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University of Florida Thesis Or Dissertation Formatting DYNAMICS AND MAGNETIZATION DYNAMICS OF MAGNETIC NANOPARTICLES IN APPLIED MAGNETIC FIELDS By ZHIYUAN ZHAO 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 2019 © 2019 Zhiyuan Zhao To my parents Wenzhong Zhao and Mei Zhu ACKNOWLEDGMENTS At first, I would like to express my deepest gratitude to my adviser Dr. Carlos Rinaldi for giving me this opportunity to pursue doctoral studies and guiding me on the research scopes and skills. I will also appreciate for his advice and encouragement during my doctoral study, for his teaching in Continuum Basis class that has a great influence on my life, and for his help on my professional presenting and writing skills. I would like to thank Dr. David P. Arnold, Dr. Jason Butler and Dr. Ranga Narayanan, for their guidance, suggestions and support on my doctoral research and dissertation writing. I would like to give a special thank to Dr. Isaac Torres-Díaz for his patient guidance and help on my learning of coding and computational simulations. The impressive and encouraging talks with him not only contributed to my research, but also motivated me to do better in both work and life. I would like to thank Camilo Velez Cuervo and Nicolas Garraud for their hard work and contributions to my research. I would like to thank all the members in the research group, for their helps and supports in my daily life. I would like to thank my parents for supporting me to pursue my dream, and for their understanding and encourage when I got frustrated. I would like to thank the Department of Chemical Engineering for giving me the opportunity to study in the University of Florida. The advanced research facilities and inspiring academic atmosphere provided me with higher perspectives and pave me way towards further study. 4 TABLE OF CONTENTS page ACKNOWLEDGMENTS ...................................................................................................... 4 LIST OF TABLES ................................................................................................................ 7 LIST OF FIGURES .............................................................................................................. 8 LIST OF ABBREVIATIONS ............................................................................................... 11 ABSTRACT ........................................................................................................................ 12 CHAPTER 1 SCOPE OF THE DISSERTATION ............................................................................. 14 2 BROWNIAN DYNAMICS SIMULATIONS OF MAGNETIC NANOPARTICLES CAPTURED IN STRONG MAGNETIC FIELD GRADIENTS .................................... 18 2.1 Background and Motivation .................................................................................. 18 2.2 Simulation Method ................................................................................................ 22 2.2.1 Model of Magnetic Dipole for Different Relaxation Mechanisms ............... 22 2.2.2 Motion Equation .......................................................................................... 25 2.2.3 Methods to Identify and Quantify Magnetically Captured Nanoparticles .. 32 2.2.4 Simulation Parameters and Conditions ...................................................... 33 2.3 Results .................................................................................................................. 34 2.3.1 Particle Motion ............................................................................................ 34 2.3.2 Magnetic Capture Rates for Different Relaxation Mechanisms ................ 35 2.3.3 Magnetic Capture Rates for Various Strengths of The External Magnetic Field Gradient.................................................................................... 36 2.3.4 Magnetic Capture Rates for Various Nanoparticle Volume Fractions ....... 37 2.3.5 Shape of Magnetic Nanoparticle Aggregates ............................................ 38 2.4 Conclusions .......................................................................................................... 39 3 MAGNETIZATION DYNAMICS AND ENERGY DISSIPATION OF INTERACTING MAGNETIC NANOPARTICLES IN ALTERNATING MAGNETIC FIELDS WITH AND WITHOUT A STATIC BIAS FIELD ............................................ 47 3.1 Background and Motivation .................................................................................. 48 3.2 Simulation Method ................................................................................................ 51 3.2.1 Brownian Dynamics Simulations ................................................................ 51 3.2.2 Simulation Parameters and Conditions ...................................................... 52 3.2.3 Simulations of Magnetorelaxometry ........................................................... 53 3.2.4 Simulations of Dynamic Magnetic Susceptibility ........................................ 55 3.2.5 Calculation of Energy Dissipation Rate ...................................................... 56 5 3.3 Results .................................................................................................................. 56 3.3.1 Equilibrium Response of Magnetization ..................................................... 56 3.3.2 Simulations of Magnetorelaxometry ........................................................... 57 3.3.3 Energy Dissipation Rate in An Alternating Magnetic Field ........................ 60 3.3.4 Effect of Static Bias Magnetic Field on Energy Dissipation Rate .............. 63 3.4 Conclusions .......................................................................................................... 64 4 EFFECTS OF PARTICLE DIAMETER AND MAGNETOCRYSTALLINE ANISOTROPY ON MAGNETIC RELAXATOIN AND MAGNETIC PARTICLE IMAGING PERFORMACE OF MAGNETIC NANOPARTICLES ............................... 79 4.1 Background and Motivation .................................................................................. 80 4.2 Simulation Method ................................................................................................ 85 4.2.1 The Landau-Lifshitz-Gilbert (LLG) Equation .............................................. 85 4.2.2 Simulation Parameters and Conditions ...................................................... 88 4.2.3 Simulations of Magnetorelaxometry ........................................................... 89 4.2.4 Simulation Parameters and Conditions ...................................................... 91 4.3 Results .................................................................................................................. 93 4.3.1 Equilibrium Response of Magnetization ..................................................... 93 4.3.2 Simulations of Magnetorelaxometry ........................................................... 94 4.3.3 Magnetization Signal in An Alternating Magnetic Field ............................. 99 4.4 Conclusions ........................................................................................................102 5 CONCLUSION REMARKS .......................................................................................118 LIST OF REFERENCES .................................................................................................123 BIOGRAPHICAL SKETCH ..............................................................................................133 6 LIST OF TABLES Table page 3-1 Diameters used in simulations (퐷p) and corresponding diameters (퐷p,fit) obtained by applying a nonlinear fit to the Langevin function. .............................. 67 3-2 Magnetic relaxation time (휏̃) for the case that an applied static magnetic field is suddenly turned on and off for various Langevin parameters and strengths of inter-particle interactions. ................................................................................... 69 4-1 Scaled anisotropy energy ∆퐸ani⁄푘B푇 for a representative anisotropy constant value of 퐾 = 13.5 kJ⁄m3 and various nanoparticle diameters. ...........................104 7 LIST OF FIGURES Figure page 2-1 Magnetic field gradients in simulations. ................................................................. 41 2-2 Zoomed-in 3D configurations snapshots close to the capture line at various times for magnetic nanoparticles that relax by different mechanisms. ................. 42 2-3 Trajectories of representative magnetic nanoparticles that respond to the applied magnetic field by different mechanisms.................................................... 43 2-4 Number of captured magnetic nanoparticles as a function of capture time for magnetic nanoparticles that relax by the Brownian and Néel relaxation mechanisms............................................................................................................ 43 2-5 Number of captured magnetic nanoparticles as a function of capture time for various maximum Langevin parameters and magnetic nanoparticles that relax by different mechanisms. .............................................................................. 44 2-6 Number percentage of captured magnetic nanoparticles as a function of capture time for various particle volume fractions and magnetic nanoparticles that relax by different mechanisms. ....................................................................... 45 2-7 Average height and width of magnetic nanoparticle aggregates as a function of capture
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