, 20120263, published 4 March 2013371 2013 Phil. Trans. R. Soc. A H. N. W. Lekkerkerker and G. J. Vroege mineral colloids: new life from old rootsLiquid crystal phase transitions in suspensions of  

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ResearchCite this article: Lekkerkerker HNW, VroegeGJ. 2013 Liquid crystal phase transitions insuspensions of mineral colloids: new life fromold roots. Phil Trans R Soc A 371: 20120263.http://dx.doi.org/10.1098/rsta.2012.0263

One contribution of 14 to a Theo MurphyMeeting Issue ‘New frontiers in anisotropicfluid–particle composites’.

Subject Areas:liquid crystals, colloids

Keywords:colloids, nanoscience, liquid crystals

Author for correspondence:H. N. W. Lekkerkerkere-mail: h.n.w.lekkerkerker@uu.nl

Liquid crystal phase transitionsin suspensions of mineralcolloids: new life from old rootsH. N. W. Lekkerkerker and G. J. Vroege

Van’t Hoff Laboratory for Physical and Colloid Chemistry, DebyeInstitute for Nanomaterials Science, Utrecht University, Padualaan8, 3584 CH Utrecht, The Netherlands

A review is given of the field of mineral colloidal liquidcrystals: liquid crystal phases formed by individualmineral particles within colloidal suspensions. Startingfrom their discovery in the 1920s, we discussdevelopments on the levels of both fundamentalsand applications. We conclude by highlighting somepromising results from recent years, which may pointthe way towards future developments.

1. IntroductionIn this contribution, we discuss the field of mineralcolloidal liquid crystals (MCLCs), which we define asphases with a liquid crystal (LC) (super)structureformed by individual mineral particles within colloidalsuspensions (for extensive reviews, see [1–3]). SinceLCs display a partially ordered long-range structure,which always involves orientational order, these colloidalmineral particles necessarily have to be sufficientlyanisometric (i.e. of different size in at least two differentdirections). Such mineral colloidal particles can be of bothnatural and synthetic origin.

Naturally occurring clays show beautiful examplesof sheet (or plate)-like particles (e.g. bentonite), rod-likeparticles (e.g. sepiolite) or even tubular particles (e.g.imogolite). While some of these systems do formLCs when brought into suspension, often the predictedLC formation is pre-empted by a sol/gel transition.An example is discussed in more detail in the paperby Cui et al. [4]. Colloidal mineral particles can alsobe synthesized by traditional inorganic precipitationreactions, sometimes followed by a phase transformation,and more recently by metallo-organic methods, ‘softchemistry’ [5] or compartmentalized growth.

c© 2013 The Author(s) Published by the Royal Society. All rights reserved.

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The crowning event of the early years of MCLCs is without doubt Onsager’s explanation inthe 1940s of the formation of a nematic phase—a decrease in excluded volume compensating fora loss of orientational entropy. Not only does Onsager’s explanation of the formation of a nematicphase remain a cornerstone in the field of MCLCs after 70 years, its extension by computersimulations has considerably widened the scope of the original argument. Furthermore, it hasenriched several fields. One may think of the implications of Onsager’s concepts for the study notonly of colloids in general (potential of mean force), but also of statistical mechanics in general(entropy-driven phase transitions).

The number of MCLCs has steadily increased. By tuning the size and shape of the particles andtheir mutual interactions, novel and interesting phase behaviour has been observed. Moreover,in the last decade, the potential of wet chemical synthesis routes to provide high-aspect-ratiocolloidal nanorods with interesting directional, optical, electronic and catalytic properties hasgrown drastically.

We discuss the present state of MCLCs using examples partly based on our own work.Building on these developments, we outline new frontiers where we feel future (r)evolutionsin the field may take place. From a fundamental point of view, this includes the observationthat, by tuning the long-range repulsion, LC phases are realized (lamellar and smectic B (SmB)phases), which so far have not been predicted by theory or simulation. From the point of view ofapplications, LC formation in principle provides a simple and cost-efficient strategy to produceorganized structures of nanorods. While some promising steps have been made towards usingthis to realize interesting devices involving nanorods with special directional, optical, electronicand catalytic properties, commercial exploitation is still in its infancy

2. Mineral colloidal liquid crystals: the early years (1925–1949)Within the first half of the last century, important progress in the field of MCLCs had already beenmade by Zocher joining the group of Freundlich at the Kaiser-Wilhelm-Institut für PhysikalischeChemie und Elektrochemie in Berlin-Dahlem, Germany. In a seminal paper of 1925—onlya few years after the classification of LC phases was introduced by Friedel [6]—Zocher [7]recognized the formation of nematic LCs in the guise of birefringent spindle-shaped areas(which subsequently became known as tactoids) in colloidal suspensions of what he presumedto be needle-like vanadium pentoxide (V2O5) particles. Following up on his previous work ontemporary alignment leading to streaming birefringence at lower concentrations [8], he nowrecognized these tactoids to be orientationally ordered (nematic) droplets of higher particledensity within an isotropic background of lower particle density deformed by the elastic forcesacting within the anisotropic structure of the tactoids. He argued that, in low-molecular-weightLCs, these elastic forces are generally too small to deform the spherical shape caused by thesurface tension of droplets. Zocher also noticed so-called atactoids consisting of spindle-shapedareas of dilute isotropic droplets deformed by the elastic forces in the surrounding nematicregion. In a subsequent paper with Jacobsohn [9], Zocher placed his findings on V2O5 particlesin the context of the famous work on spherical colloidal particles by 1926 Nobel Prize laureateJean Perrin [10], discussing the occurrence of Brownian motion, sedimentation (profiles) anddeviations from Van’t Hoff’s ideal (gas) law at higher concentrations. However, although he alsoconsidered repulsive forces protecting the colloidal particles against coagulation, he explained theoccurrence of phase coexistence by explicitly invoking attractive forces as an anisotropic analogueof the liquid–vapour coexistence described by van der Waals. In contrast to the situation of twoimmiscible fluids, he also noted the completely flat interface between the phases after completesedimentation of the tactoids, which he ascribed to a very low interfacial tension.

In the same paper [7] describing his clear recognition of the isotropic–nematic (I–N) phasetransition in suspensions of V2O5, Zocher also reported the observation of a smectic phase in15–30 year old suspensions of iron (hydr)oxide. He deduced this from the observation ofiridescent layers (‘Schillerschichten’) in the bottom layer of the suspension, which—when mixed

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into a homogeneous dispersion with some drops of the isotropic upper layer—spontaneouslyreformed in between two microscope slides. Zocher assigned the bright colours characterizingthese ‘Schillerschichten’ to Bragg reflection of visible light on regularly stacked layers ofsupposedly plate-like FeO(OH) particles (more particularly identified by X-ray diffraction on thedispersion by Böhm [11] as the mineral goethite). In 1930, Zocher & Heller [12] pursued thistopic trying to synthesize particles by hydrolysing iron chloride in a better controlled way. Thisindeed again led to the formation of ‘Schillerschichten’. Zocher correctly referred to these as (thecolloidal analogue of) the smectic phase, although he and his co-workers assumed that FeO(OH)particles were plate-like, whereas these turned out to be rod-like β-FeO(OH) as described later. In1937, Coper & Freundlich [13], former collaborators of Zocher, reported the first nematic phase insuspensions of goethite, α-FeO(OH).

In the meantime, Bawden et al. had also observed I–N phase separation in suspensions oftobacco mosaic virus (TMV) [14]. Although of course not of mineral origin, suspensions of rigid,cylindrical, rod-like TMV behave completely analogously and this observation turned out to beof crucial importance for the historical development (for an extensive review of these and otherLC viruses, see [15,16]).

All the previously cited work and many more experiments on concentrated suspensions andgels of charged colloids were extensively discussed in an ambitious paper by Langmuir [17],which was part review, part theoretical analysis but also reported new experiments on plate-likebentonite. In this clay suspension, Langmuir observed a clear phase separation at around the 2per cent volume fraction, which strongly suggested an I–N coexistence although it easily formedgels, and Langmuir primarily discussed it in terms of three-dimensional order.

Inspired by the experiments collected by Langmuir—although only explicitly citing hispaper—Onsager announced a theory of the I–N transition in 1942 in a remarkable abstract [18],postponing the publication of his full theory to 1949 [19]. In a both physically and mathematicallyvery lucid and elegant analysis, he showed that LC ordering can occur in suspensions in whichinterparticle forces are purely repulsive. The first-order I–N transition for hard anisometricparticles can be understood as the result of a competition between orientational entropy andfree volume entropy (using a virial expansion for the excluded volume interactions): a decreasein orientational entropy is compensated by an increase in the translational entropy owing to areduced excluded volume between the particles within the orientationally ordered nematic phaseat higher volume fractions. Onsager argued that his theory became increasingly accurate forincreasingly anisometric rod-like particles. He also indicated that the I–N transition that he foundfor thin rods could be mapped on the case of thin plate-like particles, although conceding that inthis case his theory became more approximate owing to the fact that plates have two long axesinstead of only one. From Onsager’s work, it follows that ordering can be driven by entropy alone,a concept which remained counterintuitive for a long time but has proved to be very importantin statistical mechanics and extends far beyond LC phase transitions. The use of the potential ofaverage/mean force introduced by Onsager and applied in this paper to provide a description ofelectrostatic double-layer repulsion for charged colloids dominates modern colloid science.

3. Mineral colloidal liquid crystals: the fallow years (1950–1980)In the decades after the publication of Onsager’s theory, the activity on viruses continued, forexample, with the subsequent discovery of smectic phases in suspensions of TMV by Oster in 1950[20], later supplemented by LCs found in other rod-like (although semiflexible) viruses such asfd virus [21]. However, there was little activity to prepare new rod- or plate-like mineral colloidswith the exception of continued efforts on Zocher’s part leading to his discovery of a nematicphase in colourless suspensions of fibrous rod-like γ-AlO(OH) particles [22], independently foundby Bugosh [23].

Within the same period, the interest in phase transitions in suspensions of spherical colloidssteadily grew. The preparation of monodisperse spherical polymer colloids (latices) in the 1950sled to the observation of colloidal crystals [24] a few years after their viral counterpart was

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found in Tipula iridescent virus [25]. Zocher followed these developments closely and relatedthem to superstructures identified in his dispersions of anisometric particles [26]. In parallel withthis, early computer simulations starting at the end of the 1950s by Alder among others [27,28]demonstrated a fluid–crystal transition in a system of hard spheres. Even so, it took until the1970s before the connection between an earlier theory by Kirkwood [29], computer simulationsand observations of colloidal crystals was made, when the Japanese school coined the nameKirkwood–Alder transition [30]. Soon afterwards, Hachisu et al. [31] were the first to suggest aconnection between Onsager’s work and this ‘Kirkwood–Alder transition’.

In the late 1970s, strong interest developed in the structure and dynamics of concentratedcolloidal suspensions as model liquids to approximate hard spheres [32,33]. This in turn generatedinterest in the preparation of monodisperse spherical (model) colloids with well-defined size andtuneable interactions.

4. Mineral colloidal liquid crystals: renewed activity (1980–2012)Inspired by the developments in the field of concentrated suspensions of spherical colloidsexhibiting the remarkable phenomenon of the spontaneous transition from fluid-like structuresto crystal structures, renewed interest in the field of mineral colloidal crystals can be seen as theresult of a combination of several factors:

1. Although in early work the nature of the LC phase was often correctly identified, theintroduction of electron microscopy (EM) and small-angle X-ray scattering (SAXS) oftenled to better identification of particle shapes.

2. A wider range of ‘model’ systems were developed in which the particles have knownshapes, sizes, better controlled polydispersity and (tuneable) interactions.

3. Techniques such as EM, advanced optical microscopy and the scattering of X-rays,neutrons and light were more widely used to study LC phases.

4. The continued development of statistical mechanics, in general, and advances in liquidstate theories, in particular, created powerful concepts and tools which were increasinglysupported and guided by computer simulations.

In the following, we describe how this revitalized the field of MCLCs.

(a) Rods: theory, simulation and selected experimental systems(i) Theory and computer simulation

Extensions of the Onsager theory. Although the results of Onsager’s theory are of great fundamentaland methodological interest, they refer strictly speaking to infinitely thin hard rods. Hence, theapplicability of the theory to experimental results is very limited. In real suspensions of rod-likeparticles, we have to take into account one or more of the following aspects:

— particles are not infinitely thin (or at least their aspect ratio L/D � 1, where L is the rodlength and D the rod diameter);

— particles may be polydisperse (mineral particles in particular);— particles are not hard but may show (long-range) repulsions and attractions; and— particles (such as viruses or polymers) may be semiflexible.

In his original paper [19], Onsager had already indicated how to address the issues of particlerepulsions and polydispersity and analysed the influence of the aspect ratio. All issues raisedabove have already been comprehensively reviewed by us [34]. A remarkable result is that forsufficiently polydisperse particles two nematic phases may be in equilibrium with an isotropicphase [35]. This has indeed been observed experimentally [36,37], as we will discuss below.

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1.00

ABC crystal phases AAA

Sm

N

nematic

smecticbiphasic regions

0.80 P

0.60

0.40

norm

aliz

ed d

ensi

ty, r

–

0.20

0 0.5log (L/D + 1)aspect ratio

1.0 1.5 2.0

Figure 1. The phase diagram of spherocylinders from computer simulations. Adapted from Bolhuis & Frenkel [41]. c© 1997,American Institute of Physics. (Online version in colour.)

Computer simulation

As mentioned before, in the early days, Zocher [7,12] observed smectic phases in suspensions ofiron (hydr)oxide and by 1983 Maeda & Hachisu [38] proved by optical microscopy and EM thatthe smectic phase of β-FeO(OH) consisted of layers of perpendicular rod-like particles of squarecross section interacting under unmistakably predominant repulsive conditions. However, untilthe mid-1980s, it was generally accepted in the literature that smectic LC ordering demanded thatattractive forces operate between the particles. This observation raised the fundamental questionof whether a thermodynamic stable smectic phase can occur in a system of particles with purelyrepulsive interactions. This question was addressed with computer simulations by Frenkel et al.[39], who presented convincing evidence that hard spherocylinders (of aspect ratio 6) with bothtranslational and orientational freedom can form a thermodynamically stable smectic phase. Thisissue was further addressed by McGrother et al. [40] and Bolhuis & Frenkel [41] for a wide rangeof L/D values. A remarkable result of these simulations is that the smectic phase—appearing firstfor spherocylinders with aspect ratio 4.1—requires fewer anisometric particles than the nematicphase where the aspect ratio should be least 4.7 (figure 1).

(ii) Selected systems of rod-like particles

Colloidal boehmite (γ-AlO(OH)) rods. Colloidal boehmite has been studied for a long time [11], andis of considerable industrial importance as a catalyst carrier. Incidentally, γ-AlO(OH) is namedboehmite after Böhm [11], although he denoted it as bauxite at the time of his collaboration withZocher around 1925. Inspired by Zocher & Török’s [22] and Bugosh’s [23] work in the early1960s, Buining et al. [42] explored the preparation of colloidal boehmite rods by hydrothermaltreatment of aluminium alkoxide precursors in the early 1990s. Colloidal boehmite rods with anaverage particle length L between approximately 100 and 400 nm (controlled by varying the initialamounts of alkoxide and acid) and aspect ratio L/D varying from 10 to 30 were obtained in thisway, showing (some) polydispersity in both the particle length and diameter.

Subsequently, these boehmite particles were sterically stabilized by grafting a layer oflow-molecular-weight poly(isobutene) (PIB) molecules on their surface [36]. Dispersed incyclohexane, the sterically stabilized boehmite rods repel each other as a result of steric

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hindrance of the grafted polymer chains and can be modelled as nearly hard rods. Abovea critical concentration dispersion, these sterically stabilized boehmite rods show a fast I–Nphase transition. After months of standing, a second nematic phase emerged in the biphasicdispersion. Comparison of the coexisting concentrations with Onsager’s theory extended toa (bidisperse) mixture of two particle lengths [35] gives remarkably good agreement. Thisstudy shows that Onsager’s theory extended to take into account polydispersity applies well toexperimental results.

Colloidal β-FeO(OH) rods

In a remarkable study, Maeda & Hachisu [38,43] proved by optical microscopy andEM that in low-salt (10−4 mol l−1 or less monovalent salt) aqueous suspensions ofβ-FeO(OH) colloids a biphasic equilibrium arises between an isotropic and a smectic phase,the latter consisting of layers of perpendicular rod-like particles of square cross section.The ratio of the bare length, L = 350 nm, to the bare thickness, D = 60 nm, is approximately 6.However, taking into account the double-layer repulsion, the effective thickness may increase by30 nm, so that the length-to-effective diameter ratio drops below 4, and hence a direct transitionfrom the isotropic to the smectic phase takes place as expected from the computer simulations. Ittestifies to the insight of Hachisu that, long before the computer simulations revealed this feature,he surmised that the absence of the nematic phase was due to the fact that the particles were notsufficiently anisometric.

The work of Maeda and Hachisu was elaborated upon in a number of publications byMaeda and Maeda. They used atomic force microscopy to investigate the smectic structures ofβ-FeO(OH)rods [44,45], confirming the earlier results of Maeda and Hachisu. Furthermore, theyinvestigated the role of long-range forces in smectic ordering [46] by changing pH over a widerange. Finally, with optical microscopy, they observed the nucleation and growth of the smecticphase [47]. In pre-smectic transition regions, lateral clustering of the particles and subsequentlayering of the clusters were observed, representing a novel pathway to phase formation.

Colloidal silica rods

A beautiful example of the development of the ever wider range of ‘model’ systems in whichthe particles have known shapes, sizes and (tuneable) interactions is provided by the synthesisof almost monodisperse, rod-like silica colloids by Kuijk et al. [48]. Bullet-like silica rods wereproduced with diameters of 200 nm and higher and lengths up to 10 μm, resulting in aspect ratiosfrom 1 to 25. The growth mechanism of these rods involves emulsion droplets inside which silicacondensation takes place. Owing to an anisotropic supply of reactants from the droplet to thenucleus, the nucleus grows to one side only, resulting in rod (bullet) formation. In concentrateddispersions, these rods self-assemble into LC phases, which can be studied quantitativelyon the single particle level in three-dimensional real space (figure 2), since the particles canbe fluorescently labelled in various ways. For a system of these silica rods with L/D = 5 insedimentation equilibrium, a multi-phase equilibrium involving an isotropic, nematic, smecticand SmB phase was observed [49]. While the I–N–Sm equilibrium follows from the equationsof state provided by computer simulations [41], the SmB phase has so far not been predicted bytheory or simulations in systems of rod-like particles with purely repulsive interactions. Kuijk [49]puts forward as a possible explanation that the SmB phase is the result of the length polydispersityof the rods, which prevents them from forming a truly three-dimensional-ordered crystal phase.

(b) Plates: theory, simulation and selected experimental systems(i) Theory and computer simulation

As mentioned in §2, the work of Langmuir [17] was an important source of inspiration forOnsager [19] in his theoretical treatment of the I–N phase transition in systems of anisometric

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gE

5 µm

2 µm5 µm

(a) (b) (c)

Figure 2. Bullet-like silica rods: (a) transmission electron microscopy image of L/D= 5 after synthesis; (c) scanning electronmicroscopy image of a highly concentrated smectic dispersion; (b) confocal microscopy image of a paranematic phase inducedby an electric field. Adapted from Kuijk et al. [48]. c© 2011, American Chemical Society. (Online version in colour.)

1.0

solid

columnar

nematic

isotropic

CUB

0.8

0.6

0.4

0.2

0 0.1 0.2

L/D

r*

0.3 0.4

Figure 3. Phase diagram of platelets (cut spheres) as density (scaled to the close-packed density) versus aspect ratioby computer simulations (CUB indicates the cubatic region). Adapted from Veerman & Frenkel [51]. c© 1992, AmericanPhysical Society.

particles with purely repulsive interactions. Langmuir recognized that the particles of the clayhe used (referred to by Langmuir as Californian bentonite, but which is now recognized to behectorite [50]) were flat plates or discs. While the theory of Onsager is quantitatively correct onlyfor (infinitely) long hard thin rods, the Onsager argument that the first-order I–N transition forhard anisometric particles can be understood as the result of a competition between orientationalentropy and free volume entropy remains valid for the I–N transition in a system of hardplates. This was confirmed by the computer simulations of Veerman & Frenkel [51] (figure 3).In addition to the I–N transition, they observed a columnar phase in a system of hard cutspheres. In fact, the ratio of diameter to thickness has to be larger than 7 in order to observethe nematic phase; otherwise, there is a direct transition from the isotropic phase to the columnarphase. Furthermore, a very remarkable cubatic phase was reported by Veerman & Frenkel [51]in between the isotropic and the columnar phase. In this phase, the particles form small stacksof almost cube-like dimensions, which tend to align perpendicular to each other. However,

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I

N N C

41volume fraction (%)

472819

CN

Figure4. Experimental phases for sterically stabilized gibbsite (I, isotropic;N, nematic; C, columnar) observed between crossedpolarizers. Adapted from van der Kooij et al. [58]. c© 2000, Macmillan Publishers Ltd. (Online version in colour.)

the thermodynamic stability of the cubatic phase was questioned by Duncan et al. [52,53].Recently, Marechal et al. [54] showed with computer simulations that the pressure at whichthe columnar phase becomes more stable than the isotropic phase is lower than the pressure atwhich long-range cubatic order was found, which unambiguously shows that the cubatic phaseis thermodynamically unstable with respect to the columnar phase. The apparent stability of thecubatic phase could be due to dynamic arrest. This is confirmed by experiments [55] that will bediscussed below.

(ii) Selected systems of plate-like particles

Gibbsite. The mineral gibbsite (γ-Al(OH)3) is an important intermediate in the Bayer process foraluminium production in the form of agglomerates of small crystals. Starting from the materialsused in the Buining method [42] to produce boehmite rods, Wierenga et al. [56] discovered asynthesis route which yields well-formed hexagonal plate-like gibbsite crystals (diameter 100–200 nm and thickness 5–15 nm). Subsequently, van der Kooij & Lekkerkerker [57] succeededin sterically stabilizing these gibbsite platelets by grafting a layer of low-molecular-weight PIBmolecules onto their surface following the method of Buining & Lekkerkerker [36]. This novelmodel system of hard colloidal platelets was observed to phase-separate into an isotropic and anematic LC phase [57]. Upon further increasing the particle concentration, van der Kooij et al. [58]observed that suspensions of these sterically stabilized plate-like gibbsite colloids also display acolumnar phase (figure 4) in good agreement with the computer simulation results of Veerman &Frenkel [51].

In a suspension of charged gibbsite platelets, the particles interact through double-layerrepulsions, which differentiates these particles from hard platelets. Not surprisingly, the LCphase behaviour now depends sensitively on the ionic strength [59–61]. By lowering thesalt concentration and/or increasing the gibbsite concentration, the nematic phase graduallytransforms from a discotic nematic (ND) into a columnar nematic (NC) phase with much strongerside-to-side interparticle correlations. Subsequently, this NC structure can be either transformedinto the hexagonal columnar phase or arrested into a birefringent repulsive gel state with NCstructure. Kleshchanok et al. [62] studied colloidal gibbsite platelets suspended in dimethylsulphoxide (DMSO). They did not observe a nematic and a columnar phase but rather a layeredLC phase consisting of hexagonally ordered particles, that is, an SmB phase. The use of DMSO,a polar aprotic solvent, leads to a long range of the electrostatic Coulomb repulsion betweenplatelets, which the authors believe to be responsible for the formation of the SmB phase. Recently,high-quality computer simulations on systems of charged colloidal platelets have been reported[63], which support the transitions from a discotic nematic phase (ND), via a columnar nematic(NC) to a columnar phase (C). However, the SmB phase observed by Kleshchanok et al. [62] wasnot detected in these simulations.

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Nickel hydroxide

Brown et al. [64,65] prepared monodisperse plate-like particles of Ni(OH)2 by controlledprecipitation from dilute aqueous solutions of nickel(II) nitrate and ammonium hydroxide. Theseparticles were sterically stabilized by adsorbing a sodium polyacrylate layer on the surface,providing particles that have short-range, repulsive interactions. They observed that theseparticles form a highly ordered phase when prepared as a concentrated dispersion, which wasidentified as a columnar phase using neutron scattering. Given the fact that the particles havean effective diameter of 103 nm and a thickness of 23 nm (hence D/L = 4.5), the observation thatonly a columnar phase is observed is in complete agreement with the computer simulation resultsof Veerman & Frenkel [51]. In 2010, Qazi et al. [55] put forward experimental evidence for theexistence of cubatic order in suspensions of these Ni(OH)2 plate-like particles. Given the fact thatcomputer simulations have shown unambiguously that the cubatic phase is thermodynamicallyunstable with respect to the columnar phase, it seems reasonable to assume that the observedcubatic phase is a dynamically arrested state.

Layered double hydroxides: hydrotalcite

The layered double hydroxide (LDH) platelets are particularly interesting, since they forman easy-to-synthesize class of colloidal, disc-shaped materials that can be adapted chemicallyto contain different metal ions and intercalated anions. The general formula for LDHs is[(M2+)1−x(M3+)x(OH)2]x+[Ay−

x/y]x−· mH2O with M2+ and M3+ different divalent and trivalentmetal cations. LDHs are obtained by substituting part of the divalent cations by trivalent cationswith a similar ionic radius while the brucite-like structure is maintained. The possibility tointroduce significant amounts of trivalent cations allows the LDH particles to have interestingtuneable optical and magnetic properties. Hydrotalcite is the LDH that contains Mg2+ and Al3+.Colloidal platelets of hydrotalcite in the size range diameter 100–200 nm and thickness 10 nmhave been prepared by co-precipitation of magnesium salts and aluminium salts [66–68]. By usingdifferent magnesium to aluminium ratios, one can tune the charge of the LDH particles.

Liu et al. [69] and Wang et al. [70] observed that hydrotalcite suspensions with Mg/Al molarratios 2 : 1 and 1 : 1 show different LC phase behaviour. The former shows a nematic phase[69] while, in the latter, a lamellar phase is observed [70]. As the net positive surface chargeof Mg/Al LDHs comes from the replacement of a fraction of divalent Mg2+ ions by trivalentAl3+ ions, it can be presumed that the sample of (1 : 1) Mg/Al LDH has a charge density 1.5times higher than that of (2 : 1) Mg/Al LDH. This is indeed reflected by a higher zeta potential(+43.6 mV versus +39 mV). Wang et al. [70] conjecture that the lamellar phase observed in (1 : 1)Mg/Al LDH suspensions arises from the stronger double-layer repulsion, although, in recentcomputer simulations on systems of charged colloidal platelets [63], the lamellar phase wasnot detected. Clearly, understanding this remarkable phase behaviour represents a challengingtheoretical endeavour.

(c) Board/lath-like particles: theory, simulation and selected experimental systemsIn the previous sections, we discussed systems in which two of the particle’s axes were (at leastroughly) equally sized. If one allows three different dimensions (length L, width W and thicknessT with T < W < L) for the particle axes, additional LC phases are expected. This expectation isinspired by the prediction of so-called biaxial nematic (Nb) phases by Freiser in 1970 [71]. In thistype of nematic phase, not only the most extreme axis of the particles is orientationally ordered, asin the usual (uniaxial) nematic Nu phases, but perpendicular to that also the two other axes havea preferred orientation. The search for such phases has turned out to be elusive for a long time,with the exception of the observation of a biaxial nematic phase in micellar systems [72] located inbetween two uniaxial phases of rod-like and disc-like micelles, respectively. However, it should beborne in mind that, in contrast to MCLCs, micelles are adaptive systems where particle shape and

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8.5

Nu, rodlike Nu, platelike

Nb

1.51 y

L/W = W/T

rod plate

isotropic

10

bP

Figure 5. Simulated phase diagram (pressure P versus y ≡ W/T) of a hard fluid of biaxial ellipsoids with L/T = 10. Adaptedfrom Camp & Allen [73]. c© 1997, American Institute of Physics.

phase symmetry mutually influence each other. Before we discuss potential examples of biaxialMCLCs, we briefly review what theory and simulations predict about typical size ratios for purelyrepulsive particles needed to observe a biaxial phase.

(i) Theory and computer simulation

Monte Carlo simulations on biaxial hard ellipsoids interpolating between rods and plates wereperformed by Camp & Allen [73] as shown in figure 5. They predict uniaxial rod-like andplate-like nematic phases bordering a rather small area of biaxial nematic exactly in the middle,when the variable width W is close to the geometric mean of the other two dimensions,

W ≈√

LT or equivalentlyLW

≈ WT

. (4.1)

A full phase diagram, including other (liquid) crystalline phases, was given by Taylor &Herzfeld [74] on the basis of scaled particle theory and cell models, where they found that theformation of a biaxial layer-like smectic (SmAb) phase strongly competes with the Nb phase, whichonly consists in a very small area (although incorporating length polydispersity could destabilizethe smectic phase and might reduce this effect [75]).

(ii) Selected systems of board/lath-like particles

Vanadium pentoxide. A first potential experimental example is Zocher’s vanadium pentoxide—recently reviewed by Davidson [76]—which turns out to consist of long, thin ribbons ofapproximate thickness T = 1 nm, width W = 25 nm and persistence length Lp = 300 nm (i.e. thelength over which the ribbons are rigid and straight: their actual length may be much longer).From 0.5 to 0.7 per cent volume fraction dispersions display an isotropic–(uniaxial) nematiccoexistence gap, which first extends into a true nematic phase but forms a nematic gel beyond1.5 per cent volume fraction. Aligning particles within a modest shear field, a uniaxial alignmentappeared persisting up to 4 per cent volume fraction, above which SAXS suddenly displayedpatterns with biaxial nematic symmetry persisting for hours once the shear flow was stopped.This observation and a simultaneous change in the swelling behaviour could be indicative of abiaxial nematic phase, but the SAXS pattern might also be explained as induced by the shearand subsequently trapped in a gel state. Nevertheless, this system remains very alluring since

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I

N

Sm

C + Sm

columnar

smectic A

nematic

isotropic

(c)(b)(a)

Figure 6. Coexisting phases of polydisperse goethite: (a) sample between crossed polarizers, (b) SAXS and (c) schematicrepresentation of the particles within the phases. (Online version in colour.)

a true biaxial nematic phase seems to underlie the gel state, especially when realizing that itsdimensions closely approach the relationship Lp/W ≈ W/T (where the persistence length Lp ofthese semiflexible ribbons takes the place of the total length L in equation (4.1)).

Goethite

A true biaxial nematic mineral LC has been found [77,78] for goethite (α-FeOOH). Understrongly basic conditions, goethite crystallites slowly grow and form approximately rectangularboard-like particles (of length L, width W and thickness T), which can subsequently beelectrostatically stabilized at pH = 3. Depending on the details of the reaction and the subsequentcentrifugation procedure, different (relative) sizes and polydispersities can be obtained. Samplesof different volume fractions quickly performed an I–N phase separation, which throughsedimentation and fractionation (continuing over months to years) formed clear isotropic,nematic [79] and smectic [80] phases (at polydispersities above 20% in combination with columnarphases [81]; figure 6).

One specific system of average dimensions L × W × T = 254 × 83 × 28 nm3 with typicalpolydispersities around 25 per cent was particularly close to the canonical relationship of equation(4.1). Microradian SAXS within the nematic phase revealed three strong liquid-like correlationpeaks perpendicular to each other. The ratios between the correlation lengths corresponding to

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these peaks closely agreed with the ratios between the average particle dimensions (especiallywhen supplemented by the Debye length to take the soft repulsion between the double layersinto account), providing conclusive evidence for a simple biaxial nematic phase [77]. At thelower osmotic pressures higher up in the sample, the biaxiality remained (although with slightlyincreasing correlation lengths, which is to be expected for a sedimented sample) without passingthrough a uniaxial nematic region before entering the isotropic phase. At first sight, this suggeststhat the sample is very close to passing through the bicritical point in the centre of figure 5, butit turns out that the polydispersity may play a significant role [82]. Also the smectic phase—displaying optical Bragg reflections—below the nematic phase was clearly biaxial. All reflectionsremain mutually perpendicular and are consistent with a biaxial smectic A phase. Batches ofgoethite with aspect ratios further away from relation (4.1) sometimes showed double correlationrings [78], but were never proved to be truly biaxial.

5. New frontiersOver the last decade, the number of wet chemical synthesis routes providing high-aspect-ratio colloidal nanorods with interesting optical, electronic and catalytic properties has grownconsiderably (for reviews, see [83,84]). The challenge is to generate organized structures of thesenanorods as they provide the basis for the engineering of new materials and the fabrication ofdevices. LC formation of nanorods provides in principle a simple and cost-efficient strategy forproducing such structures (for a tutorial review of self-assembly of inorganic nanorods, see [85]).Before we highlight the difficulties and opportunities to master the self-assembly of this class ofnanorods on the basis of a few representative examples, we illustrate some of the unique featuresMCLCs can display in external fields.

(a) Novel colloidal liquid crystal phases in external fieldsAlthough low-molecular-weight LCs are commonly aligned and switched by applying externalelectric or magnetic fields, MCLCs are special in that individual particles can be highly susceptibleto these fields. Since this already leads to orientational ordering of the particles within theoriginally isotropic (now called the paranematic) phase, the coexistence with the nematic phaseshifts to lower volume fractions as predicted by Khokhlov & Semenov [86] and observed for rod-like TMV [87] and plate-like gibbsite [88] in magnetic fields. Depending on whether or not theeasy axis of the particle coincides with its symmetry axis, the originally first-order I–N transitionmay vanish at a critical point or become second order [86].

As was discovered by Lemaire et al. [79,89], at colloidal dimensions, anti-ferromagneticgoethite displays very special magnetic properties. It aligns the long axis of its crystallites parallelto a low magnetic field (owing to a small uncompensated permanent magnetic moment alongthis axis) but their shortest axis parallel to a high magnetic field (the easy axis of magnetizationbeing along the shortest axis). Depending on the particle size and the polydispersity, the transitionfrom parallel to perpendicular alignment takes place around a magnetic field of 200–400 mT. Thisis accompanied by completely new phenomena such as a field-induced phase transition from aparallel nematic to a perpendicular columnar LC phase [90]. Furthermore, within an originallyuniform nematic phase, a separation into two nematic phases can be induced by a magnetic fieldresulting in coexistence between a uniaxial nematic phase along the field and a biaxial nematicphase perpendicular to the field [91] (figure 7). The relative amounts turn out to depend on thefield strength and polydispersity of the system.

For silica rods, the application of an external electric field leads to induced orientational orderand the formation of nematic and smectic order at different volume fractions from those withoutan applied field (figure 2) and even a new C3-symmetric crystal structure owing to the interactionbetween the induced electric dipoles [49].

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B = 300 mT

(a) (b)

Figure 7. An originally homogeneous nematic goethite dispersion after 20 h in an externalmagnetic field: (a) sample betweencrossed polarizers, and (b) SAXS, proving nematic–nematic phase separation with two perpendicular orientations in the upperand lower phase. Adapted from van den Pol et al. [91]. c© 2010, American Chemical Society. (Online version in colour.)

(b) Colloidal liquid crystals of mineral nanorods with special optical, electronic andcatalytic properties

(i) Gold nanorods

Colloidal gold nanorods have received considerable attention in the last two decades becauseof their remarkable optical properties and potential applications (for a comprehensive review,including a historical perspective on colloidal gold dispersions, see [83]). The past two decadeshave witnessed rapid advances in the wet chemical synthesis of high-aspect-ratio cylindricalgold nanorods. Particularly interesting is the seed-mediated growth approach in the presenceof surfactant [92]. Jana et al. [93] observed the formation of a nematic phase in concentratedsuspensions of high-aspect-ratio gold nanorods. In addition to the nematic phase in suspension,nematic-like and smectic-like structures mediated by drying-induced self-assembly have beenobserved on a transmission electron microscopy (TEM) grid [83,94]. Remarkably, for longnanorods (of aspect ratio = 6 (figure 8)) isotropic, nematic-like and smectic-like assemblieshave been observed in this way, while for short (aspect ratio = 3) nanorods the nematic-likeassemblies were absent. This observation is highly reminiscent of the aspect-ratio-dependentphase behaviour of rods observed in suspension (see §4a(i)) and suggests that the LC structuresobserved after drying on a TEM grid are formed in the precursor suspension. To prove thisunequivocally, the challenge remains to observe them in situ.

It has long been known that the colour of colloidal dispersions of gold particles varies fromred to blue, depending upon the size and shape of the particles [83]. Potential applications ofLCs of colloidal gold nanorods lie in their remarkable optical properties originating from twodistinct surface plasmon resonance (SPR) absorption bands of individual rods. The transverseSPR absorption band—due to the excitation across the short dimension of the rods—is relativelyinsensitive to the rod aspect ratio and coincides spectrally with the SPR absorption around520 nm of spherical nanoparticles (origin of their reddish colour). In contrast, the longitudinalSPR band—associated with the excitation along the long axis of the rods—is greatly red shiftedand very sensitive to the aspect ratio.

Caseri [95] made clever use of these dichroic properties by stretching a PVA/gold spherenanocomposite film. The spherical gold nanoparticles can form ‘pearl necklace type arrays’ byaggregating along the stretching direction. Placing this nanocomposite film in an optical device

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100 nm 100 nm 200 nm

(a) (b) (c)

Figure 8. TEM images of gold nanorod assemblies. Aspect ratio is 6. (a) Isotropic assembly, (b) nematic-like assembly and(c) smectic-like assembly from Sharma et al. [83]. (Online version in colour.)

with switchable polarization direction (a twisted nematic cell), he could produce a bicoloureddisplay. While interesting, this device is clearly a long way from the ideal of a switchable gold rodnematic LC.

(ii) CdSe and CdSe/CdS nanorods

Like colloidal gold nanorods, both CdSe and CdSe/CdS semiconductor nanorods have receivedconsiderable attention in the last two decades; in the latter case, because of their remarkablephotoluminescence properties. Colloidal CdSe and CdSe/CdS semiconductor nanorods havethe interesting property that they exhibit linearly polarized emission perpendicular to the longaxis [96]. Moreover, CdSe/CdS heteronanorods present the appealing characteristics of strongand tuneable light emission from green to red depending on the ratio between the CdS roddiameter and the CdSe nuclear diameter [97]. The ability to control the shape of CdSe andCdSe/CdS semiconductors has grown dramatically in recent years (for a critical review of thesynthesis methods of semiconductor nanoparticles, see [84]). Peng et al. [98] demonstrated that bycontrolling the growth kinetics the shapes of the resulting cadmium selenide nanoparticles can betuned to vary from a nearly spherical morphology to a rod-like one, with aspect ratios as large as10 to 1. Li et al. [99,100] observed the formation of a nematic LC phase in suspensions of these CdSesemiconductor nanorods. Smectic-like LC structures mediated by drying-induced self-assemblyon a TEM grid were observed for CdSe nanorods by Li & Alivisatos [101] and for CdSe/CdSheteronanorods by Carbone et al. [97], while Talapin et al. [102] took the drying-induced self-assembly method one step further to produce highly luminescent smectic three-dimensionalstructures of CdSe and CdSe/CdS.

More recently, Baranov et al. [103] succeeded in producing two-dimensional smecticmonolayers of close-packed hexagonally ordered arrays of nanorods directly in solution bytuning the depletion attraction forces between CdSe/CdS nanorods with surfactant micelles asillustrated in figure 9.

The origin of the depletion attraction lies in the unbalanced osmotic pressure between twocolloidal particles when the depletion layers of the added (non-absorbing) species around thecolloidal particles overlap. This mechanism was first put forward by Asakura & Oosawa [104] onthe basis of a simple statistical mechanical theory (for an overview of the depletion interactionin colloidal suspensions see [105]). Clearly, the assembly of colloidal nanorods in solution bythe depletion attraction has the potential to enable fabrication procedures for materials based onself-organized colloidal structures.

(iii) TiO2 rutile nanorods

A nice example of the potential of LC nanorods for catalytic purposes was given by Dessombzet al. [106], who synthesized rutile (TiO2) nanorods of average length 160 nm and averagediameter 15 nm that displayed an I–N phase separation in aqueous solution. These LC

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solvent

additive

surfactant

Figure9. Illustration of the formationof two-dimensional smecticmonolayers using thedepletion attraction inducedby addedsurfactantmicelles (see text). Adapted fromBaranov et al. [103]. c© 2010, American Chemical Society. (Online version in colour.)

suspensions could be spin-coated into well-aligned rutile films, the photocatalytic properties ofwhich were examined by monitoring the decomposition of methylene blue under UV light. It wasdemonstrated that UV light polarized along the quadratic axis of the rutile nanorods was mostefficient for this photocatalytic reaction.

6. Synopsis and outlookLooking back upon the preceding sections, we may conclude that, almost a century aftertheir discovery, MCLCs remain a vibrant field of research with a distinguished past and anexciting future.

Although after 70 years Onsager’s explanation of the formation of a nematic phase—a decreasein excluded volume compensating for a loss of orientational entropy—remains unassailed,its extension by computer simulations has considerably widened the scope of the Onsagerargument, including more highly ordered LC phases which have been observed in suspensions ofanisometric mineral colloids. While the entropy-driven self-organization of anisometric colloids isdetermined by their shape, it was observed that by tuning the long-range repulsion LC phases areobserved (lamellar and SmB phases) which so far have not been predicted by theory or simulationand still present a challenge.

In the last decade, the potential of wet chemical synthesis routes to provide high-aspect-ratiocolloidal nanorods with interesting directional, optical, electronic and catalytic properties hasgrown drastically. Through innovative and ingenuous approaches, significant progress has beenmade in arranging these anisotropic nanoparticles into ordered assemblies. While LC formation ofnanorods in principle provides a simple and cost-efficient strategy for producing such structuresand some promising steps have been made (such as the use of the depletion interaction), clearlythe field is still in its infancy leaving significant opportunities for future developments, wherealso the unique behaviour of mineral LCs in external fields can play an important role.

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We thank all our collaborators and colleagues, who were essential for our continued efforts and interest inthis field, and Jeroen van Duijneveldt for critically reading our manuscript.

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