142 Advances in Polymer Science Editorial Board: A. Abe. A.-C ...

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196 J. Roovers, B. Comanita Fig. 4. Dependence of radii on the molecular weight of PAMAM dendrimers in methanol; m R g ; D R h ; o R h pactness of the dendrimers. The exponent n in Eq. (4) is equal to 1/3, a value expected for equal density spheres. No full account of a systematic study of dendrimer dimensions is at present available in spite of the great interest. Preliminary values of R g , obtained by SANS on dilute PAMAM solutions in CD 3OH, have recently appeared [70]. The MW dependence is shown in Fig. 4. The dependence of R g on MW is stronger for low MW dendrimers (n=0.36) than for the high MW dendrimers (n=0.20). This latter exponent is probably a minimum value because the nominal rather than the measured MWs have been used in Fig. 4 and synthetic problems suggest that the real MWs are lower than the nominal ones. The low exponent for the high MW dendrimers is in the range predicted by various models discussed in Sect. 3.1. The 1/3 slope predicted for high MW dendrimers synthesized under conditions of saturation substitution [49] is clearly not observed. Some data have also appeared for the first five generations of the smaller DAB(CN) x and DAB(NH 2) x dendrimers (see Scheme 1 for structure). For DAB(CN) x in acetone-d 6 SANS yields n=0.31 (generations 2–5). For DAB(NH 2) x in D 2 O the low MW dendrimers follow R g ~M 0.30 [71]. In general, it is difficult to determine R g of low MW dendrimers accurately [70]. Furthermore, all dendrimers studied have ionizable groups and may act like polyelectrolytes. Therefore solvent conditions need to be carefully controlled and specified.
Dendrimers and Dendrimer-Polymer Hybrids 197 3.2.2 Hydrodynamic Radii More extensive data are available for the hydrodynamic radii of dendrimers than for the radii of gyration, because they can be derived from intrinsic viscosity measurements according to R h =(3[h]M) 1/3 (10pN A ) –1/3 (5) or from the translational diffusion coefficient, D o, according to R h=kT(6ph sD o) –1 (6) where N A is Avogadro's number, k is the Boltzmann constant, and h s the solvent viscosity. R h and R h are the radii of the equivalent sphere of constant density. Equations (5) and (6) may not apply to the smallest dendrimers whose dimensions are comparable to the dimensions of the solvent molecules. Furthermore, R h and R h cannot be compared directly to the predictions of the models because the ratio R h/R g and R h/R g are not independent of the mass and branching architecture of the dendrimers [52]. The earliest hydrodynamic radii have been obtained on poly (a,e-L-lysine) dendrimers [72] (see Fig. 3b). For these dendrimers it was found that [h]=2.5 ml/g independent of generation. It follows from Eq. (5) that R h~M 1/3 , this exponent is expected for equal-density spheres and is unusual for dendrimers and ascribed to the asymmetric nature of the branching pattern in poly (a,e,-L-lysine) [73]. The experimental ratio R h/R g for these dendrimers varies between 1.14 and 1.0. Hydrodynamic radii of poly(benzyl ether) dendrimers are shown in Fig. 5. Data for monodendrons with a hydroxyl focal group and tridendrons fall on the same curve. The value of the exponent n in Eq. (4) is 0.46 of low MW. At high MW it is 0.26 [48]. Data on low MW linear polystyrene in benzene [74] have been included in Fig. 5 for comparison. They highlight the little difference in the actual values of the hydrodynamic radii of linear polystyrene and low MW poly(benzyl ether) dendrimers. Deviations are observed only when MW>5·10 3 . Furthermore, the MW dependence of the radii of polystyrene and poly(benzyl ether) dendrimers are the same at low MW. This indicates that it remains impossible to draw major conclusions about the conformation of the low MW dendrimers from their global properties. The low values of the hydrodynamic radii of the high MW dendrimers, on the other hand, attest to their compact conformation. A similar transition to more compact dendrimers has recently been shown in a direct comparison of linear and dendritic poly(benzyl ethers) [75]. Recently, Stechemesser and Eimer published hydrodynamic radii obtained from translational diffusion coefficients measured by means of recovery after photobleaching experiments on selected generations of PAMAM dendrimers [76]. The values of R h obtained in methanol are compared with R g data on the same dendrimers in Fig. 4. It can be calculated that the ratio R h/R g~1.4 for all but the tenth generation dendrimer. This ratio is somewhat higher than expect-
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142 Advances in Polymer Science Edi
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Branched Polymers I Volume Editor:
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Volume Editor Dr. Jacques Roovers I
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Preface While books have been writt
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Contents Synthesis of Branched Poly
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Synthesis of Branched Polymers by C
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72 N. Hadjichristidis, S. Pispas, M
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100 N. Hadjichristidis, S. Pispas,
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Poly(macromonomers): Homo- and Copo
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Poly(macromonomers), Homo- and Copo
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142 Advances in Polymer Science Editorial Board: A. Abe. A.-C ...

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