Raman spectroscopy and molecular dynamics simulations of aqueous two-phase systems for the purification of phosphoric acid.

In this work, Raman spectroscopy and molecular dynamics simulations were used to elucidate key interactions between polyethylene glycol (PEG) and phosphoric acid (H3PO4) in aqueous two-phase systems for the extraction of phosphoric acid. Extensive molecular dynamics simulations were performed, and radial distribution functions as well as hydrogen bonds between PEG and other molecules were measured. Experimental data were used in combination with the slope method to infer PEG-H3PO4 interactions, and the interpretation is consistent with molecular simulation results. Based on our experimental and simulation results, we propose a solvation mechanism governed by hydrogen bonding interactions: at low concentrations of H3PO4 within the polymer-rich aqueous solution, entropy dominates and phosphoric acid molecules have weak interactions with PEG; as the concentration of phosphoric acid increases above a certain critical value, enthalpy dominates with PEG molecules interacting strongly with H3PO4 molecules via hydrogen bonds.

Curvature and confinement effects on chiral liquid crystal morphologies.

Chiral liquid crystals (ChLCs) exhibit an inherent twist that originates at the molecular scale and can extend over multiple length scales when unconstrained. Under confinement, the twist is thwarted, leading to formation of defects in the molecular order that offer distinct optical responses and opportunities for colloidal driven assembly. Past studies have explored spheroidal confinement down to the nanoscopic regime, where curved boundaries produce surface defects to accommodate topological constraints and restrict the propagation of cuboidal defect networks. Similarly, strict confinement in channels and shells has been shown to give rise to escaped configurations and skyrmions. However, little is known about the role of extrinsic curvature in the development of cholesteric textures and Blue Phases (BP). In this paper, we examine the palette of morphologies that arises when ChLCs are confined in toroidal and cylindrical cavities. The equilibrium morphologies are obtained following an annealing strategy of a Landau-de Gennes free energy functional. Three dimensionless groups are identified to build phase diagrams: the natural twist, the ratio of elastic energies, and the circumscription of a BP cell. Curvature is shown to introduce helical features that are first observed as a Double Twist, and progress to Chiral Ribbons and, ultimately, Helical BP and BP. Chiral ribbons are examined as useful candidates for driven assembly given their tunability and robustness.

Determination of liquid-vapor equilibrium and critical properties of fatty acids for biodiesel production through molecular dynamics.

In recent years, biodiesel production has emerged as an option for renewable and green fuel generation due to the constant reduction of fossil fuel reservoirs. Biofuels as biodiesel also show valuable attributes, environmentally speaking, due to their low environmental impact, contributing to the achievement of sustainability. However, costs are not allowable for large-scale production. Thereby, several novel processes have been proposed (e.g., reactive distillation) to solve this issue. An inconvenience for the development of these processes is the little information in the literature about the critical properties of fatty acids, which are precursors of biodiesel. Determination of critical properties for fatty acids through experimentation is difficult. The reason is that fatty acids tend to self-associate (to dimerize) due to carboxylic groups presence through hydrogen bonds, and consequently, have higher boiling points than other compounds of similar molecular mass (e.g., hydrocarbons, esters). Therefore, alternative methods for this determination are required. One choice is the group-contribution method, which is based on the structure of the molecule; however, results can significantly vary among different group-contribution approaches. Another alternative (and the focus of this research) for the determination of these properties is molecular simulation techniques. In this work, the liquid-vapor equilibrium as a function of temperature and the surface tension of three pure fatty acids of long chain (linoleic, oleic, and palmitic acid) have been calculated. Simulations have been performed by molecular dynamics using the method of direct determination of phase coexistence with the software GROMACS; in which the transferable potentials for phase equilibria united atom forcefield (TraPPE-UA) have been implemented for these specific molecules. Orthobaric densities and surface tension values have been reported at temperatures near the critical point (from 650 K to 800 K). Critical properties (temperature, pressure, density) have been extrapolated from trajectories obtained in these simulations using scaling law relations. Critical properties for these compounds are not available experimentally, therefore, group contribution calculations from the literature were used as a reference. In this comparison, the palmitic acid properties calculated in this work, show the best agreement among the three substances investigated.

Dynamics and phase behavior of two-dimensional size-asymmetric binary mixtures of core-softened colloids.

The self-assembly of binary colloidal mixtures provides a bottom-up approach to create novel functional materials. To elucidate the effect of composition, temperature, and pressure on the self-assembly behavior of size-asymmetric mixtures, we performed extensive dynamics simulations of a simple model of polymer-grafted colloids. We have used a core-softened interaction potential and extended it to represent attractive interactions between unlike colloids and repulsions between like colloids. Our study focused on size-asymmetric mixtures where the ratio between the sizes of the colloidal cores was fixed at σBσA=0.5. We have performed extensive simulations in the isothermal-isobaric and canonical (NVT) ensembles to elucidate the phase behavior and dynamics of mixtures with different stoichiometric ratios. Our simulation results uncovered a rich phase behavior, including the formation of hierarchical structures with many potential applications. For compositions where small colloids are the majority, sublattice melting occurs for a wide range of densities. Under these conditions, large colloids form a well-defined lattice, whereas small colloids can diffuse through the system. As the temperature is decreased, the small colloids localize, akin to a metal-insulator transition, with the small colloids playing a role similar to electrons. Our results are summarized in terms of phase diagrams.

Directing the far-from-equilibrium assembly of nanoparticles in confined liquid crystals by hydrodynamic fields.

The assembly of nematic colloids relies on long-range elastic interactions that can be manipulated through external stimuli. Confinement and the presence of a hydrodynamic field alter the defect structures and the energetic interactions between the particles. In this work, the assembly landscape of nanoparticles embedded in a nematic liquid crystal confined in a nanochannel under a pressure-driven flow is determined. The dynamics of the liquid crystal tensor alignment field is determined through a Poisson-Bracket framework, namely the Stark-Lubensky equations, coupled with the zero-Reynolds momentum equations and the liquid crystal Landau-de Gennes free energy functional. A second order semi-implicit time integration and a three-dimensional Galerkin finite element method are used to resolve flow and nematic fields under several conditions. In general, the zero Reynolds flow displaces the defects around the particles in the upstream direction and renders the surface anchoring ineffective when the flow strength dominates over the nematic elasticity. More importantly, the potential of mean force for particle assembly is non-monotonic independent of surface anchoring. Our results show that the confinement length scale determines the repulsion/attraction transition between colloids, while the flow strength modifies the static defect structure surrounding the particles and determines the magnitude of the energetic barrier for successful assembly. In the attractive regime, the particles move at different rates through the nematic until one particle eventually catches up with the other. This process occurs against or along the direction of flow depending on the flow strength. Ultimately, these results provide a template for engineering and controlling the transport and assembly of nanoparticles under far-from equilibrium conditions in anisotropic media.

Cuboidal liquid crystal phases under multiaxial geometrical frustration.

Cuboidal liquid crystal phases - the so-called blue phases - consist of a network of topological defects arranged into a cubic symmetry. They exhibit striking optical properties, including Bragg reflection in the visible range and fast response times. Confining surfaces can interfere with the packing of such a network, leading to structures that have not been explored before. In this work, a Landau-de Gennes free energy formalism for the tensor alignment field Q is used to investigate the behavior of chiral liquid crystals under non-isotropic confinement. The underlying free energy functional is solved by relying on a Monte Carlo method that facilitates efficient exploration of configuration space. The results of simulations are expressed in terms of phase diagrams as a function of chirality and temperature for three families of spheroids: oblate, spherical, and prolate. Upon deformation, blue phases adapt and transform to accommodate the geometrical constraints, thereby resulting in a wider range of thermal stability. For oblate spheroids, confinement interferes with the development of a full blue phase structure, resulting on a combination of half skyrmions. For prolate spheroids, the blue phases are hybridized and exhibit features of blue phases I and II. More generally, it is shown that mechanical deformation provides an effective means to control, manipulate and stabilize blue phases and cholesterics confined in tactoids.

Hierarchical complex self-assembly in binary nanoparticle mixtures.

Hierarchical self-assembly of soft matter provides a powerful route to create complex materials with enhanced physical properties. The understanding of the fundamental processes leading to such organization can provide design rules to create new functional materials. In this work, we use a simple model of polymer-grafted nanoparticles to explore the self-assembly of binary mixtures. By using Monte Carlo simulations we study the interplay of composition, density and particle sizes on the self-organization of such nanoparticle systems. It is found that complex hierarchical organization can take place for conditions where one-component systems form simple lattices. In particular, a mixture where one component forms a structure with 18-fold symmetry in a sea of an apparent disordered phase of the second component is observed to emerge for certain parameter combinations.

Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density.

In this work, we explore fluctuations during phase transitions of uniaxial and biaxial liquid crystals using a phenomenological free energy functional. We rely on a continuum-level description of the liquid crystal ordering with a tensorial parameter and a temperature dependent Landau polynomial expansion of the tensor's invariants. The free energy functional, over a three-dimensional periodic domain, is integrated with a Gaussian quadrature and minimized with a theoretically informed Monte Carlo method. We reconstruct analytical phase diagrams, following Landau and Doi's notations, to verify that the free energy relaxation reaches the global minimum. Importantly, our relaxation method is able to follow the thermodynamic behavior provided by other non-phenomenological approaches; we predict the first order character of the isotropic-nematic transition, and we identify the uniaxial-biaxial transition as second order. Finally, we use a finite-size scaling method, using the nematic susceptibility, to calculate the transition temperatures for 4-Cyano-4'-pentylbiphenyl (5CB) and N-(4-methoxybenzylidene)-4-butylaniline (MBBA). Our results show good agreement with experimental values, thereby validating our minimization method. Our approach is an alternative towards the relaxation of temperature dependent continuum-level free energy functionals, in any geometry, and can incorporate complicated elastic and surface energy densities.

Sharp Morphological Transitions from Nanoscale Mixed-Anchoring Patterns in Confined Nematic Liquid Crystals.

Liquid crystals are known to be particularly sensitive to orientational cues provided at surfaces or interfaces. In this work, we explore theoretically, computationally, and experimentally the behavior of liquid crystals on isolated nanoscale patterns with controlled anchoring characteristics at small length scales. The orientation of the liquid crystal is controlled through the use of chemically patterned polymer brushes that are tethered to a surface. This system can be engineered with remarkable precision, and the central question addressed here is whether a characteristic length scale exists at which information encoded on a surface is no longer registered by a liquid crystal. To do so, we adopt a tensorial description of the free energy of the hybrid liquid-crystal-surface system, and we investigate its morphology in a systematic manner. For long and narrow surface stripes, it is found that the liquid crystal follows the instructions provided by the pattern down to 100 nm widths. This is accomplished through the creation of line defects that travel along the sides of the stripes. We show that a "sharp" morphological transition occurs from a uniform undistorted alignment to a dual uniform/splay-bend morphology. The theoretical and numerical predictions advanced here are confirmed by experimental observations. Our combined analysis suggests that nanoscale patterns can be used to manipulate the orientation of liquid crystals at a fraction of the energetic cost that is involved in traditional liquid crystal-based devices. The insights presented in this work have the potential to provide a new fabrication platform to assemble low power bistable devices, which could be reconfigured upon application of small external 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.

Demixing by a Nematic Mean Field: Coarse-Grained Simulations of Liquid Crystalline Polymers.

Liquid crystalline polymers exhibit a particular richness of behaviors that stems from their rigidity and their macromolecular nature. On the one hand, the orientational interaction between liquid-crystalline motifs promotes their alignment, thereby leading to the emergence of nematic phases. On the other hand, the large number of configurations associated with polymer chains favors formation of isotropic phases, with chain stiffness becoming the factor that tips the balance. In this work, a soft coarse-grained model is introduced to explore the interplay of chain stiffness, molecular weight and orientational coupling, and their role on the isotropic-nematic transition in homopolymer melts. We also study the structure of polymer mixtures composed of stiff and flexible polymeric molecules. We consider the effects of blend composition, persistence length, molecular weight and orientational coupling strength on the melt structure at the nano- and mesoscopic levels. Conditions are found where the systems separate into two phases, one isotropic and the other nematic. We confirm the existence of non-equilibrium states that exhibit sought-after percolating nematic domains, which are of interest for applications in organic photovoltaic and electronic devices.

Mesoscale structure of chiral nematic shells.

There is considerable interest in understanding and controlling topological defects in nematic liquid crystals (LCs). Confinement, in the form of droplets, has been particularly effective in that regard. Here, we employ a Landau-de Gennes formalism to explore the geometrical frustration of nematic order in shell geometries, and focus on chiral materials. By varying the chirality and thickness in uniform shells, we construct a phase diagram that includes tetravalent structures, bipolar structures (BS), bent structures and radial spherical structures (RSS). It is found that, in uniform shells, the BS-to-RSS structural transition, in response to both chirality and shell geometry, is accompanied by an abrupt change of defect positions, implying a potential use for chiral nematic shells as sensors. Moreover, we investigate thickness heterogeneity in shells and demonstrate that non-chiral and chiral nematic shells exhibit distinct equilibrium positions of their inner core that are governed by shell chirality c.

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.

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.

Homeotropic nano-particle assembly on degenerate planar nematic interfaces: films and droplets.

A continuum theory is used to study the effects of homeotropic nano-particles on degenerate planar liquid crystal interfaces. Particle self-assembly mechanisms are obtained from careful examination of particle configurations on a planar film and on a spherical droplet. The free energy functional that describes the system is minimized according to Ginzburg-Landau and stochastic relaxations. The interplay between elastic and surface distortions and the desire to minimize defect volumes (boojums and half-Saturn rings) is shown to be responsible for the formation of intriguing ordered structures. As a general trend, the particles prefer to localize at defects to minimize the overall free energy. However, multiple metastable configurations corresponding to local minima can be easily observed due to the high energy barriers that separate distinct particle arrangements. We also show that by controlling anchoring strength and temperature one can direct liquid-crystal mediated nanoparticle self-assembly along well defined pathways.

Nanoparticle self-assembly at the interface of liquid crystal droplets.

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.

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.

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.