Star polymer model

Fig. 3.16 Star polymer model for chains tethered to a curved surface. Chains are represented as a string of blobs extending radially from the core of the star.

SANS measurements were performed at room temperature (25 °C) in order to determine the sizes of the micellar self-assembled aggregates of octyl glucoside. The SANS curves of the OG micellar solutions, obtained at OG concentrations 0.038 M and 0.061 M (which are above the CMC value of OG), are shown in Eigure 1. To fit the small angles scattering intensity, /, we used the Dozier star polymer model [39] ... 

The distinctive properties of densely tethered chains were first noted by Alexander [7] in 1977. His theoretical analysis concerned the end-adsorption of terminally functionalized polymers on a flat surface. Further elaboration by de Gennes [8] and by Cantor [9] stressed the utility of tethered chains to the description of self-assembled block copolymers. The next important step was taken by Daoud and Cotton [10] in 1982 in a model for star polymers. This model generalizes the... 

For star polymers a value of e = 0.5 has been obtained (1, V7) and studies (18) of model comb polymers indicate a value of 1.5. Other work (191 has suggested that e is near 0.5 at low LCB frequencies. For a random LCB conformation of higher branching frequency an e value between 0.7 and 1.3 might be expected, i.e. somewhere between a star and a comb configuration. 

The core first method starts from multifunctional initiators and simultaneously grows all the polymer arms from the central core. The method is not useful in the preparation of model star polymers by anionic polymerization. This is due to the difficulties in preparing pure multifunctional organometallic compounds and because of their limited solubility. Nevertheless, considerable effort has been expended in the preparation of controlled divinyl- and diisopropenylbenzene living cores for anionic initiation. The core first method has recently been used successfully in both cationic and living radical polymerization reactions. Also, multiple initiation sites can be easily created along linear and branched polymers, where site isolation avoids many problems. 

Schematically, model regular star polymers are obtained directly from living anionic polymers where (Si-Cl p is a multifunctional carbosilane coupling agent, MeSiCl3, SiCl4, Cl3SiCH2CH2SiCl3, etc. including dendritic carbosilanes...

The tube model gives a direct indication of why one might expect the strange observations on star melts described above. Because the branch points themselves in a high molecular weight star-polymer melt are extremely dilute, the physics of local entanglements is expected to be identical to the linear case each segment of polymer chain behaves as if it were in a tube of diameter a. However, in... 

The approximate treatment described above accounts rather well for the linear rheology of star polymer melts. In fact it has been remarked that the case for the tube model draws its real strength from the results for star polymers rather than for linear chains, where the problems of constraint release and breathing modes are harder to account for (but see Sect. 3.2.4.). However, there are still some outstanding issues and questions ... 

The conLguration of the polymers in the micelle has also been studied within the framework of the Daoud-Cotton model (Daoud and Cotton, 1982) for star polymers. However, this model assumes that all the chain ends lie at the outer surface of the corona, therefore overlooking the possibility of a chain-end distribution Marques (1997). 

The g factors of some star-shaped polymacromonomers with relatively limited number of arms have been investigated and compared with the theory mentioned above. Tsukahara et al. [61] estimated the g factors of PSt polymacromonomers from 24 by SEC-LALLS measurement and compared with Eqs. (6) and (8). The results suggest that these poly(macromonomers) behave like star polymer. The experimental value of g is larger than the theoretical one based on Eq. (6) in agreement with results of studies on model star polymers [62]. 

The spectroscopic data have been compared with the theoretical predictions of the Doi- Edwards model. In the time scale of our experiments, a quantitative agreement between experiment and theory is obtained if chain length fluctuations, retraction and reptation are taken into account. In the case of star polymers, the large scale fluctuation mechanism as proposed by Pearson and Helfand associated with the retraction process is accounting for... 

Despite these complications, there are now numerous evidences that the tube model is basically con-ect. The signatory mark that the chain is trapped in a tube is that the chain ends relax first, and the center of the chain remains unrelaxed until relaxation is almost over. Evidence that this occurs has been obtained in experiments with chains whose ends are labeled, either chemically or isotopically (Ylitalo et al. 1990 Russell et al. 1993). These studies show that the rate of relaxation of the chain ends is distinctively faster than the middle of the chain, in quantitative agreement with reptation theory. The special role of chain ends is also shown indirectly in studies of the relaxation of star polymers. Stars are polymers in which several branches radiate from a single branch point. The arms of the star cannot reptate because they are anchored at the branch point (de Gennes 1975). Relaxation must thus occur by the slower process of primitive-path fluctuations, which is found to slow down exponentially with increasing arm molecular weight, in agreement with predictions (Pearson and Helfand 1984). 

Figure 1 (a) Reptation of a linear polymer molecule in a tube, (b) Arm retraction mechanism in the tube model for a star polymer... 

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