Computer simulation of three-arm star polymers

Polymeric liquids have unique dynamical properties that distinguish them from small molecule fluids . One of the most important examples is the strong dependence of the transport properties on the degree of polymerization N. For linear polymer chains (the most extensively studied architecture) one finds two different regimes. For chains shorter than a crossover chain length Nc the selfdiffusion coefficient D and the shear viscosity g scale as D l Nÿ1 and g l N, whereas for longer chains the length dependence is much stronger, D l Nÿ2 and g l N, respectively. This transition occurs in melts of flexible, linear polymer chains regardless of the chemical identity of the monomeric units, and is attributed to the onset of intermolecular entanglements. The exact nature of entanglements is unclear; however, they undoubtedly originate from chain uncrossability. Several different theoretical treatments of the entanglement phenomenon have been proposed. The most popular approach 12) uses a concept of “reptation”. It postulates that a polymer chain in the melt is confined to a “tube”, the size and shape of which are given by the constraints of surrounding (uncrossable) chains. A given chain can only move along its tube. This amounts to suppression of transverse motions, and large-scale diffusive motion that occurs through snake-like “slithering” along the tube. With some caveats, reptation theory and most other theoretical approaches to the dynamics of entangled polymer melts lead to predictions that agree with experimental data for linear chains. In order to distinguish between different theories it is worthwhile to investigate polymeric liquids consisting of molecules of different architectures. Of particular interest are non-linear architectures such as star or ring polymers . An additional incentive to study non-linear architectures comes from their practical importance: most of the polymers used in industry are branched chains of various types. It is known that the dynamical properties of branched chains (especially non-linear flow properties) are very different from those of linear chains. The systematic study of branched polymer dynamics has just begun . In this paper we describe a computer simulation study of three-arm star polymers in the melt. It is believed that in dense systems of star polymers reptation is strongly suppressed. De Gennes and other workers 18) have argued that large (spatial) scale diffusive motions are enabled by an “arm-retraction” mechanism which leads to an exponential dependence of both the self-diffusion coefficient and viscosity on the length of the arm. Experimental data of Bartels et al. on three-arm star polymer melts show a stronger-than-power-law dependence of the self-diffusion coefficient on arm length. A plot of their data suggests exponential dependence over roughly five orders of magnitude. Similarly, experiments by Fetters et al. find the coefficient of viscosity to have a fasterthan-power-law dependence on arm length. Their data also show an exponential dependence on arm length. These experiments are probably the strongest argument in favor of reptation. However, it should be emphasized that the evidence provided by these experiments is indirect and that the arm retraction mechanism has not been directly observed. On a computational side, there have been several simulations of an isolated star polymer in a fixed lattice of linear obstacles. These simulations find that diffusion decreases exponentially with increasing arm length. A recent simulation by Sikorski et al. of a single star in a