Starburst limit

The sequential growth and branching involved in the preparation of dendrimers had been considered by Flory many years before they were actually prepared. Flory developed a sound understanding of the kind of processes that would occur in the self-polymerization of a molecule of the type ABj most of which have been shown to be correct by the relatively recent experimental studies. In particular, the existence of a limit to growth was predicted. This limit has become known as the starburst limit, and is the reason for the highly monodisperse nature of fully developed dendrimers. 

Fig. 1.19 Attainment of the limiting generation in dendrimer growth as a result of the starburst limit effect (schematic idealised)...

As early as 1983, de Gennes and Hervet [85] proposed a simple equation derived from fundamental principles, to predict the Starburst limited or dense-packed generation mt for PAM AM dendrimers. Based on ideal dendrimer growth, with tertiary amine branch junctures connected by linear, flexible branch cell segments P, this equation relates m, to the branch cell segment length 1 or P ... 

The starburst point occurs at a well-defined limit for each dendrimer system, and its occurrence is dependent mainly on (a) the functionality of the core, (b) the multiplicity of the branches and (c) the branch length. However, the volume of the core itself, and the length of the monomer branches also have an influence. The end groups may occupy the outer surface of the dendrimer, or the branches may fold inwards, thus distributing the end-groups within the dendrimer. The factors that control this behaviour of the branches are not fully understood, but include the nature of the solvent and the detailed chemistry of the dendrimer branches. 

De Gennes (Nobel prize in Physics, 1991) and Hervet 51] published a statistical treatment of starburst dendrimers. They concluded from a mathematical growth model that steric hindrance limiting continued tier addition was dictated by the length of the spacer units that connect the branching centers. This reinforced the dense packing concept. 

In this fashion, it is possible to control the critical molecular design parameters (CMDPs, i.e., size, shape, topology, flexibility, and surface chemistry) and grow predictable, stoichiometric structures up to a self-limited dimension (generation) which is determined by Nc and Nb as well as by the dimensions of the structural components. Such space-filling, terminally functionalized molecular organizations have been coined Starburst dendrimers [2]. Two dimensional projections of such molecular morphogenesis [1] are as illustrated in Fig. 2. 

Dendrimers (sometimes called arbor, cascade, or starburst molecules) share some characteristics with polymers but also manifest critical differences. Whereas linear polymers like polystyrene are polydisperse (have a range of molecular weights and character), dendrimers, synthesized in a stepwise manner, are monodisperse (have uniform molecular mass). Unlike polymers, their growth becomes at some stage self-limiting as the molecule folds into itself. Unlike linear polymers, which present countless rapidly interconverting shapes, dendrimers are nearly spherical in shape with diameters typically between 2 and 10 nm. 

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