From c15660a15d2ac72ad8b385ac9d54fbc0e257af65 Mon Sep 17 00:00:00 2001 From: Blaise Thompson Date: Sun, 15 Apr 2018 14:12:07 -0500 Subject: 2018-04-15 14:12 --- PEDOT_PSS/chapter.tex | 295 +++++++++++++++++++++++++++++--------------------- 1 file changed, 169 insertions(+), 126 deletions(-) (limited to 'PEDOT_PSS/chapter.tex') 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 -- cgit v1.2.3