Branch cells multiplicity

Where Nc = initiator core multiplicity Nb = branch cell multiplicity NcNbM = number of covalent bonds formed/step... 

It is apparent that both the core multiplicity (Nc) and branch cell multiplicity (Nh) determine the precise number of terminal groups (Z) and mass amplification as a function of generation (G). One may view those generation sequences as quantized polymerization events. The assembly of reactive monomers [48, 78], branch cells [48, 83, 89] or dendrons [85, 90] around atomic or molecular cores... 

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 ... 

Figure 1.21 Periodic properties for poly(amidoamine) (PAMAM) dendrimers as a function of generation G = 0-10 (I) flexible scaffolding (G = 0-3) (II) container properties (G = 4-6) and (III) rigid surface scaffolding (G = 7-10) various chemo/ physical dendrimer surfaces amplified according to Z = NCN where Nc = core multiplicity, Nb = branch cell multiplicity, G = generation...

Control and development of branch cell multiplicities (Nb) and core multiplicities (Ne). 

The stfucture of dendrimer depends on the core multiplicity (N ), the branch-cell multiplicity (N ), and the critical molecular design parameters (CMDPs) [30]. A typical branching structure is given below [31],... 

FIGURE 42.9. Mathematical expressions for calculating the theoretical number of surface groups (Z), branch cells (BC) and molecular weights (MW) as a function of generation, A/o = core multiplicities and A/b = branch cell multiplicity. 

Figure 3 Adendrimer series with core multiplicity (Nc = 3) and branch-cell multiplicity (Afc = 2) illustrating molecular shape changes, surface branch cells, surface Z-groups, and molecular weights as a function of generation.

Fig. 30 Congestion-induced dendrimer shape changes (/, //, III) with development of nanocontainer properties for a family of [core l,2-diaininoethane] (4 2) dendn-poly (amidoamine)-(NH2)z (G = 0-10) PAMAM dendiimers with core multiplicity = 4 and branch cell multiplicity A/b = 2. Distances between Z surface groups are shown as a fimction of generation [138]...

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