ISSN 0036-0244, Russian Journal of Physical Chemistry A, 2009, Vol. 83, No. 7, pp. 1170–1175. © Pleiades Publishing, Ltd., 2009. Original Russian Text © O.V. Alekseeva, N.A. Bagrovskaya, S.M. Kuz’min, A.V. Noskov, I.V. Melikhov, V.N. Rudin, 2009, published in Zhurnal Fizicheskoi Khimii, 2009, Vol. 83, No. 7, pp. 1320–1326.
PHYSICAL CHEMISTRY OF NANOCLUSTERS AND NANOMATERIALS
The Influence of Fullerene Additives on the Structure of Polystyrene Films O. V. Alekseevaa, N. A. Bagrovskayaa, S. M. Kuz’mina, A. V. Noskova, I. V. Melikhovb, and V. N. Rudinb a Institute
of the Solution Chemistry, Russian Academy of Sciences, Ivanovo, Russia of Chemistry, Moscow State University, Moscow, Russia e-mail:
[email protected]
b Faculty
Received May 8, 2008
Abstract—It was shown by electron microscopy and X-ray diffraction that a polystyrene solid with a threelevel hierarchical structure was formed when the solvent was evaporated from a solution of polystyrene in o-xylene (polystyrene molecules stuck together united to form a framework). The kinetics of the transformation of formerly dissolved molecules into aggregates could be described by a Fokker–Planck-type equation. Fullerenes introduced into a solution of polystyrene in amounts less than 0.1 wt % transformed aggregated polystyrene molecules into nanocrystals and accelerated the formation of aggregates. The influence of fullerenes on the kinetics of the processes could be correctly described in the continuum approximation taking into account aggregation rate fluctuations. DOI: 10.1134/S0036024409070218
INTRODUCTION Many polymeric solids have multilevel hierarchical structures, that is, consist of separate polymeric molecules united into primary aggregates, which are in turn united into secondary aggregates, and so on [1–3]. The hierarchical structure determines many properties of polymeric solids, and the determination of the kinetics of its formation is an important problem. This approach was repeatedly applied to fractal structures [4, 5], spherical particles [6, 7], and colloidal crystals [8, 9]. The conditions studied were those under which process rate fluctuations were unnoticeable. In this work, we make an attempt to take into account the role played by fluctuations in terms of a continuum description of the hierarchical structure with the use of Fokker–Plancktype kinetic equations [10–12]. Such a description was performed for the formation of a polystyrene film containing fullerenes as modifiers. Polymeric composites containing fullerenes find use in industry, laboratories, and medicine [13–15], and a study of polystyrene films with fullerenes is therefore of interest of its own. PROBLEM STATEMENT Suppose that the initial system is a solution of a polymer from which the solvent is removed. In solution, separate polymeric molecules predominate; they collide and stick together into primary aggregates. During solvent evaporation, the number and size of primary aggregates increase, and secondary aggregates appear. These aggregates grow by adding separate molecules and primary aggregates. Primary aggregates incorpo-
rated into secondary aggregates remain individual until the solvent is completely removed. Secondary aggregates combine into tertiary aggregates and so on. In the continuum approximation, the condition of the conservation of the number of aggregates of each type has the form ˆ i gradϕ i ) + ϕ i – ∂ϕ i /∂t = div ( G i ϕ i – D
∑Q j>i
ij
(1)
ˆ i gradϕ i ) i = i = J i , at ( G i ϕ i – D 0 where ϕi = ϕi (l, t) is the distribution function of particles of the ith kind over their state parameters l = {l1, …, li, …, lm}, Gi is the m-dimensional vector of the rates of ˆ i is the tensor of the changes in the state of particles, D fluctuation coefficient l, Qij is the frequency of the transfer of particles i into a collective of particles j, l0 denotes the parameters of the smallest aggregate capable of growing at the rate Gi , and J is the intensity of the appearance of aggregates in the system at time t. If the li parameters are functionally related to each other, we can single out one determining parameter l = l from the set l and use the distribution
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ψ i ( l, t ) =
∫ ϕ ( l, t ) dl … dl i
l
2
m
THE INFLUENCE OF FULLERENE ADDITIVES
and the equation
Table 1. Spheroid-size distribution function parameters
∂ψ ∂ψ ∂ – --------i = ---- ⎛ G i ψ i – D i --------i⎞ + ψ i ⎝ ∂l ∂l ⎠ ∂t
∑Q
ij .
(2)
j>i
According to [10, 16, 17], the rate Gi of directional changes in l and the coefficient Di of its fluctuations can be written as Gi = ai ωi ,
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1 2 D i = --- a i ω i , 2
(3)
where ai is the change in the l parameter caused by the attachment or detachment of a separate molecule and ωi is the frequency of attachments or detachments. The passage from the complete ϕi (l, t) function to ψi (l, t) involves loss of information about the state of aggregates, and its expediency should be proved experimentally. In this work, we tried to do this by comparing the experimental ψi (l, t) function with the solution to (2) for primary aggregates of polystyrene molecules containing fullerenes. We selected the size of aggregates measured by electron microscopy as a determining parameter. We also determined the characteristics of the structure of polymeric molecules and aggregates to reveal the possibility of the transition from the oneparameter distribution ψi (l, t) to the ϕi (l, t) function taking into account different aggregate structures. EXPERIMENTAL Fullerene soot was prepared by the Huffman– Kratschmer method [18]. Fullerenes present in the soot were extracted with o-xylene at T = 303 K. The concentrations of various fullerenes were determined using a LIQUOCHROME 2010 chromatograph with a UV detector. The film was prepared by pouring a solution in o-xylene containing polystyrene and fullerene followed by the evaporation of o-xylene at T = 295 K during 105 s. The conditions c0 = 0.154 g/cm3, H0 = tk 0.1 mm, Mp = 4.25 g, Φ = Mf /Mp = 0–10–3 were satisfied. Here, H0 is the thickness of the layer of the initial solution containing polystyrene, ë60, and ë70 in the concentrations c0, cF1, and cF2, respectively, and Mp and Mf are the masses of polystyrene and fullerenes in the system. We used fullerenes in amounts satisfying the condition cF1/cF2 = 4.0 ± 0.1. The film was studied by X-ray diffraction and IR spectroscopy, and the relief of its surface, using a scanning electron microscope. We determined the ψi (l, τk) function for the subsurface film region at time tk of evaporation completion. This function was compared with a solution to (2). X-ray diffraction studies were performed on a DRON-UM1 diffractometer (åÓKα radiation, λ = 0.071 nm, Zr filter as a monochromator) modernized for work with amorphous and polycrystalline substances. Measurements were taken over the angle range RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A
Φ
A, nm
a21, nm
–
l , nm
Df
0 23.0 ± 1.1 0.51 ± 0.02 47.0 ± 0.8 1.1 ± 0.2 3.5 × 10–4 26.1 ± 1.2 0.45 ± 0.02 55.1 ± 0.7 1.7 ± 0.3 1.0 × 10–3 39.2 ± 1.1 1.45 ± 0.015 65.5 ± 1.0
θ = 0.01–0.53 rad following the Debye–Scherrer scheme [19]. The X-ray patterns were processed using the Grafula II and OriginPro packages according to the equation D
I = I 0 ( S/S 0 ) f ,
(4)
where I is the intensity of radiation scattering at angle θ corresponding to the wave vector modulus S = 4πsinθ/λ, I0 and S0 are the reference I and S values, and Df is the empirical exponent sometimes treated as “fractal dimension.” The relief of the surface of films was revealed using a CamScan scanning microscope after the deposition of a layer of Au ~20 nm thick. It was determined by multiply depositing Au layers how the distribution of relief structural element images changed as the layer thickened. We developed a system of corrections that allowed us to assuredly observe and measure particles on film surfaces at l > 20 nm. The data on the size l of particles were used to determine the functions N dN ( l ) ψ ( l, t k ) = ------k- -------------- , N E dl where N(l) is the number of particles with size smaller than l, NE is the total number of changed particles, and Nk is the number of particles in the system at time tk per unit volume. The IR spectra of the films were recorded on an Avatar 360 FT-IR ESP spectrophotometer. The sample for recording the spectra of fullerenes was a pellet pressed with KBr. A semiquantitative analysis of the spectra of films was performed using the base line and internal reference method [20]. The internal reference was the absorption band of out-of-plane ring C–H bond vibrations with a maximum at 906 cm–1. The spectra were used to calculate the Zj = DjF/Dj0 factor, where DjF and Dj0 are the optical densities of absorption bands j in the presence and absence of fullerenes, respectively. The thickness of the films was measured using a micrometer to within 0.01 mm. RESULTS According to the electron microscopy data, subsurface film regions consisted of round particles (spheroids) (Fig. 1) l = 30–150 nm in diameter. The particles were sometimes united into chains. Their mean size is given in Table 1. The ψi (l, tk) functions for spheroids are shown in Fig. 2. At Φ = 1.0 × 10–3, some spheroids con-
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0.5 µm
(‡)
0.5 µm
(b)
Fig. 1. Electron microscopic image of the surface of a polystyrene film at Φ = (a) 0 and (b) 3.5 × 10–4.
1/Npψ(l, tk)
0.08 1
2 3
0.04
0
0.06
0.02
0.10
l, µm
Fig. 2. Size distribution of spheroids at time tk. The experimental data at Φ = (1) 0, (2) 3.5 × 10–4, and (3) 1.0 × 10–3. Solid lines are solutions to Eqs. (2) and (3).
tained visible particles with size ~20 nm. The film thickness ç found by direct measurements at the moment of complete solvent removal was H = 2.4 × 10 ( 1 + 1.0 × 10 î ) l 0 , 2
5
(5)
where l 0 is the mean size of spheroids without fullerenes. The X-ray patterns of films (Figs. 3, 4) were described by (4) over the interval S/S0 = 0.01–0.07 with Df = 1.1 ± 0.1 for Φ = 0 and Df = 1.7 ± 0.2 for Φ = 3.5 × 10–4. At Φ = 3.5 × 10–4, the X-ray pattern contained a diffraction maximum at θ = 0.09 rad. This maximum was related to the interplanar distance 0.39 nm calculated according to the Wulf–Bragg condition. The
width of the coherent scattering region corresponding to this maximum was ~1.2 nm according to the Scherrer condition [21, 22]. Fragments of the IR spectra of films and fullerenes are shown in Fig. 5. We see that there are certain differences between the spectra of films without fullerenes and doped with fullerenes. In the spectra of modified films, we observe overlapping of bands corresponding to phenyl ring (1500–1400 cm–1) and fullerene (1429 cm–1) vibrations, changes in the intensities of these bands and the band at 1600–1585 cm–1, and a change in the contour of a wide band at 1380–1190 cm–1. Table 2 contains Z factor values for the characteristic band at 1452 cm–1.
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THE INFLUENCE OF FULLERENE ADDITIVES
particles commensurate with polystyrene molecules (~10 nm). The micro level was separate polystyrene and fullerene molecules. 0), polystyrene and fullerene At short times (tk molecules predominated in the system. Primary aggregates formed during the whole tk interval. Secondary aggregates largely appeared at the end of the tk interval, when spheroids inevitably came into contact with each other because of a decrease in the volume of the layer. We were unable to estimate the ψi (l, tk) function for secondary aggregates. As concerns the ψi (l, tk) function for primary aggregates, the following conclusions could be drawn. Since the size of the smallest observed aggregate was commensurate with the size of the polystyrene molecule, it could be assumed that aggregation started with dimers, and
I/I0 0.8
0.4 1
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2
J i = J 0 [ ( c/c 0 ) – ( c k /c 0 ) ]. 2
0
0.1
0.3
0.5 θ, rad
2
(6)
Here, J0 is the specific frequency of the formation of dimers at t = 0, c0 and c are the initial and current concentrations of polystyrene molecules in solution, and ck is the concentration at which the rate of dimer formation was compared with the rate of their decomposition. Primary aggregates grew under the conditions ψi (l, 0) = 0 and
Fig. 3. X-ray patterns of films; Φ = (1) 0 and (2) 3.5 × 10–4.
DISCUSSION
∞
It follows from the electron microscopic data and Eq. (5) that the films had a three-level hierarchical structure. Its macro level consisted of secondary aggregates of spheroids stuck together. They formed the framework of the films, the presence of which follows from Eq. (5) (in the absence of a framework, film thickness would be independent of Φ, which contradicts Eq. (5)). The meso level consisted of spheroids, which were primary aggregates of polystyrene and fullerene molecules. This follows from the presence of ~20 nm
π 3 c = c 0 – --- ρ A l ψ i ( l, t ) dl, 6
∫
where ρA is the number of polymer molecules in unit volume of aggregates and l0 = 20 nm. Polystyrene molecules attached to and detached from aggregates independently of each other; therefore, G = a 21 ω 0 ( c – c k ),
D i /G i = a 21 ,
where ω0 is the frequency of attachment at t = 0.
log(I/I0) 2.00
1.95
1.90
1.85 2
1
1.80 0.6
0.7
0.8
0.9 log(S/S0)
Fig. 4. I(S) function in logarithmic coordinates over the S/S0 range 0.01–0.07 rad at Φ = (1) 0 and (2) 3.5 × 10–4. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A
(7)
l0
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(8)
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ALEKSEEVA et al. 1 2
3
~ ~
3500
3000
2000
1500
1000
500 ν, Òm–1
Fig. 5. IR spectra of polystyrene films at Φ = (1) 0 and (2) 3.5 × 10–4. (3) Spectrum of a layer of fullerene particles.
Secondary aggregates formed much more slowly, and the condition Qij = 0. (9) was satisfied during the main period of time. The a21 and A = [ω0ck/(I0ρ)]1/3 values were as listed in Table 1. The coincidence of the solution to (2) and (3) with the experimental data (Fig. 2) under conditions (6)–(9) and at a21 and A values given in Table 1 substantiates the validity of these conclusions. This solution was obtained by numerical methods following the algorithms described in [21]. Its correspondence with experiment is likely not fortuitous, as follows from the closeness of the a21 values to the size of the polystyrene molecule. The conclusion can be drawn that the formation of primary aggregates from polystyrene molecules at l > l0 = 20 nm can be described by the equation ∂ψ ∂ 1 ∂ – --------i = a 21 ---- ω 0 ψ i – --- a 21 ---- ( ω 0 ψ i ) . ∂l 2 ∂l ∂t
(10)
Equation (10) is the main kinetic equation at the meso kinetic level. We see that a continuum description of the meso level was possible even to molecular sizes. The Df and Table 2. Spectral characteristics of unmodified polystyrene films and films modified with fullerene Φ
D1452
D1452 /D906
Z
0 3.5 × 10–4
5.75 2.19
14.67 7.48
1 0.51
a21 parameters (Table 1) show that the properties of polystyrene molecules transferred into aggregates change as follows. According to [22, 23], the Df exponent characterizes the main type of packing of polymeric molecule chains. Df 1 if chains are arranged predominantly parallel to each other, and Df 3 if chains form a quasi-homogeneous coil. In our films, intramolecular chain packings were different. The Df exponent, however, remained constant over a fairly wide range of S values for every film (Fig. 4), which was indicative of similar packings of all given film particles. In films without fullerenes (Df = 1.1), packing of straightened chains parallel to each other predominated. This shows that a polystyrene molecule, which had the shape of a coil in solution, straightened and stretched itself along the surface of an aggregate when attached to it. In the case of complete “surface” straightening, the a21 parameter should be commensurate with the diameter of polystyrene chain “cross section,” which was indeed the case (a21 = 0.5 nm). It follows that polystyrene molecules transferred from solution onto the surface of aggregates changed their configuration and settled along aggregate surfaces. At Φ = 3.5 × 10–4 (one fullerene per 7–10 polystyrene molecules), the addition to aggregates occurred similarly, as follows from the a21 parameter value. However, under the influence of fullerene molecules, polystyrene molecules straightened with the formation of ordering elements in the arrangement of chains. Ordering occurred in two steps. At the first short-term stage, chains were arranged with elements of twodimensional ordering, and the exponent Df increased to
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Df = 1.7. At the second stage, chains assembled into nanocrystals with an interplanar distance of 0.39 nm; that is, the nanocrystallization of polystyrene occurred. Nanocrystallization developed slowly, and, in time tk, only part of molecules could be crystallized into aggregates, as is seen from the X-ray diffraction pattern, Fig. 3. The active centers of crystallization were fullerene molecules. At 3.5 × 10–4, the number of fullerene molecules was too small for each of them to induce ordering of one polystyrene molecule. It is likely that a process similar to relay crystallization occurred during aggregation [24]. At Φ = 1.0 × 10–3, the configuration of molecules on the surface was essentially different, which manifested itself by an increase in the a21 parameter. This increase substantiates the role played by fullerenes as modifiers of the molecular structure of polystyrene. As follows from Table 2, the relative intensity of the IR band at 1452 cm–1 decreases in the spectra of polystyrene films modified with fullerenes (the Z factor lowers). Changes in the spectra of modified films compared with the initial samples are likely caused by the influence of fullerene on the orientation of polystyrene chains with respect to each other. We believe that the results of this work will be of use for solving problems of the kinetics of formation of polymeric solids [25] and the behavior of fullerenes extensively used in medicine [26, 27]. ACKNOWLEDGMENTS The authors thank V.I. Korobkov for detailed discussions and valuable comments. REFERENCES 1. Hierarchical Structures in Biology as a Guide for New Material Technology, Ed. by D. A. Tirrell (National Acad. Press, Washington, DC, 1994). 2. D. Braga and F. Czepioni, Acc. Chem. Res. 27 (1), 51 (1994). 3. Handbook of Nanostructured Materials and Nanotechnology, Vol. 5: Organics, Polymer and Biological Compounds, Ed. by H. S. Nalws (Academic, Boston, 2000). 4. J. Feder, Fractals (Plenum Press, New York, 1988; Mir, Moscow, 1991). 5. P. Meakin and R. Jullien, J. Chem. Phys. 89, 246 (1988).
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A
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6. H. J. Herrman, P. Steuter, and D. P. Landay, J. Phys. A 16, 1221 (1983). 7. B. M. Smirnov, Usp. Fiz. Nauk 163 (7), 51 (1993) [Phys. Usp. 36, 592 (1993)]. 8. Polymer Colloids, Ed. by J. W. Goodwin and D. J. Buscall (Academic, New York, 1995). 9. J. D. Jornpoulos, P. R. Villeineuve, and S. Fan, Nature 386, 143 (1997). 10. I. V. Melikhov, A. S. Kelebeev, and S. J. Basic, J. Colloid Interface Sci. 112 (1), 54 (1986). 11. I. V. Melikhov and V. E. Bozhevolnov, J. Nanopart. Res. 5 (5–6), 465 (2003). 12. I. V. Melikhov, Physicochemical Evolution of Solid Matter (Binom, Moscow, 2006) [in Russian]. 13. D. V. Konarev and G. N. Lyubovskaya, Usp. Khim. 68 (1), 22 (1999). 14. M. A. Sibileva, E. V. Tarasova, and N. I. Matveeva, Zh. Fiz. Khim. 78 (4), 626 (2004) [Russ. J. Phys. Chem. 78, 526 (2004)]. 15. G. P. Okatova and N. A. Svidunovich, Ross. Khim. Zh. 50 (1), 68 (2006). 16. E. T. White and P. G. Whright, Chem. Eng. Prog. Symp. 67, 81 (1971). 17. I. V. Melikhov and P. G. Pamiatnikh, J. Cryst. Growth 102, 885 (1990). 18. W. Kratschmer and D. R. Huffman, Phil. Trans. Roy. Soc. A London 343, 33 (1993). 19. A. Guinier, X-Ray Diffraction: In Crystal, Imperfect Crystal, and Amorphous Bodies (Dover, New York, 1994). 20. A. Smith, Applied IR-Spectroscopy (Wiley, New York, 1979; Mir, Moscow, 1982). 21. L. B. Berliner and I. V. Melikhov, Teor. Osn. Khim. Tekhnol. 19 (1), 24 (1985). 22. R. Zhyul’en, Usp. Fiz. Nauk 157 (2), 339 (1989). 23. V. G. Baranov, S. Ya. Frenkel’, and Yu. V. Brestkin, Dokl. Akad. Nauk SSSR 290, 369 (1986). 24. I. V. Melikhov, V. F. Komarov, and V. Kibal’chits, Dokl. Akad. Nauk SSSR 256, 1406 (1981). 25. M. G. Krakovyak, T. N. Nekrasova, T. D. Arsen’eva, and E. V. Anufrieva, Vysokomol. Soedin. B 44, 1853 (2002) [Polymer Sci. B 44, 271 (2002)]. 26. B. M. Ginzburg, E. Yu. Melenevskaya, A. V. Novoselova, et al., Vysokomol. Soedin. A 46, 295 (2004) [Polymer Sci. A 46, 169 (2004)]. 27. B. M. Ginzburg, Sh. Tuichiev, S. Kh. Tabarov, et al., Zh. Tekh. Fiz. 75 (11), 65 (2005) [Tech. Phys. 50, 1458 (2005)].
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