Star polymer viscosity

Shell International Research (2000) Star Polymer Viscosity Index Improver for Oil Compositions , US Patent 6,034,042. 

Block (Star) Arrangement. The known star polymers, like their linear counterparts, exhibit microphase separation. In general, they exhibit higher viscosities in the melt than their analogous linear materials. Their rheological behavior is reminiscent of network materials rather than linear block copolymers (58). Although they have been used as compatibiUzers in polymer blends, they are not as effective at property enhancements as linear diblocks... 

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. 

Star-shaped polymer molecules with long branches not only increase the viscosity in the molten state and the steady-state compliance, but the star polymers also decrease the rate of stress relaxation (and creep) compared to a linear polymer (169). The decrease in creep and relaxation rate of star-shaped molecules can be due to extra entanglements because of the many long branches, or the effect can be due to the suppression of reptation of the branches. Linear polymers can reptate, but the bulky center of the star and the different directions of the branch chains from the center make reptation difficult. 

Figure 16 shows the viscometer and DRI traces of another star-branched polystyrene. This sample contained about 12% of the starting linear arm precursor which eluted at retention volume ca. 52 ml. The kinetic molecular weight of the linear precursor was 260,000. The results obtained for the individual peak through the SEC/Viscosity methodology are summarized in Table 7. It is seen that the measured of the linear arm is very closed to the kinetic value. The average functionality of this star polymer is calculated to be f = 10. 

Wyman and co-workers (120) studied the viscosity of narrow MWD linear and 4-armed star polystyrenes as a function of shear rate. At low shear rates, the star polymers (of MW 204000 and 430000) had low-shear viscosities much lower than linear ones of the same MW it may be remarked that the branch length... 

The synthesis of various multi-arm star polymers has long been of growing practical and theoretical interest to a variety of industries. Star polymers have shown to be useful as surfactants, lubricants, rheology modifiers, and viscosity modifiers. Actually, star polymers are considered as viscosity modifiers and oil additives (15). 

The branched architecture has great influence on the packing of molecular chains. In general, dendrimers have smaller hydrodynamic radius and the melt and solution viscosity of a hyperbranched polymer is expected to be lower than that of a parent linear polymer. Viscosity measurements performed with a cone viscometer confirmed the decrease of viscosity of star-shape polymers compared to the respective high molecular weight arms (polymers B-R-4 and C-R-4, Tables 1 and 2). This observation is consistent with the decrease of hydrodynamic volume observed for... 

Masuda et a/.[30] reported data collected for a series of polystyrene star polymers that seemingly conflict with the discovery made by Quack and Fetters [27]. They showed that the viscosity of polystyrene star polymers was dependent on the number of arms. Specifically, they showed that viscosity increased with the number of branches for a series of polystyrene stars with Mw, arm = 55 000 g/mol and the number of arms ranging from 7 to 39. However, the level of arm entanglement for the polystyrene stars was far lower than that of the polyisoprene stars studied by Quack and Fetters [27]. 

Clearly, in order for the viscosity of star polymers to be independent of the number of branches, a certain level of entanglement needs to be present. 

Following the initial discovery [27] that rj0 depends on just arm molecular weight for star polymers with sufficiently high levels of branching, this type of dependence was confirmed by others both theoretically [32] and experimentally [33]. Pearson and Helfand [32] predicted that the zero shear viscosity of star polymers should scale with arm molecular weight (Afa) as... 

For the subsequent generation of arborescent graft polystyrenes, a dramatic increase in rj0 was observed by Hempenius et al. [43] for each of the three series included in their study. However, despite this increase in viscosity, the rj0 for each of these is still lower than that of the linear homologue polystyrenes of the same overall molecular weight. This jump in viscosity is due to an increase in branch density which in turn results in increase in chain extension similar to that observed by Roovers [31] for highly branched star polymers. 

Gyration and Viscosity of Linear and Star Polymers in Different Regimes. 

Expressions for Viscosity and Recoverable Compliance of Entangled Star Polymers... 

Copolymerization of di- and trimethacrylates with functionalized monomers, like glycidyl methacrylate, leads to low-viscosity oligomers capable of nonradical cross-linking. This process promises substantial value for industrial applications. Star polymers useful in coatings were prepared by copolymerizing methacrylate macromonomers with diacrylates.519 For instance, a star polymer was synthesized by copolymerization of a 2-ethylhexyl methacrylate/isobutyl methacrylate/hydroxyethyl methacrylate macromonomer with butanediol diacrylate. 

Viscosity of polyisoprene star polymers with various numbers of arms at 60 C. The left plot shows that viscosity is only a function of the number of entanglements per arm and that the viscosity of entangled linear... 

Entangled star polymers relax by arm retractions with relaxation times and viscosities exponentially large in the number of entanglements per arm NJNg [Eqs (9.58) and (9.61)]. This leads to exponentially small diffusion coefficients [Eq. (9.62)] for entangled star polymers. 

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