Regular dendrimers

Cayley tree or Bethe lattice with functionality/ = 3. 

The number of monomers in generation g (the last generation) of the Tiendrimer is n f- 1) while the total number of monomers in the dendrimer (from the core to generation g) is 

The ratio of the number of monomers in the last generation of a very large dendrimer n f- 1) to the number of monomers in the rest of the dendrimer -1 is 

for f—3 approximately half of the monomers are in the last generation of the dendrimer For higher functionalities (/ 3), an even larger fraction of monomers are in the last generation of the dendrimer. 

The volume occupied by the polymer is v Ng, where vq is the monomer volume and the maximum accessible volume for a fully stretched dendrimer is (47r/3)(g/), where / is the monomer size. I he occupied volume cannot exceed the maximum accessible volume, leading to the maximum possible generation g iax for a perfect dendrimer  

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While it can be expected that a number of physical properties of hyperbranched and dendritic macromolecules will be similar, it should not be assumed that all properties found for dendrimers will apply to hyperbranched macromolecules. This difference has clearly been observed in a number of different areas. As would be expected for a material intermediate between dendrimers and linear polymers, the reactivity of the chain ends is lower for hyperbranched macromolecules than for dendrimers [125]. Dendritic macromolecules would therefore possess a clear advantage in processes, which require maximum chain end reactivity such as novel catalysts. A dramatic difference is also observed when the intrinsic viscosity behavior of hyperbranched macromolecules is compared with regular dendrimers. While dendrimers are found to be the only materials that do not obey the Mark-Houwink-Sakurada relationship, hyperbranched macromolecules are found to follow this relationship, albeit with extremely low a values when compared to linear and branched polymers [126]. 

As cheaper and readily accessible alternatives to regular dendrimers, hyper-branched polymers are increasingly being used as catalyst platforms. Rainer Haag has been one of the leaders in this field. He and C. Hajji provide an overview of an area for which commercial applications are most likely. Finally, all of these catalysis-related topics are complemented by a review of metallo-dendritic exoreceptors for the redox recognition of oxo-anions and halides, written by D. Astruc. This field offers new perspectives both for catalytic transformation and the development of molecular sensors. 

Use Flory theory to determine the end-to-end distance of a linear strand that runs from the core to any end at generation g of the regular dendrimer in Problem 6.9 with excluded volume v > 0 (in good solvent). 

AFM has also been used to study adsorbed dendrimers of increasing generation number. When this is done, it is found that there is a steady and regular rise in the diameters of the adsorbed dendrimers with each additional generation number, but that each generation of dendrimers remains highly homogeneous. 

The interest in hyperbranched polymers arises from the fact that they combine some features of dendrimers, for example, an increasing number of end groups and a compact structure in solution, with the ease of preparation of hn-ear polymers by means of a one-pot reaction. However, the polydispersities are usually high and their structures are less regular than those of dendrimers. Another important advantage is the extension of the concept of hyperbranched polymers towards vinyl monomers and chain growth processes, which opens unexpected possibilities. 

Metal-acetylide complexes including metal-poly(yne) polymers often show unique properties [21-23]. Thus, metal-acetylide dendrimers are of interest because amplification of the functionality due to metal-acetylide units based on three-dimensional assembly with a regular dendritic structure is expected. 

Transfer experiments of the Langmuir films onto solid substrates and the preparation of LB films were investigated for 43. The deposition of films of 43 occurred regularly on quartz sHdes or silicon wafers with a transfer ratio of 1 0.05. The diblock structure of dendrimer 43 also appeared crucial for efficient transfers of the Langmuir films in order to obtain well-ordered multilayered LB films. Effectively, the transfer of the Langmuir films of the dendrimer 42 with the small polar head group was found to be difficult with a transfer ratio of about... 

The architecture of macromolecules is another important synthetic variable. New materials with controlled branching sequences or stereoregularity provide tremendous opportunity for development. New polymerization catalysts and initiators for controlled free-radical polymerization are driving many new materials design, synthesis, and production capabilities. Combined with state-of-the-art characterization by probe microscopy, radiation scattering, and spectroscopy, the field of polymer science is poised for explosive development of novel and important materials. New classes of nonlinear structured polymeric materials have been invented, such as dendrimers. These structures have regularly spaced branch points beginning from a central point—like branches from a tree trunk. New struc-... 

Very recently, highly regular, highly controlled, dense branching has been developed. The resulting dendrimers often have a spherical shape with special interior and surface properties. The synthesis and properties of dendrimers has been reviewed (see e.g. G.R. Newkome et al. Dendritic Molecules , VCH, 1996). In this series, a chapter deals with the molecular dimensions of dendrimers and with dendrimer-polymer hybrids. One possible development of such materials may be in the fields of biochemistry and biomaterials. The less perfect hyper-branched polymers synthesized from A2B-type monomers offer a real hope for large scale commercialization. A review of the present status of research on hyperbranched polymers is included. 

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