Modeling and Simulation of Poly (Lactic Acid) Polymerization

Abstract

During the past 15 years, a number of aliphatic polyesters have aroused considerable interest due to their biodegradability and biocompatibility. Poly(lactic acid) (PLA) is the main biodegradable polyester of interest, primarily due to its biomedical and pharmacological applications. Since the syntheses of PLA by Carothers in 1932, hundreds of research papers and patents have appeared in the literature. Now large size PLA manufacturing units are being set-up. But, there is a lack of data concerning the rate constants for initiation, propagation and termination steps of PLA polymerization though some data about the apparent rate constant are available. Also, it is extremely difficult to experimentally find the absolute values of different rate constants. Thus, there is a need for mathematical modeling which when used with the readily available experimental data for the average molecular weights, can predict the polymerization rate constants with sufficient accuracy. This thesis embodies the subject matter resulting out of this study. It is arranged in six different chapters. A brief introduction about the need for non-degradable polymers and a brief history along with the current industrial status of PLA is given in the introduction. Since it is the lactic acid, which starts the PLA lifecycle, its importance is also discussed. Also the future prospects and advantages of PLA are mentioned. This is followed by an introduction to synthesis of PLA by ring-opening polymerization (ROP) of lactide. Focus is then shifted to a discussion of why are mathematical models useful, in general, followed by the need for mathematical modeling of the ring-opening polymerization of PLA. A brief description of the methodology used is also given. The progress of lactide polymerization has been modeled by assuming a ring opening reaction mechanism comprising of chain initiation, chain propagation, and chain termination. Appropriate differential equations have been developed incorporating the rate controlling reaction(s)/step(s). The resulting differential equations with appropriate boundary conditions were solved using a numerical technique. Effect of unequal reactivity has also been incorporated in the model. The efficacy of model has been tested by comparing the predicted results on molecular weight and molecular weight distribution with those available in the published literature. The kinetic rate constants have been arrived at, for various PLA polymerization catalysts, by matching the simulated results with the experimental data. The method is extended to quantitatively predict the effect of water present as an impurity in the reactor on the PLA molecular weight. A mechanistic model to simulate the ring-opening polymerization of PLA for a batch reactor is developed. A number of checks are made to verify the correctness of the solutions in the limiting case of Poisson distribution. Here the molecular weight change as a function of polymerization time, in a homogeneous ring-opening polymerization of PLA, is considered. The results of simulations performed on the model developed in conjunction with the reported experimental data for various catalysts are discussed. The sensitivity of the present technique with respect to ko, kp and kt (rate constants for initiation, propagation and termination by transfer to monomer, respectively) are discussed. The molecular weight of polymer formed is more sensitive to kp than kt for shorter reaction time whereas effect of kt is pronounced for prolonged reaction time. Mn, however, is not very sensitive to ko. Initiation rate constant has a very peculiar behavior: with a decrease in ko, the number average molecular weight, Mn, is lower for short eaction time, and as reaction proceeds Mn becomes higher. This interesting result is due to the fact that due to low ko, the number of initiated chains are less and with the availability of same monomer molecules for the growth of fewer number of chains, the average chain length increases. It is shown that ko values can be fine-tuned if the polydispersity (Mw/Mn) data is also considered. Based on this methodology, the values of different rate constants for the polymerization of PLA in presence of four catalysts:aluminum isopropoxide, iron trifluoroacetate, iron isobutyrate and zinc lactate are arrived at. A discussion of simulations performed without the assumption of propagation rate constant being chain length independent is also presented. Above model is applied to the polymerization data in the form of degree of polymerization as a function of monomer-to-initiator ratio. The polymerization data is available in literature for the stannous octoate catalyst for PLLA and PDLLA. Additionally, a second model (Model 2) is developed which considers cationic ring- opening polymerization mechanism where termination by transfer to polymer and unimolecular termination (first order relative to active species) and intramolecular termination, are considered. The differential equations for the formation and disappearance of the living i-mers P1, P2, â Pj, as well as for the consumption of monomer and initiator, along with the formation of deactivated polymer, Mj, for a batch reactor, using above kinetic scheme is written and solved. The typical computing time for Model 1 was 30 min and the Model 2 run took nearly a week. The simulations were matched with the reported data to get the individual rate constants for the ring-opening polymerization of lactide, using stannous octoate as a catalyst. Another objective was to find out if the difference in the degree of closeness of the curves to the experimental points is sufficient to ascribe a polymerization mechanism for the stannous octoate catalyst. However, it is not possible to ascribe a specific mechanism to PLLA and PDLLA polymerization on the basis of experimental data used in modeling. These experimental data points are characterized by poor reproducibility. However, it should be pointed out that for ROP this type of poor reproducibility is expected. The parity plots for the calculated and reported experimental values of average molecular weights show an excellent agreement. An attempt has also been made to quantify the effect of water as impurity on the polymer molecular weight. The model considers termination by transfer to monomer and by transfer to water. A value of rate constant of chain transfer to water for ionic reaction is taken from the literature and used for the evaluation of rate constants by solving the appropriate differential equations. Although the amount of water present in reaction mixture was not known, simulations reveal that water concentration in the reported data was about 0.5 ppm. It is quantitatively shown that there is a marked decrease in the degree of polymerization in presence of even small concentrations of water in the reaction vessel.