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 deletions(-) delete mode 100644 PEDOT:PSS/chapter.tex (limited to 'PEDOT:PSS/chapter.tex') diff --git a/PEDOT:PSS/chapter.tex b/PEDOT:PSS/chapter.tex deleted file mode 100644 index 1e26434..0000000 --- a/PEDOT:PSS/chapter.tex +++ /dev/null @@ -1,303 +0,0 @@ -\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