Deuterium Exchange of

Colloidal Silica Suspension by Contrast-Variation Small-Angle Neutron. Scattering. Takuya Suzuki, Hitoshi Endo, and Mitsuhiro Shibayama*. Institute fo...
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Langmuir 2008, 24, 4537-4543

4537

Analysis of Surface Structure and Hydrogen/Deuterium Exchange of Colloidal Silica Suspension by Contrast-Variation Small-Angle Neutron Scattering Takuya Suzuki, Hitoshi Endo, and Mitsuhiro Shibayama* Institute for Solid State Physics, The UniVersity of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan ReceiVed December 17, 2007. In Final Form: February 20, 2008 The microscopic surface structure and hydrogen/deuterium exchange effect were investigated by contrast-variation small-angle neutron scattering (CV-SANS) for three different-sized amorphous colloidal silica aqueous suspensions. The results show that the fraction of hydrogen/deuterium exchange per nanoparticle, φH/D, strongly depends on the size of silica nanoparticles. This finding supports that the hydrogen/deuterium exchange occurs exclusively within a finite surface layer of silica nanoparticles, while the inner component remained unchanged. Detailed analyses of the scattering intensity functions led to the estimation of (1) φH/D and (2) the thickness of the surface layer as functions of the particle radius. The surface layer thickness was found to increase from 18 to 35 Å with decreasing the particle radius from 165 to 71.2 Å. The surface area per unit weight of silica estimated with the CV-SANS results are comparable to those reported in the literature.

1. Introduction Colloidal particles have been widely used in both industry and daily life as basic constituents covering areas from commodities such as foods and cosmetics, to advanced materials such as ultrathin membrane films or magnetic materials. They have also been extensively studied in materials science, biochemistry, surface chemistry, and so forth. These wide varieties of applications are due to the fact that colloidal particles can modify the physical properties of the targeting materials by tuning the kinds of colloids, the size and composition, the degree of crystallization, surface structure, and so forth. In the field of material science, representative examples of colloids include slurries, clays, silica colloids, minerals, and Au, Ag, or Pt sols.1,2 Among various kinds of colloidal particles, colloidal silica has been one of the most widely used materials in industry as fillers, abrasives, flocculants, pigments, and insulating films.3-6 These applications are owing not only to the intrinsic properties originating from the shape and size, but also to surface modification. Surface modification is usually carried out via chemical modification of the hydroxyl groups on the silica surface. Therefore, the microstructure of the silica surface including a large number of OH groups greatly influences the physical properties of colloidal silica, and hence the properties of the targeting materials in which the colloidal silica is embedded. There have been several reports that investigated the surface structures of colloidal particles. Zhuravlev investigated the silanol number, ROH, for a fully hydroxylated surface with mass spectrometric analysis and obtained the physicochemical constant, i.e., ROH ) 0.046 ( 0.005 Å-2.7 On the other hand, Yamauchi * Author to whom correspondence should be addressed. E-mail: [email protected]. (1) Xia, Y.; Gates, B.; Yin, Y.; Lu, Y. AdV. Mater. 2000, 12, 693. (2) Grange, J. D. L.; Markham, J. L. Langmuir 1993, 9, 1749. (3) Otterstedet, O. E.; Otterstedet, J.-E. A.; Ekdahl, J. J. Appl. Polym. Sci. 1987, 34, 2575. (4) Arai, Y.; Segawa, H.; Yoshida, K. J. Sol-Gel Sci. Technol. 2004, 32, 79. (5) Vaslin-Reimann, S.; Lafuma, F.; Audebert, R. Colloid Polym. Sci. 1990, 268, 476. (6) Matsumoto, H.; Mizukoshi, T.; Nitta, K.; Minagawa, M.; Tanioka, A.; Yamagata, Y. J. Colloid Interface Sci. 2005, 286, 414. (7) Zhuravlev, L. T. Langmuir 1987, 3, 316.

et al. analyzed the structure of the adsorbed layer of water on a hydrophilic surface of well-defined silica gels under the assumption of geometrical heterogeneity of the surface by Fourier transform near-infrared analysis (FT-NIR).8 They clarified the existence of three adsorbed layers of water molecules and elucidated the number of water molecules showing a decrease of OH fraction as a function of position along the radial direction. However, their methodology had some kind of complication because the mixture of isotopic compound after deuteration was exposed in an atmosphere of high-temperature degassing, resulting in a possible change of the isotopic composition. Recently Christy et al. determined the concentration of silanol groups on silica gel surfaces by attenuation total reflection infrared spectroscopy (ATR-IR) for dried silica pellets before and after D2O substitution. Their methods were rather simple and effective because they did not involve high-temperature degassing. The evaluated values were 0.029-0.036 OH groups/Å2, which is somewhat lower than the value reported by Zhuravlev.7 As for another experimental approach to investigate the surface structure of colloidal silica, Li et al. performed a small-angle X-ray scattering (SAXS) study about colloidal silica and estimated the average core size by considering a core-layer structure.9 Among various methods to analyze the fraction of H/D exchange, contrast-variation small-angle neutron scattering (CVSANS) is one of the most powerful methods because it directly provides the information of H/D exchange as changes of (1) the zero-angle scattering intensities and (2) the information about the structure of the silica particles, e.g., the size and shape.10-12 This method allows one to carry out an in situ analysis about the surface structure and surface layer without complicated procedure, such as high-temperature degassing or pressurizing. Moreover, a simultaneous fitting of a series of scattering functions obtained by various scattering length densities provides a concrete structure (8) Yamauchi, H.; Kondo, S. Colloid. Polym. Sci. 1988, 266, 855. (9) Li, Z. H.; Gong, Y. J.; Pu, M.; Wu, D.; Sun, Y. H. J. Mater. Sci. Lett. 2003, 22, 33. (10) Kohlbrecher, J.; Buitenhuis, J.; Meier, G.; Lettinga, M. P. J. Chem. Phys. 2006, 125, 044715. (11) Zackrisson, M.; Stradner, A.; Schurtenberger, P.; Bergenholtz, J. Langmuir 2005, 21, 10835. (12) Endo, H. Physica B 2006, 385-386, 682.

10.1021/la7039515 CCC: $40.75 © 2008 American Chemical Society Published on Web 03/29/2008

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model including the core radius and the surface layer thickness. To our knowledge, there have been no reports that comprehensively and quantitatively investigated the H/D exchange effect and the structure of the surface layer by CV-SANS. In this study, we discuss the microstructures of colloidal silica, especially the surface structure and H/D change in a solvent.

2. Theoretical Background 2.1. Contrast Matching/Contrast Variation. In the case of two-component systems consisting of silica particles and water, the scattering intensity function in absolute intensity scale, I(q), is written as follows:

I(q) ) nV2(FS - FW)2P(q)S(q)

(1)

where q, n, V, FS, FW, P(q), and S(q) are the magnitude of the scattering vector, the number density and volume of the silica particle, the scattering length densities of silica and of water, the form factor of the particle, and the structure factor, respectively. At q ) 0, the form factor is unity, i.e., P(0) ) 1. Hence, eq 1 becomes

I(0) ) nV2{FS - FW(φD2O)}2S(0)

(2)

where FW(φD2O) is the scattering length density of the solvent with the volume fraction of D2O in the solvent, φD2O. FW(φD2O) can be varied as φD2O, i.e., the H/D exchange. Here, the scattering length density, F, for an arbitrary system is given by the sum of the scattering length densities of its components, Fi, i.e.,

F)

∑i φiFi

∫∞W(R)P(q,R)dR I(q) ) n〈V〉 (FS - FW) ∫0∞W(R)dR 2 0

(4)

(5)

where, n, 〈V〉, and P(q,R) are the number density of particles, the average volume of scatterers, and the form factor for the spherical particles of radius R, respectively. Here, the structure factor was assumed to be unity. On the other hand, the accurate description for S(q) is obtained from the PY approximation for the systems having a hard sphere potential.13,14 Note that we should introduce (13) Percus, J. K.; Yevick, G. J. Phys. ReV. 1958, 110, 1. (14) Wertheim, M. S. Phys. ReV. Lett. 1963, 10, 321.

(6)

h(r) ) (2πσ2)-2/3 exp(-r2/2σ2)

(7)

and

Here, g(r) is a step function indicating the density profile for the sphere having the sharp interface with t ) 0, and the asterisk means a convolution product. Hashimoto et al. investigated the interfacial thickness for microdomain structures of block copolymers. The interfacial thickness t was defined by the density profile near the interface, which was obtained by SAXS experiments.19-21 A physical meaning of t is the inverse tangent of the interface function as given by

t ≡ F0/|dη(r)/dr|r)R

(8)

where F0 ) F1 - F2 is the density difference between two phases of 1 and 2. From eqs 6-8, η(r) is given by

[ ( ) ( )

η(r) ) F0π-1/2 Erf

where bi, di, and Mi are the scattering length, the mass density, and the formula weight of component i, respectively, and NAv is Avogadro’s number. 2.2. The Form Factor and Percus-Yevick (PY) Theory. The scattering amplitude for a spherical object with radius R is given by F(q,R) ) 3{sin(qR) - qR cos(qR)}/(qR)3. Then P(q,R) is given by P(q,R) ≡ |F(q,R)|2. For a colloidal dispersion in a solvent, however, the polydispersity of the colloidal particles has to be taken into account. One common way is to introduce a Gaussian distribution, W(R), with the average radius of the silica sphere, RS, and the standard deviation, ∆RS. Hence, eq 1 has to be rewritten as 2

η(r) ) g(r) / h(r)

(3)

where the subscript i denotes the ith component. The scattering length density of the component Fi is given by

bidiNAv Fi ) Mi

two length parameters, i.e., the radius of particles, RS, and the interparticle distance, 2RHS.15-17 This is because our system has a longer-range repulsive interaction as a result of electrostatic repulsive interaction between silica particles than that of the hard-sphere potential created by RS. Although the application of the PY theory to this system is not rigorous due to the size polydispersity as well as the electrostatic repulsion, the PY structure factor can fairly reproduce the experimental results within good approximation because of very low concentration and very low size distribution of the silica particles. Basically, the effect of the electrostatic force and the polydispersity are roughly included in RHS. 2.3. Interfacial Thickness. If there is an interface layer between two phases, the density profile near the interface, η(r), is given by18

{ ( )} { ( ) }]

r+R r+R 2 σ + exp x2σ x2r x2σ σ r-R r-R 2 + exp Erf x2σ x2r x2σ

(9)

Because of the definition, t is given as follows:

t = (2π)1/2σ

(10)

3. Experimental Section 3.1. Samples. Three types of colloidal silica suspensions were prepared. The colloidal silica particles, Snowtex-OXS, SnowtexOS, and Snowtex-O-40 were kindly supplied by Nissan Chemical Industries, Ltd. (Tokyo, Japan). These colloidal silica dispersions were used without further purification. The nominal values of the radius of silica particles, RS, the solid contents of the silica dispersions, and the surface area per unit mass, AS, provided by the manufacturer are given in Table 1. The pH range was 2-4 for each sample. We diluted these as-received dispersions by H2O or D2O and prepared a series of samples with different scattering length densities of solvent. The sample codes of silica solutions were denoted as Silica-S for Snowtex-OXS solution, Silica-M for Snowtex-OS solution, and (15) Yarusso, D. J.; Cooper, S. L. Macromolecules 1983, 16, 1871. (16) Kinning, D.; Thomas, E. L. Macromolecules 1984, 17, 1712. (17) Fournet, P. G. Acta Crystallogr. 1951, 4, 293. (18) Ruland, W. J. Appl. Crystallogr. 1971, 4, 70. (19) Hashimoto, T.; Fujimura, N.; Kawai, H. Macromolecules 1980, 13 (6), 1660 (20) Hashimoto, T.; Shibayama, M.; Kawai, H. Macromolecules 1980, 13, 1237. (21) Hashimoto, H.; Fujimura, M.; Hashimoto, T.; Kawai, H. Macromolecules 1981, 14, 844.

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Figure 1. Scattering profiles of (a) Silica-L, (b) Silica-M, and (c) Silica-S. The upward arrows and the downward arrow denote the scattering maximum originating from S(q) and P(q), respectively. Table 1. Sample Characteristics a

concentration dsilica (g/cm3) ASa RS (Å) as received as received (wt %) as received (m2/g) Silica-L Silica-M Silica-S a

100-150 40-55 20-30

40.7 20.3 10.6

2.26 2.21 2.23

120 290 540

φS 0.012 0.006 0.012

Provided by the manufacturer.

Silica-L for Snowtex-O-40 solution. The volume fractions of the silica, φS, were 0.012 for Silica-S, 0.006 for Silica-M, and 0.012 for Silica-L, as also shown in Table 1. 3.2. SANS. SANS experiments were performed at the SANS instrument (SANS-U) of Institute for Solid State Physics, The University of Tokyo.22,23 The neutron wavelength was 7.0 Å, and its distribution was ca. 10%. The sample-to-detector distance was chosen to be 2 and 8 m, and the q range was from 0.005 to 0.15 Å-1. The necessary corrections were made, such as air scattering, cell scattering, and incoherent background subtraction. After these corrections, the scattering intensity was normalized to the absolute intensity with a polyethylene secondary standard sample.24 The temperature of the samples was regulated to be 25 °C with a watercirculating bath controlled with a Neslab RTE-111 thermocontroller with a precision of (0.1 °C.

4. Results and Discussion 4.1. SANS Results. Figure 1 shows the absolute scattering intensity functions, I(q), of (a) Silica-L, (b) Silica-M, and (c) Silica-S in solvents with different D2O fractions. There are three distinct peaks marked with up-arrows and a down-arrow, indicating the interparticle interference, S(q), and the peak from the particle factor, P(q), respectively. By decreasing the particle size, the scattering intensity decreases, and the interference peaks gradually disappeared with a shift to the high q region. It should be also noted that I(q) varies depending on the solvent composition. That is, I(q) decreases with increasing φD2O for φD2O < 0.49 and then increases with further increase of φD2O for each sample. Figure 2 shows the results of simultaneous curve fitting for Silica-L, Silica-M, and Silica-S, which were carried out by fitting all of the I(q)’s obtained with different φD2O’s with the same set of structural parameters. The broken line, the chain line, and the thick-solid line denote P(q), S(q), and the total scattering intensity, I(q), respectively. P(q), designated by the down-arrow, is the leading term in the high q region. On the other hand, S(q) is the (22) Okabe, S.; Nagao, M.; Karino, T.; Watanabe, S.; Adachi, T.; Shimizu, H.; Shibayama, M. J. Appl. Crystallogr. 2005, 38, 1035. (23) Okabe, S.; Karino, T.; Nagao, M.; Watanabe, S.; Shibayama, M. Nucl. Instrum. Methods Phys. Res., Sect. A 2007, 572, 853. (24) Shibayama, M.; Nagao, M.; Okabe, S.; Karino, T. J. Phys. Soc. Jpn. 2005, 74, 2728.

leading term in the low q region responsible for the scattering peaks in I(q) shown by the up-arrow. Here, we carried out the curve fitting of the observed SANS functions with eqs 1 and 5, by considering the fact that the hard-sphere potential has a larger excluded volume 2RHS than the particle size 2RS as a result of the electrorepulsive interaction.16 In this case, the volume fraction of the spheres, φS, is given by φS ) (RS/RHS)3η. As shown in the figure, the curve fitting is quite successful. The evaluated volume fraction of the spheres, φS, satisfies the volume fraction of silica at sample preparation. The obtained parameters from the curve fitting are listed in Table 2. The values of the number density of scatterers, n, obtained via eqs 1 and 2, are also listed in the table. In Table 2 are also shown the calculated values for the surface area, AS,0, by using the following equation:

AS,0 )

4πRS2n dsilicaφS

(11)

and the ratio of the surface areas, AS/AS,0. The ratio is larger than unity and is increasing with decreasing RS, indicating that there exists a rough surface depending on RS. Figure 3a shows the double logarithmic plot of the interparticle distance D () 2π/qmax) as a function of RS3/φS. Note that the slope is exactly 1/3. This value means that the silica was uniformly distributed in the solvent by keeping an equi-interparticle distance due to repulsive interactions resulting from the surface charge and excluded volume effects. Figure 3b shows the plot of (3φS/4π)(D/RS)3 vs RS. As shown in the figure, the plot is independent of RS. If the spheres are packed in a lattice of the unit cell D, the volume fraction is given by

()

4π Rs 3 D

φs ) (RS/RHS)3η ≈ k

3

(12)

where k is a numerical factor depending on the packing of the sphere in the unit cell, i.e., k ) 1 (simple cubic), k ) 2 (bodycentered cubic), and k ) 4 (face-centered cubic). The evaluated value of k is 0.44, indicating that the particles are loosely packed, even lower than the case of simple cubic packing, as a result of the repulsive interactions. 4.2. Evaluation of the H/D Exchange Fraction. Figure 4 shows the variations of I(0)/φS’s with the solvent composition. Here, I(0)’s were normalized by φS. The inset is the expanded plot in the direction of the ordinate. As shown in the figure, the obtained values for I(0)’s well fit to the parabolic function with φD2O. The absolute values of I(0)’s vary with the size of the silica. On the other hand, the contrast matching points where

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Figure 2. Fitting result for Silica-L, Silica-M, and Silica-S. The broken line, the chain line, and solid line indicate P(q), S(q), and I(q) calculated with eqs 1 and 5. Table 2. Structural Parameters Obtained by SANS RS (Å)

RHS (Å)

D (Å)

Silica-L 165 ( 0.2 414 ( 0.9 878 Silica-M 95.5 ( 0.4 303 ( 1.9 638 Silica-S 71.2 ( 0.2 173 ( 0.9 385

AS,0 n × 109 (Å-3) (m2/g)a AS/AS,0 0.638 1.64 7.94

80.5 142 189

1.49 2.04 2.85

a Calculated with the structural parameters obtained by SANS by assuming a smooth surface.

I(0)’s become a minimum are almost the same, irrespective of the silica size, i.e., φD2O ≈ 0.60 ( 0.017. Figure 5 shows the scattering length densities of Silica-L, Silica-M, Silica-S, and the solvent as a function of φD2O. The scattering length densities of each sample were evaluated with eq 2 and the following equation: FW(φD2O) ) (1 - φD2O)FH2O + φD2OFD2O. Here, the scattering length densities of H2O and D2O are FH2O ) -0.559 × 1010 cm-2 and FD2O ) 6.35 × 1010 cm-2, respectively. Thus calculated FW(φD2O) is designated by the broken line in the figure. It should be noted that the FS of each sample depends not only on φD2O but also on the radius of silica. The φD2O dependence of FS means that the degree of H/D exchange is influenced significantly by the solvent composition. Note that both solid and broken lines crossover at a single point (φD2O ≈ 0.6) as discussed above. This means that the scattering length densities of each component, i.e., the solvent and the silica particle, exactly match, independent of the difference of the size of the silica particles. In order to elucidate the physical implication of the φD2O dependence of FS, we investigated the variation of FS in detail. First, we evaluated the mass density of pure silica, dsilica. FS is given by the fraction of H/D substitution of the silica, φH/D, and the scattering length density of pure-silica, Fsilica, with eq 3 as mentioned above, i.e.,10

FS ) (1 - φH/D)Fsilica + φH/D{(1 - φD2O)FH2O + φD2OFD2O} (13) ) (FD2O - FH2O)φH/DφD2O + (1 - φH/D)Fsilica + φH/DFH2O The solid lines in Figure 5 are the fitted lines obtained with eq 13. Thereafter, we evaluated the dsilica using the obtained values of Fsilica with eq 4. The evaluated value of dsilica ≈ 2.23 [g/cm3] is in good agreement with not only those calculated from the values received by the manufacture as listed in Table 1, but also those of the bulk silica glass. The fraction, φH/D, is obtained by

dFS 1 φH/D ) dφD2O (FD O - FH O) 2

2

(14)

Figure 3. (a) Double logarithmic plot of the interparticle distance D () 2π/qmax) as a function of RS3/φS, (b) (3φS/4π)(D/RS)3 as a function of RS.

If H/D exchange occurs exclusively at the silica surface, the slope of the scattering length density with respect to φD2O, dFS/ dφD2O, should be exactly proportional to the specific surface, Ssp, i.e., the surface area divided by the volume of the particle. If the particle is a spherical object with radius RS and has a smooth surface, Ssp is given by

Ssp ≡ S/V ) 4πRS2/(4πRS3/3) ) 3/RS

(15)

where S and V are the surface and the volume of the spherical particle, respectively.

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Figure 6. RS-1 dependence of the slope of the scattering length densities of Silica-L, Silica-M, and Silica-S. Figure 4. φD2O dependences of the normalized scattering intensities for Silica-L, Silica-M, and Silica-S. The solid lines are fits calculated with parabolic functions. The inset shows expanded plots.

Figure 7. Comparison of the H/D exchange fractions obtained by SANS (this work; solid circles), by the specific surface (open triangles), and by the surface area AS (open circles). Figure 5. φD2O dependences of the scattering length densities of Silica-L, Silica-M, and Silica-S. The broken line shows the scattering length density of the solvent.

Figure 6 shows the slope of FS(φD2O), i.e., dFS/dφD2O as a function of RS-1. The solid line is the fitted result with a linear function proportional to RS-1. These results indicate that H/D exchange occurred exclusively at the surface while the chemical structure of the inner part is not influenced by the composition of solvent. The horizontal chain line indicates the dF/dφD2O evaluated with the assumption that no H/D exchange occurred, i.e., dF/dφD2O) 0 (see eq 14). The H/D exchange fraction, φH/D, evaluated by SANS can be compared with those obtained from (1) the specific surface by assuming smooth surface and from (2) the surface area, As, determined by other methods, e.g., Brunauer-Emmett-Teller (BET) gas absorption method.7 Those φH/D’s are defined by

φH/D ≈

3 ROH Vsilica RS Nsilica VOH (from the specific surface with smooth surface) (16)

ROH Vsilica (from the surface area) φH/D ≈ Asdsilica Nsilica VOH

that obtained by AS compared with that obtained by Ssp. Since AS is directly related to the active surface area, this agreement seems to be reasonable. On the other hand, the underestimation of φH/D by the specific surface is due to the assumption of a “smooth surface”. Hence, Figure 7 clearly indicates that the surface of the silica nanoparticles is rough. Now, let us estimate the thickness of the surface layer. A structure model including the interfacial layer consisting of pure silica and an outer shell of silica and substituted OH groups would be more appropriate to obtain the surface layer thickness and reproduce the observed SANS functions (Figure 1). However, it is rather difficult to obtain a precise surface thickness for the following reason. There are too many free parameters in the fit, namely, the scattering length densities of silica, the radius of silica, the interfacial thickness, and RHS. In addition, the surface thickness is so small that the measured intensities originating from the scattering of surface layer is dominated by the incoherent background scattering. We circumvented this problem as follows. 4.3. Interfacial Layer Thickness. We estimate the interfacial layer thickness, t, from the radial profile of the volume fraction of pure silica, φsilica(r), calculated from eqs 6-10, i.e.,

(17)

where Nsilica is the bulk number density of SiO2, and ROH is the surface hydroxyl number density (aOH ) 0.046 ( 0.005 Å-2).7 Nsilica is assumed to be Nsilica ) dsilicaNAv/MSilica, where Msilica is the formula weight of SiO2, that is, Nsilica ) 0.0223 Å-3. Vsilica and VOH are the reduced volumes of silica and hydroxyl groups per unit, i.e., Vsilica ) Msilica/dsilicaNAv and VOH ≈ MH2O/dH2ONAv, respectively. Figure 7 shows the comparison of the φH/D’s evaluated by SANS (this work; filled circles), by the specific surface (eq 16; open triangles), and by the surface area (eq 17; the open circles). The solid line is a guide for the eye. This figure shows that φH/D obtained by SANS is in good agreement with

φsilica ) 1 - φH/D )

∫η(r)/F04πR2dR 4πRS3/3

(18)

Here, we should pay attention to the fact that the φH/D becomes close to unity at R ) RS. The radius of pure silica (i.e., the core radius), Rcore, is given by Rcore) RS - t. As a result of the calculation with eq 18, the thicknesses of the shell, t’s, were estimated as shown in Table 3 for Silica-L, Silica-M, and SilicaS, respectively. As was expected, the surface layer thickness increases with decreasing RS. The structures of Silica-L, SilicaM, and Silica-S nanoparticles are schematically shown in Figure 8. There exists a surface layer having a finite thickness as shown

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Figure 8. Schematic models of Silica-L, Silica-M, and Silica-S. The concentration variation of OH groups is designated by gradation.

Figure 9. The reproduced scattering functions for Silica-L, Silica-M, and Silica-S. Table 3. Fitting Parameters Used in Figure 9 Silica-L Silica-M Silica-S

Fcore × 10-10 (cm-2)

Rcore (Å)

t (Å)

3.57 ( 0.01 3.52 ( 0.05 3.63 ( 0.04

146 66.4 35.9

18 29 35

by gradation. The thickness of the surface layer is dependent on the silica size, and H/D substitution occurs in this surface layer. Although H/D substitution occurs only at the silica surface with a penetration depth of atomic order, the roughness of the silica surface allows a significant depth for H/D substitution over the range of the surface layer. Figure 9 shows the reproduced scattering functions for SilicaL, Silica-M, and Silica-S with the form factor for core-shell model and the structure factor for the PY model (see Appendix). Thus obtained scattering functions are denoted by the solid lines. Here, the core radii, Rcore’s, the shell radii, Rshell’s, and the scattering length densities of core, Fsilica’s, were set as fixed parameters. On the other hand, the scattering length densities of the shell were evaluated from simultaneous curve fitting of a series of scattering intensities with different φD2Os for each sample. As shown by the solid line, the experimental scattering intensities, I(q)’s, were successfully reproduced by using the structural parameters obtained in the discussions. It should be noted that, as discussed so far, the interfacial shell thicknesses, t’s, were successfully obtained not by focusing on the high q region that provides a rather uncertain value, but by the following procedures. At first, simultaneous curve fitting to the all the experimental data having different contrasts was performed. Second, the average scattering length densities, FS’s, were calculated with eq 2. Third, the volume fraction of the deuterated OH group, φH/D, and the interfacial layer thickness, t, were estimated. Finally I(q)’s were

successfully reproduced with the obtained parameters using the core-shell model.

5. Concluding Remarks The hydrogen/deuterium exchange effect and the local structures near the surface of silica nanoparticles with different sizes were investigated by CV-SANS. The observed contrastmatching points between the silica particles and aqua solutions coincided well with different particle sizes. On the other hand, it was found that the average scattering length densities of the silica particles were significantly affected by not only the D2O fraction but also their sizes. Our detailed analyses of scattering intensities concluded that the hydrogen/deuterium exchange occurs only within a finite surface layer having rough surface with exposed OH groups. The numbers of exchangeable OH groups on the surface are in good agreement with those predicted by the surface area obtained by gas adsorption method, but not with those predicted by smooth-surface assumption. The H/D exchange fraction, φH/D, increases with lowering the radius of particle, e.g., φH/D ) 0.47 for Rs ) 71 Å. The corresponding surface-layer thicknesses are evaluated to be ca. 18-35 Å, depending on the size of silica nanoparticles. Acknowledgment. This work was partially supported by the Ministry of Education, Science, Sports and Culture, Japan (Grantin-Aid for Scientific Research (A), 2006-2008, No. 18205025, and for Scientific Research on Priority Areas, 2006-2010, No. 18068004). The SANS experiment was performed with the approval of the Institute for Solid State Physics, The University of Tokyo (Proposal No. 7404), at the Japan Atomic Energy Agency, Tokai, Japan. The authors are indebted to Nissan Chemical Industries, Co., Ltd., Tokyo, Japan, for the kind supply of colloidal silica suspensions.

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Appendix: The Form Factor for Core-Shell Structure with Size Distributions The form factor for a spherical structure with size distribution represented by the Schulz distribution is given by25

[[ { }

} [

4q2jrc2 1 ) 6 6 (1 + Z) 1 + 2q jrc Γ(1 + Z) (1 + Z)2

[{

1+

{

4q jrc

2

Z/2

3

}[

( )}] ( )}]]

{

{

]

{

(1 + Z)2}2Γ(Z - 4) sin (Z - 4) arctan

( )}] 2qrjc 1+Z

where rc and jrc are the radii of the sphere and their average, respectively. The Schulz distribution function G(rc) is defined by

rcZ

( )

Z+1 Γ(Z + 1) jrc

Z+1

[

rc exp - (Z + 1) jrc

]

sin(x) - x‚cos(x)

F(x) ) 3

x3

Z is related to the normalized polydispersity σc of rc distribution by

σc ) 2

〈rc2〉 〈rc〉

2

-1)

1 Z+1

Considering the Schulz distribution, the volume of a sphere V(rjc) is given by

4π 3

( )} {

∫0∞ G(rc)rc3drc )

4πrjc3 Γ(4 + Z) 3 (1 + Z)3Γ(1 + Z)

The scattering amplitude for a spherical structure where the size distribution is expressed by the Schulz distribution is given by

Asphere(qrjc) )

∫0

∞

G(rc)F(qrc)drc

(25) Bartlett, P.; Ottewill, R. H. J. Chem. Phys. 1992, 96, 3306.

( )}]] qrjc 1+Z

Therefore, the scattering intensity, I(q), for the spherical structure is expressed by

[

I(q) ) ∆F nVs Psphere(qrj) 1 + 2

2

{Asphere(qrj)}2 Psphere(qrj)

{S(q) - 1}

]

with the scattering contrast ∆F, the number density of spherical particles, n, and an appropriate structure factor, S(q). [1 + {Asphere(q)}2/P(q) × {S(q) - 1}] represents the interparticle interaction with a size distribution.26 The above discussion can be easily expanded to the coreshell structure27 with average core and shell radii jrc and jrshell having size distributions represented by the Schulz distribution with Zc and Zshell, respectively. In the case of a core-shell structure, the scattering intensity is defined as

[

{Acore-shell(q)}2 I(q) ) nPcore-shell(q) 1 + {S(q) - 1} Pcore-shell(q)

with Gamma function Γ(x), and F(x) is the scattering amplitude for a spherical structure defined as

V(rjc) )

q2jrc2

{q2jrc2(Z - 5)(Z - 4) + (Z + 1)2} +

(1 + Z)2 4q2jrc2 3/2

G(rc) )

1+

-qrjc(1 +

(1 + Z)2}Γ(Z - 2) sin (Z - 2) arctan

-{4q2jrc2 + (1 + Z)2}cos (Z - 5)arctan (1 + Z)2 2qrjc + q2jrc2(Z - 5)(Z - 4) cos (Z - 3) arctan 1+Z 2qrjc Γ(Z - 5) - 2qrjc{4q2jrc2 + 1+Z

1+

{

-Z/2

(1 + Z)

x

} [ -Z/2

Γ(Z - 1) × (1 + Z)2 qrjc + {q2jrc2 + cos (-1 + Z) arctan 1+Z Z)

∫0∞ G(rc){F(qrc)}2drc

PSphere(qrjc) )

2

[ {

q2jrc2 1 ) 3 3 (1 + Z) 1 + q jrc Γ(1 + Z) (1 + Z)2

]

where

Pcore-shell(q) ) ∆Fshell2V(rjs)2Psphere(qrjs) + 2∆FshellV(rjs)Asphere(qrjs)∆Fcore-shellV(rjc)Asphere(qrjc) + ∆Fcore-shell2V(rjc)2Psphere(qrjc) and

Acore-shell(q) ) ∆FshellV(rjs)Asphere(qrjs) + ∆Fcore-shellV(rjc)Asphere(qrjc) with the scattering contrast ∆Fshell ) Fshell - Fsolvent as well as ∆Fcore-shell ) Fcore - Fshell, in which Fshell, Fcore, and Fsolvent are the scattering length densities of the shell, core, and solvent, respectively. In this study, the PY theory is used for S(q) as described in the theoretical section. LA7039515 (26) Kotlarchyk, M.; Chen, S.-H. J. Chem. Phys. 1983, 79, 2461. (27) Poppe, A.; Willner, L.; Allgaier, J.; Stellbrink, J.; Richter, D. Macromolecules 1997, 30, 7462.