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 second 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 potenti...

We examine in full generality the phase behavior of systems whose constituent particles interact by means of potentials which do not diverge at the origin, are free of attractive parts and decay fast enough to zero as the interparticle separation r goes to infinity. By employing a mean fielddensity functional theory which is shown to become exact at high temperatures and/or densities, we establish a criterion which determines whether a given system will freeze at all temperatures or it will display reentrant melting and an upper freezing temperature.

Abstract. We study the structural and thermodynamic properties of a model of point particles interacting by means of a Gaussian pair potential first introduced by Stillinger (Stillinger F H 1976 J. Chem. Phys. 65 3968). By employing integral equation theories for the fluid state and comparing with Monte Carlo simulation results, we establish the limits of applicability of various common closures and examine the dependence of the correlation functions of the liquid on the density and temperature. We employ a simple, mean-field theory for the high-density domain of the liquid and demonstrate that at infinite density the mean-field theory is exact and that the system reduces to an 'infinite-density ideal gas', where all correlations vanish and where the hypernetted-chain (HNC) closure becomes exact. By employing an Einstein model for the solid phases, we subsequently calculate quantitatively the phase diagram of the model and find that the system possesses two solid phases, face-centred cubic and body-centred cubic, and also displays re-entrant melting into a liquid at high densities. Moreover, the system remains fluid at all densities when the temperature exceeds 1% of the strength of the interactions.

Phys. Rev. Lett. 82, 5289 (1999)) The phase diagram of star polymer solutions in a good solvent is obtained over a wide range of densities and arm numbers by Monte Carlo simulations. The effective interaction between the stars is modeled by an ultrasoft pair potential which is logarithmic in the core-core distance. Among the stable phases are a fluid as well as body-centered cubic, face-centered cubic, body-centered orthogonal, and diamond crystals. In a limited range of arm numbers, reentrant melting and reentrant freezing transitions occur for increasing density.PACS numbers: 82.70.Dd, 61.25.Hq A major challenge in statistical physics is to understand and predict the macroscopic phase behavior from a microscopic many-body theory for a given interaction between the particles [1]. For a simple classical fluid [2], this interaction is specified in terms of a radially symmetric pair potential V (r) where r is the particle separation. Significant progress has been made during the last decades in predicting the thermodynamically stable phases for simple intermolecular pair potentials, such as for Lennard-Jones systems, plasmas or hard spheres, using computer simulations [1] and density functional theory [3]. An important realization of classical many-body systems are suspensions of colloidal particles dispersed in a fluid medium. A striking advantage of such colloidal samples over molecular ones is that their effective pair interaction is eminently tunable through experimental control of particle and solvent properties [4]. This brings about more extreme pair interactions, leading to novel phase transformations. For instance, if the colloidal particles are sterically stabilized against coagulation, the 'softness' of the interparticle repulsion is governed by the length of the polymer chains grafted onto the colloidal surface, their surface grafting density and solvent quality. Computer simulations and theory have revealed that a fluid freezes into a body-centered-cubic (bcc) crystal for soft long-ranged repulsions and into a face-centeredcubic (fcc) one for strong short-ranged repulsions [5]. This was confirmed in experiments on sterically stabilized colloidal particles [6]. A similar behavior occurs for charge-stabilized suspensions where the softness of V (r) is now controlled by the concentration of added salt [7]. Less common effects were observed for potentials involving an attractive part aside from a repulsive core. In reducing the range of the attraction, a vanishing liquid phase has been observed [8] and an isostructural solidsolid transition was predicted [9]. More complicated pair potentials can even lead to stable quasicrystalline phases and a quadruple point in the phase diagram [10].The aim of this letter is to study the phase diagram of an ultrasoft repulsive pair potential V (r) which is logarithmic in r inside a core of diameter σ and vanishes exponentially in r outside the core. The motivation to do this is twofold: first, such a potential is a good model for the effective interaction betwee...

The distance-resolved effective interaction between two star polymers in a good solvent is calculated by Molecular Dynamics computer simulations. The results are compared with a pair potential proposed recently by Likos et al. [Phys. Rev. Lett. 1998, 80, 4450] which is exponentially decaying for large distances and crosses over, at the corona diameter of the star, to an ultrasoft logarithmic repulsion for small distances. Excellent agreement is found in a broad range of star arm numbers.