Capillary condensation of a nematic liquid crystal observed by force spectroscopy

Dynamics and Topology of Symmetry Breaking with Skyrmions

We observe that pretransitional order parameter fluctuations of a skyrmion-forming chiral nematic liquid crystal are slowed down for 4 orders of magnitude, if confined to ≲100  nm thin layers. Fluctuating fragments of half-skyrmions are observed in a narrow temperature interval and are explained by thermally activated hopping between the various energy states. Skyrmion fluctuations are accompanied by imbalanced topological charge: positive charges appear at higher temperatures and dominate in the fluctuating region until skyrmions fully condense and negative charges appear at lower temperatures.

2D isotropic-nematic transition in colloidal suspensions of ellipsoids

Liquid crystals are important condensed matter systems for technological applications, as well as for fundamental studies. An important unresolved issue is the nature of the phase transition in a two-dimensional (2D) liquid crystal system. In contrast to numerous computational studies reported in the last few decades, there have been no convincing experiments to verify these numerical results. Anisotropic colloids provide an excellent experimental model system to study phase transitions, such as crystallization and glass transition in condensed matter physics with single particle resolution. However, using colloids to probe the two-dimensional liquid crystal transition remains a challenge, since the condensed anisotropic colloids usually become stuck in the metastable glassy state rather than approaching their equilibrium liquid crystal phase. Here we report a method of using an external magnetic field to assist a colloidal system of super-paramagnetic anisotropic particles to overcome the local free energy barriers in the metastable states and approach the equilibrium phase. The experiments demonstrate a 2D isotropic-nematic phase transition with increasing packing density. The effects of the anisotropy of the colloidal particles on the 2D isotropic-nematic transition are explored. Our experimental results are compared with those from previous computational work, and quantitative agreements are reached.

Effect of the anchoring strength on the phase behaviour of discotic liquid crystals under face-on confinement

In this study we have performed molecular dynamics simulations to study a Gay-Berne discotic fluid confined in a slab geometry for a fixed confinement length. Four different anchoring strengths with a homeotropic (face-on) configuration were studied. We found that changing the anchoring strength changes the normal component of the stress tensor, which in turn changes the density of the system's bulk. This phenomenon leads to a shift in the isotropic-nematic transition temperature. We observe that the temperature regions where the nematic phase is present diminishes as the anchoring strength increases. The anchoring strength also affects the nematic-columnar coexistence temperature-region: it spans over more temperatures at higher anchoring strengths.

Validation study of using the free volume approximation to confined thermotropic and lyotropic liquid-crystalline fluids

We examined the accuracy of the free volume approximation (FVA) to calculate the isotropic-nematic (IN) transition properties of thermotropic and lyotropic rods between two parallel hard walls. This approximation has been proposed to ease the calculation of the confined systems. It approximates the free energy of the confined particles with a bulk free energy. It predicts a special point for these two types of liquid crystals where the first-order IN transition changes to the second one by decreasing either the temperature, the density or the pore width. This prediction is in contradiction (in spite of some qualitative agreement) with those of the other publications where the authors note that the discontinuous transition terminates at the critical point when the walls are completely impenetrable.

Controlling Stiction in Nano-Electro-Mechanical Systems Using Liquid Crystals

Stiction is one of the major reliability issues limiting practical application of nano-electro-mechanical systems (NEMS), an emerging device technology that exploits mechanical movements on the scale of an integrated electronic circuit. We report on a discovery that stiction can be eliminated by infiltrating NEMS with nematic liquid crystals. We demonstrate this experimentally using a NEMS-based tunable photonic metamaterial, where reliable switching of optical response was achieved for the entire range of nanoscopic structural displacements admitted by the metamaterial design. Being a more straightforward and easy-to-implement alternative to the existing antistiction solutions, our approach also introduces an active mechanism of stiction control, which enables toggling between stiction-free and the usual (stiction-limited) regimes of NEMS operation. It is expected to greatly expand the functionality of electro-mechanical devices and enable the development of adaptive and smart nanosystems.

Nanocapillary Adhesion between Parallel Plates

Molecular dynamics simulations are used to study capillary adhesion from a nanometer scale liquid bridge between two parallel flat solid surfaces. The capillary force, Fcap, and the meniscus shape of the bridge are computed as the separation between the solid surfaces, h, is varied. Macroscopic theory predicts the meniscus shape and the contribution of liquid/vapor interfacial tension to Fcap quite accurately for separations as small as two or three molecular diameters (1-2 nm). However, the total capillary force differs in sign and magnitude from macroscopic theory for h ≲ 5 nm (8-10 diameters) because of molecular layering that is not included in macroscopic theory. For these small separations, the pressure tensor in the fluid becomes anisotropic. The components in the plane of the surface vary smoothly and are consistent with theory based on the macroscopic surface tension. Capillary adhesion is affected by only the perpendicular component, which has strong oscillations as the molecular layering changes.

Electroclinic effect in a chiral paranematic liquid-crystal layer above the bulk nematic-to-isotropic transition temperature

Electroclinic measurements are reported for two chiral liquid crystals above their bulk chiral isotropic-nematic phase transition temperatures. It is found that an applied electric field E induces a rotation θ [∝Ε] of the director in the very thin paranematic layers that are induced by the cell's two planar-aligning substrates. The magnitude of the electroclinic coefficient dθ/dE close to the transition temperature is comparable to that of a bulk chiral nematic, as well as to that of a parasmectic region above a bulk isotropic-to-chiral smectic-A phase. However, dθ/dE in the paranematic layer varies much more slowly with temperature than in the parasmectic phase, and its relaxation time is slower by more than three orders of magnitude than that of the bulk chiral nematic electroclinic effect.

Capillary and winding transitions in a confined cholesteric liquid crystal

We consider a Lebwohl-Lasher model of chiral particles confined in a planar cell (slit pore) under different boundary conditions, and solve it using mean-field theory. The phase behaviour of the system with respect to temperature and pore width is studied. Two phenomena are observed: (i) an isotropic-cholesteric transition, which exhibits an oscillatory structure with respect to pore width, and (ii) an infinite set of winding transitions caused by commensuration effects between cholesteric pitch and pore width. The latter transitions have been predicted and analysed by other authors for cholesterics confined in a fixed pore and subjected to an external field promoting the uniaxial nematic phase; here we induce winding transitions solely from geometry by changing the pore width at zero external field (a setup recently explored in atomic-force microscopy experiments). In contrast with previous studies, we obtain the phase diagram in the temperature vs. pore width plane, including the isotropic-cholesteric transition, the winding transitions and their complex relationship. In particular, the structure of winding transitions terminates at the capillary isotropic-cholesteric transition via triple points where the confined isotropic phase coexists with two cholesterics with different helix indices. For symmetric and asymmetric monostable plate anchorings the phase diagrams are qualitatively similar.

Soft matter in hard confinement: phase transition thermodynamics, structure, texture, diffusion and flow in nanoporous media

Spatial confinement in nanoporous media affects the structure, thermodynamics and mobility of molecular soft matter often markedly. This article reviews thermodynamic equilibrium phenomena, such as physisorption, capillary condensation, crystallisation, self-diffusion, and structural phase transitions as well as selected aspects of the emerging field of spatially confined, non-equilibrium physics, i.e. the rheology of liquids, capillarity-driven flow phenomena, and imbibition front broadening in nanoporous materials. The observations in the nanoscale systems are related to the corresponding bulk phenomenologies. The complexity of the confined molecular species is varied from simple building blocks, like noble gas atoms, normal alkanes and alcohols to liquid crystals, polymers, ionic liquids, proteins and water. Mostly, experiments with mesoporous solids of alumina, gold, carbon, silica, and silicon with pore diameters ranging from a few up to 50 nm are presented. The observed peculiarities of nanopore-confined condensed matter are also discussed with regard to applications. A particular emphasis is put on texture formation upon crystallisation in nanoporous media, a topic both of high fundamental interest and of increasing nanotechnological importance, e.g. for the synthesis of organic/inorganic hybrid materials by melt infiltration, the usage of nanoporous solids in crystal nucleation or in template-assisted electrochemical deposition of nano structures.

Capillary adhesion at the nanometer scale

Molecular dynamics simulations are used to study the capillary adhesion from a nonvolatile liquid meniscus between a spherical tip and a flat substrate. The atomic structure of the tip, the tip radius, the contact angles of the liquid on the two surfaces, and the volume of the liquid bridge are varied. The capillary force between the tip and substrate is calculated as a function of their separation h. The force agrees with continuum predictions based on macroscopic theory for h down to ∼5 to 10 nm. At smaller h, the force tends to be less attractive than predicted and has strong oscillations. This oscillatory component of the capillary force is completely missed in the macroscopic theory, which only includes contributions from the surface tension around the circumference of the meniscus and the pressure difference over the cross section of the meniscus. The oscillation is found to be due to molecular layering of the liquid confined in the narrow gap between the tip and substrate. This effect is most pronounced for large tip radii and/or smooth surfaces. The other two components considered by the macroscopic theory are also identified. The surface tension term, as well as the meniscus shape, is accurately described by the macroscopic theory for h down to ∼1 nm, but the capillary pressure term is always more positive than the corresponding continuum result. This shift in the capillary pressure reduces the average adhesion by a factor as large as 2 from its continuum value and is found to be due to an anisotropy in the pressure tensor. The component in the plane of the substrate is consistent with the capillary pressure predicted by the macroscopic theory (i.e., the Young-Laplace equation), but the normal pressure that determines the capillary force is always more positive than the continuum counterpart.

Optical imaging of liquid crystals at the nanoscale

The instrumentation associated with near-field scanning optical microscopy (NSOM) can be exploited to provide three-dimensional structure and dynamic information about liquid crystals at scales not possible with diffraction-limited tools. This Minireview focuses on our use of NSOM techniques to probe spatial variations of the nematic director and the nematic orientational order parameter on length scales as small as a few nanometers.

Dynamics of order reconstruction in a nanoconfined nematic liquid crystal with a topological defect

At the wall in a hybrid nematic cell with strong anchoring, the nematic director is parallel to one wall and perpendicular to the other. Within the Landau-de Gennes theory, we have investigated the dynamics of s = ±1/2 wedge disclinations in such a cell, using the two-dimensional finite-difference iterative method. Our results show that with the cell gap decreasing, the core of the defect explodes, and the biaxiality propagates inside the cell. At a critical value of dc* ≈ 9ξ (where ξ is the characteristic length for order-parameter changes), the exchange solution is stable, while the defect core solution becomes metastable. Comparing to the case with no initial disclination, the value at which the exchange solution becomes stable increases relatively. At a critical separation of dc ≈ 6ξ, the system undergoes a structural transition, and the defect core merges into a biaxial layer with large biaxiality. For weak anchoring boundary conditions, a similar structural transition takes place at a relative lower critical value. Because of the weakened frustration, the asymmetric boundary conditions repel the defect to the weak anchoring boundary and have a relatively lower critical value of da, where the shape of the defect deforms. Further, the response time between two very close cell gaps is about tens of microseconds, and the response becomes slower as the defect explodes.

Liquid-crystal mediated nanoparticle interactions and gel formation

Colloidal particles embedded within nematic liquid crystals exhibit strong anisotropic interactions arising from preferential orientation of nematogens near the particle surface. Such interactions are conducive to forming branched, gel-like aggregates. Anchoring effects also induce interactions between colloids dispersed in the isotropic liquid phase, through the interactions of the pre-nematic wetting layers. Here we utilize computer simulation using coarse-grained mesogens to perform a molecular-level calculation of the potential of mean force between two embedded nanoparticles as a function of anchoring for a set of solvent conditions straddling the isotropic-nematic transition. We observe that strong, nontrivial interactions can be induced between particles dispersed in mesogenic solvent, and explore how such interactions might be utilized to induce a gel state in the isotropic and nematic phases.

Attractive interaction and bridging transition between neutral colloidal particles due to preferential adsorption in a near-critical binary mixture

We examine the solvent-mediated interaction between two neutral colloidal particles due to preferential adsorption in a near-critical binary mixture. We take into account the renormalization effect due to the critical fluctuations using the recent local functional theory [J. Chem. Phys. 136, 114704 (2012)]. We calculate the free energy and the force between two colloidal particles as functions of the temperature T, the composition far from the colloidal particles c(∞), and the colloid separation ℓ. The interaction is much enhanced when the component favored by the colloid surfaces is poor in the reservoir. For such off-critical compositions, we find a surface of a first-order bridging transition ℓ=ℓ(cx)(T,c(∞)) in the T-c(∞)-ℓ space in a universal, scaled form, across which a discontinuous change occurs between separated and bridged states. This surface starts from the bulk coexistence surface (CX) and ends at a bridging critical line where ℓ is determined by T as ℓ=ℓ(c)(T). On approaching the critical line, the discontinuity vanishes and the derivatives of the force with respect to T and ℓ both diverge. Furthermore, bridged states continuously change into separated states if c(∞) (or T) is varied from a value on CX to a value far from CX with ℓ kept smaller than ℓ(c)(T).

Surface-induced weak orientational order and role of isotropic-nematic interface fluctuations in the appearance of an induced nematic film

Recently the nontrivial spatial and temperature dependence of the surface-induced weak planar orientational order parameter Q(z, T) was determined just above the isotropic-nematic (IN) phase transition point (Ji-H. Lee et al., Phys. Rev. Lett. 102, 167801 (2009)). In this paper we present a theoretical explanation of the observed behaviour. We obtain expressions for the short-range and long-range contributions to the interface potential of the induced nematic film and specify the repulsive character of the interaction between the soft IN interface and the external bounding substrate. It is shown that the small value of the IN interfacial tension results in the renormalization of the repulsive interaction potential due to the thermal fluctuations of the soft IN interface. This leads to an increase of the equilibrium thickness of the induced nematic film and the appearance of a step-like orientational order parameter profile. We find that only renormalized short-range and thermal pseudo-Casimir interactions are essential for the appearance of the induced nematic film, which provide the observed thickness, h ~ 30 nm, of this film. The long-range van der Waals interaction is shown to be negligibly small and the dominant role is played by the renormalized short-range repulsion. Fitting of the experimental order parameter profiles (Ji-H. Lee et al. (2009)) with the expressions based on these interactions makes it possible to determine the material parameters of the system, including the amplitudes of the surface interaction, the IN interfacial tension and the interfacial coherence length. The agreement between theory and experiment confirms the importance of the interface fluctuation renormalization of the interface potentials for soft interfaces.

Structural forces in liquid crystalline blue phases

We show numerically that the interaction potential or force mediated by a liquid crystalline blue phase (BP) between two parallel plates exhibits oscillatory behavior with variation of the interplate distance, when the parallel plates impose strong normal anchoring. Its periodicity is approximately half of the unit-cell dimension of the bulk BP. The interaction arises from the deformation of the confined BP structure around the midplane of the system. The oscillatory interaction can be regarded as a clear manifestation of the BP ordering, because the cholesteric helical alignment adopted by a chiral liquid crystal cannot yield an oscillatory interaction.

Controlling the formation of capillary bridges in binary liquid mixtures

We study the formation of capillary bridges between micrometer-sized glass spheres immersed in a binary liquid mixture using bright field and confocal microscopy. The bridges form upon heating due to the preferential wetting of the hydrophilic glass surface by the water-rich phase. If the system is cooled below the demixing temperature, the bridges disappear within a few seconds by intermolecular diffusion. Thus, this system offers the opportunity to switch the bridges on and off and to tune precisely the bridge volume by altering the temperature in a convenient range. We measure the bridge geometry as a function of the temperature from bright field images and calculate the cohesive force. We discuss the influence of the solvent composition on the bridge formation temperature, the strength of the capillary force, and the bridge volume growth rate. Furthermore, we find that the onset of bridge formation coincides with the water-lutidine bulk coexistence curve.

Smectic membranes in aqueous environment

We present a study of thermotropic smectic liquid crystal films in aqueous environment. Macroscopic freely suspended films in water with a size up to 7.4 × 15 mm2 were prepared with the help of a surfactant, which ensures a strong homeotropic anchoring at liquid crystal/water interfaces. The films were studied by optical microscopy and ellipsometry. Attention was paid to the stability and the thinning transitions which occurred at temperatures above the bulk smectic- A -isotropic transition temperature. In addition, we investigated the formation and rupture kinetics of thin smectic membranes separating water droplets in microfluidic devices. Besides possible applications in discrete microfluidics, smectic films in aqueous environment may expand the general range of possible studies of freely suspended smectic films.

Competition between capillarity, layering and biaxiality in a confined liquid crystal

The effect of confinement on the phase behaviour and structure of fluids made of biaxial hard particles (cuboids) is examined theoretically by means of Onsager second-order virial theory in the limit where the long particle axes are frozen in a mutually parallel configuration. Confinement is induced by two parallel planar hard walls (slit-pore geometry), with particle long axes perpendicular to the walls (perfect homeotropic anchoring). In bulk, a continuous nematic-to-smectic transition takes place, while shape anisotropy in the (rectangular) particle cross-section induces biaxial ordering. As a consequence, four bulk phases, uniaxial and biaxial nematic and smectic phases, can be stabilised as the cross-sectional aspect ratio is varied. On confining the fluid, the nematic-to-smectic transition is suppressed, and either uniaxial or biaxial phases, separated by a continuous transition, can be present. Smectic ordering develops continuously from the walls for increasing particle concentration (in agreement with the supression of nematic-smectic second-order transition at confinement), but first-order layering transitions, involving structures with n and n + 1 layers, arise in the confined fluid at high concentration. Competition between layering and uniaxial-biaxial ordering leads to three different types of layering transitions, at which the two coexisting structures can be both uniaxial, one uniaxial and another biaxial, or both biaxial. Also, the interplay between molecular biaxiality and wall interactions is very subtle: while the hard wall disfavours the formation of the biaxial phase, biaxiality is against the layering transitions, as we have shown by comparing the confined phase behaviour of cylinders and cuboids. The predictive power of Onsager theory is checked and confirmed by performing some calculations based on fundamental-measure theory.

Direct measurement of surface-induced orientational order parameter profile above the nematic-isotropic phase transition temperature

The spatial and temperature dependence of the surface-induced orientational order parameter S(z,T) was determined in the isotropic phase. An optical fiber was immersed in a thin liquid crystal layer and the retardation was measured as a function of the fiber's height above the surface, from which the model-independent S(z,T) was deduced with resolution <or=2 nm. It was found that (i) S(z=0) <or=0.12 close to the nematic transition temperature, (ii) the susceptibility is mean-field-like, and (iii) S(z,T) deviates significantly from exponential spatial decay. The results are discussed in terms of a nonlocal potential.

Normal capillary forces

A liquid meniscus between two lyophilic solid surfaces causes an attractive force, the capillary force. The meniscus can form by capillary condensation or by accumulation of adsorbed liquid. Under ambient conditions and between hydrophilic surfaces, capillary forces usually dominate over other surface forces. They are relevant in many processes occurring in nature and technical applications, for example the flow of granular materials and friction between surfaces. Here we review normal capillary forces, focusing on a quantitative description with continuum theory. After introducing the capillary force between spherical surfaces, we extend the discussion to other regular and irregular surfaces. The influence of surface roughness is considered. In addition to capillary forces at equilibrium, we also describe the process of meniscus formation. Assumptions, limits, and perspectives for future work are discussed.

Colloid-wall interaction in a nematic liquid crystal: the mirror-image method of colloidal nematostatics

The new area of nematic colloidal systems (or nematic emulsions) has been greatly guided by the fruitful analogy between the colloidal nematostatics and electrostatics. The elastic charge density representation of the colloidal nematostatics [V. M. Pergamenshchik and V. O. Uzunova, Eur. Phys. J. E 23, 161 (2007); Phys. Rev. E 76, 011707 (2007)] develops this analogy at the level of charge density and Coulomb interaction. It shows, however, that the colloidal nematostatics in three dimensions substantially differs from the electrostatics both in its mathematical structure and physical implications: the elastic charge and multipoles are dyads; similar charges attract while opposite charges repel each other, and so on. In this paper we consider the interaction between an elastic charge and elastic dipole with a nematic surface (wall) at which the director alignment is fixed. Using the mirror image method of electrostatics as a guiding idea, we develop the mirror image method in the nematostatics for arbitrary director tilt at the wall. A wall is shown to induce a repulsive 1R{4} force on the elastic dipole which, in general, is accompanied by its reorientation. External torque on the colloid induces an elastic charge therein and triggers switching to the 1R{2} repulsion. The dyadic nature of an elastic dipole is shown to be essential: a particle-wall interaction potential cannot be obtained in phenomenological theories with a single component dipole. In the introductory sections we discuss connection between the director-mediated interaction in two and three dimensions and the electrostatic interaction and consider different symmetries of elastic dipoles. Conservation of the torque components exerted upon colloids is shown to play the role of Gauss' theorem and determines the elastic charge dyad.

Dynamical numerical model for nematic order reconstruction

In highly frustrated calamitic nematic liquid crystals, a strong elastic distortion can be confined on a few nanometers. The classical elastic theory fails to describe such systems and a more complete description based on the tensor order parameter Q is required. A finite element method is used to implement the Q dynamics by a variational principle and it is shown that a uniaxial nematic configuration can evolve passing through transient biaxial states. This solution, which connects two competing uniaxial nematic textures, is known as "nematic order reconstruction."

Surface ordering and capillary phenomena of confined hard cut-sphere particles

Isothermal-isobaric and Gibbs ensemble Monte Carlo (GEMC) computer simulations of = 1500 and = 3000 hard cut spheres of aspect ratio / = 0.1, respectively, are carried out in order to investigate the effects of confinement on the isotropic (I)-nematic (N) phase transition. We first consider the free system, and confirm the stabilisation of isotropic (I), nematic (N) and columnar (Col) states. We examine in detail the I-N transition and find coexistence densities of =0.355 and =0.368. A slab geometry is then considered for two types of walls: a hard wall, which excludes the particles entirely, and an 'adsorbent' wall which excludes the centre of mass of the particles. The adsorbent wall is found to favour planar (edge-on) alignment, which results in the formation of a first layer of adsorbed molecules, which then acts as a rough hard wall for subsequent particles, and promotes disordered states. Using Gibbs ensemble simulations we determine the capillary phase diagram of the system, and the adsorption as a function of pore width. The capillary phase diagram obtained from Gibbs ensemble simulations corresponds to one with a first-order capillary isotropisation transition, with an associated capillary critical point for a wall separation of ∼3. The hard walls are seen to promote homeotropic (face-on) alignment of the cut spheres, and promote the stabilisation of the nematic phase. In this case the capillary phase diagram obtained from the GEMC simulations exhibits a first-order capillary nematisation transition, and a capillary critical point for a wall separation of ∼4.

Capillary effects in a confined smectic phase of hard spherocylinders: influence of particle elongation

A system of hard rods confined into a pore with slit geometry (two parallel planar substrates) is studied theoretically in the regime of high packing fraction. In this regime the bulk system exhibits a nematic phase as well as a smectic-A (spatially layered) phase. When the system is confined, strong commensuration effects between the layer spacing and the pore width bring about a rich phenomenology, with a phase diagram showing layering and capillary transitions. The latter include capillary smectization transitions whereby a confined smectic phase occurs at conditions of saturation different from those of the corresponding bulk fluid. These transitions are seen to be intimately connected with layering transitions involving discontinuous changes in the number of layers inside the pore. This rich phenomenology is obtained by use of a sophisticated density-functional, Onsager-theory-based approach, especially suited to deal with strongly inhomogeneous fluids. The theory allows for a unified description of ordering and phase behavior of the fluid in confined geometry, and permits us to correlate the above behavior with the wetting properties of the fluid on a single substrate.

Lateral and normal forces between patterned substrates induced by nematic fluctuations

We consider a nematic liquid crystal confined by two parallel flat substrates whose anchoring conditions vary periodically in one lateral direction. Within the Gaussian approximation, we study the effective forces between the patterned substrates induced by the thermal fluctuations of the nematic director. The shear force oscillates as a function of the lateral shift between the patterns on the lower and the upper substrates. We compare the strength of this fluctuation-induced lateral force with the lateral van der Waals force arising from chemically structured adsorbed monolayers. The fluctuation-induced force in the normal direction is either repulsive or attractive, depending on the model parameters.

Colloidal interactions in nematic fluids

Microscopic theory is used to obtain effective interactions between colloidal particles in nematic fluids subjected to an external orienting field. It is shown that the field can dramatically change the effective intercolloidal interactions without altering the symmetry of the director configuration around a single particle. Our calculations suggest that a rich variety of colloidal structures can be promoted by varying the external field.

Atomic force microscope study of presmectic modulation in the nematic and isotropic phases of the liquid crystal octylcyanobiphenyl using piezoresistive force detection

Using a temperature controlled atomic force microscope (AFM), we have studied surface induced pre-smectic order in the nematic and isotropic phases of 4-cyano- 4'-n -octylbiphenyl. A modified AFM head with piezoresitive cantilevers has been used to measure the structural force between a flat BK7 glass plate and a 10 microm glass sphere, both being treated to induce homeotropic alignment of the confined liquid crystal layer in between. We have observed surface-induced presmectic force not only in the isotropic, but also in the nematic phase. We have measured the temperature dependencies of the presmectic force, the smectic correlation length xi and the smectic order parameter psi at the surface. The correlation length xi(T) shows a power-law temperature dependence with a critical exponent of nu=0.67 +/- 0.03 and the bare correlation length of xi(0) = (0.39 +/- 0.08) nm, in good agreement with x-ray data. The smectic density at the surface is psi(2)(S) =0.4 in the nematic phase and decreases in the isotropic phase.

Capillary smectization and layering in a confined liquid crystal

Using density-functional theory, we have analyzed the phase behavior of a model liquid crystal confined between two parallel, planar surfaces (i.e., the so-called slit pore). As a result of confinement, a rich phase behavior arises. The complete liquid-crystal phase diagram of the confined fluid is mapped out as a function of wall separation and chemical potential. Strong commensuration effects in the film with respect to wall separation lead to enhanced smectic ordering, which gives capillary smectization (i.e., formation of a smectic phase in the pore), or frustrated smectic ordering, which suppresses capillary smectization. These effects also produce layering transitions. Our nonlocal density-functional-based analysis provides a unified picture of all the above phenomena.

Numerical investigation of liquid crystal colloids using a continuum description

We investigate numerically the configuration of a nematic liquid crystal around two spherical particles. For the description of the orientational order of a nematic liquid crystal, we adopt a Landau-de Gennes continuum theory in terms of a second-rank tensor order parameter Q(ij) together with the use of bispherical coordinates to describe the geometry of the system with two spherical particles. Above but close to the nematic-isotropic transition point, we observe capillary condensation of a nematic liquid crystal between the two particles under appropriate conditions. Below the transition point where liquid crystals possess nematic order, a point-like defect called a hyperbolic hedgehog appears close to a particle when strong normal anchoring is imposed. With the aid of an adaptive mesh refinement scheme to achieve sufficient numerical resolution to describe topological defects, we present our numerical results showing how the orientation profile of a nematic liquid crystal is distorted when the distance between two particles is small enough.

Capillary bridging and long-range attractive forces in a mean-field approach

When a mixture is confined, one of the phases can condense out. This condensate, which is otherwise metastable in the bulk, is stabilized by the presence of surfaces. In a sphere-plane geometry, routinely used in atomic force microscope and surface force apparatus, it can form a bridge connecting the surfaces. The pressure drop in the bridge gives rise to additional long-range attractive forces between them. By minimizing the free energy of a binary mixture we obtain the force-distance curves as well as the structural phase diagram of the configuration with the bridge. Numerical results predict a discontinuous transition between the states with and without the bridge and linear force-distance curves with hysteresis. We also show that similar phenomenon can be observed in a number of different systems, e.g., liquid crystals and polymer mixtures.

Capillary condensation in liquid-crystal colloids

We study capillary condensation between two spherical particles dispersed in the isotropic phase of a nematic liquid crystal. Within the Landau-de Gennes theory, we calculate interaction energies due to the formation of capillary bridges that reproduce experimental observations. Close to the critical point of the transition line separating the no-bridge from the bridge configuration, fluctuations in the particle cluster might be described by an effective two-state system. We show that the transition line vanishes for small particles and that the shape of the interaction potential depends on particle size.

Surface-induced ordering of nematics in an external field: the strong influence of tilted walls

Microscopic theory is used to investigate surface-induced order in a model nematic subjected to an external orienting field. The wall-particle interaction tends to orient particles perpendicular to the surface. It is shown that if the wall is tilted at approximately 45 degrees to the field, the reorientational effects can be an order of magnitude larger than those observed for perpendicular or parallel orientations. The surprising observation is associated with the breaking of a particular bulk symmetry. A possible practical application of the tilted geometry is briefly discussed.

Effects of wetting and anchoring on capillary phenomena in a confined liquid crystal

A fluid of hard spherocylinders of length-to-breadth ratio L/D=5 confined between two identical planar, parallel walls--forming a pore of slit geometry--has been studied using a version of the Onsager density-functional theory. The walls impose an exclusion boundary condition over the particle's centers of mass, while at the same time favoring a particular anchoring at the walls, either parallel or perpendicular to the substrate. We observe the occurrence of a capillary transition, i.e., a phase transition associated with the formation of a nematic film inside the pore at a chemical potential different from micro(b)-the chemical potential at the bulk isotropic-nematic transition. This transition terminates at an Ising-type surface critical point. In line with previous studies based on the macroscopic Kelvin equation and the mesoscopic Landau-de Gennes approach, our microscopic model indicates that the capillary transition is greatly affected by the wetting and anchoring properties of the semi-infinite system, i.e., when the fluid is in contact with a single wall or, equivalently, the walls are at a very large distance. Specifically, in a situation where the walls are preferentially wetted by the nematic phase in the semi-infinite system, one has the standard scenario with the capillary transition taking place at chemical potentials less than micro(b) (capillary nematization transition or capillary ordering transition). By contrast, if the walls tend to orientationally disorder the fluid, the capillary transition may occur at chemical potentials larger than micro(b), in what may be called a capillary isotropization transition or capillary disordering transition. Moreover, the anchoring transition that occurs in the semi-infinite system may affect very decisively the confinement properties of the liquid crystal and the capillary transitions may become considerably more complicated.

Wetting of a spherical particle by a nematic liquid crystal

We discuss how the curvature of a substrate influences wetting by a nematic liquid crystal concentrating on the surface of a spherical particle. Our investigation is based on Landau-de Gennes free energy formulated in terms of second-rank nematic order parameter Q(ij). We review the method to treat wetting transitions in curved geometries and calculate the wetting phase diagram in terms of the temperature and a surface coupling parameter. We find that the length of the prewetting line which corresponds to the boundary-layer transitions introduced by Sheng [Phys. Rev. A 26, 1610 (1982)] gradually decreases with a decrease in particle radius until it vanishes completely below a critical radius of about 100 nm. The prewetting line ends at a critical point which we study in detail. By interpreting the effect of curvature as an effective shift in temperature in Landau-de Gennes theory, we are able to formulate a good estimate for the critical temperature as a function of the inverse particle radius. It demonstrates that splay deformations around the particle significantly influence nematic wetting of curved surfaces.

Structural Forces near Phase Transitions of Liquid Crystals

The structure of the fragile liquid-crystalline phases has a strong impact on the forces between bodies immersed in a liquid crystal (LC). We have equipped an atomic force microscope with a precise temperature control and measured various liquid-crystalline structural forces at temperatures close to the phase transitions. The observed forces agree well with predictions of Landau--de Gennes phenomenological theory of LCs, even at a nanoscale length. In addition to this, we have observed a molecular layer, adsorbed on the surfactant-covered glass surface, and determined its thickness and elastic properties.

Capillary forces in a confined isotropic-nematic liquid crystal

We have investigated nematic capillary condensation in the isotropic phase of nematic liquid crystals 5CB (4-cyano-4(')-n-pentylbiphenyl) and 8CB (4-cyano-4(')-n-octylbiphenyl) confined to nanometer thick layers between two orienting surfaces. The capillary condensation was induced by decreasing the liquid crystal layer thickness using an atomic force microscope, and the onset of condensation was detected by monitoring the structural force on a confining surface. Very strong and long-ranged capillary forces were observed at temperatures close to the isotropic-nematic transition. We have analyzed the temperature dependence of the thickness of the liquid crystal layer, at which the condensation occurs, with a thermodynamic Kelvin equation and determined the interfacial tension between the isotropic and nematic phases. The separation dependence of capillary forces was analyzed within the Landau-de Gennes approach, including electrostatic interaction due to surface charging. The quantitative agreement between the measured and calculated force profiles is very good, and a single set of parameters is needed to describe a set of measured force profiles at different temperatures. Surface charge density, surface potential, and Debye screening length were determined directly from the observed surface forces.

Interaction and flocculation of spherical colloids wetted by a surface-induced corona of paranematic order

Particles dispersed in a liquid crystal above the nematic-isotropic phase transition are wetted by a surface-induced corona of paranematic order. Such coronas give rise to pronounced two-particle interactions. In this paper, we report details on the analytical and numerical study of these interactions published recently [Phys. Rev. Lett. 86, 3915 (2001)]. We especially demonstrate how for large particle separations the asymptotic form of a Yukawa potential arises. We show that the Yukawa potential is a surprisingly good description for the two-particle interactions down to distances of the order of the nematic coherence length. Based on this fact, we extend earlier studies on a temperature induced flocculation transition in electrostatically stabilized colloidal dispersions [Phys. Rev. E 61, 2831 (2000)]. We employ the Yukawa potential to establish a flocculation diagram for a much larger range of the electrostatic parameters, namely, the surface charge density and the Debye screening length. As a distinguished feature, a kinetically stabilized dispersion close to the nematic-isotropic phase transition is found.

Geometric view on colloidal interactions above the nematic-isotropic phase transition

Particles dispersed in a liquid crystal above the nematic-isotropic phase transition are surrounded by a surface-induced nematic wetting layer. When the nematic coronas of two particles overlap, they experience a strong attraction since the volume of nematic ordering and therefore the free energy is reduced. For normal anchoring of the liquid-crystal molecules on the particles' surfaces, we demonstrate that the implementation of this geometric view reproduces the Yukawa interaction derived by Galatola and Fournier in a recent paper [Phys. Rev. Lett. 86, 3915 (2001)], however with half the strength. To understand the factor 2, we rederive the Yukawa potential with the approximation of linear superposition of two one-particle profiles. At the end, we comment on the similarities of our approach to the screened electrostatic interaction of charged colloids.

Observation of an electrostatic force between charged surfaces in liquid crystals

We report on the atomic force microscope observation of an electrostatic force between glass surfaces immersed in cyanobiphenil liquid crystals. The measured force is repulsive and decays exponentially with increasing surface separation. A mean field description of the electrostatic interaction in liquids has been used to determine the Debye screening length, the concentration of dissolved ions, and the surface electric potential. The effect of the observed interfacial electric field on the liquid crystal orientation at the surface has been discussed. It has been found that the coupling between the liquid crystal order and the surface electric field does not contribute considerably to the surface orienting action.

Forces in the isotropic phase of a confined nematic liquid crystal 5CB

Using a temperature controlled atomic force microscope, we have measured the temperature dependence of the force between a flat silanated glass surface and a silanated glass microsphere, immersed in the isotropic phase of the nematic liquid crystal 5CB (4'-n-pentyl 4-cyanobiphenyl). At separations of several nanometers, we observed a weak, short range attractive force of the order of 100 pN, which was increased by decreasing the temperature. The temperature dependence of the amplitude and the range of this attractive force can be described by a combination of van der Waals and a mean-field prenematic force due to the surface-induced nematic order. This is supported by ellipsometric study and allows for the determination of the surface coupling energy of 5CB on a silanated glass surface.