(255ay) Modeling of Microgel Synthesis By Precipitation Polymerization
Good progress has been achieved in the study of correlations of the internal structure and the resulting properties . However, tailoring microgels with desired properties demands an in-depth understanding of the synthesis process and the influence of its controlling factors on the internal microgel structure. This is best accomplished by mathematical modeling techniques to gain insight on the microgel synthesis and driving reaction kinetics. To obtain a validated process model, it is necessary to have suitable experimental data.
N-Vinylcaprolactam (VCL) based microgels can be synthesized by precipitation polymerization . Initially, monomer and the cross linker N-Nâ??-Methylenebisacrylamide (BIS) are completely soluble in water. Free radical polymerization of the monomer and cross linker is initiated by 2,2â??-Azobis(2-methypropyonamidine)dihydrochloride (AMPA). Polymerization continues until radical oligomers reach a critical chain length, collapse due to their insolubility in water, and form precursor particles. The precipitation creates a second, polymer-rich phase where further polymerization reactions occur and contribute to particle growth. Size of the microgel particles is determined by several competing growth mechanisms, most importantly represented by precursor particle agglomeration and absorption of monomer, radicals as well as precursor particles by larger particles. The cross linker is central to establish a stable polymer structure and governs the microgel properties significantly.
In this work, a continuous kinetic model is developed for microgel synthesis by precipitation polymerization in an isothermal batch process. Mass balances for initiator, monomer and cross linker as well as oligomer and polymer are used to describe the liquid and the microgel phase. The incorporation of cross linker is described by the copolymerization mechanism. To account for the formation of cross-links by reactions of the pendant double bonds, additional balances for these species are introduced. The model covers a broad range of reaction steps which are assumed to occur in both phases. Assuming that the reactions are not affected by simultaneously occurring particle formation mechanisms as described above , the reaction kinetics can be determined.
To comprehensively determine the reaction kinetics, dedicated experiment series performed in a real-time calorimeter provide measurements of the heat flux from reactor content to the cooling jacket. This allows computing the heat of reaction by means of an energy balance for the entire reactor. Simultaneous Raman spectroscopy measurements provide mass fractions of monomer and polymer  of an average of liquid and gel phase.
Morphology of the microgel particles and their high water content makes a continuous distinction of the ratio of the phases and the growth of microgels to this time impossible. The ratio is, however, necessary to describe the transfer of polymer from the liquid to the gel phase. To account for the transfer of radicals by precipitation, the experimentally determined critical chain length is utilized. For the liquid phase, reaction rate coefficients for propagation were derived from quantum chemical calculations. This enables the prediction of the extent of the liquid phase as reaction locus which would have been difficult to determine experimentally. Partition coefficients from quantum chemical calculations provide additional information on concentrations of small molecules in both phases.
The proposed model enables a quantitative description of the synthesis for cross-linked VCL-based microgels. Reaction kinetics of homopolymerization as well as cross reaction coefficients were derived from a range of experiments with varying composition ratios of VCL and BIS. The determined propagation reaction rate coefficients of homopolymerization and cross reactions of monomer and cross linker differ significantly which leads to a faster consumption of cross linker. This aligns with the results of experimental characterization of VCL-based microgel particles to have an uneven distribution of cross-links in the microgel particle .
Furthermore, the model indicates that growth of the gel phase is also a product of absorption and reaction of monomers. Since the critical chain length for precipitation is small, concentration of oligomers in the liquid phase is low, which consequently limits the reactions in the liquid phase. With the partition coefficients from quantum chemical calculations indicating an accumulation of monomer in the gel phase, this implies that that the impact of polymerization reactions in the liquid phase is small.
For the complex microgel system, with limited experimental information of the complex polymerization behavior, integration of experimental measurements and quantum chemical calculation led to an accurate kinetic model. The model enables the reproduction of experimentally observed phenomena and allows predictability and insights in the kinetics of microgel synthesis. This builds the first step towards model-based process design and operation of synthesis of functional microgels.
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