Hyperbranched structures, fractal

In this subsection we will consider (distinct from the dendrimers of Sect. 8) another class of regular hyperbranched polymers. We recall that the quest for simpUcity in the study of complex systems has led to fruitful ideas. In polymers such an idea is seating, as forcefully pointed out by de Gennes [4j. Now, the price to be paid in going from linear chains to star polymers [33,194[, dendrimers [13,33,194,205] and general hyperbranched structures [216[ is that scaling (at least in its classical form) is not expected to hold anymore (at least not in a simple form, which implies power-law dependences on the frequency CO or on the time f). One of the reasons for this is that while several material classes (such as the Rouse chains) are fractal, more general structures do not necessarily behave as fractals. 

Does Hyperbranched Structure Still Hold the Fractal Nature ... 

Keywords Macromolecules m Dendrimers m Fractal Structure m Hyperbranched Polymers m Nanostructure m Divergent Synthesis m Convergent Synthesis m Dendrylation... 

Keywords. Solution properties. Regularly branched structures. Randomly and hyperbranched polymers. Shrinking factors. Fractal dimensions. Osmotic modulus of semi-di-lute solutions. Molar mass distributions, SEC/MALLS/VISC chromatography... 

Our review starts with the general formulation of the GGS model in Sect. 2. In the framework of the GGS approach many dynamical quantities of experimental relevance can be expressed through analytical equations. Because of this, in Sect. 3 we outline the derivation of such expressions for the dynamical shear modulus and the viscosity, for the relaxation modulus, for the dielectric susceptibility, and for the displacement of monomers under external forces. Section 4 provides a historical retrospective of the classical Rouse model, while emphasizing its successes and limitations. The next three sections are devoted to the dynamical properties of several classes of polymer networks, ranging from regular and fractal networks to network models which take into account structural heterogeneities encountered in real systems. Sections 8 and 9 discuss dendrimers, dendritic polymers, and hyperbranched polymers. 

Chain stiffness and the effects of excluded volume became the dominating issue in the years between 1980 and the start of the new millennium. Percolation simulations indicated strong effects on the unperturbed polymer conformations due to excluded volume interactions [4]. With specially synthesized model substances (prepared by the Burchard group), the transition from mean-field to highly perturbed conformation was explored [5-17]. Studies in 1996 [8] on randomly branched, and in 2004 on hyperbranched polymers [8, 18-20], showed that the fractal conception could be quantitatively adjusted to the scattering behavior of linear and branched structures over the whole (/-domain and offered valuable insight into the structure in space [16]. 

The fractionation of each resultant broadly distributed hyperbranched polystyrene sample by precipitation led to a set of perfect narrowly distributed hyperbranched polystyrene chains with uniform subchains but different overall molar masses. We have, for the first time, experimentally elucidated their formation kinetics and established scaUng laws between their size and overall mass. Armed with such prepared hyperbranched chains, we will be able to further study correlations between their microscopic structures and macroscopic properties. In this section, we wiU focus on the formation kinetics section, and the fractal properties of these perfect hyperbranched polystyrenes will be discussed in the next chapter. 

As mentioned in Chap. 1, randomly hyperbranched chains are even more complicated than dendrimers. It has not been completely clear whether they are fractal objects [11, 12] and whether those previously reported M-dependent intrinsic viscosities from an on-line combination of the size exclusion chromatograph (SEC) with viscosity and multi-angle laser light scattering (MALLS) detectors actually captured its structure-property relationship [11, 13]. In the next section, we ll discuss our experimental results in detail. 

Previous results of hyperbranched polystyrene homopolymers showed that the hyperbranched homopolymer chains keep the fractal structure [60] namely, their size (R) and intrinsic viscosity ([ ]) in tolnene are scaled to their overall weight average molar masses (Mw) and the weight average subchain molar mass as R with Y = 0.47 0.01 and = 0.10 0.01 and [tj] ... 

Successfully prepared Seesaw-type diblock macromonomer (Na-PS- -PCL-N3) and model hyperbranched hetero-subchain copolymer [HB-(PS-f>-PCL)n] with controllable and uniform PS and PCL subchains, and found that such prepared hyperbranched copolymer chains still have a fractal-like structure, and the PCL subchains inside HB-(PS-f>-PCL)n crystallize less as the branching degree increases and the PS subchain becomes longer. This work demonstrates that we can use the chain topology to control the crystallization of PCL subchains inside hyperbranched copolymers to regulate their biodegradation for biomedical applications. 

Dendritic macromolecules are hyperbranched fractal-like structures that emanate from a central core and contain a large number of terminal groups. Two synthetic approaches have been reported for the preparation of these macromolecules the divergent [76-78] and convergent growth approaches [79-82]. In both methods many synthetic steps are necessary to produce high molecular weight materials. To avoid synthetic problems, the macromonomer with hyperbranched dendritic moiety may be one of the most useftil materials for the dendritic macromolecules. 

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