Balaji Narasimhan

Mathematical models describing polymer dissolution: consequences for drug delivery.

Polymer dissolution is an important phenomenon in polymer science and engineering that has found applications in areas like microlithography, controlled drug delivery, and plastics recycling. This review focuses on the modeling efforts to understand the physics of the drug release process from dissolving polymers. A brief review of the experimentally observed dissolution behavior is presented, thus motivating the modeling of the mechanism of dissolution. The main modeling contributions have been classified into two broad approaches - phenomenological models and Fickian equations, and anomalous transport models and scaling law-based approaches. The underlying principles and the important features of each approach are discussed. Details of the important models and their corresponding predictions are provided. Experimental results seem to be qualitatively consistent with the present picture.

Zero-order release of micro- and macromolecules from polymeric devices: the role of the burst effect

A mathematical analysis is presented to elucidate the role of the burst effect in an essentially zero-order controlled release coated hemispherical polymeric device containing a single, small orifice in its center face. Asymptotic solutions of the model show that the burst effect is controlled by the solubility of the drug in the release medium and by the drug diffusion coefficient. The effect of the above mentioned parameters on the cumulative drug released from coated hemispherical devices was also studied. It was shown that as drug solubility increased, the drug released faster and the velocity of the interface between dissolved and dispersed drug is higher. The model solutions established that the burst behavior could be manipulated by using different initial drug distributions. Using the model, conditions under which the burst effect could be minimized/maximized were established. The model predictions were compared to experimental studies of sodium salicylate release from polyethylene hemispheres and bovine serum albumin release from ethylene-vinyl acetate copolymer hemispheres.

Microphase separation in bioerodible copolymers for drug delivery

This research examines the microstructure of bioerodible polyanhydrides with an eye towards precise design of drug delivery devices. Our main hypothesis is that the bioerodible copolymer poly(1,6-bis-p-carboxyphenoxyhexane-co-sebacic anhydride) (CPH : SA) undergoes micro-phase separation at certain copolymer compositions due to differences in relative hydrophobicity of the co-monomers, resulting in thermodynamic partitioning of drugs incorporated into these copolymers. We investigate the thermal properties, degree of crystallinity, and surface microstructure of several compositions of CPH : SA using differential scanning calorimetry (DSC), wide-angle X-ray diffraction (WAXD), and atomic force microscopy (AFM). We observe that the degree of crystallinity decreases, while the crystal lamellar thickness increases with CPH content. Phase-imaging using AFM indicates the presence of micro-domains in 20 : 80 and 80 : 20 CPH : SA, while poly(SA) and 50 : 50 CPH : SA show no micro-phase separation. Finally, drug-polymer interactions are studied by loading the polymers with different amounts of brilliant blue (hydrophilic) and p-nitroaniline (hydrophobic). DSC and WAXD analysis shows that loading hydrophobic drugs into relatively hydrophobic polymers (poly(SA)) lowers melting point that becomes more pronounced with increased drug loading.

Disentanglement and reptation during dissolution of rubbery polymers

The dissolution mechanism of rubbery polymers was analyzed by dividing the penetrant concentration field into three regimes that delineate three distinctly different transport processes. The solvent penetration into the rubbery polymer was assumed to be Fickian. The mode of mobility of the polymer chains was shown to undergo a change at a critical penetrant concentration expressed as a change in the diffusion coefficient of the polymer. It was assumed that beyond the critical penetrant concentration, reptation was the dominant mode of diffusion. Molecular arguments were invoked to derive expressions for the radius of gyration, the plateau modulus, and the reptation time, thus leading to an expression for the reptation diffusivity. The disentanglement rate was defined as the ratio between the radius of gyration of the polymer and the reptation time. Transport in the second penetrant concentration regime was modeled to occur in a diffusion boundary layer adjacent to the polymer-solvent interface, where a Smoluchowski type diffusion equation was obtained. The model equations were numerically solved using a fully implicit finite difference technique. The results of the simulation were analyzed to ascertain the effect of the polymer molecular weight and its diffusivity on the dissolution process. The results show that the dissolution can be either disentanglement or diffusion controlled depending on the polymer molecular weight and the thickness of the diffusion boundary layer.

The physics of polymer dissolution: Modeling approaches and experimental behavior

Polymer dissolution is an important phenomenon in polymer science and engineering that has found applications in areas like microlithography, controlled drug delivery, and plastics recycling. This review focuses on the modeling efforts to understand the physics of the dissolution mechanism of glassy polymers. A brief review of the experimentally observed dissolution behavior is presented, thus motivating the modeling of the mechanism of dissolution. The main modeling contributions have been classified into four broad approaches — phenomenological models and Fickian equations, external mass transfer-control based models, stress relaxation models, and anomalous transport models and scaling law-based approaches. Another approach discussed is the appropriate accommodation of molecular theories in a continuum framework. The underlying principles and the important features of each approach are discussed in depth. Details of the important models and their corresponding predictions are provided. Experimental results seem to be qualitatively consistent with the present picture.

Self-diffusion and molecular mobility in PVA-based dissolution-controlled systems for drug delivery

Nuclear magnetic resonance (NMR) microscopy has been used to monitor the hydration of poly(vinyl alcohol) (PVA) samples of varying molecular weight. One-dimensional profiles weighted to predominantly show the variation of water concentration were acquired every 3 min during the first 30 min of hydration and subsequently at 1 and 2 h. Diffusion-weighted profiles obtained after 30 min and 1 and 2 h were used to calculate the spatial variation of the water self-diffusion coefficient. The resulting data provide supporting evidence for the hypothesis that phenomena such as reptation are important near the glassy/rubbery interface of polymers during dissolution, while the diffusion gradually changes to Zimm type near the rubbery/solvent interface.

High-yield resin fractionation using a liquid/liquid centrifuge

Resins used in photoresist manufacturing are often relatively expensive once processing steps (fractionation e.g.) and yield losses are factored into the net cost. We have previously reported on the merits of using an economically more attractive fractionation process using a liquid/liquid centrifuge. Further refinements of this method indicate that waste streams could be reduced by recycling the extractant phase and that lower molecular weight fractions removed from the starting resin might be used in making other resist ingredients [speed enhancers, photoactive compound (PAC) backbones e.g.]. Both of these improvements would reduce the overall manufacturing costs of making resist raw materials and the final products made with them.

Alternate novolak resin fractionation

Novolak resins fractionated using a unique method, were compared to resins fractionated with conventional methods. The potential for improving the fractionation/separation process and for making improved or more consistent resist with the resins was identified. Several experimental designs were run to determine optimum conditions needed to achieve better separation. Isolated resins were used to make experimental i-line photoresists which were tested against resists made with the conventional processes.

Preparation of lower-dispersity fractionated novolak resins by ultracentrifugation

The need to make well characterized resins consistently is paramount to the preparation of high performance photoresists. Solid resins fractionated by selective precipitation have been separated by ultracentrifugation at varying temperatures. At sufficiently high revolutions per minute, solvents and oligomers are efficiently squeezed out leaving behind polymer with higher average molecular weight and lower dispersity than resins obtained by more common isolation techniques. By controlling isolation conditions, resins with desired dissolution rates could be produced. Lithographic test confirmed that resists properties could effectively be controlled by manipulation of process conditions to isolate resins used in the formulations.