Analytical study coupling partial differential equations using Green's function method with numerical validation: photo thermal response of a multilayer structure

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2023

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Abstract

In this thesis, an analytical study is determined through a multiphysics problem to solve for the photothermal response of a one-dimensional multilayer nanostructure containing a layer doped with Smart Nanoshells (SNS) by coupling the electromagnetic and thermodynamic equations. The SNS consists of a gold (Au) shell and a core of the phase change material (PCM) vanadium dioxide (VO2), where the core transitions from a semiconductor state to a conductor state at the critical temperature of 68˚C. This behaviour results in thermal induced optical tunability through this reversible phase change of the VO2, due to the temperature dependent optical and thermal properties. This layer that is doped with SNS is approximated as an effective medium using Maxwell-Garnett Theory to allow for an analytical solution. In this work, the optical response of the multilayer nanostructure is determined through the Transfer Matrix Method (TMM) and the thermal response of the stationary and transient states is solved with Green’s Function Method and Kirchhoff’s Transformation. These equations are coupled together by the continuous wave (CW) laser that is introduced to the multilayer structure, as this is also the heat source. The solutions found through this analytical study will show that at the wavelengths of 658 nm and 737 nm, there will be two distinct photothermal responses due to the phase change of the SNS core, where the absorption of light will increase and decrease for these two wavelengths respectively. Not only does this analytical method have many potential applications such as for solar cells and photothermal therapy, but this method provides a comprehensive study of the photothermal response of these applications.

Description

This thesis was completed and submitted at Nipissing University, and is made freely accessible through the University of Toronto’s TSpace repository

Keywords

Differential equations, Mathematical physics, Green's functions, Solar cells Research, Phototherapy Research

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