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1036986140-MIT.Pdf Simulating Energy Transfer Between Nanocrystals and Organic Semiconductors by Nadav Geva B.S.E., University of Michigan (2013) Submitted to the Department of Materials Science and Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Materials Science and Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY February 2018 @ Massachusetts Institute of Technology 2018. All rights reserved. Author ............ Signature redacted ....... Department of Materials Science and Engineering Signature redacted January 3, 2017 Certified by / Troy Van Voorhis Haslam and Dewey Professor of Chemistry Signature redacted Thesis Supervisor Certified by .................... Jeffrey C. Grossman Professor of Materials ien l Engineering 7"/3 4~hesis Reader Accepted by... ......... Signature redacted ARCHIVES Donald R. S1dway John F. Elliot Professor of Materials Chemistry MASSACHUSETTS INSTITUTE OFTECHNOLOGY Chair, Department Committee on Graduate Theses MAR 01 Z018 LIBRARIES 77 Massachusetts Avenue Cambridge, MA 02139 MITLibraries http://Iibraries.mit.edu/ask DISCLAIMER NOTICE Due to the condition of the original material, there are unavoidable flaws in this reproduction. We have made every effort possible to provide you with the best copy available. Thank you. The images contained in this document are of the best quality available. 2 Simulating Energy Transfer Between Nanocrystals and Organic Semiconductors by Nadav Geva Submitted to the Department of Materials Science and Engineering on December 22, 2017, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Materials Science and Engineering Abstract Recent trends in renewable energy made silicon based photovoltaics the undisputed leader. Therefore, technologies that enhance, instead of compete with, silicon based solar cells are desirable. One such technology is the use of organic semiconductors and noncrystalline semiconductors for photon up- and down-conversion. However, the understanding of energy transfer in these hybrid systems required to effectively engineer devices is missing. In this thesis, I explore and explain the mechanism of energy transfer between noncrystalline semiconductors and organic semiconductors. Using a combination of density functional calculations, molecular dynamics, and ki- netic theory, I have explored the geometry, morphology, electronic structure, and coarse grained kinetics of these system. The result is improved understanding of the transfer mechanism, rate, and the device structure needed for efficient devices. I have also looked at machine learning inspired algorithm for acceleration of density func- tional theory methods. By training machine learning models on DFT data, a much improved initial guess can be made, greatly accelerating DFT optimizations. Gen- erating and examining this data set also revealed a remarkable degree of structure, that perhaps can be further exploited in the future. Thesis Supervisor: Troy Van Voorhis Title: Haslam and Dewey Professor of Chemistry 3 4 Acknowledgments What a ride. 9.5 years ago, I came to the US for undergrad. Since then, I finished my undergrad, got married, had 2 kids, bought a house, and now I'm finishing my PhD. I would like to start by thanking my advisor, Prof. Troy Van Voorhis, for taking a chance on a Materials grad student with no computational background. You were my model for a scientist in my time at MIT. Next is my office mate Alex Kohn. Getting a PhD is mentally challenging, and having someone who is going through the same ordeal to share the misery and the triumph was indispensable. Thank you Alex, for being that person. Another such person was James Shepherd. Our long conversions, on anything from science to politics, shaped me as much as all my previous experiences combined. The life of a grad student can be very lonely, and I am grateful I had you to break from that loneliness. While lonely, I was not alone. I would like to thank the present and past zoo community, for creating an inspiring, productive, and social work environment. I would like to thank Matt Welborn, Mike Mavros, Tianyu Zhu, Eric Hontz, Takashi Tsuchimochi, Churn Chang, Dave McMahon, Thomas Avila, Hungzho Ye, Zhou Lin, Piotr deSilva, Lexie Mclsaac, Nathan Ricke, Kaitlyn Dwelle, Amr Dodin and all other visitors to the zoo. It's been an honor being your volleyball captain and colleague. Finally, I would like to thank my family. My wife, Ceit, who's support and love kept me going through the worst of it, I couldn't have done it without you. And to my two kids, Adam and Ella. You made this twice as hard, and twice as worth it. This thesis is dedicated to you. 5 "Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrationaland contrary to the spirit of chemistry... If mathematical analysis should ever hold a prominent place in chemistry - an aberration which is happily almost impossible - it would occasion a rapid and widespread degeneration of that science." -Auguste Comte, Cours de philosophie positive, 1830 6 Contents 1 Introduction 19 1.1 M otivation ... ............ ................ 20 1.2 M ethods .. ............. .. ...... ..... ... 22 1.2.1 Molecular Dynamics (MD) .. .. ............. 22 1.2.2 Constrained Density Functional Theory - Configuration Inter- action (CDFT-CI) . ..... ......... .. 24 2 Morphology of passivating organic ligands around a nanocrystal 29 2.1 Introduction . ... .. 29 2.2 Simulations . ... .. 31 2.3 Experiment ... ... 40 2.4 Theory ... .... .. 43 2.5 Conclusion .. ..... 45 3 Reaching the Speed Limit for Triplet Transfer in Solid-State Lead Sulfide Nanocrystal Sensitized Photon Upconversion 49 3.1 Introduction ...................... .......... 49 3.2 Results and Discussion .......................... 51 3.3 C onclusion ................................. 62 3.4 Materials and Methods .......................... 63 4 Mean Field Treatment of Heterogeneous Steady State Kinetics 69 4.1 Introduction ............ .................... 69 7 4.2 Working example ............... 71 4.3 The self consistent mean field approach .. .. 74 4.4 R esults .. ...... ....... ...... 77 4.5 Conclusion ...... ....... ...... 81 5 A disordered kinetics model for triplet transfer 83 5.1 Introduction .... ..... ...... .... 83 5.2 Methods ...... ........ ....... 85 5.3 Results and Discussion .... ......... 88 5.4 Conclusions . ........ ........ .. 90 6 WDA with exact condition: An acceleration scheme 93 6.1 Introduction ....... 93 6.2 Theoretical Background 95 6.3 Method ..... .... 96 6.4 Computational Details 97 6.5 Results and discussion 98 6.6 Conclusion ...... .. 102 7 Optimal Tuning in Machine Learning 103 7.1 Introduction . ...... 103 7.2 Methods ....... .. 104 7.3 Results and Discussion . 106 7.4 Conclusions ....... 107 8 Conclusion 109 8 List of Figures 2-1 Steps of the simulation are ordered as follows: a) the nanocrystal as carved from bulk; b) which is then decorated with ligands in a 'spiky ball' conformation; c) the geometry after energy minimization; d) the geometry after molecular dynamics ...... ............. 32 2-2 Thickness of the ligand shell as a function of stretched ligand length for three dot sizes. Two linear eye-guides are also provided: the first (- -) has a slope of one, shifted by the Cd-N bond length: x + bCd-N- The second (-.-.) has a slope one half: x/2 + bCd-N. Representative error bars are shown for the smallest dot size, where we averaged over six independent runs of Fig. 2-1. These show that the shell thickness does not vary significantly with diameter over the range shown here. 34 2-3 Calculation of the order parameter: For each ligand, we calculate two vectors: the first is the vector from the geometric center of the nanocrystal to the ligand head group, the second is the vector from the head group to the tail group (shown in (a)). The order parameter is then the dot product of the normalized vectors. This distribution varies according to ligand length (shown in (b)), with ligand repeat units shown in the key as n in CH3 (CH 2)nNH 2 . The dot size is 3.56nm. 35 9 2-4 Illustrative snapshots from simulations of a 3.56nm nanocrystal. From left to right, these correspond to ligand lengths of n=3 to 17 in in- crements of two. The surface ligands are colored by their orientation relative to the surface. Red-colored molecules are sticking straight out, as quantified by an order parameter greater than 0.6, whereas turquoise-colored molecules lay flat. ..... ...... ...... 36 2-5 Mode of the order parameter distribution as a function of ligand size, for three nanocrystal sizes. ......... ............ ... 37 2-6 Anisotropy of the relative ligand shell thickness is shown for a pair of dots. The thickness (indicated by color) is plotted against two angular parameters which describe a location on a dot's spherical surface (for details, see Eq. (2.1)). Here, we have used the height of the location of the end group (C in CH 3 , red points) as a way of mapping thickness. Color is used to indicate height as a heat map, where blue locations are increased ligand height, white are decreased. At the start of the simulation (left) the height distribution is uniform within projection error but over the course of the simulation it becomes increasingly anisotropic (right). Since we are measuring the height only at the head group location, white areas are not necessarily bare. The dot size is 3.56 nm .. ........ ........ ........ ....... 37 2-7 Transmission electron microscopy (TEM) was performed to make com- parison with computational results. (a) An example of a TEM micro- graph of a layer of PbS nanocrystals with carboxylic acid ligands. (b) TEM data compares well with simulation data (here, taken from the 1.00 nm dot size). The thickness in this plot is corrected for the bond length that joins the ligand to the surface i.e. Cd-N or Pb-O. The red, dashed line shows the fit to Eq. (2.2) for the whole data set. The black, dashed line is a line of slope one. ...... ...... ...... 40 10 2-8 Two explanations for how dots are separated by a distance of approx- imately one ligand length.
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