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Gelation

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Introduction to Sol-Gel Processing
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Abstract

This chapter is devoted to the phenomenon of gelation. It gathers the theoretical models of gelation, comprising the Flory-Stockmayer model, percolation models, fractal structure, and gelation by random growth, such as by diffusion-limited aggregation of sol particles. The experimental techniques to study this phenomenon are next reviewed, in particular the methods based on the determination of viscous behavior. The experimental gelation behavior of a few inorganic and organic materials is finally analyzed.

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References

  • G.C. Abell, Phys. Rev. B 31, 6184–6196 (1985)

    Article  CAS  Google Scholar 

  • H. Aguiar, J. Serra, P. González, B. León, J. Non-Cryst. Solids 355, 475–480 (2009)

    Article  CAS  Google Scholar 

  • R.M. Almeida, A.C. Marques, Chapter 2.1: Characterization of Sol–Gel Materials by Infrared Spectroscopy, in Handbook of Sol-Gel Science and Technology, ed. by L. Klein, M. Aparicio, A. Jitianu, (Springer, New York, 2016)

    Google Scholar 

  • T.S. Asche, M. Duderstaedt, P. Behrens, A.M. Schneider, Chapter 1.13: Atomistic Simulation of Sol–Gel-Derived Hybrid Materials, in Handbook of Sol-Gel Science and Technology, ed. by L. Klein, M. Aparicio, A. Jitianu, (Springer, New York, 2016)

    Google Scholar 

  • M. Avrami, J. Chem. Phys. 7, 1103–1112 (1939). and 8, 212–224 (1940)

    Article  CAS  Google Scholar 

  • W.T. Barrett, M.G. Sanchez, J.G. Smith, Adv. Catal. 9, 551–557 (1957)

    Google Scholar 

  • M.D. Bechtold, R.D. Vest, L. Plambeck Jr., J. Am. Chem. Soc. 90, 4590–4598 (1968)

    Article  CAS  Google Scholar 

  • D. Bensimon, E. Domany, A. Aharony, Phys. Rev. Lett. 51, 1394 (1983)

    Article  CAS  Google Scholar 

  • R.K. Bharadwaj, Polymer 41, 7209–7221 (2000)

    Article  CAS  Google Scholar 

  • K. Binder, Monte Carlo Methods in Statistical Physics, 2nd edn. (Springer, Berlin, 1986)

    Book  Google Scholar 

  • S. Bizet, J. Galy, J.-F. Gérard, Polymer 47, 8219–8227 (2006)

    Article  CAS  Google Scholar 

  • P. Bouguer, Essai d’optique sur la gradation de la lumière [Optics essay on the attenuation of light] (in French) (Claude Jombert, Paris, France, 1729), pp. 16–22

    Google Scholar 

  • R.J. Bratton, Am. Ceram. Soc. Bull. 48, 759–762 (1969)

    CAS  Google Scholar 

  • D.W. Brenner, Phys. Rev. B 46, 1948 (1992)

    Article  CAS  Google Scholar 

  • D.W. Brenner, J.A. Harrison, C.T. White, R.J. Colton, Thin Solid Films 206, 220–223 (1991)

    Article  CAS  Google Scholar 

  • C.J. Brinker, B.C. Bunker, D.R. Tallant, K.J. Ward, J. Chim. Phys. 83, 851–858 (1986)

    Article  CAS  Google Scholar 

  • C.J. Brinker, K.D. Keefer, D.W. Schaefer, C.S. Ashley, J. Non-Cryst. Solids 48, 47–64 (1982)

    Article  CAS  Google Scholar 

  • C.J. Brinker, G.W. Scherer, Sol-Gel Science. The Physics and Chemistry of Sol-Gel Processing (Academic Press, New York. ISBN: 0-12-134970-5, 1990)

    Google Scholar 

  • D.A.G. Bruggeman, Ann. Phys. (Leipzig) 24, 636–664 (1935)

    Article  CAS  Google Scholar 

  • K. Burke, J. Werschnik, E.K.U. Gross, J. Chem. Phys. 123, 062206 (2005)

    Article  CAS  Google Scholar 

  • F. Burmeister, S. Steenhusen, R. Houbertz, T.S. Asche, J. Nickel, S. Nolte, N. Tucher, P. Josten, K. Obel, H. Wolter, S. Fessel, A. Schneider, K.-H. Gartner, C. Beck, P. Behrens, A. Tunnermann, H. Walles, Chapter 5: Two-Photon Polymerization of Inorganic–Organic Polymers for Biomedical and Microoptical Applications, in Optically Induced Nanostructures, ed. by K. König, A. Ostendorf, (Walter de Gruyter Inc, Boston, 2015), pp. 239–266

    Google Scholar 

  • I.C. Callaghan, R.H. Ottewill, Faraday Discuss. Chem. Soc. 57, 110–118 (1974)

    Article  CAS  Google Scholar 

  • F. Carmona, F. Barreau, P. Delhaes, R. Canet, J. Phys. Lett. 41, L531–L533 (1980)

    Article  Google Scholar 

  • R. Chandler, J. Koplik, K. Lerman, J.F. Willemsen, J. Fluid Mech. 119, 249–267 (1982)

    Article  Google Scholar 

  • P.J. Chupas, D.R. Corbin, V.N.M. Rao, J.C. Hanson, C.P. Grey, J. Phys. Chem. B 107, 8327–8336 (2003)

    Article  CAS  Google Scholar 

  • A. Cotton, H. Mouton, Ann. Chim. Phys. 11, 145–205 (1907). and 289–347

    CAS  Google Scholar 

  • A.F. Craievich, Chapter 4.17: Small-Angle X-Ray Scattering by Nanostructured Materials, in Handbook of Sol-Gel Science and Technology, ed. by L. Klein, M. Aparicio, A. Jitianu, (Springer, New York, 2016)

    Google Scholar 

  • P.G. de Gennes, J. Phys. 37, L1 (1976)

    Article  Google Scholar 

  • D.H. de Jong, G. Singh, W.F.D. Bennett, C. Arnarez, T.A. Wassenaar, L.V. Schafer, X. Periole, D.P. Tieleman, S.J. Marrink, J. Chem. Theory Comput. 9, 687–697 (2013)

    Article  CAS  Google Scholar 

  • J.C. Debsikdar, Adv. Ceram. Mater. 1, 93–98 (1986)

    CAS  Google Scholar 

  • J.M. Deutch, P. Meakin, J. Chem. Phys. 78, 2093–2094 (1983)

    Article  CAS  Google Scholar 

  • A. Dimitrov, J. Koch, S.I. Troyanov, E. Kemnitz, Eur. J. Inorg. Chem. 35, 5299–5301 (2009)

    Article  CAS  Google Scholar 

  • F. Dumont, D. Tan, A. Watillon, J. Colloid Interface Sci. 55, 678–687 (1976)

    Article  CAS  Google Scholar 

  • M. Eden, in “Proceedings of the 4∗” Berkeley Symposium on Mathematical Statistics and Probability, ed. by J. Neyman, vol. 4, (University of California Press, Berkeley, 1961), p. 223

    Google Scholar 

  • M. Elanany, P. Selvam, T. Yokosuka, S. Takami, M. Kubo, A. Imamura, A. Miyamoto, J. Phys. Chem. B 107, 1518–15124 (2003)

    Article  CAS  Google Scholar 

  • S. Fessel, A.M. Schneider, S. Steenhusen, R. Houbertz, P. Behrens, J. Sol-Gel Sci. Technol. 63, 356–365 (2012)

    Article  CAS  Google Scholar 

  • M.E. Fisher, J.W. Essam, J. Math. Phys. 2, 609–619 (1961)

    Article  Google Scholar 

  • J.P. Flory, J. Am. Chem. Soc. 63, 3083–3100 (1941)

    Article  CAS  Google Scholar 

  • J.P. Flory, J. Am. Chem. Soc. 65, 372–382 (1943)

    Article  CAS  Google Scholar 

  • J.P. Flory, Principles of Polymer Chemistry (Comell Univer. Press, Ithaca, New York, 1953)

    Google Scholar 

  • R.W. Ford, Drying, Institute of Ceramics Textbook Series (MacLaren and Sons, London, England, 1964)

    Google Scholar 

  • A. Frey-Wyssling, K. Miihlthaler, Vierteljahrenchr Naturf. Ges., Zurich 89, 214–215 (1944)

    CAS  Google Scholar 

  • J. Fricke, J. Non-Cryst. Solids 100, 169–173 (1988)

    Article  CAS  Google Scholar 

  • H.L. Frisch, J.M. Hammersley, D.J.A. Welsch, Phys. Rev. 126, 949–951 (1962)

    Article  CAS  Google Scholar 

  • C. Fritz, Inorganic–Organic Composite Systems Based on Nanoscopic Aluminium Fluoride. Berlin Thesis, Humboldt-Universität zu Berlin (2012)

    Google Scholar 

  • B. Gauthier, E. Guyon, S. Roux, S. Gits, F. Lefaucheux, J. Phys. Fr. 48, 869–875 (1987)

    Article  Google Scholar 

  • N. Gharbi, C. Sanchez, J. Livage, J. Chim. Phys. 82, 755–759 (1985)

    Article  CAS  Google Scholar 

  • J.M. Guenet, Le Courrier du CNRS 63, 50–53 (1985)

    Google Scholar 

  • A. Guinier, G. Fournet, Small-Angle Scattering of X-Rays (Wiley, New York, 1955)

    Google Scholar 

  • J.M. Hammersley, Proc. Camb. Philos. Soc. 53, 642–645 (1957)

    Article  CAS  Google Scholar 

  • H. Henschel, A.M. Schneider, M.H. Prosenc, Chem. Mater. 22, 5105–5111 (2010)

    Article  CAS  Google Scholar 

  • P.H. Hermans, Reversible Systems, in Colloid Science, ed. by H. R. Kruyt, vol. II, (Elsevier, New York, 1952), pp. 483–650

    Google Scholar 

  • H. Hu, H. Hou, Z. He, B. Wang, Phys. Chem. Chem. Phys. 15, 15027–15032 (2013)

    Article  CAS  Google Scholar 

  • R.K. Iler, The Chemistry of Silica (Wiley, New York, 1979)

    Google Scholar 

  • B.J. Ingebrethsen, E. Matijevic, J. Aerosol Sci. 11, 271–280 (1980)

    Article  CAS  Google Scholar 

  • M. Ionita, Compos. Part B Eng. 43, 3491–3496 (2012)

    Article  CAS  Google Scholar 

  • C. Jang, T.E. Lacy, S.R. Gwaltney, H. Toghiani, C.U. Pittman, Macromolecules 45, 4876–4885 (2012)

    Article  CAS  Google Scholar 

  • E. Kemnitz, Chapter 2.18: Fluorolytic Sol-Gel Processes, in Handbook of Sol-Gel Science and Technology, ed. by L. Klein, M. Aparicio, A. Jitianu, (Springer, New York, 2016)

    Google Scholar 

  • E. Kemnitz, U. Gross, S. Rudiger, G. Scholz, D. Heidemann, S.I. Troyanov, I.V. Morosov, M.H. Lemee-Cailleau, Solid State Sci. 8, 1443–1452 (2006)

    Article  CAS  Google Scholar 

  • D. Kindu, D. Ganguli, J. Mater. Sci. Lett. 5, 293–295 (1986)

    Article  Google Scholar 

  • S. Kirkpatrick, Rev. Mod. Phys. 45, 574–588 (1973)

    Article  Google Scholar 

  • L.C. Klein, G.L. Garvey, J. Non-Cryst. Solids 38–39, 45–50 (1980)

    Article  Google Scholar 

  • M. Kolb, R. Botet, R. Julien, Phys. Rev. Lett. 51, 1123–1126 (1983)

    Article  Google Scholar 

  • S. Komarneni, R. Roy, E. Breval, J. Am. Ceram. Soc. 68, C41–C42 (1985)

    CAS  Google Scholar 

  • P. Larkin, Infrared and Raman Spectroscopy. Principles and Spectral”.. ISBN: 978-0-12-386984-5 (Elsevier, Amsterdam, 2011), p. 228

    Google Scholar 

  • J. Lemerle, L. Nejem, J. Lefebvre, J. Inorg. Nucl. Chem. 42, 17–20 (1980)

    Article  CAS  Google Scholar 

  • Y.K. Leung, B.E. Eichinger, J. Chem. Phys. 80, 3877–3891 (1984)

    Article  CAS  Google Scholar 

  • Y.G. Lin, D.T. Mallin, J.C.W. Chien, H.H. Winter, Macromolecules 24, 850–854 (1991)

    Article  CAS  Google Scholar 

  • J. Livage, J. Lemerle, Annu. Rev. Mater. Sci. 12, 103–122 (1982)

    Article  CAS  Google Scholar 

  • D.A. Loy, Chapter 3-18: Mesoporous Polysilsesquioxanes: Preparation, Properties, and Applications, in Handbook of Sol-Gel Science and Technology, ed. by L. Klein, M. Aparicio, A. Jitianu, (Springer, New York, 2016)

    Google Scholar 

  • D.T. Mallin, J.C.W. Chien, H.H. Winter, Dynamic mechanical measurement of crystallization-induced gelation in thermoplastic elastomeric poly(propylene). Macromolecules 24, 850–854 (1991)

    Article  Google Scholar 

  • B. Mandelbrot, Fractals: Form, Chance and Dimension (Freeman, San Francisco, 1977)

    Google Scholar 

  • P. Manneville, L. De Seze, Percolation and Gelation by Additive Polymerization, in Numerical Methods in the Study of Critical Phenomena, ed. by L. Delia Dora, J. Demangeot, B. Lacolle, (Springer, Berlin, 1981), pp. 116–124

    Chapter  Google Scholar 

  • G. Martini, H. Burlamacchi, J. Phys. Chem. 83, 2505–2511 (1979)

    Article  CAS  Google Scholar 

  • M.C. Matos, L.M. Ilharco, R.M. Almeida, J. Non-Cryst. Solids 147 and 148, 234 (1992)

    Google Scholar 

  • K.S. Mazdiyasni, Ceram. Int. 8, 42–56 (1982)

    Article  CAS  Google Scholar 

  • G.J. McIntosh, Phys. Chem. Chem. Phys. 15, 17496 (2013)

    Article  CAS  Google Scholar 

  • P. Meakin, Phys. Rev. Lett. 51, 1119–1122 (1983a)

    Article  Google Scholar 

  • P. Meakin, Phys. Rev. B 28, 6718–6732 (1983b)

    Article  Google Scholar 

  • P.J. Melling, Am. Ceram. Soc. Bull. 63, 1427–1429 (1984)

    CAS  Google Scholar 

  • M. Moner-Girona, A. Roig, E. Molins, J. Sol. Gel. Sci. Technol. 26, 645–649 (2003)

    Article  CAS  Google Scholar 

  • S.P. Mukherjee, Final Report on Sol-Gel Coatings for Si-Ge Substrates. Sandia Laboratories (DOE Contract/DE-AC04-IG-DP00789) (Oct 22, 1979)

    Google Scholar 

  • H.T. Nguyen, J.C. Dubois, J. Malhete, C. Destrade, C.R. Heb. Sean. Acad. Sci. C 286, 463–464 (1978)

    Google Scholar 

  • G. Nicolaon, D.D. Cooke, M. Kerker, E. Matijevic, J. Colloid Interface Sci. 34, 534–544 (1970)

    Article  CAS  Google Scholar 

  • G.Y. Onoda, J. Toner, J. Am. Ceram. Soc. 69, C278–C279 (1986)

    Article  Google Scholar 

  • B.P. Partlow, B.E. Yoldas, J. Non-Cryst. Solids 46, 153–161 (1981)

    Article  CAS  Google Scholar 

  • J.C.G. Pereira, C.R.A. Catlow, G.D. Price, J. Phys. Chem. A 103, 3268–3284 (1999)

    Article  CAS  Google Scholar 

  • J.C.G. Pereira, C.R.A. Catlow, G.D. Price, R.M. Almeida, J. Sol-Gel Sci. Technol. 8, 55–58 (1997)

    CAS  Google Scholar 

  • H.P. Peters, D. Stauffer, H.P. Holter, K. Loewenich, Z. Phys. B 34, 399–408 (1979)

    Article  Google Scholar 

  • A.C. Pierre, The Gelation of Colloidal Gels and the Derjaguin-Landau-Verwey-Overbeek (or DLVO) Theory, in Ultrastructure Processing of Advanced Materials, ed. by D. R. Uhlmann, D. R. Ulrich, (Wiley, New York, 1992), pp. 103–110

    Google Scholar 

  • A.C. Pierre, J. Chim. Phys. 93, 1065–1079 (1996)

    Article  CAS  Google Scholar 

  • A.C. Pierre, K. Ma, J. Mater. Sci. 32, 2937–2947 (1997)

    Article  CAS  Google Scholar 

  • A.C. Pierre, K. Ma, C. Barker, J. Mater. Sci. 30, 2176–2181 (1995)

    Article  CAS  Google Scholar 

  • A.C. Pierre, D.R. Uhlmann, Mater. Res. Soc. Symp. Proc. 73, 481–487 (1986a)

    Article  CAS  Google Scholar 

  • A.C. Pierre, D.R. Uhlmann, J. Non-Cryst. Solids 82, 271–276 (1986b)

    Article  CAS  Google Scholar 

  • A.C. Pierre, D.R. Uhlmann, J. Am. Ceram. Soc. 70, 28–32 (1987)

    Article  CAS  Google Scholar 

  • W.J. Platzer, M. Bergkvist, Sol. Energy Mater. Sol. Cells 31, 243–251 (1993)

    Article  CAS  Google Scholar 

  • E.J.A. Pope, J.D. Mackenzie, J. Non-Cryst. Solids 101, 198–212 (1988)

    Article  CAS  Google Scholar 

  • G. Porod, Kolloid Z. 124, 83–114 (1951)., 125, 51–57 and 108–122 (1952)

    Article  CAS  Google Scholar 

  • S. Prakash, N.R. Dhar, J. Ind. Chem. Soc. 6, 391–409 (1929)

    CAS  Google Scholar 

  • S. Prakash, N.R. Dhar, J. Ind. Chem. Soc. 7, 417–432 (1930)

    CAS  Google Scholar 

  • G. Reichenauer, Chapter 21: Structural Characterization of Aerogels, in Aerogels Handbook, Advanced in Sol-Gel Derived Materials and Technology, ed. by M. A. Aegerter, N. Leventis, M. M. Koebel, (Springer Science+Business Media, New York, 2011), p. 449

    Google Scholar 

  • P.A. Rikvold, Phys. Rev. A 26, 647–650 (1982)

    Article  CAS  Google Scholar 

  • G. Rossi, L. Monticelli, S.R. Puisto, I. Vattulainen, T. Ala-Nissila, Soft Matter 7, 698–708 (2011)

    Article  CAS  Google Scholar 

  • S.B. Ross-Murphy, H. McEvoy, Brit. Polym. J. 18, 2–7 (1986)

    Article  CAS  Google Scholar 

  • S. Sakka, Gel Method for Making Glass, in Treatise on Materials Science and Technology, ed. by M. Tomazawa, R. H. Doremus, vol. 22, (Academic Press, New York, 1982), pp. 129–167

    Chapter  Google Scholar 

  • L.M. Sander, Theory of Fractal Growth Processes, in Kinetics of Aggregation and Gelation, ed. by P. Family, D. P. Landau, (Elsevier, Amsterdam, 1984), pp. 13–17

    Chapter  Google Scholar 

  • A.Y. Sane, Refractory Metal Borides, Carbides and Nitrides, and Composites Containing Them, European Patent 0115745, Eltech Systems Corporation, 15. 08 (1984)

    Google Scholar 

  • L.R.B. Santos, A.F. Craievich, C.V. Santilli, S.H. Pulcinelli, J. Appl. Crystallogr. 33, 609–613 (2000)

    Article  Google Scholar 

  • L.R.B. Santos, C.V. Santilli, S.H. Pulcinelli, J. Non-Cryst. Solid 247, 153–157 (1999)

    Article  CAS  Google Scholar 

  • Y. Sawada, S. Ohta, M. Yamazaki, H. Honjo, Phys. Rev. A 26, 3557–3563 (1982)

    Article  Google Scholar 

  • D.W. Schaefer, MRS Bull. 8, 22–27 (1988)

    Article  Google Scholar 

  • D.W. Schaefer, J.E. Martin, P. Wiltzius, D.S. Cannell, Aggregation of Colloidal Silica, in Kinetics of Aggregation and Gelation, ed. by F. Family, D. P. Landau, (Elsevier Science Publishers B.V., Amsterdam, 1984), pp. 71–74

    Chapter  Google Scholar 

  • D.L. Segal, J. Non-Cryst. Solids 63, 183–191 (1984)

    Article  CAS  Google Scholar 

  • S.-C. Shiu, J.-L. Tsai, Compos. Part B Eng. 56, 691–697 (2014)

    Article  CAS  Google Scholar 

  • A. Shokuhfar, B. Arab, J. Mol. Model. 19, 3719–3723 (2013)

    Article  CAS  Google Scholar 

  • S.K. Sinha, T. Freltoft, J. Kjems, Observation of Power-Law Correlations in Silica Particles Aggregates by Small-Angles Neutron Scattering, in Kinetics of Aggregation and Gelation, ed. by F. Family, D. P. Landau, (Elsevier Science Publishers B.V., Amsterdam, 1984), pp. 87–90

    Chapter  Google Scholar 

  • M.E. Smith, D. Holland, Chapter 1-12: Atomic-Scale Structure of Gel Materials by Solid-State NMR, in Handbook of Sol-Gel Science and Technology, ed. by L. Klein, M. Aparicio, A. Jitianu, (Springer, New York, 2016)

    Google Scholar 

  • X. Song, Y. Sun, X. Wu, F. Zeng, Comput. Mater. Sci. 50, 3282–3289 (2011)

    Article  CAS  Google Scholar 

  • H.E. Stanley, R.J. Birgeneau, P.J. Reynolds, J.F. Nicoll, J. Phys. C 9, L553–L560 (1976)

    Article  Google Scholar 

  • H.E. Stanley, F. Family, H. Gould, J. Polym. Sci. Pol. Sym. 73, 19–37 (1985)

    Article  CAS  Google Scholar 

  • D. Stauffer, A. Conoglio, M. Adam, Adv. Pol. Sci. 44, 103–158 (1982)

    Article  CAS  Google Scholar 

  • W.H. Stockmayer, J. Chem. Phys. 11, 45–55 (1943)

    Article  CAS  Google Scholar 

  • S.J. Stuart, A.B. Tutein, J.A. Harrison, J. Chem. Phys. 112, 6472–6486 (2000)

    Article  CAS  Google Scholar 

  • H. Sun, D. Rigby, Spectrochim. Acta A Mol. Biomol. Spectrosc. 53, 1301–1323 (1997)

    Article  Google Scholar 

  • T. Tanaka, G. Swislow, I. Ohmine, Phys. Rev. Lett. 42, 1556–1559 (1979)

    Article  CAS  Google Scholar 

  • T. Tanigami, K. EN, K. Yamaura, S. Matsuzawa, Polym. J. 18, 31–34 (1986)

    Article  CAS  Google Scholar 

  • Y. Taniguchi, K. Susuki, J. Phys. Chem. 78, 759–761 (1974)

    Article  CAS  Google Scholar 

  • P. Terech, J. Colloid Interface Sci. 107, 244–255 (1985)

    Article  CAS  Google Scholar 

  • P. Terech, C. Chachaty, J. Galllard, A.M. Giroud-Godquin, J. Phys. Paris 48, 663–671 (1987)

    Article  CAS  Google Scholar 

  • J. Tersoff, Phys. Rev. B 37, 6991–7000 (1988)

    Article  CAS  Google Scholar 

  • I.L. Thomas, K.H. McCorkle, J. Colloid Interface Sci. 36, 110–118 (1971)

    Article  CAS  Google Scholar 

  • C.Y.M. Tung, P.J. Dynes, J. Appl. Pol. Sci. 27, 569–574 (1982)

    Article  CAS  Google Scholar 

  • J.J. Uusitalo, H.I. Ingólfsson, P. Akhshi, D.P. Tieleman, S.J. Marrink, J. Chem. Theory Comput. 11, 3932–3945 (2015)

    Article  CAS  Google Scholar 

  • A.C.T. van Duin, S. Dasgupta, F. Lorant, W.A. Goddard, J. Phys. Chem. A 105, 9396–9409 (2001)

    Article  CAS  Google Scholar 

  • L. Vidal, L.A. Gharzouni, S. Rossignol, Chapter 1-5: Alkaline Silicate Solutions: An Overview of Their Structure, Reactivity, and Application, in Handbook of Sol-Gel Science and Technology, ed. by L. Klein, M. Aparicio, A. Jitianu, (Springer, New York, 2016)

    Google Scholar 

  • M. Visca, E. Matijevic, J. Colloid Interface Sci. 68, 308–319 (1979)

    Article  CAS  Google Scholar 

  • P.P. Von Weimarn, Rev. Gen. Colloids 7, 153–158 (1929)

    Google Scholar 

  • R.F. Voss, Bull. Am. Phys. Soc. 28, 487 (1983)

    Google Scholar 

  • Z. Wang, Q. Lv, S. Chen, C. Li, S. Sun, S. Hu, Mol. Simul. 41, 1515–1527 (2015)

    Article  CAS  Google Scholar 

  • G.C. Wei, C.R. Kennedy, L.A. Harris, Am. Ceram. Soc. Bull. 63, 1054–1061 (1984)

    CAS  Google Scholar 

  • D.A. Weitz, J.S. Huang, Self-Similar Structures and the Kinetics of Aggregation of Gold Colloids, in Kinetics of Aggregation and Gelation, ed. by F. Family, D. P. Landau, (Elsevier Science Publishers B.V., Amsterdam, 1984), pp. 19–28

    Chapter  Google Scholar 

  • C.E. White, J.L. Provis, G.J. Kearley, D.P. Riley, J.S.J. van Deventer, Dalton Trans. 40, 1348–1355 (2011)

    Article  CAS  Google Scholar 

  • H.H. Winter, F. Chambon, J. Rheol. 30, 367–382 (1987)

    Article  Google Scholar 

  • T.A. Witten Jr., P. Meakin, Phys. Rev. B 28, 5632–5642 (1983)

    Article  Google Scholar 

  • T.A. Witten Jr., L.M. Sander, Phys. Rev. Lett. 47, 1400–1403 (1981)

    Article  CAS  Google Scholar 

  • C. Wu, W. Xu, Polymer 47, 6004–6009 (2006)

    Article  CAS  Google Scholar 

  • D. Xin, Q. Han, Mol. Simul. 41, 1081–1085 (2015)

    Article  CAS  Google Scholar 

  • S. Yamagishi, K. Takahashi, J. Nucl. Mater. 144, 244–251 (1987)

    Article  CAS  Google Scholar 

  • B.E. Yoldas, J. Mater. Sci. 10, 1856–1860 (1975)

    Article  CAS  Google Scholar 

  • K. Yoshizawa, H. Kato, M. Kakihana, J. Mater. Chem. 22, 17272–17277 (2012)

    Article  CAS  Google Scholar 

  • R. Zallen, The Physics of Amorphous Solids (Wiley, New York, 1983)

    Book  Google Scholar 

  • B.J.J. Zelinski, D.R. Uhlmann, Gel Technology in Ceramics. J. Phys. Chem. Solids 45, 1069–1090 (1984)

    Article  CAS  Google Scholar 

  • J. Zou, A.C. Pierre, J. Mater. Sci. Lett. 11, 664–665 (1992)

    Article  CAS  Google Scholar 

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Pierre, A.C. (2020). Gelation. In: Introduction to Sol-Gel Processing. Springer, Cham. https://doi.org/10.1007/978-3-030-38144-8_7

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