Computer simulation of a liquid-crystal anchoring transition

Evidence of T-type structures of hard square boards in capillary confinement

We employ Onsager's second virial density functional theory combined with the Parsons-Lee theory within the restricted orientation (Zwanzig) approximation to examine the phase structure of hard square boards of dimensions (L×D×D) uniaxially confined in narrow slabs. Depending on the wall-to-wall separation (H), we predict a number of distinctly different capillary nematic phases, including a monolayer uniaxial or biaxial planar nematic, homeotropic with a variable number of layers, and a T-type structure. We determine that the favored phase is homotropic, and we observe first-order transitions from the homeotropic structure with n layers to n+1 layers as well as from homeotropic surface anchoring to a monolayer planar or T-type structure involving both planar and homeotropic anchoring at the pore surface. By increasing the packing fraction, we further demonstrate a reentrant homeotropic-planar-homeotropic phase sequence in a particular range (i.e., H/D=1.1 and 0.25≤L/D<0.26). We find that the T-type structure is more stable when the pore is wide enough with respect to the planar phase. The enhanced stability of the mixed-anchoring T-structure is unique for square boards and becomes manifest at pore width exceeding L+D. More specifically, the biaxial T-type structure emerges directly from the homeotropic state without intervention of a planar layer structure as observed for other convex particle shapes.

Capillary-driven biaxial planar and homeotropic nematization of hard cylinders

We use the Parsons-Lee modification of Onsager's second virial theory within the restricted orientation (Zwanzig) approximation to analyze the phase behavior of hard cylindrical rods confined in narrow pores. Depending on the wall-to-wall separation we predict a number of distinctly different surface-generated nematic phases, including a biaxial planar nematic with variable number of layers, a monolayer homeotropic, and a hybrid T-type structure (a planar layer combined with a homeotropic one). For narrow pores, we find evidence of two types of second-order uniaxial-biaxial transitions depending on the aspect ratio of the particles. More specifically, we observe a continuous crossover from n to n+1 layers, each with a distinct planar anchoring symmetry as well as first-order transitions from planar to homeotropic surface anchoring. Contrary to the previously studied case of parallelepipeds we find that the surface anchoring transition from planar to homeotropic symmetry occurs at much lower overall rod packing fractions. This renders the observation of homeotropic capillary nematics much more realistic in experimental systems of strongly confined anisotropic colloids. Unlike confined parallelepipeds, cylindrical rods gradually increase the number of the nematic planar layers (without any phase transitions). However, a weakly first-order transition was observed between two planar structures with n and n+1 layers in wide pores and longer rods. In addition, the cylindrical rods exhibit a first-order transition from the homeotropic structure to the uniaxial (or biaxial) T phase that has not been observed in confined hard parallelepipeds. We further demonstrate a reentrant uniaxial-biaxial-uniaxial-biaxial phase sequence for confined cylinders at small aspect ratio. Our results also clearly demonstrate that stable T-type surface ordering is a subtle capillary effect that only becomes manifest in sufficiently narrow pores away from the two-dimensional bulk limit.

Pressure-tensor method evaluation of the interfacial tension between Gay-Berne isotropic fluid and a smooth repulsive wall

The interfacial properties of a confined thermotropic liquid crystalline material are investigated using a molecular dynamics simulation technique. The pairwise interaction among the soft ellipsoidal particles is modeled by the Gay-Berne (GB) potential. The GB ellipsoids are confined by two soft, smooth, repulsive walls defined by the Weeks-Chandler-Andersen (WCA) potential. The aperiodic confinement due to walls makes the system mechanically anisotropic. Hence using the pressure-tensor method, the interfacial tension of an interface between the bulk isotropic (I) phase and WCA wall at various number densities (ρ) is calculated. From the pressure tensor and orientational order profiles, the arrangement of ellipsoids in the bulk and the vicinity of the wall is determined. The effect of system size and the wall-particle interaction strength (ε_W) on is also analyzed by varying the system size and ε_W.

From n-layer planar ordering to the monolayer homeotropic structure of confined hard rods: The effect of shape anisotropy and wall-to-wall separation

Using the Parsons-Lee theory, we examined the effect of shape anisotropy and the wall-to-wall separation (H) on the phase behavior of the hard parallelepiped rods with dimensions L, D, and D (L>D) in such narrow slitlike pores which only one homeotropic layer can form. The phase structures, including biaxiality, planar nematic layering transition as well as planar to homeotropic, were studied for some separations in the range 2.5D≤H≤10.0D for H-D≤L<H.

Ordering transitions of weakly anisotropic hard rods in narrow slitlike pores

The effect of strong confinement on the positional and orientational ordering is examined in a system of hard rectangular rods with length L and diameter D (L>D) using the Parsons-Lee modification of the second virial density-functional theory. The rods are nonmesogenic (L/D<3) and confined between two parallel hard walls, where the width of the pore (H) is chosen in such a way that both planar (particle's long axis parallel to the walls) and homeotropic (particle's long axis perpendicular to the walls) orderings are possible and a maximum of two layers is allowed to form in the pore. In the extreme confinement limit of H≤2D, where only one-layer structures appear, we observe a structural transition from a planar to a homeotropic fluid layer with increasing density, which becomes sharper as L→H. In wider pores (2D<H<3D) planar order with two layers, homeotropic order, and even combined bilayer structures (one layer is homeotropic, while the other is planar) can be stabilized at high densities. Moreover, first-order phase transitions can be seen between different structures. One of them emerges between a monolayer and a bilayer with planar orders at relatively low packing fractions.

Structure and Interfacial Tension of a Hard-Rod Fluid in Planar Confinement

The structural properties and interfacial tension of a fluid of rodlike hard-spherocylinder particles in contact with hard structureless flat walls are studied by means of Monte Carlo simulation. The calculated surface tension between the rod fluid and the substrate is characterized by a nonmonotonic trend as a function of the bulk concentration (density) over the range of isotropic bulk concentrations. As suggested by earlier theoretical studies, a surface-ordering scenario is confirmed by our simulations: the local orientational order close to the wall changes from uniaxial to biaxial nematic when the bulk concentration reaches about 85% of the value at the onset of the isotropic-nematic phase transition. The surface ordering coincides with a wetting transition whereby the hard wall is wetted by a nematic film. Accurate values of the fluid-solid surface tension, the adsorption, and the average particle-wall contact distance are reported (over a broad range of densities into the dense nematic region for the first time), which can serve as a useful benchmark for future theoretical and experimental studies on confined rod fluids. The simulation data are supplemented with predictions from second-virial density functional theory, which are in good qualitative agreement with the simulation results.

Concentration-induced planar-to-homeotropic anchoring transition of stiff ring polymers on hard walls

We study the structure and interfacial ordering of stiff ring polymers close to repulsive walls. For this purpose, we employ an anisotropic effective model in which the rings are pictured as soft, penetrable discs [P. Poier, C. N. Likos, A. J. Moreno and R. Blaak, Macromolecules, 2015, 48, 4983]. We have studied this model in the bulk and in the presence of a wall, employing Density Functional Theory and computer simulations. While the Ornstein-Zernike equation in combination with the Hypernetted Chain Approximation gives results that are in quantitative agreement with computer simulations, a simple Mean Field approximation strongly overestimates the interaction between the effective particles in the bulk. We discover that by increasing density one can induce a reorientation of the effective rings in the vicinity of a wall, which prefer to orient themselves parallel to the surface (face-on or planar) for low densities ρ and reorient orthogonal to the wall (edge-on or homeotropic) for higher values of ρ. This transition in the surface-structure can be observed in both computer simulations, as well as in an appropriate density functional theory. We trace its physical origin in the penetrable character of the rings, which allows for a reduction of the surface tension contribution due to ring-ring interactions upon the emergence of homeotropic ordering on the wall and increasing the density of the system.

Competition of lattice and basis for alignment of nematic liquid crystals

Due to elastic anisotropy, two-dimensional patterning of substrates can promote weak azimuthal alignment of adjacent nematic liquid crystals. Here we consider how such alignment can be achieved using a periodic square lattice of circular or elliptical motifs. In particular, we examine ways in which the lattice and motif can combine to favor differing orientations. Using Monte Carlo simulation and continuum elasticity we find, for circular motifs, that the coverage fraction controls both the polar anchoring angle and a transition in the azimuthal orientation. If the circles are generalized to ellipses, arbitrary control of the effective easy axis and effective anchoring potential becomes achievable by appropriate tuning of the ellipse motif relative to the periodic lattice patterning. This has possible applications in both monostable and bistable liquid crystal device contexts.

Thermotropic interface and core relaxation dynamics of liquid crystals in silica glass nanochannels: a dielectric spectroscopy study

We report dielectric relaxation spectroscopy experiments on two rod-like liquid crystals of the cyanobiphenyl family (5CB and 6CB) confined in tubular nanochannels with 7 nm radius and 340 micrometer length in a monolithic, mesoporous silica membrane. The measurements were performed on composites for two distinct regimes of fractional filling: monolayer coverage at the pore walls and complete filling of the pores. For the layer coverage a slow surface relaxation dominates the dielectric properties. For the entirely filled channels the dielectric spectra are governed by two thermally-activated relaxation processes with considerably different relaxation rates: a slow relaxation in the interface layer next to the channel walls and a fast relaxation in the core region of the channel filling. The strengths and characteristic frequencies of both relaxation processes have been extracted and analysed as a function of temperature. Whereas the temperature dependence of the static capacitance reflects the effective (average) molecular ordering over the pore volume and is well described within a Landau-de Gennes theory, the extracted relaxation strengths of the slow and fast relaxation processes provide an access to distinct local molecular ordering mechanisms. The order parameter in the core region exhibits a bulk-like behaviour with a strong increase in the nematic ordering just below the paranematic-to-nematic transition temperature TPN and subsequent saturation during cooling. By contrast, the surface ordering evolves continuously with a kink near TPN. A comparison of the thermotropic behaviour of the monolayer with the complete filling reveals that the molecular order in the core region of the pore filling affects the order of the peripheral molecular layers at the wall.

Competing alignments of nematic liquid crystals on square-patterned substrates

A theoretical analysis is presented of a nematic liquid crystal confined between substrates patterned with squares that promote vertical and planar alignment. Two approaches are used to elucidate the behavior across a wide range of length scales: Monte Carlo simulation of hard particles and Frank-Oseen continuum theory. Both approaches predict bistable degenerate azimuthal alignment in the bulk along the edges of the squares; the continuum calculation additionally reveals the possibility of an anchoring transition to diagonal alignment if the polar anchoring energy associated with the pattern is sufficiently weak. Unlike the striped systems previously analyzed, the Monte Carlo simulations suggest that there is no "bridging" transition for sufficiently thin cells. The extent to which these geometrically patterned systems resemble topographically patterned substrates, such as square wells, is also discussed.

Diffusivity maximum in a reentrant nematic phase

We report molecular dynamics simulations of confined liquid crystals using the Gay–Berne–Kihara model. Upon isobaric cooling, the standard sequence of isotropic–nematic–smectic A phase transitions is found. Upon further cooling a reentrant nematic phase occurs. We investigate the temperature dependence of the self-diffusion coefficient of the fluid in the nematic, smectic and reentrant nematic phases. We find a maximum in diffusivity upon isobaric cooling. Diffusion increases dramatically in the reentrant phase due to the high orientational molecular order. As the temperature is lowered, the diffusion coefficient follows an Arrhenius behavior. The activation energy of the reentrant phase is found in reasonable agreement with the reported experimental data. We discuss how repulsive interactions may be the underlying mechanism that could explain the occurrence of reentrant nematic behavior for polar and non-polar molecules.

Orientational prewetting of planar solid substrates by a model liquid crystal

We present grand canonical ensemble Monte Carlo simulations of prewetting transitions in a model liquid crystal at structureless solid substrates. Molecules of the liquid crystal interact via anisometric Lennard-Jones potentials and can be anchored planar or homeotropically at the substrates. Fluid-substrate attraction is modeled by a Yukawa potential of variable range. By monitoring the grand-potential density and the nematic order parameter as functions of the chemical potential μ, several discontinuous prewetting, wetting, and isotropic-nematic phase transitions are observed. These transitions depend on both the range of the fluid-substrate attraction and the specific anchoring at the substrate. Our results show that at substrates characterized by degenerate anchoring prewetting occurs at lower μ compared with cases in which the anchoring is monostable. This indicates that prewetting transitions are driven by orientational entropy because degenerate anchoring allows for more orientationally distinct configurations of molecules compared with monostable anchoring. In addition, by analyzing local density and various local order parameters, a detailed picture of the structure of various phases emerges from our simulations.

Density functional theory of liquid crystals and surface anchoring: hard Gaussian overlap-sphere and hard Gaussian overlap-surface potentials

This article applies the density functional theory to confined liquid crystals, comprised of ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The extended restricted orientation model proposed by Moradi and co-workers [J. Phys.: Condens. Matter 17, 5625 (2005)] is used to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the optimized sum of Percus-Yevick and Roth DCF for hard spheres; the anisotropy introduced by means of the closest approach parameter, the expression proposed by Marko [Physica B 392, 242 (2007)] for DCF of HGO, and hard ellipsoids were used. In this study we extend an our previous work [Phys. Rev. E 72, 061706 (2005)] on the anchoring behavior of hard particle liquid crystal model, by studying the effect of changing the particle-substrate contact function instead of hard needle-wall potentials. We use the two particle-surface potentials: the HGO-sphere and the HGO-surface potentials. The average number density and order parameter profiles of a confined HGO fluid are obtained using the two particle-wall potentials. For bulk isotropic liquid, the results are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 71, 021705 (2005)]. Also, for the bulk nematic phase, the theory gives the correct density profile and order parameter between the walls.

Nematic liquid-crystal alignment on stripe-patterned substrates

Here, we use molecular simulation to consider the behavior of a thin nematic film confined between two identical nanopatterned substrates. Using patterns involving alternating stripes of homeotropic-favoring and homogeneous-favoring substrates, we investigate the influence of the relative stripe width and the film thickness. From this, we show that the polar anchoring angle can be varied continuously from planar to homeotropic by appropriate tuning of these parameters. For very thin films with equal stripe widths, we observe orientational bridging, the surface patterning being written in domains which traverse the nematic film. This dual-bridging-domain arrangement breaks down with increase in film thickness, however, being replaced by a single tilted monodomain. Strong azimuthal anchoring in the plane of the stripe boundaries is observed for all systems.

Effective free-energy method for nematic liquid crystals in contact with structured substrates

We study the phase behavior of a nematic liquid crystal confined between a flat substrate with strong anchoring and a patterned substrate whose structure and local anchoring strength we vary. By first evaluating an effective surface free-energy function characterizing the patterned substrate, we derive an expression for the effective free energy of the confined nematic liquid crystal. Then we determine phase diagrams involving a homogeneous state in which the nematic director is almost uniform and a hybrid aligned nematic state in which the orientation of the director varies through the cell. Direct minimizations of the free-energy functional were performed in order to test the predictions of the effective free-energy method. We find remarkably good agreement between the phase boundaries calculated from the two approaches. In addition, the effective free-energy method allows one to determine the energy barriers between two states in a bistable nematic device.

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.

Lennard-Jones sticks: A new model for linear molecules

We consider the anisotropic interaction between two line segments consisting of a homogeneous distribution of Lennard-Jones centers. The potential energy of such a pair cannot be expressed in closed form. However, we show that it may be approximated in a way that renders this intuitively appealing model competitive both for simulations and theory.

Effect of nanoconfinement on liquid-crystal polymer chains

We apply a Monte Carlo polymerization model for Gay-Berne [J. Chem. Phys. 74, 3316 (1981)] monomers that we have recently introduced [J. Chem. Phys. 121, 9123 (2004)] to investigate with computer simulations the effects of nanoconfinement and anchoring type on the structure of the main-chain liquid-crystal polymers formed in thin films, in the presence of several types of surface alignment: parallel to the interface (random and uniform) or perpendicular to it (homeotropic). We perform first a study of the confined monomers and then we examine the features of the polymer chains obtained from an isotropic or nematic sample. We find a significant effect of the anchoring conditions on the characteristics of the chains and particularly striking differences between planar and homeotropic boundaries. Furthermore, our results indicate that the choice of different anchorings could be used to tune the linearity and degree of polymerization of the chains.

Density functional theory of liquid crystals and surface anchoring

This paper applies the density functional theory to confined liquid crystals comprising ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The restricted orientation model proposed by Rickayzen [Mol. Phys. 95, 393 (1998)] is extended to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the Percus-Yevick DCF for hard spheres; the anisotropy is introduced by means of the closest approach parameter. The average number density and orientational order parameter profiles of a HGO fluid confined in between planar walls are obtained using a hard needle-wall potential to represent the particle-wall interactions. For short and long needle lengths, the homeotropic and planar anchoring are observed, respectively. For the bulk isotropic phase the calculated density and order parameter profiles are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 69, 61705 (2004)]. However, for the bulk nematic phase the theory gives the correct density profile between the walls. The correct order parameters are obtained close to the walls whereas for the region in the middle of the walls, the agreement is less satisfactory.

Density profile and order parameter of a hard ellipsoidal fluid confined to a slit

The density profile and order parameter of a fluid of hard axially symmetric ellipsoids confined in between two parallel hard walls is obtained by using the density functional theory. The required input direct correlation function of the homogeneous fluid is calculated by the variational method introduced by Marko (1989 Phys. Rev. 39 2050) and the modified closest approach method proposed by Rickayzen (1998 Mol. Phys. 95 393). Here the restricted orientation model, ROM, is extended to study a fluid comprising molecules which can be aligned in more than six directions, making it more representative of a normal fluid. The density profiles, the average number density and order parameter are obtained for different values of density and elongations. The results are in agreement with the previous theory and available Monte Carlo simulation results.

Anchoring and structural transitions as a function of molecular length in confined liquid crystals

Using deuteron nuclear magnetic resonance to study liquid crystals confined to cylindrical pores, an anchoring transition has been found. The transition exhibits an unexpected sharp dependence of the anchoring strength on cyanobiphenyl liquid crystal molecular length. A structural transition from a parallel axial to a planar radial configuration occurs due to an anchoring transition from planar to weakly homeotropic orientation at the walls. The anchoring strength is at a minimum near the decylcyanobiphenyl (10CB) liquid crystal length. Long chain liquid crystal configurations depend on thermal cycling and on the equilibrium atmosphere leading to a bistable SmA structure. Orientational order wetting in the isotropic phase also depends on molecular length.

Using particle shape to induce tilted and bistable liquid crystal anchoring

We use Monte Carlo simulations of hard Gaussian overlap (HGO) particles symmetrically confined in slab geometry to investigate the role of particle-substrate interactions on liquid crystalline anchoring. Despite the restriction here to purely steric interactions and smooth substrates, a range of behaviors are captured, including tilted anchoring and homeotropic-planar bistability. These macroscopic behaviors are all achieved through appropriate tuning of the microscopics of the HGO-substrate interaction, based upon nonadditive descriptions for the HGO-substrate shape parameter.