Crossover from gas-like to liquid-like molecular diffusion in a simple supercritical fluid.

According to textbooks, no physical observable can be discerned allowing to distinguish a liquid from a gas beyond the critical point. Yet, several proposals have been put forward challenging this view and various transition boundaries between a gas-like and a liquid-like behaviour, including the so-called Widom and Frenkel lines, and percolation line, have been suggested to delineate the supercritical state space. Here we report observation of a crossover from gas-like (Gaussian) to liquid-like (Lorentzian) self-dynamic structure factor by incoherent quasi-elastic neutron scattering measurements on supercritical fluid methane as a function of pressure, along the 200 K isotherm. The molecular self-diffusion coefficient was derived from the best Gaussian (at low pressures) or Lorentzian (at high pressures) fits to the neutron spectra. The Gaussian-to-Lorentzian crossover is progressive and takes place at about the Widom line intercept (59 bar). At considerably higher pressures, a liquid-like jump diffusion mechanism properly describes the supercritical fluid on both sides of the Frenkel line. The present observation of a gas-like to liquid-like crossover in the self dynamics of a simple supercritical fluid confirms emerging views on the unexpectedly complex physics of the supercritical state, and could have planet-wide implications and possible industrial applications in green chemistry.

Role of the single-particle dynamics in the transverse current autocorrelation function of a liquid metal.

A recent simulation study of the transverse current autocorrelation of the Lennard-Jones fluid [Guarini et al., Phys. Rev. E 107, 014139 (2023)] revealed that this function can be perfectly described within the exponential expansion theory [Barocchi et al., Phys. Rev. E 85, 022102 (2012)]. However, above a certain wavevector Q, not only transverse collective excitations were found to propagate in the fluid, but a second oscillatory component of unclear origin (therefore called X) must be considered to fully account for the time dependence of the correlation function. Here, we present an extended investigation of the transverse current autocorrelation of liquid Au as obtained by ab initio molecular dynamics in the very wide range of wavevectors 5.7 ≤ Q ≤ 32.8 nm-1 in order to also follow the behavior of the X component, if present, at large Q values. A joint analysis of the transverse current spectrum and its self-portion indicates that the second oscillatory component arises from the longitudinal dynamics, as suggested by its close resemblance with the previously determined component accounting for the longitudinal part of the density of states. We conclude that such a mode, albeit featuring a merely transverse property, fingerprints the effect of longitudinal collective excitations on single-particle dynamics, rather than arising from a possible coupling between transverse and longitudinal acoustic waves.

The Effect of Embedded Nanoparticles on the Phonon Spectrum of Ice: An Inelastic X-ray Scattering Study.

As a contribution to the ongoing effort toward high-frequency sound manipulation in composite materials, we use Inelastic X-ray Scattering to probe the phonon spectrum of ice, either in a pure form or with a sparse amount of nanoparticles embedded in it. The study aims at elucidating the ability of nanocolloids to condition the collective atomic vibrations of the surrounding environment. We observe that a nanoparticle concentration of about 1 % in volume is sufficient to visibly affect the phonon spectrum of the icy substrate, mainly canceling its optical modes and adding nanoparticle phonon excitations to it. We highlight this phenomenon thanks to the lineshape modeling based on a Bayesian inference, which enables us to capture the finest detail of the scattering signal. The results of this study can empower new routes toward the shaping of sound propagation in materials through the control of their structural heterogeneity.

Onset of collective excitations in the transverse dynamics of simple fluids.

A thorough analysis of the transverse current autocorrelation function obtained by molecular dynamics simulations of a dense Lennard-Jones fluid reveals that even such a simple system is characterized by a varied dynamical behavior with changing length scale. By using the exponential expansion theory, we provide a full account of the time correlation at wavevectors Q between the upper boundary of the hydrodynamic region and Q_{p}/2, with Q_{p} being the position of the main peak of the static structure factor. In the Q range studied, we identify and accurately locate the wavevector at which shear wave propagation starts to take place, and show clearly how this phenomenon may be represented by a damped harmonic oscillator changing, in a continuous way, from an overdamped to an underdamped condition. The decomposition into exponential modes allows one to convincingly establish not only the crossover related to the onset of transverse waves but, surprisingly, also the existence of a second pair of modes equivalent to another oscillator that undergoes, at higher Q values, a similarly smooth over to underdamped transition.

Altering Terahertz Sound Propagation in a Liquid upon Nanoparticle Immersion.

One of the grand challenges of new generation Condensed Matter physicists is the development of novel devices enabling the control of sound propagation at terahertz frequency. Indeed, phonon excitations in this frequency window are the leading conveyor of heat transfer in insulators. Their manipulation is thus critical to implementing heat management based on the structural design. To explore the possibility of controlling the damping of sound waves, we used high spectral contrast Inelastic X-ray Scattering (IXS) to comparatively study terahertz acoustic damping in a dilute suspension of 50 nm nanospheres in glycerol and on pure glycerol. Bayesian inference-based modeling of measured spectra indicates that, at sufficiently large distances, the spectral contribution of collective modes in the glycerol suspension becomes barely detectable due to the enhanced damping, the weakening, and the slight softening of the dominant acoustic mode.

The damping of terahertz acoustic modes in aqueous nanoparticle suspensions.

In this work, we investigate the possibility of controlling the acoustic damping in a liquid when nanoparticles are suspended in it. To shed light on this topic, we performed Inelastic X-Ray Scattering (IXS) measurements of the terahertz collective dynamics of aqueous suspensions of nanospheres of various materials, size, and relative concentration, either charged or neutral. A Bayesian analysis of measured spectra indicates that the damping of the two acoustic modes of water increases upon nanoparticle immersion. This effect seems particularly pronounced for the longitudinal acoustic mode, which, whenever visible at all, rapidly damps off when increasing the exchanged wavevector. Results also indicate that the observed effect strongly depends on the material the immersed nanoparticles are made of.

Searching for a second excitation in the inelastic neutron scattering spectrum of a liquid metal: a Bayesian analysis.

When probed at nanometer and picosecond scales, the properties of a liquid present striking analogies with the ones of the corresponding solid, one of the most surprising is the ability of supporting shear wave propagation, as a rigid medium. Although this evidence is being reported by a growing number of terahertz scattering measurements, it remains an open question whether it is universal or rather typical of some liquids only. Furthermore, given its elusive signatures in the scattering signal, the detection of this effect appears as a typical case where an unintentional "bias of confirmation" can mislead experimentalists. We thus decided to use a Bayesian inference approach to achieve a probabilistically grounded and evidence-based lineshape modeling of the inelastic neutron scattering spectra from liquid silver, whose simulated density autocorrelations bear evidence of a shear mode propagation over very short distances. The result of our analysis indicates that the observation of any additional, non-longitudinal, acoustic modes in this simple system goes beyond the accuracy of the used scattering method.

Molecular Dynamics of Lysozyme Amyloid Polymorphs Studied by Incoherent Neutron Scattering.

Lysozyme amyloidosis is a hereditary disease, which is characterized by the deposition of lysozyme amyloid fibrils in various internal organs. It is known that lysozyme fibrils show polymorphism and that polymorphs formed at near-neutral pH have the ability to promote more monomer binding than those formed at acidic pH, indicating that only specific polymorphs become dominant species in a given environment. This is likely due to the polymorph-specific configurational diffusion. Understanding the possible differences in dynamical behavior between the polymorphs is thus crucial to deepen our knowledge of amyloid polymorphism and eventually elucidate the molecular mechanism of lysozyme amyloidosis. In this study, molecular dynamics at sub-nanosecond timescale of two kinds of polymorphic fibrils of hen egg white lysozyme, which has long been used as a model of human lysozyme, formed at pH 2.7 (LP27) and pH 6.0 (LP60) was investigated using elastic incoherent neutron scattering (EINS) and quasi-elastic neutron scattering (QENS). Analysis of the EINS data showed that whereas the mean square displacement of atomic motions is similar for both LP27 and LP60, LP60 contains a larger fraction of atoms moving with larger amplitudes than LP27, indicating that the dynamical difference between the two polymorphs lies not in the averaged amplitude, but in the distribution of the amplitudes. Furthermore, analysis of the QENS data showed that the jump diffusion coefficient of atoms is larger for LP60, suggesting that the atoms of LP60 undergo faster diffusive motions than those of LP27. This study thus characterizes the dynamics of the two lysozyme polymorphs and reveals that the molecular dynamics of LP60 is enhanced compared with that of LP27. The higher molecular flexibility of the polymorph would permit to adjust its conformation more quickly than its counterpart, facilitating monomer binding.

Onset of interfacial waves in the terahertz spectrum of a nanoparticle suspension.

We used inelastic x-ray scattering to gain insight into the complex terahertz dynamics of a diluted Au-nanoparticle suspension in glycerol. We observe that, albeit sparse, Au nanoparticles leave clear signatures on the dynamic response of the system, the main one being an additional mode propagating at the nanoparticle-glycerol interface. A Bayesian inferential analysis of the line shape reveals that such a mode, at variance with conventional acoustic modes, keeps a hydrodynamiclike behavior well beyond the continuous limit and down to subnanometer distances.

The Terahertz Dynamics of an Aqueous Nanoparticle Suspension: An Inelastic X-ray Scattering Study.

We used the high-resolution Inelastic X-ray Scattering beamline of the Advanced Photon Source at Argonne National Laboratory to measure the terahertz spectrum of pure water and a dilute aqueous suspension of 15 nm diameter spherical Au nanoparticles (Au-NPs). We observe that, despite their sparse volume concentration of about 0.5%, the immersed NPs strongly influence the collective molecular dynamics of the hosting liquid. We investigate this effect through a Bayesian inference analysis of the spectral lineshape, which elucidates how terahertz transport properties of water change upon Au-NP immersion. In particular, we observe a nearly complete disappearance of the longitudinal acoustic mode and a mildly decreased ability to support shear wave propagation.

Neutron spin echo monitoring of segmental-like diffusion of water confined in the cores of carbon nanotubes.

Following the stream of increasing scientific interest in condensed-matter systems under ultra-hydrophobic confinement, the present work reports the first incoherent neutron spin echo assessment of the dynamics of water axially confined inside single-wall carbon nanotubes of diameter d∼ 1.4 nm. At the time scale of nanoseconds, two water populations are retrieved, whose relative proportion matches the one expected for a concentric shell + chain arrangement with cylindrical symmetry. The time dependence of the mean square displacement related to the external component is found to be subdiffusive, with peculiar resemblance to segmental diffusion typical of entangled polymeric systems.

Interpreting the Terahertz Spectrum of Complex Materials: The Unique Contribution of the Bayesian Analysis.

In the last few decades, experimental studies of the terahertz spectrum of density fluctuations have considerably improved our knowledge of the mesoscopic dynamics of disordered materials, which also have imposed new demands on the data modelling and interpretation. Indeed, lineshape analyses are no longer limited to the phenomenological observation of inelastic features, as in the pioneering stage of Neutron or X-ray spectroscopy, rather aiming at the extraction from their shape of physically relevant quantities, as sound velocity and damping, relaxation times, or other transport coefficients. In this effort, researchers need to face both inherent and practical obstacles, respectively stemming from the highly damped nature of terahertz modes and the limited energy resolution, accessible kinematic region and statistical accuracy of the typical experimental outcome. To properly address these challenges, a global reconsideration of the lineshape modelling and the enforcement of evidence-based probabilistic inference is becoming crucial. Particularly compelling is the possibility of implementing Bayesian inference methods, which we illustrated here through an in-depth discussion of some results recently obtained in the analysis of Neutron and X-ray scattering results.

Model-free description of polymer-coated gold nanoparticle dynamics in aqueous solutions obtained by Bayesian analysis of neutron spin echo data.

We present a neutron spin echo study of the nanosecond dynamics of polyethylene glycol (PEG) functionalized nanosized gold particles dissolved in D_{2}O at two temperatures and two different PEG molecular weights (400D and 2000D). The analysis of the neutron spin echo data was performed by applying a Bayesian approach to the description of time correlation function decays in terms of exponential terms, recently proved to be theoretically rigorous. This approach, which addresses in a direct way the fundamental issue of model choice in any dynamical analysis, provides here a guide to the most statistically supported way to follow the decay of the intermediate scattering functions I(Q,t) by basing on statistical grounds the choice of the number of terms required for the description of the nanosecond dynamics of the studied systems. Then, the presented analysis avoids from the start resorting to a preselected framework and can be considered as model free. By comparing the results of PEG-coated nanoparticles with those obtained in PEG2000 solutions, we were able to disentangle the translational diffusion of the nanoparticles from the internal dynamics of the polymer grafted to them, and to show that the polymer corona relaxation follows a pure exponential decay in agreement with the behavior predicted by coarse grained molecular dynamics simulations and theoretical models. This methodology has one further advantage: in the presence of a complex dynamical scenario, I(Q,t) is often described in terms of the Kohlrausch-Williams-Watts function that can implicitly represent a distribution of relaxation times. By choosing to describe the I(Q,t) as a sum of exponential functions and with the support of the Bayesian approach, we can explicitly determine when a finer-structure analysis of the dynamical complexity of the system exists according to the available data without the risk of overparametrization. The approach presented here is an effective tool that can be used in general to provide an unbiased interpretation of neutron spin echo data or whenever spectroscopy techniques yield time relaxation data curves.

Multiple Interacting Collective Modes and Phonon Gap in Phospholipid Membranes.

We combine Brillouin neutron scattering measurements with recent inelastic X-ray scattering [ Zhernenkov et al. Nat. Commun. 2016 , 7 , 11575 ] to propose a model for the collective dynamics of phospholipid bilayers. Neutron and X-ray spectra were fitted by the model response function associated with the Hamiltonian of an interacting-phonon system. This approach allows for a comprehensive and unprecedented picture of the vibrational collective features of phospholipids. At low wavevectors Q, the dispersion relations can be interpreted in terms of two acoustic-like modes, one longitudinal and one transverse, plus a dispersionless optic-like mode. The transverse mode of the liquid phase shows a phonon gap that can be linked to a passive transport mechanism through membranes, an interpretation that was proposed in Zhernenkov et al. At higher Q values, the interaction of the longitudinal acoustic excitation with the dispersionless mode gives rise to a pattern that is consistent with avoided-crossing behavior. Evidence is found for a slow- to fast-sound transition, similar to bulk water and other biomolecules.

Damping Off Terahertz Sound Modes of a Liquid upon Immersion of Nanoparticles.

The control of phonon propagation in nanoparticle arrays is one of the frontiers of nanotechnology, potentially enabling the discovery of materials with unknown functionalities for potential innovative applications. The exploration of the terahertz window appears quite promising as phonons in this range are the leading carriers of heat transport in insulators and their control is the key to implement devices for heat flow management. Unfortunately, this scientific field is still in its infancy, and even a basic topic such as the influence of floating nanoparticles on the terahertz phonon propagation of a colloidal suspension still eludes a firm answer. Shedding some light on this topic is the main motivation of the present work, which focuses an inelastic X-ray scattering (IXS) measurements on a dilute suspension of Au nanospheres in water. Measured spectra showed a nontrivial shape displaying multiple inelastic features that, based on a Bayesian inference analysis, we assign to phonon modes propagating throughout the nanoparticle interior. Surprisingly, the spectra bear no evidence of propagating modes, which are known to dominate the spectrum of pure water, owing to the scattering that these modes suffer from the sparse nanoparticles in suspension. In perspective, this finding may inspire simple routes to manipulate high-frequency acoustic propagation in hybrid-liquid and solid-materials.

Water Collective Dynamics in Whole Photosynthetic Green Algae as Affected by Protein Single Mutation.

In the context of the importance of water molecules for protein function/dynamics relationship, the role of water collective dynamics in Chlamydomonas green algae carrying both native and mutated photosynthetic proteins has been investigated by neutron Brillouin scattering spectroscopy. Results show that single point genetic mutation may notably affect collective density fluctuations in hydrating water providing important insight on the transmission of information possibly correlated to biological functionality. In particular, we highlight that the damping factor of the excitations is larger in the native compared to the mutant algae as a signature of a different plasticity and structure of the hydrogen bond network.

Vibrational collective dynamics of dry proteins in the terahertz region.

The coherent density fluctuations of a perdeuterated dry protein have been studied by Brillouin neutron spectroscopy. Besides a nearly wavevector-independent branch located around 5 meV, a propagating mode with a linear trend at low wavevector Q is revealed. The corresponding speed of 3780 ± 130 m/s is definitely higher than that of hydrated proteins. Above Q = 0.8 Å(-1), this mode becomes overdamped, with lifetimes shorter than 0.1 ps, in fashion similar to glassy materials. The present results indicate that dry proteins sustain coherent density fluctuations in the THz frequency regime. The trend of the longitudinal modulus indicates that in this frequency range dry biomolecules are more rigid than hydrated proteins.

Collective density fluctuations of DNA hydration water in the time-window below 1 ps.

The coherent density fluctuations propagating through DNA hydration water were studied by neutron scattering spectroscopy. Two collective modes were found to be sustained by the aqueous solvent: a propagating excitation, characterised by a speed of about 3500 m/s, and another one placed at about 6 meV. These results globally agree with those previously found for the coherent excitations in bulk water, although in DNA hydration water the speed of propagating modes is definitely higher than that of the pure solvent. The short-wavelength collective excitations of DNA hydration water are reminiscent of those observed in protein hydration water and in the amorphous forms of ice.

Collective dynamics of protein hydration water by brillouin neutron spectroscopy.

By a detailed experimental study of THz dynamics in the ribonuclease protein, we could detect the propagation of coherent collective density fluctuations within the protein hydration shell. The emerging picture indicates the presence of both a dispersing mode, traveling with a speed greater than 3000 m/s, and a nondispersing one, characterized by an almost constant energy of 6-7 meV. In agreement with molecular dynamics simulations [Phys. Rev. Lett. 2002, 89, 275501], the features of the dispersion curves closely resemble those observed in pure liquid water [Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2004, 69, 061203]. On the contrary, the observed damping factors are much larger than in bulk water, with the dispersing mode becoming overdamped at Q = 0.6 A(-1) already. Such novel experimental findings are discussed as a dynamic signature of the disordering effect induced by the protein surface on the local structure of water.