De Gennes’ “dense-packing

As a consequence of the excluded volume associated with the core, interior and surface branch cells, steric congestion is expected to occur due to tethered connectivity to the core. Furthermore, the number of dendrimer surface groups, Z, amplifies with each subsequent generation (G). This occurs according to geometric branching laws, which are related to core multiplicity (iVc) and branch cell multiplicity (iVb). These values are defined by the following equation  

Since the radii of the dendrimers increase in a linear manner as a function of G, whereas the surface cells amplify according to NCN°, it is implicit from this equation that generational reiteration of branch cells ultimately will lead to a so-called dense-packed state. 

Dendrimer surface congestion can be appraised mathematically as a function of generation, from the following simple relationship  

The dendrimer density z (atomic mass units per unit volume) clearly minimizes 

The affect of architecture on small molecular properties has been recognized since the historical Berzelius (1832) discovery that defined the following premise substances of identical compositions but different architectures - skeletal isomers - will differ in one or more properties [15]. These effects are very apparent when comparing the fuel combustion benefits of certain isomeric octanes or the dramatic property differences observed in the three architectural isomers of carbon namely graphite, diamond and buckminsterfullerene. 

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May be used to prepared high generation (i.e. G = 0-12) dendrimers that precede and exceed the de Gennes dense packed state. 

Molecular modeling techniques are a powerful tool to obtain 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 polypropylene imine) dendrimers and radial density profiles in order to estimate the free volume inside the dendrimers, as well as to make predictions about de Gennes dense-packed generations. The molecular modeling work by Coussens and co-workers [20] was focused on the generations 1-5 of the DAB-dendr-(CN)n and DAB-dendr-(NH2)n (n = 4, 8, 16,32, 64). 

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

Dendrimer Structure Ideality — A Signature for Self-Assembly and for de Gennes Dense Packing ... 

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