Evidence of the hexagonal columnar liquid-crystal phase of hard colloidal platelets by high-resolution SAXS

Beek, D. van der; Petukhov, Andrei V.; Oversteegen, S. M.; Vroege, G. J.; Lekkerkerker, H. N. W.

doi:10.1140/epje/i2004-10080-6

Cited by 50 publications

(52 citation statements)

References 65 publications

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“…Likewise, one could expect that translational ordering in polydisperse colloidal suspensions may be inhibited [8][9][10][11][12][13]. Surprisingly, colloidal platelike particles with a diameter polydispersity as high as 25% appear to form spontaneously hexagonal columnar liquid crystals [14,15]. Here, we demonstrate that it is the hexatic intercolumnar structure of the novel columnar phase, which allows for the accommodation of the particle polydispersity.…”

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Observation of a Hexatic Columnar Liquid Crystal of Polydisperse Colloidal Disks

et al. 2005

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We report the observation of a new type of columnar liquid crystal phase, which is formed by thin hard colloidal disks in a dense suspension. High-resolution small-angle x-ray diffraction reveals a combination of long-range bond-orientational order and short-range translational order between the columns, the hallmark of the hexatic phase. Our results imply that geometric frustration related to the size polydispersity of the particles destroys long-range translational order and therefore promotes the formation of this novel phase. DOI: 10.1103/PhysRevLett.95.077801 PACS numbers: 61.30.2v, 61.10.2i, 64.70.Md, 82.70.Dd The hexatic phase, which was first suggested as an intermediate state between a crystal and a liquid [1] in the theory of two-dimensional melting [1][2][3][4], is characterized by short-range translational order while its bondorientational order is long ranged. This paradigm was subsequently broadened to three dimensions, where 2D hexatic layers can stack into a smectic hexatic structure with interplanar bond-orientational correlations [5,6]. The hexatic structure can be induced by thermally excited free dislocations or by the geometric frustration between the units that constitute the system [4]. A simple example of the latter is a planar array of ball bearings of two different sizes, which retains bond-orientational order although it loses translational order [7]. Likewise, one could expect that translational ordering in polydisperse colloidal suspensions may be inhibited [8][9][10][11][12][13]. Surprisingly, colloidal platelike particles with a diameter polydispersity as high as 25% appear to form spontaneously hexagonal columnar liquid crystals [14,15]. Here, we demonstrate that it is the hexatic intercolumnar structure of the novel columnar phase, which allows for the accommodation of the particle polydispersity.We used the recently developed high-resolution smallangle x-ray scattering (SAXS) setup [16] of the DutchBelgian beam line BM-26B at the ESRF (Grenoble, France). The instrumental resolution function had a full width at half maximum of hor 0:0008 nm ÿ1 and ver 0:0015 nm ÿ1 in the horizontal and vertical directions, respectively. To fully exploit the capabilities of SAXS, samples with large oriented domains are necessary [16,17]. In suspensions of hard spheres the addition of a depleting polymer at concentrations close to phase separation is known to promote the formation of large single crystals [16,17]. Following this scheme, we added the nonadsorbing polymer (poly-dimethylsiloxane, M w 423 kDa) at a concentration of 0:8 g=l to a suspension of sterically stabilized colloidal gibbsite platelets (with diameter D 237 49 nm and a thickness of L 18 3 nm) in toluene. Suspensions were placed in flat capillaries (internal cross section 0:3 3 mm 2 ) and stored upright for the period of at least 7 months to allow for the establishment of a gravity-controlled profile of the osmotic pressure [18]. Figure 1 shows the three-phase equilibrium of the isotropic, nematic, and columnar phases as observ...

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“…The difference in the crystal size between the hexagonal columnar and the hexatic columnar phase can be related to the structural flexibility of the latter. It also explains the relative easiness [14] of crystallization of discotic colloids and allows for growth of large domains [15] out of highly diverse building blocks.…”

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Observation of a Hexatic Columnar Liquid Crystal of Polydisperse Colloidal Disks

et al. 2005

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“…Examples of such systems are clay suspensions [1,2], dispersed gibbsite platelets [3], mixtures of silica spheres and silica-coated boehmite rods [4], wax disks [5], or nonaqueous suspensions of laponite and montmorillonite [6]. While already pure systems often possess complex liquid crystal phase behavior, binary mixtures additionally may demix into bulk phases with different chemical compositions, e.g.…”

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Density functional theory for colloidal mixtures of hard platelets, rods, and spheres

2006

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A geometry-based density functional theory is presented for mixtures of hard spheres, hard needles and hard platelets; both the needles and the platelets are taken to be of vanishing thickness.Geometrical weight functions that are characteristic for each species are given and it is shown how convolutions of pairs of weight functions recover each Mayer bond of the ternary mixture and hence ensure the correct second virial expansion of the excess free energy functional. The case of sphere-platelet overlap relies on the same approximation as does Rosenfeld's functional for strictly two-dimensional hard disks. We explicitly control contributions to the excess free energy that are of third order in density. Analytic expressions relevant for the application of the theory to states with planar translational and cylindrical rotational symmetry, e.g. to describe behavior at planar smooth walls, are given. For binary sphere-platelet mixtures, in the appropriate limit of small platelet densities, the theory differs from that used in a recent treatment [L. Harnau and S. Dietrich, Phys. Rev. E 71, 011504 (2004)]. As a test case of our approach we consider the isotropic-nematic bulk transition of pure hard platelets, which we find to be weakly first order, with values for the coexistence densities and the nematic order parameter that compare well with simulation results.

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“…3 [28] and hexagonal C [29] phases were found. The arrow pointing down in one of the orange circles means that the values of (δ h , δ l ) correspond to the parent phase.…”

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Interplay between columnar and smectic stability in suspensions of polydisperse colloidal platelets

Velasco

Martı́nez-Ratón

2014

Phys. Chem. Chem. Phys.

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The phase behavior of a model suspension of colloidal polydisperse platelets is studied using density-functional theory. Platelets are modelled as parallel rectangular prisms of square section l and height h, with length and height distributions given by different polydispersities δ l and δ h .We obtain the phase behavior of the model, including nematic, smectic and columnar phases and its dependence with the two polydispersities δ l and δ h . When δ l > δ h we observe that the smectic phase stabilises first with respect to the columnar. If δ h > δ l we observe the opposite behavior.Other more complicated cases occur, e.g. the smectic stabilises from the nematic first but then exists a first-order transition to the columnar phase. Our model assumes plate-rod symmetry, but the regions of stability of smectic and columnar phases are non-symmetric in the δ l − δ h plane due to the different dimensionality of ordering in the two phases. Microsegregation effects, i.e. different spatial distribution for different sizes within the periodic cell, take place in both phases.

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Evidence of the hexagonal columnar liquid-crystal phase of hard colloidal platelets by high-resolution SAXS

Cited by 50 publications

References 65 publications

Observation of a Hexatic Columnar Liquid Crystal of Polydisperse Colloidal Disks

Observation of a Hexatic Columnar Liquid Crystal of Polydisperse Colloidal Disks

Density functional theory for colloidal mixtures of hard platelets, rods, and spheres

Interplay between columnar and smectic stability in suspensions of polydisperse colloidal platelets

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