Superfluid Helium Droplets Research Articles

Electron diffraction of foam-like clusters between xenon and helium in superfluid helium droplets.

We report electron diffraction results of xenon clusters formed in superfluid helium droplets, with droplet sizes in the range of 105-106 atoms/droplet and xenon clusters from a few to a few hundred atoms. Under four different experimental conditions, the diffraction profiles can be fitted using four atom pairs of Xe. For the two experiments performed with higher helium contributions, the fittings with one pair of Xe-He and three pairs of Xe-Xe distances are statistically preferred compared with four pairs of Xe-Xe distances, while the other two experiments exhibit the opposite preference. In addition to the shortest pair distances corresponding to the van der Waals distances of Xe-He and Xe-Xe, the longer distances are in the range of the different arrangements of Xe-He-Xe and Xe-He-He-Xe. The number of independent atom pairs is too many for the small xenon clusters and too few for the large clusters. We consider these results evidence of xenon foam structures, with helium atoms stuck between Xe atoms. This possibility is confirmed by helium time-dependent density functional calculations. When the impact parameter of the second xenon atom is a few Angstroms or longer, the second xenon atom fails to penetrate the solvation shell of the first atom, resulting in a dimer with a few He atoms in between the two Xe atoms. In addition, our results for larger droplets point toward a multi-center growth process of dopant atoms or molecules, which is in agreement with previous proposals from theoretical calculations and experimental results.

Precision engineering of nano-assemblies in superfluid helium by the use of van der Waals forces

The ability to precisely engineer nanostructures underpins a wide range of applications in areas such as electronics, optics, and biomedical sciences. Here we present a novel approach for the growth of nanoparticle assemblies that leverages the unique properties of superfluid helium. Unlike viscous solvents at or near room temperature, superfluid helium provides an unperturbed and cold environment in which weak van der Waals interactions between molecular templates and metal atoms become significant and can define the spatial arrangement of nanoparticles. To demonstrate this concept, diol and porphyrin-based molecules are employed as templates to grow gold nanoparticle assemblies in superfluid helium droplets. After soft-landing on a solid surface to remove the helium, transmission electron microscopy (TEM) imaging shows the growth of gold nanoparticles at specific binding sites within the molecular templates where the interaction between gold atoms and the molecular template is at its strongest.

Infrared spectroscopy of isomers of C3H4+ in superfluid helium droplets.

Superfluid helium nanodroplets are unique nanomatrices for the isolation and study of transient molecular species, such as radicals, carbenes, and ions. In this work, isomers of C3H4+ were produced upon electron ionization of propyne and allene molecules and interrogated via infrared spectroscopy inside He nanodroplet matrices. It was found that the spectrum of C3H4+ has at least three distinct groups of bands. The relative intensities of the bands depend on the precursor employed and its pickup pressure, which indicates the presence of at least three different isomers. Two isomers were identified as allene and propyne radical cations. The third isomer, which has several new bands in the range of 3100-3200cm-1, may be the elusive vinylmethylene H2C=CH-CH+ radical cation. The observed bands for the allene and propyne cations are in good agreement with the results of density functional theory calculations. However, there is only moderate agreement between the new bands and the theoretically calculated vinylmethylene spectrum, which indicates more work is necessary to unambiguously assign it.

Quantized vortex nucleation in collisions of superfluid nanoscopic helium droplets at zero temperature.

We address the collision of two superfluid 4He droplets at non-zero initial relative velocities and impact parameters within the framework of liquid 4He time-dependent density functional theory at zero temperature. Despite the small size of these droplets (1000 He atoms in the merged droplet) imposed by computational limitations, we have found that quantized vortices may be readily nucleated for reasonable collision parameters. At variance with head-on collisions, where only vortex rings are produced, collisions with a non-zero impact parameter produce linear vortices that are nucleated at indentations appearing on the surface of the deformed merged droplet. Whereas for equal-size droplets, vortices are produced in pairs, an odd number of vortices can appear when the colliding droplet sizes are different. In all cases, vortices coexist with surface capillary waves. The possibility for collisions to be at the origin of vortex nucleation in experiments involving very large droplets is discussed. An additional surprising result is the observation of the drops coalescence even for grazing and distal collisions at relative velocities as high as 80 and 40m/s, respectively, induced by the long-range van der Waals attraction between the droplets.

Formation of heterogeneous clusters in superfluid helium nanodroplets: phthalocyanine and water.

Clusters consisting of a single phthalocyanine molecule and a single water molecule are investigated by means of electronic spectroscopy in superfluid helium droplets. A recent spectroscopic study of those clusters [J. Fischer, F. Schlaghaufer, E.-M. Lottner, A. Slenczka, L. Christiansen, H. Stapelfeldt, M. Karra, B. Friedrich, T. Mullan, M. Schütz and D. Usvyat, J. Phys. Chem. A, 2019, 123, 10057-10064] which all exhibit a water induced electronic shift to the red is now complemented by the corresponding clusters exhibiting a water induced shift to the blue. These clusters will be analyzed by means of fluorescence excitation spectra, dispersed emission spectra, and additional experimental observations made feasible by helium droplets as cryogenic reactor. Together with the blue shifted clusters a total number of at least 6 isomeric variants could be identified in helium droplets. This contrasts to a number of only three isomeric variants obtained from quantum chemical calculations [J. Fischer, F. Schlaghaufer, E.-M. Lottner, A. Slenczka, L. Christiansen, H. Stapelfeldt, M. Karra, B. Friedrich, T. Mullan, M. Schütz and D. Usvyat, J. Phys. Chem. A, 2019, 123, 10057-10064] disregarding the helium environment and to a single isomer identified in a molecular beam experiment [J. Menapace and E. Bernstein, J. Chem. Phys., 1987, 87, 6877-6889]. The discrepancy in the number of isomers provides evidence of a profound involvement of helium in clustering. Moreover, the discrepancies between the gas phase experiment and quantum chemical calculations similarly reveal the influence of the dynamics of cluster formation on the population of global and local minima that are accessible as isomeric variants.

Resolving the interlayer distance of cationic pyrene clusters embedded in superfluid helium droplets using electron diffraction.

We report the electron diffraction of cationic pyrene (C16H10) clusters embedded in superfluid helium droplets. The diffraction profile contains a significant contribution from helium, but interferences of atomic pairs of pyrene are still recognizable. From least-squares fittings, we determine an interlayer distance of 3.0 Å for the cationic cluster, shortened from 3.5 Å in neutral clusters. The relative contributions of dimers and trimers are about 2:1, in qualitative agreement with the doping statistics. Limited by the detection range of the experimental data, we cannot distinguish further structure details. The predominant contribution of helium also prevents observations of the solvation shell of the ionic cluster. Nevertheless, the success of this experiment demonstrates the feasibility of electron diffraction from an ionic all-light-atom system, dispelling the concern over limited particle concentration of ionic species in the diffraction region, and the need of heavy atoms for diffraction intensity.

Sizes of pure and doped helium droplets from single shot x-ray imaging.

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 5μm diameter nozzle at 20 bars and nozzle temperatures ranging from 4.2 to 9K. 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.

First-principles modelling of the new generation of subnanometric metal clusters: Recent case studies

The very recent development of highly selective techniques making possible the synthesis and experimental characterization of subnanometric (subnanometer-sized) metal clusters (even single atoms) is pushing our understanding far beyond the present knowledge in materials science, driving these clusters as a new generation of quantum materials at the lower bounds of nanotechnology. When the size of the metal cluster is reduced to a small number of atoms, the d-band of the metal splits into a subnanometric d-type molecular orbitals network in which all metal atoms are inter-connected, with the inter-connections having the length of a chemical bond (1–2 Å). These molecular characteristics are at the very core of the high stability and novel properties of the smallest metal clusters, with their integration into colloidal materials interacting with the environment having the potential to further boost their performance in applications such as luminescence, sensing, bioimaging, theranostics, energy conversion, catalysis, and photocatalysis. Through the presentation of very recent case studies, this Feature Article is aimed to illustrate how first-principles modelling, including methods beyond the state-of-the-art and an interplay with cutting-edge experiments, is helping to understand the special properties of these clusters at the most fundamental level. Moreover, it will be discussed how superfluid helium droplets can act both as nano-reactors and carriers to achieve the synthesis and surface deposition of metal clusters. This concept will be illustrated with the quantum simulation of the helium droplet-assisted soft-landing of a single Au atom onto a titanium dioxide (TiO2) surface. Next, it will be shown how the application of first-principles methods have disclosed the fundamental reasons why subnanometric Cu5 clusters are resistant to irreversible oxidation, and capable of increasing and extending into the visible region the solar absorption of TiO2, of augmenting its efficiency for photo-catalysis beyond a factor of four, also considering the decomposition and photo-activation of CO2 as a prototypical (photo-) catalytic reaction. Finally, I will discuss how the modification of the same material with subnanometric Ag5 clusters has converted it into a “reporter” of a surface polaron property as well as a novel two-dimensional polaronic material.

Electron diffraction of 1,4-dichlorobenzene embedded in superfluid helium droplets.

We perform electron diffraction of 1,4-dichlorobenzene (C6H4Cl2, referred to as 2ClB) embedded in superfluid helium droplets to investigate the structure evolution of cluster growth. Multivariable linear regression fittings are used to determine the concentration and the best model structures of the clusters. At a droplet source temperature of 22 K with droplets containing on average 5000 He atoms, the fitting results agree with the doping statistics modeled using the Poisson distribution: the largest molecular clusters are tetramers, while the abundances of monomers and dimers are the highest and are similar. Molecular dimers of 2ClB are determined to have a parallel structure with a 60° rotation for the Cl-Cl molecular axes. However, a better agreement between experiment and fitting is obtained by reducing the interlayer distance that had been calculated using the density functional theory for dimers. Further calculations using the highest level quantum mechanical calculations prove that the reduction in interlayer distance does not significantly increase the energy of the dimer. Cluster trimers adopt a dimer structure with the additional monomer slanted against the dimer, and tetramers take on a stacked structure. The structure evolution with cluster size is extraordinary, because from trimer to tetramer, one monomer needs to be rearranged, and neither the trimer nor the tetramer adopts the corresponding global minimum structure obtained using high level coupled-cluster theory calculations. This phenomenon may be related to the fast cooling process in superfluid helium droplets during cluster formation.

Electron diffraction as a structure tool for charged and neutral nanoclusters formed in superfluid helium droplets.

This perspective presents the current status and future directions in using electron diffraction to determine the structures of clusters formed in superfluid helium droplets. The details of the experimental setup and data treatment procedures are explained, and several examples are illustrated. The ease of forming atomic and molecular clusters has been recognized since the invention of superfluid helium droplet beams. To resolve atomic structures from clusters formed in droplets, substantial efforts have been devoted to minimizing the contribution of helium to diffraction signals. With active background subtraction, we have obtained structures from clusters containing a few to more than 10 monomers, with and without heavy atoms to assist with the diffraction intensity, for both neutral and ionic species. From fittings of the diffraction profiles using model structures, we have observed that some small clusters adopt the structures of the corresponding solid sample, even for dimers such as iodine and pyrene, while others require trimers or tetramers to reach the structural motif of bulk solids, and smaller clusters such as CS2 dimers adopt gas phase structures. Cationic clusters of argon clusters contain an Ar3+ core, while pyrene dimers demonstrate a change in the intermolecular distance, from 3.5 Å for neutral dimers to 3.0 Å for cations. Future improvements in reducing the background of helium, and in expanding the information content of electron diffraction such as detection of charge distributions, are also discussed.

Micrometer-sized droplets from liquid helium jets at low stagnation pressures

Droplets and droplet beams produced from the breakup of micrometer-sized liquid helium jets in vacuum were studied in this work, advancing into previously unexplored regimes of low stagnation pressures. Using a 5 μm orifice, the droplet beam shows surprisingly diverse characteristics at increasing nozzle pressures from 0.6 to 100 bar: a well-collimated beam at low stagnation pressures, a spray at some intermediate values, and a less-collimated beam at high pressures. Focusing on a nozzle stagnation of 0.6 bar and 2.7 K, we highlight the spectrum of jet disturbances, resulting in different droplet beam behaviors. On some occasions, we observed uniformly sized and equidistant droplets with diameters ranging from 11 up to more than 25 μm and separations from 15 to 100 μm. From simple estimates using the ratio between the droplet separations and diameters, we determined the disturbance frequencies benchmarking the production of repeatable targets for future experiments with superfluid helium droplets. Further analysis of the droplet beam behavior at farther distances from the nozzle revealed that the droplet diameter grew downstream up to 22 μm from an initial value of 13 μm, while their aspect ratio decreased from 1.33 to 1.16. These results indicate that droplet coagulation and superfluidity both influence the droplet beam up to several hundreds of millimeters after the nozzle exit.

Electron Diffraction of Ionic Argon Nanoclusters Embedded in Superfluid Helium Droplets.

We report electron diffraction of cationic argon nanoclusters embedded in superfluid helium droplets. Superfluid helium droplets are first doped with neutral argon atoms to form nanoclusters, and then the doped droplets are ionized by electrons. The much lower ionization energy of argon ensures that the positive charge resides on the Ar nanocluster. Using different stagnation temperatures and therefore droplets with different sizes, we have been able to preferentially form a small ionic cluster containing 2-4 Ar atoms and a larger cluster containing 7-11 atoms. The fitting results of the diffraction profiles agree with structures reported from theoretical calculations, containing a cationic trimer core with the remaining atoms largely neutral. This work testifies to the feasibility of performing electron diffraction from ionic species embedded in superfluid helium droplets, dispelling the concern over the particle density in the diffraction region. However, the large number of neutral helium atoms surrounding the cationic nanoclusters poses a challenge for the detection of the helium solvation layer, and the detection of which awaits further technological improvements.

Coexistence of vortex arrays and surface capillary waves in spinning prolate superfluid He4 nanodroplets

Within Density Functional Theory, we have studied the interplay between vortex arrays and capillary waves in spinning prolate He-4 droplets made of several thousands of helium atoms. Surface capillary waves are ubiquitous in prolate superfluid He-4 droplets and, depending on the size and angular momentum of the droplet, they may coexist with vortex arrays. We have found that the equilibrium configuration of small prolate droplets is vortex-free, evolving towards vortex-hosting as the droplet size increases. This result is in agreement with a recent experiment [S.M. O'Connell et al., Phys. Rev. Lett. 124, 215301 (2020)], where it has been disclosed that vortex arrays and capillary waves coexist in the equilibrium configuration of very large drops. Contrarily to viscous droplets executing rigid body rotation, the stability phase diagram of spinning He-4 droplets cannot be universally described in terms of dimensionless angular momentum and angular velocity variables: instead, the rotational properties of superfluid helium droplets display a clear dependence on the droplet size and the number of vortices they host.

Density functional theory of superfluid helium at finite temperatures.

A density functional theory-based method is developed to describe the static and dynamic response of superfluid helium at finite temperatures. The model relies on the well-established 0K Orsay-Trento functional, which has been extensively used to study the response of bulk superfluid helium as well as superfluid helium droplets. By including a phenomenological stochastic term in this model, it is possible to obtain thermodynamic equilibrium corresponding to a given temperature by propagating the system in imaginary time. The temperature dependence of thermodynamic quantities, such as the internal energy and entropy, is computed and is compared well with experimental reference data for the bulk liquid up to about 2K, but begins to gradually deviate above that temperature. Inspection of pseudovorticity during real-time evolution of the system near 2K reveals the presence of roton quasiparticles, which are suggested to be precursors for quantized vortex rings (Onsager's ghosts), as well as weaker analogs of extended vortex loops.

Bimodal velocity and size distributions of pulsed superfluid helium droplet beams.

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.

Impact and lifecycle of superfluid helium drops on a solid surface

Superfluid helium droplets impacting on a solid surface behave much differently than any other fluid. After a short period of initial spreading that is similar to classical fluids, superfluid helium drops quickly shrink and disappear as the superfluid drains out through a thin adsorbed layer of helium on the surface. The lifetime and contact angle of these drops is strongly temperature-dependent, and colder drops (with high superfluid fractions) maintain a constant contact angle throughout the contraction. Above ${T}_{l\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}m\phantom{\rule{0}{0ex}}b\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}a}$, helium spreads slowly like other classical fluids.

Electron diffraction of CS2 nanoclusters embedded in superfluid helium droplets.

We report experimental results from electron diffraction of CS2 nanoclusters embedded in superfluid helium droplets. From detailed measurements of the sizes of doped droplets, we can model the doping statistics under different experimental conditions, thereby obtaining the range of cluster sizes of CS2. Using a least squares fitting procedure, we can then determine the structures and contributions of dimers, trimers, and tetramers embedded in small droplets. While dimers prefer a stable gas phase structure, trimers and tetramers seem to forgo the highly symmetric gas phase structures and prefer compact cuts from the crystalline structure of CS2. In larger droplets containing more than 12 CS2 monomers, the diffraction profile is consistent with a three-dimensional nanostructure of bulk CS2. This work demonstrates the feasibility of electron diffraction for in situ monitoring of nanocluster formation in superfluid helium droplets.

Ultrashort XUV pulse absorption spectroscopy of partially oxidized cobalt nanoparticles

High-order harmonic generation (HHG) based transient extreme ultraviolet (XUV) absorption spectroscopy is an emerging technique to trace photoinduced charge carrier dynamics in condensed phase materials with femtosecond and even attosecond temporal resolution and elemental specificity. However, its application to nanoparticulate samples that are relevant, for example, for novel photocatalytic light harvesting concepts, has been limited. This is in part due to the challenge to produce residual-free samples on ultrathin, XUV-transparent substrates as well as a widespread understanding that sparsely distributed nanoparticles do not provide sufficient contrast for XUV absorption measurements. Here, we present static XUV absorption spectra of partially oxidized Co nanowire-structures with diameters of approximately 4.5 nm and lengths between 10 and 40 nm, recorded with an ultrashort pulse HHG light source. Nanoparticles are synthesized by the agglomeration of Co atoms inside superfluid helium droplets, followed by surface deposition and oxidation in ambient air. The method is uniquely suited for residual-free synthesis of transition metal nanowires and their deposition on ultrathin substrates. Analysis by high-resolution transmission electron microscopy reveals the formation of CoO nanowires with regions of unoxidized Co in their interior. The nanoparticle samples are investigated in an HHG-driven ultrafast XUV absorption setup. Despite the low surface coverage of only 23%, the recorded spectrum exhibits a distinct absorption feature at the Co M2,3(2p) edge near 60 eV with a peak height of about 40 mOD. The results support the feasibility of table-top ultrafast transient XUV absorption studies of photoinduced dynamics in transition metal oxide nanoparticles with sub-monolayer surface coverage.

Electron Diffraction of Pyrene Nanoclusters Embedded in Superfluid Helium Droplets.

We report electron diffraction of pyrene nanoclusters embedded in superfluid helium droplets. Using a least-squares fitting procedure, we have been able to separate the contribution of helium from those of the pyrene nanoclusters and determine the most likely structures for dimers and trimers. We confirm that pyrene dimers form a parallel double-layer structure with an interlayer distance of 3.5 Å and suggest that pyrene trimers form a sandwich structure but that the molecular planes are not completely parallel. The relative contributions of the dimers and trimers are ∼6:1. This work is an extension of our effort of solving structures of biological molecules using serial single-molecule electron diffraction imaging. The success of electron diffraction from an all-light-atom sample embedded in helium droplets offers reassuring evidence of the feasibility of this approach.

The impact of swift electrons on the segregation of Ni-Au nanoalloys

We report on the electron beam-induced segregation of alloyed Ni-Au clusters into a Ni and Au rich phase at temperatures above the miscibility gap of a binary system. The nanoparticles, with diameters less than 10 nm, are grown fully inert in superfluid helium droplets with a Ni-Au core-shell morphology. Upon heating, the clusters are alloyed and subsequently transformed to a Janus-type morphology under irradiation with swift electrons. The underlying mechanisms are studied experimentally via in situ scanning transmission electron microscopy and theoretically via atomistic simulation techniques under consideration of elastic electron interactions. We find that the segregation kinetics is highly temperature-dependent and attribute this behavior to diffusive relaxation processes. The presented results shed light on radiation induced phenomena using clusters as a model system and suggest new routes for the synthesis of structures in nonequilibrium configurations.