We measured the density of vibrational states (DOS) and the specific heat of various glassy and crystalline polymorphs of SiO 2 . The typical (ambient) glass shows a well-known excess of specific heat relative to the typical crystal (α-quartz). This, however, holds when comparing a lower-density glass to a higherdensity crystal. For glassy and crystalline polymorphs with matched densities, the DOS of the glass appears as the smoothed counterpart of the DOS of the corresponding crystal; it reveals the same number of the excess states relative to the Debye model, the same number of all states in the low-energy region, and it provides the same specific heat. This shows that glasses have higher specific heat than crystals not due to disorder, but because the typical glass has lower density than the typical crystal. DOI: 10.1103/PhysRevLett.112.025502 PACS numbers: 63.20.-e, 07.85.-m, 76.80.+y The low-temperature thermodynamic properties of glasses are accepted to be anomalously different from those of crystals due to the inherent disorder of the glass structure. At temperatures of ∼10 K, the specific heat of glasses shows an excess relativetothatofthecorrespondingcrystals.Theexcessspecific heat is related to a distinct feature in the spectrum of the atomic vibrations: At frequencies of ∼1 THz, glasses exhibit an excess of states above the Debye level of the acoustic waves, the socalled "boson peak." The excess of specific heat and the boson peak are universally observed for all glasses and by all relevant experimental techniques. However, the results still do not converge to a unified answer to how disorder causes these anomalies.Themajorityofthemodelsexplainthebosonpeakbyappealing tovarious glass-specific features. Theseincludelow-energy optical modes [1], onset of mechanical instability related to saddle points in the energy landscape [2] or to jamming [3][4][5], local vibrationalmodes of clusters [6] or locally favoured structures [7], librations [8] or other coherent motions [9] of molecular fragments, crossover of local and acoustic modes [10], quasilocal vibrations of atoms in an anharmonic potential [11], broadening of vibrational states in the Ioffe-Regel crossover regime [12], spatial variation of the elastic moduli [13], breakdown of the continuum approximation [14,15], and topologically diverse defects [16], to cite the most important ones.Alternatively, the boson peak is identified as the counterpart of the acoustic van Hove singularities of crystals, i.e., explained by the piling up of the vibrational states of the acousticlike branches near the boundary of the pseudoBrillouin zone [17][18][19][20].Diverging in explanations of the boson peak, all models agree that the excess states and the excess specific heat of

An integrated experimental approach, based on inelastic light-scattering techniques, has been here employed for a multilength scale characterization of networking properties of cyclodextrin nanosponges, a new class of cross-linked polymeric materials built up from natural oligosaccharides cyclodextrins. By using Raman and Brillouin scattering experiments, we performed a detailed inspection of the vibrational dynamics of these polymers over a wide frequency window ranging from gigahertz to terahertz, with the aim of providing physical descriptors correlated to the cross-linking degree and elastic properties of the material. The results seem to suggest that the stiffness of cross-linked polymers can be successfully tuned by acting on the type and the relative amount of the cross-linker during the synthesis of a polymer matrix, predicting and controlling their swelling and entrapment properties. The proposed experimental approach is a useful tool for investigating the structural and physicochemical properties of polymeric network systems.

We report measurements of the sound attenuation coefficient in vitreous silica, for sound waves of wavelength between 50 and 80 nm, performed with the new inelastic UV light scattering technique. These data indicate that in silica glass a crossover between a temperature-dependent (at low frequency) and a temperature-independent (at high frequency) acoustic attenuation mechanism occurs at Q 0:15 nm ÿ1 . The absence of any signature in the static structure factor at this Q value suggests that the observed crossover should be associated with local elastic constant fluctuations. DOI: 10.1103/PhysRevLett.97.035501 PACS numbers: 61.43.Fs, 63.50.+x The sound attenuation in disordered materials and its frequency and wavelength dependence are the result of the interplay between two physical mechanisms: one is due to the anharmonicity of the interparticle interactions, and the other to the structural disorder.The anharmonic attenuation of an acoustic sound wave, identified by its wavelength , frequency , and wave vector Q 2 = , is characterized by a specific, temperature-dependent, relaxation time r [1]. At low frequency (! r < 1) this process dominates the sound absorption through mechanisms such as, e.g., the Akhiezer mechanism [2,3]. Accordingly, the sound attenuation coefficient, as measured by the broadening ÿ of the Brillouin peak in the dynamic structure factor S Q; ! , scales as ! 2 and Q 2 . At high frequency ÿ! r > 1, i.e., Q > Q r 1=v r , where v is the sound velocity, the anharmonic attenuation becomes frequency independent [1][2][3].The sound attenuation associated with topological disorder gives rise to a steeper Q dependence of ÿ Q . If Rayleigh scattering is responsible for this attenuation, ÿ / Q 4 is expected for wavelengths larger than the typical defects size 2 =Q R . For Q > Q R , when the Rayleigh scattering regime is abandoned, one expects that ÿ Q is no longer / Q 4 . Experimentally, for Q larger than 1 nm ÿ1 , all glasses studied so far show ÿ / Q x , with x very close to 2 [4,5].This scenario can be summarized by a three-regime behavior of ÿ Q : (i) at low Q, ÿ Q is determined by anharmonic processes, and ÿ Q / Q 2 up to a first (temperature-dependent) crossover Q r 1=v r ; (ii) an intermediate regime, where the Q dependence of ÿ Q is determined by the system dependent strengths of anharmonicity and structural disorder processes; (iii) a high-Q regime, where ÿ Q is determined by the topological disorder and ÿ Q / Q 2 with a temperature-independent coefficient. This picture is highly debated because it critically depends on the location of Q r and Q R in different glasses. In densified v-SiO 2 , for example, the crossover Q R has been hypothesized to be around 2 nm ÿ1 [6].In the most studied case of vitreous silica, similarly to what happens in many other glasses, both Q r and Q R belong to a Q region which is not directly accessed by traditional scattering probes. In the case of v-SiO 2 , clear evidence is reported for the low-and high-Q quadratic behaviors of ÿ Q , using Brillouin light scat...

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.

The dynamic structure factor, S(Q, ω), of vitreous silica, has been measured by inelastic X-ray scattering in the exchanged wavevector (Q) region Q=4÷16.5 nm −1 and up to energies ω=115 meV in the Stokes side. The unprecedented statistical accuracy in such an extended energy range allows to accurately determine the longitudinal current spectra, and the energies of the vibrational excitations. The simultaneous observation of two excitations in the acoustic region, and the persistence of propagating sound waves up to Q values comparable with the (pseudo-)Brillouin zone edge, allow to observe a positive dispersion in the generalized sound velocity that, around Q≈5 nm −1 , varies from ≈6500 to ≈9000 m/s: this phenomenon was never experimentally observed in a glass.

Raman, Brillouin light, and x-ray scattering measurements have been carried out to characterize the low-frequency vibrational dynamics of the SiO(2) glass as function of its density. The obtained results demonstrate that while the distribution of the low-frequency states in the boson peak range is conserved under densification, these modes do not shift as a function of density as the acoustic modes do. The clear difference between the behavior of the vibrational states in the Boson peak range and that of the acoustic modes, could be explained considering the contribution of specific nonacoustic modes (tetrahedra rotation

The study of the effects of the density variations on the vibrational dynamics in vitreous silica is presented. A detailed analysis of the dynamical structure factor, as well as of the current spectra, allows the identification of a flattened transverse branch which is highly sensitive to the density variations. The experimental variations on the intensity and position of the Boson Peak (BP) in v-SiO2 as a function of density are reproduced and interpreted as being due to the shift and disappearance of the latter band. The BP itself is found to correspond to the lower energy tail of the excess states due to the piling up of vibrational modes at energies corresponding to the flattening of the transverse branch.

The vibrational dynamics of a new class of cross‐linked polymers obtained from both native and modified cyclodextrin, referred to as cyclodextrin nanosponges, is here investigated. The main purpose is to spot the structure of these materials at molecular level unlikely to be characterized by diffraction methods due to the low or null degree of crystallinity. The analysis of the spectral features of the vibrational bands observed between 1650 and 1800 cm−1 in both Raman and infrared spectra, and assigned to the carbonyl stretching modes of the polymeric network, is performed by using band deconvolution procedures. At the same time, a detailed inspection of the low‐wavenumber vibrational dynamics of these polymers is carried out, focusing on the modifications occurring on the so‐called boson peak. The simultaneous analysis of different wavenumber ranges in Raman and infrared spectra of cyclodextrin nanosponges allows us to develop a reliable strategy for exploring both the cross‐linking degree and the elastic properties of these innovative materials. The overall results give a complete characterization of the structural and dynamical properties of the system, in turn strictly connected to the entrapment/transport ability of these polymeric matrices. Copyright © 2013 John Wiley & Sons, Ltd.