## Shape And Size

(E)-stilbene and (E,E)-1,4-distyrylbenzene, the building blocks of the stilbenoid dendrimers, are planar molecules, but their activation barriers for torsions are low because the energy hypersurface is very flat around the planar minima [50, 51]. Thus, one could have the idea that planar cores with stilbenoid dendrons yield altogether planar compounds. However, this is only true for low generations. An X-ray crystal structure analysis of the first generation 1a (R1 = R2 = OC3H7) proved planar molecules, whose torsional angles in the stilbenoid skeleton are, at most, ±6°. The free or dissolved molecule has a D3h symmetry [20, 39]. In order to imagine the shape of the higher generations, we developed molecular models of 1a-e with the CERIUS 2.0 program [20]. The models revealed that the second generation 1b is still a flat disk; however, from the third generation onwards, the steric crowding becomes so severe that the repulsions force an extension into the third dimension. The

disk-like shape is transformed to a cylindrical shape. Figure 1 illustrates the model of the fifth generation.

The enormous steric interactions are in accord with the fast growing number of atoms and molecular masses with increasing generation n. Table 1 gives a survey over the series 1a-e with R1 = R2 = OC6H13.

The dependence of the diameter 0 and the height h of the disks or cylinders on the generation n is shown in Figure 2.

Good indications of the size of the particles can be obtained by gel permeation chromatography (GPC) measurements. The retention time t is an exponential function of the diameter 0 [Eq. (1)]. Figure 3 shows the corresponding curve. The excellent fit parameter (x2 = 0.012) reveals the consistency of the 0 values within the series.

where tO = (16.63 ± 0.49) min is the retention time corresponding to the total volume of the mobile phase, tt = (5.37 ± 0.47) min is the retention time corresponding to the volume of the stationary phase, e(^Gp/kT) = e-a97±a17 is the distribution coefficient for the substrate-sorbent interaction, and s = 0.66 ± 0.11 nm-1 is the surface area per unit pore volume.

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