Low-Frequency Vibrational Density of States of Nanophase-Separated Poly(n‑alkyl methacrylate)s: Confined Phonons and Relationship to Specific Heat.

This study investigates the low-frequency vibrational density of states of nanophase-separated poly-(n-alkyl methacrylate)-s (PnMAs) and its relationship to specific heat. This system undergoes a nanophase separation for n > 1 in alkyl side chain-rich domains and a backbone-rich matrix. Using inelastic neutron scattering, the low-frequency vibrational density of states (Boson peak, BP) of PnMAs with varying alkyl side chain lengths (methyl, butyl, hexyl, and octyl) is measured. The results reveal that the BP shifts to higher frequencies with increasing side chain length reaching a maximum. This result indicates a counterbalance of confinement effects and the scattering of the matrix. The behavior of the Boson peak of the PnMAs is compared to other nanophase-separated systems, such as Janus-polynorbornenes and hexakis-(n-alkyloxy)-triphenylene discotic liquid crystals. The study also explores the connection between the BP and specific heat capacity, showing a linear relationship between the maximum frequency of the BP and the maximum temperature of the specific heat capacity anomaly. Moreover, from the measured vibrational density of states, the specific heat capacity is calculated and compared to experimental results. The comparison reveals qualitative agreement between the calculated and experimental data. These findings provide evidence for the sound wave interpretation of the Boson peak.