Polyisoprene star polymers

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... 

Fig.5. The elastic modulus G (co) and dissipative modulus G (co) for linear top) and three-arm-star branched (bottom) polyisoprene from [5]. Note the broad range of relaxation times indicated by the width of the peak in the star-polymer...

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]. 

It is not clear why this transition should occur at such a higher level of arm entanglement for polystyrene stars than for other star polymers. This observation is in direct conflict with the standard assumption that through a proper scaling of plateau modulus (Go) and monomeric friction coefficient (0 that rheological behavior should be dependent only on molecular topology and be independent of molecular chemical structure. This standard assumption was demonstrated to hold fairly well for the linear viscoelastic response of well-entangled monodisperse linear polyisoprene, polybutadiene, and polystyrene melts by McLeish and Milner [24]. 

Figure 13.22 Damping functions hf y) and hs y) for the fast and slow relaxation processes of a 15 wt% solution of a micelle-forming polystyrene-polyisoprene diblock copolymer (molecular weights, respectively, of 14,000 and 29,000) in a low-molecular-weight (A/ = 4,000) polyisoprene. Damping functions for linear and star polymers and for silica dispersion are shown for comparison. (From Watanabe et al. 1997, with permission from Macromolecules 30 5905. Copyright 1997, American Chemical Society.)...

The viscoelastic behavior in the melt state of end-fiinctionalized polyisoprenes was also investigated (30). The results can be compared with predictions based on the star model for the aggregates. It is well known that the viscoelastic properties of star polymers in the melt state depend on arm molecular weight and they are insensitive to their functionality (31). 

For the diblock copolymer, which exhibits a flow region at longer times than pure polyisoprene, the relaxation of the isoprene sequence is treated like the relaxation of the arm of a star polymer. We have followed the description proposed by McLeish [17, 18] for star homopolymers. The distribution of relaxation times is given by Eq. (9), where Mb is the molecular weight of one branch (here the molecular weight of the polyisoprene sequence), s ranges be-... 

FIGURE 1.7 Plots of viscomelric branching parameter, g, versus branch functionahty, p, for star chains on a simple cubic lattice (unfilled circles), together with experimental data for star polymers in theta solvents , polystyrene in cyclohexane , polyisoprene in dioxane. Solid and dashed lines represent calculated values via Eqs. (1.70) and (1.71), respectively. (Adapted... 

Reliable theoretical expressions for the -parameter in good solvents are not yet available. However, a semiempirical equation for gr, has been suggested by Douglas et al. [1990] based on a fit to experimental data for polystyrene (PS), polyisoprene (PIP), and polybutadiene (PBD) star polymers. The equation is... 

Figure 8.12 Comparison of of ( ) 340, (0) 800, and (O) 6300 kDa 18-arm star polyisoprenes and ( ) 302 kDa linear polyisoprene, all in CCI4. Solid and dashed lines represent Eqs. 8.1 and 8.2, respectively, for the star polymers. Original measurements are by Xuexin, et al.(23).

Solution studies showing a transition include Colby, et al. (36), Malkin, et al. (38), and Raspaud, et al. (44) on linear polybutadiene solutions, Mochalova, et al. (39) on polyisobutylene solutions, Roovers(43) on many-arm polybutadiene star polymers, Graessley, et al. (54) on linear polyisoprenes, Koenderinck, et a/. (48) and Milas, et al. (49) on xanthan water, Lin and Phillies(45,46) on polyacrylic acid water, Ohshima, et al. (41,42) on poly- -hexyUsocyanate in dichloromethane and toluene, and Phillies and collaborators(15,47) on hydroxypropylcellulose water. 

Raju, et al. report an extremely extensive set of measurements of the dynamic moduli of linear and star polymers in systems ranging from the moderately concentrated up to the melt(25). The complete study examined linear polymers fully hydrogenated polyisoprene, polyisoprene, polystyrene, polybutadiene, and fully hydrogenated polybutadiene, as well as three-arm and four-arm polybutadiene stars, a total of 19 polymers having molecular weights between 4.6 and 860 kDa, at various temperatures. 

Measurements on the poly-a-methylstyrenes and polyisoprenes cover both linear and star polymers. For both species, more prominently for the poly-a-methylstyrenes (filled and open circles), the correlation lines between r o and a are the same for star polymers as for linear polymers. 

Star polymers, indeed, have enormous viscosities and very low diffusion coefficients, reflecting the exponential dependence of the time for complete contraction on molecular weight. A time of 1600s, characterizing complete escape of a polyisoprene arm of molecular weight 100,000, has been observed. 

Figure 5 Zero-concentration form factors of star polymers with different functionalities. Data obtained in a good solvent, methylcyclohexane-di4 with SANS. From bottom to top /= 8 (polyisoprene),/=18 (polyisoprene),/= 32 (polybutadiene),/= 64 (polybutadiene), and/= 128 (polybutadiene). The data are offset vertically for clarity. The solid line represents Eq. (27). Arrows indicate Q=the onset of the asymptotic regime in which scattering is caused by the swollen blobs in the corona. (From Ref 31.)...

For star polymers the temperature at which 2 = 0 is lower than the Floiy 0-temperature of the linear polymer and depends on the molecular weight and the functionality [103]. Several studies have confirmed this phenomenon for polystyrene stars [37,38] and polyisoprene stars [41-43]. All studies have assumed that the lower temperature of the star polymer is exclusively due to their branched structure and is not affected by the increased weight fraction of foreign chemical groups present in the multiple chain ends or in the central coupling unit of the star. There is experimental evidence that such groups affect the observable [104]. Furthermore, in the discussion it should be kept in mind that determination of 0 usually has a 1 to 2 K accuracy. 

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