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

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194 J. Roovers, B. Comanita 3 Conformation of Dendrimers 3.1 Theoretical Models The first model for the conformation of a dendrimer was proposed by de Gennes and Hervet [49]. It is based on a modified Edwards self-consistent field for dendrimers with large linear segments between consecutive branch points in a good solvent. It places the spacers of consecutive generations in concentric shells. The segment density is rather low in the center and increases parabolically (according to r 2 , r being the distance from the center) to a generation for which the segment density approaches unity. As a consequence, the radius of dendrimers, R, increases according to M 0.2 up to the steric saturation generation. The radius of incomplete dendrimers grown beyond this generation increases according to R~M 1/3 , i.e., like constant density objects. This model is related to the Maciejewski box [50] and may have merit when phase separation forces the end-standing groups to lie on the surface of the dendrimer or in case the spacers are stiff and cannot fold back. Simulations and models developed more recently for dendrimers with flexible spacers provides a quite different picture. Generally, the segment density decreases from the center of the dendrimer to zero at the surface [51–54]. In particular, some studies suggest a small minimum in the segment density near the core [52], others show evidence for an extended plateau region of near constant segment density [52, 54]. The end-standing groups are found throughout the entire dendrimer volume [52, 54] as a result of backfolding of the spacers, although most of them are found in the large volume near the dendrimer surface. Segments of lower generation spacers are more localized in the interior of the dendrimer [54] and have a stretched conformation [53]. The dependence of the radius of gyration, R g , on the mass of the dendrimer is complex. For small generation dendrimers the exponent n in R g ~M n (4) is 0.5 [51], 0.4 [52], and 0.5 [53]. For high generation dendrimers the limiting value for n is 0.22 [51], 0.24 [52], 0.20 [53], and 0.3 [54]. The latter exponents are comparable with n=0.25 for randomly branched polymers [55, 56]. There is general agreement on the increasing sphericity of dendrimers as the number of generations increases [57] and on a limited overlap of different dendrons inside the dendrimer volume [54, 58]. Based on a calculation of the intrinsic viscosity of model dendrimers, Mansfield and Klushin concluded that the hydrodynamic radius, R h , of low generation dendrimers is smaller than R g but that the reverse is true for high generation dendrimers [59]. The variation of the size of the dendrimer with the number of segments, n, between two branch points, at constant architecture (generation), has been consid-
Dendrimers and Dendrimer-Polymer Hybrids 195 ered. Lescanec and Muthukumar found R g ~n 0.5 [51]. Others have established that the good solvent limit for dendrimers and linear polymers is the same, i.e., R g ~n 3/5 [60, 61]. Many of these conclusions on the conformation of dendrimers are in qualitative agreement with the known behavior of other types of branched polymers. For example, the preferred stretching of the lower generation segments in a dendrimer is comparable to the increased expansion of the interior segments of star polymers with many arms [62, 63], and with the preferential expansion of the backbone segments in comb polymers. The limited overlap of dendrons is comparable with the limited long range interaction of the two halves of a linear polymer in a good solvent or of the different blocks in a block copolymer. The ratio R h/R g1 is, however, observed in star polymers with many arms. It would be interesting to see whether for large dendrimers R h/R g=1.29, the value for equal density spheres, or approaches R h/R g=1.00, the asymptotic value for a hollow sphere. The effect of the quality of the solvent on the dimensions of dendrimers has been considered [54]. The size of the dendrimers increases with an increased interaction with solvent. However, in contrast to linear polymers or regular star polymers, the exponent n in Eq. (4) was found to be independent of the quality of the solvent for high MW dendrimers [54]. The structure factor for dendrimers has also been calculated. The structure factor provides a description of the relative scattering intensity from a collection of scatterers as a function of the scattering vector q=(4p/l)sin(q/2). l is the wavelength of the radiation in the medium and q is the angle between incident and scattered radiation. The calculated structure factor is necessary for comparison with experimental scattering curves. The structure factor of dendritic polymers has been calculated on the assumption of Gaussian statistics, i.e., with “ghost” segments [67, 68]. Burchard also studied the dynamic structure factor and established the limiting value for R h /R g =1.023 for high generation dendritic polymers. Structure factors can also be computed from simulated segment density distributions [52, 53]. 3.2 Experimental Dimensions of Dendrimers 3.2.1 Radius of Gyration The earliest systematic study of the radii of gyration of dendrimers was performed on poly (a,e-L-lysine) dendrimers up to generation 10 (see Fig. 3b for the branch unit). The polylysine dendrimers are atypical in so far as only one of each consecutive generation is placed end-standingly. Radii of gyration between 0.8 nm (generation 3, MW=1900) and 4.3 nm (generation 10, MW= 2.3·10 5 ) have been obtained [69]. These small dimensions attest to the com-
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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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