Angewandte Chemie Dense-Shell Dendrimers Analysis of the Spatial Dimensions of Fully Aromatic Dendrimers Sabine Rosenfeldt,* Nico Dingenouts, Dominic Ptschke, Matthias Ballauff, Alexander J. Berresheim, Klaus M"llen, and Peter Lindner Dendrimers present a fascinating class of molecules because of their regularly branched structure and their unusual properties.[1–4] Most of the dendrimers described so far are composed of flexible repeating units. Such a molecule can assume a vast number of conformations that are generated by rotation about the bonds between these units (Figure 1 b). In particular, the terminal groups can fold back into the interior of the molecule. A totally different situation arises when considering the stiff, fully aromatic dendrimer G4-M (Figure 1 a): In this case the benzene rings are either linear or form an angle of 608 or 1208 to each other. Therefore, rotation about the bonds between the rings cannot change the structure of the molecule profoundly. Most importantly, no backfolding of the terminal groups is possible in such a molecule. The structure shown in Figure 1 b suggests a “dense-shell” structure of flexible dendrimers, which consists of a hollow core closed by a densely packed shell of end groups. Such a dendritic box could be used, for example, as a molecular container. Hence, many ideas for possible applications of dendrimers originated from this picture.[1–3] These ideas were further encouraged by an early publication by de Gennes and Hervet in which the first theoretical treatment of such denseshell structures was presented.[5] Subsequent theoretical work, however, has demonstrated convincingly that flexible dendrimers exhibit their maximum density in the core of the molecule (“dense-core model”) and that there is a finite probability for the end groups to be located at any position within the molecule.[6–9] Experimental studies by small-angle neutron scattering (SANS[10]) have fully corroborated this result (see the review of this work in reference [11]). In [*] Dr. S. Rosenfeldt,+ Dr. N. Dingenouts, D. Ptschke, Prof. Dr. M. Ballauff + Polymer-Institut Universit%t Karlsruhe Kaiserstrasse 12, 76128 Karlsruhe (Germany) Fax: (+ 49) 721-608-3153 E-mail: matthias.ballauff@uni-bayreuth.de Dr. A. J. Berresheim, Prof. Dr. K. M<llen Max-Planck-Institut f<r Polymerforschung Postfach 3148, 55021 Mainz (Germany) Dr. P. Lindner Institut Laue-Langevin B.P. 156X, 38042 Grenoble Cedex (France) [+] Present Address: Physikalische Chemie I Universit%t Bayreuth 95440 Bayreuth (Germany) Angew. Chem. Int. Ed. 2004, 43, 109 –112 particular, the distribution of end groups in a flexible fourthgeneration dendrimer was determined experimentally for the first time by use of SANS.[12] Thus a change of paradigm has occurred, as the previous assumption of the dense-shell model has been replaced by a model based on well-established results of polymer physics. Herein we elucidate this point further by analyzing the spatial structure of the stiff, fully aromatic dendrimer G4-M.[12–17] It has been demonstrated by SANS[11, 18–22] that such a stiff dendrimer has a dense-shell structure as expected. In accordance with results obtained by NMR spectroscopy[17] it is shown that a high segment density must result in the periphery of the molecule if the number of generations is high enough. The analysis employed herein consists of measuring the SANS intensities I0(q) at different contrast. This method, termed contrast variation, has been applied frequently to colloidal systems.[10, 11] Hence, it suffices to delineate the main points of this analysis:[11, 24] The intensity I0(q) of an isolated molecule dissolved in a suitable solvent is governed by the contrast 1̄1m, where 1̄ is the average scattering-length density of the molecule and 1m is the scattering-length density of the solvent. The scattering length defines the strength of the scattered radiation emanating from a given atom or segment. Since the scattering intensity is always related to the corresponding scattering volume, the scattering-length densities are the decisive quantities. The quantity q is the magnitude of the scattering vector and can be calculated from the scattering angle q and the wavelength l of the radiation employed (q = (4p/l)sin(q/2)).[10] The contrast in the SANS experiments can be changed by using mixtures of deuterated and nondeuterated solvents, because the scattering-length density of the solvent depends strongly on the degree of deuteration.[10] The average scattering-length density 1̄ can be obtained directly from experimental data because I0(q) can be approximated by the Guinier law for small scattering angles, that is, small q values [Eq. (1)]. In this equation, N/V is the number of I0 ðqÞ ﬃ R2g N 2 V pð 11m Þ2 exp q2 3 V ð1Þ dissolved molecules, Vp their volume, and Rg the radius of gyration.[10, 11] The volume Vp can be used to calculate the molecular weight M according to M = NL Vp v̄, where v̄ is the partial specific volume determined experimentally.[18–20] First, however, the experimental scattering intensities must be extrapolated carefully to vanishing concentration, and the incoherent contribution always present in neutron scattering must be subtracted before Equation (1) is applied.[22] Figure 2 shows the Guinier plot of the SANS data for the dissolved dendrimer G4-M according to Equation (1). The curves differ with respect to the contrast 1̄1m obtained through mixtures of deuterated and nondeuterated toluene. It is evident that the extrapolation to q = 0 provides no difficulty, so that Vp (= 30.3 nm3) and 1̄ (= 2.42 = 1010 cm2) can be obtained. From these data and the measured specific volume the molecular weight M was determined to be 22 250 g mol1, which is in agreement, within experimental DOI: 10.1002/anie.200351810 2004 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 109 Communications Figure 1. a) The stiff dendrimer G4-M.[12, 13] b) A flexible dendrimer that has been studied by small-angle neutron scattering.[8, 18, 21–23] dendrimer G4-M is displayed in Figure 3. A weak side maximum is visible at about 1.7 nm1, which already points to a well-defined structure of G4-M. Figure 2. Guinier plot[10] [see Eq. (1)] of the scattering intensities obtained at different contrast. The contrast between the dissolved dendrimer G4-M and the solvent was adjusted through the use of mixtures of deuterated and nondeuterated toluene. The ratio of the deuterated to nondeuterated toluene is given. All data have been extrapolated to vanishing concentration, and the incoherent background has been removed. error ( 600 g mol1), with the calculated value (22 927 g mol1) and the value determined by mass spectrometry. Moreover, the radius of gyration Rg, which also depends on contrast, can be determined from this plot and extrapolated to infinite contrast by an appropriate procedure.[11] For the dendrimer G4-M Rg turns out to be 2.6 nm. If 1̄ is known, the measured scattering intensity I0(q) can be expanded in powers of the contrast 1̄1m [Eq. (2)],[11, 18, 20, 21] which provides the partial intensities I0 ðqÞ ¼ ½ 11m 2 IS ðqÞ þ 2 ½ 11m ISI ðqÞ þ II ðqÞ ð2Þ IS(q), ISI(q), and II(q). The first term IS(q) contains information on the spatial structure of the dissolved molecule. In contrast, the second and third terms are related to the variation of the scattering-length density within the molecule[25] and therefore cannot be used for analyzing the shape of the molecule. The resulting partial intensity IS(q) of the stiff 110 2004 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Figure 3. Modeling of the partial scattering intensity IS(q) (triangles) obtained from the experimental SANS data by contrast variation. Solid lines: fit obtained by the model described in Figure 4. Inset: number of spheres N(r) located within the distance r from the center of the molecule. The distribution of the end groups is shown by a dashed line. The transformation of IS(q) into real space can not be done by the method employed for flexible dendrimers as shown in Figure 1 b. Simulations demonstrated that the direct Fourier transformation of IS(q) only leads to correct results for fully flexible dendrimers, that is, if the structure is averaged over a sufficiently high number of conformers.[8, 9] The dendrimer G4-M under consideration in this case, however, hardly has any flexibility as a result of its rigid structure. Moreover, it has no radial symmetry.[26] Therefore, IS(q) was analyzed by the model shown in Figure 4. In general, small-angle scattering does not have atomic resolution and parts of the molecule such as the benzene rings can be rendered in a suitably coarse-grained model when evaluating IS(q). Thus the central biphenyl unit is represented by two spheres, and each of the four dendrons emanating from this central unit is modeled by eight spheres www.angewandte.org Angew. Chem. Int. Ed. 2004, 43, 109 –112 Angewandte Chemie (Figure 4). Hence, each sphere represents five benzene rings. The distance between the centers of these spheres must approximately be the dimensions of two benzene rings, and Figure 4. Model used to determine the partial scattering intensity IS(q) [Eq. (2)]. The molecular structure of the dendrimer is represented by spheres connected by freely rotating bonds. The central biphenyl unit is modeled by two small spheres (diameter: 0.4 nm). Each dendron emanating from this center is modeled by eight spheres whose distance (0.87 nm) and radius (0.8 nm) are treated as fit parameters in the simulation. this parameter therefore determines the overall dimensions of the molecule. Since each sphere must provide the scattering power of five benzene rings, the diameter was increased appropriately. Hence, neighboring spheres overlap. For the sake of clarity, however, this overlap is not shown in Figure 4. Finally, the bonds between all spheres can be rotated freely. The scattering intensity can now be calculated as follows: Different conformers are generated by a set of torsional angles chosen at random. If a given torsional angle leads to an overlap between two spheres that do not belong to the same dendron, this angle is dismissed and a new one is generated. To obtain sufficient accuracy, about 500 conformers were generated in this way. The scattering intensity IS(q)conformer of each conformer results from the scattering contribution of all the spheres and their positions in the conformer according to Equation (3),[10] where dij denotes the distance between the IS ðqÞconformer ¼ X i;j Ai ðqÞ Aj ðqÞ sin q dij q dij ð3Þ spheres i and j with radius R in the corresponding conformer. The scattering amplitudes Aj(q) of the spheres are given by Equation (4).[10] The average over all conformations results Ai ðqÞ ¼ 4p 3 sin q Rq R cos q R R 3 3 qR ð4Þ from the arithmetic mean of all IS(q)conformer values calculated in this way. The only fit parameters are the distance of the spheres and their radius R [see Eq. (4)]. From this modeling of IS(q) (optimal fit, solid line in Figure 3) the distance between the spheres d turns out to be 0.87 nm and the radius R is 0.8 nm. These values lead to full agreement between theory and experiment within the limits of error. The distance between the spheres corresponds approximately to the length of a biphenyl unit. The diameter Angew. Chem. Int. Ed. 2004, 43, 109 –112 of the spheres (1.6 nm) fits well to the average dimensions of the subunits, which consist of five benzene rings each. The inset in Figure 3 shows the number N(r) of spheres located within distance r from the center of the molecule. While the first generation is still strictly localized, higher generations are spread out over larger distances due to the averaging of different conformers. Therefore, SANS shows that the dendrimer G4-M has a stiff structure in which the segments have a well-defined distance from the center. The above conclusions derived from SANS measurements were corroborated by an investigation by Saalw?chter and coworkers[17] by using solid-state NMR spectroscopy. In this case the marked slowing of the terminal phenyl groups could be proved directly and traced back to their mutual steric hindrance. Moreover, this study demonstrated that the dendrons can not reorient even at high temperatures. This again points to a strong mutual steric hindrance between the dendrons. The conclusions drawn from the present work are related to our basic understanding of dendrimers and their molecular shape: The dendrimer G4-M exhibits a molecular structure that can be described by the dense-shell model hitherto applied to all dendrimers. Such a stiff shape, however, in which all end groups are located in the periphery of the molecule (see Figure 3, inset) can only be realized by a concomitantly stiff chemical structure. Flexible dendrimers, on the other hand, are characterized by a segmental distribution that exhibits its maximum in the center of the molecule.[11, 18–23] in such a structure the end groups can fold back easily.[18] Consequently, flexible dendrimers exhibit the dense-core structure discussed above that was predicted by theory quite some time ago. On the other hand, dense-shell dendrimers can only be formed from stiff units, as shown for the dendrimer G4-M. Experimental Section The dendrimer was synthesized as previously described.[12, 13] Toluene (Merck, p.a.) and deuterated toluene (C7H8 ; Euriso-top, degree of deuteration: 99.96 %) were used as received. The specific volume ((0.82 0.04) cm3 g1) of G4-M was determined by using a DMA-60 densitometer (Paar, Graz, Austria). All SANS data were obtained by using the beamline D11 of the Institut Laue-Langevin in Grenoble. The data were corrected to obtain the absolute intensities by use of the software directly available at the beamline. The extrapolation of the data to vanishing concentration and the subtraction of the incoherent background were carried out as described in reference [22]. Received: May 6, 2003 [Z51810] . Keywords: dendrimers · small-angle neutron scattering · structure elucidation [1] F. VGgtle, S. Gestermann, R. Hesse, H. Schwierz, B. Windisch, Prog. Polym. Sci. 2000, 25, 987 – 1041. [2] S. M. Grayson, J. M. J. FrJchet, Chem. Rev. 2001, 3819 – 3867. [3] S. Hecht, J. Polym. Sci. Part A 2003, 41, 1047 – 1058. [4] Dendrimers and other Dendritic Polymers (Eds.: J. M. J. FrJchet, D. A. Tomalia), Wiley-VCH, Weinheim, 2002. www.angewandte.org 2004 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 111 Communications [5] P. G. de Gennes, H. Hervet, J. Phys. (Paris) 1983, 44, L351 – L360. This much-cited publication has a problem, however, as was recently pointed out (T. C. Zook, G. T. Pickett, Phys. Rev. Lett. 2003, 90, 15502-1-015502-4): The method of de Gennes and Hervet leads to a maximum segment density in the core of the dendrimers if applied correctly. [6] R. L. Lescanec, M. Muthukumar, Macromolecules 1990, 23, 2280 – 2288. [7] D. Boris, M. Rubinstein, Macromolecules 1996, 29, 7251 – 7260. [8] H. M. Harreis, C. N. Likos, M. Ballauff, J. Chem. Phys. 2003, 118, 1979 – 1988. [9] I. GGtze, C. N. Likos, Macromolecules, 2003, 36, 8189 – 8197. [10] J. S. Higgins, H. C. Benoit, Polymers and Neutron Scattering, Clarendon Press, Oxford, England, 1994; the radius of gyration is equal to the root mean square distance of the units from the center of mass of the dendrimer. [11] “Structure and Dimensions of Polymer and Colloidal Systems”: M. Ballauff, NATO Sci. Ser. Ser. C 2002, 568. [12] K. MLllen, F. Morgenroth, Tetrahedron 1997, 53, 15349 – 15366. [13] F. Morgenroth, C. KLbel, K. MLllen, J. Mater. Chem. 1997, 7, 1207 – 1211. [14] K. MLllen, A. J. Berresheim, M. MLller, Chem. Rev. 1999, 99, 1747 – 1785. [15] U.-M. Wiesler, A. J. Berresheim, F. Morgenroth, G. Lieser, K. MLllen, Macromolecules 2001, 34, 187 – 199. [16] H. Zhang, P. C. M. Grim, P. Foubert, T. Vosh, P. Vanoppen, U.M. Wiesler, A. J. Berresheim, K. MLllen, P. C. de Schryver, Langmuir 2000, 16, 9009 – 9014. [17] M. Wind, K. Saalw?chter, U.-M. Wiesler, K. MLllen, H. W. Spiess, Macromolecules 2002, 35, 10071 – 10086. [18] S. Rosenfeldt, N. Dingenouts, M. Ballauff, N. Werner, F. VGgtle, P. Lindner, Macromolecules 2002, 35, 8098 – 8105. [19] D. PGtschke, M. Ballauff, P. Lindner, M. Fischer, F. VGgtle, Macromolecules 1999, 32, 4079 – 4087. [20] D. PGtschke, M. Ballauff, P. Lindner, M. Fischer, F. VGgtle, Macromol. Chem. Phys. 2000, 201, 330 – 339. [21] N. Dingenouts, S. Rosenfeldt, N. Werner, F. VGgtle, P. Lindner, A. Roulamo, K. Rissanen, M. Ballauff, J. Appl. Cryst. 2003, in press. [22] S. Rosenfeldt, N. Dingenouts, M. Ballauff, P. Lindner, C. N. Likos, N. Werner, F. VGgtle, Macromol. Chem. Phys. 2002, 203, 1995 – 2004. [23] C. N. Likos, S. Rosenfeldt, N. Dingenouts, M. Ballauff, P. Lindner, C. N. Likos, N. Werner, F. VGgtle, J. Chem. Phys. 2002, 117, 1869 – 1877. [24] See M. Ballauff in reference [4], pp. 176–194. [25] Both terms need to be subtracted carefully before evaluating the scattering intensity to deduce the spatial structure. This problem is of central importance when analyzing dendrimers, which are rather small objects. The analysis of I0(q) without this correction may lead to incorrect conclusions.[11, 24] [26] Central to this analysis is the description of flexible dendrimers by an average segment density termed T(r), which is of central symmetry and leads to IS(q) upon Fourier transformation.[8] For stiff systems, however, the deviations of an averaged intensity would be too high, so that no meaningful description of IS(q) would be possible. This can be seen from the fact that the description through an averaged T(r) would lead to pronounced minima (zeros) of I0(q). The experimental scattering intensity, however, exhibits only a weak side maximum (see Figure 3). Moreover, this demonstrates that G4-M does not have radial symmetry, and models that assume distributions with central symmetry can not be applied. 112 2004 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.angewandte.org Angew. Chem. Int. Ed. 2004, 43, 109 –112

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