Modelling the Frequency Dependency of the Photothermal Signal From Single Aerosol Particles at Low Relative Humidity
FELIX STOLLBERGER, Alexander Bergmann, Graz University of Technology
Abstract Number: 133
Working Group: Aerosol Physics
Abstract
Photoacoustic spectroscopy (PAS) and photothermal interferometry (PTI) are two closely related experimental techniques used to probe the optical and physicochemical properties of aerosol particles. Along with numerous experimental studies, the modeling of PAS has evolved significantly from energy-balance models over complex, fully analytical approaches solving the Naiver-Stokes equations to recent multilayer heat and mass-transfer models. In general, the simulations show that the excitation frequency dependency of the photoacoustic signal contains information about evaporation-condensation and thermal equilibrium effects. However, this dependency has not been further investigated, as it is not experimentally accessible with PAS.
PTI allows to investigate this effect for the first time experimentally on single particles. However, theoretical models capable of simulating the measured size and frequency-resolved photothermal signal are currently unavailable. Therefore, we present a novel semi-analytical model combining the advances in photoacoustic modeling with the detection mechanism used in PTI.
In our model, we use the existing framework of PAS to compute the temperature of a single, isolated particle exposed to a sinusoidally modulated excitation laser in a dry environment. The heat flux from the droplet is used as a boundary condition to solve the heat equation for radially-symmetric outgoing thermal waves. Evaluating the amplitude and phase of the thermal wave in terms of a refractive index shift allows to determine a local optical path-length difference (δOPL), affecting the phase of the interferometer beam. Integrating δOPL over the intensity-weighted volume of the probe beam yields the experimentally accessible photothermal amplitude (PTA) and phase (PTP).
We validated our model with experimental data, indicating a good agreement of the PTA and PTP for frequencies lower than 6kHz in the investigated size range of 1.5–4.5µm. A systematic, radius-dependent phase shift was observed for frequencies higher than 10kHz, which could be linked to the so far excluded mass flux from the particle.
Overall, we successfully proved the validity of our model for, highlighting its future applicability to retrieving optical or thermodynamic properties of single aerosol particles by fitting experimental data with the presented theoretical model.