Highly charged droplets of superfluid helium
Felix Laimer, Lorenz Kranabetter, Lukas Tiefenthaler, Simon Albertini, Fabio Zappa, Andrew M. Ellis, Michael Gatchell, Paul Scheier
HHighly charged droplets of superfluid helium
Felix Laimer, Lorenz Kranabetter, Lukas Tiefenthaler, Simon Albertini, Fabio Zappa,
1, 2
Andrew M. Ellis, Michael Gatchell,
1, 4, ∗ and Paul Scheier Institut f¨ur Ionenphysik und Angewandte Physik,Universit¨at Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria Departamento de F´ısica-ICE, Universidade Federal de Juiz de Fora,Campus Universit´ario, 36036-900, Juiz de Fora, MG, Brazil Department of Chemistry, University of Leicester,University Road, Leicester, LE1 7RH, United Kingdom Department of Physics, Stockholm University, 106 91 Stockholm, Sweden (Dated: December 4, 2019)We report on the production and study of stable, highly charged droplets of superfluid helium.Using a novel experimental setup we produce neutral beams of liquid helium nanodroplets containingmillions of atoms or more that can be ionized by electron impact, mass-per-charge selected, andionized a second time before being analyzed. Droplets containing up to 55 net positive chargesare identified and the appearance sizes of multiply charge droplets are determined as a function ofcharge state. We show that the droplets are stable on the millisecond time scale of the experimentand decay through the loss of small charged clusters, not through symmetric Coulomb explosions.
Since their introduction several decades ago, liquidhelium nanodroplets have been used to study a widerange of unusual physical and chemical phenomena [1–4]. These droplets allow the investigation of superfluidbehavior on the nanoscale, often through probing of theweak interaction of the helium with a dopant moleculelocated within the droplet [2–4]. Alternatively, this weakinteraction with helium can be exploited in spectroscopicstudies of atoms, molecules and their clusters [3, 5, 6].Recently, experiments have been performed utilizing newultrafast diffraction technology to establish the sizes andshapes of individual helium nanodroplets [7]. However,the ionization of helium nanodroplets has long thoughtto be a largely settled matter, with most studies showingsingly charged cluster ions emanating from droplets sub-jected to electron ionization [4]. The possibility of cre-ating multiply charged helium droplets has rarely beenconsidered and there is no prior evidence for species otherthan doubly charged droplets [8]. Using a new experi-mental approach, this study shows that helium dropletswith at least several tens of charges are readily formedat sufficiently high electron energies and electron cur-rents. Furthermore, these ions are stable on the mil-lisecond timescale of these experiments. Evidence is pre-sented that the charges are distributed as multiple sin-gle charge sites across the droplets which are kept apartby Coulomb repulsion. These multiply charged heliumdroplets offer the potential for other new and transforma-tory experiments, including for the nucleation of clustersand nanoparticles and as a new means of molecular ionspectroscopy based on helium tagging.Neutral He droplets are formed in the expansion of Hegas (Messer, 99.9999% purity) with stagnation pressureof 20–25 bar through a 5 µ m nozzle orifice in a copper ∗ [email protected] block that is mounted to the second stage of a closed cir-cuit cryocooler. The temperature of the nozzle can becontrolled down to 4.2 K and depending on the tempera-ture, different mechanisms will dictate the size distribu-tion of the droplets that are formed [2]. The droplets passthrough a skimmer on their way into the first ionizationsource where they are ionized by the impact of electronswith kinetic energies up to a few hundred eV. Chargeddroplets are then mass-per-charge-selected by a spher-ical electrostatic analyzer. The m/z -selected chargeddroplets can then be ionized further by a second elec-tron impact ionization source. A second electrostatic an-alyzer, identical to the first one, is then employed to ana-lyze the final mass per charge ratio of the droplets, whichare detected with a single channel electron multiplier de-tector. The velocity spread of droplets in the beam froma continuously operated nozzle is exceptionally small andthe average velocity depends strongly on the temperatureof the helium before the expansion. This is used to de-termine the absolute sizes of our droplets [9, 10]. Moreexperimental details are given in the supporting informa-tion.Droplets that are produced from the expansion ofcooled and compressed He gas form broad log-normal sizedistributions in the size regime (millions of atoms) stud-ied here [4, 11]. In Figure 1a we show two size-per-chargedistributions of He droplets formed under identical con-ditions, but where the current and energy of electronsin the first ion source differ. Here, droplets were ionizedby electrons with kinetic energies of 22.6 eV and 150 eV,respectively, with the latter also at a higher electron cur-rent. The red dataset shows a broad log-normal size dis-tribution of negatively charged droplets that peaks near 3million He atoms per unit charge. Since negative chargecenters are heliophobic and form voids in the droplets,they are readily expelled from the droplets if multiplecharges are present [4, 8]. The distribution of anions canthus be assumed to mainly contain only singly charged a r X i v : . [ phy s i c s . a t m - c l u s ] D ec FIG. 1. a Mass per charge distributions of cationic He droplets (150 eV electrons at 105.4 µ A, blue curve) and anionic droplets(22.6 eV electrons at 0.3 µ A, red curve) by electron bombardment. The droplets were produced under identical conditions witha 8.5 K nozzle temperature. The lower energy gives a distribution of essentially purely singly charged droplets that peaks near3 million atoms and closely matches to the neutral distribution. The distribution of positively charged droplets is pushed tolower mass per charge ratios. b–d
Distributions of He droplets that are m/z -selected slices from the blue distribution in panela and ionized a second time. The parent ions have sizes of 8 . × , 1 . × , and 2 . × He atoms per charge (indicatedby arrows), respectively, and the products all have rational fractions of the parent mass per charge ratio. droplets and represent the neutral size distribution. Atthe higher electron energy, multiple positive charges maybe formed in the He droplets. This increases the energydeposited into the droplets, which could cause them toboil off He atoms and shrink in size. However, as willbe discussed, the dominant mechanism is the accumula-tion of charges in the droplets that leads to a decrease intheir mass per charge ratio and, if the charge density ishigh enough, to the ejection of low mass fragment ions.The blue dataset shows that this leads to an apparentsize distribution that, while still close to log-normal inshape, now peaks at less than 1 million He atoms perunit charge.A novel feature of the experimental setup is that wecan mass-select droplets after the first ionization sourceand let them interact with energetic electrons for a secondtime. In Figures 1b, c, and d, we show some illustrativedistributions of charged He droplets that have been m/z -selected, with narrow size distributions of about 8 . × ,1 . × , and 2 . × He atoms per charge, respec-tively. All three of these distributions were produced inthe same way from the same initial distribution, with150 eV electrons in the first ionization source and 200 eVelectrons in the second (at 105.4 µ A and 197.1 µ A, respec-tively). Now, instead of the intact distributions beingshifted continuously towards lower masses, we see a seriesof narrow peaks (FWHMs ∼
3% of mass per charge ra-tio, limited by experimental resolution) centered aroundrational fractions of the mass per charge ratio of the par-ent clusters. While one might expect that this effect iscaused by the nearly symmetrical fission of large mul- tiply charged droplets into smaller droplets with lowercharge states, this is not what we are actually observing.Instead, we find that these peaks result from stable, mul-tiply charged droplets. The fractional relative mass percharge ratios of the droplets correspond to the ratios be-tween the charge state of the parent droplet and those ofthe daughter droplets, z p /z d , which remain intact afterthe second ionizing process. By tuning the settings of thetwo ion sources, as well as the mass per charge ratio ofthe parent droplets that are selected after the first ioniza-tion process, we can discern parent and daughter dropletswith up to several tens of charges that give a range ofdifferent rational fractions of the parent mass per chargeratio. It is the wide range of higher charge states presentin the parent droplets and the overlap of the numerousdaughter droplets with different charge stats that are re-sponsible for the broad features seen below the the nar-row peaks. Interestingly, all three panels show a pileupof peaks around the same mass per charge ratio, about3 × He atoms per charge. This specific value dependson the experimental conditions, but the trend is easilyreproducible in different measurements and is a result ofthe different electron impact cross sections of droplets inthe sample.In Figure 2a we show mass spectra from m/z -selectedparent droplets containing 3 . × He atoms per charge(formed by 40 eV electrons in the first ion source) thathave been impacted a second time with electrons at ki-netic energies of 22 eV and 80 eV, respectively. The differ-ent setting used compared to Figure 1 were chosen to besthighlight the buildup of discrete charges in the selected Y i e l d ( H z ) a
80 eV22 eV 0 2 4 6 8 10 12 10 Y i e l d ( H z ) b FIG. 2. a Mass-per-charge-selected (3 . × He atoms per charge from 7 K nozzle) droplets ionized a second time with 80 eV(blue) and 22 eV (red) electrons. The higher energy leads mainly to an increase in charge state and narrow peaks with massper charge ratios at distinct rational fractions of the parent. At 22 eV, the droplets are for the most part partially neutralizedby helium anions, causing their mass per charge ratios to increase. b Wider range spectrum which shows that parent dropletscontaining up to 12 charges have had their net charge state reduced to +1. Peaks at half-integer positions show that dropletscontaining up to at least 17 charges have had their net charge reduced to +2. droplets. At the higher energy, the impacting electronsmay produce several He + ions (IE(He) = 24.6 eV) alongtheir trajectory through a droplet, resulting in an in-crease in the net positive charge. As the parent dropletscarry several different charge states, all with the samemass per charge ratio, the result is a swarm of differentdaughter peaks. For example, the peak at 1 / /
4, 2 /
3, 1 /
2, 1 /
3, and 1 /
4, although several otherpeaks are clearly visible at other fractions.When lower energy electrons are used to impact the m/z -selected He droplets it is possible to neutralize andreduce their charge states. This can be seen from the redcurves in Figures 2a and 2b. Here, the energy of the elec-trons from the second ionization source has been tuned tobelow the ionization threshold of He. At this energy theelectrons may lose energy as they scatter off of the neu-tral He, forming electronically excited He ∗ . The slowedelectrons, which form voids in the droplets, or the He ∗− that are formed by the capture of the slow electrons byHe ∗ [12], may then neutralize positive charge centers inthe parent droplets, effectively increasing their mass percharge ratios. Numerous examples of multiply chargeddroplets having their net charge reduced are clearly seenin Figures 2a and 2b where several peaks with mass per charge ratios with rational numbers greater than oneare visible. The peaks with integer values are predomi-nantly from daughter droplets with a charge state of +1,originating from parents with up to 12 charges, all withthe same initial mass per charge. Likewise, several half-integer peaks (up to at least 8.5 times the mass per chargeratio of the parent) are visible from even larger daughterdroplets that still contain two positive charges.There is a general consensus that the charge centersof multiply charged He droplets are promptly ejected assmall He + n clusters [13], leaving at most a single chargein the remaining droplet. In the present measurementswe resolve and identify multiply charged He droplets con-taining up several tens of positive charges, presumably inthe form of solvated He + n cores [13–15]. In Figure 3 weshow the appearance sizes of droplets for a range of highcharge states. We find that the critical size of a dropletthat can contain a given number of charges scales withthe square of the radius of the droplet (determined by as-suming spherical geometries and using the mean densityof bulk superfluid He). This dependence could indicatethat the appearance size of a multiply charged dropletscales with the cross section of the ionization processes.Another possibility is that the critical size is dictatedby the multiple charges residing on the surface of thedroplets, as would be expected for highly mobile inter-acting charge centers.Doubly charged He droplets have been reported pre-viously by F´arn´ık et al. [8], who identified a thresholdsize of approximately 2 × He atoms for observingthese ions. In our measurements we find a significantlysmaller appearance size. For the doubly charged dropletswe measure a minimum size of (1 . ± . × atomsand our threshold for triply charged droplets is (1 . ± . × . The largest systems we have measured theappearance sizes for are droplets containing 55 charges,the smallest of which consists of (9 . ± . × atoms.The reason for the discrepancy in appearance size be-tween our measurements and those by F´arn´ık et al. [8] isunclear, but could be the result of limitations in the olderexperiments (e.g. fixed electron energy). Using a classicalliquid droplet model, Echt et al. determined the criticalsize of He droplets containing up to 4 positive charges tobe about 2 × atoms [16]. Within this framework, fordroplets with continuous charge distributions, the crit-ical sizes of higher charge states can be determined as n ( z ) = z / ( z c /n c ), where n c is the known critical sizeof droplets with z c charges [17]. With this, the pre-dicted appearance size of droplets containing 55 chargesis 3 . × He atoms, about four times larger than theexperimentally measured limit. This discrepancy is con-sistent with results for multiply charged Ne droplets [18]where it was explained by quantum effects and discretecharge distributions in the real droplets. The compari-son with the model and previous results with charge raregas droplets suggests that the cohesive forces in the Hedroplets are enough to explain the stability of our highlycharged systems [18]. Above the charge states shown inFigure 3, larger droplets with even higher charge statesare expected to remain stable but unresolved in our mea-surements as the mass per charge selected, singly chargedparent droplets used will be too heavy to be deflectedin our electrostatic sectors. Based on the source set-tings, the largest droplets we can produce are expectedto have radii greater than 1 µ m ( > He atoms), whichcould contain many thousands of charges. Noteworthy isthat we find no evidence for ongoing droplet decay af-ter the highly charged droplets are produced, indicatingthat they are indeed stable on the ms timescale of ourexperiment.For a spherical droplet containing more than a few tensof thousands of atoms, charges produced by the electronimpact will initially be situated near the surface facingthe electron source [14]. However, the charges will behighly mobile in the superfluid and should swiftly re-structure to minimize the total repulsion energy. Thepositions of the charge centers in the stable, multiplycharged droplets could therefore be considered to be sim-ilar to the solutions of the Thomson problem of pointcharges confined in a sphere [19], as has been shown formobile charges in other liquids [20]. Droplets with anoverabundance of charges appear to behave similar toclassical liquids as they approach the Rayleigh stabilitylimit [21], losing only small portions of mass as chargesare expelled [22, 23]. The expelled charged centers likelyconsist of small He + n units in densely packed Atkins snow-balls [24], ions that are commonly found in experimentslimited to studying lower masses [4, 25, 26]. Given thelow interaction energy of He atoms, it is also possible thatthe charges lead to a shell of densely packed He + n snow- balls around the center of the droplets where the densityis lowered, which could ultimately lead to an empty voidforming in the center akin to a soap bubble. )0102030405060 C h a r g e S t a t e ( e ) Fit: z ( r ) = − .
544 + 0 . r Experimental Data
FIG. 3. Plot of the droplet charge state versus the squareof the minimum droplet radius needed to form that particu-lar charge state. The red curve is a fit to the experimentaldata. The horizontal error bars originate from the statisti-cal uncertainties in determining the sizes of the droplets andthe vertical bars from the uncertainties in the appearance ofspecific charge numbers amongst the series of higher chargestates.
In experiments where neutral
He droplets are dopedwith atomic or molecular species and then ionized, thesmall charged products that can be studied there ap-pear to only constitute a fraction of the overall charge,since these new results show that a large number of thecharges remain in the droplets. This opens the doorto new experimental techniques where multiply charged droplets are seeded with dopants. For example, chargeddroplets could be used as a weakly interacting matrixfor ion spectroscopy where, a single droplet can providemultiple, separated ion nucleation sites. This approachhas the potential to provide a new form of spectroscopicexperiments facilitated by helium-tagging and promiseshigh signal levels because of the multiple sites availablein each droplet. Each charge center can also be used as adistinct nucleation site for the production of clusters andnanoparticles. Since the cross section of the multiplycharged droplets can be selected before dopant pickup,the size distribution of particles grown in this way canbe narrowed and more finely tuned compared to the casewhen neutral droplets of random sizes are used to cap-ture gas phase building blocks and grow nanoparticlesand nanowires.This work was supported by the EU commission,EFRE K-Regio FAENOMENAL EFRE 2016-4, the Aus-trian Science Fund FWF (P31149 and W1259) and theSwedish Research Council (contract No. 2016-06625). FZacknowledges support from Brazilian agency CNPq. [1] J. A. Northby,
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