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Structural Features of Molecular-Colloidal Solutions of C60 Fullerenes in Water by Small-Angle Neutron Scattering M. V. Avdeev,*,† A. A. Khokhryakov,†,‡ T. V. Tropin,†,§ G. V. Andrievsky,| V. K. Klochkov,| L. I. Derevyanchenko,| L. Rosta,⊥ V. M. Garamus,# V. B. Priezzhev,† M. V. Korobov,§ and V. L. Aksenov†,§ Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia, Kyiv Taras Shevchenko National University, Volodymyrska Street 64, 01033 Kyiv, Ukraine, Lomonosov Moscow State University, Vorobjovy Gory, 119899 Moscow, Russia, Institute for Therapy of Ukrainian AMS, Postyshev Avenue 2-a, 61039 Kharkov, Ukraine, Research Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary, and GKSS Research Centre, 21502 Geesthacht, Germany Received November 23, 2003. In Final Form: February 27, 2004 Highly stable and reproducible molecular-colloidal water solutions of C60 fullerenes (FWS) obtained by transferring fullerenes from an organic solution into an aqueous phase with the help of ultrasonic treatment are investigated by means of small-angle neutron scattering (SANS). A polydispersity in the size of detected particles up to 84 nm is revealed. These particles are slightly anisotropic and have a characteristic size of ∼70 nm. Along with it, there are some indications that a significant part of fullerenes composes particles with the size of the order of 1 nm. The contrast variation based on mixtures of light and heavy water shows that the mean scattering length density of the particles is close to that of the packed fullerene associates as well as that the characteristic size of possible fluctuations of the scattering length density within the particles does not exceed 2 nm. A smooth surface resulting in the Porod law for the scattering is detected. A number of models discussed in the literature are considered with respect to the SANS data.
Introduction Since the discovery of fullerenes,1 their biological activity was a question of particular interest.2-10 The corresponding investigations were connected mainly with the socalled water-soluble fullerenesshydrophilic chemical derivatives of fullerenes3-8 or water-soluble complexes containing fullerenes.8-10 Also, some methods for solubilizing fullerenes by surfactants were realized.9-12 The development of the indicated approaches was determined by the fact that fullerenes are typical hydrophobic molecules13 and cannot form true solutions in water. †
Joint Institute for Nuclear Research. Kyiv Taras Shevchenko National University. Lomonosov Moscow State University. | Institute for Therapy of Ukrainian AMS. ⊥ Research Institute for Solid State Physics and Optics. # GKSS Research Centre. ‡ §
(1) Kroto, H. W.; Heath, J. P.; O’Brien, S. C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162-163. (2) Wilson, S. R. In Chemistry, Physics, and Technology; Kadish, K., Ruoff, R., Eds.; John Wiley and Sons: New York, 2000. (3) Tokuyama, H.; Yamago, S.; Nakamura, E. J. Am. Chem. Soc. 1993, 115, 7918-7919. (4) Friedman, S. H.; DeCamp, D. L.; Sijbesma, R. P.; Srdanov, G.; Wudl, F.; Kenyon, G. L. J. Am. Chem. Soc. 1993, 115, 6505-6509. (5) Dugan, L. L.; Turetsky, D. M.; Du, C.; Lobner, D.; Weeler, M.; Almli, C. R.; Shen, C. K.-F.; Luh, T.-Y.; Choi, D. W.; Lin, T.-S. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 9434-9439. (6) Sano, M.; Oishi, K.; Ishi-i, T.; Shinkai, S. Langmuir 2000, 16, 3773-3776. (7) Sijbesma, R. P.; Srdanov, G.; Wudl, F.; Castoro, J. A.; Wilkins, C.; Friedman, S. H.; DeCamp, D. L.; Kenyon, G. L. J. Am. Chem. Soc. 1993, 115, 6510-6509. (8) Andersson, T.; Nilsson, K.; Sundahl, M.; Westman, G.; Wennerstroem, O. J. Chem. Soc., Chem. Commun. 1992, 604-606. (9) Yamakoshi, Y.; Yagami, T.; Fukuhara, K.; Sueyoshi, S.; Miyata, N. J. Chem. Soc., Chem. Commun. 1994, 517-518. (10) Lai, D. T.; Neumann, M. A.; Matsumoto, M.; Sunamoto, J. Chem. Lett. 2000, 29, 64-65. (11) Hungerbuehler, H.; Guldi, D. M.; Asmus, K.-D. J. Am. Chem. Soc. 1993, 115, 3386-3387. (12) Eastoe, J.; Crooks, E. R.; Beeby, A.; Heenan, R. K. Chem. Phys. Lett. 1995, 245, 571-577.
Recently, several methods for producing stable aqueous dispersions of native fullerenes without the addition of any stabilizers were reported.14-16 These methods are based on the exchange of molecules of an organic solvent, which covers fullerenes, with water molecules. The stabilization mechanism of such dispersions is not clear at the moment, which raises an interesting problem from the viewpoint of colloidal chemistry. Nevertheless, a negative charge of colloidal particles detected in different works16,17 (ζ-potential, 9-30 mV) seems to play a significant role in the stabilization, while its origin is still under discussion. The appearance of aqueous fullerene dispersions gives promise that the biological activity of unmodified fullerenes may be used. In the present work, small-angle neutron scattering (SANS) was applied to the fullerene dispersions produced by the method developed by Andrievsky and co-workers.15 In this method, the fullerenes are transferred from an organic solution (toluene or benzene) into an aqueous phase with the help of ultrasonic treatment. These dispersions, denoted below as FWS, show high stability and partially exhibit properties of molecular solutions.18,19 The last fact explains the term “molecular-colloidal solutions” used often for FWS. The aim of the current work was to obtain structural characteristics of FWS with (13) Ruoff, R. S.; Tse, D. S.; Malhotra, R.; Lorents, D. C. J. Phys. Chem. 1993, 97, 3379-3383. (14) Scrivence, W. A.; Tour, J. M. J. Am. Chem. Soc. 1994, 116, 45174518. (15) Andrievsky, G. V.; Kosevich, M. V.; Vovk, O. M.; Shelkovsky, V. S.; Vashchenko, L. A. J. Chem. Soc., Chem. Commun. 1995, 12, 12811282. (16) Deguchi, S.; Alargova, R. G.; Tsujii, K. Langmuir 2001, 17, 60136017. (17) Mcheldov-Petrossyan, N. O.; Klochkov, V. K.; Andrievsky, G. V. J. Chem. Soc., Faraday Trans. 1997, 93, 4343-4346. (18) Andrievsky, G. V.; Klochkov, V. K.; Bordyuh, A.; Dovbeshko, G. I. Chem. Phys. Lett. 2002, 364, 8-17. (19) Adamenko, I. I.; Moroz, K. O.; Durov, S. S.; Prylutskyy, Y. I.; Scharff, P.; Braun, T. High Pressure Res. 2003, 23, 271-273.
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respect to the particle size distribution as well as the scattering length density distribution inside the particles using the contrast variation in different mixtures of heavy and light water. It should be pointed out that the use of SANS to study fullerene solutions is limited by two factors emphasized first in ref 20. As a rule, the solubility of fullerenes is not sufficient to resolve the coherent scattering signal against the incoherent background of hydrogen containing solvents (H-solvents). The use of the corresponding deuterated analogues (D-solvents), which possess a small incoherent background, is not effective either, since the mean coherent scattering length density of fullerenes is close to that of the D-solvents and, hence, results in a poor contrast. For the systems studied in the present work, the combination of fullerene concentration and the characteristic size of colloidal particles makes it possible to obtain structural information from the SANS signal in addition to other methods. Below, after the description of the experimental details and the results, different models based on the data of complementary techniques, such as UV-vis and IR spectroscopy,18 transmission electron microscopy (TEM),21 dynamical light scattering (DLS),22 differential scanning calorimetry (DSC),22 and others, are discussed with respect to the SANS data. Experimental Section Sample Preparation. Colloidal solutions of fullerenes were prepared according to the procedure described in ref 15. Fullerene C60 (MER Corporation; purity, 99.5%) was dissolved initially in benzene (purity, g99.5%; thiophene free; Aldrich). After emulsification of this solution in water with high power ultrasound treatment (frequency, 22-44 kHz; output power within 400600 W), a transparent brown-reddish dispersion formed. Then, it was filtered through microfilters (Millipore; pore size, 0.22 µm.). Residual benzene was removed from the dispersion by means of the azeotropic distillation of the water-organic phase under reduced pressure at 65-70 °C. The final FWS (C60 concentration, 252 µM) were stable and did not show any significant changes in UV-vis spectra for at least three months. By diluting these dispersions, different aqueous solutions with C60 concentrations down to 126 µM were prepared for SANS experiments. The C60 concentration in all of the samples was determined from UV-vis spectra obtained with the Hitachi2000 spectrophotometer using the extinction coefficient 68 000 dm3 mol-1 cm-1 at λ ) 340 nm.18 Several solutions for the contrast variation were prepared by dissolving the initial H2O-based samples with D2O, so that the relative content, η, of heavy water changed within an interval of 0-40%. SANS Measurements. SANS experiments were performed on the YuMO time-of-flight small-angle diffractometer at the IBR-2 pulsed reactor of the Joint Institute for Nuclear Research, Dubna, Russia, on the small-angle diffractometer at the research steady-state reactor of the Budapest Neutron Centre (BNC), Hungary, and on the SANS-1 instrument of the GKSS Research Centre, Geesthacht, Germany. On the YuMO diffractometer, neutron wavelengths within an interval of 0.05-0.5 nm and a sample-detector distance (SD) of 16 m were used to obtain scattering curves isotropic over the radial φ-angle in a q-range of 0.08-2 nm-1. The calibration procedure was performed using vanadium.23 At the BNC, fixed wavelengths of 0.45 and 1.2 nm (resolution, 13%) and sample-detector distances of 2 and 5.5 m made it possible to increase the minimal detected q-values down (20) Affholter, K. A.; Henderson, S. J.; Wignall, G. D.; Bunick, G. J.; Haufler, R. E.; Compton, R. N. J. Chem. Phys. 1993, 99, 9224-9229. (21) Andrievsky, G. V.; Klochkov, V. K.; Karyakina, E. L.; MchedlovPetrossyan, N. O. Chem. Phys. Lett. 1999, 300, 392-396. (22) Korobov, M. V.; Stukalin, E. B.; Ivanova, N. I.; Avramenko, N. V.; Andrievsky, G. V. In The exciting world of Nanocages and Nanotubes, Proceedings of the 201st meeting of The Electrochemical Society, Pennington, NJ, 2002; Kamat, P., Guldi, D., Kadish, K., Eds.; Electrochemical Society: Pennington, NJ, 2002; Vol. 12, pp 799-804. (23) Ostanevich, Yu. M. Macromol. Chem. 1988, 15, 91-103.
Avdeev et al. to 0.05 nm-1. The calibration on water24 was made. To calibrate the curves at a neutron wavelength of 1.2 nm and a SD of 5.5 m, the overlap of the data with those obtained at the same SD and a wavelength of 0.45 nm was used. On the SANS-1 instrument,25 measurements were made at a neutron wavelength of 0.81 nm (resolution, 10%) and a series of sample-detector distances within an interval of 1-9 m to cover a q-range of 0.04-2 nm-1. As in the previous case, H2O was used to calibrate the curves. At large sample-detector distances (>4.5 m), the calibrating curves were obtained by the recalculation of the curves obtained at a SD of 4 m with the corresponding distance coefficient. Since the volume fraction of fullerenes in the dispersions did not exceed a value of 10-4, the scattering from H2O and the corresponding H2O/D2O mixtures during the contrast variation without any additives was subtracted to remove the incoherent background effect in all cases. Data Treatment. The indirect Fourier transform (IFT)26 of the obtained scattering curves was performed to analyze the p(r) correlation function (pair distance distribution in the case of homogeneous particles) and the particle size distribution function. To determine the size distribution function, colloidal particles were assumed to be homogeneous and of spherical shape. The programs presented in the works of Glatter,26 Svergun,27 and Pedersen28 were used and gave close results. The resolution function of the setups calculated according to Pedersen and coworkers29 was taken into account. The intensity in zero angle, I(0), and the mean radius of gyration, R h g ) 〈R2g〉1/2, of the particles were determined by the obtained p(r) function.30 The definition of the mean radius of gyration as well as other parameters implies that averaging over the particle size distribution should be done. The intensity in zero angle can be expressed as
I(0) ) n〈(Fj - Fs)2V2〉
(1)
Here, n is the particle concentration, Fj and Fs are the mean scattering length densities of the particle and solvent, respectively, and V is the particle volume. The particle concentration is connected with the fullerene concentration, c, as follows:
n)
c 〈F0V〉
(2)
where F0 is the mean mass density of the particle. We note here that eqs 1 and 2 suggest that in the general case of polydisperse multicomponent systems the mean scattering length and mass densities of the particles can depend on the particle volume and, hence, should be included in the average over the sizes. If the particles are quite homogeneous, at sufficiently large q-values, the scattering is determined by the surface structure. In the case of a smooth surface, it satisfies the Porod law:
I(q) ) qf∞
2πn(Fj - Fs)2〈S〉 q4
(3)
where S is the surface area of a particle. The cases when the exponent in the denominator differs from 4 correspond to fractal (between 3 and 4) and diffusive (between 4 and 6) surfaces, respectively.31 The power-law model was fitted to the obtained scattering curves at large q-values to determine the surface character of the particles. (24) Jacrot, B. Rep. Prog. Phys. 1976, 39, 911-953. (25) Stuhrmann, H. B.; Burkhardt, N.; Dietrich, G.; Ju¨nemann, R.; Meerwinck, W.; Schmitt, M.; Wadzack, J.; Willumeit, R.; Zhao, J.; Nierhaus, K. H. Nucl. Instrum. Methods Phys. Res., Sect. A 1995, 356, 124-132. (26) Glatter, O. In Modern Aspects of Small-Angle Scattering; Brumberger, H., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1995. (27) Svergun, D. I. J. Appl. Crystallogr. 1992, 25, 495-503. (28) Pedersen, J. S. Adv. Colloid Interface Sci. 1997, 70, 171-210. (29) Pedersen, J. S.; Posselt, D.; Mortensen, K. J. Appl. Crystallogr. 1990, 23, 321-333. (30) Feigin, L. A.; Svergun, D. I. Structure Analysis by Small-Angle X-Ray and Neutron Scattering; Plenum Press: New York, 1987.
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Figure 1. Experimental SANS curves obtained at different setups for 252 µM dispersions. Two samples (denoted conditionally as sample 1 and sample 2) are prepared by the same procedure as described in the Experimental Section. The solid line illustrates the scattering corresponding to the Porod law. The dashed and dotted lines are the curves calculated for the monodisperse case of the sphere and spherical shell, respectively, with the same parameters Rg and I(0) as those found from experimental data. During the contrast variation with mixtures of heavy and light water, the scattering data were treated by IFT, as described above, and the changes in the resulting parameters I(0) and R hg versus contrast were analyzed. The match pointsthe relative content of D2O when the scattering from the particles disappears against the scattering of the solventswas determined by the intersection of the function (I(0)/c)1/2 with the η-axis and is denoted below as γ. The mean scattering length density of the particles in the match point is equal to that of the solvent and can be found by the following expression:
Fj ) γFD2O + (1 - γ)FH2O
(4)
where FD2O and FH2O are the scattering length densities of heavy and light water, respectively. Along with it, the analysis of the R h g parameter as a function of contrast makes it possible to conclude at what extent the distribution of the scattering length density inside the particles is nonhomogeneous.30
Results The SANS curves for different samples of FWS with a C60 concentration of 252 µM are presented in Figure 1. The absence of specific peculiarities in the curves suggests that the particles are quite polydisperse (see examples of calculated scattering curves for the monodisperse case in Figure 1). Fits of the power-law scattering to the curves over the q-interval 0.2-2 nm-1 result in the exponent -(3.96 ( 0.07) (Figure 1), which corresponds to the Porod law (3) and points to the smooth surface of the particles. It should be pointed out that the polydispersity may affect the exponent of the power-law scattering when the size distribution function is of the power-law type,31 so that smooth and fractal surfaces become indistinguishable. However, we suppose that this possibility is unlikely, since the Porod law is satisfied with good precision. A deviation from the power-law scattering in all curves at q below 0.1 nm-1 is indicative of the characteristic size close to 60 nm for the detected particles. To avoid any instrumental artifact connected with calibration, the experiments for several samples were repeated on different SANS instru(31) Schmidt, P. W. In Modern Aspects of Small-Angle Scattering; Brumberger, H., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1995.
Figure 2. (a) Experimental SANS curves (BNC) from the dispersions with different fullerene concentrations and IFT fitting of experimental data according to ref 27. (b) Resulting p(r) functions normalized on the concentration. The asymmetrical view of the p(r) function points to a slight anisotropy in the shape of the particles.
ments (see above) with different calibration procedures and showed complete consistence over the whole q-range covered (Figure 1). A comparatively high background in the curves decreases significantly with the dilution (Figure 2a) and seems to be connected with a significant fraction of smaller particles (size, ∼1 nm) in the dispersions. This conclusion is in agreement with the transmission electron microscopy data,21 revealing a polydispersity over the interval 1-72 nm. The structure of the small particles is strongly affected by the C60 concentration, since the background is not proportional to the concentration (in Figure 2a, the concentration and background change by different factors, which are 2 and 5, respectively). In particular, such a situation can take place if these particles dissociate into smaller subunits when the concentration decreases and the mean particle size becomes less. The IFT procedure for the p(r) function gives stable solutions within a q-interval of 0.04-0.4 nm-1 and requires a maximal particle size of ∼84 nm (Figure 2). Slight anisotropy in the particle shape can be revealed from the p(r) graph (Figure 2b). The resulting R h g value, 28 ( 3 nm (the corresponding radius for homogeneous spheres is 36 nm), is in close agreement with the radius determined by h ) 34 nm. Thus, one can say that the SANS and DLS22, R DLS data indicate that within the size interval of ∼10100 nm the characteristic size is ∼70 nm. Below, the particles from this interval are discussed. The character of the p(r) function as well as the R h g values reveals the independence of Rg from the dilution within the concentration range 100-300 µM (Figure 2b). With respect to the size distribution function, the IFT procedure in all used programs does not give a single result for the assumed
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for single fullerenes (Figure 3b). The experiments with the contrast variation were repeated twice in different ways. In the first case, the initial solution was dissolved by D2O, resulting in a decrease of the fullerene concentration. In the second case, the solution was dissolved by a mixture of D2O and H2O, so that the samples with different contents of D2O had one C60 concentration. No significant difference in the match points obtained by these two procedures was revealed, which shows that the inner structure of the detected particles is independent from the fullerene concentration within the interval 50-300 µM. Special attention was given to the reproducibility of the results. A series of SANS experiments was performed for the same samples of FWS several months apart as well as for newly prepared samples. The obtained SANS curves repeat each other well (see the example in Figure 1), which gives an indication of both the high stability of the studied FWS and the full reproducibility of their preparation procedure. Discussion
Figure 3. Contrast variation with the 126 µM dispersion (IBR2). (a) Experimental (points) and IFT (lines) scattering curves at different contents of D2O in the solvent. (b) Dependence of the (I(0)/c)1/2 variable on the content of D2O in the solvent (points) and linear approximation (solid line). The star indicates the match point of the system. The dashed line corresponds to the situation that would happen if fullerenes did not aggregate and were in a single state in the solution (values multiplied by 500).
spherical form-factor of the particles, and its solutions depend strongly on the parameters of the procedure. This can be explained by both the wide size distribution function and the deviation from the spherical shape used to model particles. The determination of the mean scattering length density of the particles in FWS by the contrast variation using different mixtures of H2O and D2O is illustrated in Figure 3. Changes of the mean radius of gyration during the contrast variation lie within the experimental errors; thus, from the viewpoint of SANS experiments, the particles are homogeneous in respect to the scattering length distribution. This conclusion is testified by the linear dependence of the combination (I(0)/c)1/2 on the scattering length density of the solvent (Figure 3b). It is seen from eq 1 that this can take place only if the mean scattering length density does not depend on the particle volume and, hence, can be excluded from the average over the particle sizes:
I(0) ) n(Fj - Fs)2〈V2〉
(5)
So, the possible density fluctuations do not exceed the size 2 nm, which is determined by the resolution of the SANS method. It follows from eq 5 that I(0) can be matched (see also Figure 3b). The match point, γ, is found to be ∼0.87 (F ) (5.44 ( 0.20) × 1010 cm-2) in comparison with the calculated value 1.18 (F ) (7.60 ( 0.08) × 1010 cm-2)
Here, we discuss a number of models proposed on the basis of data from other methods with respect to the characteristics of the system revealed by SANS. The obtained value of the mean scattering length density of the particles is close to that for the face-centered cubic (fcc) crystalline state of fullerenes with the lattice parameter a ) 1 nm32 (corresponding match point, γ ) 0.90, and scattering length density, F ) 5.62 × 1010 cm-2) or, as reported in ref 33, the possible cluster state of fullerenes (γ ) 0.89 and F ) 5.58 × 1010 cm-2). Such closeness may be considered as an argument for the statement that the detected particles have a mainly crystalline or rather dense structure with a packing density of ∼0.75. The formation of such a structure may be responsible for the bands in the UV-vis spectra at 460 and 610 nm,18 which are close to the peaks in the absorption spectrum of fullerene crystals and fullerene films at 460 and 625 nm, respectively.32,34,35 A filmlike fullerene structure was also proposed36 for the particles in aqueous dispersions of fullerenes produced from a tetrahydofuran (THF)/water mixture16 as well as in binary solutions of fullerenes based on mixtures of nonpolar and polar solvents.36 A difference in the values of scattering length density calculated for crystals and obtained experimentally can be caused by systematic errors in the second value. One more reason is the presence of a second component in the particles different from fullerene. For example, one can assume that residual molecules of the initial solvent are included in the particles such as in solvated crystals of fullerenes in aromatic solvents37-40 or in the colloidal particles of C60 fullerenes in pyridine/water solutions, (32) Kra¨tschmer, W.; Lamb, L. D.; Fostiropoulos, K.; Huffman, D. R. Nature 1990, 347, 354-358. (33) Prilutski, Yu. I.; Durov, S. S.; Yashchuk, V. N.; Ogul’chansky, T. Yu.; Pogorelov, E. V.; Astashkin, Yu. A.; Buzaneva, E. V.; Kirghisov, Yu. D.; Andrievsky, G. V.; Scharff, P. Eur. Phys. J. 1999, D9, 341-343. (34) Kazaoui, S.; Ross, R.; Minami, N. Solid State Commun. 1994, 90, 623-628. (35) Hebard, A. F.; Haddon, R. C.; Fleming, R. M.; Kortan, A. R. Appl. Phys. Lett. 1991, 59, 2109-2111. (36) Alargova, R. G.; Deguchi, S.; Tsujii, K. J. Am. Chem. Soc. 2001, 123, 10460-10467. (37) Dresselhaus, M. S.; Dresselhaus, G.; Eclund, P. C. Science of Fullerenes and Carbon Nanotubes; Academic Press: San Diego, CA, 1996. (38) Talyzin, A. V. J. Phys. Chem. B 1997, 101, 9679-9681. (39) Talyzin, A. V.; Engstro¨m, I. J. Phys. Chem. B 1998, 102, 64776481. (40) Korobov, M. V.; Mirakian, A. L.; Avramenko, N. V.; Ollofson, G.; Ruoff, R.; Smith, A. L. J. Phys. Chem. B 1999, 103, 1339-1346.
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where pyridine molecules are assumed to form a thin solvation shell.41-43 Water inclusions are another candidate for the additional component in the particles. The volume fraction, R, of the second component in the particles can be determined from the following equation analogous to eq 4:
Fj ) (1 - R)F0 + RF1
(6)
where F0 and F1 are the scattering length densities of the crystal and the second component, respectively. For the mean scattering length density of water (-0.56 × 1010 cm-2 in bulk) or benzene (1.182 × 1010 cm-2 in bulk), eq 6 results in estimates for R within an interval of 1-5 vol %. Thus, if water or benzene are included in the crystalline particles, their contents do not exceed 5 vol %. However, the IR spectra obtained following the procedure in refs 18 and 44 for the studied system show the absence of benzene impurities in the system. As suggested in refs 18 and 21, water can form supramolecular donor-acceptor complexes of the C60@{H2O}n type (hydrated fullerenes) in the considered system. The origin of such complexes is determined by the charge transfer from oxygen atoms of H2O (electron donors) to C60 (electron acceptor) due to the comparatively high electron affinity of the latter. This reaction requires special conditions, which are realized in the course of the preparation, and does not proceed for a pure fullerene in water. The acceptance of electrons by fullerenes (up to six) in varied conditions was reported also in refs 39 and 45-47. This, in turn, can determine the appearance of the negative charge on the surface of the crystalline particles, resulting in somewhat of a shell, which stabilizes the particle growth. The shell fraction against the particle volume is small, so that no influence on the radius of gyration during the contrast variation is seen. The observed high polydispersity in the solutions may be explained by the fact that both the association of fullerenes and the formation of the donor-acceptor complexes proceed approximately at the same time scale. The anisotropy in the particle shape observed in the p(r) function (Figure 2b) is testified by the moments of the size distribution obtained from eqs 1-3 using the value 〈R2g〉1/2 from the IFT procedure and by the assumption that the crystalline particles (F0 ) 1.69 g/cm3) are spherical. In this case, 〈R2〉1/2 ) (5/3)1/2R h g ) 36 nm. Then, from eqs 2 and 3, one can estimate the ratio 〈S〉/〈V〉 ) 〈R2〉/〈R3〉, giving 〈R3〉1/3 ) 19 nm. Analogously, eqs 1 and 2 result in the ratio 〈V2〉/〈V〉 ) 〈R6〉/〈R3〉 and allow one to determine 〈R6〉1/6 ) 42 nm. One can see that the obtained relation 〈R3〉1/3 < 〈R2〉1/2, which cannot take place for the size (41) Mrzel, A.; Mertelj, A.; Omerzu, A.; Opi, M.; Mihailovic, D. J. Phys. Chem. B 1999, 103, 11256-11260. (42) Aksenov, V. L.; Avdeev, M. V.; Mihailovic, D.; Mrzel, A.; Vasiliev, V. D.; Timchenko, A. A.; Serdyuk, I. N. In Electronic properties of novel materialssmolecular nanostructures, AIP Conference Proceedings; Kuzmany, H., Fink, J., Mehring, M., Roth, A., Eds.; American Institute of Physics: Melville, NY, 2001. (43) Aksenov, V. L.; Avdeev, M. V.; Timchenko, A. A.; Serdyuk, I. N.; May, R. P. In Frontiers of Multifunctional Nanosystems; Buzaneva, E., Scharff, P., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2002. (44) Seniavin, V. M.; Kurskaya, A. A.; Odinets, I. L.; Korobov, M. V.; Ruoff, R. S. In Recent advances in the chemistry and physics of fullerenes and related materials; Kadish, K., Ruoff, R., Eds.; Electrochemical Society: Pennington, NJ, 1997; Vol. 4. (45) Ohsawa, Y.; Saji, T. J. Chem. Soc., Chem. Commun. 1992, 781782. (46) Xie, Q.; Perez-Cordero, E.; Echegoyen, L. J. Am. Chem. Soc. 1992, 114, 3978-3980. (47) Sension, R. J.; Szarka, A. Z.; Smith, G. R.; Hochstrasser, R. M. Chem. Phys. Lett. 1991, 185, 179-183.
distribution function defined for positive R, shows that the assumed shape of the particles is not correct and the anisotropy should be taken into account. We note here that for the current model and other models, by analogy with solutions of C60 fullerenes in pyridine/water mixtures,43 the secondary aggregation may be responsible for the anisotropy; that is, the particles are elongated associates of a number (less than 10) of smaller aggregates. It seems that the high polydispersity is the property of the studied FWS prepared with ultrasound. For aqueous dispersions of fullerenes prepared by nitrogen purging16 as well as for fullerene dispersions in other polar liquids,36 quasi-monodisperse colloidal particles were reported. The alternative model18 for the discussed particles suggests that they represent associates of single hydrated C60 fullerenes [C60@{H2O}n]m. In this case, the stability of the particles in FWS may be a reflection of the stage of the independent growth48 in the frame of the nucleation theory. In fact, this means that the associates (clusters) of hydrated fullerenes are unstable, but the combination of thermodynamic parameters is so that the regime, when the mean cluster size in the system does not change within a significant time period, is realized. A similar model was discussed for the particles in the C60/pyridine/water system41 but was not confirmed in the SANS experiments with contrast variation.42,43 The number of water molecules in the hydration shell was estimated18 to be 24. A part of the molecules in the shell may form donor-acceptor bonds, which determines the fact that FWS have properties of polyacids. Below, we estimate from the SANS data the mean specific volume of a shell molecule as a function of the packing density of the hydrated complexes in the particles. Because of the D/H exchange, the mean scattering density of the particles in the discussed model depends on the rate of solvent deuteration. In the match point, it is determined by equation analogues of eq 6 but with a different meaning for F0 and F1, which are now the scattering length density of a single fullerene and hydration shell, respectively. Let us rewrite eq 6 in the following way:
(
Fj ) ξ
) (
)
V1 n1b1 V0 V0 F0 + F1 ) ξ F0 + V V V V
(7)
where V ) V0 + V1 is the volume of the hydrated complex consisting of a single fullerene volume, V0, and a shell volume, V1; b1 and n1 are the scattering length and the number of molecules in the shell, respectively; and ξ is the packing density of the complexes in the particles. Assuming the equality of specific volumes of H2O and D2O in the shell, the b1 value is determined by the following proportion:
b1 ) γbD2O + (1 - γ)bH2O
(8)
where bD2O and bH2O are the scattering lengths of heavy and light water, respectively. Equation 8 suggests that the deuteration rate in the shell is the same as it is in bulk. From eq 7, we can obtain the specific volume of water molecules in the shell:
ν1 ) ξ
F0V0 + n1b1 V0 Fjn1 n1
(9)
The dependence of ν1(ξ) for n1 ) 24 calculated according to eqs 8 and 9 is presented in Figure 4. In the calculations, (48) Schmelzer, J.; Lembke, U., Jr.; Kranold, R. J. Chem. Phys. 2000, 113, 1268-1275.
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give 54 and 30 nm, respectively,22 which are of the same order as the particle size revealed by DLS and SANS. From the homogeneity of the particles observed in the SANS experiments, it follows that the second component in the particles cannot compose large isolated inclusions of more than 2 nm in size, which is at least 1 order of magnitude smaller than the size estimated from DSC. Thus, if the observed depression of the melting point relates to water constrained inside the fullerene particles, one has to assume a relatively free H2O/D2O exchange between the captured and bulk water, so that only the fullerene moiety produces a SANS signal against the solvent. Conclusions
Figure 4. Calculated dependence (solid line) of the specific volume of the water molecules at the fullerene surface on the packing density, ξ (according to eqs 8 and 9), of the hydrated complexes in particles. The horizontal dashed lines correspond 2O to the van der Waals volume (VH 0 ) and the specific volume in H 2O bulk (ν1 ) for the water molecules. The vertical dashed line indicates the maximum possible packing density of the complexes. The bold line denotes intervals of possible values of ν1 and ξ.
the radius of the fullerene is 0.5 nm,20 while that of H2O is 0.16 nm.49 One can see that, to satisfy the condition when the specific volume of a water molecule is equal to or more than what it is in bulk, the packing density must lie within an interval of 0.85-1, which is more than the maximum possible packing density of spherical complexes (ξ ) 0.74) and, hence, cannot be realized. Moreover, if one considers water around the fullerene as a uniform shell, the thickness of this shell is smaller than the approximate diameter of water for any value of ξ (the maximal thickness is 0.208 nm at ξ ) 1). So, water must be considered as localized on the fullerene surface. In this case, the van der Waals volume of the water molecule (1.72 × 10-2 nm3) plays the role of the limiting parameter, and one can restrict intervals of possible values of the specific volume of water in the shell and packing density (Figure 4). One can see in Figure 4 that the packing density of the complexes cannot be less than 0.64. The last model of the particles in FWS to be discussed is based on the results of differential scanning calorimetry (DSC) measurements performed on the gel-like solids precipitated from various FWS similar to the studied ones. Two endothermic peaks are observed22 in the DSC traces around T ) 273 K. One of them, at T ) 270.7 K, can be interpreted as the melting of nanosized clusters of water constrained in the fullerene matrix.22 To estimate the characteristic size of the water inclusion, one can use the molar ratio of the constrained water to the fullerene (20: 1), the mean size of the particles measured by DLS and SANS, and the molar volumes of C60 and water, which are 420 and 18 cm3, respectively. The alternative way is to use the Gibbs-Thomson equation of the melting point (∆T ) -2.3 K) for the constrained water. In the assumption of the spherical shape of water inclusions, these ways (49) Richards, F. M. Annu. Rev. Biophys. Bioeng. 1977, 6, 151-176.
Small-angle neutron scattering experiments reveal that colloidal particles in FWS are highly polydisperse (up to 84 nm). They are slightly anisotropic and have a characteristic size of ∼70 nm. Their inner structure is quite homogeneous within the density fluctuation in size of no more than 2 nm. The studied system is highly stable, and good reproducibility of the preparation procedure takes place. Taking into account the data of complementary techniques (UV-vis, IR, EM, DLS, and DSC), three models for describing the particle structure can be considered. The first model implies that the particles are fullerene crystallites or rather dense clusters covered with charged thin shells of hydration water, which stabilize the solutions. According to the SANS data, in this case, the fraction of the hydration shell in the particles must not exceed 5 vol %. The second model suggests that the particles represent associates of single hydrated C60 fullerenes. In this case, hydration water must be localized on the fullerene surface. For the suggested18 hydration shell of 24 water molecules, the minimum possible packing density of the complexes in the particles is 0.64. The last model intended to explain an additional peak in the DSC traces different from the water peak considers the particles in FWS as closed filmlike structures with water captured inside. The estimated size of such inclusions is of the same order as the particle size revealed by SANS. To satisfy the SANS data, the free exchange of the captured and bulk water must take place. Finally, it should be noted that there are some indications of the fact that, in addition to the particles detected in SANS and DLS, a significant part of fullerenes also composes particles with the size of the order of 1 nm. The possibility of the separation of the particles in FWS by size and their SANS study is under discussion. Acknowledgment. We are grateful to Dr. J. Schmelzer for his attention to this work and helpful discussions. The work has been performed with the support of the Russian Ministry of Industry, Science and Technologies, State Contract No. 40.012.1.1.1148. M.V.K. thanks the Russian Foundation of Basic Research (RFBR) for the financial support (Grant 03-03-32186). Coauthors from IT of Ukrainian AMS are grateful to the U.S. Civilian Research and Development Foundation for the financial support (Cooperative Grant UC2-2440-KH-02). LA0361969
