve!2Q2/2M. . . . 41 iv 2.7 Intensity of the one-phonon peak Z(Q), the multiexcitationcomponent S (q,ω),andtheirsumS(Q)measuredintheneutronscatteringexper- M iment.[1]Thedashedlineshowesthestaticstructurefunctionmeasured byX-ray scattering.[2] (Thefigureistaken from [1]) . . . . . . . . . . 43 2.8 ThestaticstructurefunctionS (q)forthedropletswith20,40,112and dr 1000 atoms calculated by HNC/EL method (solid lines) [8] and by the DMCmethod[7](dottedlines). Thestaticstructurefunctionforthebulk heliumS (q)[23]is shownby thedashedline. . . . . . . . . . . . . . 48 ∞ 2.9 Surface excitations energies for the droplets of different sizes. [8]. The lowest excitations with l 9 are shown. R 5/3r is a hard rms ≤ ≡ sphere radius. Dashed line denotes the lowest excitation energy of a ! heliumfilmadsorbedongraphitesurface[9]. Thesolidlineshowsfitting curvegivenbyequation(2.59) . . . . . . . . . . . . . . . . . . . . . . 50 2.10 Dynamicstructurefunctions of helium droplets containing N =112(a), 240(b) and 1000(c) helium atoms. [8] The solid line shows Feynman’s energy spectrum forbulk helium. Dashed lines showripplondispersion curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.11 Dynamic structure functions of SF doped helium droplet containing 6 N =112 He atoms [8]. The solid line shows Feynman’s energy spec- trumforbulkhelium. Thedashed lineshowsripplondispersioncurve. . 55 2.12 Lindermanmechanismofchemical reaction in conditionsofcollisional energy transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.13 Vectordiagramoftheelementary scatteringevent. k and k initialand i f finalwavevectorsoftheparticle,q isthewavevectorofthequasiparticle created in collisionandθ is thescattering angle. . . . . . . . . . . . . . 62 2.14 Sketch of the energy transfer function R(∆E), ∆E = E E . The i f − Feynman excitation spectrum curve is shown below. (Spikes at ∆E = E and ∆E = E aredueto "(q) = 0 at thesepoints.) . . . . . . 68 roton roton E 3.1 Schematicrepresentationoftheprocessthemassdepletionspectroscopic technique is based on. Step (1) represents the doping of the helium droplet with the molecule. Step (2) showes the photon-induced excita- tion of the molecule. The excitation energy is transfered to the helium droplet(3)andcausesevaporationofthehelium(4)resultingindecrease ofionizationcross section. . . . . . . . . . . . . . . . . . . . . . . . . 74 v 3.2 Experimentalarrangement(nottoscale). Thesource,pickup,anddetec- tion chambers are pumped separately. The nozzle is at 14.5 K, and the He pressure behind the nozzle is 40 bar. The laser beam is brought to a focusin thedetectionchamberto avoiddamagingthenozzle. . . . . . . 78 4.1 (a) Mass spectrometer depletion spectrum. (b) Frequencies and inten- sities of R lines recorded by using LIF are taken from Georges et al. 0 [10] (c) All of the lines in (b) have been assigned 7 cm−1 widths and blue-shifted by 7 cm−1. The intensities are fitted to the experimental spectrum. (d)Theexperimentaland simulatedspectraare overlapped. . 86 4.2 CollisionaldeactivationofNO moleculebyliquidheliumenvironment 90 2 4.3 Calculationofthehomogeneousspectrallinebroadening. Thesketchof theenergytransferfunctionforthemoleculedeactivationisshowninthe upper part of the plot. Vertical lines represent NO levels starting from 2 theonethatwasinitiallyexcited. Thespectrallinewidthisgivenbythe sum of the function values at the positionscorresponded to NO levels. 2 The lower part of the plot shows the Feynman excitation spectrum of liquidhelium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.4 Thedepletionsignalversuslaserfluence can befittedwith astraightline. 98 5.1 Mass spectrometer depletion spectra for m/z values of: (a) 8 (He+); 2 (b) 46 (NO+); (c) 30 (NO+). When error bars are not visible, they are 2 smallerthanthepoints. . . . . . . . . . . . . . . . . . . . . . . . . . . 114 vi Abstract Heliumnanodropletisolationtechniqueprovideanuniqueopportunitytostudyelemen- tary chemical reactions in the ultracold liquid helium environment. The main question addressed in this work ishowdoes theliquidheliumenvironmentaffect chemical reac- tiondynamics. Thediscussionis limitedtothecaseofunimolecularreactions. First, it is shown how the spectrum of elementary excitation of helium droplets can be obtained. This spectrum is then used for evaluation of microcanonical thermody- namic functions of helium droplets at low temperature, as well as description of the process knownas evaporativecooling. Second, Feynman’s microscopictheory of liquid helium is exctended to the case of helium droplets and other systems of liquid helium in confined geometries. Possible effects due to the finite size of helium droplets are also discussed. The extention of the microscopic theory allows for the prediction of the dynamic properties of helium droplets. Themodelofunimolecularreactionsinconditionsofcollisionalenergy trans- fer, is adapted for the case of unimolecular reactions in the liquid helium environment. Theenergy transfer ratefunctionin thiscase isevaluatedbased on thedynamicproper- tiesofliquidheliumand heliumdroplets. Finally,theexperimentsonmassdepletionspectroscopyoftheNO moleculeinthe 2 regions below and above its gas phase dissociation threshold are described. In the first experiment a mass depletion spectrum in the region 17700-18300 cm−1 is recorded. vii Gas phase NO is believed to be vibronically chaotic at these energies. Transitions 2 are broadened and blue-shifted relative to those of the gas phase by 7 cm−1. Modest dispersion(i.e. 90%liewithin2cm−1ofthecentralvalues)areconsistentwithquantum chaos in NO . It is shown that the relaxation is dominated by interactions of NO with 2 2 itsnon-superfluidheliumnearest neighbors. Inthesecondexperiment,theguest-hostdynamicsofNO embeddedinHe droplets 2 n havebeenexaminedbyrecordingdepletionspectraofmassspectrometersignalsatm/z values of 8 (He+), 30 (NO+), and 46 (NO +), throughout the wavelength range 340- 2 2 402 nm. Above the gas-phase dissociation threshold (D ), it is shown that there is 0 no net unimolecular decomposition all the way up to D + 4300 cm−1. At the upper 0 end of this range, gas-phase NO decomposes with rate coefficients whose values are 2 5 1012s−1,whichisexpectedtobelargerthanthedeactivationratesinliquidhelium. ∼ × Towithintheexperimentaluncertainty,itisfoundthatreactionproductsdonotleavethe droplets. Thisisattributedto efficientrelaxation and(at thehighestenergies examined) recombination within the droplets. On the basis of these results, it is concluded that smallpolyatomicsembeddedinHe dropletsthathave n valuesof 104orlargerwill n & ’ ∼ not undergo net unimolecularreaction if the gas-phase pathway is barrierless, with two possible exceptions:(i) if one or both of the products has a positive chemical potential and (ii)ifthescatteringcross sectionoftheproduct(s)withheliumis small. viii Preface Reactions proceeding at low temperatures have attained great interest over the past decades. These kinds of reactions can be considered as a versatile means of preparing new types of compounds. Liquid helium is a perfect environment for this kind of reac- tion. However, the study of a chemical reactions in bulk liquid helium is complicated duetothecoalescenceofreacting species thatentanglesthereaction mechanism. Discovery of helium nanodroplets, i.e. clusters containing 103 106 helium atoms − signified a new era in experimental cryochemistry. It has been found that the helium nanodropletsnotonlyinherituniquepropertiesofliquidheliumsuchassuperfluiditybut alsocanbeeasilydopedwithforeignatomsormolecules. Thusthecoalescenceproblem can be avoided. It provides an unique opportunity to observe and study elementary chemical reactions. The interaction between embedded species and liquid helium environment is rather weak. Neither the interaction changes the chemical identities of reactants nor does it restrict their mutual motion during the reaction. However, liquid helium acts as an efficientcoolant. Themajorinfluenceoftheliquidheliumenvironmentonthechemical reactionisthatliquidheliumdrainstheenergyofthereactingmolecules. Thus,dynamic properties of liquid helium are of primary concern. The dynamic properties of bulk liquidheliumdifferfromthedynamicpropertiesofliquidheliuminconfinedgeometries ix andhencetheinfluenceofliquidheliumonachemicalreactionisdifferentinthesetwo cases. This thesis is organized in the following way: chapter 1 will use the normal mode approach to find the elementary excitation spectrum of helium droplets at low temper- atures. There are two types of elementary excitations of helium nanodroplets:surface and compression modes. Then the microcanonical thermodynamic functions based on the spectrum obtained will be evaluated and the rate of evaporative cooling of helium droplets will be calculated. The latter process allows droplets to maintain the tempera- tureof 0.37K. ∼ In chapter 2, the microscopic theory of bulk liquid helium introduced by R. Feyn- manwillbeextendedtothecaseofheliumdropletsandothersystemsofliquidheliumin confined geometries, taking into account the possible finite size effects. This approach generalizes the consideration of the bulk liquid helium and the liquid helium in con- fined geometries, and hence helps to find differences and similarities of these systems. Laterthischapterwilldevelopthemodelofunimolecularreactionsintheliquidhelium environment. It isbasedonthemodelofan unimolecularreactionthatproceeds incon- ditions of collisional energy transfer. The energy transfer rate function of this model is evaluated based on dynamical properties of liquid helium and helium nanodroplets givenby themicroscopictheory. Spectroscopy is a reliable tool to explore molecular dynamics. Thus, comparing a spectrum of a free molecule with a spectrum of the molecule in liquid helium envi- ronment, the influence of the liquid helium environment on the molecular dynamics is revealed. Results of the experiment on measuring absorption spectra of NO molecule 2 belowand aboveits gas phase dissociationthreshold are also discussedin chapters 3, 4 and 5. TheNO moleculewas chosenas thecandidateforthisstudybecause itexhibits 2 x