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|Title: ||Modeling And Simulation Frameworks For Synthesis Of Nanoparticles|
|Authors: ||Chakraborty, Jayanta|
|Advisors: ||Kumar, Sanjeev|
|Keywords: ||Nanoparticles - Modeling and Simulation|
Multidimensional Population Balance Equations
|Submitted Date: ||Aug-2008|
|Series/Report no.: ||G22884|
|Abstract: ||Nanoparticles are used in various applications like medical diagnostics, drug delivery, energy technology, electronics, catalysis etc. Although particles of such small dimensions can be synthesized through various methods, the liquid phase synthesis methods stands out for their simplicity. Typically, these methods involve reaction of precursors to form solute. At high concentration of solute, nucleation commences and nuclei are formed. These nuclei grow in size by assimilating solute from the bulk. Stabilizers or capping agents compete with solute for adsorption on the surface of a growing particle. Two partially protected particles can form bigger particle by coagulation. Uncontrolled turbulent flow field in laboratory scale reactors combined with all the above quite fast and poorly understood steps often lead to poorly controlled synthesis of particles. In many a systems, it also leads to very poor reproducibility. Any attempt to synthesis nanoparticles at engineering scale, with good control on mean size and polydispersity, requires quantitative understanding of the synthesis process. It can then be combined with description of other transport processes in reactors to optimize synthesis protocols.
Two main factors hinder progress in this direction: complex and often poorly understood chemistry, and inefficient tools to simulate particle synthesis. In the first part of the thesis, a quantitative model is developed for tannic acid method of synthesis of gold nanoparticles. It showcases the approach used to model a system with poorly understood chemistry and which defies an understanding through the widely used homogeneous nucleation based mechanism for particle synthesis. An organizer based mechanism in which tannic acid brings together nucleating species to facilitate nucleation is invoked. Simple reaction network based models however fail to explain the experimental findings. The underlying chemistry is explored to develop a comprehensive reaction network. This network is used as a guide to seek pathways which can mimic burst of nucleation, a characteristic of homogeneous nucleation based mechanism, through self-limiting nucleation, and various other features present in the experimental data. After successful prediction of all the features of the experimental data through this network, a minimal organizer based mechanism which leads to self-limiting nucleation is developed. The minimal organizer model offers itself as a competing and alternative mechanism to explain nanoparticle synthesis. A few new predictions made by the new model are verified by others in our group.
Monte-Carlo (MC) simulations are used as a powerful tool to simulate stochastic processes. Their application to nanoparticle synthesis is limited by three problems: (i) zero initial rate of stochastic processes which leads to infinite time step at the beginning of the simulation, (ii) sensitively time dependent rate of stochastic processes, and (iii) computation intensive simulations. We propose a new approach to carry out MC simulations. It makes use of simulation results obtained with systems of extremely small sizes. These system size dependent predictions, obtained at substantially reduced computational cost are used to construct results for system of infinite size. The approach is based on a new power law scaling that we have found in this work. An efficient implementation of MC simulation for time dependent rate processes is also developed. In this method, an additional variable is introduced for inter-event evolution. It increases the number of differential equation by one, but significantly reduces the computational effort required to estimate the interval of quiescence for time dependent rate processes. All the above ideas are combined in the new approach to simulate complete size distribution for simultaneous nucleation and growth of nanoparticles for a system of infinite size from erroneous simulations carried out with three extremely small size systems.
A new framework for solving multidimensional population balance equations (PBEs) which routinely arise in modeling of nanoparticle synthesis is also developed. The new framework advances the concept of minimal internal consistency of discretization. It suggests that an n dimensional PBE is a statement of evolution of population of particles while accounting for how n internal attributes of particles change in particulate events. Thus, a minimum of n + 1 attributes of particles, instead of 2n attributes used hitherto, need to be represented perfectly in discrete representation. This is termed as the concept of minimum internal consistency of discretization in this work. The elements used for discretization should therefore be triangles for 2-d, tetrahedrons for 3-d, and an object with n + 1 vertices in n-d space for the solution of a n-d PBE. The results presented for the solutions for 2-d and 3-d PBEs show the superiority of this framework over the earlier framework. The present work also shows that directionality of elements plays a critical role in the solution of multi-dimensional PBEs. A mere change in connectivity of pivots in space, which changes their directionality, is shown to influence numerical results. This work led to new radial discretization of space, which has been followed up by others in the group and demonstrated to be quite powerful.
A physical model is developed to understand digestive ripening of nanoparticles, a technique which is in extensive use in the literature to improve monodispersity of nanoparticles. The physical model is based on critical analysis of the large body of experimental findings available in the literature on several variations of this technique. The physical model is the first one to consistently and qualitatively explain all the reported experimental findings.|
|Appears in Collections:||Chemical Engineering (chemeng)|
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