Understanding the emergence of the boson peak in molecular glasses

Abstract

A common feature of glasses is the "boson peak", observed as an excess in the heat capacity over the crystal or as an additional peak in the terahertz vibrational spectrum. The microscopic origins of this peak are not well understood; the emergence of locally ordered structures has been put forward as a possible candidate. Here, we show that depolarised Raman scattering in liquids consisting of highly symmetric molecules can be used to isolate the boson peak, allowing its detailed observation from the liquid into the glass. The boson peak in the vibrational spectrum matches the excess heat capacity. As the boson peak intensifies on cooling, wide-angle x-ray scattering shows the simultaneous appearance of a pre-peak due to molecular clusters consisting of circa 20 molecules. Atomistic molecular dynamics simulations indicate that these are caused by over-coordinated molecules. These findings represent an essential step toward our understanding of the physics of vitrification.

Fig. 1. Optical Kerr-effect (OKE) spectra of supercooled and vitrified tetrabutyl orthosilicate (TBOS).

a All data from 90 to 440 K. b, c Two representative temperatures and fits. The black line in (b) is the component due to diffusive α relaxation fitted to a Havriliak–Negami function, which freezes out below the glass transition and is therefore absent in (c). The two green bands at low frequency are intermolecular modes fitted to two Gaussian functions. The blue band is an intramolecular vibration fitted to a Brownian oscillator function with constant amplitude. The yellow curves are additional intramolecular vibrations. d Temperature-dependent amplitudes of the low-frequency (A_G1, red disks) and high-frequency (A_G2, blue squares) intermolecular modes. The lines are guides to the eye. While these amplitudes change, the amplitude of the higher frequency intramolecular modes remain unchanged with temperature as expected.

Fig. 2. Temperature dependence of the fit parameters for the intermolecular modes.

a Ratio of the amplitude of the low-frequency intermolecular mode over that of the high-frequency one. The solid red line is an exponential fit to guide the eye (The data point at 200 K was omitted in this fit on account of the noise at low frequencies in the corresponding OKE data). b Centre frequency ω₀ of the two intermolecular modes (blue squares and red disks, also shown are linear and exponential fits to guide the eye) and the corresponding widths σ (green triangles and yellow diamonds respectively, also shown are an exponential fit and a horizontal line to guide the eye).

Fig. 3. Analysis of temperature-dependent WAXS data.

a Experimental SAXS and WAXS data taken at 298 K (red) and 92 K (blue) and fit to four Gaussians and a Lorentzian (black). The average of the nine data sets at 110 K and below is shown (yellow) with a fit including an additional Gaussian to account for the pre-peak (black). b Variation of the peak of the first (q₃, red) and second (q₅, blue) sharp diffraction peaks in the WAXS data obtained from fits to a Gaussian and a Lorentzian, respectively. The green line is an exponential fit to guide the eye. c Variation of the width of the first (γ₃, red) and second (γ₅, blue) sharp diffraction peaks.

Fig. 4. Results of the temperature-dependent molecular dynamics simulations of TBOS.

a Power spectra obtained from the Fourier transform of the Si–Si velocity–velocity autocorrelation functions. b Static structure factor, including Si, O and C atoms. c Si–Si pair correlation functions. d running Si–Si coordination number.

Fig. 5. Temperature-dependent Voronoi analysis of TBOS models.

a Probability density function of the number of faces characterising the Voronoi polyhedra (VP) for each Si atom, averaged over 1000 frames across a 10 ns long MD trajectory. b Probability density function of the volume of the VP. c Frequency of the occurrence of selected VP as a function of temperature. See Supplementary Table 4 for information about the indices of each VP. The green dotted line indicated the value of (computationally obtained) T_g. d Power spectra obtained from the Fourier transform of the Si–Si velocity–velocity autocorrelation functions at 90 K. The purple and light blue lines refer to the result obtained considering all the Si atoms (same as Fig. 4a) and those Si atoms characterised by VP with 16 faces only, respectively.

Fig. 6. Histograms of various physicochemical properties of conformers of TBOS calculated using DFT.

Shown are the distributions of the relative energy of each conformer, their permanent dipole moment, and (an)isotropic polarizabilities estimated using 100 TBOS conformers.

Fig. 7. SiO skeletons for different energy minima.

The SiO skeletons for the four lowest energy minima on the Si3(OMe)12 potential energy surface based on DFT calculations.