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...