Symmetric Star Polymers

The simple slip link algorithm described above applies most obviously to star polymers, which relax by primitive path fluctuations combined with constraint release. As mentioned above the equilibrium (or average) number of slip links is Nq = IMf, with the arm molecular 

More sophisticated slip link models can predict not only linear viscoelasticity, but also center-of-mass diflusion and nonlinear viscoelasticity of both linear and branched polymers [17, 64]. These models are discussed briefly in Section 11.5.2.2. 

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The deliberate introduction of multifunctional branching into anionically prepared polydiene and poly (diene-co-styrene) polymers produces materials with unique morphological and viscoelastic properties (1-3). Work has included synthesis of symmetric star polymers produced by reaction of living polyanionic "arms" with multi-functional chlorosilane (4-9),... 

Star polymers, with a structure where chains of different molecular weight and/or chemical nature radiate from a common junction point, are expected to have different solution behavior compared to regular or symmetric star polymers. By forcing chemically different arms to be joined, expansion of the molecular dimensions is predicted (see Sect. 3.1.1) as a consequence of the increase in the number of heterocontacts in good and theta solvents or new kinds of structures can be formed in selective solvents. 

Calculate the radius of gyration of an ideal symmetric /-arm star polymer with N monomers of length b. Hint Each arm of a symmetric star polymer... 

It has been reported that observed values of cj for symmetrical star polymers in 0-solvents are approximately equal to g112 if / is not very large (62-64) but otherwise are smaller than g112 (65). However, smaller values are also reported even for small number of branches (66). Although Eq. (2.39b) was obtained for star polymers, it is expected to be applicable to other types of branches to some extent. However, the result of its application to comb polymers is not very encouraging (64,67). The effect of the excluded volume has not been studied so much theoretically. Recent experimental results by Kamada and Sato (65) and by Kurata et al. (69,70) revealed that (f is approximately equal to g1/2 for randomly branched polymers in good solvents. 

Studies on two symmetrical star polymers have been reported by Schrag, Ferry et al. for dynamic properties at infinite dilution. One is for a four armed polybutadiene in two good solvents, a-chloronaph-thalene and chlorinated diphenyl (Aroclor 1232) (101). The polymer... 

Q1A Qian, Z., Miiuiikanti, V.S., Sauer, B.B., Dee, G.T., and Archer, L.A., Surface tension of symmetric star polymer melts (experimental data by Z. Qian), Macromolecules, 41, 5007,2008. 

Asymmetric star polymers are megamolecules [1] emanating from a central core. In contrast to the symmetric stars very little was known, until recently, about the properties of the asymmetric stars. This was due to the difficulties associated with the synthesis of well-defined architectures of this class of polymeric materials. The synthesis, solution and bulk properties, experimental and theoretical, of the following categories of asymmetric stars will be considered in this review ... 

These structures are schematically shown in Scheme 21. The synthesis of asymmetric stars can be accomplished by the same general methods reported for the symmetric stars but in such way that a controlled incorporation of the arms, differing in molecular weight, end functional groups, or topology is achieved. Efficient methods for the synthesis of asymmetric star polymers were developed only recently. 

Other measurements reported (103) are for a symmetrical star polystyrene of nine arms. The polymer was synthesized by Zilliox et al. (65,107) by the addition of a small amount of divinyl benzene to a... 

Symmetric 3-arm star polymers based on the arm-first technique were synthesized by clicking azide end-functionalized PS, PtBuA, or poly(ethylene glycol) (PEG) with a ttialk5me LA. The coupling efficiendes of PS-N3, PtBuA-N3, and PEG-N3 with the triallqme linking agent were 87%, 85%, and 82%, respectively. 

Figure 28 Phase diagram of ABC star polymers with arm-length ratio 1 1with symmetric interaction parameters. Morphologies are lamella+sphere (L+S), five cylindrical structures in sectional view, perforated layer (PL), lamella + cylinder (L + C), columnar piled disk (CPD), and lamella in sphere (L-in-S). Reprinted from Gemma, T. Hatano, A. Dotera, T. MacromoleculesZOOZ, 35,3225. ...

Into a special category should be placed starburst dendrimer polymers. These molecules are formed by growing them in three dimensions. These materials often possess radially symmetrical star-shaped structures with successive cascades of branched polymer structures. For additional discussions see Chap. 6. 

For the calculation of the form factors of unperturbed central regions of the stars, one has to take into account that (1) the central-symmetrical unperturbed polymer density profile c(r)... 

In the case of star polymers (Scheme 2.28), these include symmetric, asymmetric, and miktoarm stars, which are prepared by reacting active chain ends with a core using the arm-first method or via the core-first method. Miktoarm stars have been reported using anionic, cationic, and ATRP methodologies and typically have AB o "... 

Table 10. Characterization of symmetrical, four-armed star polymers [203]...

In order to investigate the reliability and usefulness of this star-branched polymer synthesis, a series of symmetrical, four-armed star polymers was prepared using the procedure outlined in Scheme 34. The results of the analyses of these polymers are shown in Table 10. It is perhaps most noteworthy... 

In the above expression for the viscosity of entangled stars, we note that M/f is the molecular weight per arm of the star polymer, and this implies that the viscosity of symmetric stars with entangled branches depends only on the length of the branch and not the number of branches. It has been found that this holds for functionalities up to at least 33 [90], except for a modest deviation from the rule for /= 3. Thus, data for stars with various numbers of arms can be plotted versus M3 to form a master curve. The dependence of rjg on M3 is found to be approximately exponential, and theoretical arguments [91, 92] suggest a relationship of the following form ... 

The success of the slip link model for symmetric and asymmetric star polymers inspires its application to more complex architectures, such as H polymers. The mechanisms of relaxation and branch point motion were established in studies of symmetric and asymmetric star polymers, as were the parameters (Mf,, and Tg) that allow the simulations to be compared... 

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