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Organic Supercapacitors on Paper Substrates


Probably many people are aware of the efforts by the electronics industry to make wearable or, at least, flexible electronics. Smartphones that could be folded in half like a piece of paper and put in a pocket would certainly be desirable. Eventually, they could even be included in clothing or, rather, clothing could be included in a smartphone.

The challenge in making effective wearables and other flexible electronics is almost entirely a materials-issue: Materials must be developed to provide identical functionality as those used in modern electronics but they must also be both flexible and durable, meaning that their potency diminishes with use and repeated folding no faster than a rigid electronic device. A consumer device might need a flexible touch-display or other interface of some sort, circuit elements, and a power supply at minimum. Probably we also want some form of contactless charging too, perhaps an integrated solar cell. This is a lot of functionality to re-engineer. On top of that, some papers have explored the ambitious goal of directly printing these materials as a fully-formed device from something as simple as an inkjet printer.

I report here my work on a material that may be a potential power supply for flexible electronics on paper or textile substrates. I was responsible for the synthesis and materials characterization of PEDOT films on nylon paper substrates. This involved using oxidative chemical vapor deposition (oCVD) processes developed in Gleason Group at MIT to deposit PEDOT from monomeric EDOT. Over the course of the project I performed various tests and experiments involving thermogravimetric analysis (TGA, to observe how stable the film was), differential scanning calorimetry (DSC, also to check for stability and other thermal properties), and lots of scanning electron microscopy (SEM, to perform elemental analysis on cross-sections and check for conformal coating of the CVD layer as well as general surface morphology).


A couple interesting problems came up while working with the SEM. We wanted to perform elemental analysis using energy-dispersive x-ray spectroscopy (EDX) but we noticed that a sulfur peak (sulfur indicating the presence or lack of PEDOT) lined up with a gold peak in the spectrum making it difficult to differentiate between the two. We had to start carbon-coating our samples instead of using the standard gold-palladium sputtering to get better elemental maps like the ones in the paper. Another problem we had in getting nice images of the cross-section was that cutting our paper samples with scissors or razor blades would crush the fine mesh structure of the paper and yield poor images. We tried using a focused ion beam (FIB) with mixed results but ultimately resorted to snapping our samples in cryogenic conditions.


Here is a link to a folder containing the paper itself and the supporting information document. Please use the following citation:

Liu, Andong, Peter Kovacik, Nolan Peard, Wenda Tian, Hilal Goktas, Jonathan Lau, Bruce Dunn, and Karen K. Gleason. 2017. “Monolithic Flexible Supercapacitors Integrated into Single Sheets of Paper and Membrane via Vapor Printing.” Advanced Materials, 1606091. doi:10.1002/adma.201606091.

This work was performed at the Institute for Soldier Nanotechnologies and Gleason Lab under the supervision of Andong Liu and Karen Gleason.






Notes on Textbooks

In the physical sciences (as with other fields, I assume), there are certain texts that are considered "the classics" in that they tend to be used by the vast majority of students during their studies over multiple generations. It can take a fair amount of Internet searching or exposure to academics to figure out which books are genuine classics, so I am compiling here a tentative list of essential texts for physics and some other other topics. These recommendations are the result of my own studies and experience, recommendations from other academics, and texts used in MIT courses or recommended by students on MIT mailing lists. I will attempt to keep it updated and I have included a few notes of description (again, either from my own experience or conversations with others). Feel free to contact me if you have any additional notes or recommendations.

Electromagnetism

Jackson: Classical Electrodynamics - Treatment of Bessel function not found in most other texts, more comprehensive than Griffiths. The standard reference for classical electrodynamics.
Griffiths: Introduction to Electrodynamics - Solid introduction to electrodynamics. Used in 8.07 at MIT with some references to Jackson.
Schwinger: Classical Electrodynamics and Particles, Sources, and Fields

Quantum Optics

Wolf: Introduction to the Theory of Coherence and Polarization of Light - Brief introduction to some specialized topics.
Goodman: Fourier Optics
Mandel and Wolf: Optical Coherence and Quantum Optics - The "bible" of quantum optics.
Loudon: The Quantum Theory of Light - Offers the basics, but will need extra references for the gritty details
GlauberQuantum Theory of Optical Coherence

XFELs

Saldin: The Physics of Free Electron Lasers
Philip Willmott: An Introduction to Synchrotron Radiation - Focus on application rather than theory, brief and to-the-point.

Quantum Mechanics

Griffiths: Introduction to Quantum Mechanics - Too brief usually, but everyone starts here.
Landau and LifshitzQuantum Mechanics - Non-Relativistic Theory

Quantum Field Theory

Dirac: The Principles of Quantum Mechanics
Peskin and SchroederAn Introduction to Quantum Field Theory - Standard reference for QFT
LifshitzQuantum Electrodynamics

Particle Physics

Griffiths: Introduction to Elementary Particles

Quantum Chemistry

Szabo and Ostlund: Modern Quantum Chemistry - Focused on electronic structure theory
CramerEssentials of Computational Chemistry - Explanation and application of common models with case-studies
Jensen: Introduction to Computational Chemistry - Same as Cramer but with more focus on computational details
Craig and Thirunamachandran: Molecular Quantum Electrodynamics

Condensed Matter

Ashcroft and Mermin: Solid State Physics - The go-to reference
Altland and Simons: Condensed Matter Field Theory
Ohring: Materials Science of Thin Films

Superconductivity

Tinkham: Introduction to Superconductivity
Annett: Superconductivity, Superfluids, and Condensates

Mathematics 

Algebra:

Strang: Linear Algebra and Its Applications - Used by 18.06 at MIT
Artin: Algebra - Artin's 18.701 book is more physics-oriented than most algebra books and the chapter on representation theory is just what a physicist needs.
Dummit and Foote: Abstract Algebra
Gallian: Contemporary Abstract Algebra
Lorenzo Sadun: Applied Linear Algebra

Topology

Munkres: Topology

Differential Equations

Evans: Partial Differential Equations
Simmons: Differential Equations with Applications and Historical Notes
Strauss: Partial Differential Equations
Brauer: The Qualitative Theory of Differential Equations
Hirsch: Differential Equations, Dynamical Systems, and an Introduction to Chaos


Analysis

Rudin: Principles of Mathematical Analysis
Apostol: Calculus
Ablowitz and Fokas: Complex Variables - It's a huge book and I've only used it as a reference, but anything you might need involving complex analysis is in here somewhere.

Calculus of Variations

Geland: Calculus of Variations
Forsyth: Calculus of Variations

Mathematics in Physics

(A useful, free online resource: http://www.physics.miami.edu/~nearing/mathmethods/)
Byron and FullerMathematics of Classical and Quantum Physics
Fleisch: Div, Grad, Curl and All That

Schwichtenberg: Physics from Symmetry - A really great book for introducing Lie groups and their applications to a bunch of different fields in physics.
Jeevanjee: Tensors and Group Theory for Physicists
Stillwell: Naive Lie Theory
These would be helpful for 8.033 and anything involving Lie groups, requires only 18.03 as background. They introduce the Lie stuff with a more physical and mathematical bent respectively but are written in a super casual and friendly style. In particular they staunchly avoid any differential geometry, everything here is plain old matrix multiplication.

David Skinner: Mathematical Methods - These are the lecture notes for a sophomore-level course at Cambridge. It's also relatively easy reading, requiring just 18.03; it taught me where all those weird orthogonal polynomials come from and what Green's functions are.
Zee: Group Theory in a Nutshell for Physicists - I really enjoyed Zee; it runs through a ton of group theory with minimal math prerequisites and a super casual style, showing by example. Without a proof anywhere in sight, he manages to get to grand unification in just a few hundred pages.
Schutz: Geometrical Methods of Mathematical Physics
Baez: Gauge Fields, Knots, and Gravity
Kobayashi and Nomizu: Foundations of Differential Geometry
Choquette-Bruhat and Morette: Analysis, Manifolds, and Physics
Arnold: Mathematical Methods of Classical Mechanics - A manifold underpinning of Lagrangian and Hamiltonian mechanics - less of a methods, more of a theory.
Kentaro Hori: Mirror Symmetry - The first half discusses algebraic geometry and toric geometry and I would highly recommend it if you are interested in String theory.

Plotting Transport Coefficients from BoltzTraP

BoltzTraP puts the traces of the various transport coefficient tensors (such as the conductivity tensor) in a *.trace. The trace of the conductivity tensor can be plotted using this gnuplot script. Remember to select the size to fit your display. Note that the "trace" as reported by BoltzTraP 1.2.5 is actually the trace divided by 3.
set terminal png size 2720,1800 font "Helvetica,30" linewidth 5
set output "ConductivitySym.png"
set title "Conductivity/Relaxation Time (Symmetrised)"
set xlabel "Chemical Potential (eV)"
set ylabel "1/(Ω*m*s)"

set grid

plot "data.trace" using ($1*13.605698066):6 with lines title "Conductivity/Tau"

reset
Note that this script converts the x-axis to units of electron-volts. Also remember that BoltzTraP uses the constant relaxation time approximation, so one must supply a relaxation time to get the true conductivity or mobility. The mobility is related to the conductivity by this simple formula: \(\sigma = ne\mu_e\) where \(n = N/V_{cell}\), where N is an output from BoltzTraP.
set terminal png size 2720,1800 font "Helvetica,30" linewidth 5
set output "MobilitySym.png"
set title "Mobility (Symmetrised)"
set xlabel "Chemical Potential (eV)"
set ylabel "cm^{2}/(V*s)"

set grid

set xrange [-2:2]
#Unit cell volumes in cm^3
V_cell = 10

plot "data.trace" using ($1*13.605698066):($6*tau/($3/V_cell*1.6022*10**-19)) with lines title "Mobility/Tau"

reset
Individual components of the tensors may be plotted from the corresponding file; for conductivity, this file is *.condtens.
set terminal png size 2720,1800 font "Helvetica,30" linewidth 5
set output "Conductivity_xx.png"
set title "Conductivity/Relaxation Time"
set xlabel "Chemical Potential (eV)"
set ylabel "1/(Ω*m*s)"

set grid

plot "data.condtens" using ($1*13.605698066):4 with lines title "XX",
"data.condtens" using ($1*13.605698066):5 with lines title "XY",
"data.condtens" using ($1*13.605698066):6 with lines title "XZ",
"data.condtens" using ($1*13.605698066):7 with lines title "YZ",
"data.condtens" using ($1*13.605698066):8 with lines title "YY",
"data.condtens" using ($1*13.605698066):9 with lines title "YZ",
"data.condtens" using ($1*13.605698066):10 with lines title "ZX",
"data.condtens" using ($1*13.605698066):11 with lines title "ZY",
"data.condtens" using ($1*13.605698066):12 with lines title "ZZ"

reset
As this paper points out, the effective mass can be a more useful quantity to plot from calculations because conductivity/mobility are dependent on the scattering time and mix knowledge of the electronic structure (which, in principle, we know from the DFT calculation) and the scattering properties of the material and its carriers (which we probably do not know at all). The effective mass is, in this sense, more useful because it gives information about the electronic structure without requiring any knowledge of scattering in the material. The paper gives the formula \(m^* = \frac{e^2 \tau |N|}{\sigma V_{cell}}\) where \(\tau/\sigma\) is the reciprocal of an output from BoltzTrap. \(N\) is another output from BoltzTraP in the *.trace file.
set terminal png size 2720,1800 font "Helvetica,30" linewidth 5
set output "MassSym.png"
set title "Effective Mass"
set xlabel "Chemical Potential (eV)"
set ylabel "Mass in m_{e}"

set grid

set xrange [-2:2]
#Unit cell volumes in m^3
V_cell = 10

# tau = 10**-12 #Guess relaxation time
# sigma = n * e * mu
# 1/m = sigma/(e**2 * tau) * 1/n
# n = abs(N)/V_cell
# Checked, relations used below have proper units of mass

plot "data.trace" using ($1*13.605698066):(abs($3)/V_cell*(1.602177*10**-19)**2/$6)/(9.1093836*10**-31) with lines title "Mass"

reset

N.B.: Do not trust WolframAlpha to correctly convert cubic Angstroms to cubic centimeters!

References
Gibbs, Zachary M., Francesco Ricci, Guodong Li, Hong Zhu, Kristin Persson, Gerbrand Ceder, Geoffroy Hautier, Anubhav Jain, and G. Jeffrey Snyder. 2017. “Effective Mass and Fermi Surface Complexity Factor from Ab Initio Band Structure Calculations.” npj Computational Materials. Springer US: 1–6. doi:10.1038/s41524-017-0013-3.