Faraday Discuss. Chem. SOC., 1983, 76, 53-63 Neutron-scattering Studies of Concentrated Oxide Sols BY JOHN D. F. RAMSAY, RONALD G. AVERY AND LANCE BENEST Chemistry Division, B.429, AERE, Harwell, Oxfordshire OX1 1 ORA Received 28th April, 1983 Small-angle neutron scattering (SANS) and light scattering have been used to study the interactions between particles (diameter < 20 nm) in silica and ceria sols covering a wide range of concentration. Structure factors, S(Q), have been determined which have been com- pared with those calculated for a model hard-sphere (HS) potential. At low sol concentrations ( 5 lo-, g ern-,) interactions are dominated by double-layer repulsion which is most pro- nounced at low electrolyte concentrations (ca. lop4 mol dm-,). At higher sol concentrations (2 10- g cm-3) the effects of electrolyte concentration become less important and the form of S(Q) is similar to that of a HS system, in which the effective interaction diameter is greater than the diameter of the sol particles. Preliminary SANS studies on mixtures of titania and iron oxide sols using the contrast variation technique are also described from which inform- ation on the compatibility and structure of each component has been obtained.A knowledge of the structure and nature of the interactions in concentrated oxide dispersions is important in many technological applications but also has a wider significance for a better understanding of colloid stability and the properties of oxide/water interfaces. * - Small-angle neutron scattering (SANS) has been used recently4 to study the structural changes which occur when silica and ceria sols, containing discrete and approximately spherical particles, are progressively concen- trated and finally converted into solid gels.A feature illustrated was the importance of interparticle repulsion forces in promoting short-range order and the formation of a regular porous gel structure. In this paper more detailed SANS investigations of the interactions in these sols are described, together with complementary light-scattering measurements made on less concentrated dispersions. The versatility of SANS is also demonstrated by pre- liminary studies made with mixtures of titania and a-FeOOH sols, where the dif- ference between the scattering length densities of the oxides is exploited. Possible applications of this technique in studies of structure and interactions in mixed sol systems are discussed.EXPERIMENTAL MATERIALS The concentrated silica sol was a commercial sample (LUDOX HS40) and the cerium oxide sol was prepared by peptising a hydrous oxide precipitate with nitric acid, as previously described. These stock sols were dialysed repeatedly against dilute electrolytes (NaNO, and KNO,, respectively) of different ionic strengths, having a fixed pH (ca. 8 for SiO,; ca. 3.6 for CeO,). Silica sols used for SANS were prepared in deuterium oxide (> 99% D20) to elimin- ate the background incoherent scattering from water; ceria sols were prepared in H 2 0 to achieve greater contrast. Individual samples of known concentration were prepared either by dilution with equilibrium dialysates or by concentrating further using an ultrafiltration cell.Particle-size distributions, determined by transmission electron microscopy as already de-54 INTERACTIONS IN OXIDE SOLS ~ c r i b e d , ~ showed discrete, almost spherical, particles. Mean diameters, d,, were 16.5 nm (stan- dard deviation 0.21) for silica and ca. 6 nm for ceria (majority in range 4.5-7.5 nm). Titania and iron hydroxide sols were prepared by hydrolysing solutions of TiC14 and Fe(N03)3, respectively. A cooled solution of TiC14 (2.0 mol dmP3) was neutralised rapidly with NH40H to pH z 3. The dispersion formed was dialysed repeatedly against water (pH ca. 3) to give a stock sol containing small (ca. 4 nm) particles of poorly crystalline anatase.A solution of Fe(N03)3 (2.0 mol dmd3) was dialysed to pH 3.1, concentrated by ultrafiltration and aged (7 months) to give a stock sol containing thin (ca. 5-10 nm) needle-shaped particles (length ca. 8 nm) of goethite. Samples for SANS were prepared from these stock sols by dialysing (five times) against H 2 0 + D,O mixtures (pH ca. 3.2). LIGHT SCATTERING Measurements (SOFICA, model 4200) were made with vertically polarised light with a wavelength of 546 nm as previously described.6 Scattered intensities on an absolute basis (viz. Rayleigh ratios) were obtained using a benzene standard for calibration. SMALL-ANGLE NEUTRON SCATTERING Measurements were made at wavelengths of 6 and 10 A on samples of sols contained in silica cells (path length 1 and 2 mm), using a multidetector instrument’ installed in the PLUTO reactor at AERE, Harwell.At 10 A the incident flux was considerably lower ( x 0.1) than at 6 A, although measurements could be extended to smaller Q (0.08 and 0.15 A- for 10 and 6 A, respectively). Data were analysed using standard programmes to normalise counter efficiencies and to correct for sample self-absorption and incoherent background. Absolute scattered intensities, expressed as macroscopic cross-sections, [dC/dlI],,h, were obtained using a water standard. DATA TREATMENT AND ANALYSIS NEUTRON SCATTERING For the case of coherent small-angle scattering from a concentrated colloidal dispersion of identical particles the scattered intensity is given by ItQ) = F(pp - pJ2Vp2npP(Q)S(Q) where Q is the scattering vector, defined as IQI = 4nsinO/A for a scattering angle 28 and wavelength A, F is an experimental factor, pp and ps are, respectively, the mean scattering length densities of the particles and solvent (which here is water), V, is the volume of each particle, np is the particle number density and P(Q) is the particle form factor, which for spheres of radius R is given by 3(sinQR - QRcosQR) = ( Q3R3 (3) The structure factor, S(Q), which describes the effects of interparticle interactions, is related to the particle pair-distribution function, g(r), by the Fourier transform to obtain details of the spatial distribution of the particles as a function of the mean inter- particle separation, r.In very dilute dispersions (viz. np -, 0) containing widely separated non-interacting particles, S ( Q ) = 1 .Hence S(Q) can be obtained experimentally by eliminating P(Q) from eqn (1) using the normalisation relationshipJ. D. F. RAMSAY, R. G . AVERY AND L. BENEST 55 LIGHT SCATTERING For incident unpolarised light, the scattered intensity, expressed in an equivalent form to eqn (l), is given by Re = K*McP(Q)S(Q)n (6) where Re is the Rayleigh ratio, M is the molecular weight of the particles with a mass concentration c and K* is an optical constant given by (7) K* = 2~~fio(dfi/d~)’&-~ N - ‘. Here fi0 is the refractive index of the solvent, dfi/dc is the refractive index increment and lo and N are the wavelength of the incident light and Avogadro’s number, respectively. The equivalent normalisation to eqn (S), from which S(Q) is obtained, is thus S(Q) = [&/cll[Re/clc-o. (8) HARD-SPHERE STRUCTURE FACTORS A very satisfactory interaction model for describing the properties of simple liquids,* which has more recently been applied to colloidal di~persions,~-’~ is the hard-sphere (HS) potential. In this model the particle is regarded as a non-attracting rigid sphere of diameter Q? with potential energy @(r) = a for r < Q and @(r) = 0 for r > Q.Here S(Q)Hs, solved using the Percus-Yevick approximation 1 3 , l4 for appropriate values of HS number density, nHS, and volume fraction, <pHs [where <DHs = (n/6)03nHs], has been compared with that obtained experimentally. RESULTS AND DISCUSSION INTERACTIONS AND STRUCTURE IN SILICA AND CERIA SOLS LIGHT SCATTERING Measurements of scattered intensity, Re, at eleven fixed angles (28 from 30 to 1500) were made on silica and ceria sols covering a wide range of concentration, c, from ca.5 x to ca. 3 x lov2 g ~ m - ~ . Over this range of c the attenuation of the transmitted beam was very low (c 573, even for the silica sol of highest con- centration, and complicating effects due to multiple scattering were not considered significant. Plots of RB/C against Q were horizontal, an indication that P(Q) x 1 in the range of Q/A-l covered here (ca. 8 x loM4 to 3 x Values of (RB/c)~-,o and other scattering data for the two sols are given in table 1. Table 1. Light-scattering results for sols sol (dn”/dc)/cm3 8-l (R&)c-to/cm2 g-’ K*/mol cm2 g-I M W silica 0.064 0.212 2.68 x 7.96 x lo6 ceria 0.157 0.822 1.61 x lo-’ 5.10 x lo6 Values of S(Q)Q-+~, obtained from eqn (8), are plotted for each value of c for both silica and ceria sols of two different ionic strengths in fig.1. The importance of interactions between the electrical double layers of the sol particles is apparent from the steep decline in S(Q)o which occurs at low ionic strength, where the effective56 INTERACTIONS IN OXIDE SOLS 0 2 4 0.01 0.05 iPHS 0 - 1 0.2 0.3 c/10p2g cm-3 Fig. 1. Dependence of S(Q)Q-.O and corresponding q H S on concentration, c, for sols of silica (0 and.) and ceria (0 and m) having electrolyte concentrations of (0 and 0) and 5 x mol dm-3 (@ and H). thicknesses of the diffuse double layers are correspondingly greater. This effect is more marked for the ceria sol, which might be expected, on account of its consider- ably smaller particle size.As c is increased, and the average particle separation is accordingly decreased, interactions in the sols of high ionic strength become increas- ingly important and S(Q) shows less sensitivity to differences in ionic strength and tends to approach a level which is similar for both sols. The particle interaction behaviour can be related to that for a HS potential by comparing the calculated l4 value of q H S , which corresponds with the experimentally determined S(Q)o for a given c and ionic strength, q, as is shown in fig. 1 . The effective hard-sphere diameter, a, is then given by where R and q p p ( = c S - l ) are the radius and volume fraction of the sol particles, respectively. Plots of a against ( p p in fig.2 reflect the influence of c, on the range of double-layer repulsion between the sol particles. This can be further demonstrated by the accord between (a - 2R)/2 and the Debye-Hiickel screening distances, K - ~J. D. F. RAMSAY, R. G . AVERY AND L. BENEST 57 (viz. 30.4 and 4.3 mm), for the two different electrolyte concentrations of 5 x and mol dm-3, respectively, where15 60 LO --- L3 20 0 \ \ \ \ \ 2 Fig. 2. Dependence of effective HS diameter, g, of particles on volume fraction, (pp, for silica [(i) and (ii)] and ceria [(iii) and (iv)] sols having different electrolyte concentrations, ci, of ca. low4 [(i) and (iii)] and 5 x [(ii) and (iv)] mol dm-3 SMALL-ANGLE NEUTRON SCATTERING The dependence of scattered neutron intensity, I @ ) , on momentum transfer, Q, for more concentrated silica sols (ci = 5 x mol drne3) is illustrated in fig.3. The development of the maxima in I(Q) is caused by interparticle interference effects and indicates that the particles are not arranged at random but have some short- range ordering. Thus the movement of the maxima to higher values of Q with increasing concentration, c, reflects a reduction in the equilibrium separation dis- tance between the particles as already discussed.4* ti The spatial distribution can be described by the radial distribution function, g(r), which defines the probability that the centres of a pair of particles will be separated by a distance Y. Values of Y at the first maximum in g(r), viz. r,,,, derived from eqn (4) are given in table 2.It can furthermore be shown that as c is increased the interparticle separation decreases inversely as c1/3 and approaches that of the particle diameter, 2R. From further SANS measurements it was shown that a reduction of ionic strength to mol dm-3 had no apparent effect on the development of structure in sols of similar concentration, a feature which can be demonstrated more clearly from a comparison of S(Q).58 INTERACTIONS IN OXIDE SOLS 100 ,- I L. I ,- 3 2 5 0 3 0 0.0 5 Q/A-l 0.1 Fig. 3. Small-angle neutron-scattering curves for silica sols of different concentrations, c, in 5 x lop3 mol dm-3 sodium nitrate solution: 0,0.014; 0,0.14; e, 0.27 and 0,0.55 g ~ m - ~ . Table 2. Hard-sphere simulation results for silica sols silica conc., ionic strength, clg cm-3 [Na+]/mol dm-3 n,/1016 rrnax/nm VHS a/nm 0.137 5 x 10-3 1.74 38 0.27 30.9 0.266 5 x 10-3 3.37 29 0.28 25.1 0.550 5 x 10-3 7.46 21 0.32 20.2 0.08 1 5 1 x 10-4 1.02 46 0.28 37.4 0.175 5 1 x 10-4 2.2 1 36 0.29 29.3 0.384 5 1 x 10-4 4.85 26 0.32 23.3 Two procedures were necessary to calculate S(Q).At high Q (Q/A- 2 0.02) eqn (5) was used to normalise intensity data against that for the sol of lowest con- centration (0.014 g cmW3) measured at 6 A. In this range of Q, interactions in the dilute sol had an insignificant effect on I@), viz. S(Q)dil x 1 [n.b. S(Q) + 1 as Q -+ a]. Such effects were, however, apparent for Q/A 5 0.02, and in the range 0.01 c Q/A- < 0.025 corrected intensity data were normalised against the theoretical P(Q) [cf. eqn (3)], giving a satisfactory range of overlap as shown (by the solid and open symbols) in fig.4, [The latter procedure was unsatisfactory for Q/A- 5 0.03 because both polydispersity and polychromaticity of the neutron beam resulted in a marked departure from the theoretical P(Q), calculated for a monodispersed system, as has been discus~ed.'~]J. D. F. RAMSAY, R. G. AWRY AND L. BENEST r--r-- 59 2 4 0 2 L 6 Q/IO-2 A-l Fig. 4. Structure factors, S(Q), for silica sols of different concentrations, c, and ionic strengths, ci: (i) 0.08, (ii) 0.17 and (iii) 0.38 g cm-3 (c; z mol dm-3); (iv) 0.14, (v) 0.27 and (vi) 0.55 g cmb3 (c, = 5 x mol dm-3). Full lines correspond to S(Q) for HS systems with qHS of 0.28, 0.29, 0.32, 0.27, 0.28 and 0.32 for (i)-(vi), respectively. The form of the plots of S(Q) against Q can be ascribed to a system of spherical particles which are maintained in a partially ordered structure by repulsion forces.Two features are also apparent: first, the ionic strength has no apparent effect on S(Q), and hence the interaction potential; secondly, increases in sol concentration, although resulting in shifts in S(Q)max, do not cause a marked increase in repulsive potential, as might at first be expected. These features are demonstrated more clearly by comparing the experimental S(Q) data with those calculated for a HS potential. A unique solution for the S(Q) of a HS system is obtained by fixing any two of the three interdependent parameters: 0, qHS and nHs; viz. qHS and nHS in the present case, where nHS is identical to np (=6qP/ndv3), which is already known. Results obtained (fig.4) by varying qHS to give the closest match with the experimental data in the region of S(Q)max show that qHS increases only slightly over the range of concentrations examined. This implies that for the more dilute sols, 0 is relatively large and corresponds to an effective diameter which is considerably greater than the particle diameter, d,, of 16.5 nm. As the sol concentration, c, is increased, o de- creases progressively (table 2) until in the gel it can be shown that the two are of comparable size.60 INTERACTIONS IN OXIDE SOLS 10 Although the HS model does not give a completely satisfactory simulation with the experimental S(Q), the similarity is nevertheless remarkable, because a slowly decaying potential would be expected to result from the interaction between the electrostatic double layers surrounding the particles.Indeed there is evidence that at the lower sol concentrations a 'softer' potential would be more suitable for simulat- ing the more gradual increase in S(Q) which occurs initially. This possibility has been examined more recently by applying the screened Coulomb potential model of Hayter and Penfold. * Although a detailed description is not yet appropriate,lg initial results show improved fits to experimental data compared with that obtained with the HS model. Satisfactory fits are, however, obtained with an effective surface charge on the particles which is considerably lower (viz. from ca. 0.3 to 0.7 ,uC cm-2) than the typical total surface charge density (> 2 ,uC cmP2) of silica sols, as determined under similar conditions by conductimetric titrations.20 This would sug- gest that a considerable uptake of counterions occurs, either at the oxide interface or within the Stern layer, which reduces the effective potential of the diffuse double layer markedly, so that the interaction becomes more similar to that of an HS system.The dependence of I(Q) on Q for ceria sols covering a range of concentration with an ionic strength of 5 x mol dmP3 is illustrated in fig. 5. Again marked - I 1 e 00 0 0 8 . 0 - 0 0 0 o""., . 0 0.0 5 0.1 QIA- 0.15 Fig. 5. Small-angle neutron-scattering curves for ceria sols of different concentrations, c, in 5 x mol dm-3 potassium nitrate solution: 0, 0.032; 0, 0.080; a, 0.16 and 0 , 0 .3 2 g C M - ~ . interference is observed, for reasons already described. The maxima in l ( Q ) occur at considerably larger Q values compared with those for the silica sols of similar vol- ume fraction, on account of the smaller size of the ceria particles. This feature is illustrated more clearly by the dependence of rg(r)max on c, which has been des- cribed previously for this ~ y s t e m . ~ Further measurements on sols having an ionic strength of mol dmP3 showed that the behaviour of I(Q) at corresponding ceria concentrations was very similar, an indication that the repulsive interaction was not appreciably enhanced, as already noted with the silica sols. The interaction properties of these concentrated sols are of particular interest because the particlesJ.D. F. RAMSAY, R. G. AVERY AND L. BENEST 61 are much smaller, although more polydispersed, than those of model latex disper- sions studied recently. Consequently the interparticle separation is considerably less than the screening length, K - even at relatively high electrolyte concentrations. SMALL-ANGLE NEUTRON SCATTERING OF MIXED OXIDE SOLS In principle an understanding of the interactions and homogeneity of the differ- ent components in mixed oxide sols may be obtained from SANS by exploiting the contrast variation technique, which has been employed extensively in the study of biological structures.21 In the present study of mixtures of iron hydroxide and titania sols, the oxides have a large difference in scattering length density, &xi& (see table 3), and thus under contrast match conditions for one component the scattering from the other will be considerable.This is important experimentally with very small colloidal particles, as studied here, because I(Q) is relatively weak [cf. eqn (l)]. Table 3. Molecular scattering lengths, Cibi for different oxides and corresponding scattering-length densities, p, for mass densities, 6 oxide Zihi/10-'2 cm S/g cmP2 p/lO'O cmP2 H2O -0.168 1 .oo - 0.56 D20 1.914 1.10 6.36 SiOz 1.575 2.20 3.47 Ce02 1.642 7.13 4.10 Ti02 0.825 3.84 2.39 FeOOH 1.737 4.28 5.04 FeOOD 2.778 4.28 7.96 To determine the contrast match condition for each oxide sol, measurements of I(Q) against Q were made with samples having different H 2 0 : D 2 0 solvent ratios, as shown in fig.6. For titania [fig. 6(a)] a match was obtained at ca. 50 volume % D 2 0 (data had poor statistics and are not shown) corresponding to a scattering length density, pTiO,, of 2.9 x 1 O l o cm-2. This is significantly larger than the calculated value of 2.39 x 1 O l o cmP2 for bulk anatase (cf. table 3) and suggests that the sol particles contain protons, possibly as hydroxyl groups, which are readily exchange- able. The contrast match condition for the iron hydroxide sol was never reached, even at 100% D 2 0 [fig. 6(b)]; however, from an extrapolation of plots of I(Q)* against psolvent a value of ca. 8.4 x 1 O l o cm cm-3 was obtained. This is close to that calculated for a-FeOOD and is an indication that exchange of structural protons occurs readily.The form of the scattering curve of the titania sol, which can be ascribed to a dispersion containing very small polydispersed spherical particles (diameter 6-8 nm), remains unchanged when the titania and FeOOH sols are mixed [cf. fig, 6(a), (i) and (ii)]. This shows that the dispersions are mutually stable, probably because both oxides are positively charged at this pH. An interparticle separation of ca. 30 nm can be estimated from the position of the interface maximum observed at ca. 1.9 x 10- A - 1 for the titania sol. The slight shifts in this maximum with the mixed sols (ca. 1.6 x l o p 2 and 2.2 kl, respective1y)~are dependent on the concentration of titania and suggest that the particles are grouped together around the larger a-FeOOH particles.1 0 INTERACTIONS IN OXIDE SOLS I I 1 '.0.1 0 0.1 0.2 QIA -- Fig. 6. SANS results for ( a ) titania and (6) iron hydroxide sols and their mixtures in water with different H20/D20 volume fractions. (a) Titania (ca. 0.028 g cmP3), volume % D20: U, 0; A, 20; V, 40; +, 70; e, 100; (i) and (ii) mixed sols (100% D20) with concentrations (Ti02 + FeOOH) of (0.014 + 0.015) and (0.1 1 + 0.12) g crnp3, respectively. (b) Iron hy- droxide (ca. 0.030 g cm-3), vol % D20: U, 0; 0 , 50; x , 80; a, 100; (iii) mixture (50% D20) concentrations as in (i). The scattering from the a-FeOOH sols [fig. 6 (b)] is consistent with that expected for thin rod-like particles, with diameter D, for which it can be shown22 that [I(Q)Q]cc exp( - Q2D2/16). 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