RICERCA ITALIANA     

Research program

Multiscale modelling and development of process reactors for polymeric nanoparticle precipitation

University Co-ordinator

Politecnico di TORINO - SCIENZA DEI MATERIALI E INGEGNERIA CHIMICA - ()

Research Unit Leader

Marco Vanni

Description

The research work of our unit is finalised to increase the knowledge on the fundamental processes involved in the formation of organic nanoparticles with a polymeric structure by solvent displacement method. The work plan includes both modelling and experimental activities and has as specific objectives:
a) development of mathematical tools for the simulation of the micro and nano-scale phenomena and their implementation in a commercial CFD code;
b) better understanding of the mechanisms of condensation, precipitation, growth and aggregation that determines the evolution of the nanoparticles;
c) analysis of the potential and of the limitations of the two reactor configurations (impinging jet and vortex reactor) for the production of the considered nanoparticles.
The development of mathematical tools for the simulation of the micro and nano-scale phenomena is a purely theoretical and independent line of research (line a); on the contrary, the other two objectives will be pursued by combining the experimental investigation performed in the reactors with modelling analysis of the nanoprecipitation process (line b).


Line a) Development of modelling tools for the simulation of subgrid scale processes

This research line is dedicated to the development of the mathematical methods that will be implemented in the computational fluid dynamics code for the simulation of subgrid-scale processes, that is, of the processes occurring at scales significantly smaller than the size of the computational mesh. We will consider the implementation of the population balance and of the micro-mixing model. The CFD code Fluent will be used in this and in the subsequent phases of the project.

Concerning the population balance equation, we will adopt the approach called DQMOM (Direct Quadrature Method Of Moments). It is a method of moments capable of evaluating the integral properties of the population with good accuracy and low computational load. Since the structure of the moment transport equations for this method are very similar to those of the equations for scalar transport, the DQMOM method can be implemented very effectively in CFD codes. The main problem in this case will be to develop the ability to deal with bivariate or multivariate particle populations, required to characterize our product. During this phase most of the development and validation work will be performed on simplified configurations by comparison with the results of Monte Carlo simulations, that are capable of dealing with multivariate populations in a very simple way.

The description of micro-mixing will be based on a finite-mode pdf method, which will be improved and implemented in the CFD code. The model currently used by our research group is based on the investigation of the evolution of the probability density function (pdf) only monitoring its first three moments with respect to a non-reacting scalar, the so-called mixture fraction. Using this approach we are able to model the properties of the distribution up to the variance, that corresponds to the second order moment. Recently the integration of this approach with the quadrature method of moments has been investigated. Using this innovative approach it is possible to guarantee a better description of higher order moments of the pdf of all scalars involved, comparable to that of the full pdf approach but with much lower computational costs. Actually a full pdf approach would be intractable in this case, because of the computational load. In addition the DQMOM implementation of the finite mode pdf and of the population balance share the same mathematical framework, making their integration in the CFD code very effective.

The micromixing models and the population balance solver will be implemented in Fluent as "user defined subroutines". These subroutines will be used also by the research unit of Bologna for the simulation of their systems.

This phase will be completed within the first 9 months of the project.


Line b) Analysis of the process of nanoprecipitation in the impinging jet and in the vortex reactor

The main scope of the analysis performed by our unit is to elucidate and to evaluate quantitatively the processes of micro and nanoscale that take place in the production of nanoparticles. The nanoprecipitation will be characterized in the confined impinging jet reactor and in the vortex reactor, which are two of the configurations tested in the global project for a comparison of different reactor solutions. The experimental study will be coupled with theoretical analysis of the mechanisms of micro and nanoscale. The work will be divided in the following steps:

1. Set-up of the reactors
The confined impinging jet reactor is formed by a cylinder where the two colliding jets of water and solvent are injected. The system is very small, the volume being about 1 cm3. This configuration generates intense turbulence with extremely low local mixing time: this feature makes the reactor particularly suited for precipitation processes, since the properties of the precipitate depend mostly on the slower processes, which are nucleation, growth and condensation in this case, if the reactor is operated under appropriate conditions. The properties of the precipitate thus become nearly independent from the chaotic effects of turbulence on mixing and the formed solid phase is more uniform. Proper operation of the impinging jet reactor requires the two colliding jets to have similar strength, and consequently its use is limited to systems with ratio between solvent and water flow rates close to one. From this point of view, greater flexibility is provided by the second configuration studied in this research project, the vortex reactor, in which the two jets are injected circumferentially in the cylindrical chamber, in such a way as to generate a vortex pattern.
RANS type CFD simulations of the flow field (that is, simulations based on the Reynolds Averaged Navier Stokes equations) in these reactor configurations will be tuned and validated by comparison with DNS (Direct Numerical Simulation) and LES (Large Eddy Simulation) of the same system obtained by the research unit of Udine. DNS does not use any closure assumption for turbulence and therefore it should be regarded as a having the same reliability of a true experiment, but giving results with a detail and a level of information highly superior. The requirement for accurate RANS simulations is essential for the subsequent studies of micromixing and of particle formation in the system, which cannot be modelled by DNS, due to the extremely small scales involved.

2. Characterization of micromixing and precipitation for simple reacting systems
In order to verify the quality of our modelling approach we plan to adopt at first the large amount of experimental data on fast competitive reactions collected by Johnson and Proud'homme (AIChE J., 49, p. 2264, 2003) for an impinging jet reactor similar to our one. This information will be used to tune and validate our micromixing model. Furthermore, to characterize the ability of our models to predict the precipitation process, we plan to perform a set of experiments concerning the precipitation of barium sulphate in aqueous solution. A similar analysis will be performed in parallel also by the other research units of Bologna and Palermo for a first comparison of the different tested reactor configurations. Even if it is not a system of practical interest, barium sulfate will be adopted in this step of the project because is produced by inexpensive reactants, does not present any problem of waste disposal, and kinetic laws are well known. There exists an extensive literature on the subject and our research unit has wide expertise with this system due to its past activity. Therefore it will provide the other units with information concerning modelling and experimental methods of analysis. The effect of operating conditions on particle morphology and size distribution will be investigated in detail. The size distribution of the solid precipitate will be characterized through laser light scattering. Precipitate morphology will be studied by using both conventional and high resolution Scanning Electron Microscopy.
The phases 1 and 2 of line b) will be developed in parallel with research line a), described previously. They will be completed within the first 9 months of the project.

3. Precipitation of polymeric nanoparticles
In these tests we will investigate the precipitation (induced by solvent displacement) of nanoparticles formed exclusively by polymer, without active principle. A first series of experiments will be performed by precipitating polycaprolactone (PCL) by displacement of acetone with water. PCL with narrow and well characterised molecular weight distribution is available commercially and provides a simple case to test the ability of our model to predict the turbulent precipitation of organic substances. Since the condensation of the polymeric chains depends on the insolubility of the polymer in the presence of water, in order to characterize the mechanism of condensation, the knowledge of the solubility of the polymer in water-solvent mixtures is required. Experimental determination of the solubility of PCL in water-acetone mixtures through turbidimetry is thus planned.
As a second part of this step, we will consider the polymer chosen for the production of the drug nanoparticles, poly(methoxy polyethylene glycol cyanoacrylate-co-hexadecylcyanoacrylate). The polymer will be produced by our unit according to the indications given by research unit of Torino-University (which has good expertise in this field) and characterised by light scattering for the distribution of molecular weights. As before, an experimental determination of solubility is planned. Due to their expertise, the unit of Torino-Università will give us also preliminary information on suitable operating conditions and the proper solvents for the precipitation process.
The block co-polymer structure of this macromolecule allows the attainment of precipitated particles with a core formed by the hydrophobic aliphatic chains and an external region rich in polyethylene-glycol groups, but makes the analysis of the process much more complex than in the case of PCL. With this new polymer the formation and the morphology of the particles is strongly affected by the mutual interaction between the hydrophilic and the hydrophobic polymeric chains and thus on their relative lengths.

During this phase too, the effect of operating conditions on particle morphology and size distribution will be investigated by laser light scattering and electronic microscopy.

4. Precipitation tests performed with the polymer and an organic active principle.
The tests performed with the polymer and the organic active principle are aimed to the identification of the operating condition required for the reactor. To obtain the required product, with the active principle included in a polymer matrix, the characteristic times for condensation/aggregation of the polymer and nucleation/growth of the active principle must be similar, otherwise the product would be formed either by the polymer or by the active principle only. In order to obtain such a result, one can act on the operating variables, particularly the concentration of the reactants dissolved in the organic solution. The information provided by the research unit of Udine, about the detailed history of the concentration field seen by the particles or by small lumps of fluid during their life, obtained by Lagrangian analysis based on DNS, will be fundamental in order to understand in detail the mechanism of precipitation. The evolution of the population of particles for this process has to be modelled by a population balance at least bivariate (i.e., with two internal coordinates), capable of considering simultaneously the amount of polymer and of active principle contained in the particles. The identification of birth and growth mechanisms is likely to be particularly critical, but the interaction with the unit of Palermo should help in addressing this point, due to the simple one-dimensional flow configuration of their equipment (Couette cell). In these conditions the solution of the population balance is much simpler and can be performed even by MonteCarlo methods, which make it possible to test easily different mechanisms for growth, nucleation and aggregation. After their validation in the simple flow configuration, the mechanisms can be safely transferred to more complex approaches, such as the classes method (Palermo) or the DQMOM (Torino). In this case too, the characterization of the product will be performed by laser light scattering and electron microscopy, integrated by microanalysis performed by the research unit of Palermo.
Since anti-tumour drugs are very expensive and, above all, extremely toxic, the experimental work will be performed by substituting the drug with a model molecule (probably a fluorescent dye), with behaviour similar to that of pharmaceutical active agents, and chosen on the basis of the suggestions coming from the unit of Torino-University.
Points 3 and 4 will be characterized by continuous exchange of information with the group of Torino-University, in order to optimise composition and operating conditions. We plan to complete the two phases within the 21st month of the project.

5. Analysis of potential and of limitations of the impinging jet and of the vortex reactor
As a final point we intend to verify the ability of the considered reactors to reach specific targets for the properties of the produced particles, concerning average particle size, width of the size distribution, morphology, ratio between active principle and polymer. As said previously, the production of the nanoparticles requires good matching among the characteristic times of the different processes involved. Therefore the development of an accurate model of the process, planned at point 4, should help considerably in identifying new operating conditions suited for specific targets and in understanding the limitations of the process in the considered reactors. The results obtained for our configurations will be compared with those of the other studied precipitators, developed by the research units of Bologna and of Palermo, in order to set up guidelines to choose the best configuration on the basis of the specific objective.
Phase 5 will be performed during the last 3 months of the project.