Control of liquid crystals combining surface acoustic waves, nematic flows, and microfluidic confinement.

The optical properties of liquid crystals serve as the basis for display, diagnostic, and sensing technologies. Such properties are generally controlled by relying on electric fields. In this work, we investigate the effects of microfluidic flows and acoustic fields on the molecular orientation and the corresponding optical response of nematic liquid crystals. Several previously unknown structures are identified, which are rationalized in terms of a state diagram as a function of the strengths of the flow and the acoustic field. The new structures are interpreted by relying on calculations with a free energy functional expressed in terms of the tensorial order parameter, using continuum theory simulations in the Landau-de Gennes framework. Taken together, the findings presented here offer promise for the development of new systems based on combinations of sound, flow, and confinement.

Control of Monodomain Polymer-Stabilized Cuboidal Nanocrystals of Chiral Nematics by Confinement.

Liquid crystals are important components of optical technologies. Cuboidal crystals consisting of chiral liquid crystals-the so-called blue phases (BPs), are of particular interest due to their crystalline structures and fast response times, but it is critical that control be gained over their phase behavior as well as the underlying dislocations and grain boundaries that arise in such systems. Blue phases exhibit cubic crystalline symmetries with lattice parameters in the 100 nm range and a network of disclination lines that can be polymerized to widen the range of temperatures over which they occur. Here, we introduce the concept of strain-controlled polymerization of BPs under confinement, which enables formation of strain-correlated stabilized morphologies that, under some circumstances, can adopt perfect single-crystal monodomain structures and undergo reversible crystal-to-crystal transformations, even if their disclination lines are polymerized. We have used super-resolution laser confocal microscopy to reveal the periodic structure and the lattice planes of the strain and polymerization stabilized BPs in 3D real space. Our experimental observations are supported and interpreted by relying on theory and computational simulations in terms of a free energy functional for a tensorial order parameter. Simulations are used to determine the orientation of the lattice planes unambiguously. The findings presented here offer opportunities for engineering optical devices based on single-crystal, polymer-stabilized BPs whose inherent liquid nature, fast dynamics, and long-range crystalline order can be fully exploited.

Sculpted grain boundaries in soft crystals.

Engineering the grain boundaries of crystalline materials represents an enduring challenge, particularly in the case of soft materials. Grain boundaries, however, can provide preferential sites for chemical reactions, adsorption processes, nucleation of phase transitions, and mechanical transformations. In this work, "soft heteroepitaxy" is used to exert precise control over the lattice orientation of three-dimensional liquid crystalline soft crystals, thereby granting the ability to sculpt the grain boundaries between them. Since these soft crystals are liquid-like in nature, the heteroepitaxy approach introduced here provides a clear strategy to accurately mold liquid-liquid interfaces in structured liquids with a hitherto unavailable level of precision.

Specific inter-domain interactions stabilize a compact HIV-1 Gag conformation.

HIV-1 Gag is a large multidomain poly-protein with flexible unstructured linkers connecting its globular subdomains. It is compact when in solution but assumes an extended conformation when assembled within the immature HIV-1 virion. Here, we use molecular dynamics (MD) simulations to quantitatively characterize the intra-domain interactions of HIV-1 Gag. We find that the matrix (MA) domain and the C-terminal subdomain CActd of the CA capsid domain can form a bound state. The bound state, which is held together primarily by interactions between complementary charged and polar residues, stabilizes the compact state of HIV-1 Gag. We calculate the depth of the attractive free energy potential between the MA/ CActd sites and find it to be about three times larger than the dimerization interaction between the CActd domains. Sequence analysis shows high conservation within the newly-found intra-Gag MA/CActd binding site, as well as its spatial proximity to other well known elements of Gag -such as CActd's SP1 helix region, its inositol hexaphosphate (IP6) binding site and major homology region (MHR), as well as the MA trimerization site. Our results point to a high, but yet undetermined, functional significance of the intra-Gag binding site. Recent biophysical experiments that address the binding specificity of Gag are interpreted in the context of the MA/CActd bound state, suggesting an important role in selective packaging of genomic RNA by Gag.

Free-energy model for nanoparticle self-assembly by liquid crystal sorting.

We modeled the experimentally observed self-assembly of nanoparticles (NPs) into shells with diameters up to 10 µm, via segregation from growing nematic domains. Using field-based Monte Carlo simulations, we found the equilibrium configurations of the system by minimizing a free-energy functional that includes effects of excluded-volume interactions among NPs, orientational elasticity, and the isotropic-nematic phase-transition energy. We developed a Gaussian-profile approximation for the liquid crystal (LC) order-parameter field that provides accurate analytical values for the free energy of LC droplets and the associated microshells. This analytical model reveals a first-order transition between equilibrium states with and without microshells, governed mainly by the competition of excluded-volume and phase-transition energies. By contrast, the LC elasticity effects are much smaller and mostly confined to setting the size of the activation barrier for the transition. In conclusion, field-based thermodynamic methods provide a theoretical framework for the self-assembly of NP shells in liquid crystal hosts and suggest that field-based kinetic methods could be useful to simulate and model the time evolution of NP self-assembly coupled to phase separation.

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.

Room temperature ionic liquids: A simple model. Effect of chain length and size of intermolecular potential on critical temperature.

A model of a room temperature ionic liquid can be represented as an ion attached to an aliphatic chain mixed with a counter ion. The simple model used in this work is based on a short rigid tangent square well chain with an ion, represented by a hard sphere interacting with a Yukawa potential at the head of the chain, mixed with a counter ion represented as well by a hard sphere interacting with a Yukawa potential of the opposite sign. The length of the chain and the depth of the intermolecular forces are investigated in order to understand which of these factors are responsible for the lowering of the critical temperature. It is the large difference between the ionic and the dispersion potentials which explains this lowering of the critical temperature. Calculation of liquid-vapor equilibrium orthobaric curves is used to estimate the critical points of the model. Vapor pressures are used to obtain an estimate of the triple point of the different models in order to calculate the span of temperatures where they remain a liquid. Surface tensions and interfacial thicknesses are also reported.

Liquid-vapor equilibria of ionic liquids from a SAFT equation of state with explicit electrostatic free energy contributions.

Statistically associating fluid theory (SAFT) provides closed-form free energies by perturbation methods. We propose here a SAFT equation of state for ionic liquids that models the contribution from Coulomb forces after that of the Restricted Primitive Model (RPM) in the Mean Spherical Approximation (MSA). The resulting SAFT-MSA equation, fitted to simulated orthobaric curves of imidazolium based ionic liquids, predicts experimental density data with errors ≈1% and the characteristic decrease of all critical coordinates with increasing cation size. The SAFT-MSA equation can be applied to calculate thermodynamic coefficients, the speed of sound and surface tension (among other properties) of pure ionic liquids and can be generalized straightforwardly to mixtures.

Self-assembly of kagome lattices, entangled webs and linear fibers with vibrating patchy particles in two dimensions.

A vibrating version of patchy particles in two dimensions is introduced to study self-assembly of kagome lattices, disordered networks of looping structures, and linear arrays. Discontinuous molecular dynamics simulations in the canonical ensemble are used to characterize the molecular architectures and thermodynamic conditions that result in each of those morphologies, as well as the time evolution of lattice formation. Several versions of the new model are tested and analysed in terms of their ability to produce kagome lattices. Due to molecular flexibility, particles with just attractive sites adopt a polarized-like configuration and assemble into linear arrays. Particles with additional repulsive sites are able to form kagome lattices, but at low temperature connect as entangled webs. Abundance of hexagonal motifs, required for the kagome lattice, is promoted even for very small repulsive sites but hindered when the attractive range is large. Differences in behavior between the new flexible model and previous ones based on rigid bodies offer opportunities to test and develop theories about the relative stability, kinetics of formation and mechanical response of the observed morphologies.

Measuring liquid crystal elastic constants with free energy perturbations.

A first principles method is proposed to calculate the Frank elastic constants of nematic liquid crystals. These include the constants corresponding to standard splay, twist and bend deformations, and an often-ignored surface-like contribution known as saddle-splay. The proposed approach is implemented on the widely studied Gay-Berne (3, 5, 2, 1) model [J. G. Gay and B. J. Berne, J. Chem. Phys., 1981, 74, 3316], and the effects of temperature and system size on the elastic constants are examined in the nematic phase. The results of simulations for splay, twist, and bend elastic constants are consistent with those from previous literature reports. The method is subsequently applied to the saddle-splay elastic constant k24 which is found to exist at the limits of the Ericksen inequalities governing positive definite free energy. Finally, extensions of the method are discussed that present a new paradigm for in silico measurements of elastic constants.

Analytical equation of state with three-body forces: application to noble gases.

We developed an explicit equation of state (EOS) for small non polar molecules by means of an effective two-body potential. The average effect of three-body forces was incorporated as a perturbation, which results in rescaled values for the parameters of the two-body potential. These values replace the original ones in the EOS corresponding to the two-body interaction. We applied this procedure to the heavier noble gases and used a modified Kihara function with an effective Axilrod-Teller-Muto (ATM) term to represent the two- and three-body forces. We also performed molecular dynamics simulations with two- and three-body forces. There was good agreement between predicted, simulated, and experimental thermodynamic properties of neon, argon, krypton, and xenon, up to twice the critical density and up to five times the critical temperature. In order to achieve 1% accuracy of the pressure at liquid densities, the EOS must incorporate the effect of ATM forces. The ATM factor in the rescaled two-body energy is most important at temperatures around and lower than the critical one. Nonetheless, the rescaling of two-body diameter cannot be neglected at liquid-like densities even at high temperature. This methodology can be extended straightforwardly to deal with other two- and three-body potentials. It could also be used for other nonpolar substances where a spherical two-body potential is still a reasonable coarse-grain approximation.

Steric contribution of macromolecular crowding to the time and activation energy for preprotein translocation across the endoplasmic reticulum membrane.

Protein translocation from the cytosol to the endoplasmic reticulum (ER) or vice versa, an essential process for cell function, includes the transport of preproteins destined to become secretory, luminal, or integral membrane proteins (translocation) or misfolded proteins returned to the cytoplasm to be degraded (retrotranslocation). An important aspect in this process that has not been fully studied is the molecular crowding at both sides of the ER membrane. By using models of polymers crossing a membrane through a pore, in an environment crowded by either static or dynamic spherical agents, we computed the following transport properties: the free energy, the activation energy, the force, and the transport times for translocation and retrotranslocation. Using experimental protein crowding data for the cytoplasm and ER sides, we showed that dynamic crowding, which resembles biological environments where proteins are translocated or retrotranslocated, increases markedly all the physical properties of translocation and retrotranslocation as compared with translocation in a diluted system. By contrast, transport properties in static crowded systems were similar to those in diluted conditions. In the dynamic regime, the effects of crowding were more notorious in the transport times, leading to a huge difference for large chains. We indicate that this difference is the result of the synergy between the free energy and the diffusivity of the translocating chain. That synergy leads to translocation rates similar to experimental measures in diluted systems, which indicates that the effects of crowding can be measured. Our data also indicate that effects of crowding cannot be neglected when studying translocation because protein dynamic crowding has a relevant steric contribution, which changes the properties of translocation.

Boundary-layer method for the analytical calculation of stable textures of bent-core liquid crystal fibers.

We study the equilibrium textures of molecular orientation inside cylindrical fibers made of coaxial layers of bent-core smectics. We propose a free-energy model taking into account surface-like and bulk contributions--including layer-compression and electrostatic terms among others--with constant values of the material parameters. We follow the usual variational procedure of minimization of the free energy with respect to the tilt-angle profile θ(r) and obtain an Euler-Lagrange equation and its boundary condition. We solve the variational equations for the equilibrium configurations using a boundary-layer approximation and find multiple solutions. Since the equilibrium tilt profiles are found to be radially inhomogeneous, we select those with minimum distortions in order to find the lowest free-energy state. We minimize further the free energy of the system with respect to the fiber radius and find wider intervals of stability than those previously reported, depending on the balance of the material's spontaneous polarization, elastic and electric divergence-of-polarization constants, and surface-tension coefficients. The bulk and surface-layer structures thus found could be used to calculate the allowed modes of propagation of electromagnetic waves inside the fiber.

Anisotropic nanoparticles immersed in a nematic liquid crystal: defect structures and potentials of mean force.

We report results for the potential of mean force (PMF) and the defect structures that arise when spherocylindrical nanoparticles are immersed in a nematic liquid crystal. Using a dynamic field theory for the tensor order parameter Q of the liquid crystal, we analyzed configurations, including one, two, and three elongated particles, with strong homeotropic anchoring at their surfaces. For systems with one nanoparticle, the most stable configuration is achieved when the spherocylinder is placed with its long axis perpendicular to the far-field director, for which the defect structure consists of an elongated Saturn ring. For systems with two or three nanoparticles with their long axes placed perpendicular to the far-field director, at small separations the defect structures consist of incomplete Saturn rings fused with new disclination rings orthogonal to the original ones, in analogy to results previously observed for spherical nanoparticles. The shape of these orthogonal rings depends on the nanoparticles' configuration, i.e., triangular, linear, or parallel with respect to their long axis. A comparison of the PMFs indicates that the latter configuration is the most stable. The stability of the different arrays depends on whether orthogonal disclination rings form or not, their size, and the curvature effects in the interparticle regions. Our results suggest that the one-elastic-constant approximation is valid for the considered systems; similar results were obtained when a three-constant expression is used to represent the elastic free energy. The attractive interactions between the elongated particles were compared to those observed for spheres of similar diameters. Similar interparticle energies were observed for linear arrays; in contrast, parallel and triangular arrays of spherocylinders yielded interactions that were up to 3.4 times stronger than those observed for spherical particles.

Anchoring energies of liquid crystals measured on surfaces presenting oligopeptides.

We report a methodology that permits quantitation of the azimuthal anchoring energy of the nematic liquid crystal 4-cyano-4'-pentyl-biphenyl on surfaces patterned with oligopeptides. The oligopeptide (IYGEFKKKC), an optimized substrate for the Src protein kinase, was covalently immobilized via the terminal cysteine to monolayers of amine-terminated tetra(ethylene glycol) formed on gold films. The measurements of anchoring energies, which were based on a torque-balance method, revealed a systematic decrease in anchoring energy from 3.7 +/- 0.6 microJ/m2 with increasing surface density of oligopeptide. We calculate that a mass density of oligopeptide of less than 1 ng/cm2 can lead to a measurable change in the anchoring energy of the nematic liquid crystal. These results suggest that measurements of anchoring energies of liquid crystals on surfaces may offer the basis of quantitative and label-free methods for detecting biomolecules on surfaces.

Measurement of the azimuthal anchoring energy of liquid crystals in contact with oligo(ethylene glycol)-terminated self-assembled monolayers supported on obliquely deposited gold films.

We report measurements of the orientations and azimuthal anchoring energies of the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) on polycrystalline gold films that are deposited from a vapor at an oblique angle of incidence and subsequently decorated with organized monolayers of oligomers of ethylene glycol. Whereas the gold films covered with monolayers presenting tetra(ethylene glycol) (EG4) lead to orientations of 5CB that are perpendicular to the plane of incidence of the gold, monolayers presenting tri(ethylene glycol) (EG3) direct 5CB to orient parallel to the plane of incidence of the gold during deposition of the gold film. We also measure the azimuthal anchoring energy of the 5CB to be smaller on the surfaces presenting EG3 (3.2 +/- 0.8 microJ/m2) as compared to EG4 (5.5 +/- 0.9 microJ/m2). These measurements, when combined with other results presented in this paper, are consistent with a physical model in which the orientation and anchoring energies of LCs on these surfaces are influenced by both (i) short-range interactions of 5CB with organized oligomers of ethylene glycol at these surfaces and (ii) long-range interactions of 5CB with the nanometer-scale topography of the obliquely deposited films. For surfaces presenting EG3, these short- and long-range interactions oppose each other, leading to small net values of anchoring energies that we predict are dependent on the level of order in the EG3 SAM. These measurements provide insights into the balance of interactions that control the orientational response of LCs to biological species (proteins, viruses, cells) on these surfaces.

Interactions of liquid crystal-forming molecules with phospholipid bilayers studied by molecular dynamics simulations.

Recent experiments have shown that liquid crystals can be used to image mammalian cell membranes and to amplify structural reorganization in phospholipid-laden liquid crystal-aqueous interfaces. In this work, molecular dynamics simulations were employed to explore the interactions between commonly used liquid crystal-forming molecules and phospholipid bilayers. In particular, umbrella sampling was used to obtain the potential of mean force of 4-cyano-4'-pentylbiphenyl (5CB) and 4'-(3,4-difluor-phenyl)-4-pentyl-bicylohexyl (5CF) molecules partitioning into a dipalmitoylphosphatidylcholine bilayer. In addition, results of simulations are presented for systems consisting of a fully hydrated bilayer with 5CB or 5CF molecules at the lowest (4.5 mol %) and highest (20 mol %) concentrations used in recent laboratory experiments. It is found that mesogens preferentially partition from the aqueous phase into the membrane; the potential of mean force exhibits highly favorable free energy differences for partitioning (-18 k(B)T for 5CB and -26 k(B)T for 5CF). The location and orientation of mesogens associated with the most stable free energies in umbrella sampling simulations of dilute systems were found to be consistent with those observed in liquid-crystal-rich bilayers. It is found that the presence of mesogens in the bilayer enhances the order of lipid acyl tails, and changes the spatial and orientational arrangement of lipid headgroup atoms. These effects are more pronounced at higher liquid-crystal concentrations. In comparing the behavior of 5CB and 5CF, a stronger spatial correlation (i.e., possibly leading to aggregation) is observed between 5CB molecules within a bilayer than between 5CF molecules. Also, the range of molecular orientations and positions along the bilayer normal is larger for 5CB molecules. At the same time, 5CF molecules were found to bind more strongly to lipid headgroups, thereby slowing the lateral motion of lipid molecules.

Interactions between spherical colloids mediated by a liquid crystal: a molecular simulation and mesoscale study.

Monte Carlo simulations and dynamic field theory (DyFT) are used to study the interactions between dilute spherical particles, dispersed in nematic and isotropic phases of a liquid crystal. A recently developed simulation method (expanded ensemble density of states) was used to determine the potential of mean force (PMF) between the two spheres as a function of their separation and size. The PMF was also calculated by a dynamic field theory that describes the evolution of the local tensor order parameter. Both methods reveal an overall attraction between the colloids in the nematic phase; in the isotropic phase, the overall attraction between the colloids is much weaker, whereas the repulsion at short range is stronger. In addition, both methods predict a new topology of the disclination lines, which arises when the particles approach each other. The theory is found to describe the results of simulations remarkably well, down to length scales comparable to the size of the molecules. At separations corresponding to the width of individual molecular layers on the particles' surface, the two methods yield different defect structures. We attribute this difference to the neglect of density inhomogeneities in the DyFT. We also investigate the effects of the size of spherical colloids on their interactions.

Prevención y manejo del riesgo de inundaciones

El HIMAT es una institución que se encuentra vinculada con investigaciones y estudios relacionados con la "Prevención y Manejo de Catástrofes Naturales". Este trabajo hace referencia a la Prevención y Manejo de Riesgo de Inundaciones, evento que todos los años ocurre, causando graves problemas en las cuencas de los ríos Magdalena y Cauca donde se encuentra el mayor polo de desarrollo del país; contempla asuntos relacionados con la filosofía general de la prevención de inundaciones, red de comunicaciones, sistemas de transmisión, producción de pronósticos, automatización de la red, resultados y conclusiones