Influence of pressure on the boson peak: stronger than elastic medium transformation

Stringlet excitation model of the boson peak

The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations ("stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency ωBP in the temperature regime well below the observed glass transition temperature Tg. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above Tg. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above Tg, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.

Effect of the alkali vs iron ratio on glass transition temperature and vibrational properties of synthetic basalt-like glasses

Volcanic eruptions generate huge amounts of material with a wide range of compositions and therefore different physicochemical properties. We present a combined Raman and calorimetric study carried out on four synthetic basaltic glasses with different alkali vs iron ratio which spans the typical compositions of basalts on Earth. Differential scanning calorimetry shows that changes of this ratio modify the glass transition interval whereas Raman spectra allow to gain insight about the structure of the glass in the microscopic and macroscopic range. Indeed, our Raman analysis is extended from the high frequency region, characterized by the molecular peaks, to the very low frequency region where glasses exhibit the boson peak. Spectra show a variation of the non-bridging oxygens number that affects the medium range order of the glass and the network interconnections. In the considered substitution interval, the boson peak shape is conserved while its position shift upwards. This means that increasing the alkali vs iron content, the elastic medium hardens but it does not change nature. This study emphasizes the importance of considering the full-range spectra when analysing multicomponent or natural systems with small chemical variations.

Vibrational disorder and densification-induced homogenization of local elasticity in silicate glasses

We report the effect of structural compaction on the statistics of elastic disorder in a silicate glass, using heterogeneous elasticity theory with the coherent potential approximation (HET-CPA) and a log-normal distribution of the spatial fluctuations of the shear modulus. The object of our study, a soda lime magnesia silicate glass, is compacted by hot-compression up to 2 GPa (corresponding to a permanent densification of ~ 5%). Using THz vibrational spectroscopic data and bulk mechanical properties as inputs, HET-CPA evaluates the degree of disorder in terms of the length-scale of elastic fluctuations and the non-affine part of the shear modulus. Permanent densification decreases the extent of non-affine elasticity, resulting in a more homogeneous distribution of strain energy, while also decreasing the correlation length of elastic heterogeneity. Complementary 29Si magic angle spinning NMR spectroscopic data provide a short-range rationale for the effect of compression on glass structure in terms of a narrowing of the Si-O-Si bond-angle and the Si-Si distance.

Understanding the scaling of boson peak through insensitivity of elastic heterogeneity to bending rigidity in polymer glasses

Amorphous materials exhibit peculiar mechanical and vibrational properties, including non-affine elastic responses and excess vibrational states, i.e., the so-called boson peak (BP). For polymer glasses, these properties are considered to be affected by the bending rigidity of the constituent polymer chains. In our recent work [Tomoshige,et al2019,Sci. Rep.919514], we have revealed simple relationships between the variations of vibrational properties and the global elastic properties: the response of the BP scales only with that of the global shear modulus. This observation suggests that the spatial heterogeneity of the local shear modulus distribution is insensitive to changes in the bending rigidity. Here, we demonstrate the insensitivity of elastic heterogeneity by directly measuring the local shear modulus distribution. We also study transverse sound wave propagation, which is also shown to scale only with the global shear modulus. Through these analyses, we conclude that the bending rigidity does not alter the spatial heterogeneity of the local shear modulus distribution, which yields vibrational and acoustic properties that are controlled solely by the global shear modulus of a polymer glass.

Reaching the Ideal Glass in Polymer Spheres: Thermodynamics and Vibrational Density of States

The existence of an ideal glass and the resolution to the Kauzmann paradox is a long-standing open question in materials science. To address this problem, we exploit the ability of glasses with large interfacial area to access low energy states. We submit aggregates of spheres of a polymeric glass former to aging well below their glass transition temperature, T_{g}; and characterize their thermodynamic state by calorimetry, and the vibrational density of state (VDOS) by inelastic neutron scattering (INS). We show that, when aged at appropriate temperatures, glassy spheres attain a thermodynamic state corresponding to an ideal glass in time scales of about one day. In this state, the boson peak, underlying the deviation from the Debye level of the VDOS, is essentially suppressed. Our results are discussed in the framework of the link between the macroscopic thermodynamic state of glasses and their vibrational properties.

Disentangling Self-Atomic Motions in Polyisobutylene by Molecular Dynamics Simulations

We present fully atomistic molecular dynamics simulations on polyisobutylene (PIB) in a wide temperature range above the glass transition. The cell is validated by direct comparison of magnitudes computed from the simulation and measured by neutron scattering on protonated samples reported in previous works. Once the reliability of the simulation is assured, we exploit the information in the atomic trajectories to characterize the dynamics of the different kinds of atoms in PIB. All of them, including main-chain carbons, show a crossover from Gaussian to non-Gaussian behavior in the intermediate scattering function that can be described in terms of the anomalous jump diffusion model. The full characterization of the methyl-group hydrogen motions requires accounting for rotational motions. We show that the usually assumed statistically independence of rotational and segmental motions fails in this case. We apply the rotational rate distribution model to correlation functions calculated for the relative positions of methyl-group hydrogens with respect to the carbon atom at which they are linked. The contributions to the vibrational density of states are also discussed. We conclude that methyl-group rotations are coupled with the main-chain dynamics. Finally, we revise in the light of the simulations the hypothesis and conclusions made in previously reported neutron scattering investigations on protonated samples trying to address the origin of the dielectric β-process.

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 ω_BP is proportional to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{G}$$\end{document}G. These results provide a positive correlation between the boson peak, shear elasticity, and the glass transition temperature.

Boson Peak Decouples from Elasticity in Glasses with Low Connectivity

We perform molecular-dynamics simulations of the vibrational and elastoplastic properties of polymeric glasses and crystals and the corresponding atomic systems. We evidence that the elastic scaling of the density of states in the low-frequency boson peak (BP) region is different in crystals and glasses. Also, we see that the BP of the polymeric glass is nearly coincident with the one of the atomic glasses, thus revealing that the former-unlike the elasticity-is controlled by nonbonding interactions only. Our results suggest that the interpretation of the BP in terms of the macroscopic elasticity, discussed in highly connected systems, does not hold for systems with low connectivity.

Local Deformation of Glasses is Mediated by Rigidity Fluctuation on Nanometer Scale

Microscopic deformation processes determine defect formation on glass surfaces and, thus, the material's resistance to mechanical failure. While the macroscopic strength of most glasses is not directly dependent on material composition, local deformation and flaw initiation are strongly affected by chemistry and atomic arrangement. Aside from empirical insight, however, the structural origin of the fundamental deformation modes remains largely unknown. Experimental methods that probe parameters on short or intermediate length-scale such as atom-atom or superstructural correlations are typically applied in the absence of alternatives. Drawing on recent experimental advances, spatially resolved Raman spectroscopy is now used in the THz-gap for mapping local changes in the low-frequency vibrational density of states. From direct observation of deformation-induced variations on the characteristic length-scale of molecular heterogeneity, it is revealed that rigidity fluctuation mediates the deformation process of inorganic glasses. Molecular field approximations, which are based solely on the observation of short-range (interatomic) interactions, fail in the prediction of mechanical behavior. Instead, glasses appear to respond to local mechanical contact in a way that is similar to that of granular media with high intergranular cohesion.

Damping of vibrational excitations in glasses at terahertz frequency: The case of 3-methylpentane

We report a compared analysis of inelastic X ray scattering (IXS) and of low frequency Raman data of glassy 3-methylpentane. The IXS spectra have been analysed allowing for the existence of two distinct excitations at each scattering wavevector obtaining a consistent interpretation of the spectra. In particular, this procedure allows us to interpret the linewidth of the modes in terms of a simple model which relates them to the width of the first sharp diffraction peak in the static structure factor. In this model, the width of the modes arises from the blurring of the dispersion curves which increases approaching the boundary of the first pseudo-Brillouin zone. The position of the boson peak contribution to the density of vibrational states derived from the Raman scattering measurements is in agreement with the interpretation of the two excitations in terms of a longitudinal mode and a transverse mode, the latter being a result of the mixed character of the transverse modes away from the center of the pseudo-Brillouin zone.

Pressure Dependence of the Boson Peak of Glassy Glycerol

The pressure dependence of the boson peak (BP) of glycerol, including its behavior across the liquid-glass transition, has been studied using Raman scattering. A significant increase of the BP frequency was observed with pressure up to 11 GPa at room temperature. The pressure dependence of BP frequency ν_BP is proportional to (1+P/P₀)^1/3, where P and P₀ are the pressure and a constant, respectively, consistent with a soft potential model. The characteristic length of medium range order is close in size to a cyclic trimer of glycerol molecules, as predicted by the medium range order of a BP excitation using molecular dynamics simulations, and the pressure dependence of a characteristic medium range order is nearly constant. The pressure induced structural changes in glycerol can be understood in terms of the shrinkage of voids with cyclic trimers persisting to at least 11 GPa. Pressure dependence of the intermolecular O-H stretching mode indicates that the intermolecular hydrogen bond distances gradually decrease up to the glass transition pressure of ∼5 GPa and become nearly constant in the glassy state, indicating the disappearance of free volume in the dense glass.

Evidence for Marginal Stability in Emulsions

We report the first measurements of the effect of pressure on vibrational modes in emulsions, which serve as a model for soft frictionless spheres at zero temperature. As a function of the applied pressure, we find that the density of states D(ω) exhibits a low-frequency cutoff ω^{*}, which scales linearly with the number of extra contacts per particle δz. Moreover, for ω<ω^{*}, our results are consistent with D(ω)∼ω^{2}/ω^{*2}, a quadratic behavior whose prefactor is larger than what is expected from Debye theory. This surprising result agrees with recent theoretical findings [E. DeGiuli, A. Laversanne-Finot, G. A. Düring, E. Lerner, and M. Wyart, Soft Matter 10, 5628 (2014); S. Franz, G. Parisi, P. Urbani, and F. Zamponi, Proc. Natl. Acad. Sci. U.S.A. 112, 14539 (2015)]. Finally, the degree of localization of the softest low frequency modes increases with compression, as shown by the participation ratio as well as their spatial configurations. Overall, our observations show that emulsions are marginally stable and display non-plane-wave modes up to vanishing frequencies.

Pressure Effect on the Boson Peak in Deeply Cooled Confined Water: Evidence of a Liquid-Liquid Transition

The boson peak in deeply cooled water confined in nanopores is studied to examine the liquid-liquid transition (LLT). Below ∼180  K, the boson peaks at pressures P higher than ∼3.5  kbar are evidently distinct from those at low pressures by higher mean frequencies and lower heights. Moreover, the higher-P boson peaks can be rescaled to a master curve while the lower-P boson peaks can be rescaled to a different one. These phenomena agree with the existence of two liquid phases with different densities and local structures and the associated LLT in the measured (P, T) region. In addition, the P dependence of the librational band also agrees with the above conclusion.

Elasticity and Inverse Temperature Transition in Elastin

Elastin is a structural protein and biomaterial that provides elasticity and resilience to a range of tissues. This work provides insights into the elastic properties of elastin and its peculiar inverse temperature transition (ITT). These features are dependent on hydration of elastin and are driven by a similar mechanism of hydrophobic collapse to an entropically favorable state. Using neutron scattering, we quantify the changes in the geometry of molecular motions above and below the transition temperature, showing a reduction in the displacement of water-induced motions upon hydrophobic collapse at the ITT. We also measured the collective vibrations of elastin gels as a function of elongation, revealing no changes in the spectral features associated with local rigidity and secondary structure, in agreement with the entropic origin of elasticity.

Signature of a polyamorphic transition in the THz spectrum of vitreous GeO2

The THz spectrum of density fluctuations, S(Q, ω), of vitreous GeO2 at ambient temperature was measured by inelastic x-ray scattering from ambient pressure up to pressures well beyond that of the known α-quartz to rutile polyamorphic (PA) transition. We observe significant differences in the spectral shape measured below and above the PA transition, in particular, in the 30-80 meV range. Guided by first-principle lattice dynamics calculations, we interpret the changes in the phonon dispersion as the evolution from a quartz-like to a rutile-like coordination. Notably, such a crossover is accompanied by a cusp-like behavior in the pressure dependence of the elastic response of the system. Overall, the presented results highlight the complex fingerprint of PA phenomena on the high-frequency phonon dispersion.

Acoustic excitations in glassy sorbitol and their relation with the fragility and the boson peak

We report a detailed analysis of the dynamic structure factor of glassy sorbitol by using inelastic X-ray scattering and previously measured light scattering data [B. Ruta, G. Monaco, F. Scarponi, and D. Fioretto, Philos. Mag. 88, 3939 (2008)]. The thus obtained knowledge on the density-density fluctuations at both the mesoscopic and macroscopic length scale has been used to address two debated topics concerning the vibrational properties of glasses. The relation between the acoustic modes and the universal boson peak (BP) appearing in the vibrational density of states of glasses has been investigated, also in relation with some recent theoretical models. Moreover, the connection between the elastic properties of glasses and the slowing down of the structural relaxation process in supercooled liquids has been scrutinized. For what concerns the first issue, it is here shown that the wave vector dependence of the acoustic excitations can be used, in sorbitol, to quantitatively reproduce the shape of the boson peak, supporting the relation between BP and acoustic modes. For what concerns the second issue, a proper study of elasticity over a wide spatial range is shown to be fundamental in order to investigate the relation between elastic properties and the slowing down of the dynamics in the corresponding supercooled liquid phase.

Low-energy vibrational dynamics of cesium borate glasses

Low-temperature specific heat and inelastic light scattering experiments have been performed on a series of cesium borate glasses and on a cesium borate crystal. Raman measurements on the crystalline sample have revealed the existence of cesium rattling modes in the same frequency region where glasses exhibit the boson peak (BP). These localized modes are supposed to overlap with the BP in cesium borate glasses affecting its magnitude. Their influence on the low frequency vibrational dynamics in glassy samples has been considered, and their contribution to the specific heat has been estimated. Evidence for a relation between the changes of the BP induced by the increased amount of metallic oxide and the variations of the elastic medium has been provided.

Equivalence of the boson peak in glasses to the transverse acoustic van Hove singularity in crystals

We compare the atomic dynamics of the glass to that of the relevant crystal. In the spectra of inelastic scattering, the boson peak of the glass appears higher than the transverse acoustic (TA) singularity of the crystal. However, the density of states shows that they have the same number of states. Increasing pressure causes the transformation of the boson peak of the glass towards the TA singularity of the crystal. Once corrected for the difference in the elastic medium, the boson peak matches the TA singularity in energy and height. This suggests the identical nature of the two features.

Density invariant vibrational modes in disordered colloidal crystals

We experimentally measure the density of states (DOS) and dynamical structure factor (DSF) arising from the thermal fluctuations in a colloidal crystal composed of thermally sensitive micron-sized hydrogel particles at several different particle volume fractions, ϕ's. Particle positions are tracked over long times using optical microscopy and particle tracking algorithms in a single two-dimensional (2D) [111] plane of a 3D face-centered-cubic single crystal. The dynamical fluctuations are spatially heterogeneous while the lattice itself is highly ordered. At all ϕ's, the DOS exhibits an excess of low frequency modes, a so-called boson peak (BP), and the DSF exhibits a cross-over from propagating to nonpropagating behavior, a so-called Ioffe-Regel crossover, at a frequency somewhat below the BP for both longitudinal and transverse modes. As we tune ϕ from 0.64 to 0.56, the Lindemann parameter grows from ~3% to ~8%; however, the shape of the DOS and DSF remain largely unchanged when rescaled by the Debye level. This invariance indicates that the effective degree of disorder remains essentially constant even in the vicinity of melting.

High pressure effect on the ultrafast energy relaxation rate of LDS698 (C19H23N2O4Cl) in a solution

Effects of high pressure in a range of up to 1.7 GPa on ultrafast energy relaxation of LDS698 (C(19)H(23)N(2)O(4)Cl) molecules in solution have experimentally been illustrated by a method of femtosecond time-resolved absorption spectroscopy. The rates of the intramolecular and intermolecular energy relaxations show quite different pressure dependences. The observed results are in good agreement with the theoretical interpretation based on the pressure influences on the molecular energy gaps, the intermolecular H-bond interaction, and the solution viscosity.

Scaling the temperature-dependent boson peak of vitreous silica with the high-frequency bulk modulus derived from Brillouin scattering data

The position and strength of the boson peak in silica glass vary considerably with temperature T. Such variations cannot be explained solely with changes in the Debye energy. New Brillouin-scattering measurements are presented which allow determining the T dependence of unrelaxed acoustic velocities. Using a velocity based on the bulk modulus, scaling exponents are found which agree with the soft-potential model. The unrelaxed bulk modulus thus appears to be a good measure for the structural evolution of silica with T and to set the energy scale for the soft potentials.

Non-Debye normalization of the glass vibrational density of states in mildly densified silicate glasses

The evolution of the boson peak with densification at medium densification rates (up to 2.3%) in silicate glasses was followed through heat capacity measurements and low frequency Raman scattering. It is shown that the decrease of the boson peak induced by densification does not conform to that expected from a continuous medium; rather it follows a two step behaviour. The comparison of the heat capacity data with the Raman data shows that the light-vibration coupling coefficient is almost unaffected in this densification regime. These results are discussed in relation to the inhomogeneity of the glass elastic network at the nanometre scale.

Connection between Boson peak and elastic properties in silicate glasses

Inelastic neutron, light, and x-ray scattering are used to investigate the vibrational density of states (VDOS) and the elastic properties of a sodium silicate glass as a function of temperature. The elastic moduli show the frequency and temperature dependence typical of anharmonic effects. The measured VDOS spectra, up to and including the excess vibrational density at the boson peak, scale with the Debye level only if this is calculated from the high-frequency values of the elastic constants. This emphasizes that conclusions on the relation between VDOS and elastic properties can be drawn only if anharmonic and relaxational effects are properly taken into account.

Influence of pressure on quasielastic scattering in glasses: relationship to the boson peak

We report unexpectedly strong variations in the quasielastic scattering (QES) intensity in glasses under pressure. Analysis of the data reveals strong correlations between pressure-induced changes in the QES intensity and the intensity of the boson peak. This observation emphasizes a direct relationship between these two components of the fast dynamics. In addition, we observe changes of the QES spectral shape that can be interpreted as pressure-induced variations in the underlying energy landscape.

Raman-scattering measurements of the vibrational density of states of a reactive mixture during polymerization: effect on the boson peak

Raman-scattering measurements are used to follow the modification of the vibrational density of states in a reactive epoxy-amine mixture during isothermal polymerization. Combining them with Brillouin light and inelastic x-ray scattering measurements, we analyze the variations of the boson peak and of the Debye level while the system changes from liquid to glass upon increasing the number of covalent bonds among the constituent molecules. The shift and intensity variation of the boson peak are explained by the modification of the elastic properties throughout the reaction, and a master curve for the boson peak can therefore be obtained. Surprisingly, bond-induced modifications of the structure do not affect this master curve.

Universal link between the boson peak and transverse phonons in glass

The physical properties of a topologically disordered amorphous material (glass), such as heat capacity and thermal conductivity, are markedly different from those of its ordered crystalline counterpart. The understanding of these phenomena is a notoriously complex problem. One of the universal features of disordered glasses is the 'boson peak', which is observed in neutron and Raman scattering experiments. The boson peak is typically ascribed to an excess density of vibrational states. Here, we study the nature of the boson peak, using numerical simulations of several glass-forming systems. We discovered evidence suggestive of the equality of the boson peak frequency to the Ioffe-Regel limit for 'transverse' phonons, above which transverse phonons no longer propagate. Our results indicate a possibility that the origin of the boson peak is transverse vibrational modes associated with defective soft structures in the disordered state. Furthermore, we suggest a possible link between slow structural relaxation and fast boson peak dynamics in glass-forming systems.