Mathematical models describing polymer dissolution: consequences for drug delivery

Abstract

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.

Introduction

Dissolution of polymers in solvents is an important phenomenon in polymer science and engineering. It has found significant applications in a variety of areas. For example, in microlithography, a process used in fabricating integrated circuits, a photosensitive polymer, called a photoresist, is coated onto a substrate to form a thin film [1], [2], [3], [4], [5]. Irradiation through a glass plate or ‘mask’ bearing an array of circuit patterns allows selected areas of the photoresist to be exposed. The modified or exposed regions of the polymer exhibit an altered rate of dissolution in certain solvents, resulting in the formation of a polymeric image of the mask pattern.

In controlled release applications of polymers, a solute is molecularly dispersed in a polymer phase, which is usually in the glassy state. In the presence of a thermodynamically compatible solvent, swelling occurs and the polymer begins to release its contents to the surrounding fluid. This release process can be controlled either by solute diffusion or by polymer dissolution. In this case, the presence of permanent entanglements in the polymer becomes significant. These systems can give constant release rates under special conditions [6], [7], [8], [9], [10], [11], [12].

Polymer dissolution finds applications in membrane science. In phase inversion, a technique to form asymmetric membranes, a thin film of polymer solution is cast onto a suitable substrate followed by immersion in a coagulation bath (quench step) [13], [14], [15]. During the quench period, solvent/nonsolvent exchange and eventual polymer precipitation occur. The extent of dissolution of the polymer is instrumental in determining the ultimate structure of the membrane. Many crystallizable polymer films such as polycarbonates can be made porous by exposing a uniform film to a beam of alpha particles. The crystalline structure is disrupted and the film then chemically treated with an etchant such as caustic potash. The pores produced are nearly cylindrical and of uniform radius. Such membranes are used for microfiltration. Another technique is to cast films from pairs of compatible, non-complexing polymers. Treatment of such films with a solvent that dissolves only one of the polymers leaves behind a polymer with interconnected microvoids. This acts as a microfiltration membrane. Knowledge of the dissolution behavior of the polymers enables us to select suitable solvents. The membranes produced by the above methods are of uniform texture and are not skinned or asymmetric [16].

Polymer dissolution has also been applied in the treatment of unsorted plastics for recycling [17], [18], [19]. A single solvent such as xylene is used to dissolve five polymers — poly(vinylchloride), polystyrene, low density polyethylene, high density polyethylene and polypropylene — at five different temperatures, ranging from room temperature to 138°C. The remaining poly(ethyleneterephthalate) can be dissolved using a separate solvent. In this process, xylene is placed in a chip-filled vat first at room temperature. Polystyrene dissolves while the other five do not. The xylene solution is then drained to a separate part of the system where it is heated under pressure to about 250°C. The solution is then sent to a vacuum chamber to undergo flash devolatilization, causing xylene to vaporize instantaneously, leaving behind pure polystyrene. The same xylene is then sent back to dissolve another polymer at a different temperature and the process continues with the other polymers.

The dissolution of novolak resins in solvents is an important process in many semiconductor applications [20], [21], [22]. Hence, it becomes necessary to understand the dissolution characteristics of novolaks. Novolak resins, as the world’s oldest synthetic materials, play an important role in today’s semiconductor industry. Their advantages are in their non-swelling nature, aqueous –base developability and etching resistance [23], [24].

Some of the potential applications of the dissolution of polymers are in scaffolding for tissue regeneration [25]. Polymers are shaped into scaffolds that resemble the structure of tissues or organs. They are treated with compounds that help cells adhere onto their surface and multiply. They are then ‘seeded’ with the cells that grow and multiply as the polymer gradually dissolves. The new permanent tissue or the organ is implanted in the patient. So far, only biodegradable polymers have been used for such purposes, thereby considerably narrowing down the number of polymers that can be used. Moreover, most degradable polymers are too weak to be used in load bearing implants [26]. By using semicrystalline polymers, which combine strength with ease of control of the degree of crystallinity, it is possible to obtain desired dissolution rates that correspond to the growth rates of different tissues.

In addition to the above, polymer dissolution rate data have been used to determine glass transition temperature and other thermodynamic parameters associated with polymorphic changes [27]. Dissolution has also found a variety of uses in the pharmaceutical sciences. In the development of microcapsules for sustained release dosage forms [28], the mechanism of drug transport is governed by the dissolution of the polymer. Cooney [29] studied the dissolution of pharmaceutical tablets in the design of sustained release forms. Ozturk and co-workers [30], [31] showed that the dissolution of the polyacid, which is used in enteric-coated tablets, was the controlling step in the release kinetics mechanism.

The dissolution of a polymer into a solvent involves two transport processes, namely solvent diffusion and chain disentanglement. When an uncrosslinked, amorphous, glassy polymer is in contact with a thermodynamically compatible solvent, the latter diffuses into the polymer. A gel-like layer is formed adjacent to the solvent–polymer interface due to plasticization of the polymer by the solvent. After an induction time, the polymer is dissolved. However, there are also cases where a polymer crazes when placed in a solvent. When semicrystalline polymers are exposed to thermodynamically compatible solvents, the unfolding of the crystalline regions is an additional step accompanying solvent diffusion and chain disentanglement. Hence, semicrystalline polymer dissolution becomes equivalent to amorphous polymer dissolution after the crystals in the polymer unfold. A schematic of polymer dissolution is shown in Fig. 1.

In general, polymer dissolution differs from dissolution of a non-polymeric material in two aspects. Polymers require an induction time before starting to dissolve, while non-polymeric materials dissolve instantaneously. Also, polymer dissolution can be controlled either by the disentanglement of the polymer chains or by the diffusion of the chains through a boundary layer adjacent to the solvent–polymer interface. However, the dissolution of non-polymeric materials is generally controlled by the external mass transfer resistance through a liquid layer adjacent to the solid–liquid interface.

This review focuses on understanding the mathematical modeling of the mechanism of polymer dissolution in drug delivery applications. An appropriate understanding of the various controlling steps in the dissolution process greatly enhances the tailoring of the polymer to achieve not only desired rates of drug release, but also the desired profiles.