pubs.acs.org/Langmuir © 2010 American Chemical Society
Experimental Observation of Fractionated Crystallization in Polydisperse Platelike Colloids D. V. Byelov,*,† M. C. D. Mourad,† I. Snigireva,‡ A. Snigirev,‡ A. V. Petukhov,† and H. N. W. Lekkerkerker† †
Van’t Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute for Nanomaterials Science, Utrecht University, Utrecht, The Netherlands, and ‡ESRF, Grenoble, France Received March 11, 2010. Revised Manuscript Received April 8, 2010
We have discovered that the long-term aging of the hexagonal columnar liquid-crystal phase of polydisperse gibbsite platelets leads to fractionated crystallization, that is, to the formation of coexisting columnar crystals with different periods. This process was revealed by microradian X-ray diffraction demonstrating the splitting of the Bragg intercolumnar reflections into sequences of sharper reflections. The fractionated crystallization was observed in a number of samples of sterically stabilized as well as charge-stabilized polydisperse gibbsite platelets.
Introduction Colloidal particles are able to spontaneously form ordered phases at the submicrometer scale. For example, spherical colloids display crystallization phenomena analogous to atomic systems.1 Anisometric colloids such as rodlike2-4 and plateletlike5-7 particles are able to form various liquid-crystalline phases: nematic with only short-range positional order, smectic with one-dimensional periodicity, and columnar with two-dimensional positional order. The influence of the polydispersity of colloids on their crystallization is well recognized in both experimental1,8-10 and theoretical11-14 studies. In particular, it was shown that a periodically ordered crystal phase of hard-sphere colloids cannot accommodate size polydispersity higher than a certain critical (or terminal) polydispersity σc.15,16 Theoretically, it has been suggested that colloidal suspensions of spherical particles with polydispersity higher than σc can still crystallize accompanied with simultaneous fractionation, that is, splitting into fractions with narrower size distributions.8,16-21 If local values of the polydispersity are then *To whom correspondence should be addressed. E-mail: dbyelov@ gmail.com. (1) Pusey, P. N.; van Megen, W. Nature 1986, 320, 340–342. (2) Dogic, Z.; Fraden, S. Phys. Rev. Lett. 1997, 78, 2417–2420. (3) Lemaire, B. J.; Davidson, P.; Panine, P.; Jolivet, J. P. Phys. Rev. Lett. 2004, 93, 267801(1)–267801(4). (4) Maeda, H.; Maeda, Y. Langmuir 1996, 12, 1446–1452. (5) Brown, A. B. D.; Clarke, S. M.; Rennie, A. R. Langmuir 1998, 14, 3129–3132. (6) van der Kooij, F. M.; Kassapidou, K.; Lekkerkerker, H. N. W. Nature (London) 2000, 406, 868–871. (7) Michot, L. J.; Bihannic, I.; Maddi, S.; Funari, S. S.; Baravian, C.; Levitz, P.; Davidson, P. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 16101–16104. (8) Pusey, P. N. J. Phys. (Paris) 1987, 48, 709–712. (9) Zhang, S. D.; van Duijneveldt, J. S. J. Chem. Phys. 2006, 124, 154910(1)– 154910(7). (10) van den Pol, E.; Thies-Weesie, D.; Petukhov, A.; Vroege, G.; Kvashnina, K. J. Chem. Phys. 2008, 129, 164715(1)–164715(8). (11) Dickinson, E.; Parker, R. J. Phys. Lett. 1985, 46, L229–L232. (12) McRae, R.; Haymet, A. D. J. J. Chem. Phys. 1988, 88, 1114–1125. (13) Fasolo, M.; Sollich, P. Phys. Rev. E 2004, 70, 041410(1)–041410(18). (14) Auer, S.; Frenkel, D. Nature (London) 2001, 413, 711–713. (15) Kofke, D. A.; Bolhuis, P. G. Phys. Rev. E 1999, 59, 618–622. (16) Bartlett, P. J. Chem. Phys. 1998, 109, 10970–10975. (17) Bartlett, P. J. Phys.: Condens. Matter 2000, 12, A275–A280. (18) Sear, R. P. Europhys. Lett. 1998, 44, 531–535. (19) Kranendonk, W. G. T.; Frenkel, D. Mol. Phys. 1991, 72, 679–697. (20) Barrat, J. L.; Hansen, J. P. J. Phys. (Paris) 1986, 46, 1547–1553. (21) Sollich, P.; Wilding, N. B. Phys. Rev. Lett. 2010, 104, 118302.
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below σc, each of these fractions can consequently form crystals with different periods. In other words, the penalty of the decrease of the entropy of mixing can be compensated by the better packing offered by a narrowly dispersed crystalline fraction. The number of coexisting crystal phases was predicted to increase upon increasing the overall particle polydispersity and external compression.16 This fractionated crystallization scenario means that one could grow high quality crystals even in highly polydisperse colloidal suspensions. However, the theoretical model was never proved by experiment. A plausible explanation of this failure could be related to the slow dynamics in crowded concentrated suspensions. Particle fractionation requires their diffusion over significant distances, much larger than the particle size. As a result, the metastable crystalline states can have extremely long lifetimes. In this study, we focus on self-organization of plateletlike colloids. They are able to form columnar liquid-crystal phases even at particle size polydispersity higher than 20%.6,22,23 Interestingly, after centrifugation, leading to fast sedimentation, clear signatures of the columnar structure are still observed.24 Still, the exact mechanism of the formation of liquid crystal phases in the suspension of colloidal platelets should be revealed. We show that columnar crystals of colloidal platelets spontaneously rearrange into coexisting domains with the same structure but distinctly different periods. We present experimental evidence that columnar phases consisting of domains with a discrete spectrum of structure periods exist in a number of aqueous suspensions of charge-stabilized gibbsite as well as in sterically stabilized suspensions of hard particles dispersed in apolar solvent toluene.
Experimental Section Hexagonal colloidal gibbsite platelets Al(OH)3 for the sterically stabilized suspension were synthesized similar to that described in the work of Wierenga et al.25 and then subsequently (22) van der Beek, D.; Petukhov, A.; Oversteegen, S.; Vroege, G.; Lekkerkerker, H. Eur. Phys. J. E 2005, 16, 253–258. (23) Harnau, L. Mol. Phys. 2008, 106(16), 1975–2000. (24) van der Beek, D.; Radstake, P.; Petukhov, A.; Lekkerkerker, H. Langmuir 2007, 23, 11343–11346. (25) Wierenga, A. M.; Lenstra, T. A. J.; Philipse, A. P. Colloids Surf., A 1998, 134, 359–371.
Published on Web 04/14/2010
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Figure 1. Microradian diffraction patterns were measured in multidomain (a) and single-domain (b) regions of a hexagonal columnar phase of sterically stabilized gibbsite particles. Azimuthally integrated profiles of 2D patterns are presented in panel (c). The profiles were shifted vertically by 1 order of magnitude for clarity. grafted26,27 with end functionalized polyisobutene and dispersed in toluene.27 The averaged diameter ÆDæ and the thickness Ælæ of dried particles were estimated from transmission electron microscopy (TEM) measurements and are equal to 237 nm (σD >21%) and 18 nm, correspondingly. The suspension of sterically stabilized gibbsite platelets in toluene was mixed with nonadsorbing polymer poly(dimethylsiloxane), Mw = 423 kDa at concentration 0.8 g/L, to promote the formation of large single crystals28 For the X-ray experiments, the suspension was placed in a flat capillary with internal cross section 0.3 3 mm2. Aqueous charge stabilized suspensions of gibbsite platelets were prepared as described by Mourad et al.29 for selected concentrations of salt (NaCl). Details about the particle synthesis can be found elsewhere;30 their subsequent surface functionalization with Al13 polycations was described by van Bruggen et al.31 Dried particles were inspected by TEM. From the micrographs, the average diameter ÆDæ = 205 nm and the standard deviation σD >23% of particles were obtained. The thickness of gibbsite platelets was estimated from TEM measurements and equal to Ælæ=14 nm. For the X-ray experiments, the suspensions were placed in round capillaries with internal diameter 1.5 mm. X-ray experiments were performed at the Dutch-Belgian beamline BM-26 (DUBBLE)32 and at the beamline ID-06 at ESRF, Grenoble, France. In order to achieve the necessary high resolution, we used a microradian X-ray diffraction setup similar to that used in the work of Petukhov et al.33 The key elements of our setup were compound refractive lenses (CRL)34 and two high resolution CCD detectors (Photonic Science, 4008 by 2671 pixels, with pixel sizes 22 and 9 μm square correspondingly). An angular resolution was of the order of 3-5 microradian. The selected X-ray wavelength was 0.1 nm. (26) Buining, P. A.; Veldhuizen, Y. S. J.; Pathmamanoharan, C.; Lekkerkerker, H. N. W. Colloids Surf. 1992, 64, 47–55. (27) van der Kooij, F. M.; Lekkerkerker, H. N. W. J. Phys. Chem. B 1998, 102, 7829–7832. (28) Petukhov, A.; van der Beek, D.; Dullens, R.; Dolbnya, I.; Vroege, G.; Lekkerkerker, H. N. W. Phys. Rev. Lett. 2005, 95, 077801(1)–077801(4). (29) Mourad, M. C. D.; Byelov, D. V.; Petukhov, A. V.; de Winter, D. A. M.; Verkleij, A. J.; Lekkerkerker, H. N. W. J. Phys. Chem. B 2009, 113, 11604–11613. (30) Wijnhoven, J. E. G. J. J. Colloid Interface Sci. 2005, 292, 403. (31) van Bruggen, M. P. B.; Donker, M.; Lekkerkerker, H. N. W.; Hughes, T. L. Colloids Surf., A 1999, 150, 115–128. (32) Borsboom, M.; Bras, W.; Cerjak, I.; Detollenaere, D.; van Loon, D. G.; Goedtkindt, P.; Konijnenburg, M.; Lassing, P.; Levine, Y. K.; Munneke, B.; Oversluizen, M.; van Tol, R.; Vlieg, E. J. Synchrotron Radiat. 1998, 5, 518–520. (33) Petukhov, A. V.; Thijssen, J. H. J.; ’t Hart, D. C.; Imhof, A.; van Blaaderen, A.; Dolbnya, I. P.; Snigirev, A.; Moussaid, A.; Snigireva, I. J. Appl. Crystallogr. 2006, 39, 137–144. (34) Snigirev, A.; Kohn, V.; Snigireva, I.; Lengeler, B. Nature (London) 1996, 384, 49–51.
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Results and Discussion We start by presenting results obtained on a dispersion of sterically stabilized gibbsite platelets in toluene. The system is similar to that reported by Petukhov et al.28 and tends to spontaneously form (from top to bottom) isotropic, nematic, and columnar coexisting liquid crystalline phases in the capillary upon the establishment of the sedimentation-diffusion equilibrium. Also, homeotropic anchoring with platelets parallel to the flat capillary walls was observed in the nematic and columnar phases. A more detailed study of the structure of the columnar phase revealed that hexagonal intercolumnar ordering is not always long-ranged as it should be in an ideal hexagonal columnar crystal.35 Instead, a hexatic-like structure with short-range positional and long-range orientational order is formed.28 We have performed a series of microradian diffraction measurements on the aged samples (from 2 to 5 years old). The bottom part of the capillary is found to contain a hexagonal columnar phase with two distinct regions yielding diffraction patterns shown in Figure 1a and b. The upper part of the columnar phase contains many small domains and leads to a powderlike pattern (Figure 1a) with reflections forming sharp rings. The most striking observation here is the separation of diffraction peaks into two sets corresponding to coexisting periodic structures with two distinct periods. Quantitatively, the radii of powder rings are assigned to the two coexisting sets of reflections at {q} = {0.0248; 0.0428; 0.0494; 0.0651} nm-1 and {q*}={0.0301; 0.0519; 0.0599} nm-1 as illustrated in Figure 1c. √ √ √ Within each set, the q-values are related as 1: 3: 4: 7. This relation is characteristic for the 100, 110, 200, and 210 Bragg reflections of the hexagonal columnar structure. Only the weaker 210* reflection is not detected. Therefore, at a fixed height in the sample, one can observe contributions from numerous domains with different orientation, each of which can only have one of the two possible periods that differ by about 20%. The lower part of the columnar phase yields a single-domainlike diffraction pattern with clear 6-fold symmetry as shown in Figure 1b. Moreover, splitting of every peak is clearly visible (Figure 1c). Even the 200 peak of the lower-q subset, which is not visible in the azimuthally averaged profile in Figure 1c due to much stronger 110* reflection from the other subset, is still detectable in the two-dimensional pattern in Figure 1b. Therefore, we again observe coexistence of domains with two distinct (35) de Gennes, P.; Prost, J. Physics of liquid crystals, 2nd ed.; Clarendon Press: Oxford, 1993.
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Figure 2. Microradian X-ray diffraction pattern measured with 1 month old (a) and 2 year old (b) aqueous suspensions of gibbsite platelets at a particle concentration of 350 g/L and a salt concentration of 10-4 M.
periods. Interestingly, domains of the two types have exactly the same orientation, meaning that the bond-orientational order is extended over the boundaries between domains of different periods. This can be caused by the free energy of the domain boundaries, which is minimized for adjacent domains with the same orientation. Next, we discuss the results obtained in aqueous suspensions of charged gibbsite platelets. The spatial extent of the Coulomb repulsion is determined by the salt concentration, which affects the phase behavior of the suspensions.29 Here, we focus on the sol region at concentrations from 300 to 350 g/L and a salt concentration from 10-3 to 10-4 M where the system forms the columnar phase. An example of the microradian X-ray diffraction pattern, which has been measured with a 1 month old sample, is presented in Figure 2a. The suspension has a particle concentration of 350 g/ L and a salt concentration of 10-4 M. The pattern shows a number of peaks at low-q range, which are characteristic for columnar hexagonal structure. In addition, one can also see an oriented broad peak at a higher-q range, which indicates the presence of the columns orthogonal to the beam. The face-to-face correlations of platelets are responsible for this peak at q001= 0.154 nm-1. The estimated correlation distance is therefore 2π/ q001=41 nm. The intercolumnar positional correlations of plateand q110 =0.048 nm-1 lets produce peaks at q100 =0.028 nm-1 √ (Figure 3). These q-values are related as 1: 3 that corresponds to the 100 and 110 Bragg reflections of the hexagonally arranged columns√of platelets with an intercolumnar distance of a=(2π/ q100)(2/ 3)=259 nm. In order to study the time evolution of the system, we measured the same sample again after 2 years. The characteristic diffraction pattern is presented in Figure 2b. The intracolumnar face-to-face correlation distance decreases to 35 nm (q001 =0.181 nm-1), and the q001 peak becomes sharper. Qualitatively, new effects appear at low q. The single and relatively broad q100 peak splits into two peaks at q100 =0.027 nm-1 and q*100 =0.031 nm-1 (a=269 nm and a*=234 nm) (see Figure 3). The same splitting is observed for the second order peak q110. The presence of two sets of the different peaks means that there are coexisting periodic structures with two distinct periods. At the same time, the ringlike appearance of the reflections suggests the presence of many domains with different orientation. In this multidomain ensemble, there are two clearly preferred periods. We also note that each of the peaks after splitting is narrower than that before fractionation. The full width at half-maximum of the q100 peak for the aged sample is 7.1 10-4 nm-1 compared to 15.3 10-4 nm-1 for the 1 month old sample. To follow the dynamics of the process at a shorter time scale, we prepared fresh aqueous suspensions of gibbsite platelets at a particle concentration of 350 g/L and a salt concentration of 6900 DOI: 10.1021/la100993k
Figure 3. Azimuthally integrated radial profiles of the scattering intensities in low-q regions of the patterns shown in Figure 2a (bottom curve) and b (top curve). The profiles were shifted vertically by 1 order of magnitude for clarity.
Figure 4. Radial profiles of the averaged scattering intensities in low-q regions of the 2D patterns from 2 year old aqueous suspensions of gibbsite platelets at a particle concentration of 300 g/L and a salt concentration of 10-3 M. The patterns were collected upon vertical scanning of the sample with the high resolution detector. Curves were shifted along the vertical axes for clarity.
10-4 M. We performed X-ray experiments at 2 weeks and 2 months after the preparation of the sample. While the fresh sample exhibits the same pattern as that for the 1 month old sample presented in Figure 2a, the 2 month old sample possesses peak splitting similar to that presented in Figure 2b. Peak splitting also has been found at different heights in the sample as illustrated in Figure 4 for the sample with a particle concentration of 300 g/L and a salt concentration of 10-3 M. One can notice that because of the gravity-induced gradient of the osmotic pressure, the q-values slightly increase upon going down in the capillary. Moreover, not only two but also three coexisting periods can be observed further down in the capillary. Qualitatively, these results agree with the theoretical prediction for spheres: the number of coexisting domains grows with increasing polydispersity and compression.16 Here we briefly highlight meanings of the term fractionation and illustrate it on selected examples. The fractionation between different phases plays an important role in various polydisperse colloidal systems. Examples for rodlike particles were discussed elsewhere,9,10,36-38 and this list is far from being complete. For (36) Vroege, G.; Thies-Weesie, D.; Petukhov, A.; Lemaire, B.; Davidson, P. Adv. Mater. 2006, 18, 2565–2568. (37) Thies-Weesie, D. M. E.; de Hoog, J. P.; Mendiola, M. H. H.; Petukhov, A. V.; Vroege, G. J. Chem. Mater. 2007, 19, 5538–5546. (38) Grelet, E. Phys. Rev. Lett. 2008, 100, 168301–168304.
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instance, significant fractionation of the particles forming different coexisting phases was observed in suspensions of polydisperse goethite rods.10 Also, it was found that polydispersity can induce a new columnar phase,36,37 which acts as a waste bin for the coexisting smectic phase (and vice versa). Still, smectic as well as columnar structures display a single period. Similarly, strong fractionation into thick and thin fractions were recently observed in coexisting isotropic, nematic, and columnar phases of polydisperse colloidal platelets leading to peculiar effects such as density inversion.39 However, all these examples involve fractionation effects between different phases. Here we present fractionation phenomena within a single phase, which is analogous to that predicted for hard spheres.8,16-18 We also note that size segregation during crystallization has been recently observed in a binary mixture of spherical colloids coated with long DNA strands40 but there is a clear difference between segregation in a binary mixture and a (39) Verhoeff, A. A.; Wensink, H. H.; Vis, M.; Jackson, G.; Lekkerkerker, H. N. W. J. Phys. Chem. B 2009, 113, 13476–13484. (40) Geerts, N.; Jahn, S.; Eiser, E. J. Phys.: Condens. Matter 2010, 22, 104111(1)–104111(5).
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fractionated crystallization in a system with a continuous size distribution. We would like to highlight a difference between the theoretical model of the crystallization of polydisperse spheres and the experimental results for the crystallization of polydisperse platelets. Spheres are suggested to undergo the fractionation, which is then followed by crystallization.16 In our observation, the platelets first crystallize into an ordered structure and only after they fractionate and (re)crystallize into better-ordered crystals with a discrete spectrum of periods. We expect that the fractionated crystallization reported here opens up a new way in fabrication of high-quality crystallites out of highly polydisperse particle ensembles. The well-defined discrete spectrum of structure periods can be exploited to create photonic crystals consisting of domains with adjacent photonic band gaps. Acknowledgment. We thank P. Bartlett for fruitful discussions. The authors are grateful to the DUBBLE and ID-6 teams for their excellent support and hospitality. The Dutch Organization for Scientific Research (NWO) and ESRF are thanked for beam time provided.
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