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Multivariate Population Balance Equations for Functional Nanoparticle Formation Stabilized by Amphiphilic Block Copolymer Directed Assembly

Chungyin Cheng1, R. Dennis Vigil, and R. O. Fox2. (1) Chemical and Biological Engineering, Iowa State University, Ames, IA 50011, (2) Department of Chemical & Biological Engineering, Iowa State University, 2114 Sweeney Hall, Ames, IA 50011-2230

Nanoprecipitation [1] is a process to produce functional nanoparticles protected by amphiphilic copolymer directed assembly. In this process, organic drug and copolymers are dissolved in solvent and rapidly mixed with nonsolvent in a customized micro-device to create high supersaturation. The growth of nanoparticles is kinetically arrested by block copolymer assembly on the surface of the organic drug, and therefore a tunable and narrow particle size distribution is achievable. In order to simulate the Nanoprecipitation process, the population balance equations (PBEs) are solved to obtain the particle size distribution (PSD) information in the particulate flow system. A bi-variate PBE model is presented to describe the particle stabilization process. Different particle compositions are represented by a bi-variate PSD with the first coordinate for the organic drug and the second for the copolymer. The detailed kinetics of micellization for the copolymer directed assembly are discussed. A two-region Brownian aggregation kernel is introduced to account for cases with larger aggregation number for micelles, where the hydrophilic block forms a corona region to prevent further aggregation. In this work, the bi-variate PBEs are solved using the quadrature method of moments (QMOM) [2] to obtain faster computations and the results (mean particle size) are compared with experimental data.

[1] B. K. Johnson and R. K. Prud'homme. Flash nanoprecipitation of organic actives and block copolymers using a confined impinging jets mixer. Australian Journal of Chemistry 56(10):10211024, 2003.

[2] Marchisio, D. L. & Fox, R. O. Solution of population balance equations using the direct quadrature method of moments Journal of Aerosol Science 36, 43-73, 2005