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University of Cincinnati UNIVERSITY OF CINCINNATI Date: ___________________8th August 2008 I, ________________________________________________Prashant Rajan _________, hereby submit this work as part of the requirements for the degree of: Master of Science in: Department of Chemical and Materials Engineering It is entitled : Understanding aggregate morphology in colloidal systems through small-angle scattering and reverse Monte Carlo (RMC) simulations This work and its defense approved by: Chair: _______________________________Dale W. Schaefer _______________________________Greg Beaucage _______________________________Jude Iroh _______________________________Steve Clarson _______________________________ Understanding aggregate morphology in colloidal systems through small- angle scattering and reverse Monte Carlo simulations A thesis submitted to the Division of Research and Advanced Studies of the University of Cincinnati in partial fulfillment of the requirements for the degree of Master of Science in the Department of Chemical and Materials Engineering of the College of Engineering 2008 by Prashant Rajan B.E. University of Pune, Pune, India Committee Chair: Professor Dale W. Schaefer Abstract We have studied the three dimensional structure of aggregated colloidal silica at sub- micron length scales. Our efforts are part of an integrated research project[1-3] focused on constructing a verifiable model for reinforcement of elastomers by colloidal fillers using small- angle scattering techniques. Our work is aimed at developing a simulation-based modeling tool that enables us to visualize the microstructure of reinforcing fillers in three dimensions by fitting small-angle scattering data. We have developed a program based on ‘ C’ programming language to describe scattering from a single aggregate. Our simulation creates the aggregate using a particle-cluster aggregation mechanism. The simulation then proceeds to make random moves on the aggregate surface while simultaneously fitting small angle scattering data on the system under study. Our results provide a real-space picture of aggregate structure that is consistent with scattering data and images obtained from electron microscopy. We estimate primary particle size accurately by generating aggregate morphology visualizations for different primary particle sizes. Visualizations for different primary particle size and size distributions provide a different qualitative picture of aggregate morphology for the same mass fractal dimension. We arrive at the correct value for primary particle size by matching the visualizations with the slopes of power-law regime in the mass fractal domain. We have also distinguished between the morphology of silica aggregates in powder and inside elastomer by applying our program to small-angle-scattering data on silica powder and silica-filled-elastomer systems. ii iii ACKNOWLEDGMENTS: A Masters thesis is not usually an incredibly hard effort but this thesis is special in that it is the cumulative result of two years worth of experiences, work and relationships. I came to this program a naïve adolescent struggling to become an adult and I leave a much-chastened youth struggling to remain responsible. For this transition I thank first and foremost my advisor Dr. Dale Schaefer. To me he does and always will symbolize simplicity, hard work and the highest ethical and research standards. My gratitude to my parents and my sister who let a floundering idiot leave their care, doubtless with much fear and trepidation. My grateful thanks to Dr. Beaucage for teaching me that action speaks much louder than words. He helped me arrive at what is probably my biggest epiphany till date – learning IS indeed an end in itself. Thank you Dr. Vasudevan, for believing in me and giving me a chance when I thought I had none. I thank Drs. Clarson and Iroh for their cheerful support through my time here in Cincinnati. I thank Dr. T.K. Hatwar for giving me the opportunity to work with him through Spring. I thank Drs. Tom Blanton and Joel Shoreman for their enthusiasm in discussing my research. I also thank Dr. Jan Ilavsky and the Advanced Photon Source at Argonne. This thesis would not be possible without availing of the world-class facilities at Argonne. A big thank you to my friends in Cincinnati and elsewhere – Dhruva you remain my guiding star! Sujit, Rohan, Johny, Sachin, Aarti, Amrita – with friends like you, who needs therapists? Thank you Aniruddha, Ashay, Ashish, Adi, Ashwin, Mangya and the rest of the gang at West Nixon. You guys got me through the tough times. I reserve special thanks for Ram, who I am sure my elder brother would have been like. He perhaps has played a more immediate role than anyone else in effecting a semblance of change in me. I would like to thank Doug Kohls for helping with USAXS in samples. Also, iv many thanks to Doug, for showing me the difference between professional and personal trust. You gave me an accurate estimate of the price of both. Last but never the least, I thank Shweta. Words fail me when I think of the efforts you have taken to get me to this stage. This is just the beginning. And the fact that I am writing this acknowledgement is proof that love is enough. v TABLE OF CONTENTS: ABSTRACT ii ACKNOWLEDGEMENTS iv LIST OF FIGURES viii LIST OF TABLES xii 1. INTRODUCTION 1 1.1 BACKGROUND AND MOTIVATION 1 1.2 FRACTAL CONCEPTS 4 1.3 SMALL-ANGLE SCATTERING 6 1.4 REVERSE MONTE CARLO (RMC) METHODS: A BRIEF REVIEW 8 2. MATERIALS AND METHODS 17 2.1 ULTRA SMALL-ANGLE X-RAY SCATTERING (USAXS) 19 2.2 STRUCTURAL MODELING 19 2.2.1 RMC MODELING 20 2.3 IMPLEMENTATION OF RMC ALGORITHM 20 2.3.1 GENERATING THE AGGREGATE 21 2.3.2 EXECUTING MONTE CARLO MOVEMENT OF BEADS 21 2.3.3 FITTING THE DATA 23 2.4 TRANSMISSION ELECTRON MICROSCOPY (TEM) 23 3. RESULTS AND DISCUSSION 38 3.1 USAXS ANALYSIS 39 3.2 RMC ANALYSIS 39 3.3 TEM RESULTS 41 3.4 ANALYSIS OF COLLOIDAL SILICA DISPERSED IN RUBBER 52 vi 3.5 RELEVANCE OF RMC AND SMALL ANGLE SCATTERING ANALYSIS TO 55 REINFORCEMENT STUDIES 3.6 UNIQUENESS OF SOLUTION 60 3.7 ACCOUNTING FOR POLYDISPERSITY BETWEEN AGGREGATES 63 4. CONCLUSIONS AND FUTURE WORK 64 REFERENCES 66 APPENDICES 68 72 vii LIST OF FIGURES Figure 1. Mass Fractal form of a Romanesco broccoli (Brassica oleracea) Figure 2. Crumpled paper as surface fractal in 3 dimensions Figure 3. Scattering intensity plotted against the scattering vector q for a sample of precipitated silica exhibiting 2 levels of structure as observed through Ultra Small Angle X-ray Scattering (USAXS) Figure 4. Unified fit model applied to USAXS data on precipitated silica sample dispersed in rubber. Rg1 and Rg2 correspond to the radius of gyration calculated for silica primary particle and aggregate respectively Figure 5. Graphical representation of initial aggregate structure for an aggregate composed of 220 beads Figure 6. Normalized analytical form factor for a solid sphere (R = 8.5 nm) having uniform scattering length density Figure 7. Effect of analytical form factor P(q) on intensity I(q) sim calculated by the RMC program Figure 8. RMC fit using level 1 Unified fit in form factor P(q) calculation Figure 9. Optimizing the structure factor S(q) calculation at each Monte Carlo step by calculating only the contribution of the move under consideration to the overall structure factor S(q). Figure 10. Structure factor evolution over the duration of a simulation Figure 11. Effect of monodisperse spherical assumption on S(q) and I(q) calculated by RMC modeling program Figure 12. Polydisperse collection of beads viii Figure 13. Effect of polydispersity on RMC calculated structure factor S(q) Figure 14. Unified fit intensity modeled with RMC for a uniform distribution of bead radii (0.5 Ǻ < R < 175 Ǻ), Aggregation number, z = 107 Figure 15. Chi square ( χ2) with no fluctuations allowed Figure 16. Chi square ( χ2) calculated with fluctuations allowed Figure 17. USAXS curves of colloidal silica samples:(a) DSI series: DSI pH6 and DSI 1289, (b) Goodyear: GY5011, (c) Nissan Snowtex. Flat background was subtracted to emphasize the power-law profiles at high q. Data have been scaled vertically to match in the high q region for comparison Figure 18. Evolution of chi square over the number of Monte Carlo moves for DSI pH6, DSI 1289, GY 5011 and Nissan Snowtex Figure 19. Graphical representatations of aggregate structures. Figure 20. Probability distributions of primary particle radii as estimated by Irena modeling of Unified fit to USAXS data Figure 21. Fits obtained from RMC modeling of Unified intensity for DSI pH6, DSI 1289, GY 5011 and Nissan Snowtex® Figure 22. Aggregate morphology visualization: Nissan Snowtex "String of pearls", slope of mass fractal domain P = - 1.68 Figure 23. Aggregate morphology visualization: GY 5011, slope of mass fractal domain P = -2.7 Figure 24. Visualizing aggregate morphology for DSI 1289, mass fractal dimension as obtained from Unified fit is -2.53 ix Figure 25. Visualizing aggregate morphology of DSI pH6 through RMC modeling. Mass fractal dimension obtained from Unified fit is - 3.0 indicating dense compact aggregates Figure 26. Unified fit to DSI pH6 for smaller sized primary particles (Rg1 = 155 Å). Figure 27. Visualizing aggregate morphology of DSI pH6 through RMC modeling. Mass fractal dimension obtained from Unified fit is - 3.06 indicating dense aggregates. Figure 28. Aggregate visualization for incorrectly calculated radius of gyration (Rg = 458 Å) of primary particles - DSI pH6.Through RMC visualization, we are able to observe an open fractal aggregate which is inconsistent with the the calculated slope of the mass fractal domain (-3.06). We understand that the intensity curve was incorrectly interpreted leading to an erroneus assumption of broad particle size distribution along with large Rg for primary particles.The aggregates are actually composed of smaller primary particles that form a dense cluster that is more representative of the slope in the mas fractal domain.
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