Swelling of Gels and Diffusion of Molecules

  • Yong Li
  • T. Tanaka
Part of the Springer Proceedings in Physics book series (SPPHY, volume 52)


The kinetics of swelling and shrinking of gels is studied. A new relation, in addition to the differential equation developed by Tanaka and Fillmore, is formulated to solve the kinetics of gels having arbitrary shape. The gel kinetics is described as a combination of the collective diffusion with finite rate and immediate relaxation of shear deformation. The relation demonstrates the fundamental differences between the gel kinetics and the molecules diffusion process. The difference is a direct result of the existence of the shear modulus of the gel network system. Some interesting details of our theory are further discussed.


Shear Modulus Diffusion Process Shear Process Pure Diffusion Longitudinal Modulus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Y. Li and T. Tanaka, J. Chem. Phys. (to be published).Google Scholar
  2. [2]
    T. Tanaka, L. Hocker and G. Benedek, J. Chem. Phys. 59(9), 5151(1973).ADSCrossRefGoogle Scholar
  3. [3]
    T. Tanaka and D. Fillmore, J. Chem. Phys. 70(3), 1214(1979).ADSCrossRefGoogle Scholar
  4. [4]
    T. Tanaka, E. Sato, Y. Hirokawa, S. Hirotsu and J. Peetermans, Phys. Rev. Lett. 55(22), 2455(1985).ADSCrossRefGoogle Scholar
  5. [5]
    E. Sato-Matsuo and T. Tanaka, J. Chem. Phys. 89(3), 1695(1988).ADSCrossRefGoogle Scholar
  6. [6]
    A. Peters and S. J. Candau, Macromolecules 19(7), 1952(1986).ADSCrossRefGoogle Scholar
  7. [7]
    A. Peters and S. J. Candau, Macromolecules 21(7), 2278(1988).ADSCrossRefGoogle Scholar
  8. [8]
    L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 1986 Pergamon Press, Oxford.Google Scholar
  9. [9]
    The boundary of the ink string can be defined as the density profile of the ink molecules at a certain value. For instance, we can define the radius of the string r as the value at which the relative density p(r)/p (0) = 0.1.Google Scholar
  10. [10]
    Due to a mistake made in the initial condition, the coefficients A n given by Eq. (6) in [6] are not correct. The correct answer should be display equation The boundary condition of a spherical gel is R = α2 n/(4 − 4αn cot αn).Google Scholar
  11. [11]
    Akira Onuki, Phys. Rev. A 38(4), 2192(1988).ADSCrossRefGoogle Scholar
  12. [12]
    This does not mean that there is no solution to this problem. Readers can verify easily that for equation x 2 + x = 1, iteration x n+1 = 1 − x 2 n does not converge 54-1.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Yong Li
    • 1
  • T. Tanaka
    • 1
  1. 1.Department of Physics and Center for Material Science and EngineeringMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations