Star Polymers Viewed as Ultrasoft Colloidal Particles

Abstract

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...

Glassy States in Asymmetric Mixtures of Soft and Hard Colloids

“…Star polymers have been explored in detail, since they exemplify stable, long hairy particles. At high concentrations, they deform but also interpenetrate via their grafted arms, as reflected by their effective interactions: their tunability at the molecular level allows repulsive pair potentials ranging from ultrasoft to hard as their functionality (number of arms) f S changes from typically below 30 to above 400 [8]. The very same deformability also determines their purely entropic interactions with planar or curved hard walls [9].…”

Generation of Defects and Disorder from Deeply Quenching a Liquid to Form a Solid

“…Such soft potentials arise as the effective interaction potential between polymers or soft macromolecules in solution [25][26][27][28][29][30][31][32][33][34][35][36][37]. Our main reason for considering this model centres on the fact that the structure and phase behaviour (i.e.…”

Colloids with polymer stars: the interaction

“…The factor 5/18 is found by matching the cone approximation for Θ (2) f f to the known values of the contact exponents for f = 1, 2 [1]. This matching in turn proposes an approximate value for the η f exponents, The prefactor Θ f 1 f 2 of the force between two star polymers at short distance calculated in non-resummed 1-loop and resummed 3-loop RG analysis in comparison to the result of the cone approximation.…”

“…While such a behavior was already predicted by early scaling arguments [4] only recently corresponding experiments have become feasible with sufficiently dense stars. In addition theory and computer simulation have refined the original estimate for the number of chains f necessary for a freezing transition from f ∼ 100 to f ∼ 34 and predicted a rich phase diagram [1]. These results were derived using an effective pair potential between stars [1] with a short distance behavior derived from scaling theory as explained below.…”

“…structures of polymer chains that are chemically linked with one end to a common core, have found recent interest as very soft colloidal particles [1,2]. Increasing the number of chains f they interpolate between the properties of linear polymers and polymeric micelles [3].…”