Vibrations of a one-dimensional host-guest system

TL;DR

This paper introduces a one-dimensional host-guest model with cages containing particles, demonstrating how internal resonance can create a vibrational frequency gap in the lattice spectrum.

Contribution

It presents a novel simple model of a host-guest chain that shows how internal resonance within cages can induce a vibrational gap in a one-dimensional lattice.

Findings

A vibrational gap appears due to internal resonance within cages.

The model demonstrates how host-guest interactions influence vibrational spectra.

The gap size correlates with the internal resonance frequency.

Abstract

A simple model shows how it is possible to create a gap in the vibrational spectrum of a one-dimensional lattice. The proposed model is a host-guest chain having, instead of point-like masses connected by spring, massive cages hosting particles inside. We imagine the cage as a rigid box containing a mass linked by a spring to the box inner wall. The presence of guests creates an energy gap in the dispersion of vibrational frequencies. The gap is about the internal resonance of the mass hidden in the cage.