MULTISCALE SIMULATION OF POLYMER NANOPARTICLES PRECIPITATION FOR PHARMACEUTICAL APPLICATIONS

This work focuses on the development and use of a multiscale computational tool for the simulation of the process of precipitation of polymeric nanoparticles in micro-mixers. This process, as will be shown through the rest of the thesis, is not very easy to model with single scale model (i.e., Computational Fluid Dy- namics, Population Balances, Molecular Dynamics). The main reason stands in the complex behaviour of the system investigated (the polymer); the behaviour at atomistic scale influences the macro-scale. With micro-scale (which is equivalent in our notation to the atomistic scale) we refer to all the phenomena occurring at length-scales of nanometres (1 nm = 10−9 m) and time-scales of picoseconds (1 ps = 10−12 s), whereas with macroscale we intend all the phenomena occur- ring at length-scale of meters and at time-scale of seconds. There are different models used to describes these (apparently) uncorrelated phenomena. Computa- tional Fluid Dynamics (CFD) which describes at the macroscale the motion of a fluid in a given domain often coupled with Population Balance Model (PBM) to describe the presence of a dispersed colloidal phase, and Molecular Dynamics (MD) which describes the motion of a collection of atoms in an interval of time. The coupling of these methods in a unique description of the problem is called multiscale modelling, a research area which has raised much interests in the last few years. In this work, precipitation of nanoparticles occurs in a micromixer, is investigated trough CFD-PBM, whilst the precipitation process is described by extracting some information from MD simulations, hence, coupling these differ- ent models in one description. The thesis is structured as follows: 1. The First Chapter is an introduction to the investigated problem. A brief description of the use of polymer nanoparticles in the pharmaceutical in- dustry is given, with the current state of the art. A brief overview of the different production processes and devices used will be also given 2. The Second Chapter in intended to give all the theoretical background re- quired for the understanding of the subsequent chapters. Starting from the very beginning, the governing equations for the generic N-body prob- lem are derived together with the description of the theoretical tools for the molecular dynamics. By using the Boltzmann Equation we show how to move from a description of the problem a the micro-scale (here repre- sented by the MD) to a description of the problem at the macro-scale (rep- resented by the CFD). The introduction of the Boltzmann equation (and the mesoscale) is also useful since the PBM is a kinetic equation very similar to the Boltzmann equation 3. The Third Chapter involves the description of the CFD model of the micro- mixer used in this study. The polymeric nanoparticles precipitation model is presented along with its intrinsic limitations highlighting the need of a more fundamental approach 4. In the Fourth Chapter we discuss the improvement of the CFD model by developing a nucleation theory adequate to the description of the polymer particle formation. The parameters appearing in this theory are estimated by using the standard full atoms MD simulations. Eventually the nucle- ation theory is integrated into the CFD-PBM and used to simulate the entire process 5. The Fifth Chapter is devoted to the extension of the MD framework. In fact, in order to further investigate the polymer particle formation process, larger systems, involving many polymeric chains have to be described. This requires some form of partial coarse-graining, resulting in hybrid atomistic/coarse-grained model. The framework to do this is in this chapter described, showing how the model allows to speed up the simulation by ne- glecting some Degrees of Freedom of the original problem but maintaining the necessary details where needed 6. In the last Chapter some conclusions from the simulations presented are drawn