Phonon Modes and Heat Capacity of Monolayer Films Adsorbed in Spherical Pores

TL;DR

This paper investigates the phonon spectrum and heat capacity of a monolayer film adsorbed in spherical pores, revealing discrete phonon modes and temperature-dependent heat capacity behaviors.

Contribution

It provides a novel analysis of phonon modes and heat capacity for monolayer films on spherical surfaces, extending previous cylindrical surface studies.

Findings

Discrete phonon spectrum due to boundary conditions

Arrhenius low-temperature heat capacity behavior

High-temperature heat capacity scales as T^2

Abstract

We examine the hydrodynamic phonon spectrum of a monolayer film adsorbed on the wall of a spherical pore. Due to the boundary conditions, the monolayer film exhibits a discrete phonon spectrum. The corresponding density of states per unit frequency is thus a set of delta functions and the heat capacity exhibits Arrhenius behavior at low temperatures. At high temperatures, the heat capacity approaches the C ~ T^2 behavior of a two-dimensional monolayer film. Our results for the spherical surface film are compared to previous calculations for films confined to a cylindrical surface.