Julio C. Armas-Pérez

Nanoparticle self-assembly at the interface of liquid crystal droplets

Significance Controlled assembly of nanoparticles at liquid crystal interfaces could lead to easily manufacturable building blocks for assembly of materials with tunable mechanical, optical, and electronic properties. Past work has examined nanoparticle assembly at planar liquid crystal interfaces. In this work, we show that nanoparticle assembly on curved interfaces is drastically different and arises for conditions under which assembly is too weak to occur on planar interfaces. We also demonstrate that liquid crystal-mediated nanoparticle interactions are strong, are remarkably sensitive to surface anchoring, and lead to hexagonal arrangements that do not arise in bulk systems. All of these elements form the basis for a highly tunable, predictable, and versatile platform for hierarchical materials assembly. Nanoparticles adsorbed at the interface of nematic liquid crystals are known to form ordered structures whose morphology depends on the orientation of the underlying nematic field. The origin of such structures is believed to result from an interplay between the liquid crystal orientation at the particles’ surface, the orientation at the liquid crystal’s air interface, and the bulk elasticity of the underlying liquid crystal. In this work, we consider nanoparticle assembly at the interface of nematic droplets. We present a systematic study of the free energy of nanoparticle-laden droplets in terms of experiments and a Landau–de Gennes formalism. The results of that study indicate that, even for conditions under which particles interact only weakly at flat interfaces, particles aggregate at the poles of bipolar droplets and assemble into robust, quantized arrangements that can be mapped onto hexagonal lattices. The contributions of elasticity and interfacial energy corresponding to different arrangements are used to explain the resulting morphologies, and the predictions of the model are shown to be consistent with experimental observations. The findings presented here suggest that particle-laden liquid crystal droplets could provide a unique and versatile route toward building blocks for hierarchical materials assembly.

Nematic and smectic ordering in a system of two-dimensional hard zigzag particles

The orientational and positional ordering of the two-dimensional system of hard zigzag particles has been investigated by means of Onsager theory. Analytical results are obtained for the transition densities of the isotropic-nematic and the nematic-smectic phase transitions. It is shown that the stability of the nematic and smectic phases is very sensitive to the molecular shape. In the hard needle limit, only the isotropic-nematic phase transition takes place, while increasing the tail length and the bent angle between the central core and the tails destabilizes the nematic phase. On the other hand the stability of the smectic phase is due to the increasing excluded area cost with bent angle and the tail length. The zigzag particles pack in a layered structure such that they are tilted and form semi-ideal gas in the layers to push the high cost excluded area regions into the interstitial regions. The predictions of Onsager theory are in good agreement with MC simulation data.

Liquid-vapor equilibrium and interfacial properties of square wells in two dimensions

Liquid-vapor coexistence and interfacial properties of square wells in two dimensions are calculated. Orthobaric densities, vapor pressures, surface tensions, and interfacial thicknesses are reported. Results are presented for a series of potential widths λ* = 1.4, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, and 5, where λ* is given in units of the hard core diameter σ. Critical and triple points are explored. No critical point was found for λ* < 1.4. Corresponding states principle analysis is performed for the whole series. For λ* = 1.4 and 1.5 evidence is presented that at an intermediate temperature between the critical and the triple point temperatures the liquid branch becomes an amorphous solid. This point is recognized in Armas-Pérez et al. [unpublished] as a hexatic phase transition. It is located at reduced temperatures T* = 0.47 and 0.35 for λ* = 1.4 and 1.5, respectively. Properties such as the surface tension, vapor pressure, and interfacial thickness do not present any discontinuity at these points. This amorphous solid branch does not follow the corresponding state principle, which is only applied to liquids and gases.

Theoretically informed Monte Carlo simulation of liquid crystals by sampling of alignment-tensor fields

A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate.

Effect of flexibility on liquid-vapor coexistence and surface properties of tangent linear vibrating square well chains in two and three dimensions

The effect of flexibility on liquid-vapor and interfacial properties of tangent linear vibrating square well chains is studied. Surface tension, orthobaric densities, vapor pressures, and interfacial thicknesses are reported and analyzed using corresponding states principles. Discontinuous molecular dynamics simulations in two and three dimensions are performed on rigid tangent linear vibrating square well chains of different lengths. In the case of two dimensions, simulation results of completely flexible tangent linear vibrating square well chains are also reported. Properties are calculated for chains of 2-12 monomers. Rigidity is controlled by trapping the first and last monomer in the chain in a vibrating well at half of the distance of the whole chain. Critical property values are reported as obtained from orthobaric densities, surface tensions, and vapor pressures. For the fully flexible chains, the critical temperatures increase with chain length but the effect saturates. In contrast, the critical temperatures increase for the rigid chains until no more critical point is found.

Directed self-assembly of nematic liquid crystals on chemically patterned surfaces: morphological states and transitions

The morphology and through-film optical properties of nematic liquid crystals (LCs) confined between two surfaces may be engineered to create switches that respond to external electric fields, thereby enabling applications in optoelectronics that require fast responses and low power. Interfacial properties between the confining surfaces and the LC play a central role in device design and performance. Here we investigate the morphology of LCs confined in hybrid cells with a top surface that exhibits uniform homeotropic anchoring and a bottom surface that is chemically patterned with sub-micron and micron- wide planar anchoring stripes in a background of homeotropic anchoring. In a departure from past work, we first investigate isolated stripes, as opposed to dense periodic arrays of stripes, thereby allowing for an in-depth interpretation of the effects of patterning on LC morphology. We observe three LC morphologies and sharp transitions between them as a function of stripe width in the submicron and micron regimes. Numerical simulations and theory help explain the roles of anchoring energy, elastic deformation, entropy, pattern geometry, and coherence length of the LC in the experimentally observed behavior. The knowledge and models developed from an analysis of results generated on isolated features are then used to design dense patterned substrates for high-contrast and efficient orientational switching of LCs in response to applied fields.

Directed Self-Assembly of Colloidal Particles onto Nematic Liquid Crystalline Defects Engineered by Chemically Patterned Surfaces

In exploiting topological defects of liquid crystals as the targeting sites for trapping colloidal objects, previous work has relied on topographic features with uniform anchoring to create defects, achieving limited density and spacing of particles. We report a generalizable strategy to create topological defects on chemically patterned surfaces to assemble particles in precisely defined locations with a tunable interparticle distance at nanoscale dimensions. Informed by experimental observations and numerical simulations that indicate that liquid crystals, confined between a homeotropic-anchoring surface and a surface with lithographically defined planar-anchoring stripes in a homeotropic-anchoring background, display splay-bend deformation, we successfully create pairs of defects and subsequently trap particles with controlled spacing by designing patterns of intersecting stripes aligned at 45° with homeotropic-anchoring gaps at the intersections. Application of electric fields allows for dynamic control of trapped particles. The tunability, responsiveness, and adaptability of this platform provide the opportunities for assembly of colloidal structures toward functional materials.

Liquid crystal free energy relaxation by a theoretically informed Monte Carlo method using a finite element quadrature approach.

A theoretically informed Monte Carlo method is proposed for Monte Carlo simulation of liquid crystals on the basis of theoretical representations in terms of coarse-grained free energy functionals. The free energy functional is described in the framework of the Landau-de Gennes formalism. A piecewise finite element discretization is used to approximate the alignment field, thereby providing an excellent geometrical representation of curved interfaces and accurate integration of the free energy. The method is suitable for situations where the free energy functional includes highly non-linear terms, including chirality or high-order deformation modes. The validity of the method is established by comparing the results of Monte Carlo simulations to traditional Ginzburg-Landau minimizations of the free energy using a finite difference scheme, and its usefulness is demonstrated in the context of simulations of chiral liquid crystal droplets with and without nanoparticle inclusions.

Phase diagram of a square-well model in two dimensions

The phase behavior of a two-dimensional square-well model of width 1.5σ, with emphasis on the low-temperature and/or high-density region, is studied using Monte Carlo simulation in the canonical and isothermal-isobaric ensembles, and discontinuous molecular-dynamics simulation in the canonical ensemble. Several properties, such as equations of state, Binder cumulant, order parameters, and correlation functions, were computed. Numerical evidence for vapor, liquid, hexatic, and triangular solid is given, and, in addition, a non-compact solid with square-lattice symmetry is obtained. The global phase diagram is traced out in detail (or sketched approximately whenever only inaccurate information could be obtained). The solid region of the phase diagram is explained using a simple mean-field model.

Liquid-vapor equilibrium and surface properties of short rigid chains with one long range attractive potential.

Liquid-vapor coexistence and interfacial properties of short lineal rigid vibrating chains with three tangent monomers in two and three dimensions are calculated. The effect of the range and position of a long ranged square well attractive potential is studied. Orthobaric densities, vapor pressures, surface tensions, and interfacial widths are reported. Two types of molecules are studied. Chains of three tangent hard sphere monomers and chains of three and five tangent hard sphere monomers interacting with a square well attractive potential with λ(∗) = λ∕σ = 1.5 in units of the hard core diameter σ. The results are reported in two and three dimensions. For both types of chains, a long ranged square well attractive potential is located at various positions in the chain to investigate its effect in the properties of the corresponding systems. Results for hard sphere chains are presented for a series of different sizes of λ(∗) between 2.5 and 5. For square well chains the position in the chain of the long ranged potential has no influence in the coexistence and interfacial properties. Critical temperatures increase monotonically with respect to λ(∗) and critical densities decrease systematically for both types of chains. When the long ranged potential is located in the middle monomer of the hard sphere chains no critical point is found for λ(∗) < 2.4. No critical point is found when the long ranged potential is located in one of the extremes of the hard sphere chains.