Langmuir 2006, 22, 9843-9845
9843
Articles Rupture and Regeneration of Colloidal Crystals As Studied by Two-Dimensional Ultra-Small-Angle X-ray Scattering Toshiki Konishi and Norio Ise* Central Laboratory, Rengo Company, Ltd., 186-1 4-chome, Ohhiraki, Fukushima, Osaka 553-0007, Japan ReceiVed May 4, 2006. In Final Form: July 19, 2006 The structure of colloidal crystals of silica particles in water was studied by using the two-dimensional (2D) ultra-small-angle X-ray scattering (USAXS) technique. By violent shaking of the dispersion, large (body-centered cubic, bcc) crystals were broken into microcrystals while the lattice structure and lattice constant were preserved. The 2D-USAXS profiles revealed that the [11h1] direction of bcc microcrystals was parallel to the capillary axis and their orientational distribution with respect to the capillary axis was random. While a prepeak was observed in the onedimensional USAXS measurements, no such peak was detected by the 2D-USAXS technique. The prepeak was concluded to be due to {110} being rotated by 54.7° (the angle between [001] and [11h1]) from the capillary axis. The diffraction from the plane was out of the horizontal plane and was observed at a lower angle as a prepeak by detector scanning in the horizontal direction.
Introduction Previously,1 we studied colloidal crystals of silica particles in water by the one-dimensional ultra-small-angle X-ray scattering (1D-USAXS) technique, with special reference to the rupture of a single crystal by shaking and subsequent regeneration of microcrystals. It was demonstrated that the single crystal was broken into microcrystals while retaining the lattice symmetry (body-centered-cubic (bcc) at a particle concentration of 1.53 vol %) and lattice constant. The scattering profile after shaking, which was not single-crystal-like or powder-like, always showed a 6-fold symmetry, suggesting that [11h1] was kept parallel to the capillary axis. We believe that this conclusion is correct but admit that our argument was indirect in a sense that the structure and its direction had to be assumed and compared with the experimental data. In the 1D-USAXS apparatus, the X-rays were not parallel in the vertical plane and the detected intensity was smeared. Owing to this smearing effect, it is difficult by the 1D-USAXS technique to obtain the scattered intensity from oriented systems as a function of the scattering vector. In other words, reliable structural information can be derived by the 1DUSAXS technique only for disoriented systems, and careful treatment is required in the analysis of the scattering data for mixed systems in which oriented structures coexist with disoriented structures. In the present study, we took advantage of two-dimensional ultra-small-angle X-ray scattering (2DUSAXS),2 in which the incident X-ray is collimated in two perpendicular (horizontal and vertical) planes, to further shed light on the very fragile nature of colloidal crystals. The 2DUSAXS incident beam has been confirmed to have a pointfocusing geometry, so the smearing effect is practically absent, enabling us to obtain scattered intensity as a function of the scattering vector and hence reliable information from oriented systems and also from mixed systems. Furthermore, structural * To whom correspondence should be addressed. Present address: 23 Nakanosaka, Kamigamo, Kita-ku, Kyoto 603-8024, Japan. E-mail:
[email protected]. (1) Konishi T.; Ise, N. Langmuir 1997, 13, 5007. (2) Konishi T.; Ise, N. Phys. ReV. 1998, B57, 2655.
information can uniquely be derived from the 2D-USAXS profiles without assuming a lattice structure and its direction a priori.2 It is fair to mention that a 2D-USAXS technique was developed successfully for structure analysis of colloidal crystals by Vos et al.3 It is worth mentioning that, for colloidal silica powder, the 1D-USAXS technique provided the same scattered intensityscattering vector curve after the desmearing procedure was applied as provided directly by the 2D-USAXS method.4 Experimental Section The colloidal silica particle, Seahoster KE-P10W, was a product of Nippon Shokubai Co., Ltd. (Osaka, Japan), which was used also in the previous work.1,2,4 The average radius was 54 nm with a standard deviation of 8% as determined by fitting the 1D-USAXS profiles under high salt conditions to the form factors for isolated spheres. The net surface charge density was determined to be 0.06 µC cm-2 by conductivity measurements.5 The sample dispersion was extensively purified according to our usual procedure. The 2DUSAXS apparatus was described previously.2 The purified dispersions were introduced into a quartz capillary2 (length 70 mm, inner diameter 2 mm). The scattered intensity measurements were carried out at a fixed scattering angle θ and at various directions of the scattering vector by rotating the sample capillary about the capillary axis by φs and about the axis of the X-ray by χ. (For notations and definitions, see a recent monograph6). The dispersions were violently shaken several times (a few seconds) to dozens of times. The shaking was done in such a way that the direction of motion of the dispersion in the capillary was repeatedly reversed in short times. The dispersions thereby lost iridescence, indicating qualitatively that the starting crystals inside were destroyed. The few seconds of shaking were adequate to give (3) Vos, W. L.; Megens, M.; Van Kats, C. M.; Bo¨secke, P. Langmuir 1997, 13, 6004. (4) Konishi, T.; Yamahara, E.; Furuta, T.; Ise, N. J. Appl. Crystallogr. 1997, 30, 854. (5) Yamanaka, J.; Hayashi, Y.; Ise, N.; Yamaguchi, T. Phys. ReV. 1997, E55, 3028. (6) Ise N.; Sogami, I. S. Structure Formation in Solution-Ionic Polymers and Colloidal Particles; Springer: Berlin, 2005.
10.1021/la061247y CCC: $33.50 © 2006 American Chemical Society Published on Web 10/28/2006
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Figure 1. Contour plot of 2D-USAXS intensity before shaking (silica particle concentration 7.5 vol %, scattering angle θ ) 200 s). The intensity was measured 13 days after the dispersion was introduced into the capillary.
Konishi and Ise
Figure 2. Contour plot of 2D-USAXS intensity measured 1 day after shaking (silica particle concentration 7.5 vol %, θ ) 188 s).
a scattering pattern similar to that in Figure 2: Longer shaking gave practically the same patterns. Thus, it was inferred that the crystals were almost completely destroyed by the shaking. The capillaries were then kept standing until the scattering measurements. The adequacy of our shaking procedures is demonstrated by the high reproducibility of the results and, more clearly, by the fact that our 1D-USAXS profiles after shaking agreed with independent results by Reus et al.,7 as far as the peak position is concerned, who employed an apparatus specially designed to carry out the measurements both at rest and under shear. Thus, we believe that the shaking procedure is satisfactory for our purpose and adopted it in the present 2DUSAXS work.
Results and Discussion Before Shaking. Figure 1 is the contour plot of the 2D-USAXS intensities against χ and φs for an aqueous (7.5 vol %) dispersion of colloidal silica, which was left standing for 13 days in the quartz capillary. The measurements were done before the capillary was shaken. The scattering angle θ was 200 s at the peak of the {110} diffraction of a bcc structure, and hence, the closest interparticle distance 2Dexp was 194 nm while the average distance 2D0 was calculated to be 226 nm from the particle concentration. We note that the inequality relation 2Dexp < 2D0 is seen to hold, though less clearly than at lower concentrations, suggesting that the dispersion contains localized ordered structures of a higher particle density in the “sea” of lower particle densities and maintains the two-state structure6 even at 7 vol %. In Figure 1, all {110} diffractions from the scattering volume (about 1 mm × 1 mm × 1.5 mm) were observed except those at φs ) 90° and 270°, where the X-ray beam was intercepted by the capillary holder. As seen in Figure 1, the number of crystal grains that gave rise to diffraction with detectable intensity was limited, and each crystal grain was relatively large compared with those after shaking (Figure 2). After Shaking. Figures 2 and 3 are the contour plots of the intensities against χ and φs for the dispersion measured at 24 h and 10 days, respectively, after shaking of the sample used in Figure 1. It is seen that the {110} planes were oriented in such a way that χ ) 0° or 55° independently of φs. It is easily shown by the bcc geometry that the observed profile can be accounted for only when [11h1] of the bcc crystal is parallel to the capillary axis and the rotational angle with respect to the capillary axis is randomly distributed. We note that this orientational distribution was concluded by the 1D-USAXS measurement in the previous paper.1 It is also noticed from Figure 2 that the number of (7) Reus, V.; Belloni, L.; Zemb, T.; Lutterbach, N.; Versmold, H. J. Phys. II 1997, 7, 603.
Figure 3. Contour plot of 2D-USAXS intensity measured 10 days after shaking (silica particle concentration 7.5 vol %, θ ) 188 s).
Figure 4. Contour plot of 2D-USAXS intensity measured about one year after shaking (silica particle concentration 1.53 vol %, θ ) 112 s).
microcrystals giving rise to diffraction with detectable intensity is large enough and their sizes are relatively small compared with those of the crystal grains before shaking. On the 10th day after shaking, some microcrystals were found to be oriented in ways different from those in Figure 2 and seemed to decrease in number and increase in size as time passed. Figure 4 gives the data at a 1.53 vol % dispersion taken 1 year after shaking. It is to be noted here that, before shaking, this sample had a 1D-USAXS profile reported in Figure 1 of ref 1 which was characteristic of a single crystal, while the 1D-USAXS profile over the period of 1-4 days after shaking was not singlecrystal-like or powder-like as shown in Figure 2 of ref 1. It is clear that Figure 4 is similar to Figure 2, though the concentration is different, but there are fewer microcrystals in the former than in the latter, while their size is larger at a lower concentration. It seems from Figures 3 and 4 that the orientation of the microcrystals at a lower concentration is more strongly regulated than at a higher concentration.
Colloidal Crystal Rupture/Regeneration by 2D-USAXS
Diffuse Peak. For the colloidal silica particle dispersion, no peaks are found by the 2D-USAXS technique at scattering vectors lower than the position of the {110} diffraction peak of the bcc crystal, while a “prepeak” was observed in the 1D-USAXS study for the colloidal dispersion under some experimental conditions.1 See Figure 2 in ref 1. Reus et al. also carried out 1D-USAXS measurements and found a powder-like scattering profile from dispersions of bromopolystyrene particles under shear, which was claimed to form a bcc structure at 2-12 vol %.7 However, a diffuse prepeak was observed for dispersions at rest. Harada et al. also observed a prepeak for an aqueous 3.8 vol % dispersion of poly(methyl methacrylate) particles by 1D-USAXS,8 which was reported to form a face-centered cubic (fcc) structure under their conditions. These authors attributed the prepeak to the existence of crystal defects. Remember that the prepeak occurred only in the 1D-USAXS measurements. In this respect, it is important to recall our previous 1D-USAXS observation,1 in which a prepeak was actually observed but its peak position varied with changing rotational angle of the capillary in the plane perpendicular to the incident X-ray, φ˜ . When the capillary was kept vertical, in other words, at φ˜ ) 0°, peaks were observed at positions relative to those of the {110} planes at 0.58, 1.00, 1.53, 1.73, and 2.00. Interestingly, the peaks reported by Reus et al. were located at 0.6, 1.0, 1.5, 1.7, and 2.0. The agreement with our 1D-USAXS observation is clear9 and implies that the peak at 0.6, which they called the diffuse prepeak, is the {110} diffraction peak observed at an apparent scattering angle θ˜ ) θ cos 54.7° (0.58), where 54.7° is the angle made between [001] and [11h1] of the bcc crystal. (For a definition, see Figure 1 of ref 10.) Since the powder sample of silica particles did not give the prepeak even in the 1D-USAXS profile, as mentioned above, the prepeak seems to have its origin in an orientational nonrandomness of microcrystals. In passing, we note that the desmearing treatment is not appropriate for the scattering data at rest reported by Reus et al., since the method is valid for isotropically disoriented systems while the actual dispersion was not disoriented. It seems that the inappropriateness is clearly demonstrated by the fact that the desmeared scattered intensity was not positive between peaks in Figure 7 of ref 7. The observation of the prepeak is related to the optical system of the 1D-USAXS apparatus. The diffracted X-ray is detected by rotating the second Ge crystal on a horizontal plane in this (8) Harada, T.; Matsuoka, T; Ikeda, H.; Yamaoka, H. Colloids Surf., A 2000, 174, 79. (9) This agreement seems to imply that “applying shear” in Reus et al.’s experiments is equivalent to “shaking” in ours and that the dispersion “at rest” contains regenerated microcrystals. (10) Konishi T.; Ise, N. J. Am. Chem. Soc. 1995, 117, 8422.
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apparatus. Diffraction from a colloidal crystal out of the horizontal plane at scattering angle θ (made by the incident X-ray in the horizontal plane with the scattered X-ray) is detected when the second Ge crystal is rotated not by θ, but by θ˜ . The 1D-USAXS optical system, which has a smearing effect in the vertical direction, gives θ˜ ) θ cos φ′, where φ′ is given by φ′ ) φ0 + φ˜ . φ0 is the angle between the diffraction plane and the capillary axis and is determined by the lattice structure and its direction (for example, 0° and (54.7° for (110) of the bcc crystal and 35.3° for (200)). Thus, the above consideration shows that the so-called diffuse prepeak reported is a diffraction of the {110} plane of the bcc crystal in the direction rotated by 54.7° from the capillary axis. As discussed in refs 1 and 10, the reason this rotation took place is that the dispersion energetically favors a crystal orientation of 6-fold symmetry ([11h1] parallel to the capillary axis), which ensures stronger stabilization due to particle-capillary wall interaction than the 4-fold symmetry ([001] parallel to the capillary axis).11 In the case of an fcc crystal, two {11h1} planes out of the four can be parallel to the capillary wall; in other words, the [110] direction is parallel to the capillary axis. Two remaining {11h1} planes form an angle of 54.7° with the capillary axis. Thus, if a prepeak is to be observed, it is located at cos 54.7° ()0.58) of the lowest position of the true {11h1} diffraction. Harada et al. observed the prepeak at around 0.6 by 1D-USAXS and ultrasmall-angle neutron scattering (USANS).12,13 In summary, the influence of shaking on a colloidal crystal of silica particles in water was studied by using the 2D-USAXS technique. By shaking, a large (bcc) crystal was broken into microcrystals while the lattice structure and lattice constant were retained. The scattering profile indicated that the [11h1] direction of bcc microcrystals was parallel to the capillary axis and their orientational distribution with respect to the capillary axis was random. This conclusion agrees with that we derived previously using the 1D-USAXS technique. While a diffuse prepeak was observed in the 1D-USAXS and USANS measurements, it was not detected in the 2D-USAXS study. It was concluded that the prepeak was caused by the orientational nonrandomness and the detection system. LA061247Y (11) Compare Figure 3 of ref 2 and Figure 3 of ref 8. (12) Matsuoka, H.; Ikeda, T.; Yamaoka, H.; Hashimoto, M.; Takahashi, T.; Amagalian, M. M.; Wignall, G. D. Langmuir 1999, 15, 293. (13) Matsuoka, H.; Yamamoto, T.; Harada, T.; Ikeda, T. Langmuir 2005, 21, 7105.
