Low-frequency Vibrational Spectra Research Articles

Enumerating low-frequency nonphononic vibrations in computer glasses

In addition to Goldstone phonons that generically emerge in the low-frequency vibrational spectrum of any solid, crystalline or glassy, structural glasses also feature other low-frequency vibrational modes. The nature and statistical properties of these modes—often termed “excess modes”—have been the subject of decades-long investigation. Studying them, even using well-controlled computer glasses, has proven challenging due to strong spatial hybridization effects between phononic and nonphononic excitations, which hinder quantitative analyses of the nonphononic contribution DG(ω) to the total spectrum D(ω), per frequency ω. Here, using recent advances indicating that DG(ω)=D(ω)−DD(ω), where DD(ω) is Debye’s spectrum of phonons, we present a simple and straightforward scheme to enumerate nonphononic modes in computer glasses. Our analysis establishes that nonphononic modes in computer glasses indeed make an additive contribution to the total spectrum, including in the presence of strong hybridizations. Moreover, it cleanly reveals the universal DG(ω)∼ω4 tail of the nonphononic spectrum, and opens the way for related analyses of experimental spectra of glasses.

Terahertz Spectroscopy Unambiguously Determines the Orientation of Guest Water Molecules in a Structurally Elusive Metal-Organic Framework.

Porous materials, particularly metal-organic frameworks (MOFs), hold great promise for advanced applications. MIL-53(Al) is an exceptionally well-studied MOF that exhibits a phase transition upon guest capture─in this case, water─resulting in a dramatic change in the pore volume. Despite extensive studies, the structure of the water-loaded narrow-pore phase, MIL-53(Al)-np, remains controversial, particularly with respect to the positions of the adsorbed water molecules. We use terahertz spectroscopy, coupled with powder X-ray diffraction and density functional theory simulations, to unambiguously resolve this controversy. We show that the low-frequency (<100 cm-1) vibrational spectrum depends on weak long-range forces that are extremely sensitive to the orientation of the adsorbed water molecules. This enables definitively determining the correct structure of MIL-53(Al)-np while highlighting the extreme sensitivity of terahertz spectroscopy to bulk structure, suggesting its potential as a robust complement to X-ray diffraction for precise characterization of host-guest complexes.

Universal scaling for disordered viscoelastic matter near the onset of rigidity.

The onset of rigidity in interacting liquids, as they undergo a transition to a disordered solid, is associated with a rearrangement of the low-frequency vibrational spectrum. In this Letter, we derive scaling forms for the singular dynamical response of disordered viscoelastic networks near both jamming and rigidity percolation. Using effective-medium theory, we extract critical exponents, invariant scaling combinations, and analytical formulas for universal scaling functions near these transitions. Our scaling forms describe the behavior in space and time near the various onsets of rigidity, for rigid and floppy phases and the crossover region, including diverging length scales and timescales at the transitions.

Application of a high-resolution terahertz gas spectroscopy method to compositional analysis of thermal decomposition products of human fluids (urine)

Subject of study. In this study, the compositions of thermal decomposition products of samples of human fluids (urine) of cancer patients obtained before and after chemotherapy were investigated to identify the markers reflecting the influence of platinum-based chemotherapy, including its nephrotoxic influence, on the human body. Method. Molecular absorption spectroscopy, including nonstationary spectroscopy in the terahertz frequency range, is a prospective approach to investigation of multicomponent gas mixtures of different origins, including those of biological origin. The rotational spectrum lines and low-frequency vibrational spectra of molecules are in the terahertz frequency range (0.100–10 THz). When radiation transmitted through a gaseous sample is detected, the absorption lines, which are a unique characteristic of specific substances, are recorded in the spectrum. These absorption lines indicate the presence of the corresponding substances in the investigated multicomponent gas mixture; thus, this technique allows the identification of potential markers for pathologies and diseases as well as markers characterizing the effects of various exposure types on the human body, including the effect of drugs. Main results. A complex of metabolites resulting from the thermal decomposition of the sample was identified. The contents of gaseous thermal decomposition products of urine obtained from sick and conditionally healthy volunteers were compared. In addition, the contents of thermal decomposition products of urine obtained from the cancer patients before and after chemotherapy were compared. Practical significance. The proposed approach is advantageous for the development of a noninvasive investigation method that facilitates the assessment of chemotherapy effects on the human body.

Unified quantifier of mechanical disorder in solids.

Mechanical disorder in solids, which is generated by a broad range of physical processes and controls various material properties, appears in a wide variety of forms. Defining unified and measurable dimensionless quantifiers, allowing quantitative comparison of mechanical disorder across widely different physical systems, is therefore an important goal. Two such coarse-grained dimensionless quantifiers (among others) appear in the literature: one is related to the spectral broadening of discrete phononic bands in finite-size systems (accessible through computer simulations) and the other is related to the spatial fluctuations of the shear modulus in macroscopically large systems. The latter has been recently shown to determine the amplitude of wave attenuation rates in the low-frequency limit (accessible through laboratory experiments). Here, using two alternative and complementary theoretical approaches linked to the vibrational spectra of solids, we derive a basic scaling relation between the two dimensionless quantifiers. This scaling relation, which is supported by simulational data, shows that the two apparently distinct quantifiers are in fact intrinsically related, giving rise to a unified quantifier of mechanical disorder in solids. We further discuss the obtained results in the context of the unjamming transition taking place in soft sphere packings at low confining pressures, in addition to their implications for our understanding of the low-frequency vibrational spectra of disordered solids in general, and in particular those of glassy systems.

A methodology for integrated performance analyses of vibration reducing gloves

This study proposes a methodology for evaluating the integrated performance of vibration reducing (VR) gloves considering four measures. These include manual dexterity, distributed palm and fingers vibration transmission and grip strength preservation, which generally pose conflicting design requirements. The weights for the conflicting performance measures are identified for the given work conditions, classified according to the frequency ranges of predominant tool handle vibration (low and high), as defined in ISO-10819 together with the assembly/disassembly tasks. An index of weighted measures is formulated for identifying the most desirable VR glove for the given work condition. The results showed the greatest weighting for the fingers vibration response for high-frequency vibration spectra. Higher weightings for palm vibration and muscles' activity, were obtained for low-frequency vibration spectra, while the weighting for manual dexterity increased when coupled with manual tasks. An integrated performance index is identified and applied to rank nine different VR gloves and a conventional glove with known individual performance measures for identifying the most desirable glove. The vibration reducing gloves included: five gloves with gel vibration isolation materials, denoted as gel1, …, gel5; two gloves with air bladder vibration isolation material, denoted as air1 and air2; one hybrid glove comprising air pocket vibration isolation material in the palm region and gel in the fingers regions, denoted as hybrid; and a rubber glove. The gel2, air2 and hybrid gloves, made of air bladder or viscoelastic gels, showed superior integrated performance for high- and low-frequency vibration spectra among the ten alternatives. The fabric and rubber gloves revealed best integrated performance for the multiple tasks in conjunction with the low-frequency vibration spectrum.

Low-frequency vibrational spectrum of mean-field disordered systems

We study a recently introduced and exactly solvable mean-field model for the density of vibrational states $\mathcal{D}(\ensuremath{\omega})$ of a structurally disordered system. The model is formulated as a collection of disordered anharmonic oscillators, with random stiffness $\ensuremath{\kappa}$ drawn from a distribution $p(\ensuremath{\kappa})$, subjected to a constant field $h$ and interacting bilinearly with a coupling of strength $J$. We investigate the vibrational properties of its ground state at zero temperature. When $p(\ensuremath{\kappa})$ is gapped, the emergent $\mathcal{D}(\ensuremath{\omega})$ is also gapped, for small $J$. Upon increasing $J$, the gap vanishes on a critical line in the $(h,J)$ phase diagram, whereupon replica symmetry is broken. At small $h$, the form of this pseudogap is quadratic, $\mathcal{D}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{2}$, and its modes are delocalized, as expected from previously investigated mean-field spin glass models. However, we determine that for large enough $h$, a quartic pseudogap $\mathcal{D}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{4}$, populated by localized modes, emerges, the two regimes being separated by a special point on the critical line. We thus uncover that mean-field disordered systems can generically display both a quadratic-delocalized and a quartic-localized spectrum at the glass transition.

Non-relaxor behaviour of low-frequency vibration spectra of relaxor ferroelectric PbCo1/3Nb2/3O3: evidences from Brillouin and Raman scattering measurements

This paper presents the results of studies of a low-frequency vibration spectrum of PbCo1/3Nb2/3O3 (PCN) relaxor ferroelectric crystal using the Brillouin and Raman light scattering in the temperature range from 80 to 750 K. The analysis of the temperature behaviour of the longitudinal acoustic phonon in Brillouin scattering spectra showed no anomalies in the vicinity of ‘diffuse phase transition’ (T m = 250 K) in PCN. Polarized Raman light scattering spectra were obtained in PCN over the entire temperature range studied. Analysis of low-frequency optical mode behaviour in PCN during temperature change also revealed no correlations with dielectric permeability anomaly in the vicinity of T m: softening of optical phonon at 43 cm−1 frequency in VV polarization is observed at 170 K. In the same temperature range, there are anomalies (a ‘narrow’ and weak component) in quasi-elastic light scattering (QELS) obtained in temperature behaviour with VH polarization in Raman spectra in PCN. A ‘wide’ and intense QELS component, obtained in Raman spectra with VV polarization, shows anomalies in the vicinity of T m. We associate the anomalies of optical phonons and QELS with structure distortions in the formation of phase stratification and the dynamics of polar nano-regions.

Universality of the Nonphononic Vibrational Spectrum across Different Classes of Computer Glasses.

It has been recently established that the low-frequency spectrum of simple computer glass models is populated by soft, quasilocalized nonphononic vibrational modes whose frequencies ω follow a gapless, universal distribution D(ω)∼ω^{4}. While this universal nonphononic spectrum has been shown to be robust to varying the glass history and spatial dimension, it has so far only been observed in simple computer glasses featuring radially symmetric, pairwise interaction potentials. Consequently, the relevance of the universality of nonphononic spectra seen in simple computer glasses to realistic laboratory glasses remains unclear. Here, we demonstrate the emergence of the universal ω^{4} nonphononic spectrum in a broad variety of realistic computer glass models, ranging from tetrahedral network glasses with three-body interactions, through molecular glasses and glassy polymers, to bulk metallic glasses. Taken together with previous observations, our results indicate that the low-frequency nonphononic vibrational spectrum of any glassy solid quenched from a melt features the universal ω^{4} law, independently of the nature of its microscopic interactions.

Manifestation of structural Higgs and Goldstone modes in the hexagonal manganites

Structural phase transitions described by Mexican hat potentials should in principle exhibit aspects of Higgs and Goldstone physics. Here, we investigate the relationship between the phonons that soften at such structural phase transitions and the Higgs- and Goldstone-boson analogues associated with the crystallographic Mexican hat potential. We show that, with the exception of systems containing only one atom type, the usual Higgs and Goldstone modes are represented by a combination of several phonon modes, with the lowest energy phonons of the relevant symmetry having substantial contribution. Taking the hexagonal manganites as a model system, we identify these modes using Landau theory, and predict the temperature dependence of their frequencies using parameters obtained from density functional theory. Separately, we calculate the additional temperature dependence of all phonon mode frequencies arising from thermal expansion within the quasi-harmonic approximation. We predict that Higgs-mode softening will dominate the low-frequency vibrational spectrum of InMnO$_3$ between zero kelvin and room-temperature, whereas the behavior of ErMnO$_3$ will be dominated by lattice expansion effects. We present temperature-dependent Raman scattering data that support our predictions, in particular confirming the existence of the Higgs mode in InMnO$_3$.

Assessing the Performance of Density Functional Theory Methods on the Prediction of Low-Frequency Vibrational Spectra

The low-frequency (terahertz) dynamics of condensed phase materials provide valuable insight into numerous bulk phenomena. However, the assignment and interpretation of experimental results require computational methods due to the complex mode types that depend on weak intermolecular forces. Solid-state density functional theory has been used in this regard with great success, yet the selection of specific computational parameters, namely the chosen basis set and density functional, has a profound influence on the accuracy of predicted spectra. In this work, the role of these two parameters is investigated in a series of organic molecular crystals, in order to assess the ability of various methods to reproduce intermolecular forces, and subsequently experimental terahertz spectra. Specifically, naphthalene, oxalic acid, and thymine were chosen based on the varied intermolecular interactions present in each material. The results highlight that unconstrained geometry optimizations can be used as an initial proxy for the accuracy of interatomic forces, with errors in the calculated geometries indicative of subsequent errors in the calculated low-frequency vibrational spectra, providing a powerful metric for the validation of theoretical results. Finally, the origins of the observed shortcomings are analyzed, providing a basic framework for further studies on related materials.

Effect of aggregated Aβ protofilaments on intermolecular vibrational spectrum of confined water

Alzheimer’s disease, one of most common neurodegenerative diseases, is believed to be caused due to the self-assembly of amyloid beta ( $$\hbox {A}\beta $$ ) peptides into insoluble fibrils in the brain. Atomistic molecular dynamics simulations have been carried out to probe the effects of non-uniform structural distortions of aggregated $${\hbox {A}\beta }_{17-42}$$ protofilaments of different sizes, ranging from pentamer to tetradecamer, on the low-frequency vibrational spectrum of water confined within their amphiphilic nanocores. The calculations revealed increased back scattering of water molecules present either at the exterior surfaces of the protofilaments or confined within their cores, thereby leading to blue shifts of the band corresponding to $$\hbox {O} \cdot \cdot \cdot \hbox {O} \cdot \cdot \cdot \hbox {O}$$ bending or restricted transverse motions of water. Due to more restricted environment, the effect is more for the core water molecules. It is observed that the extent of such shifts is sensitive to the degree of confinement within the protofilament cores and the nature of hydrogen bonding. Importantly, the structural crossover of the protofilaments with increased core volume at decamer has been found to be associated with characteristic effect on the low-frequency modes of the water molecules confined within its core. Molecular dynamics simulations were carried out to probe the effects of non-uniform structural distortions of $$\hbox {A}\upbeta _{17{-}42}$$ protofilaments on low-frequency vibrational spectrum of water confined within their amphiphilic nanocores. It is demonstrated that the structural crossover of the protofilaments with increased core volume at decamer is associated with characteristic effect on the low frequency modes of water confined within its core.

Boson peak, elasticity, and glass transition temperature in polymer glasses: Effects of the rigidity of chain bending

The excess low-frequency vibrational spectrum, called boson peak, and non-affine elastic response are the most important particularities of glasses. Herein, the vibrational and mechanical properties of polymeric glasses are examined by using coarse-grained molecular dynamics simulations, with particular attention to the effects of the bending rigidity of the polymer chains. As the rigidity increases, the system undergoes a glass transition at a higher temperature (under a constant pressure), which decreases the density of the glass phase. The elastic moduli, which are controlled by the decrease of the density and the increase of the rigidity, show a non-monotonic dependence on the rigidity of the polymer chain that arises from the non-affine component. Moreover, a clear boson peak is observed in the vibrational density of states, which depends on the macroscopic shear modulus G. In particular, the boson peak frequency ωBP is proportional to sqrt{G}. These results provide a positive correlation between the boson peak, shear elasticity, and the glass transition temperature.

Universality and Structural Implications of the Boson Peak in Proteins

The softness and rigidity of proteins are reflected in the structural dynamics, which are in turn affected by the environment. The characteristic low-frequency vibrational spectrum of a protein, known as boson peak, is an indication of the structural rigidity of the protein at a cryogenic temperature or dehydrated conditions. In this article, the effect of hydration, temperature, and pressure on the boson peak and volumetric properties of a globular protein are evaluated by using inelastic neutron scattering and molecular dynamics simulation. Hydration, pressurization, and cooling shift the boson peak position to higher energy and depress the peak intensity and decreases the protein and cavity volumes. We found the correlation between the boson peak and cavity volume in a protein. A decrease of cavity volume means the increase of rigidity, which is the origin of the boson peak shift. Boson peak is the universal property of a protein, which is rationalized by the correlation.

Ultrafast Structure and Dynamics in the Thermally Activated Delayed Fluorescence of a Carbene-Metal-Amide.

Thermally activated delayed fluorescence has enormous potential for the development of efficient light emitting diodes. A recently discovered class of molecules (the carbene-metal-amides, CMAs) are exceptionally promising as they combine the small singlet-triplet energy gap required for thermal activation with a large transition moment for emission. Calculations suggest excited state structural dynamics modulate the critical coupling between singlet and triplet, but they disagree on the nature of those dynamics. Here we report ultrafast time-resolved transient absorption and Raman studies of CMA photodynamics. The measurements reveal complex structural evolution following intersystem crossing on the tens to hundreds of picoseconds time scale, and a change in the low-frequency vibrational spectrum between singlet and triplet states. The latter is assigned to changes in Raman active modes localized on the metal center.

Еxperimental Studies of Sliding Bearings of Locomotive Turbochargers by Their Level of Vibration

The diagnostic features and sources of vibration of sliding bearings of diesel locomotive turbochargers (disappearance of the negative allowance on bearing bushings, self-oscillation in the bearing, self-oscillation when the negative allowance on the bearing bushing disappears, excitation of blade harmonics, etc.) are described in brief. The results of experimental studies of diesel locomotive turbochargers equipped with cylindrical and elliptical sliding bearings are shown. The specific spectra of vibration velocity of the bearing housings (cylindrical and elliptical) in the low-frequency range are presented. Bearing frequencies have been detected in the low-frequency vibration spectrum of the turbocharger housing with cylindrical bearings, and the connection of the detected diagnostic features with defects in sliding bearings has been established. Blade frequencies of the compressor and turbines on turbochargers with cylindrical and elliptical sliding bearings have been found in the high-frequency part of the vibration spectrum. These frequencies are necessary for identifying rotor harmonics and bearing frequencies. It has been established that for a defect-free bearing of turbochargers with elliptical and cylindrical sliding bearings, the vibration velocity of the rotor harmonics and the bearing frequency should not exceed the rated values.

Inhibiting Low-Frequency Vibrations Explains Exceptionally High Electron Mobility in 2,5-Difluoro-7,7,8,8-tetracyanoquinodimethane (F2-TCNQ) Single Crystals.

Organic electronics requires materials with high charge mobility. Despite decades of intensive research, charge transport in high-mobility organic semiconductors has not been well understood. In this Letter, we address the physical mechanism underlying the exceptionally high band-like electron mobility in F2-TCNQ (2,5-difluoro-7,7,8,8-tetracyanoquinodimethane) single crystals among a crystal family of similar compounds Fn-TCNQ (n = 0, 2, 4) using a combined experimental and theoretical approach. While electron transfer integrals and reorganization energies did not show outstanding features for F2-TCNQ, Raman spectroscopy and solid-state DFT indicated that the frequency of the lowest vibrational mode is nearly twice higher in the F2-TCNQ crystal than in TCNQ and F4-TCNQ. This phenomenon is explained by the specific packing motif of F2-TCNQ with only one molecule per primitive cell so that electron-phonon interaction decreases and the electron mobility increases. We anticipate that our findings will encourage investigators for the search and design of organic semiconductors with one molecule per primitive cell and/or the poor low-frequency vibrational spectrum.

Communication: Pseudoisomorphs in liquids with intramolecular degrees of freedom.

Computer simulations show that liquids of molecules with harmonic intramolecular bonds may have "pseudoisomorphic" lines of approximately invariant dynamics in the thermodynamic phase diagram. We demonstrate that these lines can be identified by requiring scale invariance of the inherent-structure reduced-unit low-frequency vibrational spectrum evaluated for a single equilibrium configuration. This rationalizes why generalized excess-entropy scaling, density scaling, and isochronal superposition apply for many liquids with internal degrees of freedom.

Effects of Intermolecular Charge Transfer in Liquid Water on Raman Spectra

The low-frequency vibrational spectrum of liquid water is composed of contributions from the intermolecular librational and translation modes. The existence of these two modes introduces difficulty into the simulation of experimentally obtained Raman spectra. We constructed a polarizability function for a water model that includes intramolecular charge flow (CF) effects, intermolecular charge transfer (CT) effects, and intermolecular dipole-induced-dipole (DID) effects. We computed the one-dimensional (1D) Raman and terahertz (THz) spectra with all of these effects included (CFCT-DID) and compared with experimental spectra. We find that the CFCT-DID function provides a better description of the experimental results, because the CT effects reduce the polarizability only for translational motion to which parallelly polarized (VV) and perpendicularly polarized (VH) Raman spectra are sensitive. In our calculations of two-dimensional (2D) Raman and THz-Raman spectra, we observe the enhancement of echo signals in both cases. The details of the CFCT-DID function, along with its source code, are provided in the Supporting Information.

Observation of coherent delocalized phonon-like modes in DNA under physiological conditions.

Underdamped terahertz-frequency delocalized phonon-like modes have long been suggested to play a role in the biological function of DNA. Such phonon modes involve the collective motion of many atoms and are prerequisite to understanding the molecular nature of macroscopic conformational changes and related biochemical phenomena. Initial predictions were based on simple theoretical models of DNA. However, such models do not take into account strong interactions with the surrounding water, which is likely to cause phonon modes to be heavily damped and localized. Here we apply state-of-the-art femtosecond optical Kerr effect spectroscopy, which is currently the only technique capable of taking low-frequency (GHz to THz) vibrational spectra in solution. We are able to demonstrate that phonon modes involving the hydrogen bond network between the strands exist in DNA at physiologically relevant conditions. In addition, the dynamics of the solvating water molecules is slowed down by about a factor of 20 compared with the bulk.