# Microscopyc description of the Photothermal increase of temperature for metallic nanoparticles excited with short-laser pulses

## TL;DR

This paper introduces a formalism based on Jarzynski's statistics to describe the photothermal temperature increase in metallic nanoparticles, especially gold, under short laser pulses, considering size and wavelength effects.

## Contribution

It develops a novel theoretical approach to quantify nanoscale photothermal effects using non-equilibrium thermodynamics formalism.

## Key findings

- Temperature change depends on nanoparticle size and wavelength for particles under 40 nm.
- For particles near 40 nm, the new formalism aligns with traditional macroscopic predictions.
- Size and wavelength significantly influence photothermal responses in gold nanoparticles.

## Abstract

The pulsed photothermal phenomenon due to optically absorbed energy, result from non-radiative decay mechanisms, which in nature, these imply the temporal change in the local free energy and thus a temporary change in the local temperature. At the nanoscale, this is a prediction broadly described in terms of macroscopic variables. Here we introduce a formalism based on the Jarzynski's physical statistics description, for interpreting the equilibrium free energy difference between two configurations of a metallic nanoparticle. In this way, within a finite-time span, we describe the temporal increase of the local free energy and thus of the local temperature arising from temporarily bringing the sample far from thermal equilibrium. The result is an expression for which one can get the photothermally induced change of temperature for a metallic nanoparticle. For practical purposes, we limited the study to Au nanoparticles. The study is made as function of the particle size and the optical properties for wavelengths spanning the optical range. The assessment indicates that, for nanoparticles with radii shorter than 40 nm, the temperature change is strongly dependent on particle size and on the illumination wavelength. While, for near 40 nm particle radii, the current description and the known formalism, based on macroscopic variables, predict the very same temperature change. At the closing we discuss additional possible thermodynamic consequences associated to the scale considerations.