Abstract
Diffusion in a boundary between a polymer+solvent solution and non-solvent was treated by accounting for the presence of the four diffusion coefficients that describe the isothermal transport process in a three component system. Diffusion equations were integrated assuming a concentration dependence of diffusion coefficients that account for the thermodynamic conditions on the cross diffusion terms of Eq. (1). The presence of non-zero cross terms promotes an incongruent diffusion of polymer whose concentration increases at the boundary between the polymer+solvent solution and the non-solvent. Although our model describes diffusion in the range of homogeneous solution, this incongruent polymer diffusion is a process similar to that promoted by the solvent evaporation from the polymer+solvent film that some authors suggested as an intermediate step before the film immersion into the coagulation bath to obtain good asymmetric membranes.
Similar content being viewed by others
References
M. A. Frommer and D. Lancet, inReverse Osmosis Membrane Research, H. K. Lonsdale and H. E. Podell, eds., (Plenum, New York, 1972).
J. Andersen and Ullman,J. Appl. Phys. 44, 4303 (1973).
S. Sourirajan and B. Kumst in,Reverse Osmosis and Synthetic Membranes, S. Surirajan, ed., (Natl. Res. Council of Canada, Ottawa 1977).
H. Strathman and K. Kock,Desalination 21, 241 (1977).
C. Cohen, G. B. Tanny, and S. Prager,J. Polymer Sci. Polym. Phys. 17, 477 (1979).
F. W. Altena, J. Smid, J. W. A. Van der Berg, J. G. Wijmans, and C. A. Smolders,Polymers 26, 1531 (1985).
A. J. Reuvers, J. W. A. Van der Berg, and C. A. Smolders,J. Membrane Sci. 34, 45 (1987).
A. J. Reuvers, and C. A. Smolders,J. Membrane Sci. 34, 67 (1987).
C. S. Tsay and A. J. McHugh,J. Polymer Sci. Part B: Pol. Phys. 28, 1327 (1990).
V. Vitagliano and R. Sartorio,J. Phys. Chem. 74, 2949 (1970).
V. Vitagliano, R. Sartorio, S. Scala, and D. Spaduzzi,J. Solution Chem. 7, 605 (1978).
D. G. Miller, V. Vitagliano, and R. Sartorio,J. Phys. Chem. 90, 509 (1986).
L. Ambrosone, G. Guarino, R. Sartorio, and V. Vitagliano,J. Membrane Sci. 45, 299 (1989).
A. Weissberger,Physical Methods of Chemistry, Vol 1, Part IV, (Wiley, New York, 1972).
H. J. V. Tyrrell and K. R. Harris,Diffusion in Liquids (Butteworths, London, 1984).
J. S. Kirkadly and D. J. Young,Diffusion in the Condensed State (The Institute of Metals, London, 1987).
E. L. Cussler,Diffusion. Mass Transfer in Fluid Systems (Cambridge University, London, 1984).
L. Sundelof,Ark. Kemi 20, 369 (1963).
H. Tompa,Polymer Solutions (Butterworths, London 1956) p. 182.
J. C. Jaeger and A. M. Starfield,An Introduction to Applied Mathematics, 2nd edn., (Clarendon Press, Oxford 1974), p. 419.
F. W. Altena, C. A. Smolders,Macromolecules 15, 1491 (1982).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ambrosone, L., Paduano, L., Sartorio, R. et al. Diffusion phenomena in ternary systems polymer-nonsolvent-solvent. J Solution Chem 22, 1119–1134 (1993). https://doi.org/10.1007/BF00651694
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00651694