becomes increasingly smaller and experimentally approaches the cross-sectional
area or van der Waals dimension of the surface groups Z. The generation G thus
reached is referred to as the “de Gennes dense-packed generation” [9, 26, 55]. Ideal
dendritic growth without branch defects is possible only for those generations
preceding this dense-packed state. This critical dendrimer property gives rise to
self-limiting dendrimer dimensions, which are a function of the branch cell segment
length (l), the core multiplicity N c , the branch cell juncture multiplicity N b , and the
steric dimensions of the terminal group Z (Fig. 10). Whereas the dendrimer radius
r in the above expression is dependent on the branch cell segment lengths l, large
l values delay this congestion. On the other hand, larger N c and N b values and larger
Z dimensions dramatically hasten it.
Additional physical evidence supporting the development of congestion as a
function of generation is shown in the composite comparison of dendrimer nanoperiodic property patterns as illustrated in Sect. 6.5.2. Plots of intrinsic viscosity
[η] [9, 113], density z, surface area per Z group (A z ), and refractive index n as a
function of generation clearly show maxima or minima at G ¼ 3–5, paralleling
computer-assisted molecular-simulation predictions [84, 114], as well as extensive
photochemical probe experiments reported by Turro and coworkers [105–108].
Clearly, this de Gennes dense-packed congestion would be expected to contribute to (1) sterically inhibited reaction rates and (2) sterically-induced stoichiometry [9]. Each of these effects was observed experimentally at higher
generations. The latter would be expected to induce dendrimer mass defects at
higher generations, which we have used as a diagnostic signature for appraising the
de Gennes dense packing effect.
Theoretical dendrimer mass values were compared to experimental values by
performing electrospray and MALDI-TOF mass spectrometry analysis on the
respective PAMAM families (i.e., N c ¼ 3 and 4) [88]. Note that there is essentially
complete shell filling for the first five generations of the NH 3 -core PAMAM series
(N c ¼ 3, N b ¼ 2) (Fig. 13b). A gradual digression from theoretical masses occurs
for G ¼ 5–8, followed by a substantial break (i.e., Δ ¼ 23%) between G ¼ 8 and
9. This discontinuity in shell saturation is interpreted as a signature for de Gennes
dense packing. It should be noted that shell saturation values continue to decline
monotonically beyond this breakpoint to a value of 35.7% of theoretical at G ¼ 12.
A similar trend is noted for the ethylenediamine-core PAMAM series (N c ¼ 4,
N b ¼ 2); however, the shell saturation inflection point occurs at least one generation earlier (i.e., G ¼ 4–7, see Fig. 13a). This suggests that the onset of de Gennes
dense packing may be occurring between G ¼ 7 and 8. Recent work by Halperin,
Schluter and coworkers [111] describes a simple yet elegant strategy for detecting
the onset of de Gennes dense packing by UV labeling dendrimer surfaces with the
Sanger reagent, as a function of generation, and monitoring signal regression as an
indication of congestion and dense packing. This protocol provides a photolabeling
technique that corroborates mass spectrometry data, as shown in Fig. 13.
Unique features offered by the “dendritic state” that have no equivalency in
classical polymer topologies are found almost exclusively in the dendron/
dendrimer subset and to a slightly lesser degree in the dendrigrafts. They include:
Twenty-First Century Polymer Science After Staudinger: The Emergence of. . .
347
area or van der Waals dimension of the surface groups Z. The generation G thus
reached is referred to as the “de Gennes dense-packed generation” [9, 26, 55]. Ideal
dendritic growth without branch defects is possible only for those generations
preceding this dense-packed state. This critical dendrimer property gives rise to
self-limiting dendrimer dimensions, which are a function of the branch cell segment
length (l), the core multiplicity N c , the branch cell juncture multiplicity N b , and the
steric dimensions of the terminal group Z (Fig. 10). Whereas the dendrimer radius
r in the above expression is dependent on the branch cell segment lengths l, large
l values delay this congestion. On the other hand, larger N c and N b values and larger
Z dimensions dramatically hasten it.
Additional physical evidence supporting the development of congestion as a
function of generation is shown in the composite comparison of dendrimer nanoperiodic property patterns as illustrated in Sect. 6.5.2. Plots of intrinsic viscosity
[η] [9, 113], density z, surface area per Z group (A z ), and refractive index n as a
function of generation clearly show maxima or minima at G ¼ 3–5, paralleling
computer-assisted molecular-simulation predictions [84, 114], as well as extensive
photochemical probe experiments reported by Turro and coworkers [105–108].
Clearly, this de Gennes dense-packed congestion would be expected to contribute to (1) sterically inhibited reaction rates and (2) sterically-induced stoichiometry [9]. Each of these effects was observed experimentally at higher
generations. The latter would be expected to induce dendrimer mass defects at
higher generations, which we have used as a diagnostic signature for appraising the
de Gennes dense packing effect.
Theoretical dendrimer mass values were compared to experimental values by
performing electrospray and MALDI-TOF mass spectrometry analysis on the
respective PAMAM families (i.e., N c ¼ 3 and 4) [88]. Note that there is essentially
complete shell filling for the first five generations of the NH 3 -core PAMAM series
(N c ¼ 3, N b ¼ 2) (Fig. 13b). A gradual digression from theoretical masses occurs
for G ¼ 5–8, followed by a substantial break (i.e., Δ ¼ 23%) between G ¼ 8 and
9. This discontinuity in shell saturation is interpreted as a signature for de Gennes
dense packing. It should be noted that shell saturation values continue to decline
monotonically beyond this breakpoint to a value of 35.7% of theoretical at G ¼ 12.
A similar trend is noted for the ethylenediamine-core PAMAM series (N c ¼ 4,
N b ¼ 2); however, the shell saturation inflection point occurs at least one generation earlier (i.e., G ¼ 4–7, see Fig. 13a). This suggests that the onset of de Gennes
dense packing may be occurring between G ¼ 7 and 8. Recent work by Halperin,
Schluter and coworkers [111] describes a simple yet elegant strategy for detecting
the onset of de Gennes dense packing by UV labeling dendrimer surfaces with the
Sanger reagent, as a function of generation, and monitoring signal regression as an
indication of congestion and dense packing. This protocol provides a photolabeling
technique that corroborates mass spectrometry data, as shown in Fig. 13.
Unique features offered by the “dendritic state” that have no equivalency in
classical polymer topologies are found almost exclusively in the dendron/
dendrimer subset and to a slightly lesser degree in the dendrigrafts. They include:
Twenty-First Century Polymer Science After Staudinger: The Emergence of. . .
347