Spectroscopy and Dynamics of doped helium nanodroplets Kevin K. Lehmann University of Virginia NSF
Properties of 4 He Nanodroplets Helium binding energy of ~5 cm -1 (7 K) Evaporative cooling to T ~ 0.38 K ~100% superfluid if bulk Helium We generate droplets with <N> ~ 1,000-20,000 atoms R ~ 2-7 nm Broad Log-Normal distribution of size There are no thermally populated phonons Lowest excitation energy 534 N -1/3 GHz > 3 kt Surface Ripplons form heat bath ν(l) = 78 L(L 1)(L + 2)N 1/2 GHz Lowest mode (L=2) ~ 2.2 GHz (~0.3 kt) for N = 10 4 Amplitude ~ 0.4 Å
Why Spectroscopy in He Nanodroplets? Rapid Cooling (~nsec) below 1 K Stabilize unstable species and form new compounds Vibrations and Rotations are cooled Pickup only requires vapor pressure of ~10-4 torr Allows study of very nonvolatile species Can form controlled clusters Poisson Distribution of sizes Gives Rotational Resolution -> structural information Higher Resolution and smaller shifts than other Rare gas matrices The Ultimate Spectroscopic Matrix!
Droplet Production and Detection 10 µm aperture T=16 35 K flux: 10 20 atoms/s dopant inside (except alkali) Visible, IR, or UV Microwave (rotational transitions) NEP: 35-45 fw/ Hz ~10-4 torr He 100 atm las ser cold expansion cluster formation dopant pick-up photon absorption + He evaporation (10 2-10 4 He/photon) MW multiple photon absorption + He evaporation (0.1 He/photon) detection (bolometer) Droplet sizes: 1000-10000 atoms (45-95 Å diameter) Droplet temperature: 0.4 K (evaporative cooling) Sensitivity (S/N=1@1Hz): 3 10 7 He atoms
The cluster machine cold head pump out gas in so ource BUC pick-up cell MW cavity laser in (optic fiber) bo olometer MW in
The beginning SF 6 in He droplets Goyal, Schutt and Scoles, PRL 69, 933 (1992) Narrow lines Small shifts Complexes formed (SF 6 ) 2 // SF 6 (SF 6 ) 2
Rotational resolution in 4 He droplets (Hartmann, Miller, Toennies, and Vilesov, PRL 75, 1566 (1995) Cryotip T 0 =5-30 K He P 0 =5-100 bar Interaction region Ionizer Scattering & QMS gas Window Lens Mirror SF 6 freely rotates inside the droplet, but T=0.37 K SF 6 the observed B is only P Branch R Branch 37% of the gas phase value 4 3 2 1 0 1 2 3 4 SF
OCS in 3 He and 4 He droplets: proof of superfluidity in 4 He droplets Grebenev, Toennies, and Vilesov, SCIENCE 279, 2083 (1998) 0 7 25 Free rotation is exclusive to 4 He (a boson fluid). In 3 He (a fermion fluid) free rotation does not occur, unless enough 4 He is present to form a shell around the OCS molecule. 35 60 100 P1 R0 R1-0.2 0.0 0.2 0.4
Acculight Argos OPO Approximately 1.75 W of power measured entering the machine. To Spectrometer Wavemeter S P I OPO Power meter 7.5 GHz etalon 150 MHz etalon Produces over 2 W of CW over the tunable range of 3.2 3.9 µm. Continuous scans of 45 GHz. Also produces 2-5 W of 1.5 µm light.
Methane ν 3 v 3 Q(1) line 3018 3018.5 3019 3019.5 3020 3020.5 wavenumber (cm -1 ) Found two extra lines. A second line near Q(1) and also a P(2) line. P(2) Miller Groups Methane spectra of the ν 3 band. Nauta, K., Miller, R.E. Chem Phys. Let. 350 (2001) 225. 3001.2 3001.6 3002 3002.4 3002.8
Methane ν 2 + ν 4 2830.8 2831.2 2831.6 2832 2832.4 2845.6 2846 2846.4 2846.8 Found 2 lines of a second band of methane. From these values assuming B and ζ we derived ν 0 = 2836.36 cm -1 and B = 5.2279 cm -1. The addition of an R(1) line would help solve more equations and will be searched for. Line He (cm -1 ) Gas Phase (cm -1 ) HWHM (cm -1 ) Q(1) 2831.459 2835.876 0.051 R(0) 2846.304 2851.46 0.068 Constant He Value Gas Phase Value ν 0 2836.36 cm -1 2841.009 cm -1 B 4.978 cm -1 5.2279 cm -1 Lolck, J., Robiette, A., Brown, L., Hunt, R.H. J. Mol. Spec. 92 (1982) 229.
Comparison of Widths Line Methane v 2 + v 4 He (cm -1 ) HWHM (cm -1 ) Q(1) 2831.459 0.051 R(0) 2846.304 0.068 CH 3 D v 4 Line Frequency HWHM (cm -1 ) (cm -1 ) P(1) 3008.846 0.4154 Q(1) 3016.046 0.221 R(0) 3025.345 0.120 Line CH 3 D v 1 Frequency (cm -1 ) HWHM (cm -1 ) Q(1) 2969.789 0.0289 R(0) 2977.144 0.0387 Line Line CH 2 D 2 v 1 Frequency (cm -1 ) HWHM (cm -1 ) Q(1) 2977.220 0.0107 R(0) 2982.868 0.0184 CH 2 D 2 v 4 Line Frequency HWHM (cm -1 ) (cm -1 ) Q(1) 3013.728 0.4421 R(0) 3020.253 0.1556 R(1) 3026.077 1.5522 CHD 3 v 1 Frequency (cm -1 ) HWHM (cm -1 ) Q(1) 2993.319 0.0188 R(0) 2999.289 0.0266
CH 3 Cl Line Location (cm -1 ) HWHM (cm -1 ) P 1 (2) P 0 (2) P 0 (1) Q 0 (1) R 0 (0) R 1 (1) R 0 (1) 2968.268 0.0423 2968.371 0.0334 2968.594 0.0244 2968.78 0.023 2969.135 0.0226 2969.293 0.032 2969.369 0.1041
Planned IR experiments IR-MW double resonance to determine rate of rotational relaxation in droplets IR-IR double resonance to determine rate of vibrational relaxation in droplets Visible-IR double resonance to determine cooling rate of droplets to test evaporative cooling models Study chemical reactions at very low temperatures test reactions proposed by Astrochemistry.
New Experiment: Driving Ions in Helium He droplet source Ions Lens Electrostatic energy selector Ion Multipler Atoms hν grids Figure 3: Schematic of proposed ion machine
(a) (b) (c) Figure 1: Classical Simulation of ion motion in He droplet driving by frequency swept microwave field of 20 V/cm. Red is the frequency; blue the ion kinetic energy; and black to energy deposited in droplet. Not the change in scale on the left for the second figure. This demonstrates that the ion will lock onto and follow the frequency until the ion moves at the critical velocity. Above this, the ion no longer can follow and relaxes to zero energy (c).
Proposed Experiments on ions Determine critical velocity for different ions & function of droplet size Measure rate of translational cooling Use circularly polarized radiation to pump in angular momentum (~10 9 hbar/sec) Nucleate vortices? Measure helium loss vs. energy input Nanocalorimeter to measure binding energy of clusters formed in droplets.
Evaporative Cooling of Helium Nanodroplets with Angular Momentum Conservation KKL & Adriaan Dokter Physical Review Letters 92, 173401 (2004)
Thermodynamics of Helium Droplets Statistical Evaporative cooling calculations of temperature versus cooling time. D.M. Brink & S. Stringari Z Phys. D 15 257 (1990)
There have been previous classical and quantum statistical evaporative cooling studies These predicted droplet temperatures close to those later found experimentally They ignored angular momentum constraints Droplets pick up considerable angular momentum in pickup process and possibly during formation due to droplet coalescence Can this be completely shed during cooling? Experiments of Portner, Havenith, and Vilesov interpreted as implying that droplets remember direction of initial angular momentum Droplet Energy and Angular Momentum will be stored in primarily in Ripplons
Distribution of Collisional Angular momentum for N = 10 4 Scales as N 1/3 for other droplet sizes
Monte Carlo Evaporation Start with E, L from pickup process E ~ 1700 K and L ~ 4000 for tetracene pickup Calculate number of open channels Droplet(E, L) -> Droplet(E, L ) + He(E k, J) E -2/3 k = E - E - E bind > 1.23 K J(J+1) N (centrifugal barrier) Calculate RRKM rate and increase time by lifetime Pick one decay channel at random equal probability Repeat until time > cooling time (10 or 100 µs). J = 10, 1000, 2000, 3000, 4000 & 5000 studied, 500 decay trajectories for each
Conclusions Droplets have MUCH higher internal energy and angular momentum than for a canonical ensemble at same temperature. Explains why previous attempts to predict lineshapes failed PIMC will not give exact predictions - may be substantial bias Molecular Lab frame alignment of embedded molecules should be common.
Energetic Considerations on the formation and decay of a Vortex in Helium Nanodroplets KKL & Roman Schmied
Vortices are common, basically unavoidable in bulk superfluid helium, but have not yet been observed in helium nanodroplets Simplest Vortex is a straight line In droplets must go through center Will have one quantum of angular momentum per helium atom in droplet. Previous considered by DFT and PIMC calcs. Helium flows around vortex with local velocity, v = h/2πmr; r min. distance to vortex
In bulk, Vortex may be approximated by a hollow core of radius a ~ 1.0 Å (Rayfield & Reif) Energy proportional to length of vortex Droplets will distort moderately from vortex For 10 4 He droplet: B= 4.60 nm, A= 4.88 nm Trade off Vortex energy and surface energy. Net drop in energy of -4.64 K
Comparison of Vortex Formation Energy for N=1000 droplet Density Functional 129 K Dalfovo et al. PRL 85, 1028 (2000) Hollow Core Model 103 K a=1.0 Å 500 quanta L = 2 Ripplon 167 K Same total angular momentum
Energy of Vortex normalized by Equal Angular momentum in lowest Ripplon mode DFT Theory Hollow Core Model
Curved Vortex Lines Vortex can be off centered and curved. Will then wrap around droplet, but will have greater energy per unit angular momentum. Angular Velocity is derivative of Energy with Angular momentum - Will be stable if below that of Lowest Ripplon
Energy and Angular Momentum of curved Vortex Solutions
Angular Velocity of Curved Vortex divided by Ripplons N = 10 5 N = 10 2 Distance of Closest Approach of Vortex to Axis
Lowest Angular Momentum of Stable Curved Vortex N L / h-bar 10 2 25 10 3 160 10 4 930 10 5 5400
How could Vortex be formed? Thermal angular momentum at T λ? Not enough < J > = (3 k T λ I cl ) 1/2 ~ 0.7 N 5/6 Collisional Angular Momentum of pickup? SF 6 collision should deposit several thousand units of angular momentum Enough for small smaller droplets Coalescence of droplets? For impact of 3 nm, need relative v ~ 10 m/s
Distribution of Collisional Angular momentum for N = 10 4 Scales as N 1/3 for other droplet sizes
How Can a Vortex Decay? Into Ripplons? Lowest energy N unit of angular momentum = 5.3 K N 1/2 Always more than vortex energy By Atom evaporation? Also endothermic Angular momentum loss by evaporation < mvr Also costs ~7 K per evaporation For N=10 3, Vortex energy can remove a maximum of 171 units of angular momentum
How Can a Vortex Decay? Fragment into two droplets? Must increase surface area by ~26% E suf =4.4 K N 2/3 Very strongly endothermic It appears that a vortex once formed will be highly metastable. Solute molecules will be trapped on vortex and aligned by it (Dalfovo et al).
Why have they not be yet detected? Collisional excitation with enough angular momentum to produce sufficient L will deposit far from E than that of vortex At these high E, density of states is dominated bulk excitation Perhaps cooling by evaporation will remove angular momentum fast enough to prevent trapping in basin of metastable vortex?
Energy of Straight Vortex For core radius a: h2 ρ B 2A E = e sv ln 2πm a 1
Thanks for you attention! If you find this interesting, please stop by to see me: Email: Lehmann@virginia.edu Office: Chemistry Rm 126