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Phase Behaviour of Lyotropic Liquid Crystals in External Fields And Eur. Phys. J. Special Topics 222, 3053–3069 (2013) c EDP Sciences, Springer-Verlag 2013 THE EUROPEAN DOI: 10.1140/epjst/e2013-02075-x PHYSICAL JOURNAL SPECIAL TOPICS Review Phase behaviour of lyotropic liquid crystals in external fields and confinement A.B.G.M. Leferink op Reininka, E. van den Pol, A.V. Petukhov, G.J. Vroege, and H.N.W. Lekkerkerker Van ’t Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute for Nanomaterials Science, Utrecht University, Padualaan 8, 3584 Utrecht, The Netherlands Received 6 September 2013 / Received in final form 17 September 2013 Published online 25 November 2013 Abstract. This mini-review discusses the influence of external fields on the phase behaviour of lyotropic colloidal liquid crystals. The liquid crystal phases reviewed, formed in suspensions of highly anisotropic particles ranging from rod- to board- to plate-like particles, include ne- matic, smectic and columnar phases. The external fields considered are the earth gravitational field and electric and magnetic fields. For elec- tric and magnetic fields single particle alignment, collective reorienta- tion behaviour of ordered phases and field-induced liquid crystal phase transitions are discussed. Additionally, liquid crystal phase behaviour in various confining geometries, e.g. slit-pore, circular and spherical confinement will be reviewed. 1 Introduction The vast majority of studies of colloidal suspensions deal with spherical particles [1–3]. Their behaviour in external fields was studied in detail and one can find ex- tended examples in other mini-reviews in this issue [4–8]. In contrast, here we shall only discuss the phase behaviour of suspensions of highly non-spherical particles with high aspect ratio. Anisometric colloidal particles, such as rods and platelets, have the ability to spontaneously self-organize into various liquid crystalline phases when brought in sus- pension involving isotropic (I), nematic (N), smectic (S) and columnar (C) phases. In the I phase the particles do not possess order. In the N phase the particles are orientationally ordered, but lack long-range positional order. In the S phase orienta- tionally ordered particles are stacked in layers and thus have long range positional order in one dimension. In the C phase the oriented particles stack into columns, which form a periodic structure in two dimensions. Generally, higher ordered phases (S, C ) are found for higher particle volume fractions. The spontaneous formation of lyotropic liquid crystal phases is an entropy driven process. Already in the 1940s Onsager explained in his seminal work [9]theI-N phase transition for rod-like par- ticles on basis of the particle shape alone: at sufficiently high concentration the loss in orientational entropy is smaller than the gain in excluded volume entropy. a e-mail: [email protected] 3054 The European Physical Journal Special Topics Later Frenkel and coworkers predicted the formation of N, S and C phases of hard anisotropic particles using computer simulations [10–13]. The first experimental observation of a lyotropic colloidal liquid crystal was of the N phase, which was found in a suspension of ribbon-like vanadium pentoxide (V2O5) particles [14]. Later the N phase was also found in suspensions of rod-like TMV-virus particles [15,16], board-like goethite particles [17] and clay plate-like [18] particles. The nematic phase found in systems of rod-like particles (which align their long axis) is often referred to as prolate nematic (N+), while plate-like particles display oblate nematic ordering (N−), in which the short particle axes are aligned. For particles with a shape exactly in between rod- and plate-like the rare biaxial nematic phase (NB) is predicted [19–21]. In the NB phase both particle axes are aligned [22]. Nowadays a rich variety of different liquid crystalline phases has been observed in suspensions of anisometric (mineral) particles, which has extensively been reviewed in the papers by Gabriel & Davidson [23,24] and Lekkerkerker & Vroege [25]. These include col- loidal mineral particles which are known to display rich phase behaviour [23] such as board-like goethite (α-FeOOH) which is able to form N+, NB, S and C phases and plate-like gibbsite (γ-Al(OH)3), which can form N−, C andinrarecasesevenS [26] phases. Lyotropic liquid crystals are highly susceptible to external fields and in this paper we will review the influence of several external fields, i.e. the earth gravitational field, an electric and a magnetic field, on the phase behaviour of lyotropic liquid crystals. Additionally we will discuss the influence of several types of spatial confinement in- cluding slit-pore, 2D circular and 3D spherical confinement. This paper is organised as follows: in Sect. 2 we will discuss how slow sedimentation of particles in the earth gravitational field can lead to the formation of well-ordered liquid crystals phases, even in polydisperse samples. In Sect. 3 we will describe the influence of both external electric and magnetic fields where we make a distinction between external field-induced particle alignment in the I phase, the collective reori- entation of ordered phases (N, S, C ) and field-induced phase transitions. These will be discussed in Sects. 3.1, 3.2 and 3.3 respectively. In Sect. 4 we will review the influ- ence of confining geometries. Additionally we will discuss the experimental difficulties and recent progress in analysing confinement effects on liquid crystals. Finally we will conclude in Sect. 5. 2 Earth gravitational field Generally, the influence of the gravitational field on the formation of mineral liquid crystal phases is very important. At low volume fractions a colloidal dispersion builds up a barometric concentration profile [27,28] proportional to exp(−z/lg) where z is the vertical height and lg the gravitational length. The gravitational length is inversely proportional to the mass density difference Δρ (between the particles and the solvent) and the particle volume Vparticle kBT lg = (1) gΔρVparticle where g is the gravitational acceleration and kBT the thermal energy. The gravita- tional length of larger mineral particles can easily be 1 mm or less. The sedimentation profile for more concentrated dispersions may contain different coexisting liquid crys- tal phases. However, it should be borne in mind that the osmotic pressure at each interface between different phases is different and Gibbs phase rule predicting the maximum number of coexisting phases does not necessarily hold (even for a monodis- perse system). For a (multi-component) polydisperse system the chemical potential Colloidal Dispersions in External Fields 3055 for each component must be equal at each interface and also the typical gravitational length (1) can strongly vary for components with different particle volumes. Since this effect couples to the fractionation or partitioning of particles over the different phases, sedimented colloidal systems may display very rich phase behaviour. For the nematic phase e.g. the tendency that long rods order first due to their larger excluded volume [29,30] is reinforced by sedimentation and leads to additional fractionation. Generally, in sedimentation-induced phase-separated samples the more highly ordered liquid crystal phases are formed below the less ordered and disor- dered phases. However, for polydisperse gibbsite platelets a density inversion for the isotropic-nematic transition was found [31] which could be explained by fractionation effects [32]. Thicker platelets sediment faster but they remain, due to their smaller as- pect ratio, in the isotropic phase for volume fractions (φ) at which the thinner platelets already formed the nematic phase. Liquid crystalline phases with partial positional order (S, C ) may be more difficult to form since inherent polydispersity may prevent particles to fit within the positionally ordered structures. Hence, low polydispersity rods form layer-like smectic [33,34] phases while the smectic phase destabilizes at higher polydispersity favouring the nematic phase at low density and the colum- nar phase at higher density [35–37]. Conversely, polydisperse monolayer α-Zirconium phosphate platelets sometimes form a smectic phase rather than a columnar liquid crystal [38]. These platelets are only polydisperse in diameter, which inhibits long range positional order in the columnar phase, whereas the layered smectic phase can easily accommodate the platelets due to their constant thickness. If sedimentation takes place sufficiently slowly, Brownian motion may permit particles to keep re- arranging [39] and fractionating. For gibbsite platelets sometimes a single columnar phase develops slowly [40,41], whereas fast sedimentation in a centrifugal field of 900 g [42] leads to the formation of many small columnar liquid crystals (the larger particles fractionating towards the bottom and giving larger repeat distances). However, under osmotic compression exerted by free polymer a hexatic columnar phase (without true long range positional order) was identified for gibbsite [43] below a region with small columnar liquid crystals. The electrostatically stabilised goethite system of board-like nanoparticles also showed marked influence of sedimentation and fractionation. This was already sus- pected from the observation of a smectic phase within a 55% polydisperse batch [44], i.e. far above the terminal polydispersity of 18% for the smectic phase of spherocylin- ders [36]. Careful analysis of the size distributions of coexisting isotropic, nematic, smectic and columnar phases [45] showed an almost threefold increase of the par- ticle length over 5 cm sample height, a strongly reduced polydispersity (<28%) in the smectic phase and the exclusive presence of the longest particles in the colum- nar phase, which acts as a waste disposal for particles that do not fit the smectic periodicity. In contrast, a similar system of 17% overall polydispersity only displayed a gradual shift (of 10%) in the length distribution without changing its form while a columnar phase was completely absent. SAXS measurements showed an almost constant smectic layer thickness, only slightly compressed when going down in the sample.
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