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Part of the book series: NATO ASI Series ((NSSE,volume 354))

Abstract

The geometric features of sponges, which describe polycontinuous morphologies, are discussed. The focus is on 3-periodic surfaces, which have an underlying 3-d lattice. Definitions and explanations of a range of concepts from non-euclidean geometry, topology and differential geometry are used to derive local and global features of smoothly curved sponges, facetted polyhedral sponges and reticulating networks of edges on these forms.

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References

  1. L.E. Scriven, Nature 1976, 263: 123–125.

    Article  Google Scholar 

  2. W. Fischer and E. Koch, Phil. Trans. Roy. Soc. Lond. A 1996, 354: 2105–2142.

    Article  CAS  Google Scholar 

  3. S.T. Hyde and S. Andersson, Z. Kristallogr. 1984, 168: 221–254.

    Article  Google Scholar 

  4. S. Andersson, S.T. Hyde, and J.-O. Bovin, Z. Kristallogr. 1985, 173: 97–99.

    Article  CAS  Google Scholar 

  5. S. Andersson, Angew. Chem. Int. Ed. Engl. 1983, 22: 69–81.

    Article  Google Scholar 

  6. S. Andersson, S.T. Hyde and H.-G.von Schnering, Z. Kristallogr.1984, 168: 1–17.

    Google Scholar 

  7. S. T. Hyde and S. Andersson, ibid., 1986, 174: 225–236.

    Google Scholar 

  8. M. O’Keeffe and B.G. Hyde, “Crystal Structures. 1. Patterns and Symmetry.” Washington: Mineralogical Society of America; 1996.

    Google Scholar 

  9. T. Jiang, A.J. Lough, G.A. Ozin, D. Young, and R.L. Bedard, Chem. Mater. 1995, 7: 245–248.

    Article  CAS  Google Scholar 

  10. G. Stucky, A. Monnier, F. Schüth, Q. Huo, D. Margolese, D. Kumar, M. Krishnamurty, P. Petroff, A. Firouzi, M. Jamicke and B. Chmelka, Mol. Cryst. Liq. Cryst. 1994, 240: 187–200.

    Article  CAS  Google Scholar 

  11. S. Inagaki, A. Koiwai, N. Suzuki, Y. Fukushima and K. Kuroda, Bull. Chem. Soc. Japan 1996, 96: 1449.

    Article  Google Scholar 

  12. S. Inagaki, Y. Fukushima and K. Kuroda, Chem. Comm. 1993, 8: 680–682.

    Article  Google Scholar 

  13. Q. Huo, R. Leon, P. Petroff and G. Stucky, Science 1995, 268: 1324–1327.

    Article  CAS  Google Scholar 

  14. C.-Y. Chen, S.-Q. Xiao and M.E. Davis, Microporous Materials 1995, 4: 1–20.

    Article  Google Scholar 

  15. J.S. Beck, C.T.-W. Chu, I.D. Johnson, C.T. Kresge, M.E. Leonowicz, W.J. Roth and J.C. Vartuli, U.S. Patent 5108725 (1992).

    Google Scholar 

  16. S.A. Bagshaw, E. Prouzet and T.J. Pinnavaia, Science 1995, 269: 1242.

    Article  Google Scholar 

  17. P. Behrens, Adv. Mater. 1993, 5: 127–132.

    Article  CAS  Google Scholar 

  18. K. Larsson, Nature 1983, 304: 664.

    Article  Google Scholar 

  19. K. Larsson, J. Phys. Chem. 1989, 93: 7304–7314.

    Article  CAS  Google Scholar 

  20. W. Longley and T.J. Mackintosh, Nature 1983, 303: 612–614.

    Article  CAS  Google Scholar 

  21. V. Luzzati and P.A. Spegt, Nature 1967, 215: 701–704.

    Article  CAS  Google Scholar 

  22. P. Ström and D.M. Anderson, Langmuir 1992, 8: 691–709.

    Article  Google Scholar 

  23. J. Seddon and R. Templer, Phil. Trans. R. Soc. Lond. A 1993, 344: 377–401.

    Article  CAS  Google Scholar 

  24. S.T. Hyde, S. Andersson, B. Ericsson and K. Larsson, Z. Kristallogr. 1984, 168: 213–219.

    Article  CAS  Google Scholar 

  25. D.M. Anderson and E.L. Thomas, Macromolecules 1988, 21: 3221–3230.

    Article  CAS  Google Scholar 

  26. D.A. Hajduk, P.E. Harper, S.M. Gruner, C.C. Honeker, G. Kim, E.L. Thomas and L.J. Fetters, Macromolecules 1994, 27: 4063.

    Article  CAS  Google Scholar 

  27. H. Hasegawa, H. Tanaka, K. Yamasaki and T. Hashimoto, Macromolecules 1987, 20: 1651–1662.

    Article  CAS  Google Scholar 

  28. H. Hasegawa, Y. Nishikawa, S. Koizumi, T. Hashimoto and S. Hyde, in Proc. Conference on Advanced Materials (IUMRS-ICAM-93). (1993): Elsevier S. P. MRS Japan.

    Google Scholar 

  29. E.L. Thomas, D.M. Anderson, C.S. Henkee and D. Hoffman, Nature 1988, 334: 598–601.

    Article  CAS  Google Scholar 

  30. Y.J. Bouligand, J. Phys. (Fr.) Colloque 1990, C7: 35.

    Google Scholar 

  31. T. Landh, FEBS Lett. 1995, 369 (1): 13–17.

    Article  CAS  Google Scholar 

  32. S. Hyde, B. Ninham, S. Andersson, Z. Blum, T. Landh, K. Larsson and S. Lidin, The Language of Shape“ Amsterdam: Elsevier; 1997.

    Google Scholar 

  33. G. Donnay and D.L. Pawson, Science 1969, 166, 1147; H.-U.Nissen, Science 1969, 166, 1150.

    Article  Google Scholar 

  34. G. Porte, Curr. Rev. Colloid Sci. 1996, 1: 345–349.

    Article  CAS  Google Scholar 

  35. G. Porte, R. Gomati, O. El Haitamy, J. Appell and J. Marignan, J. Phys. Chem. 1986, 90: 5746–5751.

    Article  CAS  Google Scholar 

  36. K. Fontell, ACS Symposium Series,1975,(9): 270–277.

    Google Scholar 

  37. H. Jinnai, T. Koga, Y. Nishikawa, T. Hashimoto and S.T. Hyde, Phys. Rev. Lett.,1997, 78, 2248–2251..

    Google Scholar 

  38. A.P. Roberts, D. Bentz and M.A. Knackstedt, Proc. Soc. Petrol. Eng. 37024, (SPE Conference, Adelaide, 1996 ), 551–559.

    Google Scholar 

  39. M. Knackstedt, private communication

    Google Scholar 

  40. R. Corkery, T. Senden and S.T. Hyde, in preparation.

    Google Scholar 

  41. D. Hilbert and S. Cohn-Vossen, “Geometry and the Imagination” New York: Chelsea Publishers; 1952.

    Google Scholar 

  42. D.M. Anderson, Studies in the microstructure of microemulsions (1986), Ph.D. thesis, University of Minnesota.

    Google Scholar 

  43. D. Hilbert, Trans. Am. Math. Soc. 1901, 87–99.

    Google Scholar 

  44. J.-F. Sadoc and J. Charvolin, Acta Cryst. 1989, A45: 10–20.

    Article  Google Scholar 

  45. S.H. Tolbert, T.E. Schäffer, J. Feng, P.K. Hansma and G.D. Stucky, Chem. Mater. 1997, 9: 1962–1967.

    Article  CAS  Google Scholar 

  46. J.C.C. Nitsche, “Lectures on Minimal Surfaces”, Vol. 1. Cambridge: Cambridge University Press; 1989.

    Google Scholar 

  47. D. Hoffman, Math. Intell. 1987, 9: 8–21.

    Article  Google Scholar 

  48. E. Koch and W. Fischer, Acta Cryst. 1990, A46: 33–40.

    Article  Google Scholar 

  49. W. Fischer and E. Koch, Z. Kristallogr. 1996, 211: 1–3.

    Article  CAS  Google Scholar 

  50. W. Fischer and E. Koch, Acta Cryst. 1989, A45: 726–732.

    Article  Google Scholar 

  51. A.-M. Levelut, E. Hallouin, D. Bennemann, G. Heppke and D. Lötzsch, J. Phys. II (France) 1997, 7: 981–1000.

    Article  CAS  Google Scholar 

  52. A.H. Schoen, “Infinite periodic minimal surfaces without self-intersections ”,(1970), N.A.S.A. Technical Report #D5541.

    Google Scholar 

  53. A. Schoen, in “Geometric Analysis and Computer Graphics”,R. Finn, D.A. Hoffman and P. Concus, eds. (1991), Springer-Verlag: New York. p. 147–158.

    Google Scholar 

  54. R. Kusner, in [52]. p. 103–108.

    Google Scholar 

  55. A.F. Wells, “Three-Dimensional Nets and Polyhedra” (1977). John Wiley and Sons: New York. p. 160.

    Google Scholar 

  56. H.-G. von Schnering and R. Nesper, Angew. Chem. Int. Ed. Engl. 1987, 26: 1059–1080.

    Article  Google Scholar 

  57. S.T. Hyde, Z. Kristallogr. 1989, 187: 165–185.

    Article  CAS  Google Scholar 

  58. S. Lidin, J. Phys. (France) 1988, 49: 421–427.

    Article  Google Scholar 

  59. S.-S. Chern, in “Differential geometry and complex analysis”, I.C. H.M. Farkas, eds. (1985), Springer Verlag: Berlin. p. 155–163.

    Google Scholar 

  60. A. Ramsay and R.D. Richtmyer, Introduction to Hyperbolic Geometry“, Springer Verlag New York, Inc., 1995.

    Book  Google Scholar 

  61. A. Fogden and S.T. Hyde, in preparation.

    Google Scholar 

  62. S.T. Hyde, Curr. Opinion Solid State Mat. Sci. 1996, 1: 653–662.

    Article  Google Scholar 

  63. H.S.M. Coxeter, “Twelve Geometric Essays”, Carbondale: Southern Illinois University Press; 1968.

    Google Scholar 

  64. H.S.M. Coxeter, Proc. Lond. Math. Soc.,1937,Ser. 2, 43: 33–62.

    Google Scholar 

  65. W. Fischer, Z. Kristallogr. 1974, 140: 50–74.

    Article  CAS  Google Scholar 

  66. P.A. Firby and C.F. Gardiner, “Surface Topology’; 2nd. ed., Chichester: Ellis Horwood Limited; 1991.

    Google Scholar 

  67. M. O’Keeffe, Z. Kristallogr. 1991, 196: 21–37.

    Article  Google Scholar 

  68. S. Andersson, S.T. Hyde, K. Larsson and S. Lidin, Chen. Rev. 1988, 88: 221–42.

    Article  CAS  Google Scholar 

  69. G.O. Brunner and W.M. Meier, Nature 1989, 337: 146–147.

    Article  CAS  Google Scholar 

  70. L. Stixrude and M.S.T. Bukowinski, Am. Mineral. 1990, 75: 1159–1169.

    CAS  Google Scholar 

  71. S.T. Hyde, Acta Cryst. 1993, A50: 753–759.

    Google Scholar 

  72. S.T. Hyde, Z. Blum, and B.W. Ninham, Acta Cryst.1993, A49: 586–589.

    Google Scholar 

  73. A. Fogden and M. Jacob, Z. Kristallogr. 1995, 210: 398–406.

    Article  CAS  Google Scholar 

  74. A.A. Barbosa and A.J. Palangana, Phys. Rev. E 1997, 56 (2): 2295.

    Google Scholar 

  75. A.L. Mackay and J. Klinowski, Compu. Math. Appl. 1986, 12B: 803–824.

    Article  Google Scholar 

  76. A.L. Mackay and H. Terrones, Nature 1991, 352: 762.

    Article  Google Scholar 

  77. A.L. Mackay and H. Terrones, Phil. Trans. R. Soc. Lond. A 1993, 343: 113–127.

    Article  CAS  Google Scholar 

  78. T. Lenosky, X. Gonze, M. Teter and V. Elser, Nature 1992, 355: 333–335.

    Article  CAS  Google Scholar 

  79. D. Vanderbilt and J. Tersoff, Phys. Rev. Lett. 1991, 68: 511–513.

    Article  Google Scholar 

  80. J. Gibson, M. Kolohan and H. Riley, J. Chem. Soc. 1946: 456–461.

    Google Scholar 

  81. G.B. Adams, O.F. Sankey, J.B. Page, M. O’Keeffe and D.A. Drabold, Science 1992, 256: 1792–1795.

    Article  Google Scholar 

  82. M. O’Keeffe, G.B. Adams and O.F. Sankey, Phys. Rev. Lett. 1992, 68: 2325–8.

    Article  Google Scholar 

  83. S.T. Hyde and M. O’Keeffe, Phil. Trans. R. Soc. Lond. A 1996, 354: 1999–2008.

    Article  CAS  Google Scholar 

  84. E.R. Neovius, Bestimmung Zweier Speciellen Periodische MinimaL Flaechen“ Helsinki: Frenckel Son; 1883.

    Google Scholar 

  85. P. Pearce, “Structure In Nature is a Strategy for Design ”,Cambridge, Mass.: MIT Press; 1978.

    Google Scholar 

  86. D. Weaire, ed. “The Kelvin Problem”, London: Taylor and Francis; 1996.

    Google Scholar 

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Hyde, S.T. (1999). Sponges. In: Sadoc, J.F., Rivier, N. (eds) Foams and Emulsions. NATO ASI Series, vol 354. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9157-7_26

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  • DOI: https://doi.org/10.1007/978-94-015-9157-7_26

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5180-6

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