Hyperbranched molecule

AB2 reacts selectively with only one antagonist function of a second polyfunctional molecule, the other ones being protected81 (Fig. 5.16). The perfect hyperbranched molecules obtained according to that step-by-step process are called dendrimers. The degree of branching characterizes the structure of a hyperbranched polymer and has been defined by Hawker et al.82 as... 

In the ideal case, all reactive groups have the same reactivity irrespective of the shape and size of the hyperbranched molecules and no rings are formed. Then, the distribution of units in different reaction states is expressed by the following probability generating function (pgf), F0n(Z, z) ... 

Dendrigraft molecules are star-like in the Oth generation, but have a uniform interior with an exterior transition zone for G3 [17,34], Random hyperbranched molecules have broad distributions both in molecular mass and in shape [17], Scattering from hyperbranched is closer to that of linear polymers than to spheres, indicating that there is a gradually tapering distribution on units from the center to the exterior. 

We are currently investigating the synthesis and characterization of such molecules for numerous different applications such as surfactants, cosmetics, and toner resins. A point of interest in the preparation and characterization of multifunctional hyperbranched molecules is the compositional heterogeneity (how many and what type of functional groups are on a particular hyperbranched po-lyesteramide molecule) and the positional heterogeneity (spatial distribution of the functional groups on a particular hyperbranched polyesteramide molecule). 

As the hyperbranched polyesteramide resins are characterized by high poly-dispersity the distribution of the functional groups might vary greatly from one hyperbranched molecule to the other, even in that one particular molecule carries only one type of functional groups. 

The magnitude of a must always be less than ae, becausepA< 1. Thus gelation cannot occur. At high degrees of conversion, very large hyperbranched molecules may be produced, but not a network. 

Figure 1. Schematics of Boltorn hyperbranched aliphatic esters. Insert shows the network formed by covalent linking of hyperbranched molecules with diisocyanate.

Frechet, M. J. Hawker, C. J. (1996) Synthesis and properties of dendrimers and hyperbranched molecules, in AUen, G. (Ed.) Comprehensive Polymer Science, Oxford Pergamon. 

Amylopectin is responsible for the crystalline character of the starch granule and its structure can be modelled as a hyperbranched molecule [10,11, 28,29]. The model for the amylopectin molecule proposed by Robin [14] is illustrated in Figure 4.1(c). The A-chains, which are short segments of 15 D-glucopyranosyl residues, are the portion responsible for the crystalline structure of amylopectin. Starch crystallites are thus formed by compact areas made up of A-chains with DP 15. The crystallinity index of regular corn starch with 73% amylose is equivalent to that of waxy maize starch which is 100% amylose this confirms that amylose content has little effect on granule crystallinity. Starch crystallites formed in compact areas are made up of vicinal A-chains in a compact double helix conformation with two extended helices possessing 6 residues per turn that repeat every 21 A [1]. 

Hyperbranched molecules can be prepared using condensation polymerization methods and ABj-type molecules typified by the hydroxydiacids. However, a self-condensing nnimolecular initiator, such as... 

Amylopectin is a highly branched molecule which is responsible for the main crystalline charactCT of the starch granule. Its structure was modelled as a hyperbranched molecule [17, 51, 52], as proposed initially by Nikuni [53] and French [16] and later improved by Robin [37] (Fig. 15.4). In this model, short chains with 15 D-glucopyranosyl units branch out at almost regular intervals of 25 units to form either external A-chains or internal chains of amylopectin [37]. Starch crystallites are thus formed in compact areas made up of A-chains with DP 15. Less compact areas mainly occupied by B-chains, where the (l,6)-a-D-branching points are located, are placed between these compact areas. 

In addition to porphyrins, phthalocya-nines have been placed in the middle of hyperbranched molecules. Cobalt phthalo-cyanines with dendritic branches have been synthesized, and the analysis of their electrochemical behavior suggests that electron transfer between the phthalocya-nine core and an electrode is considerably hindered by the dendritic structure [51]. Dendrimers with phthalocyanine cores and electroactive tetrathiafulvalene (TTF) branches have also been synthesized and examined [52]. 

Figure 3 The chemical structure of a hyperbranched molecule. The dendritic molecular structure contains a core (I), the bulk (II) and the shell (III).

Keywords linear elastic fracture mechanics, critical strain energy release rate, precipitating elastomers, hyperbranched molecules, preformed rubber particles, core-shell latex particles, treated rubber, precipitating thermoplastic particles, preformed thermoplastic particles, crack bridging, shear banding, cavitation. 

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