Branch cells

Figure 1.6 Examples of (a) branch cell, (b) dendritic assembly of branch cells and (c) crosslinked nano-networks derived from branch cells...

A comparison of the covalent connectivity associated with each of these architecture classes (Figure 1.7) reveals that the number of covalent bonds formed per step for linear and branched topology is a multiple (n = degree of polymerization) related to the monomer/initiator ratios. In contrast, ideal dendritic (Class IV) propagation involves the formation of an exponential number of covalent bonds per reaction step (also termed G = generation), as well as amplification of both mass (i.e. number of branch cells/G) and terminal groups, (Z) per generation (G). 

III.) BRANCHED Thermoplastic Divalent Branch Cell Monomers V 0 "AiQrr 0 Z J n... 

IV.) DENDRITIC Thermoplastic Polyvalent Branch Cell Monomers ( l) Z /vZ ( L)... 

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

Figure 1.8 Branch cell structural parameters (a) branching angles, (b) rotation angles, (/) repeat units lengths, (Z) terminal groups and dendritic subclasses derived from branches (IVa) random hyperbranched, (IVb) dendrigrafts and (IVc) dendrons/dendrimers...

New advances beyond the traditional AB2 Flory-type branch cell monomers have been reported by Frechet et al [65, 66]. They have introduced the concept... 

In contrast to traditional polymers, dendrimers are unique core-shell structures possessing three basic architectural components namely, (I) a core, (II) an interior of shells (,generation) consisting of repetitive branch cell units and (III) terminal functional groups (i.e. the outer shell or periphery) as illustrated in Figures 1.13 and 1.14. 

Cores Monomers Branch Cells Dendrons Dendrimers... 

Figure 1.13 Overview of synthetic strategies for (a) branch cell construction, (b) dendron construction and (c) dendrimer construction annotated with discovery scientists...

PAMAM dendrimers are synthesized by the divergent approach. This methodology involves the in situ branch cell construction in stepwise, iterative stages (i.e. generation = 1, 2, 3. ..) around a desired core to produce mathemat-... 

This first reaction sequence on the exposed dendron (Figure 1.14) creates G = 0 (i.e. the core branch cell), wherein the number of arms (i.e. dendrons) anchored to the core is determined by Nc. Iteration of the alkylation/amidation sequence produces an amplification of terminal groups from 1 to 2 with the in situ creation of a branch cell at the anchoring site of the dendron that constitutes G = 1. Repeating these iterative sequences (Scheme 3), produces additional shells (generations) of branch cells that amplify mass and terminal groups according to the mathematical expressions described in the box opposite. 

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... 

Figure 1.15 Comparison of molecular shape change, two-dimensional branch cell amplification surface branch cells, surface groups (Z) and molecular weights as function of generation G= 0-6...

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. 

Important physical property subtleties were noted within the dendrimer subset. For example, dendrimers possessing asymmetrical branch cells (i.e. Den-kewalter type) exhibit a constant density versus generation relationship (Figure 1.20). This is in sharp contrast to symmetrical branch cell dendrimers (Tomalia-type PAMAM) that exhibit a minimum in density between G = 4 and G = 7 (NH3 core) [48, 96]. This is a transition pattern that is consistent with the observed development of container properties described in Figure 1.21. 

Tomalia (PAMAM) (symmetrical) branch cell dendrimers... 

Figure 1.20 Comparison of densities as a function of generation for (A) asymmetrical branch cell in DenkewaIter-type dendrimers, (B) symmetrical branch cell in Tomalia-type dendrimers ([densities calculated from experimental hydrodynamic diameters and theoretical, D.A. Tomalia, M. Hall, D.M. Hedstrand, J. Am. Chem. Soc., 109,1601 (1987))...

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...

The precise structure subset, dendrimers are prepared using iterative protection-condensation-deprotection reaction cycles. These reiterative cycles incorporate ABn monomers (i.e. branch cell units) into structural domains referred to as dendrons. Assembly of these dendrons can proceed in a divergent [1] (core... 

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