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Criticality in the Linear Response of Disordered Solids Carl Peter Goodrich University of Pennsylvania, [email protected]

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Criticality in the Linear Response of Disordered Solids Carl Peter Goodrich University of Pennsylvania, Carlpgoodrich@Gmail.Com University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 1-1-2015 Unearthing the Anticrystal: Criticality in the Linear Response of Disordered Solids Carl Peter Goodrich University of Pennsylvania, [email protected] Follow this and additional works at: http://repository.upenn.edu/edissertations Part of the Physics Commons Recommended Citation Goodrich, Carl Peter, "Unearthing the Anticrystal: Criticality in the Linear Response of Disordered Solids" (2015). Publicly Accessible Penn Dissertations. 1743. http://repository.upenn.edu/edissertations/1743 This paper is posted at ScholarlyCommons. http://repository.upenn.edu/edissertations/1743 For more information, please contact [email protected]. Unearthing the Anticrystal: Criticality in the Linear Response of Disordered Solids Abstract The fact that a disordered material is not constrained in its properties in the same way as a crystalline one presents significant and yet largely untapped potential for novel material design. However, unlike their crystalline counterparts, disordered solids are not well understood. Though currently the focus of intense research, one of the primary obstacles is the lack of a theoretical framework for thinking about disorder and its relation to mechanical properties. To this end, we study a highly idealized system composed of frictionless soft spheres at zero temperature that, when compressed, undergos a jamming phase transition with diverging length scales and clean power-law signatures. This critical point is the cornerstone of a much larger ``jamming scenario" that has the potential to provide the essential theoretical foundation that is sorely needed to develop a unified understanding of the mechanics of disordered solids. We begin by showing that jammed sphere packings have a valid linear regime despite the presence of a new class of ``contact nonlinearities," demonstrating that the leading order behavior of such solids can be ascertained by linear response. We then investigate the critical nature of the jamming transition, focusing on two diverging length scales and the importance of finite-size effects. Next, we argue that this jamming transition plays the same role for disordered solids as the idealized perfect crystal plays for crystalline solids. Not only can it be considered an idealized starting point for understanding the properties of disordered materials, but it can even influence systems that have a relatively high amount of crystalline order. As a result, the behavior of solids can be thought of as existing on a spectrum, with the perfect crystal at one end and the jamming transition at the other. Finally, we introduce a new principle for disordered solids wherein the contribution of an individual bond to one global property is independent of its contribution to another. This principle allows the different global responses of a disordered system to be manipulated independently of one another and provides a great deal of flexibility in designing materials with unique, textured and tunable properties. Degree Type Dissertation Degree Name Doctor of Philosophy (PhD) Graduate Group Physics & Astronomy First Advisor Andrea J. Liu Second Advisor Sidney R. Nagel This dissertation is available at ScholarlyCommons: http://repository.upenn.edu/edissertations/1743 Keywords critical phenomena, disordered solids, elasticity, jamming Subject Categories Physics This dissertation is available at ScholarlyCommons: http://repository.upenn.edu/edissertations/1743 UNEARTHING THE ANTICRYSTAL: CRITICALITY IN THE LINEAR RESPONSE OF DISORDERED SOLIDS Carl P. Goodrich A DISSERTATION in Physics and Astronomy Presented to the Faculties of the University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 2015 Andrea J. Liu, Professor of Physics and Astronomy Supervisor of Dissertation Sidney R. Nagel, Professor of Physics (University of Chicago, Chicago, IL) Co-Supervisor of Dissertation Marija Drndic, Professor of Physics and Astronomy Graduate Group Chairperson Dissertation Committee Douglas J. Durian, Professor of Physics and Astronomy Eleni Katifori, Assistant Professor of Physics and Astronomy Tom C. Lubensky, Professor of Physics and Astronomy Rob Riggleman, Assistant Professor of Chemical and Biomolecular Engineering David Srolovitz, Professor of Materials Science and Engineering UNEARTHING THE ANTICRYSTAL: CRITICALITY IN THE LINEAR RE- SPONSE OF DISORDERED SOLIDS COPYRIGHT 2015 Carl P. Goodrich Dedication For my mother, whom I miss every day. iii Acknowledgements This dissertation would never have been possible without the tremendous support and guidance I have received from countless individuals. First and foremost, I thank my advisors, Andrea Liu and Sid Nagel, for their unwavering support, advice, patience, encouragement, and confidence. More than anything, Andrea and Sid have taught me what it means to be a scientist, and I am forever humbled to have been able to work with and learn from them. Thank you for the countless opportunities, and for challenging me every day. I am also very grateful for the considerable financial support they have provided for me to attend numerous conferences and schools, which has been an essential part of my education and development. I have been extremely lucky not only to have two outstanding advisors but to be in an ideal environment for a graduate student to learn and grow. I sincerely thank Randy Kamien for challenging me each and every day, for making DRL a fun and enjoyable work environment, and for always being generous with his time. It is an understatement to say that Randy has had a significant and profound effect on me iv both as a scientist and a person. Furthermore, I thank Tom Lubensky for many stimulating discussions and interactions over the years. I am also grateful to Doug Durian, Eleni Katifori, Allison Sweeney, and Arjun Yodh for countless interactions that have been invaluable to my education. I have also had the privilege to work alongside many amazingly talented, in- sightful and kind students and postdocs at Penn. I sincerely thank the entire soft matter theory group, particularly Ed Banigan, for teaching me to love biophysics and for always explaining things in a clear and concise way so that even I could understand; Bryan Chen, for many invaluable discussions regarding isostaticity, the \pebble game," and the like; Wouter Ellenbroek, for taking me under his wing when I was first learning about jamming; Timon Idema, for teaching me, both directly and by example, more about science and about life than I can possibly put in words; Anton Souslov, for helping me think clearly about criticality and jamming; and finally my jamming brethren Sam Schoenholz and Daniel Sussman, for numer- ous discussions and for their constant insight, feedback and support. I also owe a tremendous amount to others at Penn that are outside of the soft matter theory group. I thank Dave Srolovitz and Spencer Thomas for teaching me how to generate polycrystals and for other invaluable discussions. I thank the entire DISCONAP community, especially John Crocker, Jennifer Rieser, and Rob Riggleman, as well as the entire Yodh lab, especially Matt Gretale, Matt Lohr, Tim Still, and Peter Yunker. v In addition, I have benefitted greatly from numerous interactions with researchers outside of Penn. I especially thank Lisa Manning, Brian Tighe, and Martin van Hecke for countless discussions that never failed to teach me something new. I am also grateful for many fruitful interactions with, among others, Justin Burton, Patrick Charbonneau Eric Corwin, Simon Dagois-Bohy, Eric DeGiuli, Amy Graves, Silke Henkes, Stan Leibler, Edan Lerner, Michael Mitchell, Corey O'Hern, Ken Schweizer, Jen Schwartz, Jim Sethna, Mark Shattuck, Mike Thorpe, Tsvi Tlusty, Sal Torquato, Vincenzo Vitelli, Matthieu Wyart, Ning Xu, and Zorana Zeravcic. Finally, I thank my fathers Bill and Scot, and my sister Kirstin. I could not have done any of this without your unyielding love and support. Thank you for always being there for me. I also thank my cousin Elaine and her wonderful family for giving me a home away from home. vi ABSTRACT UNEARTHING THE ANTICRYSTAL: CRITICALITY IN THE LINEAR RESPONSE OF DISORDERED SOLIDS Carl P. Goodrich Andrea J. Liu Sidney R. Nagel The fact that a disordered material is not constrained in its properties in the same way as a crystalline one presents significant and yet largely untapped potential for novel material design. However, unlike their crystalline counterparts, disordered solids are not well understood. Though currently the focus of intense research, one of the primary obstacles is the lack of a theoretical framework for thinking about disorder and its relation to mechanical properties. To this end, we study a highly idealized system composed of frictionless soft spheres at zero temperature that, when compressed, undergos a jamming phase transition with diverging length scales and clean power-law signatures. This critical point is the cornerstone of a much larger \jamming scenario" that has the potential to provide the essential theoretical foundation that is sorely needed to develop a unified understanding of the mechanics of disordered solids. We begin by showing that jammed sphere packings have a valid linear regime despite the presence of a new class of \contact nonlinearities," demonstrating that the leading order behavior of such solids can vii be ascertained by linear response. We then investigate the critical nature of the jamming
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