Pressure and density dependence of the boson peak in polymers

The nature of the low-frequency vibrations, the so-called boson peak, in spectra of glass-forming systems remains a subject of active discussions. It appears that densification of glasses leads to significant change of the boson peak vibrations and opens additional possibility to verify different model predictions. We present light (Raman and Brillouin) scattering studies of the influence of pressure (up to 1.5 GPa) on the boson peak vibrations and elastic properties of five different polymers. We demonstrate that the pressure-induced shift of the boson peak frequency in all cases is significantly stronger than change of sound velocities. This result clearly shows the failure of the homogeneous elastic continuum approximation. The boson peak amplitude decreases strongly with pressure. However, the major part of these variations (but not all) can be related to the change of the Debye level. We emphasize a correlation between pressure-induced variations of the boson peak frequency and intensity. Surprisingly, the spectral shape of the boson peak remains the same at all pressures indicating that the frequency distribution of the vibrational modes remains essentially unaltered even when the boson peak frequency doubles. The results are compared to predictions of different models and results of recent computer simulations.

Figure 1

Depolarized light scattering intensity measured on PBD at $T=140\text{K}$ and $P=0.57\text{GPa}$. The spectrum shows transverse Brillouin mode (TM), longitudinal Brillouin mode (LM, leak of intensity due to nonperfect polarization scheme), the boson peak (BP), and the microscopic peak (MP).

Figure 2

(Color online) Brillouin scattering spectra of PIP at 140 K at different pressures: (a) Transverse modes; (b) Longitudinal modes. Symbols—experimental data and lines are the fits by a Lorentzian function.

Figure 3

(Color online) Depolarized light scattering spectra of PIP presented as a spectral density at $T=140\text{K}$ and three different pressures indicated in the plot: Symbols are experimental data and lines are fits with Eq. (3).

Figure 4

(Color online) Microscopic peak in PIP (spectra presented as the susceptibility for more clear observation of the peak): Symbols are experimental data and lines are the fits by a Lorentzian function.

Figure 5

(Color online) Pressure variations of relative density at 140 K calculated for all the studied polymers using Brillouin scattering data; ${\rho }_0$ is the density at ambient pressure.

Figure 6

(Color online) Pressure induced variations of vibrational frequencies at $T=140\text{K}$ in PBD (a), PMPS (b), PS (c), PIP (d), and PIB (e). All the frequencies are normalized to their values at initial pressure (see Table ). The symbols present: (▲)-boson peak; (▼)-microscopic peak; (◼)-longitudinal modes, and (●)-transverse modes.

Figure 7

(Color online) Pressure dependence of the boson peak frequency in PIP compared to the prediction of the soft potential model. Symbols are experimental data and lines are the fit: (a) The fit assumes $P_0$ is independent of pressure [Eq. (12)]; (b) The fit takes into account variations of the bulk modulus $K$ [Eq. (14)]. Here $K_0$ is the bulk modulus at ambient pressure. Similar results have been obtained for all other polymers.

Figure 8

(Color online) Pressure dependence of the ratio between frequency of the transverse Brillouin mode and the frequency of the boson peak at $T=140\text{K}$: (a) PBD; (b) PMPS; (c) PS; (d) PIP; and (e) PIB. Symbols are experimental data and lines present the fits to a power law [Eq. (16)] with the ambient pressure point excluded from the fit; $x$ is the value of the exponent obtained from the fit.

Figure 9

The exponent $x$ vs fragility $m$ of the studied polymers. Fragility data are from Refs. 23, 41.

Figure 10

(Color online) (a) Changes of the boson peak intensity under pressure in all studied polymers at $T=140\text{K}$; (b) The same changes of the boson peak intensity scaled by the expected variations of the Debye level [Eq. (17)].

Figure 11

Relationship between variations of the boson peak intensity and the inverse boson peak frequency at $T=140\text{K}$: (a) PBD; (b) PMPS; (c) PS; (d) PIP; and (e) PIB.

Figure 12

(Color online) The spectra of the boson peak at different pressures scaled at the boson peak maximum: (a) PBD; (b) PMPS; (c) PS; (d) PIP; and (e) PIB.