J. Phys. II France
Volume 6, Numéro 5, May 1996
Page(s) 587 - 591
DOI: 10.1051/jp2:1996199
J. Phys. II France 6 (1996) 587-591

Static Properties of a Star Polymer in a High Molecular Weight Solvent

C. Gay and E. Raphaël

Laboratoire de Physique de la Matière Condensée U.R.A. 792 C.N.R.S., Collège de France, 11 Place Marcelin Bertholot, 75231 Paris Cedex 05, France

(Received 15 January 1996, received in final form 11 March 1996, accepted 20 March 1996)

Recently, Raphaël, Pincus and Fredrickson considered the static properties of an isolated star polymer ( f arms, N monomers per arm) dissolved in a melt of linear chains of degree of polumerization P<N, which are chemically identical to the star arms ( Macromolecules 26 (1993) 1996). In the present article we show that the results obtained by these authors are valid only for stars with a high enough number f>P1/2. For f<P1/2, a new Gaussian region appears within the star structure. We predict that the N-monomer volume fraction varies as $\phi (r)\cong 1$ (dense region) for r<af, $\phi (r)\cong f(r/a)^{-1}$ for af < r < aPf-1 and $\phi (r)\cong
P^{1/3}f^{2/3}(r/a)^{-4/3}$ for r>aPf-1. Our study is restricted to scaling laws; the exact prefactores in our formulae remain undetermined.

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