Swelling-Controlled Release

  • Liang-tseng Fan
  • Satish Kumar Singh
Part of the Polymers book series (POLYMERS, volume 13)


Consider a monolithic polymeric device containing an active agent introduced into the elution medium. If the elution medium is not thermodynamically compatible with the polymer or if the polymer is well above its glass transition temperature, the morphological structure is time independent and the device belongs to the diffusion-controlled category. However, if the elution medium or a constituent component is thermodynamically compatible with a polymer in the glassy state, its glass transition temperature may be lowered below the system temperature. Subsequently, the glassy polymer begins to undergo a glass-to-gel transition. The polymer chains in the gel state, being more mobile than those in the glassy state, allow the active agent to diffuse (more rapidly) out of the matrix. Such a device in which the change of polymer morphology, caused by interaction with the elution medium, controls or influences the release is classified as being swelling controlled. A distinction has been made between two types of systems formed by such swellable polymers (Peppas, 1984). A swellable controlled-release system comprising the first type, consists of a hydrophilic polymer that undergoes swelling more or less continuously throughout the matrix. This glass-to-gel transition loosens the matrix and the active agent is able to diffuse out, with the release rate determined by the diffusion process. A swelling-controlled system belonging to the second type, comprises a polymeric system exhibiting spatially discontinuous swelling.


Active Agent Glassy Polymer Fickian Diffusion Deborah Number Anomalous Transport 
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  1. Ahn, B. J., Smith, J. M., Parrish, W. R.: Non-Fickian Diffusion Through Polymer Films, AIChE J. 31, 874–876 (1985)CrossRefGoogle Scholar
  2. Alfrey, T.: Glassy Polymer Diffusion is often Tractable. Chem. Eng. News 43 (41), 64–65 (1965)CrossRefGoogle Scholar
  3. Alfrey, T., Gurnee, E. F., Lloyd, W. G.: Diffusion in Glassy Polymers. J. Polym. Sci.: Part C., 12, 249–261 (1966)Google Scholar
  4. Astarita, G., Joshi, S.: Sample-Dimension Effects in the Sorption of Solvents in Polymers — A Mathematical Model, J. Membrane Sci. 4, 165–182 (1978)CrossRefGoogle Scholar
  5. Astarita, G., Nicolais, L.: Physics and Mathematics of Heat and Mass Transfer in Polymers, Pure & Appl. Chem. 55, 727–736 (1983)CrossRefGoogle Scholar
  6. Astarita, G., Sarti, G. C.: A Class of Mathematical Models for Sorption of Swelling Solvents in Glassy Polymers, Polym. Eng. Sci. 18, 388–395 (1978)CrossRefGoogle Scholar
  7. Bagley, E., Long, F. A.: Two-Stage Sorption and Desorption of Organic Vapors in Cellulose Acetate, J. Am. Chem. Soc. 77, 2172–2178 (1955)CrossRefGoogle Scholar
  8. Baird, B. R., Hopfenberg, H. B., Stannett, V. T.: The Effect of Molecular Weight and Orientation on the Sorption on n-Pentane by Glassy Polystyrene, Polym. Eng. Sci. 11, 274–283(1971)CrossRefGoogle Scholar
  9. Baker, R. W.: Controlled Release of Biologically Active Agents, pp. 179–184, John Wiley & Sons, New York (1987)Google Scholar
  10. Bamba, M., Puisiuex, F., Marty, J.-P., Carstensen, J. T.: Release Mechanisms in Gelforming Sustained Release Preparations, Int. J. Pharm. 2, 307–315 (1979)CrossRefGoogle Scholar
  11. Bearman, R. J.: On the Linear Phenomenological Equations, J. Chem. Phys. 28, 662–664 (1958)CrossRefGoogle Scholar
  12. Bearman, R. J., Kirkwood, J. G.: Statistical Mechanics of Transport Processes. XI. Equations of Transport in Multicomponent Systems, J. Chem. Phys. 28, 136–145 (1958)CrossRefGoogle Scholar
  13. Berens, A. R., Hopfenberg, H. B.: Diffusion and Relaxation in Glassy Polymer Powders: 2. Separation of Diffusion and Relaxation Parameters, Polymer 19, 489–496 (1978)CrossRefGoogle Scholar
  14. Bernier, G. A., Kambour, R. P.: The Role of Organic Agents in the Stress Crazing and Cracking of Poly(2,6-dimethyl-l,4-phenylene oxide), Macromolecules 1, 393–400 (1968)CrossRefGoogle Scholar
  15. Bharucha-Reid, A. T.: Elements of the Theory of Markov Process and Their Applications, pp. 129–163, McGraw-Hill, New York (1960)Google Scholar
  16. Cohen, D.S.: Theoretical Models for Diffusion in Glassy Polymers, J. Polym. Sci., Polym. Phys. Ed. 21, 2057–2065 (1983)CrossRefGoogle Scholar
  17. Cohen, D. S.: Diffusive Fronts of Penetrants in Glassy Polymers, Physica 12D, 369–374 (1984)Google Scholar
  18. Cohen, D. S., Stanley, E. A.: Gaseous Diffusion in Glassy Polymers, SIAM J. Appl. Math. 43, 949–970 (1983)CrossRefGoogle Scholar
  19. Crank, J.: Diffusion in Media with Variable Properties. Part III. Diffusion Coefficients which Vary Discontinuously with Concentration, Trans. Farad. Soc. 47, 450–461 (1951)CrossRefGoogle Scholar
  20. Crank, J.: A Theoretical Investigation of the Influence of Molecular Relaxation and Internal Stress on Diffusion in Polymers, J. Polym. Sci. XI, 151–168 (1953)CrossRefGoogle Scholar
  21. Crank, J.: The Mathematics of Diffusion, pp. 290–293, Oxford University Press, London (1975)Google Scholar
  22. Davidson III, G. W. R., Peppas, N. A.: Solute and Penetrant Diffusion in Swellable Polymers. V. Relaxation-Controlled Transport in P(HEMA-co-MMA) Copolymers, J. Controlled Release 3, 243–258 (1986 a)CrossRefGoogle Scholar
  23. Davidson III, G. W. R., Peppas, N. A.: Solute and Penetrant Diffusion in Swellable Polymers. VI. The Deborah and Swelling Interface Numbers as Indicators of the Order of Biomolecular Release, J. Controlled Release 3, 259–271 (1986b)CrossRefGoogle Scholar
  24. Fan, L. T.: Mathematical Modeling and Process Optimization. In: Food Process Engineering, Vol. I, pp. 26–51, Food Processing Systems, P. Linko, Malkki, Y., Olkku, J. (Eds.), Applied Science Publishers, London (1979)Google Scholar
  25. Feynman, R. P., Leighton, R. B., Sands, M.: The Feynman Lectures on Physics, pp. 43–44, Addison-Wesley Publishing Company, Reading, Massachusetts (1963)Google Scholar
  26. Franson, N. M., Peppas, N. A.: Influence of Copolymer Composition on Non-Fickian Water Transport through Glassy Copolymers, J. Appl. Polym. Sci. 28, 1299–1310 (1983)CrossRefGoogle Scholar
  27. Frisch, H. L.: Anomalous Polymer-Penetrant Permeation, J. Chem. Phys. 37, 2408–2413 (1962)CrossRefGoogle Scholar
  28. Frisch, H. L.: Simultaneous Nonlinear Diffusion of a Solvent and Organic Penetrant in a Polymer, J. Polym. Sci. Polym. Phys. Ed. 16, 1651–1664 (1978)CrossRefGoogle Scholar
  29. Frisch, H. L.: Sorption and Transport in Glassy Polymers — A Review, Polym. Eng. Sci. 20, 2–13(1980)CrossRefGoogle Scholar
  30. Frisch, H. L., Wang, T. T., Kwei, T. K.: Diffusion in Glassy Polymers II, J. Polym. Sci.: Part A-2, 7, 879–887 (1969)CrossRefGoogle Scholar
  31. Good, W. R.: Diffusion of Water Soluble Drugs from Initially Dry Hydrogels, pp. 139–153. In: Polymeric Delivery Systems, Kostelnik, R. J. (Ed.), Gordon and Breach Science Publishers, New York (1978)Google Scholar
  32. Gostoli, C., Sarti, G. C.: Diffusion and Localized Swelling Resistances in Glassy Polymers, Polym. Eng. Sci. 22, 1018–1026 (1982)CrossRefGoogle Scholar
  33. Graham, N. B., McNeill, M. E.: Hydrogels for Controlled Drug Delivery, Biomaterials, 5, 27–36 (1984)CrossRefGoogle Scholar
  34. Hopfenberg, H. B.: Anomalous Transport of Penetrants in Polymeric Membranes, pp. 16–32. In: Membrane Science and Technology: Industrial, Biological, and Waste Treatment Processes, J. E. Flinn (Ed.), Plenum Press, New York (1970)Google Scholar
  35. Hopfenberg, H. B., Apicella, A., Saleeby, D. E.: Factors Affecting Water Sorption in and Solute Release from Glassy Ethylene-Vinyl Alcohol Copolymers, J. Membrane Sci. 8, 273–282(1981)CrossRefGoogle Scholar
  36. Hopfenberg, H. B., Frisch, H. L.: Transport of Organic Micromolecules in Amorphous Polymers, J. Polym. Sci. Polym. Letters, B7, 405–409 (1969)CrossRefGoogle Scholar
  37. Hopfenberg, H. B., Holley, R. H., Stannett, V.: The Effect of Penetrant Activity and Temperature on the Anomalous Diffusion of Hydrocarbons and Solvent Crazing in Polystyrene. Part I: Biaxially Oriented Polystyrene, Polym. Eng. Sci. 9, 242–249 (1969)CrossRefGoogle Scholar
  38. Hopfenberg, H. B., Hsu, K. C.: Swelling-Controlled, Constant Rate Delivery Systems. Polym. Eng. Sci. 18, 1186–1191 (1978)CrossRefGoogle Scholar
  39. Hopfenberg, H. B., Stannett, V. T., Folk, G. M.: Sorption Kinetics and Equilibria in Annealed Glassy Polyblends, Polym. Eng. Sci. 15, 261–267 (1975)CrossRefGoogle Scholar
  40. Jacques, C. H. M., Hopfenberg, H. B., Stannett, V.: Super Case II Transport of Organic Vapors in Glassy Polymers, pp. 73–86. In: Permeability of Plastic Films and Coatings to Gases, Vapors, and Liquids, H. B. Hopfenberg (Ed.), Plenum Press, New York (1974)Google Scholar
  41. Joshi, S., Astarita, G.: Diffusion-Relaxation Coupling in Polymers which Show Two-Stage Sorption Phenomena, Polymer 20, 455–458 (1979)CrossRefGoogle Scholar
  42. Korsmeyer, R. W.: Solute and Penetrant Diffusion in Swellable Polymers, Ph. D. Dissertation, Purdue University, West Lafayette, Indiana, pp. 28–51 (1983)Google Scholar
  43. Korsmeyer, R. W., Gurny, R., Doelker, E., Buri, P., Peppas, N. A.: Mechanisms of Solute Release from Porous Hydrophilic Polymers, Int. J. Pharm. 15, 25–35 (1983)CrossRefGoogle Scholar
  44. Korsmeyer, R. W., Lustig, S. R., Peppas, N. A.: Solute and Penetrant Diffusion in Swellable Polymers. I. Mathematical Modeling, J. Polym. Sci., Polym. Phys. Ed. 24, 395–408 (1986a)CrossRefGoogle Scholar
  45. Korsmeyer, R. W., Meerwall, E. V., Peppas, N. A.: Solute and Penetrant Diffusion in Swellable Polymers. II. Verification of Theoretical Models, J. Polym. Sci., Polym. Phys. Ed. 24, 409–434 (1086b)Google Scholar
  46. Korsmeyer, R. W., Peppas, N. A.: Effect of the Morphology of Hydrophilic Polymeric Matrixes on the Diffusion and Release of Water Soluble Drugs, J. Membrane Sci. 9, 211–227(1981)CrossRefGoogle Scholar
  47. Korsmeyer, R. W., Peppas, N. A.: Macromolecular and Modeling Aspects of Swelling-Controlled Systems, pp. 77–90. In: Controlled Release Delivery Systems, Roseman, T. J., Mansdorf, S. Z. (Eds.), Marcell Dekker, Inc., New York (1983)Google Scholar
  48. Korsmeyer, R. W., Peppas, N. A.: Solute and Penetrant Diffusion in Swellable Polymers. III. Drug Release From Glassy Poly(HEMA-co-NVP) Copolymers, J. Controlled Release 1, 89–98 (1984)CrossRefGoogle Scholar
  49. Kwei, T. K., Wang, T. T., Zupko, H. M.: Diffusion in Glassy Polymers. V. Combination of Fickian and Case II Mechanisms, Maeromolecules 5, 645–646 (1972)CrossRefGoogle Scholar
  50. Kwei, T. K., Zupko, H. M.: Diffusion in Glassy Polymers I, J. Polym. Sci: Part A-2, 7, 867–877 (1969)CrossRefGoogle Scholar
  51. Lapidus, H., Lordi, N. G.: Drug Release from Compressed Hydrophilic Matrices, J. Pharm. Sci. 57, 1292–1301(1968)CrossRefGoogle Scholar
  52. Lee, P. I.: Controlled Drug Release from Polymeric Matrices Involving Moving Boundaries, pp. 39–48. In: Controlled Release of Pesticides and Pharmaceuticals, D. H. Lewis (Ed.), Plenum Press, New York (1981)Google Scholar
  53. Lee, P. I.: Novel Approach to Zero-Order Drug Delivery via Immobilized Nonuniform Drug Distribution in Glassy Hydrogels, J. Pharm. Sci. 73, 1344–1347 (1984a)CrossRefGoogle Scholar
  54. Lee, P. I.: Effect of Non-Uniform Initial Drug Concentration Distribution on the Kinetics of Drug Release from Glassy Hydrogel Matrices, Polymer 25, 973–978 (1984 b)CrossRefGoogle Scholar
  55. Long, F. A., Richman, D.: Concentration Gradients for Diffusion of Vapors in Glassy Polymers and their Relation to Time Dependent Diffusion Phenomena, J. Am. Chem. Soc. 82, 513–519(1960)CrossRefGoogle Scholar
  56. Lustig, S. R., Peppas, N. A.: Solute and Penetrant Diffusion in Swellable Polymers. VII. A Free Volume-Based Model with Mechanical Relaxation, J. Appl. Polym. Sci. 33, 533–549(1987)CrossRefGoogle Scholar
  57. McGregor, R.: Diffusion and Sorption in Fibers and Films, Vol. I, An Introduction with Particular Reference to Dyes, pp. 210–211, Academic Press, New York (1974)Google Scholar
  58. Michaels, A. S., Bixler, H. J., Hopfenberg, H. B.: Controllably Crazed Polystyrene: Morphology and Permeability, J. Appl. Polym. Sci. 12, 991–1007 (1968)CrossRefGoogle Scholar
  59. Nagy, M.: Some New Aspects of Research on Polymer Gels, Colloid and Polymer Sci. 263, 245–265 (1985)CrossRefGoogle Scholar
  60. Neogi, P.: Anomalous Diffusion of Vapors Through Solid Polymers. Part I. Irreversible Thermodynamics of Diffusion and Solution Processes, AIChE J. 29, 829–833 (1983)CrossRefGoogle Scholar
  61. Omar, M. A.: Elementary Solid State Physics: Principles and Applications, p. 143, Addison-Wesley Publishing Company, Reading, Massachusetts (1978).Google Scholar
  62. Park, G. S.: The Glassy State and Slow Process Anomalies, pp. 141–163. In: Diffusion in Polymers, Crank, J., Parks, G. S. (Eds.), Academic-Press, London (1968)Google Scholar
  63. Paul, D. R., Garcin, M., Garmon, W. E.: Solute Diffusion Through Swollen Polymer Membranes, J. Appl. Polym. Sci. 20, 609–625 (1976)CrossRefGoogle Scholar
  64. Peppas, N. A.: Release of Bioactive Agents from Swellable Polymers: Theory and Experiments, pp. 279–289. In: Recent Advances in Drug Delivery Systems, Anderson, J. M., Kim, S. W. (Eds.), Plenum Publishing Corporation, New York (1984)CrossRefGoogle Scholar
  65. Peppas, N. A., Franson, N. M.: The Swelling Interface Number as a Criterion for Prediction of Diffusional Solute Release Mechanisms in Swellable Polymers, J. Polym. Sci., Polym. Phys. Ed. 21, 983–997 (1983)CrossRefGoogle Scholar
  66. Peppas, N. A., Gurny, R., Doelker, E., Buri, P.: Modelling of Drug Diffusion through Swellable Polymeric Systems, J. Membrane Sci. 7, 241–253 (1980)CrossRefGoogle Scholar
  67. Peppas, N. A., Meadows, D. L.: Macromolecular Structure and Solute Diffusion in Membranes: An Overview of Recent Theories, J. Membrane Sci. 16, 361–377 (1983)CrossRefGoogle Scholar
  68. Peppas, N. A., Moynihan, H. J.: Solute Diffusion in Swollen Membranes. IV. Theories for Moderately Swollen Networks, J. Appl. Polym. Sci. 30, 2589–2606 (1985)CrossRefGoogle Scholar
  69. Peppas, N. A., Reinhart, C. T.: Solute Diffusion in Swollen Membranes. Part I. A New Theory, J. Membrane Sci. 15, 275–287 (1983)CrossRefGoogle Scholar
  70. Peppas, N. A., Sinclair, J. L.: Anomalous Transport of Penetrants in Glassy Polymers, Colloid and Polymer Sci. 261, 404–408 (1983)CrossRefGoogle Scholar
  71. Peterlin, A.: Diffusion with Discontinuous Swelling. V. Type II Diffusion into Sheets and Spheres, J. Polym. Sci., Polym. Phys. Ed. 17, 1741–1756 (1979)CrossRefGoogle Scholar
  72. Petropoulos, J. H., Roussis, P. P.: A Discussion of Theoretical Models of Anomalous Diffusion of Vapors in Polymers, pp. 219–232. In: Permeability of Plastic Films and Coatings to Gases, Vapors, and Liquids, Hopfenberg, H. B. (Ed.), Plenum Press, New York (1974)Google Scholar
  73. Petropoulos, J. H., Roussis, P. P.: The Influence of Transverse Differential Swelling Stresses on the Kinetics of Sorption of Penetrants by Polymer Membranes, J. Membrane Sci. 3, 343–356(1978)CrossRefGoogle Scholar
  74. Rebenfeld, L., Makarewicz, P. J., Weignann, H.-D., Wilkes, G. L.: Interactions Between Solvents and Polymers in the Solid State, J. Macromol. Sci.-Rev. Macromol. Chem. C15, 279–393 (1976)CrossRefGoogle Scholar
  75. Reinhart, C. T., Peppas, N. A.: Solute Diffusion in Swollen Membranes. Part II. Influence of Crosslinking on Diffusive Properties, J. Membrane Sci. 18, 227–239 (1984)CrossRefGoogle Scholar
  76. Roorda, W. E., Bodde, H. E., de Boer, A. G., Junginger, H. E.: Synthetic Hydrogels as Drug Delivery Systems, Pharmaceutisch Weekblad, Scientific Edition 8, 165–189 (1986 a)Google Scholar
  77. Roorda, W. E., de Vries, M. A., Kosho, C., de Leede, L. G. T., de Boer, A. G., Junginger, H. E.: Zero-Order Release of Oxprenolol-HCl: A New Approach, pp. 206–207. In: Proceedings of the 13th International Symposium on Controlled Release of Bioactive Materials, I. A. Chaudry and C. Thies (Eds.), Norfolk, Virginia, August 3–6 (1986b)Google Scholar
  78. Rudolph, F. B.: Diffusion in a Multicomponent Inhomogeneous System with Moving Boundaries. I. Swelling at Constant Volume, J. Polym. Sci., Polym. Phys. Ed. 17, 1709–1718(1979)CrossRefGoogle Scholar
  79. Rudolph, F. B.: Diffusion in a Multicomponent Inhomogeneous Multiphase System with Moving Boundaries. II. Increasing or Decreasing Volume (Swelling or Drying), J. Polym. Sci., Polym. Phys. Ed. 18, 2323–2336 (1980)CrossRefGoogle Scholar
  80. Segot-Chicq, S., Peppas, N. A.: Solute and Penetrant Diffusion in Swellable Polymers. IV. Semicrystalline, Swelling-Controlled Release Systems of Poly(Ethylene-co-Vinyl Alcohol). J. Controlled Release 3, 193–204 (1986)CrossRefGoogle Scholar
  81. Seinfeld, J. H., Lapidus, L.: Mathematical Models in Chemical Engineering, Vol. 3, pp. 225–229, Prentice Hall, Englewood Cliff, New Jersey (1974)Google Scholar
  82. Sfirakis, A., Rogers, C. E.: Sorption and Diffusion of Alcohols in Amorphous Polymers, Polym. Eng. Sci. 21, 542–547 (1981)CrossRefGoogle Scholar
  83. Singh, S. K.: Analysis and Development of Some Controlled Release Systems, Ph. D. Dissertation, Kansas State University, Manhattan, Kansas, pp. IV.19–IV.82 (1987)Google Scholar
  84. Singh, S. K., Fan, L. T.: A Generalized Model for Swelling-Controlled Release Systems, Biotechnology Progress 2, 145–156 (1986)CrossRefGoogle Scholar
  85. Thomas, N., Windle, A. H.: Discontinuous Shape Changes Associated with Case II Transport of Methanol in Thin Sheets of PMMA, Polymer 18, 1195 (1977)CrossRefGoogle Scholar
  86. Thomas, N., Windle, A. H.: Case II Swelling of PMMA Sheet in Methanol, J. Membrane Sci. 5, 337–342 (1978 a)CrossRefGoogle Scholar
  87. Thomas, N., Windle, A. H.: Transport of Methanol in Poly(Methyl Methacrylate), Polymer 19, 255–265 (1978b)CrossRefGoogle Scholar
  88. Thomas, N. L., Windle, A. H.: A Theory of Case II Diffusion, Polymer 23, 529–542 (1982)CrossRefGoogle Scholar
  89. Tosun, L, Yilmaz, L.: On the Fickian Diffusion of Organic Penetrants in Glassy Polymers, Polym. Eng. Sci. 22, 1043–1045 (1982)CrossRefGoogle Scholar
  90. Tu, Y.-O.: A Multi-Phase Stefan Problem Describing the Swelling and the Dissolution of Glassy Polymer, Quart. Appl. Math. XXXV, 269–285 (1977)Google Scholar
  91. Tu, Y.-O., Ouano, A. C.: Model for the Kinematics of Polymer Dissolution, IBM J. Res. Develop. 12, 197–208 (1977)Google Scholar
  92. Urdahl, K. G., Peppas, N. A.: Anomalous Penetrant Transport in Glassy Polymers. V. Cyclohexane Transport in Polystyrene, J. Appl. Polym. Sci. 33, 2669–2687 (1987)CrossRefGoogle Scholar
  93. van Kampen, N. G.: Stochastic Process in Physics and Chemistry, North Holland, Netherlands (1981)Google Scholar
  94. Vieth, W. R., Howell, J. M., Hsieh, J. H.: Dual Sorption theory, J. Membrane Sci. 1, 177–220(1976)CrossRefGoogle Scholar
  95. Vieth, W. R., Sladek, K. J.: A Model for Diffusion in a Glassy Polymer, J. Colloid Sci. 20, 1014–1033(1965)CrossRefGoogle Scholar
  96. Vrentas, J. S., Duda, J. L.: Diffusion in Polymer-Solvent Systems. III. Construction of Deborah Number Diagrams, J. Polym. Sci. Polym. Phys. Ed., 15, 441–453 (1977)CrossRefGoogle Scholar
  97. Vrentas, J. S., Duda, J. L., Ling, H. C.: Enhancement of Impurity Removal from Polymer Films, J. Appl. Polym. Sci. 30, 4499–4516 (1985)CrossRefGoogle Scholar
  98. Vrentas, J. S., Jarzebski, C. M., Duda, J. L.: A Deborah Number for Diffusion in Polymer-Solvent Systems, AIChE J. 21, 894–901 (1975)CrossRefGoogle Scholar
  99. Wang, F. H. L., Duda, J. L., Vrentas, J. S.: Analysis of Impurity Migration in Plastic ontainers, Polym. Eng. Sci. 20, 120–127 (1980)CrossRefGoogle Scholar
  100. Wang, T. T., Kwei, T. K.: Diffusion in Glassy Polymers. Reexamination of Vapor Sorption Data, Macromolecules 6, 919–921 (1973)CrossRefGoogle Scholar
  101. Wang, T. T., Kwei, T. K., Frisch, H. L.: Diffusion in Glassy Polymers. III, J. Polym. Sci, Part A-2, 7, 2019–2028 (1969)CrossRefGoogle Scholar
  102. Windle, A. H.: Case II Sorption, pp. 75–118. In: Polymer Permeability, J. Comyn (Ed.), Elsevier Applied Science Publishers, London (1985)CrossRefGoogle Scholar
  103. Yariv, A.: An Introduction to Theory and Applications of Quantum Mechanics, pp. 253–259, John Wiley and Sons, New York (1982)Google Scholar
  104. Yasuda, H., Lamaze, C. E.: Permeability of Solutes in Homogeneous Water-Swollen Polymer Membranes, J. Macromol. Sci. Phys. 85, 111–134 (1971)Google Scholar
  105. Yasuda, H., Peterlin, A., Colton, C. K., Smith, K. A., Merril, E. W.: Permeability of Solutes Through Hydrated Polymer Membranes. Part III. Theoretical Background for the Selectivity of Dialysis Membranes, Die Makromolekulare Chemie 126, 177–186 (1969)CrossRefGoogle Scholar
  106. Ya’suda, H., Stannett, V., Frisch, H. L., Peterlin, A.: The Permeability of Strained Polymer Films, Die Makromolekulare Chemie 73, 188–202 (1964)CrossRefGoogle Scholar
  107. Yilmaz, L., Tosun, I., Gürkan, T., Gülcat, U.: Anomalous Diffusion of Liquids in Glassy Polymers, Mathematical Modelling 4, 535–543 (1983)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag, Berlin Heidelberg 1989

Authors and Affiliations

  • Liang-tseng Fan
    • 1
  • Satish Kumar Singh
    • 2
  1. 1.Department of Chemical EngineeringKansas State UniversityManhattanUSA
  2. 2.Kabi PharmaSolnaSweden

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