Langmuir 1997, 13, 5007-5010
5007
Orientation and Lattice Structure of Microcrystals of Colloidal Silica Particles in Dispersions Observed by Ultra-small-Angle X-ray Scattering Toshiki Konishi and Norio Ise* Central Laboratory, Rengo Co., Ltd., 186-1-4, Ohhiraki, Fukushima-ku, Osaka 553, Japan Received November 1, 1996. In Final Form: June 13, 1997X By using the ultra-small-angle X-ray scattering technique, the influence of shaking on a single crystal (body-centered-cubic (bcc) lattice) in dilute dispersions of colloidal silica particles was studied in a preliminary manner. After being vigorously shaken, the single crystal was broken into microcrystals while the lattice structure and lattice constant were retained. The scattering profile after shaking always showed a 6-fold symmetry and was not due to single crystals or powder-like. This suggests that the (110) planes (the most densely packed in bcc) of the microcrystals were unexpectedly maintained parallel to, and in contact with, the container (capillary) surface. The preference of the (110) planes over other less densely packed planes contradicts the widely accepted double layer interaction theory and provides a positive support to the largely ignored attractive interaction between charged surface and colloidal particles and between particles.
I. Introduction The ultra-small-angle X-ray scattering (USAXS) technique enables us to detect scattered X-rays at very low angles, down to 4 seconds of arc, from solid and liquid materials and opaque samples (such as turbid colloidal dispersions), where other conventional methods such as light scattering and electron microscopy are not applicable.1 By this method, we observed for the first time several orders of Bragg diffraction from a single crystal of colloidal silica particles in a dilute dispersion (3.76 vol%).2,3 A long-accepted practice has been to assume that the interaction between charged colloidal particles is purely repulsive, in conformity with the so-called DLVO (Derjaguin-Landau-Verwey-Overbeek) theory.4 This repulsion-only assumption is being questioned in the light of recent experimental results,5 for example, void formation in macroscopically “homogeneous” dispersions.6 We have recently discussed the paradoxical nature of this assumption in the light of basic knowledge and logical criteria.7 In this article, we present new results using the USAXS technique for colloidal silica particle dispersions, which are inconsistent with this assumption and testify to the presence of an attractive interparticle interaction. In our previous reports,2,3 it was concluded that a single body-centered-cubic (bcc) crystal was formed in a dilute dispersion in a capillary with the [11 h 1] or [001] direction of the crystal being parallel to the capillary axis with, respectively, 6- and 4-fold symmetries. Furthermore, the nearest neighbor interparticle distance 2Dexp derived from the lattice constant, a, was smaller than the average distance 2D0 calculated from the overall concentration and the radius of the particle.2,3 In order to confirm that the difference between 2Dexp and 2D0 is entirely due to interparticle interaction, we thought it would be of interest to examine whether or not sedimentation of the particles and concentration gradients of salt ions in the capillary were causes of the observed relationship, since the specific X
Abstract published in Advance ACS Abstracts, August 15, 1997.
(1) Matsuoka, H.; Ise, N. Adv. Polym. Sci. 1994, 114, 187. (2) Konishi, T.; Ise, N.; Matsuoka, H.; Yamaoka, H.; Sogami, I. S.; Yoshiyama, Y. Phys. Rev. B 1995, 51, 3914. (3) Konishi, T.; Ise, N. J. Am. Chem. Soc. 1995, 117, 8422. (4) Derjaguin, B. V.; Landau, L. Acta Physiochim. 1941, 14, 113. Verwey, E. J. W.; Overbeek, J. Th. G . Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948. (5) Dosho, S.; et al. Langmuir 1993, 9, 394. (6) Ito, K.; Yoshida, H.; Ise, N. Science 1994, 263, 66. (7) Ise, N.; Yoshida, H. Acc. Chem. Res. 1996, 29, 3.
S0743-7463(96)01064-5 CCC: $14.00
gravity of the silica is rather large (2.2 g/cm3) and ionexchange resin particles were not placed uniformly through the dispersion. Thus, in the present preliminary study, we measured USAXS for dispersions after the capillary had been shaken vigorously and found its unanticipated influence on ordered structures in the colloidal silica dispersion. II. Experimental Section A colloidal silica dispersion in water (KE-P10W) with a concentration of about 20 wt % was kindly donated by Nippon Shokubai Co. Ltd., Osaka. The particles had an average radius R of 560 Å with a standard deviation of 8%, as determined by fitting the USAXS profiles under high salt condition to the form factors for isolated spheres.8 The original dispersion was purified by dialysis against Milli-Q reagent-grade water for 2 weeks. The surface charge density was 0.06 µC/cm2 as determined by conductivity measurements.9 Three test dispersions with different concentrations were prepared by dilution with Milli-Q water. The volume fractions, c, of colloidal silica were determined to be 1.53, 2.89, and 3.80 vol % by dry weight.9 The dispersion was put into a quartz capillary (70 mm length) with an inner diameter of 2 mm. For further deionization, ion-exchange resin particles (AG501-X8(D), Bio-Rad Lab., Richmond, CA) were confined by a nylon mesh at the top and bottom of the dispersion, where the X-ray beam did not strike. The details of our USAXS apparatus have been described elsewhere.2,3 The scattering intensity I(2θ˜ ) was measured as a function of the rotation angle 2θ˜ of the second channel-cut crystal rotated with respect to the vertical axis. The scattering profile for the dispersion with c ) 1.53 vol % was first measured after the capillary was kept standing vertically for 9 days. USAXS was again measured after the capillary had been vigorously shaken. For other dispersions with different concentrations of silica, USAXS profiles were measured only after the capillary had been shaken. Because the scattering profiles from the dispersions were not isotropic (not powder-like), we carried out the USAXS measurements by rotating the capillary about the capillary axis by ω (ω ) 0 was where scattering was at a maximum) and also rotating in the plane at right angles to the X-ray beam by φ˜ (φ˜ ) 0 was where the capillary was vertical). It has to be mentioned that, in the present preliminary study, the dispersion capillary was vigorously shaken in order to “rectify” the putative inhomogeneous distribution of particles and salt ions and the “shaking” has not been quantified. As will be discussed below, the change of the orientation of crystals by (8) Konishi, T.; Yamahara, E .; Ise, N. Langmuir 1996, 12, 2608. (9) Yamanaka, J.; Hayashi, Y.; Ise, N.; Yamaguchi, T. Phys. Rev. E 1997, 55, 3028.
© 1997 American Chemical Society
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Figure 1. The logarithm of the USAXS intensity I(2θ˜ ) in counts per second plotted against the rotation angle 2θ˜ of the second Ge crystal. Sample: 1.53 vol % water dispersion of silica particles (radius 560 Å , standard deviation 8%). Rotation angle of the capillary ω ) 0° with respect to its axis and φ˜ ) 0° with respect to the axis which is parallel to the incident X-ray. As described in previous papers,2,3 the incident and scattered X rays were highly parallel in the horizontal plane, but not in the vertical plane. Thus, 2θ˜ does not always equal the true scattering angle 2θ, but 2θ˜ ) 2θ cos φ, with φ being the angle made by the horizontal plane with the scattering plane which is defined by the paths of the incident and scattered X-rays. We note here that the angle φ is equal to the angle between the lattice plane that gives rise to the diffraction and the vertical plane that includes the path of the incident X-ray. shaking did take place with high reproducibility. If the orientation did change at random by “shaking”, the way of shaking must have been controlled carefully. The influence of shear stress with controlled magnitude and direction on colloidal single crystals is of interest as a future study.
III. Results and Discussion Figure 1 shows the USAXS profile for a colloidal silica dispersion of c ) 1.53 vol % prior to shaking the capillary. The measurement was performed with both rotation angles ω and φ˜ equal to 0°. The same scattering profiles were obtained when ω ) (90 × m)°, with m being an integer. As seen from Figure 1, sharp peaks were observed at diffraction angles of 100 × n seconds, with n being an integer. These Bragg reflections with values of n up to 3 show that a large single crystal had grown in the capillary. Following the procedure previously described3 for crystal structure with 4-fold symmetry, we concluded that a single colloidal crystal with bcc symmetry had grown with the [001] direction being parallel to the capillary axis and with the lattice constant a ) 4400 Å. The previous papers2,3 showed that, besides the 4-fold symmetry as demonstrated in Figure 1, a 6-fold symmetry can also be observed for the same dispersion but from a different capillary. This must be kept in mind, since we observed only 6-fold symmetry after shaking as will be mentioned below. Figure 2 shows the USAXS profiles for the same dispersion measured over the period 1-4 days after the capillary was shaken. Si crystals were used for detection and ω was 0°. The same scattering profiles were obtained for all angles of ω, but the profile varied with changing angle φ˜ as shown in Figure 2. The profile at φ˜ ) 0 (top curve in Figure 2), which was obtained on the forth day, had the same shape as the one which was obtained over the period 15 min to 12 h after the capillary was shaken (data not shown), indicating that no significant change in the structure of the colloidal crystal occurred between 12 h and 4 days after shaking.10
Konishi and Ise
Figure 2. Logarithm of the relative USAXS intensity I(2θ˜ ) in counts per second plotted against the rotation angle 2θ˜ of the second Si crystal for various rotation angles φ˜ of the capillary. Sample was 1.53 vol % water dispersion of silica particles (using the same dispersion in the same capillary as in Figure 1). Scanning of 2θ˜ was carried out continuously with consecutive values of φ˜ after shaking the capillary. Rotation angle of the capillary ω ) 0 with respect to its axis, and the same USAXS profile was observed at all rotation angles ω with respect to the capillary axis. The curves were shifted vertically by an order of 10.
It can be seen that after shaking the structure is neither powder-like, as the profile is dependent on φ˜ , nor due to a single crystal as the profile is independent of ω. Because the smearing effect12 prevented us from applying the conventional analysis usually used in crystallography, we first attempted to explain the USAXS results obtained by assuming various lattice structures. Consequently, we concluded that a bcc lattice, with [11 h 1] parallel to the capillary axis and a equal to 4300 Å, was formed after shaking. Here, we emphasize that this lattice structure explains all the experimental results observed. We discuss the relation between the value of 2θ˜ at the peak position in the scattering profile and the value of φ˜ . Because of the smearing effect (see the caption to Figure 1), the rotation angle of the second crystal 2θ˜ peak at the peak in Figure 2 is related to the true diffraction angle 2θ˜ peak as follows.
2θ˜ peak ) 2θpeak cos φ
(1)
The angle φ is given by the equation
φ ) φ0 + φ˜
(2)
where φ0 is the angle made by the diffraction plane and the capillary axis. The expected values of φ0 are easily (10) The sample studied here was allowed to stand without motion after the present study and reinvestigated 12 months later by using a two-dimensional USAXS apparatus (ref 11). According to this recent study the scattering profile was still φ˜ -dependent but no longer ω-independent, indicating that microcrystals grew, though very slowly, and relatively large microcrystals were dispersed in the dispersion. (11) Konishi, T.; Ise, N. Submitted. (12) Guinier, A.; Fournet, A. Small Angle Scattering of X-rays; Wiley: New York, 1955.
Microcrystals of Colloidal Silica Particles
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Figure 3. Dependence of the rotation angle 2θ˜ peak of the second crystal of the Bonse-Hart camera at the diffraction peak in the USAXS profiles on the rotation angle φ˜ of the capillary with respect to the axis parallel to the incident X-ray beam. (open circle), observed data; (solid line) calculated data.
calculated from the geometry of the assumed lattice structure to be 0 and (54.7° for {110} planes, (35.3° for {200} planes, and 0, (28.1, and (70.5° for {211} planes. We did not take diffractions from other lattice planes into account because of their presumably low intensities. The diffraction angle 2θ is given by
sin θ ) λ/2dhkl
(3)
with dhkl being the distance between the lattice planes of Miller indices hkl. The values of dhkl are calculated assuming the value of a from
dhkl ) a/(h2 + k2 + l2)1/2
(4)
for bcc lattices. We compared the dependence of the calculated 2θ˜ peak on φ˜ with the observed values in Figure 3. One can see that there is good agreement between observed and calculated values. Thus we confirmed that the lattice structure was not changed by shaking. We noted that the lattice constant for the dispersion stayed practically unchanged before (4400 Å) and after (4300 Å) shaking. On the other hand, the orientation of the microcrystals changed; the large single crystal was broken and each of the new microcrystals had a new orientation rotated from the original one by 54.7° (the angle between [001] and [11h 1]). It should be noted that the (110) planes were kept parallel to the capillary surface whether [001] or [11 h 1] was parallel to the capillary axis. This result is consistent with microscopic observation and Kossel line analysis reported earlier,13,14 which showed that, for bcc, the (110) plane was parallel to, and in contact with, the surface of the cover glass. We imply that the phrase “in contact” means that the (110) plane was about 4000 Å (the order of magnitude of 2Dexp) distant from the glass surface on the basis of microscopic information on latex dispersions.5 Furthermore, from the fact that the USAXS profile did not depend on the rotation angle ω, we concluded that (13) Ito, K.; Nakamura, H.; Ise, N. J. Chem. Phys. 1986, 85, 6143. (14) Sogami, I. S.; Yoshiyama, T. Phase Transition 1990, 21, 171.
Figure 4. Schematic view of the distribution and orientation of microcrystals (rectangles) in capillary (bold lines and curve) after shaking. The (110) planes are denoted by dashed lines. Table 1. Values of 2Dexp and 2D0 c (vol %)
2Dexp (Å)
2D0 (Å)
1.53 2.89 3.80
3700 2800 2600
3900 3100 2800
microcrystals are large in number and that the orientation of the each microcrystal with respect to the capillary axis is same, but arranged randomly about the [11 h 1] axis. Figure 4 shows the highly schematic view of the distribution of microcrystals in the capillary. Using the methods discussed above, we determined the structures for dispersions with c ) 2.89 and 3.80 vol % to be the same as for a dispersion with c ) 1.53 vol %, namely, bcc with [11 h 1] parallel to the capillary axis but with different lattice constants. The values of 2Dexp and 2D0 are listed in Table 1, which shows 2Dexp is less than 2D0. Thus the non-space-filling nature1-3,15 of the colloidal crystals at low concentrations was again confirmed for dispersions under condition where particle sedimentation and concentration gradients are not significant. Clearly, at 2.89 vol %, the microcrystals occupy only 73.5% [)(2800/3100)3] of the total dispersion volume while 26.5% is occupied by voids and/or free (disordered) particles.16 This result supports the presence of an attractive interparticle interaction. It is interesting to note that the crystal structure itself did not change when the system was shaken and the (110) planes were kept parallel to the capillary surface, while the orientation of the microcrystals was randomized in the vertical direction. Whether the [001] or [11h 1] direction is kept parallel to the capillary axis, the {110} planes (the most densely packed plane in bcc) have to be in contact with and parallel to the surface. This fact seems not to (15) Ise, N.; et al. J. Am. Chem. Soc. 1980, 102, 7901. See also Ise, N. Angew. Chem. 1986, 25, 323; Ber. Bunsenges. Phys. Chem. 1996, 100, 841. (16) We considered here only 2.89 vol %. For other concentrations, we could not exclude the possibility that the ion-exchange resin particles added contained a small amount of water, lowering the particle concentration. If this was the case, the 2D0 values at 1.53 and 3.80 vol % could be larger than the values given in Table 1.
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be consistent with the widely accepted idea that negatively charged particles must be repelled by a (negatively charged) surface (the double layer interaction theory). If this theory is correct, less dense planes other than {110} are expected to be favored near the capillary surface. This however is not what was observed to be the case. Independently, Thomas and Ito et al.17,18 demonstrated experimentally that ionic entities are positively absorbed near a like-charged interface, and our observations are consistent with their finding. There must be an electrostatic attraction between negatively charged particles and negatively charged interface mediated via intermediary hydronium counterions.5,7,15,19 Because of this counterionmediated attraction, {110} planes are formed more easily than other less dense planes in contact with the capillary surface, upon which the second {110} planes would be then formed by the same mechanism, and so on. One might ask whether the observed attraction is due to image forces between the particle and the quartz capillary. However, this concept is originally for conductor/charge systems and therefore is not valid in the present case, since the quartz is not conductor. In this respect, it would be interesting to note that the quartz surface is covered by silanol groups, which dissociate into silanol anions and protons in dissociating solvent, and the protons in solutions may be polarized near the anionic silica particles. As a result, there might be created a “dipoleion” attraction between the quartz surface and the particles. However, at the present we have no experimental evidence of the polarization. Therefore we believe that the electrostatic potential due to the dissociated silanol groups is overwhelmingly high so that it would have a long-range effect on proton distribution in dispersions, causing the counterion-mediated attraction. The counterion-mediated attraction stabilizes the lattice, which explains why the [11 h 1] direction parallel to the capillary axis (6-fold symmetry) is preferred, since three of six {110} planes then are parallel to the capillary surface and the microcrystals are much more stabilized (in other words, a greater contact between the curved capillary surface and the planar crystal plane is realized) than when only two of the {110} planes are parallel to the surface (4-fold symmetry), namely, when the [001] direction is parallel to the axis. In other words, the lowest free energy state was chosen after shaking, and therefore it is quite reasonable that exclusively 6-fold symmetry was observed after shaking. It is surprising that the orientation mentioned above was reproducible regardless of the concentrations of particles and can be accounted for by simple energetics between the capillary surface and particles and between the particles themselves. However, the reason why many microcrystals were formed after shaking, rather than a single crystal, is not very clear. Here we point out some possibilities. The first is that the colloidal dispersion was not kept standing long enough after shaking to allow a single crystal to grow. As the second possibility, we suggest that the microcrystals produced by shaking are fairly monodisperse in size, so that the Ostwald ripening process,21 in which larger crystals grow at the expense of smaller ones, becomes too slow.10
In the above argument, the original single crystal was assumed to be broken into free particles by the shaking. Another possibility is that the single crystal was broken into small crystals, which were reoriented to the final arrangement by rotational diffusion. However, in order for this process to have taken place as described, the single crystal would have had to be cleaved along the {110} plane. One should remember that d110 is certainly the longest among the interplanar distances of bcc structures, and according to Kossel line analysis14 colloidal bcc crystal growth proceeds by stepwise stacking of {110} planes. It is to be noted that Ackerson and Clark22 investigated the structures of colloidal crystals under shear using light scattering and the slippage of the (110) planes over one another under shear was concluded. Our finding that the (110) planes were kept parallel to the surface after shaking is in line with theirs. It is worth noting that close check of their data (Figures 2 and 3 in ref 22) reveals 2Dexp ≈ 2D0 under their experimental condition, although they did not mention this. In other words, the crystal was almost space-filling. Under such a circumstance, there was naturally no need to invoke an attractive interaction between the surface and particles to explain the parallelism of the most closely packed plane and the surface. In other words, the repulsion between particles in the bulk sufficed. On the other hand, our crystal is non-space-filling, which can be accounted for by assuming an interparticle attractive interaction. Then it is difficult to interpret the parallelism of the (110) plane and the glass surface in terms of the repulsion-only assumption. This difficulty is solved by accepting an attractive interaction between the surface and particles, which was demonstrated to exist in latex dispersions by Ito et al.23 It is not clear from our experiments whether the shaking destroyed completely the original single crystal to particles or partially broke the crystal to microcrystals by shear in a manner suggested by Ackerson and Clark. Timeresolved USAXS setups and relevant experimental designs are necessary to reach a final solution. In summary, it is emphasized that the present experiments unexpectedly revealed that the capillary surface plays an important role in colloidal crystal growth at low concentrations. The fact that the most closely packed planes were preferred near the capillary surface is inconsistent with the basic idea of the established double layer interaction theory. This observation, together with the relationship 2Dexp < 2D0, adds to recognition of the counterion-mediated attraction between similarly charged particles and between the particles and similarly charged surface. We believe that the present argument may have a profound impact on not only colloid science but also complex fluid physics and chemical physics of ionic systems.
(17) Lu, J. R.; Simister, E. A.; Thomas, R. K.; Penfold, J. J. Phys. Chem. 1993, 97, 13907. (18) Ito, K.; Muramoto, T.; Kitano, H. J. Am. Chem. Soc. 1995, 117, 5005; Proc. Jpn. Acad. 1996, 72B, 62. (19) It has been often claimed that the positive adsorption is caused by the repulsion between like-charged particles in the bulk. This interpretation was ruled out by the recent observation that the adsorption is enhanced when the charge number of the interface is increased (see Figure 4 of ref 20). (20) Muramoto, T.; Ito, K.; Kitano, H. J. Am. Chem. Soc. 1997, 119, 3592.
(21) Ostwald, Wil. Z. Phys. Chem. 1900, 34, 495. (22) Ackerson, B. J.; Clark, N. A. Phys. Rev. A 1984, 30, 906. (23) As a reason why the equality relation held for the AckersonClark case whereas the inequality is observed in our case, we might suggest the difference in the charge densities of the particles used. The (effective) charge density of their particles was 0.04 µC/cm2 (based on the value of 360 e/particle obtained by fitting to a model calculation), while our particles have 0.06 µC/cm2. Although the difference is small, our sample is slightly more charged than the A-C spheres. Our experience shows that the higher the charge number, the stronger the interparticle attraction, resulting in the inequality relation.
Acknowledgment. Mr. S. Owen and Dr. B. V. R. Tata gave us kind help in preparing the manuscript and useful discussion, which are gratefully acknowledged. The authors thank Nippon Shokubai Co., Ltd., for the kind donation of the sample. LA961064J
