\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}