Hyperbranched chain

Buchard outlined some properties of hyperbranched chains. The dilute solution properties of branched macromolecules are governed by the higher segment density found with linear chains. The dimensions appear to be shmnk when compared with linear chains of the same... 

Most of the thermodynamic studies reported in literature deal with molecules of a molar mass < 100. Even polymer thermodynamics at present fails to adequately deal with simple molecules like hyperbranched chains, star-shaped macromolecules or with sequence length (distribution) and the resulting morphology in blocky co- and terpolymers. Commercialization of nanostructure-based materials most probably will take place without essential contributions from thermodynamics scientists. One may hope that these polymer thermodynamic scientists will soon get more interested in such molecules and thus become able to achieve major advances in this area and contribute to the next step, the optimization of the production processes for such nanomolecules, via supercritical separations or - modifications and high pressure processing steps. 

L. Li, Studies on Perfect Hyperbranched Chains Free in Solution and Confined in a Cylindrical Pore, Springer Theses, DOI 10.1007/978-3-3t9-06097-2 l,... 

Fig. 1.1 Schematic illustration of a perfect hyperbranched chain, where A, B, C, D, E. and F represent different branching points, and represents the degree of polymerization between neighboring branching points...

Fig. 1.3 Comparison of topological structures of a randomly branched chain and a hyperbranched chain prepared by using different types of macromonomers...

As for step-growth-based polymerization methods. Fig. 1.3 shows two typical approaches in the preparation of hyperbranched chains (A) co-polycondensation [49-56] and (B) self-polycondensation [1, 23, 30-32, 40-48]. The co-polycondensation... 

However, whether such classical mass-size scaling law is valid or not for perfect hyperbranched chains, and how the subchain length and branching degree of hyperbranched chains affect such a mass-size scaling law are still uncertain. Note... 

Investigate on the deformation property of perfect hyperbranched chains more specifically, using our developed ultrafiltration technique to explore how the branching effect affects the critical flow which hyperbranched chains need to crawl through a cylindrical nanopore. 

It should be emphasized that such formed chains are different from dendrimers. Previously, Hedrick et al. [8, 9] used this approach to synthesize hyperbranched chains, starting with short B A B oligomers containing 5-20 monomer units. Their resultant hyperbranched polymers are too small to be accurately characterized by laser light scattering (LLS), presumably because they used a relatively lower efficient esterification. 

Fig. 3.15 Schematic illustration of the topological structures of disulfide-functionalized hyperbranched chains prepared by two different approaches a Homo-polymerization of tel-echelic precursors with thiol end groups, and b Co-polymerization of disulfide-functionalized...

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. 

Figure 4.5 shows that the polydispersity index (Mw/Afn) (determined by MALLS detector) increases with the reaction time. It is known that in the selfpolycondensation process, hyperbranched chains with more azide groups are ready to react with macromonomers but more difficult to react with each other because there is only one hiding A group inside each hyperbranched chain. However, the coupling between two hyperbranched chains in the later stage of reaction makes Mw to increase much fast than Ma. This is why M IMa quickly raises to 5.8-7.7. 

Figure 4.6 shows the rafio of (L>7 )w,SEC-MAiis/(T>F)w,sEC-Ri of hyperbranched polystyrenes rapidly inaeases to 3.1 (PS-7.6K), 2.3 (PS-18.7K) and 2.1 (PS-45K), respectively, with the reaction time. The deviation of (7)P)w,sec-maij.s away from (DF)w,sec-ri clearly shows that SEC with the conventional universal polystyrene calibration leads to a much under-estimated molar mass for huge hyperbranched chains. Therefore, it should be avoided in the study of branched chains because they have a much smaller hydrodynantic volume than their linear counterparts with a similar molar mass, hi other words (7>7 )w,SEC-MALLs/(flF)w,sEC-Ri reflects the hydrodynamic volume difference between hyperbranched and linear chains namely (DP)w,sec-malls/( >F)w,sec-ri increases with the compacmess of hyperbranched chains. 

Fractal Property of Perfect Hyperbranched Chains Scaling Laws of Sizes and Intrinsic Viscosities... 

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. 

The effect of branching is even better displayed in the Kratky plot namely (qR P(qR versus qR, as shown in Fig. 5.4. Theoretically, Burchard [18] deduced the scattering factor for AB2-type hyperbranched chains as... 

In contrast, all the hyperbranched polystyrenes used in the current study were fractionated by precipitation, i.e., according to the interaction parameter xM, where M is the overall molar mass of the chain and x is the Flory-Huggins parameter, a constant, independent on M for a polymer in a given solvent. Therefore, hyperbranched chains in each fraction used here have a similar molar mass. In comparison with our results, some of previous computer simulations [27, 28] suggested that the molar mass dependence of intrinsic viscosity of irregular hyperbranched chains deviates from Eq. 5.2 because the segment density distribution is different from those predicted by de Gennes and Hervet. We will come back to this point later. 

When treating each hyperbranched chain as a suspending hard sphere and taking (P = 2.5 [1], we can rewrite Eq. 5.1 as... 

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