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Toward a Fundamental Understanding of Bubble Nucleation in Polymer Foaming Toward a Fundamental Understanding of Bubble Nucleation in Polymer Foaming DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Adam Craig Burley Graduate Program in Chemical and Biomolecular Engineering The Ohio State University 2012 Dissertation Committee: Professor Isamu Kusaka, Co-Advisor Professor David Tomasko, Co-Advisor Professor Kurt Koelling Copyright by Adam Craig Burley 2012 Abstract Polymer foams are used extensively in a variety of applications. A firm understanding of bubble nucleation is vital to predict foam properties based on process conditions. However, a number of theoretical and experimental challenges have thus far limited progress in this area. The use of a scaling theory is proposed to connect nucleation behavior to well understood bulk phase behavior of polystyrene-CO2 systems, which can be predicted by equations of state, such as the Sanchez–Lacombe or Statistical Associating Fluid Theory equation of state. Scaling theory of nucleation asserts that when the reversible work of critical nucleus formation is properly normalized and plotted against the normalized degree of supersaturation, the resulting scaling curve is insensitive to temperature and the materials being used. Once the form of the scaling function is known, it can be used to predict the nucleation barrier knowing only the initial foaming conditions and calculating only bulk thermodynamic values. Using an extension of diffuse interface theory, the slope of the scaling curve near saturation was determined. This initial slope constrains the scaling function for better predictions of the reversible work. The accuracy of the scaling theory was examined by comparison to experiments. The scaled free energy barriers determined from experiments are consistent with the scaling function so constructed, and the theoretical results qualitatively agree with those found previously. ii This document is dedicated to Grandpa George, with whom I wish I could have shared it. iii Acknowledgments I gratefully acknowledge my co-advisors, Dr. Isamu Kusaka and Dr. David Tomasko for their support, guidance, and expertise throughout my course of study. They have instilled in me a greater appreciation for multidisciplinary approaches and deep thinking. The way that Dr. Kusaka can incisively determine courses of action on the spot that I was not able to realize in days or weeks of thought will always amaze me. Dr. Tomasko’s ability to look at issues from novel angles is something that I hope I can fully develop in myself. I would also like to thank Dr. Kurt Koelling for his insights and useful comments both in group meetings and as a member of my exam committees. I would like to express my sincere thanks to Dr. Manish Talreja, Dr. Zhihua Guo, and Dr. Lu Feng for a variety of fruitful discussions, comments, and thought-provoking questions both in group meetings and in private conversations. I thank my family for their love and unflagging support of me in everything I do, and for always understanding when it seemed I might never leave grad school. Words fail to adequately describe the great debt I owe to my parents for instilling in me an insatiable spirit for the pursuit of knowledge. Everything that I have ever or will ever accomplish is in no small part thanks to you. That I am so undeniably your son is a testament to the iv great example you set for me and one of the greatest compliments I could ever hope to receive. Over the course of ten years and three degrees at The Ohio State University, I have created a cornucopia of lasting memories with countless friends. Whether we met in the dorms, as ChemEs, in grad school, through mutual friends, or just by plain chance, I am better for having known them. I will always cherish ChemE happy hour, pizza night, marathon Halo sessions, football games, Crew games, pickup soccer, and all sorts of other social events. I would like to especially thank Cory Gandert, Adam Lindsay, Jeff Svoboda, Dan Ramos, Laura Kunes, Charlie Benore, Chad Bernard, Tony and Sharon Frost, Katie Martin, Katie Richards, Lenore Jarvis, the Fujiis, Nicole Guzman, and Jenn Czocher for their help in distracting me from my worries, Dieter von Deak and Troy Vogel for also sticking around with me through grad school, and Elif Miskioglu for providing me with sanity (and sometimes cookies) over the past year. How firm thy friendship… v Vita February 17, 1984 ........................................ Born – Trenton, Ohio June 2006 .................................................... B.S. Chemical Engineering, The Ohio State University September 2006 to August 2007 .................. Distinguished University Fellow, The Ohio State University September 2007 to present .......................... Graduate Research Associate, Department of Chemical and Biomolecular Engineering March 2011 to March 2012 .......................... Distinguished University Fellow, The Ohio State University December 2011 ........................................... M.S. Chemical Engineering, Ohio State University vi Publications 1. Burley, A. C.; Feng, L.; Kusaka, I.; Tomasko, D. L.; Koelling, K.; Lee, L. J., "A Scaling Approach to Nucleation: Theory and Application in Polymer Foaming." 2011, in preparation. 2. Guo, Z.; Burley, A. C.; Koelling, K. W.; Kusaka, I.; Lee, L. J.; Tomasko, D. L., "CO2 Bubble Nucleation in Polystyrene: Experimental and Modeling Studies." Journal of Applied Polymer Science 2011, 125, 2170-2186 3. Tomasko, D. L.; Burley, A.; Feng, L.; Yeh, S.-K.; Miyazono, K.; Nirmal-Kumar, S.; Kusaka, I.; Koelling, K., "Development of CO2 for polymer foam applications." Journal of Supercritical Fluids 2009, 47, 493-499. Fields of Study Major Field: Chemical and Biomolecular Engineering vii Table of Contents Abstract .......................................................................................................................... ii Acknowledgments ......................................................................................................... iv Vita ............................................................................................................................... vi List of Tables................................................................................................................. xi List of Figures .............................................................................................................. xii Chapter 1: Literature Review ...........................................................................................1 Introduction .................................................................................................................1 Nucleation....................................................................................................................5 Nucleation Experiments ............................................................................................7 Nucleation Theory ....................................................................................................9 Simulation, SCFT, and DFT ....................................................................................... 12 Scaling Approach and Diffuse Interface Theory ......................................................... 15 Diffuse Interface Theory ......................................................................................... 16 Chapter 2: Equations of State and Phase Diagrams ........................................................ 24 Equations of State ...................................................................................................... 24 Cubic EOSs ............................................................................................................ 25 viii Lattice Fluid Theories ............................................................................................. 25 Sanchez-Lacombe .................................................................................................. 26 Off-Lattice Theories ............................................................................................... 26 Statistical Associating Fluid Theory ....................................................................... 27 Mixtures and Conformal Solution Theory ............................................................... 31 Phase Diagrams.......................................................................................................... 32 Phase Diagram Classification ................................................................................. 37 Chapter 3: Modeling Using the Sanchez-Lacombe EOS................................................. 49 Development and Formulation ................................................................................... 49 Computer Code ...................................................................................................... 53 Parameter Fitting ........................................................................................................ 54 Entropy Fitting ....................................................................................................... 57 Chapter 4: Modeling Using the iSAFT EOS .................................................................. 65 iSAFT Formulation .................................................................................................... 65 Phase Diagram Determination .................................................................................... 71 Parameter
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