One of the main goals of polymer science has been to relate the structure of macromolecular chains to their macroscopic properties. In particular, it has been hoped that one could relate the sizes of polymer coils to the degree to which they entangle with one another and thus to their viscoelasticity in the melt. In recent years, the availability of model polymers with nearly monodisperse molecular weight distributions and precisely controlled chemical structures has allowed for improved data both on rheology and on the dimensions of the chains. This has now allowed us to determine the correlations between such properties as chain dimensions, density, and plateau modulus and to show that some quite simple relations exist between them. The main body of these data is on polymers that can be considered to be models for polyolefins. These have been made by the hydrogenation of polydienes synthesized by anionic polymerization techniques. In this way the molecular weight distribution can be made to be nearly monodisperse (Afw/M" < 1.1) and the chemical structure is well controlled. For example, models of a wide range of ethylene-butene copolymers have been made by the saturation of polybutadienes with a range of vinyl content. Such polymers can be made at many molecular weights as well. The viscoelastic properties of these polymers have been measured very precisely, and their chain dimensions have been determined by small-angle neutron scattering. To a high degree of correlation, we find that the mean-square unperturbed end-to-end distance,

After many years of intense research, most aspects of the motion of entangled polymers have been understood. Long linear and branched polymers have a characteristic entanglement plateau and their stress relaxes by chain reptation or branch retraction, respectively. In both mechanisms, the presence of chain ends is essential. But how do entangled polymers without ends relax their stress? Using properly purified high-molar-mass ring polymers, we demonstrate that these materials exhibit self-similar dynamics, yielding a power-law stress relaxation. However, trace amounts of linear chains at a concentration almost two decades below their overlap cause an enhanced mechanical response. An entanglement plateau is recovered at higher concentrations of linear chains. These results constitute an important step towards solving an outstanding problem of polymer science and are useful for manipulating properties of materials ranging from DNA to polycarbonate. They also provide possible directions for tuning the rheology of entangled polymers.

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...

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The local dynamics of 1,4 polybutadiene below and above the merging of the ␣ and ␤ relaxations have been investigated by combining neutron spin echo ͑NSE͒ and dielectric spectroscopy. The study of the dynamic structure factor measured by NSE over a wide momentum transfer range allows us to characterize the ␣ relaxation as an interchain process while the ␤ relaxation originates from mainly intrachain motions. At temperatures below the merging, the dynamic structure factor can be described by a superposition of elemental processes for the ␤ relaxation as obtained from dielectric spectroscopy. The elemental motions behind this process can be related to rotational jumps of the chain building blocks around their center of mass. Furthermore, we have been able to consistently describe the dynamic structure factor above the merging of the ␣ and ␤ relaxations by assuming that both processes are statistically independent. In the framework of this scenario a procedure for analyzing the dielectric response in the ␣-␤ merging region has been developed. Its application to the dielectric data allows us to describe the dielectric response in this region on the basis of the low temperature behavior of the ␣ and ␤ processes and without considering any particular change in the relaxation mechanism of these processes. The temperature dependence found for the relaxation time of the ␣ process follows now the viscosity, a masked feature in the experimental data due to the merging process. In this way, we have been able to consistently describe the relaxation of both, the polarization and the density fluctuations, by using the same scenario, i.e., independent ␣ and ␤ processes, and considering the same functional forms and temperature dependences of the characteristic times of the two processes. ͓S1063-651X͑96͒07209-1͔