INVESTIGATION AND CHARACTERIZATION OF THE DISPERSION OF NANOPARTICLES IN A POLYMER MATRIX BY SCATTERING TECHNIQUES By MARIE CHRISTINE KISSINGER-KANE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007 © Marie Christine Kissinger-Kane 2007 To my husband, Kevin iii ACKNOWLEDGMENTS I would first like to acknowledge my husband, Kevin, and my parents for their constant love and support. Without them, I am sure this would have been much more difficult to accomplish. Secondly, I would like to thank my advisor, Dr. Brij Moudgil and my committee co-chair, Dr. Anthony Brennan. Their knowledge and guidance have been invaluable tools throughout my graduate school journey. Dr. Moudgil, I thank you for thoroughly preparing me for my future career and making me the confident person that I am today. Dr. Brennan, I thank you for your unending encouragement and for not letting me take myself too seriously. I would like to also acknowledge the rest of my graduate committee for their guidance and support: Dr. Laurie Gower, Dr. Kevin Powers, Dr. David Tanner, and Dr. Charles Beatty. My special thanks to Dr. Powers; his “out of the box” ideas and countless discussions with me, academic or not, fueled my passion for learning and discovery. I would also like to acknowledge those outside of the University of Florida that have provided assistance. Dr. Rick Beyer at the Army Research Labs at Aberdeen Proving Ground provided the small angle x-ray measurements, and Dr. J. David Londono at DuPont assisted with ultra small angle x-ray experiments. Their collaboration has been an invaluable tool and I would now consider myself among a small elite group of x-ray scattering specialists. Next, I would like to acknowledge my best friend and colleague, Sara Jensen (Homeijer), for her friendship, encouragement and assistance (patience) with TEM iv micrographs. Next, I would like to acknowledge the faculty and staff of the Particle Engineering Research Center. Especially, I would like to thank Mr. Gary Scheiffele for laboratory help and Gill Brubaker for helpful discussions on Mie Theory. I would also like to thank my friends and colleagues at the Particle Engineering Research Center for their laughter, friendship, and helpful discussions. The Particle Engineering Research Center (PERC) at the University of Florida, the National Science Foundation (NSF Grant EEC-94-02989), the United States Air Force, and the Industrial Partners of the PERC are graciously acknowledged for financial support of this research. Finally, I would like honor the memory of my late committee member, Dr. Abbas Zaman, who took the time to show me the value of rheology measurements and always had a smile and kind word for me. He will be sorely missed. v TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................................................................................. iv LIST OF TABLES............................................................................................................. ix LIST OF FIGURES .............................................................................................................x ABSTRACT..................................................................................................................... xiv CHAPTER 1 INTRODUCTION ........................................................................................................1 2 LITERATURE REVIEW .............................................................................................5 Particle Dispersion Studies...........................................................................................5 Particle Surface Modification................................................................................6 Mechanical Dispersion ..........................................................................................7 Dispersion Equations....................................................................................................9 Correlation of Dispersion with Material Properties....................................................12 Mechanical Properties .........................................................................................12 Optical Density....................................................................................................13 Molecular Modeling of Nanocomposite Dispersion...................................................13 Light Scattering ..........................................................................................................15 Background..........................................................................................................15 Particle Size Measurement ..................................................................................17 Small Angle and Ultra Small Angle X-ray Scattering................................................18 X ray Data Analysis.............................................................................................19 The Guinier regime ......................................................................................20 The power-law regime .................................................................................21 A Unified Fit model .....................................................................................22 The Porod regime .........................................................................................22 Scattering Techniques for Dispersion Measurements .........................................23 Microscopy .................................................................................................................24 ASTM Standard for Dispersion of Carbon Black in Rubber......................................24 Scope of Proposed Research.......................................................................................27 3 MATERIALS AND METHODS ...............................................................................29 vi Materials .....................................................................................................................29 Nanoparticles.......................................................................................................29 Polymer Matrix....................................................................................................32 Particle Surface Treatment- Silane Coupling Agent ...........................................34 Methods ......................................................................................................................35 Nanocomposite Formulation ...............................................................................35 Four levels of particle dispersion .................................................................36 Solvent selection for fractionated sample....................................................44 Particle agglomerate sedimentation .............................................................48 Optical Bench ......................................................................................................49 Optical components......................................................................................49 Detector Selection ........................................................................................50 Laser calibration...........................................................................................51 Instrument calibration ..................................................................................52 Snell’s Law Correction.................................................................................53 Scattering Measurements.....................................................................................55 Light scattering (3 μm < d < 90 nm) ............................................................56 Ultra small angle x-ray scattering (2 μm < d < 80 nm)................................58 Small angle x-ray scattering (100 nm < d < 1 nm).......................................59 Scattering data analysis with IGOR .............................................................60 Additional Characterization.................................................................................61 Optical density..............................................................................................61 Commercial light scattering instruments......................................................62 Transmission electron microscopy...............................................................63 Scanning electron microscopy .....................................................................64 4 SCATTERING THEORY ..........................................................................................65 General Scattering Theory..........................................................................................65 Boundary Conditions...........................................................................................67 The Amplitude Matrix.........................................................................................68 The Mueller Matrix .............................................................................................70 Scattering of a Sphere..........................................................................................71 Angular Dependent Scattering ............................................................................71 The Length Scale ........................................................................................................72