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Diffusion and Release of a Mobile Product in a Reactive Membrane System

Tsutomu Shimotori1, Edward L. Cussler2, and William A. Arnold1. (1) Civil Engineering, University of Minnesota, 500 Pillsbury Dr. SE, Minneapolis, MN 55455, (2) Chemical Engineering and Materials Science, University of Minnesota, 500 Pillsbury Dr. SE, Minneapolis, MN 55455

When a polymer membrane containing an immobilized, reactive chemical is in contact with solution containing a reactive solute, the solute diffuses into the membrane and reacts with the immobilized chemical. As a result, the reactive solute and the immobilized chemical are consumed, and at the same time, mobile products may be produced within the membrane. The mobile products will diffuse out of the membrane under the driving force of the resulting concentration gradient. This process continues until all of the immobilized chemical is consumed. In this study, diffusion and release of a mobile product produced in a reactive membrane was investigated experimentally and theoretically.

Such a reactive membrane system has many possible applications. For example, it can be applied to a controlled release of drugs [1]. Acidic conditions in the body could be used to trigger a reaction within an implanted membrane to release a drug. Similarly, it can be used for a controlled release of agricultural chemicals [2]. Also, it may be relevant to reactive barrier membranes for retarding penetration of contaminants [3] if formation of undesired by-products is possible. Thus, the diffusion of the mobile products out of the reactive membrane is of great interest.

In our experiments, a diaphragm cell in which a reactive solute challenges a reactive membrane from one side was adopted. Hydrochloric acid and a poly(vinyl alcohol) membrane containing zinc oxide particles were chosen as the reactive solute and the reactive membrane, respectively. The immobilized zinc oxide was dissolved by the penetrating hydrochloric acid. Zinc ions were formed within the membrane, and they subsequently diffused out of the membrane into the two glass chambers that comprised the diaphragm cell holding the membrane. The concentration of zinc ions and acid in the chambers were monitored using a colorimetric method and a pH meter, respectively. The experiments were conducted with varied zinc oxide loadings, acid concentrations, membrane thicknesses, and chamber volumes to determine the effects of these parameters.

Our modeling is based on a theoretical equation derived by Yang et al. to describe the breakthrough behavior of the reactive solute [4]. A diffusion equation with a reaction term describes the behavior of the mobile product before breakthrough of the reactive solute, while a diffusion equation without a reaction term governs the system after the breakthrough. Based on a pseudo-steady state assumption, an analytical solution to this problem was derived. This analytical solution closely agrees with a numerical solution without the steady state assumption. The equations were successfully used to fit and explain the experimental data.

[1] Petratos, P. B.; Chen, J.; Felsen, D.; Poppas, D. P. (2002) “Local Pharmaceutical Release from a New Hydrogel Implant,” J. Surg. Res. 103, 55-60. [2] Zhao, J.; Wilkins, R. M. (2005) “Low Molecular Weight Polylactic Acid as a Matrix for the Delayed Release of Pesticides,” J. Agric. Food Chem. 53, 4076-4082. [3] Shimotori, T.; Nuxoll, E. E.; Cussler, E. L.; Arnold, W. A. (2004) “A Polymer Membrane Containing Fe0 as a Contaminant Barrier,” Environ. Sci. Technol. 38, 2264-2270. [4] Yang, C.; Nuxoll, E. E.; Cussler, E. L. (2001) “Reactive Barrier Films,” AIChE J. 47, 295-302.