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Correlation functions in gel phase via mesoscopic cyclization theory of weak gels

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Abstract

The theory of classic sol-gel transition (SGT) in weak gels upon which the labile infinite cluster of particles bonded via weak chemical bonds (the gel fraction) appears on the background of a set of finite clusters (the sol fraction), is revisited. The basic approaches to describe the SGT (Flory approach, Stockmayer approach and the mesoscopic cyclization (MC) theory elaborated earlier by the author) are shortly outlined. The MC theory is revisited and generalized to provide description of spatially inhomogeneous weak gels, which is exemplified by calculation of the correlation function G (q) of monomer units in the gel-phase. A reduced choice of the network structural elements leads to reproducing the results obtained earlier within the Flory approach. On the contrary, an extended selection of such elements enables us to evaluate contribution to G (q) of closed trails of bonds comprised in the infinite cluster. This contribution leads to a pronounced small-angle scattering enhancement, which is especially noticeable near the sol-gel threshold.

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References

  1. P. J. Flory, Principles of Polymer Chemistry (Cornell Univ. Press, Ithaka, New York, 1953).

    Google Scholar 

  2. P. J. Flory, J. Am. Chem. Soc. 63, 3083 (1941).

    Article  CAS  Google Scholar 

  3. W. H. Stockmayer, J. Chem. Phys. 11, 45 (1943).

    Article  CAS  Google Scholar 

  4. P. G. de Gennes, Scaling Concepts in Polymer Physics (Cornell Univ. Press, Ithaca; London, 1979).

    Google Scholar 

  5. F. Tanaka, Macromolecules 22, 1988 (1989).

    Article  CAS  Google Scholar 

  6. F. Tanaka, Phys. Rev. E 73, 061405 (2006).

    Article  Google Scholar 

  7. I. Ya. Erukhimovich, PhD Thesis (Kharkiv, 1979).

    Google Scholar 

  8. A. Coniglio, H. F. Stanley, and W. Klein, Phys. Rev. Lett. 42, 518 (1979).

    Article  CAS  Google Scholar 

  9. A. A. Veitsman, J. Phys. Chem. 94, 8499 (1990).

    Article  Google Scholar 

  10. C. Panayiotou and I. C. Sanchez, J. Phys. Chem. 95, 10090 (1991).

    Article  CAS  Google Scholar 

  11. I. Ya. Erukhimovich, J. Exp. Theor. Phys. 81, 553 (1995).

    Google Scholar 

  12. A. N. Semenov and M. Rubinstein, Macromolecules 31, 1373 (1998).

    Article  CAS  Google Scholar 

  13. E. A. Muller and K. E. Gubbins, Ind. Eng. Chem. Res. 40, 2193 (2001).

    Article  Google Scholar 

  14. C. McCabe and A. Galindo, in Applied Thermodynamics of Fluids, Ed. by A. R. H. Goodwin, J. V. Sengers, and C. J. Peters (RSC Publishing, Cambridge, 2010). Chap. 8.

  15. I. Ya. Erukhimovich and A. V. Ermoshkin, J. Exp. Theor. Phys. 88, 538 (1999).

    Article  CAS  Google Scholar 

  16. I. Erukhimovich, M. V. Thamm, and A. V. Ermoshkin, Macromolecules 34, 5653 (2001).

    Article  CAS  Google Scholar 

  17. I. Ya. Erukhimovich and A.V. Ermoshkin, J. Chem. Phys. 116, 368 (2002).

    Article  CAS  Google Scholar 

  18. M. P. Tsyurupa and V. A. Davankov, React. Funct. Polym. 66, 768 (2006).

    Article  CAS  Google Scholar 

  19. M. P. Tsyurupa, Z. K. Blinnikova, Yu. A. Davidovich, S. E. Lyubimov, A. V. Naumkin, and V. A. Davankov, React. Funct. Polym. 72, 973 (2012).

    Article  CAS  Google Scholar 

  20. J. Germain, J. M. J. Frechet, and F. Svec, Small 5, 1098 (2009).

    Article  CAS  Google Scholar 

  21. A. A. Lazutin, M. K. Glagolev, V. V. Vasilevskaya, and A. R. Khokhlov, J. Chem. Phys. 140, 134903 (2014).

    Article  CAS  Google Scholar 

  22. M. K. Glagolev, A. A. Lazutin, V. V. Vasilevskaya, and A. R. Khokhlov, Polymer 86, 168 (2016).

    Article  CAS  Google Scholar 

  23. G. Medjahdi, D. Sarazin, and J. Francois, Macromolecules 24, 4138 (1991).

    Article  CAS  Google Scholar 

  24. I. Ya. Yerukhimovich and B. A. Letuchii, Polym. Sci. USSR 21, 1394 (1979).

    Article  Google Scholar 

  25. I. M. Lifshitz, Sov. Phys. J. Exp. Theor. Phys. 28, 1280 (1969).

    Google Scholar 

  26. I. M. Lifshitz, A. Yu. Grosberg, and A. R. Khokhlov, Rev. Mod. Phys. 50, 683 (1978).

    Article  CAS  Google Scholar 

  27. I. Ya. Yerukhimovich, Polym. Sci. USSR 24, 2223 (1982).

    Article  Google Scholar 

  28. I. Ya. Erukhimovich, Doctoral Thesis (Moscow, 1994).

    Google Scholar 

  29. I. M. Lifshits, A. Yu. Grosberg, and A. R. Khokhlov, Sov. Phys. JETP 44, 855 (1976).

    Google Scholar 

  30. J. S. Higgins and H. C. Benoit, Polymers and Neutron Scattering (Clarendon Univ. Press, Oxford, 1996).

    Google Scholar 

  31. S. V. Panyukov, Polym. Sci. Ser. A 58 (6), 886 (2016).

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. A.N. Nesmeyanov Institute of Organoelement Compounds of Russian Academy of Sciences, ul. Vavilova 28, Moscow, 119991, Russia

    I. Ya. Erukhimovich

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  1. I. Ya. Erukhimovich
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Correspondence to I. Ya. Erukhimovich.

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Erukhimovich, I.Y. Correlation functions in gel phase via mesoscopic cyclization theory of weak gels. Polym. Sci. Ser. A 58, 873–885 (2016). https://doi.org/10.1134/S0965545X16060043

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  • DOI: https://doi.org/10.1134/S0965545X16060043

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