Generalized Dual Sorption Theory

  • Wolf R. Vieth
  • Mary A. Amini
Part of the Polymer Science and Technology book series (PST, volume 6)


A theory is formulated to explain certain classes of negative and positive deviations from Henry’s law which are frequently observed in sorption plots of penetrants in polymers. Sorption is visualized as a process in which there are dual modes: either the penetrant molecule is normally dissolved and is free to diffuse or it is immobilized, as in a sink or well. It is the second process which gives rise to deviations from normal behavior. To explain negative deviations from Henry’s law, the solubility of the penetrant is analyzed as the sum of the contributions from these two modes. A diffusion equation, which is a modification of Fick’s second law, is derived for the rate of sorption. Numerical solutions are found for the resulting nonlinear partial differential equation using finite difference techniques. A very good correspondence of the theory and data is observed for several polymer-penetrant pairs. In the case of positive deviations from Henry’s law, the polymer network swells to expose more sites, increasing the sorption level synergistically. A statistical analysis of the phenomenon of clustering is used to aid in interpretation of the sorption isotherms. Fick’s law is modified to include a rate equation for clustering (assuming a first order reversible reaction). The correlation of the data with theory is quite good; not only in predicting the behavior of sorption transients, but also in yielding the effective steady-state diffusion coefficients.


Sorption Isotherm Positive Deviation Negative Deviation Glassy Polymer Finite Difference Technique 
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.
    W. R. Vieth and K. J. Sladek, J. Colloid Sci., 20, 1014 (1965).CrossRefGoogle Scholar
  2. 2.
    W. R. Vieth, A. S. Douglas and R. Bloch, J. Macromol. Sci., B3, 737 (1969).CrossRefGoogle Scholar
  3. 3.
    A. S. Michaels, W. R. Vieth, and J. A. Barrie, J. Appl. Phys., 34, 1 (1969).CrossRefGoogle Scholar
  4. 4.
    P. M. Tam, “High Pressure Sorption in a Glassy Polymer,” S. M. Thesis, M.I.T., Cambridge, Massachusetts (1965).Google Scholar
  5. 5.
    W. R. Vieth, C. S. Frangoulis, and J. A. Rionda, Jr., J. Colloid and Interface Sci., 22, 454 (1966).CrossRefGoogle Scholar
  6. 6.
    J. A. Eilenberg and W. R. Vieth, “Transport and Mechanical Properties of Polycarbonate” in “Advances in Polymer Science and Engineering,” K. D. Pae, D. R. Morrow, and Y. Chen, ed., Plenum Press, New York, 1972, pp. 145–162.CrossRefGoogle Scholar
  7. 7.
    J. Crank, “The Mathematics of Diffusion,” Oxford University Press, Oxford, 1956, pp. 52–56.Google Scholar
  8. 8.
    B. H. Zimm and J. L. Lundberg, J. Phys. Chem., 60, 425 (1956).CrossRefGoogle Scholar
  9. 9.
    E. R. Lieberman, “Studies on the Permeation of Gas Through Collagen Films,” Ph.D. Thesis, Rutgers University, New Brunswick, New Jersey, 1971, p. 137, 322.Google Scholar

Copyright information

© Plenum Press, New York 1974

Authors and Affiliations

  • Wolf R. Vieth
    • 1
  • Mary A. Amini
    • 1
  1. 1.Department of Chemical and Biochemical EngineeringRutgers UniversityNew BrunswickUSA

Personalised recommendations