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

## TL;DR

This paper studies how the structure of certain polymers affects their low-frequency vibrations and specific heat, finding a link between these properties.

## Contribution

The study reveals a linear relationship between the Boson peak frequency and specific heat anomaly temperature in nanophase-separated polymers.

## Key findings

- The Boson peak shifts to higher frequencies with increasing alkyl side chain length in PnMAs.
- A linear relationship is found between the Boson peak frequency and the specific heat capacity anomaly temperature.
- Calculated specific heat capacity from vibrational density of states agrees qualitatively with experimental results.

## Abstract

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.