Star-branched polystyrene molecular weight

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. 

Viscosity enhancement in branched polystyrenes would be expected to be considerably smaller than in branched diene polymers. A smaller Z factor and a higher Me for this polymer combine to reduce the V value. The star-branched polymers shown in Fig. 11 would not therefore be expected to show viscosity enhancement at a concentration of 0.25 g/ml. Experiments reported on melt viscosities of star-branched polystyrenes having f 3 on the other hand would have been expected to have shown some enhancement at least at the h est molecular weight. None was in fact foimd, the viscosities beii approximately predictable from the Bueche theory i. e. were all lower than their linear counterparts. Viscosity enhancements have been reported for multibranch star polystyrenes (f = 7 to 13) in melt flow experiments. These are of comparable magnitude to the values found for four-brandi star pedybutadienes at the same value of M /Mc. Specific effects of multiple brandling were not considered in the model described above but there is evidence that the major enhancement effect is produced at f = 3. Increase of the branch nuniber to four at constant increases the enhancement by about a factor of two but subsequent increases in f have only small effect . ... 

FIG. 9-15. Logarithmic plots of [C ] and [G"] against frequency (unreduced) calculated from Zimm-Kilb theory for star-branched polystyrenes with molecular weight 10 in a solvent with viscosity 0.01 poise at 25 C, with large N and h = 0.25 or 0.05, and different degrees of branching from/= 2 (linear) to/= 13,... 

Hancock and Synovec " have carried out rapid characterization of linear and star branched polystyrene by gradient detection using methylene dichloride solutions of the polymers. This technique measures weight average molecular weights and is more specific than results obtained using a refractive index detector. 

As an example demonstrating the effects of the chain architecture on chain dynamics, we here focus on the star-branched chain composed of monodisperse / arms. The top part of Figure 7 shows reduced moduli, [G ]r= (MG7CRT)c- and [G"]r = (M G"-(B>/s /GRT)c- o/ measured for dilute nine-arm star-branched polystyrene (PS) chains in theta solvents (decalin and dioctyl phthalate). These [G ]r and [G"]r data are plotted against a reduced frequency, orj. Here, M (= 5.0 x 10 ) and G are the molecular weight and mass concentration of the star-branched PS, respectively, is the solvent viscosity, R is the gas constant, T is the absolute temperature, and rj is the longest relaxation time (cf. eqn [54] shown later). The terminal relaxation tails of the [G ]r and [G"]r data (cf. eqn [30]) are dearly noted in Figure 7. 

The foregoing section dealt with TLC separation of linear and branched polymers, from the standpoint of resolutions with respect to molecular weight. In this section we summarize TLC results of chromatographic distinguishment of linear and star-shaped polystyrenes on the same molecular-weight level. It is now well known that... 

In several cases the melt viscosity of a series of lightly-branched polymers has been determined as a function of MW, and compared with that of linear polymers, and it has been found or may be deduced from the published data that there is a cross-over molecular weight, below which the branched polymer is less viscous, but above which it more viscous, than the linear polymer of equal MW. This behaviour is observed with some comb-shaped polystyrenes (35) and poly(vinyl acetate)s (59, 89), star polybutadienes (57, 58, 123), and randomly-branched polyethylenes (56,61). Jackson has found (141) that if the ratio ZJZC of the number of chain atoms at the cross-over point, Zx, to the number at the kink in the log 0 — logM curve, Zc, [as given in Ref. (52)], is plotted against nb, the number of branches, a reasonable straight line is obtained, as in Fig. 5.1. 

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. 

Star-branched lonomers composed of short sulfonated polystyrene outer blocks and hydrogenated butadiene or isoprene inner blocks, with narrow molecular weight distributions have been synthesized by living... 

Hadjichristidis and coworkers [230] studied the hydrodynamic behavior, in dilute solution, of miktoarm stars of the types A2B and A2B2 where A, B = PS, PI, and PBD in solvents good for both segments or theta for one of the arms and good for the others. Analysis of the results suggests that the experimentally determined values of intrinsic viscosity, [q], viscometric radius, Rv, and Rh for the copolymers are higher than the ones calculated from homopolymer star data. The phenomenon was perceived as an indication of repulsive interactions between A and B chains, which tend to increase the sizes of the individual chains and of the star molecule as a whole [230]. A similar conclusion was reached from SEC experiments on polystyrene-poly-f-butylacrylate miktoarm stars with equal number of branches of the two components [243]. The phenomenon, in this case, was more pronounced as the molecular weight of the branches increased. 

Tsitsilianis et al. recently published [245] preliminary results on the micelliza-tion behavior of anionically synthesized amphiphilic heteroarm star copolymers with polystyrene and poly(ethylene oxide) branches in THF and water. The former solvent is not very selective for one of the segments whereas the latter is strongly selective for PEO. The apparent molecular weights found for the micelles in THF were two orders of magnitude larger than the ones measured for the unimers. By increasing concentration an increase in the depolarization ratio was observed supporting the conclusion that multimolecular micelles are formed by this kind of miktoarm star copolymer. 

The efficiency of the linking reactions of polychlorosi-lanes with poly(dienyl)lithium compounds has been documented by synthesis of well-defined, narrow molecular weight distribution, 18-armed star-branched polyisoprenes, polybutadienes, and butadiene end-capped polystyrenes by linking reactions with a decaoctachlorosilane [(SiCl)ig] [256, 257]. The linking reactions of poly(butadienyl)lithium (Mjj = 5.3-89.6 x 10 g/mol) with carbosilane dendrimers with up to 128 Si-Cl bonds have been reported to proceed... 

The variation of recoverable compliance with molecular weight also differs for linear and nonlinear polymers. In contrast to the behavior of nearly monodisperse linear polymers, for which becomes a constant 2/ G ) beyond about 5Mg, for stars simply continues to increase in direct proportion to Mb, which is exemplified by the comparison of data for linear polystyrene [71] and four-arm polystyrene stars [66] in Fig. 3.47. Experimentally, the behavior of for nearly monodisperse stars, irrespective of branch-point functionality, is described well by [52]... 

---