# Bounds on quantum confinement effects in metal nanoparticles

## TL;DR

This paper derives explicit bounds on the permittivity and relaxation rates of metal nanoparticles due to quantum confinement, revealing limitations of empirical dielectric modifications for uniform particle distributions.

## Contribution

It introduces a quantum box model to establish bounds on nanoparticle permittivity and relaxation rates, improving understanding of size and frequency effects.

## Key findings

- Explicit bounds for permittivity and relaxation rates derived
- Quantum confinement significantly impacts dielectric properties
- Empirical modifications may be inaccurate for uniform particles

## Abstract

Quantum size effects on the permittivity of metal nanoparticles are investigated using the quantum box model. Explicit upper and lower bounds are derived for the permittivity and relaxation rates due to quantum confinement effects. These bounds are verified numerically, and the size-dependence and frequency-dependence of the empirical Drude size parameter is extracted from the model. Results suggest that the common practice of empirically modifying the dielectric function can lead to inaccurate predictions for highly uniform distributions of finite-sized particles.