SANS investigation of self-assembling dendrimers in organic solvents Pappannan Thiyagarajan,a* Fanwen Zeng,b C. Y. Kua and Steven C. Zimmermanb* aIPNS, Argonne National L aboratory, Argonne, IL 60439, USA bDepartment of Chemistry, University of Illinois, Urbana, IL 61801, USA The self-assembly behaviour of tetraacids 1a–c and tetraester 4 in CDCl3 and [2H8]tetrahydrofuran {[2H8 ]THF} has been investigated by the small-angle neutron scattering (SANS) technique.The experimental SANS data were compared with simulated scattering data derived from structural models proposed previously for the aggregates. These studies suggest that dendritic monomers 1b,c self-assemble into cyclic hexameric aggregates, whereas 1a forms a large tubular aggregate in CDCl3. Further study on 1c in CDCl3 as a function of concentration suggests that the cyclic hexameric aggregates strongly interact with each other at higher concentrations.The control compound 4 was shown to be monomeric in both solvents. There is significant current interest in organic compounds that information on supramolecular assemblies in their native state in aqueous solution7 and their interparticle interactions.8b form stable, discrete aggregates in solution.1 These aggregates may have a particular function or they may serve as synthetic intermediates for the construction of larger, covalently linked nano- or meso-structures.In this regard, hydrogen-bond Materials and Methods mediated self-assembly is a powerful approach because the Materials directionality of hydrogen bonding allows control over the aggregate structure, while its strength in apolar solvents pro- The synthesis and characterization of compounds 1a–c and 4 vides a considerable enthalpic driving force to overcome the were described previously3 and material was available from disfavourable entropy of aggregation.One successful approach the prior studies. [2H1 ]Chloroform and [2H8]tetrahydrofuran, to forming discrete aggregates is to target closed assemblies, purchased from Cambridge Isotope Laboratory, were used such as those formed in cyclic arrays of monomers. An added directly.benefit of the cyclic aggregation approach is the cooperativity which often manifests itself in highly stable and discrete selfassembled structures. SANS measurements One of the continuing unsolved challenges in this area is to SANS experiments of compounds 1a–c and 4 were performed characterize the aggregate structure in solution.Because there in CDCl3. The self-assembly behaviour of compounds 1c and is no single method for unambiguously determining the number 4 was also investigated in [2H8]THF to study the eect of density and structure of aggregates present, the characteriz- this solvent, which is more competitive toward hydrogen- ation is often based on a combination of several indirect bonding interactions.The corresponding solution was injected methods.2 The commonly used techniques are size-exclusion into a Suprasil cylindrical cell with a 2 mm pathlength chromatography (SEC), 1H NMR spectroscopy, vapour press- (volume=0.7 ml).SANS data were collected at the Intense ure osmometry (VPO), UV–VIS and IR spectroscopy, and Pulsed Neutron Source of Argonne National Laboratory, sometimes mass spectrometry. We recently reported that using the time-of-flight SANS instrument, Small Angle Neutron dendritic tetraacids 1b,c self-assemble into cyclic hexamer 2, Diractometer (SAND).9a This instrument uses pulsed neu- whereas 1a forms a series of linear aggregates such as 3 trons derived from spallation with wavelengths in the range (Fig. 1).3 Hexamer 2, whose structure was supported by SEC, 0.5–14 A° and a fixed sample-to-detector distance of 2 m.The VPO, and comparison with a covalently linked model, is the scattered neutrons are measured using a 128×128 array of largest known discrete abiotic aggregate formed by weak position sensitive, gas filled, 40×40 cm2, proportional counters interactions.4 Herein, we report the use of small-angle neutron with the wavelengths measured by time-of-flight through scattering (SANS) technique to characterize the self-assembly binning the pulse to 68 constant Dt/t=0.05 time channels.The behaviour of 1a–c and test the previously proposed models.size range in a SANS experiment depends on the range of SANS and small-angle X-ray scattering (SAXS) are direct momentum transfer Q [see eqn. (2)] which is determined by techniques which can yield unique information about the the geometry of the instrument and the range of wavelengths structure and interactions of macromolecules with sizes in the of the neutrons.Given the characteristics of the SAND at the range of 10 to 1000 A° . A distinguishing feature of neutron Intense Pulsed Neutron Source (IPNS), useful SANS data in scattering compared to X-ray scattering is that neutrons inter- the Q range 0.0035–0.8 A° -1 can be obtained in a single act with atomic nuclei, while X-rays interact with the electron measurement. The data for each sample is corrected for the clouds of the atoms.This property renders neutron scattering backgrounds from the instrument, the Suprasil cell, and the very sensitive to dierent isotopes, such as proton and deu- solvent as well as for detector non-linearity.9b Data are terium whose coherent lengths are quite dierent.5 SANS is presented on absolute scale by using the known scattering one of the highly applied neutron scattering techniques for the cross-section of a silica gel sample.characterization of macromolecules and several reviews dealing with the application of this technique for biological systems have been published.6 This technique allows extraction of form Small-angle neutron scattering factors, which are descriptions of macromolecular size and shape, and particle–particle structure factors in solutions.The dierential scattering cross-section I (Q) measured as a function of momentum transfer Q by SANS is a convolution SANS has also been demonstrated to provide structural J. Mater. Chem., 1997, 7(7), 1221–1226 1221Fig. 1 (a) Dendritic tetraacids 1a–c and the proposed cyclic hexameric aggregate 2 and linear aggregate 3, (b) tetraester 4 1222 J.Mater. Chem., 1997, 7(7), 1221–1226of two terms, namely, intraparticle correlations P(Q) and concentration dependent eects, such as aggregation, it is possible to obtain the true Rg of the particle by the linear interparticle correlations S(Q). extrapolation of measured Rg values at several concentrations. I(Q)=nP(Q)S(Q) (1)The magnitude of the slope of the curve (second virial coecient) in the apparent Rg vs.concentration plot yields In eqn. (1), n is the number of particles per unit volume and qualitative information on the interparticle interactions. Q=4pl-1 sin h (2) In the case of polydisperse systems, the Rg and I (0) values are respectively the Z-averaged and mass-averaged quantities. where l is the wavelength of neutrons and 2h is the scat- For example, the Z-averaged Rg value is defined as tering angle.The intraparticle structure factor P(Q) is defined as Rg2 =. NiMi2(Rg2)i . NiMi2 (7) P(Q)=T.i,j bibj exp[iQ(ri-rj )]U (3) where Ni and Mi and (Rg)i are the number density, molecular mass, and radius of gyration of the aggregates of type i, and the interparticle structure factor respectively.The shape of the scattering particles can be analysed by S(Q)=1 NT.N i=1 .N j=1 exp[iQ(Ri-Rj)]U (4) fitting the scattering pattern in the whole Q range by either using the analytical functions for the form factors of dierent In eqn. (3), ri and rj are the position vectors of the atoms in a geometrical objects,11 or by calculating the scattering pattern particle and bi and bj are the scattering lengths5 of atoms i using a suitable molecular model, as was done for proteins and j and the braces indicate that averaging for all orientations using eqn.(3).10 The molecular models of compounds 1a–c of the particles is taken. In general, the scattering power of an and 4 and their possible aggregate structures were constructed atom depends on the isotope.5 Eqn.(3) can be used to calculate with the Macromodel program12 on a Silicon Graphics workthe scattering from the particle, if atomic coordinates are station. Because of the limitations on the number of atoms available. In eqn. (4), Ri and Rj are the position vectors of the used, the dendrimer substituents and the tetraacid core unit particle centres and N is the total number of particles.were minimized separately and then covalently linked. Each In the case of dilute solutions the particles are far apart and structure was first minimized using molecular mechanics:MM2 S(Q) in the low Q region will oscillate around unity and hence force field with the Polak–Ribier conjugate gradient method I(Q) is predominantly due to P(Q). The I (Q) data can be of optimization.These minimized structures were then further readily analysed to obtain the correct size, shape and molecular minimized by molecular dynamics with automatic set-up parmass of the particle. At higher concentrations where the ameters of 300 K, initial temperature, 10 ps run with a 15 fs excluded volume eects become significant the size and molecu- timestep using SHAKE and zero momentum.lar mass parameters derived from the low-Q region become The atomic coordinates of the structures derived from the lower in values. This is due to the increased eect of S(Q) on modelling studies were used to calculate the scattering patterns. I(Q) and one has to decompose I(Q) to obtain the P(Q) and It is important to state that we used only the atomic coordi- S(Q) terms prior to analysis.This step, however, requires nates of the molecular models for calculating the scattering information on the size and morphology of the particles as curves, but did not use the neutron scattering cross-sections well as the interaction potentials. Under these conditions it of individual atoms. What this means is that the shape of the is possible to obtain the surface potentials of the colloidal scattering curve for a given system is appropriate, but the objects.8 scaling is not.We arbitrarily scaled the calculated scattering data and compared the shapes with the experimental data to test the validity of the proposed models. In the case of 10.6 mM Analysis of SANS data CDCl3 solution of 1a none of the aggregate models generated At the low-Q region, the experimental scattering intensity I(Q) by the Macromodel program could explain the measured vs.Q data can be used to obtain size information by using scattering data (discussed later) and hence modelling using the eqn. (5)11 which is an approximation of eqn. (1) in the low- form factor for a hollow cylinder was used. The form factor of Q region. a cylindrical shape particle with or without a hollow inner portion (tube vs.rod) can be written as I (Q)=I(0) exp(-Q2Rg2/3) (5) where A(Q)=2 sin(QaL /2) QaL /2 GAJ1(QcRo) QcRo B-ARi RoB2AJ1(QcRi) QcRi BH I(0)=n(rp-rs)2 V 2 (6) (8) In eqn. (6), rp and rs are the scattering length densities (r= where L is the length of the cylinder, Ro is the outer radius of S bi/V ) of the particles and the solvents, V is the volume of the cylinder, Ri is the inner radius of the cylinder, Qa is the the particle, and bi is the scattering length of individual atoms.component of Q in the axial direction, Qc is the component of The radius of gyration, Rg is the root-mean-squared distances Q in the cross-section plane, and J1 is the first-order Bessel of all of the atoms to the centroid of the scattering volume of function of the first kind.The orientationally averaged particle the particle. This parameter is shape independent and one structure factor used to fit is needs to know the shape of the particle in order to derive sizes in terms of the familiar physical dimensions. For example, for P(Q)=V 2 4p P1 -1 dm P2p 0 dw|A(Q)|2 (9) a sphere with a radius of R, Rg2=0.6R2 and for an ellipsoid, Rg2=(a2+d2+c2)/5 where a, d, c are the semiaxes of an where V=pRo2L .ellipsoid. The value of Rg is obtained from the absolute value of the slope (k) of a line in the natural log of I (Q) vs. Q2 plot (Guinier plot)11 in the Q region where QRg#1.0, as Rg2=3k. Results and Discussion In dilute solutions where the interparticle interactions are either nonexistent or minimal, this value will represent the true Fig. 2 shows the measured SANS data for 1c in CDCl3 at three concentrations. Each curve is superimposed by the size of the particle. However, in the presence of interparticle interactions the value of Rg will be smaller and this value has calculated SANS data from the coordinates generated for the cyclic hexamer 2 (see Fig. 1) proposed for this system.It is to be denoted as apparent value. In the absence of any other J. Mater. Chem., 1997, 7(7), 1221–1226 1223Fig. 2 Experimental SANS data for 1c in CDCl3 at three concentrations: (a) 12mgml-1, (b) 24mgml-1 and (c) 50mgml-1. The Fig. 3 Corresponding Guinier plots for the data in Fig. 2. The Guinier calculated scattering pattern (—) from the coordinates generated for plots for the calculated curves (+) are shown in each case.The value the cyclic hexamer model proposed for this system is superimposed of the slopes in the experimental data (—) decreases with increasing on the experimental data. concentration; all of them are smaller than that for the calculated data. clearly demonstrated that the calculated and measured data agree reasonably well for a solution with a concentration of 3.8 mM (12 mg ml-1) [Fig. 2(a)] and the agreement becomes poorer with increasing concentration. The actual disagreement is in the low-Q region of the high concentration sample which suggests the presence of interparticle interactions between these hexamer aggregates in CDCl3. The interparticle eects can be seen better in the corresponding Guinier plots (Fig. 3) which exhibit decreasing slopes (decrease of apparent Rg values) with increasing concentration, when compared to the calculated data for the cyclic hexamer. The calculated SANS data for the cyclic hexamer yields an Rg of 33.6 A° , while the apparent Rg values for the measured samples with a monomer concentration of 3.8 mM (12 mg ml-1), 7.6 mM (24 mg ml-1) and 15.7 mM (50 mg ml-1) are 30.4, 28.9 and 23.7 A° , respectively. Fig. 4 shows the linear dependence of apparent Rg as a function of concentration. The Rg value at infinite dilution from Fig. 4 is 33.1 A° which agrees quite well with the expected value of 33.6 A° on the basis of the proposed model. Thus the cyclic hexamer model (see Fig. 1) proposed for 1c in CDCl3 is consistent with the SANS results.However, it is noteworthy Fig. 4 Apparent Rg values as a function of concentration for 1c in to mention that SANS also suggests the presence of concen- CDCl3. The linearity implies that the particles are intact but interact tration-dependent interactions between these aggregates at the strongly. The extrapolated Rg value at infinite dilution agrees well with the Rg value calculated for the cyclic hexamer.high concentration range investigated here. 1224 J. Mater. Chem., 1997, 7(7), 1221–1226Fig. 6 Experimental SANS data for 16 mg ml-1 4 in [2H8 ]THF ($) and in CDCl3 (#). The lines are the calculated scattering patterns for the monomer. The dierent scaling between these data sets is due to the dierence in contrast provided by the solvent for the scattering from the monomer.[2H8]THF is due to dierent contrasts [see eqn. (6)] provided by the dierent scattering length densities of the solvents CDCl3 (3.16×1010 cm-2) and [2H8]THF (6.36×1010 cm-2). It is evident that the contrast for neutron scattering from these particles is higher in [2H8]THF when compared to that in CDCl3 as seen from the low signal intensity and large error bars for the latter, even though both samples used similar beam times. Tetraacids 1 with second- and first-generation dendritic substituents were also investigated.Experimental SANS data for an 8.5 mM solution of 1b in CDCl3 along with the calculated data derived from a cyclic hexameric aggregate are shown in Fig. 5 (a) Experimental SANS data of a 6.3 mM solution of 1c in Fig. 7. The experimental Rg of 27.1±1 A° agrees quite well with [2H8]THF ($) along with the calculated data for a monomer (%). that from the calculated data (Rg=28.6 A° ). The shapes of the (b) Guinier plots for the data in (a). scattering patterns also agree well in the whole Q region thus validating the correctness of the proposed model for this system. When 1c is dissolved in [2H8]THF the aggregation proper- Previous SEC dilution study in methylene chloride showed ties change.The I(Q) data and the corresponding Guinier that the aggregation of tetraacid 1a is concentration dependent. curves for a solution of 1c in [2H8 ]THF at a concentration of This behaviour, as well as the broadness of the SEC peak, 8.2 mM are shown in Fig. 5. Compound 1c was proposed to suggested that 1a forms a series of linear aggregates.Molecular exist as a monomer in this media as THF competes with the modelling studies suggested that this preference resulted from hydrogen-bonding contacts thus preventing aggregate forma- the small size of the first-generation dendritic substituent which tion. The measured I (Q) data for this is compared with the could be accommodated in the linear aggregate structure calculated SANS data for a monomer.The Rg value of 13.5 A° (Fig. 1). Non-specific aggregation was also observed in the for the calculated SANS curve agrees reasonably well with the SANS studies which suggest the formation of large and polydis- experimental Rg value of 14.6±1 A° obtained from the middle- perse aggregates in a 10.6 mM CDCl3 solution of 1a (Fig. 8). Q region of the data. Also the data in the high-Q region for This Fig. shows the measured SANS data and calculated form both the experimental and the calculated data for a monomer factors for linear aggregates with 8 and 20 monomers. The agree quite well. However, in the low-Q region, the two data Guinier plot for the measured data has at least two dierent sets do not agree.Interestingly, the low-Q region of the experimental data exhibits a power law [I(Q)#Q-1.8 ] which points to extremely large structures resembling mass fractals.13 Nevertheless this unusual SANS curvature in the low-Q region is not reproducible. For example, in a dierent run, the experimental SANS data fit to the calculated value for a dimeric structure.The dierences between runs may originate from a slow disassembly process of the hexameric aggregate.14 To demonstrate the appropriateness of the SANS technique for examining this class of macromolecules, as well as to probe the eect of solvent on conformation, tetraester 4 was investigated in both CDCl3 and [2H8]THF. Tetraester 4, a close analogue of 1c, was shown previously to exist as a monomer in both solvents due to the absence of hydrogen-bonding sites.3 The SANS data collected for 4 in CDCl3 and [2H8]THF at a concentration of 8.0 mM are shown in Fig. 6. These results validate the monomer model proposed for this system (see Fig. 1). Thus, these data show that the experimental scattering Fig. 7 SANS data for 1b in CDCl3 (#) along with the calculated data patterns are identical to the calculated ones for the monomer.for a cyclic hexamer. The data agree quite well, validating the proposed model. The large dierence in the scaling of data for 4 in CDCl3 and J. Mater. Chem., 1997, 7(7), 1221–1226 1225models and compared with the measured scattering data. This oers a direct way to compare the validity of the models and thus increase our understanding of these systems.The SANS studies provide strong support for the cyclic hexamer model previously proposed for 1b,c in CDCl3. SANS further suggests a concentration dependent interaction between these hexameric aggregates. The ester analogue 4 was studied in both THF and CDCl3 and found to exist as a monomer, as expected. Compound 1a seems to form large and non-discrete aggregates.However, the previously proposed linear aggregate model could not explain the experimental data rather the aggregate may have a thin, hollow, cylindrical structure. This work was supported by the US Department of Energy, Oce of Basic Energy Sciences, Division of Material Sciences, under Contract W-31-109-Eng-38 to IPNS. S.C.Z. gratefully acknowledges support from the National Institutes of Health (GM39782).F. Z. thanks the University of Illinois Department of Chemistry for a fellowship. We gratefully acknowledge the technical support provided by D. G. Wozniak at IPNS. References 1 (a) J-M. Lehn, Angew. Chem., Int. Ed. Engl., 1990, 29, 1304; (b) J. S. Lindsey, New J. Chem., 1991, 15, 153; (c) D. S. Lawrence, T. Jiang and M. Levett, Chem. Rev., 1995, 95, 2229; (d) J.F. Stoddart and D. Philp, Angew Chem., Int. Ed. Engl., 1996, 35, 1154. 2 (a) J. P. Mathias, E. E. Simanek and G. M. Whitesides, J. Am. Chem. Soc., 1994, 116, 4326; (b) G. M. Whitesides, E. E. Simanek, J. P. Mathias, C. T. Seto, D. N. Chin, M. Mammen and D. M. Gordon, Acc. Chem. Res., 1995, 28, 37; (c) N. Branda, Fig. 8 (a) SANS data for 1a in CDCl3 (#) along with the calculated R.Wyler and J. Rebek Jr., Science, 1994, 263, 1267; (d) M. R. scattering patterns for a linear aggregate with 8 monomers (,) and Ghadiri, J. R. Granja, R. A. Milligan, D. E. McRee and with 20 monomers (—). The scattering pattern has a secondary peak N. Khazanovich, Nature (L ondon), 1993, 366, 324; (e) E. E. Schrier, which indicates a more ordered structure.The linear aggregate model J. Chem. Educ., 1968, 45, 176. does not explain the data well. (b) Guinier plots for the data in (a). 3 S. C. Zimmerman, F. Zeng, D. E. C. Reichert and S. V. Kolotuchin, Experimental data (#), Rg=137±35 A° (—), Rg=36±5 A° (,); calcu- Science, 1996, 271, 1095. lated data for linear aggregates with 8 monomers ($) and with 20 4 S. C. Zimmerman, Curr.Opin. Colloid Interfac. Sci., in press. monomers (+). The experimental data indicate the presence of 5 G. E. Bacon, Neutron Diraction, Oxford University Press, polydispersity as at least two dierent linear regions are seen. Melbourne, 3rd edn., 1975. 6 (a) B. Jacrot, Rep. Prog. Phys., 1976, 39, 911; (b) H. B. Stuhrmann linear regions corresponding to Rg values of 36±5 and and A.Miller, J. Appl. Crystallogr., 1978, 11, 325; (c) L. A. Feigin and D. I. Svergun, Structure Analysis by Small Angle X-Ray and 137±35 A° . On the other hand, the Rg values for the calculated Neutron Scattering, Plenum, New York, 1987. data for the linear aggregates of 8 and 20 monomers, respect- 7 (a) B. Jacrot, Comp. V irol., 1981, 17, 129; (b) P. Thiyagarajan and ively, are 24.6 and 50.6 A° .The scattering patterns for linear D. M. Tiede, J. Phys. Chem., 1994, 98, 10 343; (c) R. P. Hjelm Jr., aggregates with dierent polymer indices were calculated, but P. Thiyagarajan and H. A. Alkan, J. Phys. Chem., 1992, 96, 8653. none of them could fit the secondary peak at Q=0.12 A° -1 in 8 (a) S. H. Chen, Annu. Rev. Phys. Chem., 1986, 37, 351; the experimental data.The best fit of the scattering data was (b) D. S. Jayasuriya, N. Tcheurekdjian, C. F. Wu, S. H. Chen and P. Thiyagarajan, J. Appl. Crystallogr., 1988, 21, 843. however accomplished by using eqn. (9) for a hollow cylindrical 9 (a) R. K. Crawford, P. Thiyagarajan, J. E. Epperson, F. Trouw, aggregate with an outer radius of 31 A° , inner radius of 26–28 A° R. Kleb, D. Wozniak and D.Leach, Proc. 13th International and a length of 49 A° . It is not obvious how 1a can form such Collaboration on Advanced Neutron Sources, Switzerland, Oct a structure, except perhaps an open helical assembly formed 11–14, 1995, PSI-Proc, 1996, 95–02, 99–117; (b) P. Thiyagarajan, from an extremely flat and extended monomer. Further SANS J. E. Epperson, R. K. Crawford, J. M. Carpenter, T. E. Klippert and molecular modelling studies are needed to elucidate the and D. G. Wozniak, J. Appl. Crystallogr., 1997, 30, in press. 10 P. Thiyagarajan, S. J. Henderson and A. Joachimiak, Structure, exact aggregate structure for compound 1a. 1996, 4, 79. 11 A. Guinier andG. Fournet, Small Angle Scattering of X-Rays, John Wiley & Sons, New York, 1955. Conclusions 12 W. C. Still, Macromodel 3.5a, Columbia University, New York, Hydrogen-bond mediated self-assembling dendrimers have 1992. been studied by a variety of techniques and structural models 13 (a) J. Feder, Fractals, Plenum, New York, 1988; (b) T. Freltoft, J. K. Kjems and S. K. Sinha, Phys. Rev. B, 1986, 33, 269; have been proposed based on the results of SEC, NMR and (c) P. McMahon and I. Snook, J. Chem. Phys., 1996, 105, 2223. VPO studies. Small-angle neutron scattering (SANS) was 14 F. Zeng and S. C. Zimmerman, unpublished work. shown to be a direct and powerful technique for studying these systems in dierent solvents. Scattering data were calculated Paper 7/00581D; Received 24th January, 1997 from the atomic coordinates generated from the proposed 1226 J. Mater. Chem., 1997, 7(7), 1221–1226