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 0 K 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 2 K, but begins to gradually deviate above that temperature. Inspection of pseudovorticity during real-time evolution of the system near 2 K 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.

Unravelling the full relaxation dynamics of superexcited helium nanodroplets.

The relaxation dynamics of superexcited superfluid He nanodroplets is thoroughly investigated by means of extreme-ultraviolet (XUV) femtosecond electron and ion spectroscopy complemented by time-dependent density functional theory (TDDFT). Three main paths leading to the emission of electrons and ions are identified: droplet autoionization, pump-probe photoionization, and autoionization induced by re-excitation of droplets relaxing into levels below the droplet ionization threshold. The most abundant product ions are He2+, generated by droplet autoionization and by photoionization of droplet-bound excited He atoms. He+ appear with some pump-probe delay as a result of the ejection He atoms in their lowest excited states from the droplets. The state-resolved time-dependent photoelectron spectra reveal that intermediate excited states of the droplets are populated in the course of the relaxation, terminating in the lowest-lying metastable singlet and triplet He atomic states. The slightly faster relaxation of the triplet state compared to the singlet state is in agreement with the simulation showing faster formation of a bubble around a He atom in the triplet state.

Peracetic acid-based advanced oxidation processes for decontamination and disinfection of water: A review.

Peracetic acid (PAA) has attracted growing attention as an alternative oxidant and disinfectant in wastewater treatment due to the increased demand to reduce chlorine usage and control disinfection byproducts (DBPs). These applications have stimulated new investigations on PAA-based advanced oxidation processes (AOPs), which can enhance water disinfection and remove micropollutants. The purpose of this review is to conduct a comprehensive analysis of scientific information and experimental data reported in recent years on the applications of PAA-based AOPs for the removal of chemical and microbiological micropollutants from water and wastewater. Various methods of PAA activation, including the supply of external energy and metal/metal-free catalysts, as well as their activation mechanisms are discussed. Then, a review on the usage of PAA-based AOPs for contaminant degradation is given. The degradation mechanisms of organic compounds and the influence of the controlling parameters of PAA-based treatment systems are summarized and discussed. Concurrently, the application of PAA-based AOPs for water disinfection and the related mechanisms of microorganism inactivation are also reviewed. Since combining UV light with PAA is the most commonly investigated PAA-based AOP for simultaneous pathogen inactivation and micropollutant oxidation, we have also focused on PAA microbial inactivation kinetics, together with the effects of key experimental parameters on the process. Moreover, we have discussed the advantages and disadvantages of UV/PAA as an AOP against the well-known and established UV/H2O2. Finally, the knowledge gaps, challenges, and new opportunities for research in this field are discussed. This critical review will facilitate an in-depth understanding of the PAA-based AOPs for water and wastewater treatment and provide useful perspectives for future research and development for PAA-based technologies.

First Observation of Bright Solitons in Bulk Superfluid

The existence of bright solitons in bulk superfluid ^{4}He is demonstrated by time-resolved shadowgraph imaging experiments and density functional theory (DFT) calculations. The initial liquid compression that leads to the creation of nonlinear waves is produced by rapidly expanding plasma from laser ablation. After the leading dissipative period, these waves transform into bright solitons, which exhibit three characteristic features: dispersionless propagation, negligible interaction in a two-wave collision, and direct dependence between soliton amplitude and the propagation velocity. The experimental observations are supported by DFT calculations, which show rapid evolution of the initially compressed liquid into bright solitons. At high amplitudes, solitons become unstable and break down into dispersive shock waves.

Application of time-resolved shadowgraph imaging and computer analysis to study micrometer-scale response of superfluid helium.

Application of inexpensive light emitting diodes as backlight sources for time-resolved shadowgraph imaging is demonstrated. The two light sources tested are able to produce light pulse sequences in the nanosecond and microsecond time regimes. After determining their time response characteristics, the diodes were applied to study the gas bubble formation around laser-heated copper nanoparticles in superfluid helium at 1.7 K and to determine the local cavitation bubble dynamics around fast moving metal micro-particles in the liquid. A convolutional neural network algorithm for analyzing the shadowgraph images by a computer is presented and the method is validated against the results from manual image analysis. The second application employed the red-green-blue light emitting diode source that produces light pulse sequences of the individual colors such that three separate shadowgraph frames can be recorded onto the color pixels of a charge-coupled device camera. Such an image sequence can be used to determine the moving object geometry, local velocity, and acceleration/deceleration. These data can be used to calculate, for example, the instantaneous Reynolds number for the liquid flow around the particle. Although specifically demonstrated for superfluid helium, the technique can be used to study the dynamic response of any medium that exhibits spatial variations in the index of refraction.

A thermodynamic model to predict electron mobility in superfluid helium.

Electron mobility in superfluid helium is modeled between 0.1 and 2.2 K by a van der Waals-type thermodynamic equation of state, which relates the free volume of solvated electrons to temperature, density, and phase dependent internal pressure. The model is first calibrated against known electron mobility reference data along the saturated vapor pressure line and then validated to reproduce the existing mobility literature values as a function of pressure and temperature with at least 10% accuracy. Four different electron mobility regimes are identified: (1) Landau critical velocity limit (T ≈ 0), (2) mobility limited by thermal phonons (T < 0.6 K), (3) thermal phonon and discrete roton scattering ("roton gas") limited mobility (0.6 K < T < 1.2 K), and (4) the viscous liquid ("roton continuum") limit (T > 1.2 K) where the ion solvation structure directly determines the mobility. In the latter regime, the Stokes equation can be used to estimate the hydrodynamic radius of the solvated electron based on its mobility and fluid viscosity. To account for the non-continuum behavior appearing below 1.2 K, the temperature and density dependent Millikan-Cunningham factor is introduced. The hydrodynamic electron bubble radii predicted by the present model appear generally larger than the solvation cavity interface barycenter values obtained from density functional theory (DFT) calculations. Based on the classical Stokes law, this difference can arise from the variation of viscosity and flow characteristics around the electron. The calculated DFT liquid density profiles show distinct oscillations at the vacuum/liquid interface, which increase the interface rigidity.

Time-resolved study of laser initiated shock wave propagation in superfluid 4He.

Intense shock waves in superfluid 4He between 1.7 and 2.1 K are generated by rapidly expanding confined plasma from laser ablation of a metal target immersed in the liquid. The resulting shock fronts in the liquid with initial velocities up to ca. Mach 10 are visualized by time-resolved shadowgraph photography. These high intensity shocks decay within 500 ns into less energetic shock waves traveling at Mach 2, which have their lifetime in the microsecond time scale. Based on the analysis using the classical Rankine-Hugoniot theory, the shock fronts created remain in the solid phase up to 1 µs and the associated thermodynamic state appears outside the previously studied region. The extrapolated initial shock pressure of 0.5 GPa is comparable to typical plasma pressures produced during liquid phase laser ablation. A secondary shock originating from fast heat propagation on the metal surface is also observed and a lower limit estimate for the heat propagation velocity is measured as 7 × 104 m/s. In the long-time limit, the high intensity shocks turn into liquid state waves that propagate near the speed of sound.

Interaction of Helium Rydberg State Molecules with Dense Helium.

The interaction potentials of the He2* excimer, in the a3Σu, b3Πg, c3Σg, and d3Σu electronic states with a ground state helium atom are presented. The symmetry of the interaction potentials closely follows the excimer Rydberg electron density with pronounced short-range minima appearing along the nodal planes of the Rydberg orbital. In such cases, a combination of the electrostatic short-range attraction combined with Pauli repulsion leads to the appearance of unusual long-range maxima in the potentials. Bosonic density functional calculations show that the 3d state excimer resides in a localized solvation bubble in dense helium at 4.5 K, with radii varying from 12.7 Å at 0.1 MPa to 10.8 Å at 2.4 MPa. The calculated 3d → 3b pressure-induced fluorescence band shifts are in good agreement with experimental results determined by application of corona discharge. The magnitude of the spectral shifts indicate that the observed He2* molecules emit from dense helium whereas the corresponding fluorescence signal from the discharge zone appears quenched. This implies that fluorescence spectroscopy involving this electronic transition can only be used to probe the state of the surrounding medium rather than the discharge zone itself.

Ejection of Metal Particles into Superfluid 4He by Laser Ablation.

The dynamics of laser ablation of a metal target immersed in superfluid 4He is studied through time-resolved shadowgraph photography. Delayed ejection of hot micrometer-sized particles from the target surface into the liquid was indirectly observed by monitoring the formation and growth of gaseous bubbles around the particles. The experimentally determined particle average velocity distribution appears to be similar to that previously measured in vacuum but exhibits a sharp cutoff at the speed of sound in the liquid. The propagation of the subsonic particles terminates in slightly elongated nonspherical gas bubbles residing near the target, whereas faster particles reveal an unusual hydrodynamic response in the liquid. On the basis of the previously established semiempirical model developed for macroscopic objects, the ejected transonic particles exhibit a supercavitating flow to reduce their hydrodynamic drag. Supersonic particles appear to follow a completely different propagation mechanism as they leave discrete and semicontinuous bubble trails in the liquid. The relatively low number density of the observed nonspherical gas bubbles indicates that only large micron-sized particles are visualized in the experiments. Although the unique properties of superfluid helium allow detailed characterization of these processes, the developed technique can be used to study the hydrodynamic response of any liquid to fast-propagating objects on the micrometer scale.

Theoretical modeling of electron mobility in superfluid (4)He.

The Orsay-Trento bosonic density functional theory model is extended to include dissipation due to the viscous response of superfluid (4)He present at finite temperatures. The viscous functional is derived from the Navier-Stokes equation by using the Madelung transformation and includes the contribution of interfacial viscous response present at the gas-liquid boundaries. This contribution was obtained by calibrating the model against the experimentally determined electron mobilities from 1.2 K to 2.1 K along the saturated vapor pressure line, where the viscous response is dominated by thermal rotons. The temperature dependence of ion mobility was calculated for several different solvation cavity sizes and the data are rationalized in the context of roton scattering and Stokes limited mobility models. Results are compared to the experimentally observed "exotic ion" data, which provides estimates for the corresponding bubble sizes in the liquid. Possible sources of such ions are briefly discussed.

Laser-Assisted Detection of Metal Nanoparticles in Liquid He-II.

The formation of gas bubbles surrounding laser heated copper nanoparticles in superfluid helium at 1.7 K is observed. Because of the effective light capture by these plasmonic particles and the subsequent heat transfer into the liquid, such bubbles grow within 3 µs to tens of micrometers in size. The Schlieren imaging technique is used to determine the spatial distribution of the nanoparticles in the liquid, and the gas bubble radii are related to the parent nanoparticle size. The presented liquid-phase particle size analysis is validated against atomic force microscopy measurements of nanoparticles deposited from the liquid onto a solid substrate.

Copper dimer interactions on a thermomechanical superfluid (4)He fountain.

Laser induced fluorescence imaging and frequency domain excitation spectroscopy of the copper dimer (B(1)Σg (+) ←X(1)Σu (+)) in thermomechanical helium fountain at 1.7 K are demonstrated. The dimers penetrate into the fountain provided that their average propagation velocity is ca. 15 m/s. This energy threshold is interpreted in terms of an imperfect fountain liquid-gas interface, which acts as a trap for low velocity dimers. Orsay-Trento density functional theory calculations for superfluid (4)He are used to characterize the dynamics of the dimer solvation process into the fountain. The dimers first accelerate towards the fountain surface and once the surface layer is crossed, they penetrate into the liquid and further slow down to Landau critical velocity by creating a vortex ring. Theoretical lineshape calculations support the assignment of the experimentally observed bands to Cu2 solvated in the bulk liquid. The vibronic progressions are decomposed of a zero-phonon line and two types of phonon bands, which correlate with solvent cavity interface compression (t < 200 fs) and expansion (200 < t < 500 fs) driven by the electronic excitation. The presented experimental method allows to perform molecular spectroscopy in bulk superfluid helium where the temperature and pressure can be varied.

Interaction of ions, atoms, and small molecules with quantized vortex lines in superfluid (4)He.

The interaction of a number of impurities (H2, Ag, Cu, Ag2, Cu2, Li, He3 (+), He(*) ((3)S), He2 (∗) ((3)Σu), and e(-)) with quantized rectilinear vortex lines in superfluid (4)He is calculated by using the Orsay-Trento density functional theory (DFT) method at 0 K. The Donnelly-Parks (DP) potential function binding ions to the vortex is combined with DFT data, yielding the impurity radius as well as the vortex line core parameter. The vortex core parameter at 0 K (0.74 Å) obtained either directly from the vortex line geometry or through the DP potential fitting is smaller than previously suggested but is compatible with the value obtained from re-analysis of the Rayfield-Reif experiment. All of the impurities have significantly higher binding energies to vortex lines below 1 K than the available thermal energy, where the thermally assisted escape process becomes exponentially negligible. Even at higher temperatures 1.5-2.0 K, the trapping times for larger metal clusters are sufficiently long that the previously observed metal nanowire assembly in superfluid helium can take place at vortex lines. The binding energy of the electron bubble is predicted to decrease as a function of both temperature and pressure, which allows adjusting the trap depth for either permanent trapping or to allow thermally assisted escape. Finally, a new scheme for determining the trapping of impurities on vortex lines by optical absorption spectroscopy is outlined and demonstrated for He(*).

Rotational superfluidity in small helium droplets.

The first minimum appearing in molecular rotational constants as a function of helium droplet size has been previously associated with the onset of superfluidity in these finite systems. We investigate this relationship by bosonic density functional theory calculations of classical molecular rotors (OCS, N2O, CO, and HCN) interacting with the surrounding helium. The calculated rotational constants are in fair agreement with the existing experimental data, demonstrating the applicability of the theoretical model. Inspection of the spatial evolution of the global phase and density shows the increase in the rotational constant after the first minimum correlates with continuous coverage of the molecule by helium and the appearance of angular phase coherence rather than completion of the first solvent shell. We assign the observed phenomenon to quantum phase transition between a localized state and one-dimensional superfluid, which represents the onset of rotational superfluidity in small helium droplets.

Solvation of intrinsic positive charge in superfluid helium.

On the basis of electronic structure calculations, the structure of intrinsic positive charge solvated in superfluid helium is identified as triatomic He3(+) ion, which is bound to the surrounding ground state helium atoms through the charge­charge induced dipole interaction in a pairwise additive manner. Bosonic density functional theory calculations show that this ion forms the well-known Atkins' snowball solvation structure where the first rigid helium shell is effectively disconnected from the rest of the liquid. Evaluation of the total energy vs helium droplet size N shows distinct regions related to the completion of solvent shells near N = 16 and N = 47. These regions can be assigned to magic numbers observed in positively charged helium droplets appearing at N = 15 and in the range between 20 and 50 helium atoms. The calculated added mass for the positive ion in bulk superfluid helium (18 mHe) is much smaller than the previous experiments suggest (30­40 mHe), indicating that there may be yet some unidentified additional factor contributing to the measured effective mass. Both previous experiments and the present calculations agree on the effective mass of the negative charge (240­250 mHe). The main difference between the solvated negative and positive charges in liquid helium is that the latter forms a chemically bound triatomic molecule surrounded by highly inhomogeneous liquid structure whereas the former remains as a separated charge with a smoothly varying liquid density around it.

Dynamics of vortex assisted metal condensation in superfluid helium.

Laser ablation of copper and silver targets immersed in bulk normal and superfluid (4)He was studied through time-resolved shadowgraph photography. In normal fluid, only a sub-millimeter cavitation bubble is created and immediate formation of metal clusters is observed within a few hundred microseconds. The metal clusters remain spatially tightly focused up to 15 ms, and it is proposed that this observation may find applications in particle image velocimetry. In superfluid helium, the cavitation bubble formation process is distinctly different from the normal fluid. Due to the high thermal conductivity and an apparent lag in the breakdown of superfluidity, about 20% of the laser pulse energy was transferred directly into the liquid and a large gas bubble, up to several millimeters depending on laser pulse energy, is created. The internal temperature of the gas bubble is estimated to exceed 9 K and the following bubble cool down period therefore includes two separate phase transitions: gas-normal liquid and normal liquid-superfluid. The last stage of the cool down process was assigned to the superfluid lambda transition where a sudden formation of large metal clusters is observed. This is attributed to high vorticity created in the volume where the gas bubble previously resided. As shown by theoretical bosonic density functional theory calculations, quantized vortices can trap atoms and dimers efficiently, exhibiting static binding energies up to 22 K. This, combined with hydrodynamic Bernoulli attraction, yields total binding energies as high as 35 K. For larger clusters, the static binding energy increases as a function of the volume occupied in the liquid to minimize the surface tension energy. For heliophobic species an energy barrier develops as a function of the cluster size, whereas heliophilics show barrierless entry into vortices. The present theoretical and experimental observations are used to rationalize the previously reported metal nanowire assembly in both superfluid bulk liquid helium and helium droplets, both of which share the common element of a rapid passage through the lambda point. The origin of vorticity is tentatively assigned to the Zurek-Kibble mechanism. Implications of the large gas bubble formation by laser ablation to previous experiments aimed at implanting atomic and dimeric species in bulk superfluid helium are also discussed, and it is proposed that the developed visualization method should be used as a diagnostic tool in such experiments to avoid measurements in dense gaseous environments.

Injection of atoms and molecules in a superfluid helium fountain: Cu and Cu2He(n) (n = 1, ..., ∞).

We introduce an experimental platform designed around a thermomechanical helium fountain, which is aimed at investigating spectroscopy and dynamics of atoms and molecules in the superfluid and at its vapor interface. Laser ablation of copper, efficient cooling and transport of Cu and Cu(2) through helium vapor (1.5 K < T < 20 K), formation of linear and T-shaped Cu(2)-He complexes, and their continuous evolution into large Cu(2)-He(n) clusters and droplets are among the processes that are illustrated. Reflection is the dominant quantum scattering channel of translationally cold copper atoms (T = 1.7 K) at the fountain interface. Cu(2) dimers mainly travel through the fountain unimpeded. However, the conditions of fountain flow and transport of molecules can be controlled to demonstrate injection and, in particular, injection into a nondivergent columnar fountain with a plug velocity of about 1 m/s. The experimental observables are interpreted with the aid of bosonic density functional theory calculations and ab initio interaction potentials.

Kinetics of UV-H2O2 advanced oxidation in the presence of alcohols: the role of carbon centered radicals.

UV photolysis of aqueous hydrogen peroxide samples was carried out in the presence of methanol, ethanol, or t-butanol. The concentrations of H(2)O(2), dissolved O(2), and the alcohols were monitored as a function of time, and a quantitative chemical kinetics model for the photolysis of the solutions is presented. The observed kinetics consisted of an initial rapid consumption of dissolved oxygen followed by a significant acceleration in the photodecomposition of hydrogen peroxide. The acceleration phase was identified to originate from the fast feedback reaction between hydrogen peroxide and the carbon centered radicals resulting from hydrogen atom abstraction from the primary alcohols. In tertiary butanol solutions the radical species formed are more stable and do not react directly with H(2)O(2). As a consequence no significant acceleration of H(2)O(2) photolysis was observed in the presence of t-butanol.

Rotation of methyl radicals in molecular solids.

Electron spin resonance (ESR) measurements were carried out to study the rotation of methyl radicals (CH(3)) in solid carbon monoxide, carbon dioxide, and nitrogen matrices. The radicals were produced by dissociating methane by plasma bursts generated by a focused 193 nm ArF excimer laser radiation during the gas condensation on the substrate. The ESR spectra exhibit anisotropic features that persist over the temperature range examined, and in most cases this indicates a restriction of rotation about the C(2) symmetry axis. A nonrotating CH(3) was also observed in a CO(2) matrix. The intensity ratio between the symmetric (A) and antisymmetric (E) nuclear spin states was recorded as a function of temperature for each molecular matrix. The rotational energy levels are modified from their gas phase structure with increasing crystal field strength. An anomalous situation was observed where the A/E ratio extended below the high temperature limit of 1/2.

Rotation of methyl radicals in a solid krypton matrix.

Electron spin resonance (ESR) measurements were carried out to study the rotation of methyl radicals (CH(3)) in a solid krypton matrix at 17-31 K temperature range. The radicals were produced by dissociating methane by plasma bursts generated by a focused 193 nm excimer laser radiation during the krypton gas condensation on the substrate. The ESR spectrum exhibits only isotropic features at the temperature range examined, and the intensity ratio between the symmetric (A) and antisymmetric (E) spin state lines exhibits weaker temperature dependence than in a solid argon matrix. However, the general appearance of the methyl radical spectrum depends strongly on temperature due to the pronounced temperature dependency of the E state linewidths. The rotational energy level populations are analyzed based on the static crystal field model, pseudorotating cage model, and quantum chemical calculations for an axially symmetric, planar rotor. Crystal field strength parameter values of -140 cm(-1) in Ar and -240 cm(-1) in Kr match most closely the experimentally observed rotational energy level shifts from the gas phase value. In the alternative model, considering the lattice atom movement in a pseudorotating cage, the effective lowering of the rotational constants B and C to 80%-90% leads to similar effects.