8964
Langmuir 2008, 24, 8964-8970
Determination of the Size, Concentration, and Refractive Index of Silica Nanoparticles from Turbidity Spectra Boris N. Khlebtsov,† Vitaly A. Khanadeev,‡ and Nikolai G. Khlebtsov*,†,‡ Institute of Biochemistry and Physiology of Plants and Microorganisms, Russian Academy of Sciences, 13 Prospekt EntuziastoV, SaratoV 410049, Russia, and SaratoV State UniVersity, 83 Ulitsa Astrakhanskaya, SaratoV 410026, Russia
Langmuir 2008.24:8964-8970. Downloaded from pubs.acs.org by KAROLINSKA INST on 01/28/19. For personal use only.
ReceiVed March 31, 2008. ReVised Manuscript ReceiVed May 11, 2008 The size and concentration of silica cores determine the size and concentration of silica/gold nanoshells in final preparations. Until now, the concentration of silica/gold nanoshells with Sto¨ber’s silica core has been evaluated through the material balance assumption. Here, we describe a method for simultaneous determination of the average size and concentration of silica nanospheres from turbidity spectra measured within the 400-600 nm spectral band. As the refractive index of silica nanoparticles is the key input parameter for optical determination of their concentration, we propose an optical method and provide experimental data on a direct determination of the refractive index of silica particles n ) 1.475 ( 0.005. Finally, we exemplify our method by determining the particle size and concentration for 10 samples and compare the results with transmission electron microscopy (TEM), atomic force microscopy (AFM), and dynamic light scattering data.
Introduction In the past few years, gold nanoshells (NSs) have attracted interest as novel plasmon-resonant structures for various applications to nanobiotechnology.1,2 These particles consist of a spherical silica core covered with a thin (15-30 nm) gold shell, which ensures both convenient surface bioconjugation with molecular probes and remarkable plasmon-resonant optical properties. It has been recognized that NSs provide an efficient platform for analytical biosensing,3–5 integrated applications to the photothermal therapy6,7 and optical imaging of cancer cells,8–10 optical coherent tomography,11 and diffusion-wave spectroscopy.12 In contrast to usual colloidal gold particles, the absorption and scattering plasmon resonance of NSs can easily be tuned from the visible (VIS) to the near-infrared (NIR) spectral band * To whom correspondence should be addressed. E-mail: khlebtsov@ ibppm.sgu.ru. † Russian Academy of Sciences. ‡ Saratov State University. (1) Hirsch, L. R.; Gobin, A. M.; Lowery, A. R.; Tam, F.; Drezek, R.; Halas, N. J.; West, J. L. Ann. Biomed. Eng. 2006, 34, 15–22. (2) Kalele, S.; Gosavi, S. W.; Urban, J.; Kulkarni, S. K. Curr. Sci. 2006, 91, 1038–1052. (3) Hirsch, L.; Jackson, J. B.; Lee, M.; Halas, N.; West, J. Anal. Chem. 2003, 75, 2377–2381. (4) Wang, Y.; Qian, W.; Tan, Y.; Ding, S. Biosens. Bioelectron. 2008, 23, 1166–1170. (5) Khlebtsov, B. N.; Dykman, L. A.; Bogatyrev, V. A.; Zharov, V. P.; Khlebtsov, N. G. Nanoscale Res. Lett. 2007, 2, 6–11. (6) Hirsch, L.; Stafford, R. J.; Bankson, J. A.; Sershen, S. R.; Rivera, B.; Price, R. E.; Hazle, J. D.; Halas, N.; West, J. Proc. Natl. Acad. Sci. U.S.A. 2003, 23, 13549–13554. (7) Khlebtsov, B. N.; Zharov, V. P.; Melnikov, A. G.; Tuchin, V. V.; Khlebtsov, N. G. Nanotechnology 2006, 17, 5267–5179. (8) Loo, C.; Lin, A.; Hirsch, L.; Lee, M.; Barton, J.; Halas, N.; West, J.; Drezek, R. Technol. Cancer Res. Treat. 2004, 3, 33–40. (9) (a) Loo, C.; Lowery, A.; Halas, N.; West, J.; Drezek, R. Nano Lett. 2005, 5, 709–711. (b) Loo, C.; Hirsch, L.; Lee, M.; Chang, E.; West, J.; Halas, N.; Drezek, R. Opt. Lett. 2005, 30, 1012–1014. (10) Park, J.; Estrada, A.; Sharp, K.; Sang, K.; Schwartz, J. A.; Smith, D. K.; Coleman, Ch.; Payne, J.D.; Korgel, B. A.; Dunn, A. K.; Tunnell, J. W. Opt. Express 2008, 16, 1590–1599. (11) (a) Lee, T. M.; Oldenburg, A. L.; Sitafalwalla, S.; Marks, D. L.; Luo, W.; Toublan, F. J.-J.; Suslick, K. S.; Boppart, S. A. Opt. Lett. 2003, 28, 1546–1548. (b) Zagainova, E. V.; Shirmanova, V. V.; Kamenskii, V. A.; Kirllin, M. Yu.; Orlova, A. G.; Balalaeva, I. V.; Khlebtsov, B. N.; Sergeev, A. M. Russ. Nanotechnol. 2007, 2, 135-143 (in Russian).
by varying the core/shell geometry.13,14 The resonance absorption and scattering efficiency of NSs exceeds that of colloidal gold particles by more than 1 order, thus having the advantage of colloidal gold as labels for optical imaging of biospecific interactions. An accurate determination of the size and concentration of NSs is essential for most biomedical applications of NSs. For instance, the size and concentration of nanoparticles are crucial parameters determining their uptake by living cells15 and their circulation and biodistribution in living bodies.16 Whereas transmission electron microscopy (TEM) is a reliable method for sizing of metal nanoparticles, there are no analogous timetested and convenient tools for concentration measurements. As a few examples, one can point out the paper by Green at al.17 on small-angle X-ray and dynamic light scattering studies performed to monitor the nucleation of Sto¨ber’s silica nanoparticles, and studies of concentrated samples by using backscattering,18 diffuse photon density,19 and fluorescence20 techniques. Here, we consider gold NSs, which are fabricated in many laboratories by a two-step protocol. First, silica nanospheres are prepared, and then gold nanoshells are formed by functionalization of the silica surface with fine (1-3 nm) gold seeds followed by (12) (a) Wu, C.; Liang, X.; Jiang, H. Opt. Commun. 2005, 253, 214–221. (b) Lin, A. W. H.; Lewinski, N. A.; Lee, M. H.; Drezek, R. A. J. Nanopart. Res. 2006, 8, 681–692. (c) Zaman, R. T.; Diagaradjane, P.; Wang, J. C.; Schwartz, J.; Rajaram, N.; Gill-Sharp, K. L.; Cho, S. H.; Rylander, H. G.; Payne, J. D.; Krishnan, S.; Tunnell, J. W. IEEE J. Sel. Top. Quantum Electron. 2007, 13, 1715–1720. (13) Oldenburg, S. J.; Averitt, R. D.; Westcott, S. L.; Halas, N. Chem. Phys. Lett. 1998, 288, 243–247. (14) Khlebtsov, N. G.; Trachuk, L. A.; Melnikov, A. G. Opt. Spectrosc. 2005, 98, 83–90. (15) Jiang, W.; Kim, B. Y. S.; Rutka, J. T.; Chan, W. C. W. Nat. Nanotechnol. 2008, 3, 145–150. (16) De Jong, W. H.; Hagens, W. I.; Krystek, P.; Burger, M. C.; Sips, A. J. A. M.; Geertsma, R. E. Biomaterials 2008, 29, 1912–1919. (17) Green, D. L.; Lin, J. S.; Lam, Y.-F.; Hu, M. Z.-C.; Schaefer, D. W.; Harris, M. T. J. Colloid Interface Sci. 2003, 266, 346–358. (18) (a) Bemer, G. G. Powder Technol. 1978, 20, 133–136. (b) Bos, A. S.; Heerens, J. J. Chem. Eng. Commun. 1982, 16, 301–311. (c) Tontrup, C.; Gruy, F. Powder Technol. 2000, 107, 1–12. (19) Taniguchi, J.; Murata, H.; Okamura, Y. Jpn. J. Appl. Phys., Part 1 2007, 46, 2953–2961. (20) Yoon, Y.; Lueptow, R. M. Colloids Surf., A 2006, 277, 107–110.
10.1021/la8010053 CCC: $40.75 2008 American Chemical Society Published on Web 07/01/2008
Study of Silica Particles Using Turbidity Spectra
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Figure 2. Optical scheme of an attachment for measurement of turbidity spectra with a Specord M-40 spectrophotometer (top view in the horizontal plane): 1, limiting diaphragm; 2, cuvette; 3, slit aperture diaphragm; and 4, photodetector.
Theory
Figure 1. Dependence of the scattering cross section, scattering efficiency, and wavelength exponent on the root-mean-squared diameter dav and size parameter x ) πdavnm/λ. Calculations for polydisperse silica particles in ethanol (n ) 1.475, nm ) 1.364, polydispersity parameter µ ) 20).
reduction of gold atoms on the adsorbed seeds. In fact, it is the size and concentration of the silica cores that determine the size and concentration of NSs in final preparations. As far as we are aware, the paper by Westcott et al.21 is the only report dealing with evaluation of the concentration of NSs and silica particles prepared by Sto¨ber’s method22 (that publication21 was later cited in ref 23 and in other works). However, the concentration of silica particles was evaluated in ref 21 by an ad hoc material balance, that is, by assuming that all of the tetraethyl orthosilicate reacted and that all silica nanoparticles have a density of 2 g/cm3. Clearly, these assumptions need validation for a particular preparation. In principle, the concentration of silica particles can be evaluated by combining the TEM particle size, the optical density measurements, and calculations of the particle extinction cross section, which equals the scattering cross section in this case. However, such an approach uses two independent methods, and, what is more important, one needs to know the refractive index of silica particles. We did not find any direct estimations of this parameter except for data available for bulk silica samples,24 whose refractive index shows significant variations depending on the technology used (one can also note an approximate contrast variation method25 which was derived from the Rayleigh-GansDebye approximation and applied to polystyrene latex, silica, and casein micelles). Thus, to the best of our knowledge, there are no available optical methods for a simple simultaneous determination of the size, concentration, and refractive index of silica nanoparticles from spectrophotometric data (turbidity spectra). The primary goal of this work was to fill this gap. Here, we describe a method based on measurements of turbidity spectra at 400-600 nm wavelengths. As noted above, the refractive index of silica nanoparticles is an important input parameter for optical determination of their concentration. In this work, we propose an optical method and provide the first, to the best of our knowledge, experimental data on a direct and accurate determination of the refractive index of silica particles prepared by Sto¨ber’s method.22 (21) Westcott, S. L.; Oldenburg, S. J.; Lee, T. R.; Halas, N. J. Langmuir 1998, 14, 5396–5401. (22) Sto¨ber, W.; Fink, A.; Bohn, J. J. Colloid Interface Sci. 1968, 26, 62–66. (23) Pham, T.; Jackson, J. B.; Halas, N. J.; Lee, T. R. Langmuir 2002, 18, 4915–4920. (24) http://www.crystran.co.uk/products.asp?productid)73. (25) Griffin, M.c. A.; Griffin, W. G. J. Colloid Interface Sci. 1985, 104, 409– 415.
The turbidity spectra method has been known for a long time, starting with the pioneering studies of Heller.26 For details, the readers are referred to the reviews27–29 and the book.30 Here, we restrict ourselves by a short summary. The optical density (extinction) A or turbidity τ ) 2.3A/l spectrum of a suspension with the layer thickness l can be approximated by a power law for a thin visible spectral interval (usually, from 400 to 600 nm27,29):
τ ) 2.3A ⁄ l ∼ λ-w
(1)
where λ is the wavelength in vacuum and w is the wavelength exponent. Experimentally, w is determined from the linear approximation of spectra plotted in the double-logarithmic coordinates:
w ) -∂ log τ ⁄ ∂ log λ = ∆ log τ ⁄ ∆ log λ
(2)
In the single-scattering approximation, the turbidity τ is proportional to the number concentration N of particles and their scattering cross section Csca(x,m):
τ ) NCsca(x, m) ) Nπ(d ⁄ 2)2Qsca(x, m)
(3)
where the scattering cross section Csca and the scattering efficiency Qsca are functions of the particle size parameter x ) πdnm/λ, d is the sphere or the equivolume sphere diameter, nm is the absolute refractive index of the surrounding medium, m ) n/nm is the relative refractive index, and n is the absolute refractive index of particles. Let us assume for a moment that n(λ) ≈ const and nm(λ) ≈ const within the ∆λ ) 200 nm (600-400 nm) spectral band. From eqs 2 and 3, we have
w ≈ w0 ) -∂ ln(Q) ⁄ ∂ ln(λ) ) ∂ ln(Q) ⁄ ∂ ln(x)
(4)
Thus, eq 2 determines an experimental value of w, whereas eq 4 relates the wavelength exponent to the average particle diameter d by plotting theoretical functions (4) versus d. After determining the average particle size, the number concentration N or the mass-volume concentration c can be calculated as follows:
N ) τ ⁄ Csca,
c ) φF(4πa3 ⁄ 3)N ≡ φF(4πa3 ⁄ 3)τ ⁄ Csca (5)
where F and φ are the particle matter density and volume fraction, respectively. For silica particles, φ should be close to 1, whereas for porous particles it may be less than 1 (for immune complexes, e.g., φ is only about 0.331). (26) (a) Heller, W.; Bhatnagar, H. L.; Nakagaki, M. J. Chem. Phys. 1962, 36, 1163–1170. (b) Heller, W. J. Chem. Phys. 1964, 40, 2700–2705. (27) Shchyogolev, S. Yu.; Khlebtsov, N. G. In Colloid and Molecular Electrooptics; Jennings, B. R., Stoylov, S. P., Eds.; IOP Publishing: Bristol and Philadelphia, 1992; pp. 141-146. (28) Crawley, G.; Cournil, M.; Di Benedetto, D. Powder Technol. 1997, 91, 197–208. (29) (a) Shchyogolev, S. Yu. J. Biomed. Opt. 1999, 4, 490–503. (b) Holoubek, J. J. Quant. Spectrosc. Radiat. Transfer 2007, 106, 104–121. (30) Klenin, V. J. Thermodynamics of Systems Containing Flexible Chain Polymers; Elsevier: Amsterdam, 1999. (31) Khlebtsov, B. N.; Burygin, G. L.; Matora, L. Yu.; Shchyogolev, S. Yu.; Khlebtsov, N. G. Biochim. Biophys. Acta 2004, 1670, 199–207.
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Figure 3. (a) TEM images of silica particles with an average diameter dTEM of 139 nm and (b) DLS intensity distribution with an average diameter of 138 nm. Panels (c) and (d) show TEM histograms for samples with dTEM ) 114 and 139 nm, together with normalized gamma-distributions calculated for a polydispersity parameter µ of 100. Note that the relative distribution width by TEM data ∆dmax/2/dm = 0.2 is essentially less than the corresponding DLS value ∆dmax/2/dm = 0.7.
Figure 4. Dependence of the extinction ratio, A(nm)/A(nm0), on the refractive index of immersion media nm. Symbols represent experimental data for 90 nm (a) and 215 nm (b) silica particles at wavelengths of 400 and 500 nm. The theoretical curves were calculated by Mie theory for gammadistribution of silica particles with a polydispersity parameter µ of 100 and refractive indices of particles n of 1.46-1.50 (step, 0.01). Most of the experimental points agree with calculations at n ) 1.48 for nm g 1.4.
The above scheme can be considered as a simplified version of the inverse light scattering problem solution32 for a dilute suspension of monodisperse spherical particles. A closely related “turbidity ratio method” has been developed in refs 33–35 Generalization of these approaches to the polydisperse particles can be found in refs 28 and 36–38 (see also the reviews in refs 27–29 for more details concerning the multiple39,40 and small(32) Shifrin, K. S.; Tonna, G. AdVances in Geophysis; Academic Press: New York, 1993, 34, 175-252. (33) Dezˇelic´, G.; Dezˇelic´, N.; Tezˇak, B. J. Colloid Sci. 1963, 18, 888–892. (34) Sedlacˇek, B. Collect. Czech. Chem. Commun. 1967, 32, 1374–1389. (35) Hosono, M.; Sugii, S.; Kusudo, O.; Tsuji, W. Bull. Inst. Chem. Res., Kyoto UniV. 1973, 51, 104–117. (36) Zollars, R. L. J. Colloid Interface Sci. 1980, 74, 163–172. (37) Melik, D. H.; Fogler, H. S. J. Colloid Interface Sci. 1983, 92, 161–180. (38) Antalik, J.; Liska, M.; Vavra, J. Ceram.-Silik. 1994, 38, 31–34. (39) Khlebtsov, N. G. J. Appl. Spectrosc. 1984, 40, 243–247. (40) Apfel, U.; Ho¨rner, K. D.; Ballauff, M. Langmuir 1995, 11, 3401–3407. (41) Deepak, A.; Box, M. A. Appl. Opt. 1978, 17, 2900-2908; 31693176.
angle41,42 scattering contributions, the particle shape,43 instrumental errors,44 and other effects45). For the goals of this paper, the spectral dependence of refractive indices46,47 is the most important effect. This can be illustrated by the following simple example. Let us consider small dielectric spheres, say, polystyrene beads in water. From the well-known classic Rayleigh law,48 Qsca ∼ Isca ∼ λ-4, one would expect that limxf0 w = 4 for very small particles. Surprisingly enough, an accurate experimental measurement26,47 results in the following (42) Khlebtsov, N. G.; Melnikov, A. G. J. Appl. Spectrosc. 1987, 47, 807–810. (43) (a) Khlebtsov, N. G.; Shchegolev, S. Yu. Opt. Spectrosc. 1977, 42, 549-552; 663-666. (b) Shchegolev, S. Yu.; Khlebtsov, N. G.; Klenin, V. I. Opt. Spectrosc. 1977, 43, 82–86. (44) Khlebtsov, N. G.; Shchygolev, S. Yu.; Klenin, V. I.; Frenkel, S. Ya. Opt. Spectrosc. 1978, 45, 654–658. (45) Shmakov, S. L. Opt. Spectrosc. 2001, 91, 283-287; 2003, 95, 461-463; 2004, 96, 275-280. (46) Cancellieri, A.; Frontali, C.; Gratton, E. Biopolymers 1974, 13, 735–743. (47) Khlebtsov, N. G.; Melnikov, A. G. J. Appl. Spectrosc. 1992, 56, 268–273.
Study of Silica Particles Using Turbidity Spectra
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Figure 5. Extinction spectra of 90 nm (a) and 215 nm (b) silica particles suspended in six immersion media with refractive indices increasing from w/4 1.362 to 1.455. Panels (c) and (d) show the extrapolation plots A/εm versus εm for determination of the particle refractive index. The curves for 400 nm include possible dispersion effects. The average extrapolation value equals n ) ε ) 1.472 ( 0.005.
unexpected limit: limxf0 w = 4.35. This contradiction can be explained by assuming that the refractive indices n(λ) and nm(λ) are decreasing functions of the wavelength because of the usual dispersion law. The experimental (w, eq 2) and theoretical (w0, eq 4) wavelength exponents can then be related by the following equation:46
w ) w0(1 - χm) -
w0m (χ - χm) m-1
(6)
where the dispersion parameters are
χ)
d ln n , d ln λ
χm )
d ln nm d ln λ
(7)
Evaluation of these dispersion parameters for various systems can be found in refs 29 and 47. For all calculations, we used Mie theory for polydisperse particles with the normalized gamma-distribution
h(d¯) ) Hd¯µ exp(-∆µd¯),
H)
∫
d¯max 2 x d¯min
h(x) dx
(8)
where dj ) d/dav is the normalized particle diameter, H is the normalization constant, dav is the average diameter, µ is the polydispersity parameter, and the normalization parameter ∆µ depends on the choice of dav. For example, ∆µ ) µ if dav is the modal diameter dm, and ∆µ ) [(µ+1)(µ+2)]1/2 if dav ) (〈d2〉)1/2 is the root-mean-squared diameter. In the case of small particles, the most appropriate average size is defined by the following equation47
dav ≡ d0 ) 〈dw+4 ⁄ dw+2 〉1⁄2
(9)
where the angular brackets designate averaging over the particle size distribution and w is the measured wavelength exponent of a polydisperse suspension. The polydispersity parameter µ can
be expressed through the relative dispersion width (∆d) at half of the distribution maximum, ∆d/dm ) 2.48/µ. Figure 1 gives a general impression about variations in the average scattering cross section 〈Csca〉, the polydisperse scattering efficiency Qsca ) 〈Csca〉/π(dav/2)2, and the polydisperse wavelength exponent w with the average size parameter x ) πdavnm/λ (bottom abscissa axis) or the average diameter dav (top abscissa axis). Here, dav is the root-mean-squared diameter, the refractive indices n ) 1.475 and nm ) 1.364 correspond to silica particles in ethanol (see below), and the polydispersity parameter µ equals 20 according to our TEM data for samples with maximal dispersion of sizes. In fact, only a small initial part of the plots in Figure 1 is of interest for silica nanoparticles with diameters of less than 200 nm.
Experimental Section The following reagents were used in the experiments: tetraethyl orthosilicate (TEOS, Aldrich), and absolute ethanol (ET0016, Scharlau Chem. S.A., Spain). Aqua ammonia (25%) and dimethyl sulfoxide (DMSO, Reachim Co., Russia) were of analytical grade. All experiments used triply distilled water. For preparation of 100 nm silica nanoparticles according to the method,22 0.62 mL of 25% aqua ammonia was added to 10 mL of absolute ethanol, and the solution was magnetically stirred (500 rpm) for 5 min at room temperature. Then, 0.3 mL of TEOS was added dropwise, and the suspension was stirred for 1 h and was then left overnight without stirring. For the preparation of particles of other sizes, the amount of added aqueous ammonia was varied as described in ref 49 and by using other recent improvements of Sto¨ber’s method.50–52 (48) Van de Hulst, H. C. Light Scattering by Small Particles; Wiley: NewYork, 1957. (49) Khlebtsov, B. N.; Bogatyrev, V. A.; Dykman, L. A.; Khlebtsov, N. G. Opt. Spectrosc. 2007, 102, 233–241.
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Figure 6. Variations in the wavelength exponent of 90 nm (a) and 215 nm (b) silica suspensions with an increase in the DMSO content in terms of the refractive index nm. The circles and triangles show independent runs, and the squares present calculations for a simple model, assuming an increase in the size parameter (x ∼ nm) without any aggregation. The dashed line in panel (a) shows a reversible behavior of the wavelength exponent after addition of 2 mL (50% [v/v]) of ethanol.
Figure 7. (a) Calibration plots for determination of the average particle size and number concentration N1 per jτ ) 1 cm-1 for polydisperse silica nanospheres in ethanol. The circles represent the TEM diameter and the STT wavelength exponent. Panel (b) shows turbidity spectra for 160 nm silica particles (two measurement runs). The insets show the calculated average STT size and concentration and the TEM image of 160 nm silica (large particles), together with a 100 nm polystyrene latex standard sample (Metachem Diagnostics, Ltd., U.K.; small particles).
Dynamic light scattering (DLS) measurements were carried out with a PotoCorr FS instrument (Photo Corr Inc., Russia). TEM characterization was made with a Libra-120 transmission electron microscope (Carl Zeiss, Germany). Atomic force microscopy (AFM) measurements were made with a Solver Bio AFM instrument (NTMDT, Russia). The refractive indices of the immersion media were measured with an IRF-23 Abbe refractometer (LOMO, Russia; the measurement accuracy was about (0.0005). Extinction spectra were recorded with UV-VIS Specord BS-250 (Analytik Jena, Germany) and Specord M-40 (Carl Zeiss, Germany) spectrophotometers. Turbidity spectra were measured with an attachment53 to the Specord M-40 spectrophotometer (Figure 2, top view in the horizontal plane). The converging light beam passes through input diaphragm 1 and cuvette 2 with a suspension, forming an image of a monochromator spectral slit in the plane of the adjustable aperture slit diaphragm 3. The width of the aperture diaphragm is 0.1-0.5 mm and defines the small-angle scattering flux reaching photodetector 4. In the vertical plane, the beam size is constant (approximately 5 mm). Figure 3 shows a typical TEM image for a sample with an average TEM diameter of 139 nm, which is in excellent agreement with the DLS diameter of 138 nm. However, the DLS size distribution width is significantly overestimated, as compared with the TEM histograms (panels c and d). This effect is known for DLS measurements of thin (50) Bogush, G. H.; Tracy, M. A.; Zukoski, C. F., IV J. Non-Cryst. Solids 1988, 104, 95–106. (51) Park, S. K.; Kim, K. D.; Kim, H. T. Colloids Surf., A 2002, 197, 7–17. (52) Rao, K. S.; El-Hami, K.; Kodaki, T.; Matsushige, K.; Makino, K. J. Colloid Interface Sci. 2005, 289, 125–131. (53) Khlebtsov, N. G. Appl. Opt. 1996, 35, 4261–4270.
particle size distributions.54 It follows from panels (c) and (d) that the typical values of the polydispersity parameter µ are close to 100. This conclusion has also been confirmed by TEM analysis of 80 and 160 nm silica samples.
Results and Discussion Determination of the Refractive Index of Silica Particles. To determine the refractive index of silica particles, we chose the immersion-media approach,34,55 in which the light scattering properties of particles are probed in a set of immersion media with refractive indices approaching that of the particles. With the scattering cross section of dielectric spheres varying as48 (n2 - nm2)2, the optical density or turbidity approaches zero with n f nm. For silica particles in ethanol, DMSO was found to be a suitable immersion liquid because of the high refractive index (1.455) and miscibility with ethanol. All refractive index determinations were carried out with several 90 and 215 nm silica particle suspensions. The actual average particle diameters were different for TEM, AFM, DLS, and spectroturbidimetry (STT) measurements and for sample preparations. For simplicity, we shall refer to these samples as 90 and 215 nm silica. A typical experimental protocol was as follows. A 1 mL portion of a silica suspension was mixed with 3.0, 2.4, 1.8, 1.2, 0.6, and (54) Berne, B. J.; Pecora, R. Dynamic Light Scattering: With Application to Chemistry, Biology, and Physics; Dover Publications: Mineola, NY, 2002. (55) Koga, S.; Fujita, T. J. Gen. Appl. Microbiol. 1961, 7, 253–261.
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Table 1. Data of TEM, DLS, AFM, and STT Analyses of Silica Samples sample no.
diameter TEM [nm]
diameter DLS/ AFM [nm]
1
92 ( 8
2
114 ( 12
3 4 5 6 7
NAb NA NA 119 ( 14 139 ( 12
8 9
NA 160 ( 17
10
217 ( 20
86 ( 15 95 ( 13 108 ( 24 133 ( 15 NA NA NA 125 ( 35 138 ( 47 150 ( 13 NA 143 ( 58 162 ( 12 216 ( 100 NA
a
Calculated with µ ) 20.
b
wavelength exponent
turbidity τ500 [cm-1]
diameter STT [nm]
number concentration N × 10-12 [cm-3]
mass-volume concentration c [mg/cm3]
3.813
1.3
92.4
9.8
6.9
3.660
2.2
111
6.1
7.4
3.700 3.753 3.743 3.355 3.282
1.9 1.4 1.8 2.64 3.4
106 99.9 101.2 122 147
6.6 6.8 8.2 4.3 2.1
7.1 6.0 7.5 7.0 6.0
3.225 3.177
4.4 4.5
152 156
2.3 2.0
7.3 7.1
2.635
10.1
218
0.6
7.2a
Not available.
0 mL of ethanol, with this being followed by addition of 0, 0.6, 1.2, 1.8, 2.4, and 3.0 mL of DMSO. The refractive index of the mixtures was roughly varied from 1.364 to 1.450 (the actual values were accurately measured with the IRF-23 refractometer). The turbidity spectra were then measured for the 400-600 nm spectral interval. For experimental data processing, we used two approaches based on the following scaling relationship,26 which holds for the extinction cross section or optical density of diluted suspensions with small (d < λ/2) particles:
(
τ ∼ Csca ∼ xw
) (
ε - εm 2 w ε - εm ∼ εm ε + 2εm ε + 2εm
)
2
(10)
where the dielectric functions ε ) n2 and εm ) nm2 have been used instead of refractive indices. It follows from eq 10 that the ratio of optical densities, A(εm)/A(εm0) ≡ A(nm)/A(nm), for two immersion media (say, with a current εm and an initial εm ) εm0 ) (1.364)2) should depend on the dielectric permittivity ε or on the refractive index n ) ε of particles. Thus, we can calculate these ratios as a function of nm ) εm for different constant n ) ε and then compare these plots with the experimental data to find the best-fitting n ) ε. Figure 4 shows theoretical dependences of the extinction ratio, A(nm)/A(nm0), on the refractive index of immersion media (ethanol + DMSO), nm. The curves were calculated by Mie theory for polydisperse spherical dielectric particles with n ) 1.46-1.50 (step, 0.01) and µ ) 100 (approximation of TEM data). The symbols represent experimental points for 90 and 215 nm silica nanospheres. Clearly, most of these points are grouped near the theoretical curves with a refractive index n of 1.48, when the refractive index of the media becomes greater than 1.4. This conclusion holds for both particle sizes. In general, the extinction ratio method seems to be not quite accurate because of evident dispersion of experimental points around different theoretical curves with unrealistic refractive indices n g 1.48. There are several possible reasons that could explain these drawbacks. First, the approximation (eq 10) may be not accurate for the largest particles (about 200 nm in diameter) and for polydisperse ensembles. Second, the presence of a small fraction of aggregated particles also may violate approximation 10. In any case, we describe below another approach to determine the refractive index of silica particles. (56) Suzuki, N.; Tomita, Y. Appl. Opt. 2004, 43, 2125–2129. (57) Scholz, S.; Althues, H.; Kaskel, S. Colloid Polym. Sci. 2007, 285, 1645– 1653.
The second approach is based on a slightly modified version of eq 10, which can be rewritten as
√A(λ) ⁄ εmw⁄4 ∼
(
ε - εm ε + 2εm
)
(11)
Suppose we have measured the wavelength exponent w and extinction at an average wavelength λj (e.g., at λj ) 500 nm) for a set of immersion media. Then, if we shall plot the (A(λj))1/2/εw/4 m quantity versus the dielectric permittivity of the immersion media, these plots will approach zero at εm f ε. Thus, the extrapolation points should give the expected permittivity of silica particles or, equivalently, their refractive index. Figure 5 shows experimental realization of this method for 90 and 215 nm silica particles. From both experiments, we found that the average extrapolated refractive index equals n ) ε ) 1.472 ( 0.005. Finally, keeping in mind the data of Figure 4, we come to the following estimation:
〈n 〉 ) 1.475 ( 0.005
(12)
A close inspection of the fitting plots in Figure 5 shows a small increase in the silica refractive index for λ ) 400 nm in comparison with other wavelengths. Specifically, n400 ) 1.472 and n500-600 ) 1.468 for 90 nm particles and n400 ) 1.474 and n500-600 ) 1.471 for 215 nm particles (our measurements did not reveal notable differences between refractive indices for 500-600 nm wavelengths). These data indicate slow spectral dispersion of the silica refractive index consistent with the Sellmeier dispersion equation. In general, our estimation of the average refractive index 1.475 ( 0.005 is somewhat higher than that of fused silica24 n ) 1.46 and Sto¨ber’s particles (n ) 1.4656 and n ) 1.4757). Note that such a small difference in the refractive index input values will result in a significant (about 25% for n ) 1.46) difference in the number concentration, which varies as (n2 - nm2)-2 at a given extinction. Liz-Marza´n et al.58 have studied the optical properties of gold (core)/silica (shell) particles assuming the refractive index of the silica shell to be 1.456. However, for thick silica shells, the experimental minimum of peak intensity was observed at the refractive index of solvent nm = 1.47 (ref 58, Figure 10, top panel), in close agreement with our estimation given by eq 12. To summarize, the above value 〈n〉 ) 1.475 ( 0.005 should be thought as an effective “turbidimetric” refractive index that ensures best agreement between the STT data for the particle size and concentration and the TEM, DLS, AFM, and material balance estimations. (58) Liz-Marza´n, L. M.; Giersig, M.; Mulvaney, P. Langmuir 1996, 12, 4329– 4335.
8970 Langmuir, Vol. 24, No. 16, 2008
Figure 5a and b shows that the wavelength exponent decreases significantly on addition of DMSO and with a corresponding increase in the refractive index of the immersion media. Such a behavior is consistent with plot in Figure 1 for the wavelength exponent, as the size parameter should increase on addition of DMSO. However, only a small part of the wavelength decrease in Figure 4a and b can be attributed to the refractive index increase. Indeed, Figure 6 clearly shows that the experimental variation of the wavelength exponent is not consistent with theoretical calculations, assuming that a progressive addition of DMSO results in a corresponding increase in the refractive index and size parameter without any aggregation. Given the strong dependence of the wavelength exponent on the presence of a small large-particle fraction,47 as well as our experimental observations for the described experiments, we may assume some aggregation of silica particles caused by DMSO addition. Interestingly, addition of ethanol to sample 6 with the maximal DMSO content (S6, Figure 6a) results in a reversion of the wavelength exponent (from 3.1 to 3.61). This indicates that the nature of aggregation is reversible and the structure of formed aggregates is loose. Accordingly, we believe that the possible aggregation cannot affect strongly our results for the refractive index determination of silica nanoparticles. Concerning the possible reasons for DMSO-induced aggregation, we note that DMSO is an aprotic solvent, whereas ethanol and water are typical protic liquids. Therefore, addition of DMSO may affect hydrogen bonds involved in the stabilization of silica particles. Furthermore, it has been shown59 that addition of DMSO to silica suspension decreased the negative surface charge density, thus decreasing the electrostatic stabilization of particles. Determination of the Particle Size and Concentration. Given the average refractive index n ) 1.475 and the polydispersity parameter µ ) 100, we have calculated calibration plots for simple and convenient determination of the average particle size and concentration, with the measured values of the wavelength exponent and turbidity at the average wavelength jτ ) 2.3A500/l (Figure 7a). For simplicity, the concentration curve N1 has been calculated with jτ ) 1 cm-1. For a particular jτ measured, one should simply multiply the number concentration N1 by the measured jτ value. To verify the accuracy of our calibration curve, we show several points that present a combination of the TEM particle sizing and the wavelength exponent measurements. In general, for the 80-250 nm particle diameter range, we have found quite satisfactory agreement between STT, TEM, DLS, and AFM data (see below). Figure 7b presents an example for STT characterization of 160 nm particles (TEM diameter, see the inset in Figure 7b). Results of the particle size and concentration analysis are collected in Table 1. First, we note good agreement between STT diameters and those determined by other methods. Second, (59) Kosmulski, M. J. Colloid Interface Sci. 1996, 179, 128–135.
KhlebtsoV et al.
the mass-volume concentration of silica is close to but somewhat lower (within the 80-100% range) than the material balance concentration of 7.3 mg/mL. Note, that the mass-volume concentrations in Table 1 have been calculated with the silica particle density of 2 g/cm3 reported in ref 21 (see also citations therein). In general, the literature data60 are within 2.0-2.3 g/cm3. Clearly, the use of 2.3 g/cm3 density would result in unacceptable overestimated mass-volume concentrations in drastic disagreement with the material balance. To fit experimental conditions, we would have to take an even more, quite unrealistic value for the refractive index of silica particles. Thus, our choice was a reasonable compromise between these alternatives.
Conclusions We have developed a new version of the immersion method for accurate measurement of the refractive index of silica particles fabricated by Sto¨ber’s22 method. The developed method seems applicable to other systems, provided that a suitable immersion liquid is selected. It should be emphasized that the turbidity spectra can be accurately measured with any commercial spectrophotometer if the particle size is not too large (say, less than 500 nm). Otherwise, one should use some kind of receiving aperture to exclude small-angle scattering effects. From the data in Table 1, one can see that TEM measurements are in excellent agreement with the STT average diameters, whereas the technically more complex and more expensive DLS method gives somewhat worse values with unrealistic dispersions. According to our synthetic protocol, all samples contained the same quantity of TEOS, which is equivalent to a silica mass-volume concentration of 7.3 mg/cm3, provided that all TEOS reacted. The last column of Table 1 shows that this assumption holds with an accuracy of 10-20%. Thus, our estimation of the refractive index n ) 1.475 ( 0.005 seems to be a best-fitting compromise, ensuring fairly accurate determination of both the particle size and the concentration, in comparison with TEM, AFM, and dynamic light scattering data. Acknowledgment. This work was partly supported by grants from RFBR (Nos. 08-02-00399a, 08-02-01074a, and 07-0201434-a). B.N.K. was supported by grants from the President of the Russian Federation (No. MK 2637.2007.2), INTAS YS Fellowship (No. 06-1000014-6421), the Russian Science Support Foundation, and RFBR (Nos. 07-04-00301a and 07-04-00302a). Supporting Information Available: Dependence of the size parameter x, the scattering efficiency Qsca, the scattering cross section 〈Csca〉, the number concentration N × 10-12 (particles per 1 cm3 at turbidity τ500 ) 1 cm-1), the mass-volume concentration c [mg/cm3] (turbidity τ500 ) 1 cm-1), and the wavelength exponent w on the average particle diameter d0. This material is available free of charge via the Internet at http://pubs.acs.org. LA8010053 (60) Patel, I. S.; Schmidt, P. W. J. Appl. Crystallogr. 1971, 4, 50–55.
