Combining statistical-mechanical theories and neutron-scattering techniques, we show that the effective pair potential between star polymers is exponentially decaying for large distances and crosses over, at a density-dependent corona diameter, to an ultrasoft logarithmic repulsion for small distances. We also make the theoretical prediction that in concentrated star polymer solutions, this ultrasoft interaction induces an anomalous fluid structure factor which exhibits an unusually pronounced

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... econd peak. [S0031-9007(98)06148-1] PACS numbers: 61.25.Hq, 61.20.Gy, 82.70.Dd Star polymers consist of a well-defined number f of flexible polymer chains tethered to a central microscopic core. By enhancing this functionality (or arm number) f which governs the interpenetrability of two stars, one can continuously switch from unbranched polymer chains (f 1, 2) to a colloidal sphere (f ¿ 1). Hence, star polymers can actually be viewed as hybrids between polymerlike entities and colloidal particles establishing an important link between these different domains of physics. Moreover, star polymer solutions reveal quite a number of novel structural and dynamical properties which occur neither in single-chain polymers nor in suspensions of colloidal spheres; for recent reviews see Refs. [1, 2] . While the polymer conformations around a single star are well understood by computer simulation [3], scaling theory [4], and small-angle neutron scattering experiments [5] , concentrated star polymer solutions are much more difficult to access due to the additional effective interactions between the stars. In particular, these interactions become relevant when the distance r between two star polymer centers is of the order of the so-called corona diameter s, which describes the spatial extension of the monomer density around a single star (see the inset of Fig. 1 ). This translates immediately into an overlap density r ‫ء‬ ϵ 1͞s 3 of the core number density r. Close to this overlap density r ‫ء‬ , there is an effective repulsion between stars resulting from the osmotic pressure arising between polymers from different cores. The repulsion is purely entropic; i.e., it simply scales with the thermal energy k B T . Witten and Pincus [6] were the first to derive the functional form of this repulsion. The effective potential between two stars, V ͑r͒, was found to depend logarithmically on r and to scale asymptotically as f 3͞2 with the arm number, i.e., V ͑r͒ 2k B T gf 3͞2 ln͑r͞s͒, where k B is Boltzmann's constant, T is the temperature, and g is an unknown numerical prefactor. Note that this result was obtained only for large f and for small distances r # s. Since this potential depends only weakly on r, the stars can be viewed as "ultrasoft" colloidal particles whose interaction is very different from common soft spheres described, e.g., by an inverse-power potential [7, 8] . The aim of this Letter is twofold: First, we describe the star polymer interaction quantitatively, proposing an explicit analytical expression for the effective pair potential V ͑r͒, similar to that in Ref. [6] which is designed, however, for arbitrary r and f. Using fluid-state theory and Monte Carlo computer simulations, we have calculated the structural correlations. At the same time, we have performed small-angle neutron scattering measurements on 18-arm polyisoprene stars over a broad density regime, ranging from r 0.07r ‫ء‬ to r 0.6r ‫ء‬ . The experimental data for the pair correlations compare favorably well with our theoretical results. Second, more qualitatively, we predict theoretically an anomalous fluid structure factor S͑q͒ with a first peak that decreases and a pronounced second peak that increases with growing density slightly above the overlap concentration. This is unknown for common simple fluids [7] whose repulsive interaction potential is governed by a single length scale. FIG. 1. The pair potential given by Eq. (1) for f 18, 32, 64, 128, and 256 (from left to right) as a function of the centerto-center separation r. Inset: two stars in the "blob" picture [4], at distance r from each other. 4450 0031-9007͞98͞80(20)͞4450(4)$15.00