STATIC PROPERTIES OF A STAR POLYMER IN A HIGH-MOLECULAR-WEIGHT SOLVENT

Recently, Raphael, Pincus and Fredrickson considered the static proper ties of an isolated star polymer (f arms, N monomers per arm) dissolve d in a melt of linear chains of degree of polymerization P < N, which are chemically identical to the star arms (Macromolecules 26 (1993) 19 96). In the present article we show that the results obtained by these authors are valid only for stars with a high enough number of arms f > p(1/2). For f < p(1/2), a new Gaussian region appears within the sta r structure. We predict that the N-monomer volume fraction varies as p hi(r) congruent to 1 (dense region) for r < af, phi(r) congruent to f( r/a)(-1) for af < r < aPf(-1) and phi(r) congruent to p(1/3)f(2/3)(r/a )(-4/3) for r > aPS(-1). Our study is restricted to scaling laws; the exact prefactors in our formulae remain undetermined.