Star Molecules

The number of branches of star molecules made this way cannot be precisely predicted. Accurate molecular weight measurements are necessary to determine the average... 

Star molecules containing branches made of two blocks have also been prepared by these methods102 103. Recently it was shown that such star-block copolymers exhibit very interesting so-called double-diamond structures in the bulk owing to segregation due to incompatibility between chemically unlike blocks 104. ... 

The theoretical approach described before dealt with the short-time dynamic response of the star molecules. However, in the case of completely labelled stars [148] it was found that the line shape of the Zimm model provides a good description of the NSE spectra not only in the short-time regime (t < 5 ns), but also on longer time scales. 

More recently Frechet and Gitsov [130] used a similar approach as above and synthesized a novel series of dendritic copolymers derived from a central penta-erythritol core unit. These hybrid star molecules behaved as unimolecular micelles with different core-shell conformational-structures as a response to the polarity of the solvent used. 

Astruc et al. [187] reported a nonairon sandwich complex by treating a nona-ol with [C5H5]Fe(q6-p-MeC6H4F)(PF6). In a subsequent report [188], Astruc and Marvaud reported the synthesis of aromatic star molecules with or without a central Fe(/f-C5H5)+ group. These bipyridine and terpyridine terminated dendrimers were further capped with [Ru(bipy)2Cl2] and [Ru(terpy)Cl3], respectively, to afford the corresponding hexa or hepta nuclear complexes. 

The living ALi chains polymerize a small amount of DVB leading to the formation of a star molecule bearing within its core (microgel nodule of DVB) a number of active sites, which is theoretically equal to the number of incorporated A arms. Subsequent addition of monomer B yields the /z-star copolymer. 

Dendrimers are nearly spherical in shape when compared to conventional linear polymers [ 17,34], The lower generation dendrimers have internal segment density distributions similar to star molecules, but even the smallest are more compact than stars. As the generation number increases, the sphere-like characteristics increase and the largest dendrimers form a population of spheres with uniform internal density (roughly half dendrimer units-half solvent) [47], sharp interfaces on the outside and a small polydispersity in shape. 

In this model the linear chains become the rays of a star molecule. The rays, consisting of m repeating units, can be considered stiff rods, but in most cases they will be flexible and can be described in a first approximation by Gaussian chain statistics. A star molecule has only one branching unit among/xm units which belong to Hnear chains. Their properties can be expected to show a close... 

Again, this structure resembles very much a linear chain, when the side chains are much shorter than the backbone. The other limit is that of a short backbone and long side chains grafted on the backbone in the densest way. This structure will approach the behavior of star molecules. It should be mentioned that a realization of complete regularity will scarcely be possible. It is almost im-... 

Fig. 2. Two limiting cases of a regular comb molecule. The flexible chain sections between two branching points may consist of m monomer units while the/flexible side chains have a length of n monomer units. The one structure (short side chains) resembles a substituted linear chain, the second one (short backbone) has similarity to star molecules...

Schaefgen and Flory [79] were the first to observe this effect. They prepared star-branched polyamides by co-condensation of A-B types of monomers with central units which carried/-functional A groups. By this technique star molecules were obtained in which the arms are not monodisperse in length. They rather obeyed the Schulz-Flory most probable length distribution with polydis-persity index However, the coupling of f arms onto a star center leads... 

Fig. 14. Dependence of the interpenetration function R on the number of arms in star molecules. The full line represents the result of the renormalization group theory [90], the data points refer to measurements [77]. Reprinted with permission from [77]. Copyright [1983] American Society...

The other extreme to star molecules are the randomly branched macromolecules. Here the branching process has an immense influence on the shape of the distribution. It was first derived by Stockmayer [ 14] and later reproduced byFlo-ry [13]. The exact and asymptotic distributions are given by the following two equations ... 

Fig. 23. The intrinsic viscosity of several end-linked PS star molecules as a function ofM [95]. In the limit of low and high molar masses asymptotic power law behavior may be derived. That at low molar masses is widely controlled by the presence of non-reacted star molecules, that at high molar masses is expected from theory for randomly branched macromolecules. The exponents of the two asymptotic lines are a =0.49 0.08 for M <0.8x10 g/mol and a =0.18 0.05 for M >2.0xl0 g/mol. Reprinted with permission from [95]. Copyright [1997] American Society...

Figure 22 shows the results of the fractions from end-linked 3-arm star molecules in comparison to linear polystyrenes in the same solvent and Fig. 23 gives the result of [i]] as a function of... 

Such behavior has not been observed. Kurata et al. [ 129] developed an empirically based suggestion after comparing the results available in those days for star molecules. He also assumes power law correlation between the two contraction factors as given by... 

Table 3. Experimentally determined contraction factors g = Rgi,IRgu and various star molecules in 0-and good solvents ...

In the meantime the precision in preparing well defined star molecules and measuring g and g have been significantly improved. Table 3 gives a hst of the data from the literature, and Fig. 25 demonstrates this dependence. Evidently the experimental data cannot be described by a power law. A possible fit curve is given by the equation [110]... 

Fig. 28. The ratio A2M [rj] at large for star molecules (symbols) and randomly branched structures [25,26,108,130,131]. The shaded area indicates the range of the experimental findings with randomly and hyperbranched samples [144]. The line was drawn to guide the eye...

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. ... 

Star-shaped macromolecules have also been synthesized by using the monofunctional "living" precursor as an Initiator for the polymerization of a small amount of a divinyl monomer. A small crosslinked nodule is formed, which is connected with the p chains that have contributed to Its Initiation. It turns out that fluctuations on the value of p within a sample remain rather small, and consequently the star polymers obtained by this method can also be considered as tailor-made polymers. Recently star molecules with deuterium labeled central nodule have been synthesized according to the... 

In these eqs. index 2 stands for two branches, i.e. for the linear molecule. is the mean square radius of gyration which is equal to < h2 >/6 for linear chains of sufficient length. As an example, the values for a star molecule of four equal branches are quoted. One obtains for the free-draining case ... 

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