Skip to main content
SpringerLink
Log in

Simulations of Sol-to-Gel Modeling: Effects of Mobility, Reversibility, and Quality of Solvent

  • Published:
Journal of Sol-Gel Science and Technology Aims and scope Submit manuscript

Abstract

Some of our recent work on computer simulation modeling of the sol-to-gel transition for the polymerization by step reaction are presented. Depending on the variants of the model, a random distribution of bifunctional and tetrafunctional monomers of concentration C2 and C4 respectively, and their chains (bond-fluctuating) are used as primary reacting units on a simple cubic lattice as the initial sol-phase. Effects of solvent, temperature, mobility of monomers, rate of reaction, and reversibility are considered in understanding the evolution of microgels, onset of gelation and the nature of sol-to-gel transition, inhomogeneity, etc. Gel point (pc, gel volume fraction (PG), weight average degree of polymerization (MW), structure factor (S(q, t)) show various interesting variations with the conversion factor (p). For example, sol-to-gel transition seems nonuniversal with respect to quality of the solvent, degree of inhomogeneity depends on the quality of solvent and rate of reaction due to interplay between the phase-separation and cross-linking.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. 1._P.J. Flory, J. Am. Chem. Soc. 63, 3083, 3091, 3096 (1941); Principle of Polymer Chemistry (Cornel University Press, 1953).

    Google Scholar 

  2. W.H. Stockmayer, J. Chem. Phys. 11, 45 (1943); 12, 125 (1944).

    Google Scholar 

  3. Kinetics of Aggregation and Gelation, edited by F. Family and D.P. Landau (North Holland, 1984).

  4. Random Fluctuations and Pattern Growth, edited by H.E. Stanley and N. Ostrowsky (Kluwer Academic Publishers, 1988).

  5. M. Kolb, in Fractals in Physics, edited by L. Pietronero and E. Tosatti (Elsevier, 1986).

  6. M. Klob and H.J. Herrmann, J. Phys. A 18, L435 (1985).

    Google Scholar 

  7. P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, 1979).

    Google Scholar 

  8. D. Stauffer, Ber. Bonsenges. Phys. Chem. 102, 1672 (1998).

    Google Scholar 

  9. D. Stauffer, A. Coniglio, and M. Adam, Adv. Polym. Sci. 41, 103 (1982).

    Google Scholar 

  10. M. Daoud, F. Family, and G. Jannink, J. Phys. Lett. Paris 45, L199 (1984).

    Google Scholar 

  11. J.E. Martin, J. Wilcoxon, and D. Adolf, Phys. Rev. A 36, 1803 (1987).

    Google Scholar 

  12. M. Adam, M. Delsanti, J.P. Munch, and D. Durand, J. Phys. France 48, 1809 (1987).

    Google Scholar 

  13. E.V. Patton, J.A. Wesson, M. Rubinstein, J.C. Wilson, and L.E. Oppenheimer, Macromolecules 22, 1946 (1989).

    Google Scholar 

  14. F. Schosseler, H. Benoit, Z. Grubisic-Gallot, Cl. Strazielle, and L. Leibler, Macromolecules 22, 400 (1989).

    Google Scholar 

  15. D. Durand, F. Naveau, and J.P. Busnel, Macromolecules 22, 2011 (1989).

    Google Scholar 

  16. M. Adam and M. Delsanti, Contemp. Phys 30, 203 (1989).

    Google Scholar 

  17. J.E. Martin and J. Wilcoxon, Phys. Rev. A 39, 252 (1989).

    Google Scholar 

  18. F. Schosseler, M. Daoud, and L. Leibler, J. Phys. France 51, 2373 (1990).

    Google Scholar 

  19. J.E. Martin and J. Odinek, Macromolecules 23, 3363 (1990).

    Google Scholar 

  20. J. Bauer, P. Lang, W. Burchard, and M. Bauer, Macromolecules 24, 2634, (1991).

    Google Scholar 

  21. M. Adam, Makromol. Chem., Macromol. Symp. 45, 1 (1991).

    Google Scholar 

  22. J.R. Colby, M. Rubinstein, J.R. Gillmor, and T.H. Mourey, Macromolecules 25, 7180 (1992).

    Google Scholar 

  23. J.R. Colby, J.R. Gillmor, and M. Rubinstein, Phys. Rev. E. 43, 3712 (1993).

    Google Scholar 

  24. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, 1994).

  25. P.G. de Gennes, J. Phys. France Lett. 37, L1 (1976).

    Google Scholar 

  26. D. Stauffer, J. Chem. Soc. Faraday Trans. II 72, 1354 (1976).

    Google Scholar 

  27. P. Manneville and L. de Seze, in Numerical Methods in the Study of Critical Phenomena, edited by I. Della Dra, J. Demongeot, and B. Lacolle (Springer-Verlag, Berlin 1981); H.J. Herrmann, D.P. Landau, and D. Stauffer, Phys. Rev. Lett. 49, 412 (1982); R. Bansil, H.J. Herrmann, and D. Stauffer, J. Polym. Sci. 17, 988 (1984); N. Jan, T. Lookman, and D. Stauffer, J. Phys. A 16, L117 (1983); R.B. Pandey, J. Stat. Phys. 34, 191 (1983); H.J. Herrmann, Phys. Rep. 136, 153 (1986).

    Google Scholar 

  28. C.N. Bowman and N.A. Peppas, Chem. Eng. Sci. 47, 1411 (1992).

    Google Scholar 

  29. Y. Liu and R.B. Pandey, J. Phys. II France 4, 865 (1994).

    Google Scholar 

  30. Y.Y. Chiu and L.J. Lee, J. Polym. Sci. A 33, 269 (1995).

    Google Scholar 

  31. P. Meakin, Phys. Rev. Lett. 51, 1119 (1983).

    Google Scholar 

  32. R. Julien and R. Bötet, Aggregation and Fractal Aggregates (World Scientific, Singapore, 1987).

    Google Scholar 

  33. P.A. Netz and D. Samios, Macromol. Theory & Simul. 3, 607 (1994).

    Google Scholar 

  34. R.M. Ziff, in Kinetics of Aggregation and Gelation, edited by F. Family and D.P. Landau (North Holland, 1984).

  35. M.H. Ernst, in Fractals in Physics, edited by L. Pietronero and E. Tosatti (Elsevier Sci. Pub., 1986).

  36. H. Boots and R.B. Pandey, Polym. Bull 11, 415 (1984).

    Google Scholar 

  37. Y. Liu and R.B. Pandey, Phys. Rev. B 55, 8257 (1997).

    Google Scholar 

  38. J.E. Martin and J. Odinek, Macromolecules 23, 3362 (1990).

    Google Scholar 

  39. E. Mendes, Jr., P. Lindner, M. Buzier, F. Boue, and J. Bastide, Phys. Rev. Lett. bf 66, 1595 (1991).

    Google Scholar 

  40. M. Najeh, J.-P. Munch, and J.-M Guenet, Macromolecules 25, 7018 (1992).

    Google Scholar 

  41. K. Chou and B.I. Lee, J. Mat. Sci. 29, 3565 (1994).

    Google Scholar 

  42. J. Bastide and L. Leibler, Macromolecules 21, 2649 (1988).

    Google Scholar 

  43. M. Rubinstein, L. Leibler, and J. Bastide, Phys. Rev. Lett. 68, 405 (1992).

    Google Scholar 

  44. F. Mallamace, N. Micali, C. Vasi, R. Bansil, S. Pajavic, and F. Sciortino, J. Phys. II France 2, 2081 (1992).

    Google Scholar 

  45. Y. Cohen, O. Ramon, I.J. Kopelman, and S. Mizrahi, J. Polym. Sci. B 30, 1055 (1992).

    Google Scholar 

  46. E.S. Matsuo, M. Orkisz, S.-T. Sun, Y. Li, and T. Tanaka, Macromolecules 27, 6791 (1994).

    Google Scholar 

  47. F. Schosseler, R. Skouri, J.P. Munch, and S.J. Candau, J. Phys. II France 2, 233 (1994).

    Google Scholar 

  48. J.M. Low and R. McPherson, J. Mat. Sci. 23, 4141 (1988).

    Google Scholar 

  49. N. Micali, C. Vasi, F. Mallamace, R. Bansil, S. Pajevic, and F. Sciortino, Phys. Rev. E 48, 4501 (1993).

    Google Scholar 

  50. A. Sainai, J. Spevacek, and J.-M. Guenet, Macromolecules 31, 703 (1998).

    Google Scholar 

  51. K. Yamanaka, Y. Takagi, and T. Inoue, Polymer 30, 1840 (1989).

    Google Scholar 

  52. J.Y. Kim, C.H. Cho, P. Palffy-Muhoray, M. Mustafa, and T. Kyu, Phys. Rev. Lett. 71, 2232 (1993).

    Google Scholar 

  53. T. Ohnaga, W. Chen, and T. Inoue, Polymer 35, 3774 (1994).

    Google Scholar 

  54. A.E. Gonzalez and G. Ramirez-Santiago, Phys. Rev. Lett. 74, 1238 (1995).

    Google Scholar 

  55. Y. Liu and R.B. Pandey, Phys. Rev. E. 54, 6609 (1996).

    Google Scholar 

  56. Finite Size Scaling and Numerical Simulation of Statistical Systems, edited by V. Privman (World Scientific, Singapore, 1990).

    Google Scholar 

  57. R.B. Pandey and D.P. Landau, J. Phys. A 17, L551 (1985).

    Google Scholar 

  58. S.C. Glotzer, M.F. Gyure, F. Sciortino, A. Coniglio, and H.E. Stanley, Phys. Rev. Lett. 70, 3275 (1993); S.C. Glotzer, M.F. Gyure, F. Sciortino, A. Coniglio, and H.E. Stanley, Phys. Rev. E 49, 247 (1994).

    Google Scholar 

  59. F. Sciortino, R. Bansil, and H.E. Stanley, Phys. Rev. E 47, 4615 (1993).

    Google Scholar 

  60. W.H. Jo and M.B. Ko, Macromolecules 27, 7815 (1994).

    Google Scholar 

  61. M. Schulz and H.L. Frisch, J. Chem. Phys. 101, 10008 (1994).

    Google Scholar 

  62. Y. Liu and R.B. Pandey, J. Chem. Phys. 105, 825 (1996).

    Google Scholar 

  63. W. Burchard, R. Stadler, L.L. Freitas, M. Möller, J. Omeis, and E. Mühleisen, in Biological and Synthetic Polymer Networks, edited by O. Kramer (Elsevier Applied Science, London, 1986).

    Google Scholar 

  64. P. Russo, Reversible Polymer Gels and Related Systems, ACS Symposium Series 350 (American Chemical Society, Washington, DC, 1988).

    Google Scholar 

  65. D.K. Rout, S.K. Pulapura, and R.A. Gross, Macromolecules 26, 6007 (1993).

    Google Scholar 

  66. H.B. Bohidar and S.S. Jena, J. Chem. Phys. 98, 8970 (1993).

    Google Scholar 

  67. M. Berghmans, S. Thijs, M. Cornette, H. Berghmans, and F.C. De Schryver, Macromolecules 27, 7669 (1994).

    Google Scholar 

  68. N. Fazel, A. BrOulet, and J.M. Guenet, Macromolecules 27, 3836 (1994).

    Google Scholar 

  69. C. Daniel, C. Dammer, and J.-M. Guenet, Polymer 35, 4243 (1994).

    Google Scholar 

  70. S. Mal, P. Maiti, and A.K. Nandi, Macromolecules 28, 2371 (1995).

    Google Scholar 

  71. R. Bansil, J. Lal, and B.L. Carvalho, Polymer 33, 2961 (1992).

    Google Scholar 

  72. Y. Cohen, O. Ramon, I.J. Kopelman, and S. Mizrahi, J. Polym. Sci. B 30, 1055 (1992).

    Google Scholar 

  73. J.Y. Kim, C.H. Cho, P. Palffy-Muhoray, M. Mustafa, and T. Kyu, Phys. Rev. Lett. 71, 2232 (1993).

    Google Scholar 

  74. E.K. Hobbie, B.J. Bauer, and C.C. Han, Phys. Rev. Lett. 72, 1839 (1994).

    Google Scholar 

  75. K.F. Silveira, I.V.P. Yoshida, and S.P. Nunes, Polymer 36, 1425 (1995).

    Google Scholar 

  76. F. Tanaka and A. Matsuyama, Phys. Rev. Lett. 62, 2759 (1989); F. Tanaka, Macromolecules 23, 3784, 3790 (1990); F. Tanaka and M. Ishida, Physica A 204, 660 (1994).

    Google Scholar 

  77. F. Tanaka and W.H. Stockmayer, Macromolecules 27, 3943 (1994).

    Google Scholar 

  78. A.N. Semenov and M. Rubinstein, Macromolecules 31, 1373 (1998); M. Rubinstein and A.N. Semenov, Macromolecules 31, 1386 (1998).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, University of Southern Mississippi, Hattiesburg, MS, 39406-5046

    R.B. Pandey

  2. Hematronix Inc., 1505 Capital Ave, Plano, Texas, 75074

    Yimin Liu

Authors
  1. R.B. Pandey
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yimin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pandey, R., Liu, Y. Simulations of Sol-to-Gel Modeling: Effects of Mobility, Reversibility, and Quality of Solvent. Journal of Sol-Gel Science and Technology 15, 147–159 (1999). https://doi.org/10.1023/A:1008739505899

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008739505899

Search

Navigation