Star polymers scaling properties

The dynamics of highly diluted star polymers on the scale of segmental diffusion was first calculated by Zimm and Kilb [143] who presented the spectrum of eigenmodes as it is known for linear homopolymers in dilute solutions [see Eq. (77)]. This spectrum was used to calculate macroscopic transport properties, e.g. the intrinsic viscosity [145], However, explicit theoretical calculations of the dynamic structure factor [S(Q, t)] are still missing at present. Instead of this the method of first cumulant was applied to analyze the dynamic properties of such diluted star systems on microscopic scales. 

The properties of the surplus segment probability p and the effective constraint coordination number z are less well established. It seems possible that p will dep d on polymer species to some extent, since loop projection may be easier for a more locally flexible chain. Weak dependences on concentration and temf rature are likely for the same reason. On the other hand, z characterizes the topology on a fairly large scale and therefore may be virtually a universal constant. Diese however are only some speculations. Values of p and z can be established by various experiments, p from the elastic properties of networks and also from the relaxation of star polymers, z from relative relaxation rates of linear and star molecules in liquids and networks and also from measurements of diffusion rates of stars in linear chain liquids. The adequacy of the... 

Beyond the overlap concentration threshold, c>c = pN/lP, star polymers form a semidilute solution. Because of the fact that the arms in a star are stretched, the scaling theory [24] predicts that the properties of semidilute solutions of star polymers are distinctively different from those of linear polymers. When the polymer concentration c > c, a semidilute solution is envisioned as a system of closely packed and virtually non-interpenetrating (segregated) polymer stars. A further increase in polymer concentration leads to a progressive contraction of the coronae of the individual stars. This contraction results in an increase in the conformational entropy of the partially stretched star arms. 

Simulations, both MC and MD, have been used to test these scaling predictions and to determine other properties of a star polymer, including the static structure factor in the dilute limit. At present, it is not possible to simulate a melt or even a semi-dilute solution of many-arm star polymers due to the long relaxation times. For few-arm stars f 12) MC methods are clearly most efficient, while for large number of arms, MD methods work very well. For small /, the density of monomers of the star is low almost everywhere and static MC methods in which one generates the chains by constructing walks can be Using this method,... 

G. D. J. Phillies. Temporal scaling analysis Viscoelastic properties of star polymers. J. Chem. Phys., Ill (1999), 8144-8150. 

Freed et al. [42,43], among others [44,45] have performed RG perturbation calculations of conformational properties of star chains. The results are mainly valid for low functionality stars. A general conclusion of these calculations is that the EV dependence of the mean size can be expressed as the contribution of two terms. One of them contains much of the chain length dependence but does not depend on the polymer architecture. The other term changes with different architectures but varies weakly with EV. Kosmas et al. [5] have also performed similar perturbation calculations for combs with branching points of different functionalities (that they denoted as brushes). Ohno and Binder [46] also employed RG calculations to evaluate the form of the bead density and center-to-end distance distribution of stars in the bulk and adsorbed in a surface. These calculations are consistent with their scaling theory [27]. 

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