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An Abstract of a Dissertation Kansas State BROWNIAN DYNAMICS STUDY OF THE SELF-ASSEMBLY OF LIGATED GOLD NANOPARTICLES AND OTHER COLLOIDAL SYSTEMS by SIDDIQUE J. KHAN M.S., PIEAS,Islamabad, 2004 AN ABSTRACT OF A DISSERTATION submitted in partial fulfillment of the requirements for the degree DOCTOR OF PHILOSOPHY Department of Physics College of Arts and Sciences KANSAS STATE UNIVERSITY Manhattan, Kansas 2012 Abstract We carry out Brownian Dynamics Simulations to study the self-assembly of ligated gold nanoparticles for various ligand chain lengths. First, we develop a phenomenological model for an effective nanoparticle-nanoparticle pair potential by treating the ligands as flexible polymer chains. Besides van der Waals interactions, we incorporate both the free energy of mixing and elastic contributions from compression of the ligands in our effective pair po- tentials. The separation of the nanoparticles at the potential minimum compares well with experimental results of gold nanoparticle superlattice constants for various ligand lengths. Next, we use the calculated pair potentials as input to Brownian dynamics simulations for studying the formation of nanoparticle assembly in three dimensions. For dodecanethiol ligated nanoparticles in toluene, our model gives a relatively shallower well depth and the clusters formed after a temperature quench are compact in morphology. Simulation results for the kinetics of cluster growth in this case are compared with phase separations in binary mixtures. For decanethiol ligated nanoparticles, the model well depth is found to be deeper, and simulations show hybrid, fractal-like morphology for the clusters. Cluster morphology in this case shows a compact structure at short length scales and a fractal structure at large length scales. Growth kinetics for this deeper potential depth is compared with the diffusion-limited cluster-cluster aggregation (DLCA) model. We also did simulation stud- ies of nanoparticle supercluster (NPSC) nucleation from a temperature quenched system. Induction periods are observed with times that yield a reasonable supercluster interfacial tension via classical nucleation theory (CNT). However, only the largest pre-nucleating clus- ters are dense and the cluster size can occasionally range greater than the critical size in the pre-nucleation regime until a cluster with low enough energy occurs, then nucleation ensues. Late in the nucleation process the clusters display a crystalline structure that is a random mix of fcc and hcp lattices and indistinguishable from a randomized icosahedra structure. Next, we present results from detailed three-dimensional Brownian dynamics simulations of the self-assembly process in quenched short-range attractive colloids. Clusters obtained in the simulations range from dense faceted crystals to fractal aggregates which show ramified morphology on large length scales but close-packed crystalline morphology on short length scales. For low volume fractions of the colloids, the morphology and crystal structure of a nucleating cluster are studied at various times after the quench. As the volume fraction of the colloids is increased, growth of clusters is controlled by cluster diffusion and cluster- cluster interactions. For shallower quenches and low volume fractions, clusters are compact and the growth-law exponent agrees well with BinderStauffer predictions and with recent experimental results. As the volume fraction is increased, clusters do not completely coalesce when they meet each other and the kinetics crosses over to diffusion-limited cluster-cluster aggregation (DLCA) limit. For deeper quenches, clusters are fractals even at low volume fractions and the growth kinetics asymptotically reaches the irreversible DLCA case. BROWNIAN DYNAMICS STUDY OF THE SELF-ASSEMBLY OF LIGATED GOLD NANOPARTICLES AND OTHER COLLOIDAL SYSTEMS by SIDDIQUE J. KHAN M.S., PIEAS, Islamabad, 2004 A DISSERTATION submitted in partial fulfillment of the requirements for the degree DOCTOR OF PHILOSOPHY Department of Physics College of Arts and Sciences KANSAS STATE UNIVERSITY Manhattan, Kansas 2012 Approved by: Major Professor Amit Chakrabarti Copyright Siddique J. Khan 2012 Abstract We carry out Brownian Dynamics Simulations to study the self-assembly of ligated gold nanoparticles for various ligand chain lengths. First, we develop a phenomenological model for an effective nanoparticle-nanoparticle pair potential by treating the ligands as flexible polymer chains. Besides van der Waals interactions, we incorporate both the free energy of mixing and elastic contributions from compression of the ligands in our effective pair po- tentials. The separation of the nanoparticles at the potential minimum compares well with experimental results of gold nanoparticle superlattice constants for various ligand lengths. Next, we use the calculated pair potentials as input to Brownian dynamics simulations for studying the formation of nanoparticle assembly in three dimensions. For dodecanethiol ligated nanoparticles in toluene, our model gives a relatively shallower well depth and the clusters formed after a temperature quench are compact in morphology. Simulation results for the kinetics of cluster growth in this case are compared with phase separations in binary mixtures. For decanethiol ligated nanoparticles, the model well depth is found to be deeper, and simulations show hybrid, fractal-like morphology for the clusters. Cluster morphology in this case shows a compact structure at short length scales and a fractal structure at large length scales. Growth kinetics for this deeper potential depth is compared with the diffusion-limited cluster-cluster aggregation (DLCA) model. We also did simulation stud- ies of nanoparticle supercluster (NPSC) nucleation from a temperature quenched system. Induction periods are observed with times that yield a reasonable supercluster interfacial tension via classical nucleation theory (CNT). However, only the largest pre-nucleating clus- ters are dense and the cluster size can occasionally range greater than the critical size in the pre-nucleation regime until a cluster with low enough energy occurs, then nucleation ensues. Late in the nucleation process the clusters display a crystalline structure that is a random mix of fcc and hcp lattices and indistinguishable from a randomized icosahedra structure. Next, we present results from detailed three-dimensional Brownian dynamics simulations of the self-assembly process in quenched short-range attractive colloids. Clusters obtained in the simulations range from dense faceted crystals to fractal aggregates which show ramified morphology on large length scales but close-packed crystalline morphology on short length scales. For low volume fractions of the colloids, the morphology and crystal structure of a nucleating cluster are studied at various times after the quench. As the volume fraction of the colloids is increased, growth of clusters is controlled by cluster diffusion and cluster- cluster interactions. For shallower quenches and low volume fractions, clusters are compact and the growth-law exponent agrees well with BinderStauffer predictions and with recent experimental results. As the volume fraction is increased, clusters do not completely coalesce when they meet each other and the kinetics crosses over to diffusion-limited cluster-cluster aggregation (DLCA) limit. For deeper quenches, clusters are fractals even at low volume fractions and the growth kinetics asymptotically reaches the irreversible DLCA case. Table of Contents Table of Contents viii List of Figuresx List of Tables xii Acknowledgements xiii Dedication xiv 1 Introduction1 2 Phenomenological Modeling of the Ligated Gold Nanoparticles9 2.1 Components of the Effective NP-NP Interaction Potential . 11 2.1.1 van der Waals Interaction between Two Gold Nanoparticles. 11 2.1.2 Free energy of mixing. 11 2.1.3 Elastic Contribution from Ligand Compression. 13 2.2 Evaluation of the Effective NP-NP Interaction Potential . 13 2.3 NP-NP Interaction Based on Denting Conformation Model. 16 2.4 NP-NP Interaction Model Without Free Energy of Mixing. 18 2.5 Conclusion. 19 3 Brownian Dynamics Simulation Method 20 3.1 Brownian Motion . 21 3.2 Verlet Algorithm For Molecular Dynamics . 23 3.3 Brownian Dynamics Algorithm . 24 3.4 Simulation Parameters . 27 4 Self-Assembly of Dodecanethiol C12 and Decanethiol C10 Ligated Gold Nanoparticles from solution 29 4.1 Nucleation of the Nanoparticle Superclusters . 30 4.1.1 Classical Nucleation Theory . 31 4.2 Dynamical and Morphological analysis of Prenucleating SCs . 38 4.2.1 Cluster Dynamics . 38 4.2.2 Morphology and Shape of the Nucleating NPSCs . 40 4.3 Induction Time Analysis using Fisher's Droplet Model . 43 4.4 Aggregation at Higher Volume Fractions . 46 4.4.1 Structure Factor . 47 viii 4.4.2 Growth Kinetics in C12 Ligated System . 48 4.4.3 Growth Kinetics in C10 Ligated System . 52 4.5 Conclusion. 57 5 Crystalline Structure of the nucleating cluster in Dodecanethiol Ligated Nanoparticles 58 5.1 Radial Distribution Function . 59 5.2 Bond-orientational order Parameter . 62 5.3 Crystalline Structure of Dodecanethiol and Decanethiol Ligated System NPSCs 63 5.3.1 Possibility of icosahedral (ich) structure . 66 5.3.2 Evaluation of Crystalline Fraction . 71 5.4 Conclusion. 74 6 Self-Assembly in a model of short-range attractive colloids 76 6.1 Interaction Model Potential and Simulation Parameters . 79 6.2 Nucleation and Crystalline Structures for short-ranged shallow quenches . 80 6.3 Symmetric Structures of Small Size Clusters and Their Distribution . 88
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