Skip to main content
SpringerLink
Log in

Stochastic Model for Diffusion in Porous or Heterogeneous Polymer Matrix

  • Chapter
Controlled Release

Part of the book series: Polymers ((POLYMERS,volume 13))

  • 245 Accesses

Abstract

A number of new polymeric materials are being explored for possible utilization as carriers for the controlled release of biologically active agents. The morphological structure of most polymers is heterogeneous, consisting of two phases, namely crystalline and amorphous. These two phases are present in varying amounts depending on the composition and the thermal and processing history of the polymer, and are dispersed throughout the body of the polymer. Transport of active agents in such materials is influenced therefore by their molecular structure since the permeabilities of the two phases are different. Crystalline domains in a semi-crystalline polymer are virtually impermeable relative to the amorphous phase; consequently, the diffusing molecule has to follow a tortuous path through the permeable amorphous phase. This permeable phase is interspersed between the impermeable domains serving as boundaries or walls. It is evident that the characteristics of transport in the permeable-impermeable domains of a heterogeneous polymer are similar to those in a porous medium. Thus the release of an active agent from either the heterogeneous polymer or the porous matrix carrier can be analyzed analogously (see, e.g., Peterlin, 1979, Harland and Peppas, 1986).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Akanni, K. A., Evans, J. W., Abramson, LS.: Effective Transport Coefficients in Heterogeneous Media, Chem. Eng. Sci. 42, 1945–1954 (1987)

    Article  CAS  Google Scholar 

  • Aris, R.: The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, Vol. I, The Theory of the Steady State, pp. 23–25, Clarendon Press, Oxford (1975)

    Google Scholar 

  • Bharucha-Reid, A. T.: Elements of the Theory of Markov Processes and Their Applications, pp. 129–163, McGraw-Hill, New York (1960)

    Google Scholar 

  • Bhatia, S. K.: Directional Autocorrelation and the Diffusional Tortuosity of Capillary Porous Media, J. Catalysis 93, 192–196 (1985)

    Article  CAS  Google Scholar 

  • Bhatia, S. K.: Stochastic Theory of Transport in Inhomogeneous Media, Chem. Eng. Sci. 41, 1311–1324(1986)

    Article  CAS  Google Scholar 

  • Chou, S. T., Fan, L. T., Nassar, R.: Stochastic Analysis of Stepwise Cellulose Degradation Data, Presented at the AIChE 1987 Summer National Meeting, Minneapolis, Minnesota, August 16–19 (1987).

    Google Scholar 

  • De Jong, G. De J.: Longitudinal and Transverse Diffusion in Granular Deposits, Trans. Am. Geophys. Union 39, 67–74 (1958)

    Google Scholar 

  • Duggirala, S. K.: Stochastic Analysis of Particulate Processes-A Study of Attrition, Sieving and Grinding, M. S. Thesis, Department of Chemical Engineering, Kansas State University, Manhattan, Kansas (1986)

    Google Scholar 

  • Fan, L. T., Shin, S. H.: Stochastic Diffusion Model of Non-Ideal Mixing in a Horizontal Drum Mixer, Chem. Eng. Sci. 34, 811–820 (1979)

    Article  CAS  Google Scholar 

  • Fatt, I.: The Network Model of Porous Media, Parts I, II, III, Petroleum Transactions, AIME 207, 144–181 (1956)

    Google Scholar 

  • Feng, C., Stewart, W. E.: Practical Models for Isothermal Diffusion and Flow of Gases in Porous Solids, Ind. Eng. Chem. Fundam. 12, 143–147 (1973)

    Article  CAS  Google Scholar 

  • Foster, R. N., Butt, J. B.: A Computational Model for the Structure of Porous Materials Employed in Catalysis, AIChE J. 12, 180–185 (1966)

    Article  CAS  Google Scholar 

  • Fox, R. O.: Master Equation Formulation and Monte Carlo Simulation of Some Multinomial Stochastic Processes from Chemical Engineering, PhD Dissertation, Kansas State University, Manhattan, Kansas (1987)

    Google Scholar 

  • Gavalas, G. R., Kim, S.: Periodic Capillary Models of Diffusion in Porous Solids, Chem. Eng. Sci. 36, 1111–1122(1981)

    Article  CAS  Google Scholar 

  • Gurny, R., Doelker, E., Peppas, N. A.: Modelling of Sustained Release of Water-Soluble Drugs from Porous, Hydrophobic Polymers, Biomaterials 3, 27–32 (1982)

    Article  CAS  Google Scholar 

  • Harland, R. S., Peppas, N. A.: Drug Diffusion in Heterogeneous Polymeric Systems with Impermeable Domains, pp. 153–154. In: Proceedings of the 13th International Symposium on Controlled Release of Bioactive Materials, Chaudry, I., Theis, C. (Eds.), August 3–6 Norfolk, Virginia (1986)

    Google Scholar 

  • Haring, R. E., Greenkom, R. A.: A.Statistical Model of a Porous Medium with Nonuniform Pores, AIChE J. 16, 477–483 (1970)

    Article  CAS  Google Scholar 

  • Johnson, M. F. L., Stewart, W. E.: Pore Structure and Gaseous Diffusion in Solid Catalysts, J. Catalysis 4, 248–252 (1965)

    Article  CAS  Google Scholar 

  • Langer, R., Folkman, J.: Sustained Release of Macromolecules from Polymers, pp. 175–196. In: Polymeric Delivery Systems, Kostelnik, R. J. (Ed.), Gordon and Breach Science Publishers, New York (1978)

    Google Scholar 

  • Lapidus, H., Lordi, N. G.: Drug Release from Compressed Hydrophilic Matrices, J. Pharm. Sci. 57, 1293–1301 (1968)

    Google Scholar 

  • Manning, J. R.: Diffusion in a Chemical Concentration Gradient, Phys. Rev. 124, 470–482 (1961)

    Article  Google Scholar 

  • Manning, J. R.: Correlated Walk and Diffusion Equations in a Driving Force, Phys. Rev. 139, A126–A135(1965)

    Article  Google Scholar 

  • Mason, E. A., Malinauskas, A. P., Evans III, R. B.: Flow and Diffusion of Gases in Porous Media, J. Chem. Phys. 46, 3199–3216 (1967)

    Article  CAS  Google Scholar 

  • McGregor, R.: Diffusion and Sorption in Fibers and Thin Films, Vol. I., pp. 193–218, Academic Press, New York (1974)

    Google Scholar 

  • Mo, W. T., Wei, J.: Effective Diffusivity in Partially Blocked Zeolite Catalyst, Chem. Eng. Sci. 41, 703–710 (1986)

    Article  CAS  Google Scholar 

  • Nassar, R., Too, J. R., Fan, L. T.: Stochastic Modeling of Polymerization in a Continuous Flow Reactor, J. Appl. Polym. Sci. 26, 3745–3759 (1981)

    Article  CAS  Google Scholar 

  • Pace, R. J., Datyner, A.: Statistical Mechanical Model for Diffusion of Simple Penetrants in Polymers. I. Theory, J. Polym. Sci., Polym. Phys. Ed. 17, 437–451 (1979)

    Article  CAS  Google Scholar 

  • Peterlin, A.: Transport Phenomena and Polymer Morphology, Makromolekulare Chem. Suppl. 3, 215–232(1979)

    Article  CAS  Google Scholar 

  • Pines, E., Prins, W.: Structure-Property Relations of Thermoreversible Macromolecular Hydrogels, Macromolecules 6, 888–895 (1973)

    Article  CAS  Google Scholar 

  • Pismen, I. M.: Diffusion in Porous Media of a Random Structure, Chem. Eng. Sci. 29, 1227–1236(1974)

    Article  CAS  Google Scholar 

  • Rajamani, K., Pate, W. T., Kinneberg, D. J.: Time-Driven and Event-Driven Monte Carlo Simulations of Liquid-Liquid Dispersions: A Comparison, Ind. Eng. Chem. Fundam. 25, 746–752 (1986)

    Article  CAS  Google Scholar 

  • Ryan, D., Carbonell, R. G., Whitaker, S.: A Theory of Diffusion and Reaction in Porous Media. In: Transport with Chemical Reactions, AIChE Symposium Series 202 77, 46–62 (1981)

    Google Scholar 

  • Saffman, P. G.: A Theory of Dispersion in a Porous Medium, J. Fluid Mech. 6, 321–349 (1959)

    Article  Google Scholar 

  • Satterfield, C. N.: Mass Transfer in Heterogeneous Catalysis, pp. 1–77, MIT Press, Cambridge, Massachusetts (1970)

    Google Scholar 

  • Scheidegger, A. E.: Statistical Approach to Miscible Displacement in Porous Media, The Canadian Mining and Metallurgical Bulletin, pp. 26–30, January (1959)

    Google Scholar 

  • Scheidegger, A. E.: Statistical Theory of Flow Through Porous Media. Trans. Soc. Rheol. 9, 313–319 (1965)

    Article  Google Scholar 

  • Seinfeld, J. H., Lapidus, L.: Mathematical Models in Chemical Engineering, Vol. 3, pp. 225–229, Prentice Hall, Englewood Cliff, New Jersey (1974)

    Google Scholar 

  • Silberberg, A.: The Hydrogel-Water Interface. In: Hydrogels for Medical and Related Applications, J. D. Andrade (Ed.), ACS Symposium Series 31, 198–205 (1976)

    Chapter  Google Scholar 

  • Singh, S. K.: Analysis and Development of Some Controlled Release Systems, pp. III.48–III.56, PhD Dissertation, Kansas State University, Manhattan, Kansas (1987)

    Google Scholar 

  • Smith, J. M.: Chemical Engineering Kinetics, pp. 268–269, McGraw-Hill, New York (1970)

    Google Scholar 

  • Theodorou, D., Wei, J.: Diffusion and Reaction in Blocked and High Occupancy Zeolite Catalysts, J. Catalysis 83, 205–224 (1983)

    Article  CAS  Google Scholar 

  • Too, J. R., Nassar, R., Chou, S. T., Fan, L. T.: Stochastic Analysis of Crystallization in an Open Flow System, J. Chinese I. Ch. E. 17, 303–313 (1986)

    CAS  Google Scholar 

  • van Kampen, N. G.: Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, Netherlands (1981)

    Google Scholar 

  • Vrentas, J. S., Duda, J. L.: Molecular Diffusion in Polymer Solutions, AIChE J. 25, 1–24 (1979)

    Article  CAS  Google Scholar 

  • Wakad, N., Nardse, Y.: Effective Diffusivities and Deadend Pores, Chem. Eng. Sci. 29, 1304–1306(1974)

    Article  Google Scholar 

  • Wakao, N., Smith, J. M.: Diffusion in Catalyst Pellets, Chem. Eng. Sci. 17, 825–834 (1962)

    Article  CAS  Google Scholar 

  • Wang, C.-T., Smith, J. M.: Tortuosity Factors for Diffusion in Catalyst Pellets, AIChE J. 29, 132–136(1983)

    Article  CAS  Google Scholar 

  • Whitaker, S.: Advances in Theory of Fluid Motion in Porous Media, Ind. Eng. Chem. 61 (12), 14–28 (1969)

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemical Engineering, Kansas State University, Durland Hall, Manhattan, KS, 66506, USA

    Professor Liang-tseng Fan

  2. Kabi Pharma, Gårdsvägen 6, Box 1828, Solna, S-171 26, Sweden

    Dr. Satish Kumar Singh

Authors
  1. Professor Liang-tseng Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dr. Satish Kumar Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag, Berlin Heidelberg

About this chapter

Cite this chapter

Fan, Lt., Singh, S.K. (1989). Stochastic Model for Diffusion in Porous or Heterogeneous Polymer Matrix. In: Controlled Release. Polymers, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-74507-2_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-74507-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-74509-6

  • Online ISBN: 978-3-642-74507-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation