Starburst dense packing

Molecular modelling techniques are a powerfiil tool for obtaining a very detailed insight in the three-dimensional structure of dendrimer molecules at the atomic level. They have been applied to calculate sizes of the poly(propylene imine) dendrimers and radial density profiles in order to estimate the amount of free volume inside the dendrimers, and to make a prediction about the starburst-dense packed generation. The molecular modelling work by Coussens et al. [33,34] was focussed on the generations 1-5 of the DAR-dendr- CH) and DAB-c(e c(r-(NH2) (n = 4, 8, 16, 32, 64). 

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. 

Starburst (de Gennes) Dense Packing — A Critical Branched... 

Starburst/cascade dendrimer dense-packing critical branching state, nanoscopic steric effects. 

CPK models of generations 0-5 (Fig. 27) show that these SPEIs are much more congested and compact than the Starburst PAMAMs. These models indicate that ideally branched generation 5 is forbidden due to dense packing as described and predicted by be Gennes and others [81, 82, 85, 86]. 

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 SEC partition coefficient [6] (.K sec) was measured on a Superose 6 column for three sets of well-characterized symmetrical solutes the compact, densely branched nonionic polysaccharide, Ficoll the flexible chain nonionic polysaccharide, pullulan and compact, anionic synthetic polymers, carboxylated starburst dendrimers. All three solutes display a congruent dependence of K ec on solute radius, R. In accord with a simple geometric model for SEC, all of these data conform to the same linear plot of i sEc versus R. This plot reveals the behavior of noninteracting spheres on this column. The mobile phase for the first two solutes was 0.2M NaH2P04-Na2HP04, pH 7.0. In order to ensure the suppression of electrostatic repulsive interactions between the dendrimer and the packing, the ionic strength was increased to 0.30M for that solute. 

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