Part of the book series: Advances in Delivery Science and Technology ((ADST))

Abstract

Porous systems play a significant role in controlled release. Porous membranes and matrices can be used to store drug prior to release, and pore structure plays a significant role in determining release kinetic profiles. In this chapter we review methods used to measure pore structure and mathematical models used to relate pore structure to drug transport properties. Steric and hydrodynamic interactions between drug and pore walls, pore tortuosity, and variation in pore width are identified as factors affecting transport. Percolation theory, which addresses connectedness of random pore networks and its effect on overall releasability of drug and release rate, is discussed. Concepts developed for porous systems can be applied, with some modifications, to transport in other heterogeneous systems, such as tissue interstitium and hydrogels.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 160.49
Price includes VAT (Germany)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 213.99
Price includes VAT (Germany)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
EUR 213.99
Price includes VAT (Germany)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Siegel RA (1989) Modeling of drug release from porous polymers. In: Rosoff M (ed) Controlled release of drugs: polymers and aggregate systems. VCH, New York, pp 1–51

    Google Scholar 

  2. Bean CP (1972) The physics of porous membranes–neutral pores. In: Eisenmann G (ed) Membranes. Marcel Dekker, New York, pp 1–54

    Google Scholar 

  3. Deen WM, Bohrer MP, Epstein NB (1981) Effects of molecular size and configuration on diffusion in microporous membranes. AIChE J 27:952–959

    Article  CAS  Google Scholar 

  4. Madou M (2002) Fundamentals of microfabrication, 2nd edn. CRC, New York

    Google Scholar 

  5. Mueller A, Hillmyer M, Bates FS (2009) Ordered network mesostructures in block polymer materials. Macromolecules 42:7221–7250

    Article  Google Scholar 

  6. Nuxoll EE, Hillmeyer MA, Wang R, Leighton C, Siegel RA (2009) Composite block polymer-microfabricated silicon nanoporous membrane. ACS Appl Mater Interf 1:889–893

    Article  Google Scholar 

  7. Anglin EJ, Cheng L, Freeman WR, Sailor MJ (2008) Porous silicon in drug delivery devices and materials. Adv Drug Deliv Rev 60:1266–1277

    Article  PubMed  CAS  Google Scholar 

  8. Slowing II, Vivero-Escoto JL, Wu C-W, Lin VS-Y (2008) Mesoporous silica nanoparticles as controlled release drug delivery and gene transfection carriers. Adv Drug Deliv Rev 60:1278–1288

    Article  PubMed  CAS  Google Scholar 

  9. Cauda V, Engelke H, Sauer A, Arcizet D, Bräuchle C (2010) Colchicine-loaded lipid bilayer-coated 50 nm mesoporous nanoparticles efficiently induce microtubule depolymerization upon cell uptake. Nano Letters 10:2484–2492

    Article  PubMed  CAS  Google Scholar 

  10. Martin F, Walczak R, Boiarski A, Cohen M, West T, Cosentino C, Ferrari M (2005) Tailoring width of microfabricated nanochannels to solute size can be used to control diffusion kinetics. J Control Release 102:123–133

    Article  PubMed  CAS  Google Scholar 

  11. Baker RW (2004) Membrane technology and applications. Wiley, Chichester

    Book  Google Scholar 

  12. Li M, Rouaud O, Poncelet D (2008) Microencapsulation by solvent evaporation: state of the art for process engineering approaches. Int J Pharm 363:26–39

    Article  PubMed  CAS  Google Scholar 

  13. Martin AN (2011) Micromeritics. In: Sinko P (ed) Martin’s physical pharmacy and pharmaceutical sciences. Kluwer, Philadelphia, pp 442–468

    Google Scholar 

  14. Chandler R, Koplik J, Lerman K, Willemsen JF (1982) Capillary displacement and percolation in porous media. J Fluid Mech 119:249–267

    Article  Google Scholar 

  15. Lane A, Shah N, Connor WC (1986) Measurement of the morphology of high-surface-area solids: porosimetry as a percolation process. J Coll Interf Sci 109:235–242

    Article  CAS  Google Scholar 

  16. Miller ES, Peppas NA, Winslow DN (1983) Morphological changes of ethylene/vinyl acetate-based controlled delivery systems during release of water-soluble solutes. J Membr Sci 14:79–92

    Article  CAS  Google Scholar 

  17. Lightfoot EN, Bassingthwaighte JB, Grabowski EF (1976) Hydrodynamic models for diffusion in microporous membranes. Ann Biomed Eng 4:78–90

    Article  PubMed  CAS  Google Scholar 

  18. Malone DM, Anderson JL (1978) Hindered diffusion of particles through small pores. Chem Eng Sci 33:1429–1440

    Article  CAS  Google Scholar 

  19. Deen WM (1989) Hindered transport of large molecules in liquid-filled pores. AIChE J 33:1409–1423

    Article  Google Scholar 

  20. Cassasa EF (1967) Equilibrium distribution of flexible polymer chains between a macroscopic solution phase and small voids. J Poly Sci Polym Lett 5:773–777

    Article  Google Scholar 

  21. Davidson MG, Suter UW, Deen WM (1987) Hydrodynamic partitioning of flexible macromolecules between bulk solution and cylindrical pores. Macromolecules 20:1141–1146

    Article  CAS  Google Scholar 

  22. Brenner H, Gaydos LJ (1977) The constrained Brownian movement of spherical particles in cylindrical pores of comparable radius. J Coll Interf Sci 58:312–356

    Article  Google Scholar 

  23. Faxen H (1923) Die Bewegung einer Einer Starren Kuegel laengs der Achse mit zaeher Fluessigkeit gefuellten Rohres. Ark Mat Astron Fys 17:1

    Google Scholar 

  24. Glandt ED (1981) Noncircular pores in model membranes: a calculation of the effect of pore geometry on the partition of a solute. J Membr Sci 8:331–336

    Article  CAS  Google Scholar 

  25. Cosentino C, Amato F, Walczak R, Boiarski A, Ferrari M (2005) Dynamic model of biomolecular diffusion through two-dimensional nanochannels. J Phys Chem B 109:7358–7364

    Article  PubMed  CAS  Google Scholar 

  26. Pricl S, Ferrone M, Fermeglia M, Amato F, Cosentino C, Ming-Cheng Cheng M, Walczak R, Ferrari M (2006) Multiscale modeling of protein transport in silicon membrane nanochannels. Part 1. Derivation of molecular parameters from computer simulations. Biomed Microdevices 8:277–290

    Article  PubMed  CAS  Google Scholar 

  27. Amato F, Cosentino C, Pricl S, Ferrone M, Fermeglia M, Ming-Cheng Cheng M, Walczak R, Ferrari M (2006) Multiscale modeling of protein transport in silicon membrane nanochannels. Part 2. From molecular parameters to a perdictive continuum diffusion model. Biomed Microdevices 8:291–298

    Article  PubMed  CAS  Google Scholar 

  28. Higuchi T (1963) Mechanism of sustained-action medication. Theoretical analysis of solid drugs dispersed in solid matrices. J Pharm Sci 52:1145–1149

    Article  PubMed  CAS  Google Scholar 

  29. Pismen LM (1974) Diffusion in porous media of a random structure. Chem Eng Sci 29:1227–1236

    Article  CAS  Google Scholar 

  30. Siegel RA, Langer R (1986) A new Monte Carlo approach to diffusion in constricted porous geometries. J Coll Interf Sci 109:426–440

    Article  CAS  Google Scholar 

  31. Siegel RA, Langer R (1990) Mechanistic studies of macromolecular drug release from macroporous polymers. II. Models for the slow kinetics of drug release. J Control Release 14:153–167

    Article  CAS  Google Scholar 

  32. Dudko OK, Berezhkovskii AM, Weiss GH (2005) Time-dependent diffusion coefficients in periodic porous media. J Phys Chem B 109:21296–21299

    Article  PubMed  CAS  Google Scholar 

  33. Maknovskii YA, Berezhkovskii AM, Zitserman VYu, Zitserman VY (2009) Time-dependent diffusion in tubes with periodic partitions. J Chem Phys 131:104705

    Article  Google Scholar 

  34. Broadbent S, Hammersley J (1957) Percolation processes: crystals and mazes. Proc Cambr Philos Soc 53:629–641

    Article  CAS  Google Scholar 

  35. Bollobas B, Riordan O (2006) Percolation. Cambridge University Press, Cambridge

    Google Scholar 

  36. Stauffer D, Aharony A (1994) Introduction to percolation theory. CRC, New York

    Google Scholar 

  37. Sahimi M (1994) Applications of percolation theory. Taylor and Francis, Boca Raton, FL

    Google Scholar 

  38. Saltzman M, Langer R (1989) Transport rates of proteins in porous materials with known microgeometry. Biophys J 55:163–171

    Article  PubMed  CAS  Google Scholar 

  39. Siegel RA, Kost J, Langer RA (1989) Mechanistic studies of macromolecular drug release from macroporous polymers. I. Experiments and preliminary theory concerning completeness of drug release. J Control Release 8:223–236

    Article  CAS  Google Scholar 

  40. Hastedt JE, Wright JL (1990) Diffusion in porous materials above the percolation threshold. Pharm Res 7:893–901

    Article  PubMed  CAS  Google Scholar 

  41. Hastedt JE, Wright JL (2006) Percolative transport and cluster diffusion near and below the percolation threshold of a porous polymeric matrix. Pharm Res 23:2427–2440

    Article  PubMed  CAS  Google Scholar 

  42. Winterfeld PH, Scriven LE, Davis HT (1981) Percolation and conduction on 3D Voronoi and regular networks: a second case study in topological disorder. J Phys C Solid State Phys 17:3429–3439

    Google Scholar 

  43. Powell MJ (1979) Site percolation in randomly packed spheres. Phys Rev B 20:4194–4198

    Article  Google Scholar 

  44. Vicsek T, Kertesz J (1981) Monte Carlo renormalization-group approach to percolation in a continuum: test of universality. J Phys A Math Gen 14:L31–L37

    Article  CAS  Google Scholar 

  45. Boissonade J, Barreau F, Carmona F (1983) The percolation of fibers with random orientations: a Monte Carlo study. J Phys A Math Gen 16:2777–2787

    Article  Google Scholar 

  46. Kirkpatrick S (1973) Percolation and conduction. Rev Mod Phys 574:574–588

    Article  Google Scholar 

  47. Brandt WW (1975) Use of percolation theory to estimate effective diffusion coefficients of particles migrating on various ordered lattices and in a random network structure. J Chem Phys 63:5162–5167

    Article  CAS  Google Scholar 

  48. Barocas V, Drasler W, Girton T, Guler I, Knapp DR, Moeller J, Parsonage E (2009) A dissolution-diffusion model for the TAXUS™ drug-eluting stent with surface burst estimated from continuum percolation. J Biomed Mater Res B Appl Biomater 90B:267–274

    CAS  Google Scholar 

  49. Schnitzer JE (1988) Analysis of steric partition behavior of molecules in membranes using statistical physics. Application to gel chromatography and electrophoresis. Biophys J 54:1065–1076

    Article  PubMed  CAS  Google Scholar 

  50. Lustig SR, Peppas NA (1988) Solute diffusion in swollen membranes. IX. Scaling laws for solute diffusion in gels. J Appl Polym Sci 36:735–747

    Article  CAS  Google Scholar 

  51. Amsden B (1998) Solute diffusion within hydrogels. Mechanisms and models. Macromolecules 31:8382–8395

    Article  CAS  Google Scholar 

  52. Masaro L, Zhu XX (1999) Physical models of diffusion for polymer solutions, gels, and solids. Progr Polym Sci 24:731–775

    Article  CAS  Google Scholar 

  53. Sakiyama-Elbert SE, Hubbell JA (2000) Controlled release of nerve growth factor from a heparin-containing fibrin-based cell ingrowth matrix. J Control Release 69:149–158

    Article  PubMed  CAS  Google Scholar 

  54. Amsden BG, Cheng Y-L (1994) Enhancement of fraction released above percolation threshold from monoliths containing osmotic excipients. J Control Release 33:99–105

    Article  Google Scholar 

  55. Eitzman DM, Melkote RR, Cussler EL (1996) Barrier membranes with tipped flakes. AIChE J 42:2–9

    Google Scholar 

  56. DeRocher JP, Gettlefinger BT, Wang J, Nuxoll EE, Cussler EL (2005) Barrier membranes with different sizes of aligned flakes. J Membr Sci 254:21–30

    Google Scholar 

  57. Lape NK, Nuxoll EE, Cussler EL (2004) Polydisperse flakes in barrier films. J Membr Sci 236:29–37

    Google Scholar 

  58. Fredrickson GH, Bicerano J (1999) Barrier properties of oriented disc composites. J Chem Phys 110:2181–2188

    Google Scholar 

  59. Liu Q, Cussler EL (2006) Barrier membranes made with lithographically printed flakes. J Membr Sci 285:56–67

    Google Scholar 

  60. Shante VKS, Kirkpatrick S (1971) An introduction to percolation theory. Adv. Phys. 20: 325–357

    Google Scholar 

  61. Nan C-W, Shen Y, Ma J (2010) Physical composites near percolation. Annu Rev Mater Res 40:131–151

    Google Scholar 

  62. Larson RG, Scriven LE, Davis HT (1977) Percolation theory of residual phases in porous media. Nature 268: 409–413

    Google Scholar 

  63. Berkowitz B, Balgerg I (1993) Percolation theory and its application to groundwater hydrology. Water Resourc Res 29:775–794

    Google Scholar 

  64. Holman LE, Leuenberger H (1988) The relationship between solid fraction and mechanical properties of compacts–the percolation theory approach. Int J Pharmaceut 46:35–44

    Google Scholar 

  65. Kuentz M, Leuenberger H (1999) Pressure susceptibility of polymer tablets as a critical property: a modified Heckel equation. J Pharm Sci 88:174–179

    Google Scholar 

  66. Balberg I, Binenbaum N, Wagner N (1984) Percolation thresholds in the three-dimensional sticks system. Phys Rev Lett 52:1465–1468

    Google Scholar 

  67. Leuenberger H, Bonny JD, Kolb M (1995) Percolation effects in matrix-type controlled release systems. Int J Pharmaceut 115:217–224

    Google Scholar 

  68. Tongwen X, Binglin H (1998) Mechanism of sustained drug release in diffusion-controlled polymer matrix--aplication of percolation theory. Int J Pharmaceut 170:139–149

    Google Scholar 

  69. Adrover A, Massimiliano G, Grassi M (1996) Analysis of controlled release in disordered structures: the percolation model. J Membr Sci 113:21–30

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ronald A. Siegel .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer US

About this chapter

Cite this chapter

Siegel, R.A. (2012). Porous Systems. In: Siepmann, J., Siegel, R., Rathbone, M. (eds) Fundamentals and Applications of Controlled Release Drug Delivery. Advances in Delivery Science and Technology. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-0881-9_9

Download citation

Publish with us

Policies and ethics

Navigation