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authorBlaise Thompson <blaise@untzag.com>2018-04-15 14:12:07 -0500
committerBlaise Thompson <blaise@untzag.com>2018-04-15 14:12:07 -0500
commitc15660a15d2ac72ad8b385ac9d54fbc0e257af65 (patch)
treec02dd6355b443b9217adfe5c7f846f66a499c3ea /PEDOT_PSS
parentb75d9d8f2ba798fbbadc975a789cf2615b743328 (diff)
2018-04-15 14:12
Diffstat (limited to 'PEDOT_PSS')
-rw-r--r--PEDOT_PSS/chapter.tex295
1 files changed, 169 insertions, 126 deletions
diff --git a/PEDOT_PSS/chapter.tex b/PEDOT_PSS/chapter.tex
index 10a7472..29b411c 100644
--- a/PEDOT_PSS/chapter.tex
+++ b/PEDOT_PSS/chapter.tex
@@ -1,4 +1,5 @@
-\chapter{PEDOT:PSS} \label{cha:pps}
+\chapter{Measurement of ultrafast dynamics within PEDOT:PSS using three-pulse photon echo
+ spectroscopy} \label{cha:pps}
\textit{This Chapter presents content first published in \textcite{HorakErikH2018a}.
The authors are:
@@ -32,32 +33,32 @@ As a polymer, PEDOT:PSS implicitly contains a large amount of structural inhomog
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)
+even more structural inhomogeneity.
+In summary, PEDOT:PSS has a complex, nested microstructure. %
+From smallest to largest:
+\begin{ditemize}
+ \item PEDOT oligomers (6---18-mers) [CITE 14]
\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
+ films to as many as 13---14 oligomers for more conductive solvent treated films [CITE 15]
+ \item nanocrystallites then arrange into globular conductive particles in a pancake-like shape
+ [CITE 16, 17]
\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. %
+ nanofibril geometry akin to a string of pearls [CITE 6, 21]
+ \item nanofibrils interweave to form thin films, with PSS capping layer at surface [CITE 19, 22]
+\end{ditemize}
+
+In order to be conductive, PEDOT:PSS needs to have good spatial and energetic overlap between
+electronic states throughout the thin film. %
+The exact energetics and dynamics of these electronic states, then, is a crucial piece of
+information needed to understand the mechanism of conductivity in PEDOT:PSS. %
+The electronic states responsible for conductivity have very broad and featureless transitions in
+the mid infrared. %
+Bulk, linear spectroscopy cannot tease out the relative contribution of homogeneous and
+inhomogeneous broadening in the breadth of these transitions. %
+Multidimensional spectroscopy is able to tease these two broadening mechanisms apart. %
+
+In this chapter, I report on my usage of three pulse echo (3PE) spectroscopy to constrain
+homogeneous and inhomgeneous linewidths in PEDOT:PSS. %
\section{Methods} % ==============================================================================
@@ -86,62 +87,74 @@ Signal was detected using an InSb photodiode (Teledyne Judson J10D-M204-R01M-3C-
Four wave mixing was isolated from excitation scatter using dual chopping and digital signal
processing. %
-\section{Transmittance and reflectance} % ========================================================
-
-\autoref{fig:PEDOTPSS_linear} shows the transmission, reflectance, and extinction spectrum of the
-thin film used in this work. %
-
-\clearpage
-\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
-
-\section{Three-pulse echo spectroscopy} % ========================================================
-
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*). %
+\autoref{pps:fig:mask} diagrams the phase matching mask used in this set of experiments. %
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] %
+Comparing both pathways, rephasing-induced peak shifts can be extracted as in 3PE.
+\cite{WeinerAM1985a} %
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. %
-\autoref{fig:PEDOTPSS_mask} diagrams the phase matching mask used in this set of experiments. %
-
\begin{figure}
\includegraphics[width=0.5\linewidth]{"PEDOT_PSS/mask"}
- \caption[PEDOT:PSS 3PE phase matching mask.]{
+ \caption[Phase matching mask for 3PE, 3PE*.]{
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}
+ \label{pps:fig:mask}
\end{figure}
-\autoref{fig:PEDOTPSS_raw} shows the ten raw 2D delay-delay scans that comprise the primary dataset
+\section{Results} % ==============================================================================
+
+\autoref{pps:fig:linear} shows the transmission, reflectance, and extinction spectrum of the
+thin film used in this work. %
+The region under investigation is shaded green. %
+Reflectance is remarkably low across the visible and near infrared, and transmission does not
+change much at all over the region under investigation. %
+
+\autoref{pps:fig:raw} shows the ten raw 2D delay-delay scans that comprise the primary dataset
described in this section. %
The rows correspond to the two phase matching conditions, as labeled. %
+The data is presented on the intensity level, as raw as possible. %
+The five repetitions of each experiment are truly remarkably similar, showing that no damage was
+being done during the experiment. %
+Each row is normalized to the same factor, showing the remarkable \emph{quantitative} agreement
+between scans. %
+In total, these 10 scans comprise roughly eight hours of continuous illumination for this
+sample. %
+
+\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{pps:fig:linear}
+\end{figure}
\begin{figure}
\includegraphics[width=\linewidth]{"PEDOT_PSS/raw"}
- \caption[PEDOT:PSS 3PE raw data.]{
- CAPTION TODO
+ \caption[Raw 3PE data.]{
+ Raw ultrafast data.
+ Unprocessed two-dimensional delay-delay plots.
+ Each discrete acquisition is plotted as a single colored pixel.
+ Grey pixels correspond to negative results, which appear in the no-signal regions due to random
+ noise.
}
- \label{fig:PEDOTPSS_raw}
+ \label{pps:fig:raw}
\end{figure}
+\section{Discussion} % ===========================================================================
+
\subsection{Assignment of zero delay} % ----------------------------------------------------------
The absolute position of complete temporal overlap of the excitation pulses (zero delay) is a
@@ -149,81 +162,88 @@ crucial step in determining the magnitude of th epeak shift and therefore the to
ability of the material. %
The strategy for assigning zero delay relies upon the intrinsic symmetry of the two-dimensional
delay space. %
-\autoref{fig:PEDOTPSS_delay_space} labels the six time-orderings (TOs) of the three pulses that are
+\autoref{pps:fig:delay_space} labels the six time-orderings (TOs) of the three pulses that are
possible with two delays. %
The TO labeling scheme follow from a convention first defined my Meyer, Wright and Thompson.
-[CITE] %
-[CITE] first discussed how these TOs relate to traditional 3PE experiments. %
+\cite{MeyerKentA2004a} %
+\textcite{KohlerDanielDavid2014a} first discussed how these TOs relate to traditional 3PE
+experiments. %
Briefly, spectral peak shifts into the rephasing TOs \RomanNumeral{3} and \RomanNumeral{5} when
inhomogeneous broadening creates a photon echo in the \RomanNumeral{3} and \RomanNumeral{5}
-rephasing pathways colored orange in \autoref{fig:PEDOTPSS_delay_space}. %
+rephasing pathways colored orange in \autoref{pps:fig:delay_space}. %
For both phase-matching conditions, there are two separate 3PE peak shift traces (represented as
-black arrows in \autoref{fig:PEDOTPSS_delay_space}), yielding four different measurements of the
+black arrows in \autoref{pps:fig:delay_space}), yielding four different measurements of the
photon echo. %
Since both 3PE and 3PE* were measured using the same alignment on the same day, the zero delay
position is identical for the four photon echo measurements. %
We focus on this signature when assigning zero delay---zero is correct only when all four peak
shifts agree. %
Conceptually, this is the two-dimensional analogue to the traditional strategy of placing zero such
-that the two conjugate peak shifts (3PE and 3PE*) agree. [CITE] %
+that the two conjugate peak shifts (3PE and 3PE*) agree. \cite{WeinerAM1985a} %
-We found that the 3PEPS traces agree best when the data in \autoref{fig:PEDOTPSS_raw} is offset by
+We found that the 3PEPS traces agree best when the data in \autoref{pps:fig:raw} is offset by
19 fs in $\tau_{22^\prime}$ and 4 fs in $\tau_{21}$. %
-\autoref{fig:PEDOTPSS_processed} shows the 3PEPS traces after correcting for the zero delay
+\autoref{pps:fig:processed} shows the 3PEPS traces after correcting for the zero delay
value. %
-The entire 3PEPS trace ($\tau$ vs $T$) is show for regions \RomanNumeral{1}, \RomanNumeral{3}
+The entire 3PEPS trace ($\tau$ vs $T$) is shown for regions \RomanNumeral{1}, \RomanNumeral{3}
(purple and light green traces) and \RomanNumeral{5}, \RomanNumeral{6} (yellow and light blue
-traces) for the [PHASE MATCHING EQUATIONS] phase matching conditions, respectively. %
+traces) for the $\vec{k_1} - \vec{k_2} + \vec{k_{2^\prime}}$ and $\vec{k_1} + \vec{k_2} -
+\vec{k_{2^\prime}}$ phase matching conditions, respectively. %
Peak-shift magnitudes were found with Gaussian figs on the intensity level, in accordance with
-3PEPS convention. [CITE]
-The bottom subplot of \autoref{fig:PEDOTPSS_overtraces} shows the agreement between the four traces
+3PEPS convention. \cite{WeinerAM1985a} %
+The bottom subplot of \autoref{pps:fig:overtraces} shows the agreement between the four traces
for $T > 50$ fs where pulse-overlap effects become negligible. %
These pulse-overlap effects cause the 3PEPS at small $T$ even without inhomogeneous broadening.
-[CITE] %
+\cite{WeinerAM1985a} %
At long $T$, the average static 3PEPS is 2.5 fs. %
+There is a deviation of the TO \RomanNumeral{1}-\RomanNumeral{3} 3PEPS* trace (green line) from the
+other traces. %
+It is attributed to a combination of excitation pulse distortions and line shape differences
+between OPA1 and OPA2 (see \autoref{pps:fig:linear}) and small errors in the zero delay
+correction. %
+\autoref{pps:fig:traces} shows what the four 3PEPS traces would llike like for different
+choices of zero-delay. %
+The inset numbers in each subplot denote the offset (from chosen zero) in each delay axis. %
+
\begin{figure}
\includegraphics[width=\linewidth]{"PEDOT_PSS/delay space"}
- \caption[PEDOT:PSS 3PE delay space.]{
- CAPTION TODO
+ \caption[3PE, 3PE* delay space.]{
+ Representation of 2D delay space.
+ Representation of symmetry between the two phase-matched experiments performed in this work.
+ In each two-dimensional delay space, the six TOs are labeled.
+ Pathways III and V are rephasing (orange), all other pathways are non-rephasing (blue).
+ Thick black arrows are drawn along the $\tau$ trace for constant T = 125 fs, with arrowheads
+ pointing in the direction of shift for positively correlated systems.
+ The region with signal above 10\% (processed dataset, amplitude level) is shaded to guide the
+ eye.
}
- \label{fig:PEDOTPSS_delay_space}
+ \label{pps:fig:delay_space}
\end{figure}
\begin{figure}
- \includegraphics[width=\linewidth]{"PEDOT_PSS/processed"}
- \caption[PEDOT:PSS 3PE processed data.]{
- CAPTION TODO
+ \includegraphics[width=\linewidth]{"PEDOT_PSS/traces"}
+ \caption[Delay offsets.]{
+ Delay offsets.
+ Comparison between 3PEPS traces at different delay offsets.
+ Inset is D1, D2 offset in fs.
}
- \label{fig:PEDOTPSS_processed}
+ \label{pps:fig:traces}
\end{figure}
\begin{figure}
\includegraphics[width=\linewidth]{"PEDOT_PSS/overtraces"}
- \caption[PEDOT:PSS 3PE traces.]{
- CAPTION TODO
+ \caption[Peak shift traces drawn in delay space.]{
+ 3PEPS traces.
+ Fully processed 2D delay scans (upper) and 3PEPS traces for both rephasing pathways and both
+ phase matching conditions.
+ The 3PEPS traces are shown mapped onto the 2D space (upper) and overlaid for comparison
+ (lower).
}
- \label{fig:PEDOTPSS_overtraces}
+ \label{pps:fig:overtraces}
\end{figure}
-\begin{figure}
- \includegraphics[width=\linewidth]{"PEDOT_PSS/traces"}
- \caption[PEDOT:PSS 3PE traces.]{
- CAPTION TODO
- }
- \label{fig:PEDOTPSS_traces}
-\end{figure}
-
-There is a deviation of the TO \RomanNumeral{1}-\RomanNumeral{3} 3PEPS* trace (green line) from the
-other traces. %
-It is attributed to a combination of excitation pulse distortions and line shape differences
-between OPA1 and OPA2 (see \autoref{fig:PEDOTPSS_linear}) and small errors in the zero delay
-correction. %
-\autoref{fig:PEDOTPSS_traces} shows what the four 3PEPS traces would llike like for different
-choices of zero-delay. %
-The inset numbers in each subplot denote the offset (from chosen zero) in each delay axis. %
-
-\subsubsection{Numerical model} % ----------------------------------------------------------------
+\subsection{Numerical model} % -------------------------------------------------------------------
We simulated the 3PEPS response of PEDOT:PSS through numerical integration of the Liouville-von
Neumann Equation. %
@@ -238,7 +258,7 @@ rates, respectively. %
A three-level system was used because a two-level system cannot explain the population relaxation
observed at long populations times, $T$. %
This slow delcay may be the same as the slowly decaying optical nonlinearities in PEDOT:PSS.
-[CITE] %
+\cite{MeskersStefanCJ2003a} %
Inhomogeneity was incorporated by convolving the homogeneous repsonse with a Gaussian distribution
function of width $\Delta_{\mathsf{inhom}}$ and allowing the resultant polarization to interfere on
the amplitude level. %
@@ -259,64 +279,87 @@ Taken together, it is clear that both pure dephasing and ensemble dephasing infl
shift so it is important to find valuse of $T_2^*$ and $\Delta_{\mathsf{inhom}}$ that uniquely
constrain the measured response. %
-\begin{figure}
- \includegraphics[width=\linewidth]{"PEDOT_PSS/parametric"}
- \caption[PEDOT:PSS 3PE traces.]{
- CAPTION TODO
- }
- \label{fig:PEDOTPSS_parametric}
-\end{figure}
-
We simulated the $\tau$ trance for a variety of $\Delta_{\mathsf{inhom}}$ and $T_2$ values. %
-The results for $\Delta_t = 40$ fs are summarized in \autoref{fig:PEDOTPSS_parametric}. %
+The results for $\Delta_t = 40$ fs are summarized in \autoref{pps:fig:parametric}. %
The lines of constant $T_2$ span from $\Delta_{\mathsf{inhom}} = 0$ (green left ends of curves) to
the limit $\Delta_{\mathsf{inhom}} \rightarrow \infty$ (blue right ends of curves). %
The lines of constant $T_2$ demonstrate that ensemble dephasing reduces the transient duration and
introduces a peak shift. %
The influence of inhomogeneity on the observables vanishes as $T_2 \rightarrow \infty$. %
-We preformed simulations analogus to those in \autoref{fig:PEDOTPSS_parametric} for pulse durations
+We preformed simulations analogus to those in \autoref{pps:fig:parametric} for pulse durations
longer and smaller than $\Delta_t = 40$ fs. %
Longer pulse durations create solutions that do not intersect our experimental point (see
-right-most subplot of \autoref{fig:PEDOTPSS_parametric}), but shorter pulse durations do. %
+right-most subplot of \autoref{pps:fig:parametric}), but shorter pulse durations do. %
[TABLE] summarizes the coherence dephasing time and inomogeneous broadening values that best
matches the experimental FWHM and inhomogeneous broadening value for $\Delta_t = 35, 40$ and 45
fs. %
Clearly, there is no upper limit that can provide an upper limit for the inhomogeneous
broadening. %
+Our model system does ans excellent job of reproducing the entire 2D transient within measurement
+error (\autoref{pps:fig:agreement}). %
+The most dramatic disagreement is in the upper right, where the experiment decays much slower than
+the simulation. %
+Our system description does not account for signal contributions in TOs \RomanNumeral{2} and
+\RomanNumeral{4}, where double quantum coherence resonances are important. %
+In additon, excitation pulse shapes may cause such distortions. %
+Regardless, these contributions do not affect our analysis. %
+
+\begin{figure}
+ \includegraphics[width=\linewidth]{"PEDOT_PSS/parametric"}
+ \caption[3PEPS parameter space.]{
+ 3PEPS parameter space.
+ Interplay of pure and ensemble dephasing on the coherent transient duration and the peak shift
+ value for the three pulse-widths considered in \autoref{pps:tab:table}.
+ Red lines represent the parameters for constant values of $T_2$ and varying amounts of
+ $\Delta_{\text{inhom}}$.
+ The domain of possible observables is bounded (blue hash for $\Delta_{\text{inhom}} \rightarrow
+ \inf$, green hash for $\Delta_{\text{inhom}} = 0$).
+ Also shown is the measured FWHM for the PEDOT:PSS thin film (star).
+ }
+ \label{pps:fig:parametric}
+\end{figure}
+
\begin{table}
\begin{tabular}{ c | c c c }
$\Delta_t$ (fs) & $T_2$ (fs) & $\hbar T_2^{-1}$ (meV) & $\Delta_{\mathsf{inhom}}$ (meV) \\ \hline
45 & --- & --- & --- \\
40 & 10 & 66 & $\infty$ \\
\end{tabular}
- \caption[]{
- CAPTION TODO
+ \caption[Fitted parameters.]{
+ Fitted parameters for the coherent transient.
+ The FWHM of the homogeneous line shape is $\hbar T_2^{-1}$.
}
- \label{tab:PEDOTPSS_table}
+ \label{pps:tab:table}
\end{table}
\begin{figure}
\includegraphics[width=\linewidth]{"PEDOT_PSS/agreement"}
- \caption[PEDOT:PSS 3PE traces.]{
- CAPTION TODO
+ \caption[Agreement between simulation and experiment.]{
+ Agreement between simulation and experiment.
+ Experiment and simulation in the full 2D representation (left) and transient grating slices
+ (right), for both phase matching conditions (top and bottom).
+ The identity of each slice can be inferred from its color.
+ In this case the displayed simulation is for $\Delta_t=35$ fs, with the appropriate $T_2$ and
+ $\Delta_{\text{inhom}}$ as seen in \autoref{pps:tab:table}.
+ Simulatinos for other pulse-widths look very similar.
}
- \label{fig:PEDOTPSS_agreement}
+ \label{pps:fig:agreement}
\end{figure}
-Our model system does ans excellent job of reproducing the entire 2D transient within measurement
-error (\autoref{fig:PEDOTPSS_agreement}). %
-The most dramatic disagreement is in the upper right, where the experiment decays much slower than
-the simulation. %
-Our system description does not account for signal contributions in TOs \RomanNumeral{2} and
-\RomanNumeral{4}, where double quantum coherence resonances are important. %
-In additon, excitation pulse shapes may cause such distortions. %
-Regardless, these contributions do not affect our analysis. %
-
-Extremely fast (single fs) carrier scattering time constants have also been observed for PEDOT-base
-conductive films. [CITES]
-
\section{Conclusions} % ==========================================================================
-% TODO \ No newline at end of file
+To asses homogeneous and inhomogeneous linewidth, we performed ultrafast four wave mixing
+spectroscopy on a drop-cast PEDOT:PSS thin film. %
+Under Redfield theory, the homogeneous linewidth of any transition is determined by pure dephasing
+and population relaxation \cite{SkinnerJL1988a}, although ensemble dephasing can become relevant
+for very inhomogeneously broadened systems. %
+Three-pulse photon echo (3PE) analysis can distinguish between homogeneous and inhomogeneous
+broadening. \cite{WeinerAM1985a} %
+We collecte the transient grating population relaxation trace and 3PE traces and find that the net
+dephasing and population relaxation are both fast, comparable to our pulse width. %
+Through numerical modeling, we extract a population time of 80 fs, a homogeneous dephasing time of
+$<18$ fs ($>73$ meV), and an inhomogeneous broadening factor of $>43$ meV. %
+Extremely fast (single fs) carrier scattering time constants have also been observed for PEDOT-base
+conductive films. \cite{ChangYunhee1999a, ChoShinuk2005a, ZhuoJingMei2008a} % \ No newline at end of file