## Optimization of Particle Synthesis - New Mathematical Concepts for a Controlled Production of Functional Nanoparticles

### Optimierung in der Partikelsynthese - Neue mathematische Konzepte für eine gezielte Herstellung funktionaler Nanopartikel

Please always quote using this URN: urn:nbn:de:bvb:29-opus4-40395
• Embedded in an interdisciplinary research project, the present work investigates the modeling, simulation, and optimization of specific processes for the production of functional nanoparticles. The examined material systems represent a selection of important core building blocks for future nanotechnologies. Depending on the application, a well-defined particle size distribution of the final product is required. The involved mechanisms (e.g. reaction, growth, ripening, and agglomeration) are described in the modeling by a hyperbolic partial integro-differential equation coupled to one or more ordinary differential equations. The successful validation against experimental data combined withEmbedded in an interdisciplinary research project, the present work investigates the modeling, simulation, and optimization of specific processes for the production of functional nanoparticles. The examined material systems represent a selection of important core building blocks for future nanotechnologies. Depending on the application, a well-defined particle size distribution of the final product is required. The involved mechanisms (e.g. reaction, growth, ripening, and agglomeration) are described in the modeling by a hyperbolic partial integro-differential equation coupled to one or more ordinary differential equations. The successful validation against experimental data combined with the techniques of optimal control theory thereby allow for a targeted manipulation of the underlying processes. The developed methods establish in many cases for the first time a systematic approach for the production of tailor-made nanoparticles.

Author: Michael Gröschel urn:nbn:de:bvb:29-opus4-40395 978-3-944057-12-5 FAU Studies Mathematics & Physics (2) FAU University Press Erlangen Günther Leugering, Wolfgang Peukert Doctoral Thesis English 2013 FAU University Press Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Naturwissenschaftliche Fakultät 2013/09/10 2013/12/10 Funktionale Nanopartikel; Integrodifferentialgleichung; Nichtlineare partielle Differentialgleichung; Partikelgrößenverteilung; Partikeltechnologie; Populationsbilanzgleichung Optimale Kontrolle; Nichtlineare Kontrolltheorie; Nichtlineare Optimierung; Numerische Mathematik; Mathematische Modellierung; Nanopartikel; Prozessoptimierung; Parameteridentifikation; Teilchentechnologie; Steife nichtlineare Differentialgleichung; Bilineares System; Adjungierte Differentialgleichung; Finite-Volumen-Methode; Verteilungsfunktion; Glattheit Mathematik VIII, 211 S. Parallel erschienen als Druckausgabe bei FAU University Press Naturwissenschaftliche Fakultät / Department Mathematik G. Mathematics of Computing 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Lxx Hyperbolic equations and systems [See also 58J45] / 35L65 Conservation laws 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q70 PDEs in connection with mechanics of particles and systems 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Rxx Miscellaneous topics (For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDE, see also 60H15) / 35R09 Integro-partial differential equations [See also 45Kxx] 74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Sxx Numerical methods [See also 65-XX, 74G15, 74H15] / 74S10 Finite volume methods 93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Cxx Control systems / 93C20 Systems governed by partial differential equations 70.00.00 CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES / 78.00.00 Optical properties, condensed-matter spectroscopy and other interactions of radiation and particles with condensed matter / 78.20.-e Optical properties of bulk materials and thin films (for optical properties related to materials treatment, see 81.40.Tv; for optical materials, see 42.70-a; for optical properties of superconductors, see 74.25.Gz; for optical properties of rocks and mine open_access Universität Erlangen-Nürnberg / FAU University Press Creative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 3.0