Star-shaped branched molecules

Discriminating branched and star polymers from linear ones can always be achieved by measuring the properties in dilute solution. In fact, molecules having the same molar mass but different macromolecular architectures exhibit different transport and light scattering properties. More specifically, a branched macromolecule is more compact than a linear molecule having the same molar mass, and therefore it will display less friction and will diffuse more easily in the solvent. Viscometry can be used to detect branched structures, since the Mark-Houwink-Sakurada exponent (Eq. 2.23) for branched and star-shaped polymers is lower tiian that for the corresponding linear chain. Unfortunately, in order to measure the difference, one must have a sample made exclusively... 

When only one type of repeat unit is found in a polymer chain it is described as a homopolymer. This illustration uses 25 units in every case so that the degree of polymerization (i.e. number of repeat units in the polymer) is the same for each. As can be seen, polymers may be linear, branched, ring- or star-shaped. The length of branches may be the same or different in the branched and star-shaped molecules. 

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. 

Moreover, star shaped polymers, which have p branches of known length connected by one of their ends to a central nodule are also of interest. The size of the nodule should be kept small with respect to the whole star molecule. The methods developed to synthesize these tailor made polymers have been reviewed recently. ... 

The main topic of interest is the properties of molecules of finite size, having no large rings, and in general having trifunctional branch-points. These are typically produced by chain-transfer with polymer in free-radical polymerizations, though they can of course be made in other ways. Molecules with branch-points of higher functionality are also of interest, especially star-shaped molecules with several arms, as these are both easy to synthesize and relatively easy to discuss theoretically. 

Chompff,A.J. Normal modes of branched polymers. I. Simple ring and star-shaped molecules. J. Chem. Phys. 53,1566-1576 (1970). 

In this model, derived originally for star-shaped branched molecules, polymer molecules are represented by beads connected by identical Hookean springs, and the decrease in viscosity with branching is expressed by the g1/2 rule. 

Cationic star-shaped molecules containing cyclopentadienyliron complexes, where the organo-metallic cations are evenly distributed throughout the molecule branches, 250, have been reported (Scheme 2.67).295 296 291 Electrochemical studies of these materials indicated that the iron centers underwent reversible reductions. For the hexametallic star-shaped molecule (n = 1), two redox potentials were observed at KU2 = I -20 and —1.30 V. 

A number of research groups have reported the preparation of a large number of star-shaped molecules and dendrimers containing ferrocenyl or arene cyclopentadienyliron complexes at the core or the peripheries.300-320 A number of these dendrimers were prepared via cyclopentadienyliron-mediated per-alkylation, -benzylation and -allylation reactions of cationic tri-, tetra- and hexamethylbenzene complexes. These dendrimers were multifunctional materials and have been used in the synthesis of branched organic and organometallic polymers. 

Zimm and Kilb have investigated theoretical formulas for the limiting viscosity number of various model, branched molecules in dilute solution. For star-shaped molecules, it was found that the ratio Mbr/Mnn varies approximately as the square root of the ratio of the mean square radii of gyration. Zimm and Kilb then postulated that branched macromolecules, of any shape, will obey this relation to a degree of approximation sufficiently good for practical purposes thus... 

Star-shaped branching radiates out from a single branch point. Combshaped molecules, on the other hand, contain branches of generally equal length joined more or less equidistantly along the main chain (see Figure 2-4). 

Branched macromolecules have a higher average segment density than unbranched macromolecules of the same molar mass, and have a lower coil volume. This is easily seen by comparing a star-shaped branched molecule with a linear one. The influence of the branching on the dimensions can be expressed by a g factor... 

An alternative to a linear polymer is a branched one. The branches can be long or short. Low-density polyethylene, for instance, can have both short and long branches. Linear and branched molecules are illustrated in Fig. 1.1a and b. Branched polymers can also be star or comb shaped (Fig. 1.1c and d). In addition to the above, polymer molecules can also be double stranded. Such polymers are called ladder polymers (Fig. 1. le). It is also possible for polymers to have semiladder structures (Fig. l.lf). 

FIGURE 1.1. Shapes of polymeric molecules, (a) linear polymer, (b) branched polymer, (c) star>shaped polymer, (d) comb-shaped polymer, (e) ladder polymei (f) semiladder polymer, and (g) network structure. 

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. 

Figure 1.2 The homopolymers illustrated are (a) linear molecule, (b) branched molecule where the branch chains are short, (c) large cyclic molecule, (d) a star-shaped molecule with arms of different size. All the molecules illustrated have the same degree of polymerization (25 repeat...

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