S. N. Upadhyay

Synthesis of Poly(Lactic Acid): A Review

Poly(lactic acid), a bio‐degradable polymer, has been studied extensively during the past 15 years. This paper presents a review on poly(lactic acid) (PLA) with focus on its stereochemistry, synthesis via ring‐opening polymerization, reaction kinetics and thermodynamics, synthesis of low molecular weight polymer, a continuous process for production of PLA from lactic acid, and blends. The different polymerization mechanisms, which have been proposed in the literature, are also summarized. Various catalyst systems, solvents, and reaction temperature and time give products of an entire range of molecular weights, ranging from a few thousand to over a million. Modeling and simulation of the ring‐opening polymerization of PLA is also discussed.

Mathematical Modeling of the Poly(lactic acid) Ring–Opening Polymerization Kinetics

The modeling of ring-opening polymerization of (D,L)-lactide to poly(lactic acid) (PLA) has been performed. Except some reported data on the apparent rate constant, there is lack of data in the literature on the rate constants for initiation, propagation and termination steps of PLA polymerization. Using a simple numerical technique, the individual rate constants are evaluated theoretically and the results are compared with the available experimental data for ring-opening polymerization of PLA. The proposed method works well without requiring a polymer chain length independent rate constant. It is also shown that presence of even small amount of impurity (e.g., water) in the reaction kettle can greatly limit the polymer molecular weight.

Computer simulation of membrane processes: ultrafiltration and dialysis units

Abstract An algorithm for computer simulation of membrane processes such as ultrafiltration and dialysis has been developed using a simplified finite volume approach. The technique used is slightly different from the standard finite difference, finite volume and finite element methods where all the parameters are considered at fixed nodal points. In the present approach the entire flow chamber is divided into a large number of volume elements and each element is considered to be an independent unit (similar to finite volume method). All mass flux and velocity components are calculated at the boundaries whereas concentration is considered at the center of the element. Thus, unlike FDM, FVM, and FEM, in the present approach nodal points for velocity and concentration are different. It has been observed that this method is more accurate and fast and requires less computational effort.

Mathematical Modeling of the Poly(lactic acid) Ring-Opening Polymerization using Stannous Octoate as a Catalyst

A novel and simple mathematical model to get the polymerization rate constants for the ring-opening polymerization of poly(lactic acid) is described. The model permits evaluation of the degree of polymerization versus monomer-to-initiator ratio curves. The predicted results are compared with the reported experimental data. The value of rate constants for initiation, propagation, and different modes of termination, are also obtained.

Mass Transfer from Spherical and Nonspherical Particles to Non-Newtonian Fluids

Abstract Mass transfer coefficients are measured for aqueous solutions of carboxy methyl cellulose (CMC) flowing past single immersed spherical and nonspherical particles of benzoic acid. The test particles used are 1.265–3.05 cm diameter spheres and 0.5388–1.1431 cm diameter cylindrical pellets, and the fluids used are demineralized water and 1% and 3% aqueous CMC solutions. The results obtained are analyzed and discussed using Acrivos and effective viscosity approaches, and empirical correlations for predicting heat and mass transfer coefficient are also proposed.

Synthesis of Polylactide: Effect of Dispersion of the Initiator

The ring opening polymerization of L-lactide was studied in bulk using stannous octoate as initiator. In some experiments, triphenylphosphine, a Lewis base was also used as co-initiator. The polymerization was carried out at 130°C up to 29 h. The monomer was used after recrystallizing three times with dry toluene. Experiments were carried out using a wide range of monomer to initiator ratio. The averages and distributions of molar masses of resulting PLA have been determined by means of size exclusion chromatography, SEC. It is shown that the (mode, process) procedure of dispersion of the catalyst in polymerization system affects the molar mass distribution of the product as is evidenced by the bimodality or even trimodality observed in the SEC chromatograms.

A colsed form solution of convective mass transfer model for intracellular calcium response of endothelial cells

Endothelial cells, lining the entire vascular system, respond to change in concentration of specific agonist like adenosine triphosphate (ATP) by increasing cytosolic Ca2

Convective-diffusive mass transfer of agonist and the intracellular calcium response of endothelial cell

Endothelial cell layer regulates several crucial physiological processes of the vascular system. The mechanism of the response of this cell layer to the flow of surrounding fluid is still largely unclear. In the present article, a comparison of the available experimental results for the intracellular calcium ion concentration and theoretical results for the extra-cellular ATP concentration obtained using a convective-diffusive mass transfer model, has been made which supports the mass transfer model for the endothelial cell response to the fluid flow. The experimental results are in excellent agreement with the calculated values assuming the effect of ATP concentration alone.

Role of important parameters in ring opening polymerization of polylactide

Abstract Different parameters, namely polymerization temperature, polymerization time, monomer/initiator ratio, nature of the initiator, amount of water or other impurities etc. are very significant for polymerization reactions either in bulk or solution. Monomer to initiator ratio has a very significant role in polymerization reactions and a value ranging from 50 to 5000 that has been reported by different researchers. Recrystallization of the monomer removes the meso compounds from the monomer, which absorbs the moisture and effects polymerization reaction. So, it is necessary to recrystallize the monomer with any anhydrous solvent like dry toluene, ethyl acetate etc. Prolonged reaction time cannot increase the polymer yield; it generally causes the decrease of molecular weight and broadening of molecular weight distribution of formed polymers. This is probably due to the transesterification side reaction in polymerization, intensifying at prolonged time periods. Several groups like hydroxyl and carboxylic acid affect the polymerization rate.

Kinetic parameters estimation of ring-opening poly(lactic acid) polymerization by modeling and simulation

Abstract The modeling of ring-opening polymerization of lactide to poly(lactic acid) (PLA) has been carried out. Carothers first synthesized PLA in 1932. Since then, hundreds of research papers and patents have appeared in the literature. However, there is a lack of data concerning the rate constants for initiation, propagation and termination steps of PLA polymerization, except some data about the apparent rate constant. This work investigates, theoretically, the individual rate constants using a simple numerical technique. The progress of lactide polymerization can be modeled by assuming a ring opening reaction mechanism comprising chain initiation, chain propagation, and chain termination. The simulator developed, based on the solutionof differential equations corresponding to the above-mentioned kinetic scheme, Generates a detailed molecular weight distribution that can be used to estimate average molecular weights (or average degree of polymerization) vs. polymerization time curves. These simulated curves, on matching with the reported experimental data (for different catalysts), yield the absolute values of rate constants. The values have been determined for zinc lactate. Rate constants could be determined by using the molecular weight and the polydispersity vs. polymerization data. This methodology offers greater opportunity for capturing high, non-equilibrium polymer yield through appropriately timed termination of the polymerization reaction.