High Pressure Light Scattering Study of Relaxation in the Glass Former Cumene*

To understand relaxation dynamics in glassy systems, a light scattering study on Cumene has been carried out in a diamond anvil cell (DAC) at pressures from 0.2 GPa to 2.5 GPa isothermally at 75 $^{\circ}$C. Polarized and depolarized spectra were taken in both near-backscattering and equal-angle 60$^{\circ}$ forward-scattering geometries at several free spectral ranges from 0.5 GHz to 300 GHz. Depolarized backscattering spectra are converted into susceptibility featuring the evolution of the $\alpha $-relaxation peak, yielding structural relaxation times $\tau _{\alpha}$ from 10 ps to 1 ns. We have also developed photon correlation spectroscopy (PCS) in a DAC, giving $\tau_{\alpha}$ from $\sim$ 1 $\mu$s to 1 s. We fit $\tau_{\alpha}$ over these many decades with a modified VFTH equation $\tau _{\alpha} = \tau_{0}$exp[DP/(P$_{0}$-P)] giving parameters $\tau _{0}=$ 9.2 ps, D$=$ 17.5, and P$_{\mathrm{0}}=$ 4.5 GPa at 75$^{\circ}$C. After the $\alpha $-relaxation peak moves into lower frequencies (P $\sim$ 1 GPa), we observe the emergence of the $\beta $-relaxation minimum region. We fit the $\beta $-minimum to a power law scaling form $\chi $''($\omega )=$b($\omega $/$\omega _{\mathrm{min}}$)$^a$ $+$ a($\omega_{\mathrm{min}}$/$\omega$)$^b$. Polarized backscattering and forward scattering gives frequency shift $\omega_{\mathrm{B}}$ and linewidth $\Gamma _{\mathrm{B}}$ values of the longitudinal acoustic modes at two different q. We observe that the usual peak in linewidths does not coincide with $\omega_{\mathrm{B}}\tau_{alpha} \approx $ 1, indicating that the longitudinal acoustic modes do not couple with structural relaxation. Tansverse acoustic modes also appear in the depolarized forward scattering spectra.