J. Phys. II France
Volume 2, Numéro 6, June 1992
Page(s) 1341 - 1344
DOI: 10.1051/jp2:1992203
J. Phys. II France 2 (1992) 1341-1344

Scaling theory of polymer solutions trapped in small pores : the $\theta$-solvent case

E. Raphael1 and P. Pincus2

1  Institute for Polymer & Organic Solids, University of California, Santa Barbara CA 93106, U.S.A.
2  Materials and Physics Departments, University of California, Santa Barbara CA 93106, U.S.A.

(Received 11 February 1992, accepted 27 February 1992)

We study theoretically the behavior of a single macromolecular chain dissolved in a $\theta$-solvent and confined in a tube with a diameter D comparable to the natural size (R0=N1/2a) of the chain ( N being the number of monomers of the chain). We find that for $D\ll R_{0}$ the longitudinal dimension $R_{\parallel}$ of the chain increases as $R_{\parallel}\cong Na(a/D)$, in contrast with the longitudinal behavior of an ideal chain which is unaffected by the confinement. We show that this extension of the chain is a consequence of the three-body interactions which are still present at the Flory temperature. We then generalize these results to semi-dilute solutions where the overlap between different chains is significant.


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