Modeling Studies on the Synthesis of Superabsorbent Hydrogels Using Population Balance Equations

Abstract

The synthesis of super‐absorbent hydrogels is simulated using a kinetic model based upon population balance equations of generating functions. Dynamics in a batch reactor of properties such as the weight fraction of gel or average molecular weights of the soluble fraction can be predicted. This kinetic model neglects intramolecular cyclization reactions for simplicity (hence predictions can be valid only for very small amounts of crosslinker) but it can accommodate the operation with different kinds of crosslinking agents, namely bifunctional (e.g. N,N′‐methylenebisacrylamide), trifunctional (e.g. trimethylolpropane triacrylate) and tetrafunctional (e.g. tetraallyloxyethane). The influence of the use of such different kinds of crosslinkers on the dynamics of gelation is discussed. It is also assessed the impacts of the rate propagation coefficient of the monofunctional monomer (typically acrylic acid), of the reactivity of the pendant double bonds (PDB) and of the initial composition on the dynamics of gel production. Some crucial details concerning the numerical solution of the two‐point boundary value problems (TPBVP) associated with this simulation tool are also presented. Predictions of the proposed kinetic approach are compared with those obtained using the Theory of the Branching Processes which is not strictly valid with kinetically controlled polymerization systems such as those here considered. Important differences between the predictions of the two approaches are shown. Superabsorbent hydrogels were synthesized with a 2.5 L batch reactor and the experimental data are used to show that the simple kinetic model developed is able to capture the main features of this polymerization system.

Modeling and experimental study of inverse suspension polymerization of acrylic acid and trimethylolpropane triacrylate for hydrogel production.

“…Table 5 shows the values of the kinetic parameters used in the model developed in the present work. As presented in Chapter 3, the model was developed on the basis of the recent study by Gonçalves et al (2011) to simulated the synthesis of acrylic acid hydrogels using a kinetic model based on the population balance equations and generating functions in order to predict the changes in the properties like the gel fraction and monomer conversion. …”

“…Termination by combination Gonçalves et al (2011) reported some values of propagation kinetic constant (Tables 7 and 8), and its dependency of temperature and monomer concentration. Table 6.…”

“…Ref: (Gonçalves et al, 2011) For generality, no particular chemical system has been selected for this study, but the chosen kinetic parameters should allow a simulation as much as possible close to the real behavior of the crosslinking copolymerization systems. A basic set of kinetic parameters were fixed in the calculations in order to have a realistic time evolution of the copolymerization; they are collected in the supplementary material.…”

“…Table 7. Reported values of the propagation rate constant (kp11) of acrylic acid in water Ref: (Gonçalves et al, 2011) which is known to depend on the presence of inhibitors MEHQ (which comes in the commercial monomers used) and oxygen (which can be dissolved in the aqueous solution). Although nitrogen was bubbled in all experiments to deoxygenate the reaction medium, the nitrogen flow rate was not precisely controlled nor was equal in all experiments.…”

“…A mathematical model for the process was developed based on the previous models reported in the literature, in special that of Gonçalves et al (2011). The model predicted the time history of monomer conversion and gel fraction to be compared with the data collected in the experiments.…”