From 3e0cce57dcd76a477207edbad02c16ae7b735ad0 Mon Sep 17 00:00:00 2001 From: Blaise Thompson Date: Wed, 4 Apr 2018 09:35:55 -0500 Subject: remove : --- PEDOT_PSS/chapter.tex | 303 ++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 303 insertions(+) create mode 100644 PEDOT_PSS/chapter.tex (limited to 'PEDOT_PSS/chapter.tex') diff --git a/PEDOT_PSS/chapter.tex b/PEDOT_PSS/chapter.tex new file mode 100644 index 0000000..10c5af2 --- /dev/null +++ b/PEDOT_PSS/chapter.tex @@ -0,0 +1,303 @@ +\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} + +\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*). % +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. % + +\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.]{ + 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} + +\autoref{fig:PEDOTPSS_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. % + +\begin{figure} + \includegraphics[width=\linewidth]{"PEDOT_PSS/raw"} + \caption[PEDOT:PSS 3PE raw data.]{ + CAPTION TODO + } + \label{fig:PEDOTPSS_raw} +\end{figure} + +\subsection{Assignment of zero delay} % ---------------------------------------------------------- + +The absolute position of complete temporal overlap of the excitation pulses (zero delay) is a +crucial step in determining the magnitude of th epeak shift and therefore the total rephasing +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 +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. % +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}. % +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 +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] % + +We found that the 3PEPS traces agree best when the data in \autoref{fig:PEDOTPSS_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 +value. % +The entire 3PEPS trace ($\tau$ vs $T$) is show 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. % +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 +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] % +At long $T$, the average static 3PEPS is 2.5 fs. % + +\begin{figure} + \includegraphics[width=\linewidth]{"PEDOT_PSS/delay space"} + \caption[PEDOT:PSS 3PE delay space.]{ + CAPTION TODO + } + \label{fig:PEDOTPSS_delay_space} +\end{figure} + +\begin{figure} + \includegraphics[width=\linewidth]{"PEDOT_PSS/processed"} + \caption[PEDOT:PSS 3PE processed data.]{ + CAPTION TODO + } + \label{fig:PEDOTPSS_processed} +\end{figure} + +\begin{figure} + \includegraphics[width=\linewidth]{"PEDOT_PSS/overtraces"} + \caption[PEDOT:PSS 3PE traces.]{ + CAPTION TODO + } + \label{fig:PEDOTPSS_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} % ---------------------------------------------------------------- + +We simulated the 3PEPS response of PEDOT:PSS through numerical integration of the Liouville-von +Neumann Equation. % +Integration was performed on a homogeneous, three-level system with coherent dynamics described by + +\begin{equation} + \frac{1}{T_2} = \frac{1}{2T_1} + \frac{1}{T_2^*}, +\end{equation} + +where $T_2$, $T_1$ and $T_2^*$ are the net dephasing, population relaxation, and pure dephasing +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] % +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. % +This strategy captures rephasing peak shifts and ensemble dephasing. % + +It is difficult to determine the coherence dephasing and the inhomogeneous broadening using 3PE if +both factors are large. % +To extract $T_2^*$ and $\Delta_{\mathsf{inhom}}$, we focused on two key components of the dataset, +coherence duration and peak shift at large $T$. % +Since dephasing is very fast in PEDOT:PSS, we cannot directly respove an exponential free induction +decay (FID). % +Instead, our model focuses on the FWHM of the $\tau$ trace to determine the coherence duration. % +At $T > 50$ fs, the transient has a FWHM of $\sim$ 80 fs (intensity level). % +For comparison, our instrumental response is estimated to be 70-90 fs, depending on the exact value +of our puse duration $\Delta_t$ (35-45 fs FWHM, intensity level). % +An experimental peak shift of 2.5 fs was extracted using the strategy described above. % +Taken together, it is clear that both pure dephasing and ensemble dephasing influence FWHM and peak +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 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 +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. % +[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. % + +\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 + } + \label{tab:PEDOTPSS_table} +\end{table} + +\begin{figure} + \includegraphics[width=\linewidth]{"PEDOT_PSS/agreement"} + \caption[PEDOT:PSS 3PE traces.]{ + CAPTION TODO + } + \label{fig:PEDOTPSS_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{Frequency-domain transient grating spectroscopy} % -------------------------------------- + +This section describes preliminary, unpublished work accomplished on PEDOT:PSS. % + + -- cgit v1.2.3