Spectroscopy and Dynamics of doped helium nanodroplets Kevin K. - - PowerPoint PPT Presentation

Spectroscopy and Dynamics of doped helium nanodroplets

Kevin K. Lehmann University of Virginia

NSF

Properties of 4He 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 – 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

– Lowest mode (L=2) ~ 2.2 GHz (~0.3 kT) for N = 104 – Amplitude ~ 0.4 Å

ν(L) = 78 L(L −1)(L + 2)N −1/2GHz

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
• 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 He 100 atm

laser

dopant inside (except alkali) Visible, IR, or UV Microwave (rotational transitions) NEP: 35-45 fW/√Hz flux: 1020 atoms/s ~10-4 torr cold expansion cluster formation dopant pick-up photon absorption + He evaporation (102-104 He/photon)

las

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): 3×107 He atoms

sour bol cold head

The cluster machine

laser in (optic fiber) source bolometer MW in gas in pump

• ut

pick-up cell BUC MW cavity MW cavity MW cavity MW cavity

The beginning

SF6 in He droplets

Goyal, Schutt and Scoles, PRL 69, 933 (1992)

SF6

• Narrow lines
• Small shifts
• Complexes formed

(SF6)2 // (SF6)2 ⊥

Window Mirror Cryotip T0=5-30 K He P0=5-100 bar Scattering gas Ionizer & QMS Interaction region Lens

SF6

T=0.37 K

Rotational resolution in

4He droplets

(Hartmann, Miller, Toennies, and Vilesov, PRL 75, 1566 (1995) SF6 freely rotates

SF6

P Branch R Branch T=0.37 K 4 3 2 1 4 3 2 1 SF6 freely rotates inside the droplet, but the observed B is only 37% of the gas phase value

Free rotation is exclusive to 4

4He

He (a boson fluid). In 3

3He

He (a fermion fluid) free rotation does not occur, unless enough 4

4He

He is present to form a shell around the OC CS molecule.

OCS in 3He and 4He droplets: proof of superfluidity in 4He droplets

Grebenev, Toennies, and Vilesov, 279, 2083 (1998)

7

OC CS molecule.

25 35 60

100

P1 R0 R1

• 0.2

0.0 0.2 0.4

Acculight Argos OPO

S P I

Wavemeter

To Spectrometer

150 MHz Approximately 1.75 W of power measured entering the machine. S P I OPO

Power meter

150 MHz

etalon

7.5 GHz etalon

Produces over 2 W of CW over the tunable range of 3.2 – 3.9 m. Continuous scans of 45 GHz. Also produces 2 - 5 W of 1.5 µm light.

Methane ν3

Found two extra lines. A

3018 3018.5 3019 3019.5 3020 3020.5 wavenumber (cm-1)

v3 Q(1) line Miller Groups Methane spectra of the ν3 band.

Found two extra lines. A second line near Q(1) and also a P(2) line.

3001.2 3001.6 3002 3002.4 3002.8

P(2)

Nauta, K., Miller, R.E. Chem Phys. Let. 350 (2001) 225.

Methane ν2 + ν4

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 ν0 = 2836.36 cm-1 and B’ = 5.2279 cm-1. The addition

• f 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 ν0 2836.36 cm-1 2841.009 cm-1 B’ 4.978 cm-1 5.2279 cm-1

2845.6 2846 2846.4 2846.8

Lolck, J., Robiette, A., Brown, L., Hunt, R.H. J. Mol. Spec. 92 (1982) 229.

Comparison of Widths

Line He (cm-1) HWHM (cm-1) Q(1) 2831.459 0.051 R(0) 2846.304 0.068 Methane v2 + v4 Line Frequency HWHM CH3D v4 Line Frequency (cm-1) HWHM (cm-1) Q(1) 2977.220 0.0107 R(0) 2982.868 0.0184 Line Frequency HWHM CH2D2 v1 CH2D2 v4 Line Frequency (cm-1) HWHM (cm-1) P(1) 3008.846 0.4154 Q(1) 3016.046 0.221 R(0) 3025.345 0.120 Line Frequency (cm-1) HWHM (cm-1) Q(1) 2969.789 0.0289 R(0) 2977.144 0.0387 CH3D v1 Line Frequency (cm-1) HWHM (cm-1) Q(1) 3013.728 0.4421 R(0) 3020.253 0.1556 R(1) 3026.077 1.5522 Line Frequency (cm-1) HWHM (cm-1) Q(1) 2993.319 0.0188 R(0) 2999.289 0.0266 CHD3 v1

CH3Cl

Line Location (cm-1) HWHM (cm-1) P1(2) 2968.268 0.0423 P0(2) 2968.371 0.0334 P0(1) 2968.594 0.0244 2968.594 0.0244 Q0(1) 2968.78 0.023 R0(0) 2969.135 0.0226 R1(1) 2969.293 0.032 R0(1) 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 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

Lens Ions He droplet source Electrostatic energy selector hν Atoms Ion Multipler grids Figure 3: Schematic of proposed ion machine

(a) (b)

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).

(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
• Use circularly polarized radiation to pump in

angular momentum (~109 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)

Statistical Evaporative cooling calculations of temperature versus cooling time. Thermodynamics of Helium Droplets 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 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 = 104

Scales as N1/3 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(Ek, J) – Ek = E - E’ - Ebind > 1.23 K J(J+1) N-2/3 (centrifugal barrier) – Ek = E - E’ - Ebind > 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 – 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 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 – 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 – Droplets will distort moderately from vortex – For 104 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

• Hollow Core Model

103 K

– a=1.0 Å

• 500 quanta L = 2 Ripplon

167 K

– Same total angular momentum

DFT Theory Energy of Vortex normalized by Equal Angular momentum in lowest Ripplon mode 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
• f Energy with Angular

momentum

• Will be stable if below that of

Lowest Ripplon

Energy and Angular Momentum

• f curved Vortex Solutions

Angular Velocity of Curved Vortex divided by Ripplons

N = 102 N = 105 Distance of Closest Approach of Vortex to Axis

Lowest Angular Momentum of Stable Curved Vortex

N L / h-bar 102 25 10 25 103 160 104 930 105 5400

How could Vortex be formed?

• Thermal angular momentum at Tλ?

– Not enough < J > = (3 k Tλ Icl)1/2 ~ 0.7 N5/6

• Collisional Angular Momentum of pickup?
• Collisional Angular Momentum of pickup?

– SF6 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 = 104

Scales as N1/3 for other droplet sizes

How Can a Vortex Decay?

• Into Ripplons? Lowest energy N unit of

angular momentum = 5.3 K N1/2

– Always more than vortex energy

• By Atom evaporation? Also endothermic

– Angular momentum loss by evaporation < mvR – Also “costs” ~7 K per evaporation – For N=103, 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% – ∆Esuf =4.4 K N2/3 – Very strongly endothermic – 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
• 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:

Esv = h2ρeB ln 2A       −1     Esv =

e

2πm ln a     −1    

Thanks for you attention!

If you find this interesting, please stop by to see me: by to see me: Email: Lehmann@virginia.edu Office: Chemistry Rm 126