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\chapter{PEDOT:PSS}
\section{Introduction}
Poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) (PEDOT:PSS) is a transparent, electrically
conductive (up to 4380 S cm$^{-1}$ \cite{KimNara2013a}) polymer. %
It has found widespread use as a flexible, cheap alternative to inorganic transparent electrodes
such as indium tin oxide. %
As a polymer, PEDOT:PSS implicitly contains a large amount of structural inhomogeneity. %
On top of this, PEDOT:PSS is a two component material, composed of PEDOT (low molecular weight,
p-doped, highly conductive) and PSS (high molecular-weight, insulating, stabilizing). %
These two components segment into domains of conductive and non-conductive material, leading to
even more structural inhomogeneity. %
Nonlinear spectroscopy may be able to shed light on the microscopic environment of electronic
states within PEDOT:PSS. %
\section{Background}
Complex microstructure:
\begin{enumerate}
\item PEDOT oligomers (6---18-mers)
\item these oligomers $\pi$-stack to form small nanocrystalites, 3 to 14 oligomers for pristine
films to as many as 13---14 oligomers for more conductive solvent treated films
\item nanocrystallites then arrange into globular conductive particles in a pancakge-like shape
\item these particles themselves are then linked via PSS-rich domains and assembled into
nanofibril geometry akin to a string of pearls
\item nanofibrils interweave to form thin films, with PSS capping layer at surface
\end{enumerate}
Prior spectroscopy (absorption anisotropy, X-ray scattering, condutivity). %
% TODO: absorption spectrum of thin film
Broad in the infrared due to midgap states created during doping from charge-induced lattice
relaxations. %
These electronic perturbations arise from injected holes producing a quinoidal distortion spread
over 4-5 monomers of the CP aromatic backbone, collectively called a polaron. %
Energetically favorable to be spin-silent bipolaron. %
\section{Methods}
PEDOT:PSS (Orgacon Dry, Sigma Aldrich) was dropcast onto a glass microscope slide at 1 mg/mL at a
tilt to ensure homogeneous film formation. %
The sample was heated at 100 $^\circ$C for $\sim$15 min to evaporate water. %
An ultrafast oscillator (Spectra-Physics Tsunami) was used to prepare $\sim$35 fs seed pulses. %
These were amplified (Spectra-Physics Spitfire Pro XP, 1 kHz), split, and converted into 1300 nm 40
fs pulses using two separate optical parametric amplifiers (Light Conversion TOPAS-C): ``OPA1'' and
``OPA2''. %
Pulses from OPA2 were split again, for a total of three excitation pulses: $\omega_1$, $\omega_2$
and $\omega_{2^\prime}$. %
These were passed through motorized (Newport MFA-CC) retroreflectors to control their relative
arrival time (``delay'') at the sample: $\tau_{21} = \tau_2 - \tau_1$ and $\tau_{22^\prime} =
\tau_2 - \tau_{2^\prime}$. The three excitation pulses were focused into the sample in a $1^\circ$
right-angle isoceles triange, as in the BOXCARS configuration. \cite{EckbrethAlanC1978a} %
Each excitation beam was 67 nJ focused into a 375 $\mathsf{\mu m}$ symmetric Gaussian mode for an
intensity of 67 $\mathsf{\mu J / cm^2}$. %
A new beam, emitted coherently from the sample, was isolated with apertures and passed into a
monochromator (HORIBA Jobin Yvon MicroHR, 140 mm focal length) with a visible grating (500 nm blaze
300 groves per mm). %
The monochromator was set to pass all colors (0 nm, 250 $\mathsf{\mu m}$ slits) to keep the
measurement impulsive. %
Signal was detected using an InSb photodiode (Teledyne Judson J10D-M204-R01M-3C-SP28). %
Four wave mixing was isolated from excitation scatter using dual chopping and digital signal
processing. %
\section{Transmittance and reflectance}
\afterpage{
\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{"PEDOT:PSS/linear"}
\caption[PEDOT:PSS transmission and reflectance spectra.]{
Thin film spectra.
Transmission, reflectance, and extinction spectrum of the thin film used in this work. %
Extinction is $\log_{10}{\mathsf{(transmission)}}$. %
}
\label{fig:PEDOTPSS_linear}
\end{figure}
\clearpage}
\autoref{fig:PEDOTPSS_linear} shows the transmission, reflectance, and extinction spectrum of the
thin film used in this work. %
\section{Three-pulse echo spectroscopy}
\afterpage{
\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{"PEDOT:PSS/mask"}
\caption[PEDOT:PSS 3PE phase matching mask.]{
Phase matching mask used in this experiment.
Each successive ring subtends 1 degree, such that the excitation pulses are each angled one
degree relative to the mask center.
The two stars mark the two output poyntings detected in this work.
}
\label{fig:PEDOTPSS_mask}
\end{figure}
\clearpage}
Two dimensional $\tau_{21}, \tau_{22^\prime}$ scans were taken for two phase matching
configurations: (1) $k_{\mathsf{out}} = k_1 - k_2 + k_{2^\prime}$ (3PE) and (2) $k_{\mathsf{out}} =
k_1 + k_2 - k_{2^\prime}$ (3PE*). %
The rephasing and nonrephasing pathways exchange their time dependance between these two
configurations. %
Comparing both pathways, rephasing-induced peak shifts can be extracted as in 3PE. [CITE] %
All data was modeled using numerical integration of the Liouville-von Numann equation. %
Continuously variable ND filters (THORLABS NDC-100C-4M, THORLABS NDL-10C-4) were used to ensure
that all three excitation pulse powers were equal within measurement error. %
\afterpage{
\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{"PEDOT:PSS/raw"}
\caption[PEDOT:PSS 3PE raw data.]{
CAPTION TODO
}
\label{fig:PEDOTPSS_raw}
\end{figure}
\clearpage}
\afterpage{
\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{"PEDOT:PSS/processed"}
\caption[PEDOT:PSS 3PE processed data.]{
CAPTION TODO
}
\label{fig:PEDOTPSS_processed}
\end{figure}
\clearpage}
\afterpage{
\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{"PEDOT:PSS/delay_space"}
\caption[PEDOT:PSS 3PE delay space.]{
CAPTION TODO
}
\label{fig:PEDOTPSS_delay_space}
\end{figure}
\clearpage}
\afterpage{
\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{"PEDOT:PSS/traces"}
\caption[PEDOT:PSS 3PE traces.]{
CAPTION TODO
}
\label{fig:PEDOTPSS_traces}
\end{figure}
\clearpage}
\afterpage{
\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{"PEDOT:PSS/overtraces"}
\caption[PEDOT:PSS 3PE traces.]{
CAPTION TODO
}
\label{fig:PEDOTPSS_overtraces}
\end{figure}
\clearpage}
\section{Frequency-domain transient grating spectroscopy}
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