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The Journal of Chemical Physics

Sizes of large He droplets

Luis F. Gomez, Evgeny Loginov, Russell Sliter, Andrey F. Vilesov

Published Oct 18, 2011• 180 citations
Publisher

Abstract

Helium droplets spanning a wide size range, N(He) = 10(3)-10(10), were formed in a continuous-nozzle beam expansion at different nozzle temperatures and a constant stagnation pressure of 20 bars. The average sizes of the droplets have been obtained by attenuation of the droplet beam through collisions with argon and helium gases at room temperature. The results obtained are in good agreement with previous measurements in the size range N(He) = 10(5)-10(7). Moreover, the measurements give the average sizes in the previously uncharacterized range of very large droplets of 10(7)-10(10) atoms. The droplet sizes and beam flux increase rapidly at nozzle temperatures below 6 K, which is ascribed to the formation of droplets within the nozzle interior. The mass spectra of the droplet beam upon electron impact ionization have also been obtained. The spectra show a large increase in the intensity of the He(4) (+) signal upon increase of the droplet size, an effect which can be used as a secondary size standard in the droplet size range N(He) = 10(4)-10(9) atoms.

DOI
10.1063/1.3650235

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Helium droplets spanning a wide size range, N(He) = 10(3)-10(10), were formed in a continuous-nozzle beam expansion at different nozzle temperatures and a constant stagnation pressure of 20 bars. The average sizes of the droplets have been obtained by attenuation of the droplet beam through collisions with argon and helium gases at room temperature. The results obtained are in good agreement with previous measurements in the size range N(He) = 10(5)-10(7). Moreover, the measurements give the average sizes in the previously uncharacterized range of very large droplets of 10(7)-10(10) atoms. The droplet sizes and beam flux increase rapidly at nozzle temperatures below 6 K, which is ascribed to the formation of droplets within the nozzle interior. The mass spectra of the droplet beam upon electron impact ionization have also been obtained. The spectra show a large increase in the intensity of the He(4) (+) signal upon increase of the droplet size, an effect which can be used as a secondary size standard in the droplet size range N(He) = 10(4)-10(9) atoms.
Factors affecting the size of liquid-helium droplets produced by a pulsed nozzle are described. The shape of the nozzle orifice is found to be important in allowing control of the size of the droplets. With an appropriate choice of nozzle geometry, the average droplet size is shown to be continuously variable over nearly two orders of magnitude by adjustment of the helium gas stagnation pressure and/or temperature. A scaling law similar to, but not identical with, that found for helium droplets produced by continuous supersonic expansion sources is found for the pulsed source. The pulsed nozzle described in this article has been used to make helium droplets ranging in size from a few thousand atoms up to nearly 105 helium atoms.
Electron impact ionization of superfluid helium droplets containing several thousand atoms produces a broad distribution of Hen+ ions that peaks at n = 2 and decreases monotonically toward larger n. In larger droplets (say 105 or more atoms), however, the He4+ signal intensity is anomalously large. We have studied the mechanism for the formation of He4+ ions in large helium droplets by varying the duration of the electron impact excitation pulse. Droplets of different average sizes were generated using the expansion of helium at 20 bars and 9-20 K through a pulsed valve nozzle. The resulting ions were analyzed by time-of-flight mass spectroscopy (TOFMS) and quadrupole mass spectroscopy (QMS). The intensity distributions obtained with the TOFMS technique initially showed much smaller He4+ signals than those obtained using QMS. However, we discovered that the intensity anomaly is associated with the duration of the electron bombardment pulse in the TOFMS instrument. Measurements with different electron bombardment pulse durations enabled us to discern a characteristic time of ∼10 μs for enhanced He4+ production in large droplets under our experimental conditions. A qualitative model is presented in which metastables interact on droplet surfaces, yielding two He2+ cores that share a Rydberg electron while minimizing repulsion between the cores. This is the He4+(4A2) state suggested by Knowles and Murrell.
Advancements in x-ray free-electron lasers on producing ultrashort, ultrabright, and coherent x-ray pulses enable single-shot imaging of fragile nanostructures, such as superfluid helium droplets. This imaging technique gives unique access to the sizes and shapes of individual droplets. In the past, such droplet characteristics have only been indirectly inferred by ensemble averaging techniques. Here, we report on the size distributions of both pure and doped droplets collected from single-shot x-ray imaging and produced from the free-jet expansion of helium through a 5 μm diameter nozzle at 20 bars and nozzle temperatures ranging from 4.2 to 9 K. This work extends the measurement of large helium nanodroplets containing 109–1011 atoms, which are shown to follow an exponential size distribution. Additionally, we demonstrate that the size distributions of the doped droplets follow those of the pure droplets at the same stagnation condition but with smaller average sizes.
We report detailed measurements of velocities and sizes of superfluid helium droplets produced from an Even-Lavie pulse valve at stagnation pressures of 20-60 atm and temperatures between 5.7 and 18.0 K. By doping neutral droplets with Rhodamine 6G cations produced from an electrospray ionization source and detecting the positively charged droplets at two different locations along the beam path, we determine the velocities of the different groups of droplets. By subjecting the doped droplet beam to a retardation field, size distributions can then be analyzed. We discover that at stagnation temperatures above 8.0 K, a single group of droplets is observed at both locations, but at 8.0 K and below, two different groups of droplets with different velocities are detectable. The slower group, considered from fragmentation of liquid helium, cannot be deterred by the retardation voltage at 9 kV, implying an exceedingly large size. The faster group, considered from condensation of gaseous helium, has a bimodal distribution when the stagnation temperatures are below 12.3 K at 20 and 40 atm, or 16.1 K at 60 atm. We also report similar size measurements using low energy electrons for impact ionization, and this latter method can be used for facile in situ characterization of pulsed droplet beams. The mechanism of the bimodal size distribution of the condensation group and the reason for the coexistence of both the condensation and fragmentation groups remain elusive.
Liquid 4He^{4}\mathrm{H}\mathrm{e}4He at pressures P0=0.5−−30  bars{P}_{0}=0.5--30\text{ }\text{ }\mathrm{\text{bars}}P0​=0.5−−30  bars and temperatures T0=1.5−−4.2  K{T}_{0}=1.5--4.2\text{ }\text{ }\mathrm{K}T0​=1.5−−4.2  K is discharged into vacuum through two different $2\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ nozzles. The velocities of the beam of particles obey the Bernoulli equation down to 15  m/sec15\text{ }\text{ }\mathrm{m}\mathrm{/}\mathrm{s}\mathrm{e}\mathrm{c}15  m/sec. With decreasing T0{T}_{0}T0​ and increasing P0{P}_{0}P0​ the velocity and angular distributions become exceedingly narrow with $\ensuremath{\Delta}v/v\ensuremath{\lesssim}1%$ and $\ensuremath{\Delta}\ensuremath{\vartheta}\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{m}\mathrm{r}\mathrm{a}\mathrm{d}$. Optical observations indicate that the beam consists of micron-sized droplets ($N\ensuremath{\gtrsim}{10}^{9}\text{ }\text{ }\mathrm{\text{atoms}}$). This new droplet source provides opportunities for novel experimental studies of superfluid behavior.
A pulsed valve connected to a closed-cycle cryostat was optimized for producing helium droplets. The pulsed droplet beam appeared with a bimodal size distribution. The leading part of the pulse consists of droplets suitable for doping with molecules. The average size of this part can be varied between 10(4) and 10(6) helium atoms, and the width of the distribution is smaller as compared to a continuous-flow droplet source. The system has been tested in a single pulse mode and at repetition rates of up to 500 Hz with almost constant intensity. The droplet density was found to be increased by more than an order of magnitude as compared to a continuous-flow droplet source.