Phase transitions and topological defects in discotic liquid crystal droplets with planar anchoring: a Monte Carlo simulation study.

In this work we present the results of Monte Carlo (MC) simulations at the isothermal-isobaric ensemble for a discotic liquid crystal (DLC) droplet whose surface promotes edge-on (planar) anchoring. For a given pressure, we simulate an annealing process that enables observation of phase transitions within the spherical droplet. In particular, we report a first order isotropic-nematic transition as well as a nematic-columnar transition at the center of the droplet. We found the appearance of topological defects consisting of two disclination lines with ends at the surface of the sphere. We also observed that both transitions, isotropic-nematic and nematic-columnar, occur at lower temperatures as compared to the unconfined system.

Packing core-corona particles on a spherical surface.

We explore the non-trivial structures that can be obtained by the assembly of repulsive core-corona particles confined on a spherical surface. Using Monte Carlo simulations, we study the low-temperature equilibrium configurations as a function of the size of the confining (spherical) surface for a small number of particles (N ≤ 12) and obtain a large variety of minimal-energy arrangements including anisotropic and chiral structures. For a small cluster (N = 4), we construct a phase diagram in the confining surface radius vs corona range plane that showed regions where configurations with a certain energy are not accessible. Also, a phase diagram in the temperature and confining surface radius plane showed the presence of reentrant phases. The assembly of Platonic and Archimedean solids and the emergence of helical structures are also discussed. When the number of particles is large (N ≥ 100), apart from the appearance of defects, the overall configurations correspond closely to the ones formed in an unconfined two-dimensional case. Interestingly, the present model reproduces the symmetry of experimentally obtained small clusters of colloidal spheres confined at the surface of evaporating liquid droplets which cannot be explained in terms of packing of hard spheres. Thus, our simulations provide insight on the role that the softness of the particles may have in the assembly of clusters of nanoparticles.

Band structure of a rotating helical phononic crystal.

We consider an elastic helical medium whose tensor stiffness twirls uniformly along the helix axis. We are interested in analyzing the band structure when the whole material is externally forced to rotate around the helix axis to a fixed constant frequency. Departing from a general dynamic description of the elastic phenomena, we establish a set of equations for the displacement vector and the stress tensor. These equations allow us to calculate the band structure parametrized by the externally imposed rotating frequency. We find that the band structure strongly depends on the rotation frequency, and we show that backward and forward modes propagate differently, particularly for the longitudinal and right-polarized modes.

Structural properties and ring defect formation in discotic liquid crystal nanodroplets.

In this work, we performedNpTMonte Carlo simulations of a Gay-Berne discotic liquid crystal confined in a spherical droplet under face-on anchoring and fixed pressure. We find that, in contrast to the unbounded system, a plot of the order parameter as function of temperature does not show a clear evidence of a first-order isotropic-nematic transition. We also find that the impossibility of simultaneously satisfy the uniform director field requirement of a nematic phase with the radial boundary conditions, results in the appearance of a ring disclination line as a stress release mechanism in the interior of the droplet. Under further cooling, a columnar phase appears at the center of the droplet.

Dependence of the elastic band structure of a helical medium on thermal dilatation.

We consider an elastic helical medium formed by uniformly rotating a triclinic crystal around a given axis to constitute a helical medium giving rise to a material whose tensor stiffness rotates uniformly and varies along the helix axis. A detailed analysis of its elastic properties has been done previously. Here, we are concerned in analyzing the role of thermal coupling with heat flow through the dilatation tensor. Starting from a general dynamic description of the thermoelastic phenomena which takes into account the finite speed of propagation of thermal waves, we establish a set of equations for the strains, stresses, temperature and heat flow. These equations allow to calculate the band structure and the logarithmic ratio between longitudinal and transverse strains. We express our results for different values of the thermoelastic coupling and period of the helix which show remarkable modifications when compared with the case in which no thermoelastic coupling is present.

Shape selection and mis-assembly in viral capsid formation by elastic frustration.

The successful assembly of a closed protein shell (or capsid) is a key step in the replication of viruses and in the production of artificial viral cages for bio/nanotechnological applications. During self-assembly, the favorable binding energy competes with the energetic cost of the growing edge and the elastic stresses generated due to the curvature of the capsid. As a result, incomplete structures such as open caps, cylindrical or ribbon-shaped shells may emerge, preventing the successful replication of viruses. Using elasticity theory and coarse-grained simulations, we analyze the conditions required for these processes to occur and their significance for empty virus self-assembly. We find that the outcome of the assembly can be recast into a universal phase diagram showing that viruses with high mechanical resistance cannot be self-assembled directly as spherical structures. The results of our study justify the need of a maturation step and suggest promising routes to hinder viral infections by inducing mis-assembly.

Self-assembly of core-corona particles confined in a circular box.

Using Monte Carlo simulations, we study the assembly of colloidal particles interacting via isotropic core-corona potentials in two dimensions and confined in a circular box. We explore the structural variety at low temperatures as function of the number of particles (N) and the size of the confining box and find a rich variety of patterns that are not observed in unconfined flat space. For a small number of particles [Formula: see text], we identify the zero-temperature minimal energy configurations at a given box size. When the number of particles is large ([Formula: see text]), we distinguish different regimes that appear in route towards close packing configurations as the box size decreases. These regimes are characterized by the increase in the number of branching points and their coordination number. Interestingly, we obtain anisotropic open structures with unexpected variety of rotational symmetries that can be controlled by changing the model parameters, and some of the structures have chirality, in spite of the isotropy of the interactions and of the confining box. For arbitrary temperatures, we employ Monte Carlo integration to obtain the average energy and the configurational entropy of the system, which are then used to construct a phase diagram as function of temperature and box radius. Our findings show that confined core-corona particles can be a suitable system to engineer particles with highly complex internal structure that may serve as building blocks in hierarchical assembly.

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

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

Influence of anchoring in the phase behaviour of discotic liquid crystals.

Molecular dynamics simulations were performed for a Gay-Berne discotic fluid confined in a slab geometry for two different anchorings: homeotropic (face-on) and planar (edge-on), and for two different confinement lengths. Our results show that the behaviour of the more confined system in the temperature region of the isotropic-nematic transition is critically influenced by the presence of the walls: the growth of the solid-liquid crystal interface spans over the entire width of the cell, and the character of the transition is changed from first order to continuous. For all the confined systems studied, we observe a higher nematic-columnar transition temperature and a smaller nematic phase region in the phase diagram, as compared with the behaviour of the infinite system.

Electronic properties of DNA: Description of weak interactions in TATA-box-like chains.

DNA is one of the most important biomolecules since it contains all the genetic information about an organism. The tridimensional structure of DNA is a determinant factor that influences the physiological and biochemical mechanisms by which this molecule carries out its biological functions. It is believed that hydrogen bonds and π-π stacking are the most relevant non-covalent interactions regarding DNA stability. Due to its importance, several theoretical works have been made to describe these interactions, however, most of them often consider only the presence of two nitrogenous bases, having a limited overview of the participation of these in B-DNA stabilization. Furthermore, due to the complexity of the system, there are discrepancies between which involved interaction is more important in duplex stability. Therefore, in this project we describe these interactions considering the effect of chain length on the energy related to both hydrogen bonds and π-π stacking, using as model TATA-box-like chains with n base pairs (n=1 to 14) and taking into consideration two different models: ideal and optimized B-DNA. We have found that there is a cooperative effect on hydrogen bond and π-π stacking mean energies when the presence of other base pairs is considered. In addition, it was found that hydrogen bonds contribute more importantly than π-π stacking to B-DNA stability; nevertheless, the participation of π-π stacking is not negligible: when B-DNA looks for a conformation of lower energy, π-π stacking interaction are the first to be optimized. All work was realized under the framework of DFT using the DMol3 code (M06-L/DNP).

Spontaneous non-canonical assembly of CcmK hexameric components from ß-carboxysome shells of cyanobacteria.

CcmK proteins are major constituents of icosahedral shells of ß-carboxysomes, a bacterial microcompartment that plays a key role for CO2 fixation in nature. Supported by the characterization of bidimensional (2D) layers of packed CcmK hexamers in crystal and electron microscopy structures, CcmK are assumed to be the major components of icosahedral flat facets. Here, we reassessed the validity of this model by studying CcmK isoforms from Synechocystis sp. PCC6803. Native mass spectrometry studies confirmed that CcmK are hexamers in solution. Interestingly, potential pre-assembled intermediates were also detected with CcmK2. Atomic-force microscopy (AFM) imaging under quasi-physiological conditions confirmed the formation of canonical flat sheets with CcmK4. Conversely, CcmK2 formed both canonical and striped-patterned patches, while CcmK1 assembled into remarkable supra-hexameric curved honeycomb-like mosaics. Mutational studies ascribed the propensity of CcmK1 to form round assemblies to a combination of two features shared by at least one CcmK isoform in most ß-cyanobacteria: a displacement of an α helical portion towards the hexamer edge, where a potential phosphate binding funnel forms between packed hexamers, and the presence of a short C-terminal extension in CcmK1. All-atom molecular dynamics supported a contribution of phosphate molecules sandwiched between hexamers to bend CcmK1 assemblies. Formation of supra-hexameric curved structures could be reproduced in coarse-grained simulations, provided that adhesion forces to the support were weak. Apart from uncovering unprecedented CcmK self-assembly features, our data suggest the possibility that transitions between curved and flat assemblies, following cargo maturation, could be important for the biogenesis of ß-carboxysomes, possibly also of other BMC.

Effective temperatures and the breakdown of the Stokes-Einstein relation for particle suspensions.

The short- and long-time breakdown of the classical Stokes-Einstein relation for colloidal suspensions at arbitrary volume fractions is explained here by examining the role that confinement and attractive interactions play in the intra- and inter-cage dynamics executed by the colloidal particles. We show that the measured short-time diffusion coefficient is larger than the one predicted by the classical Stokes-Einstein relation due to a non-equilibrated energy transfer between kinetic and configuration degrees of freedom. This transfer can be incorporated in an effective kinetic temperature that is higher than the temperature of the heat bath. We propose a Generalized Stokes-Einstein relation (GSER) in which the effective temperature replaces the temperature of the heat bath. This relation then allows to obtain the diffusion coefficient once the viscosity and the effective temperature are known. On the other hand, the temporary cluster formation induced by confinement and attractive interactions of hydrodynamic nature makes the long-time diffusion coefficient to be smaller than the corresponding one obtained from the classical Stokes-Einstein relation. Then, the use of the GSER allows to obtain an effective temperature that is smaller than the temperature of the heat bath. Additionally, we provide a simple expression based on a differential effective medium theory that allows to calculate the diffusion coefficient at short and long times. Comparison of our results with experiments and simulations for suspensions of hard and porous spheres shows an excellent agreement in all cases.

Mechanical instability at finite temperature.

Many physical systems including lattices near structural phase transitions, glasses, jammed solids and biopolymer gels have coordination numbers placing them at the edge of mechanical instability. Their properties are determined by an interplay between soft mechanical modes and thermal fluctuations. Here we report our investigation of the mechanical instability in a lattice model at finite temperature T. The model we used is a square lattice with a φ(4) potential between next-nearest-neighbour sites, whose quadratic coefficient κ can be tuned from positive to negative. Using analytical techniques and simulations, we obtain a phase diagram characterizing a first-order transition between the square and the rhombic phase and different regimes of elasticity, as well as an 'order-by-disorder' effect that favours the rhombic over other zigzagging configurations. We expect our study to provide a framework for the investigation of finite-T mechanical and phase behaviour of other systems with a large number of floppy modes.

Non-additive simple potentials for pre-programmed self-assembly.

A major goal in nanoscience and nanotechnology is the self-assembly of any desired complex structure with a system of particles interacting through simple potentials. To achieve this objective, intense experimental and theoretical efforts are currently concentrated in the development of the so-called "patchy" particles. Here we follow a completely different approach and introduce a very accessible model to produce a large variety of pre-programmed two-dimensional (2D) complex structures. Our model consists of a binary mixture of particles that interact through isotropic interactions that enable them to self-assemble into targeted lattices by the appropriate choice of a small number of geometrical parameters and interaction strengths. We study the system using Monte Carlo computer simulations and, despite its simplicity, we are able to self-assemble potentially useful structures such as chains, stripes, and Kagomé, twisted Kagomé, honeycomb, square, Archimedean and quasicrystalline tilings. Our model is designed in such a way that it may be implemented using discotic particles or, alternatively, using exclusively spherical particles interacting isotropically. Thus, it represents a promising strategy for bottom-up nano-fabrication.

Effective static and high-frequency viscosities of concentrated suspensions of soft particles.

We obtain an analytic expression that allows to determine the static η and high-frequency η(∞) viscosities as function of the volume fraction φ of a concentrated suspension of soft spherical particles in a liquid of viscosity η(0). The particles consist of a hard core of radius a covered by a porous layer of thickness d. Suspensions of hard spheres and homogeneous porous particles are limiting cases of the model. The proposed expression incorporates the results for the intrinsic viscosity obtained on the basis of a cell model [H. Ohshima, Langmuir 26, 6287 (2010)] into a recently obtained relation for the effective viscosity of concentrated colloidal suspensions [C. I. Mendoza and I. Santamaría-Holek, J. Chem. Phys. 130, 044904 (2009); J. Colloid. Interface Sci. 346, 118 (2010)]. In this model, the correlations between the particles due to crowding effects are introduced through an effective volume fraction φ(eff) which is then used as integration variable in a differential effective medium procedure. The final expression is simple, accurate, and allows to collapse all the data in a universal master curve that is independent of the parameters characterizing the system. The only difference between the static and high-frequency cases is that in the later case φ(eff) also incorporates hydrodynamic interactions arising from the so-called relaxation term. We have tested the accuracy of our model comparing with experimental results for spherical polymeric brushes and simulations for the high-frequency viscosity of homogeneous porous particles. In all cases the agreement with the data is extremely good.

The rheology of concentrated suspensions of arbitrarily-shaped particles.

We propose an improved effective-medium theory to obtain the concentration dependence of the viscosity of particle suspensions at arbitrary volume fractions. Our methodology can be applied, in principle, to any particle shape as long as the intrinsic viscosity is known in the dilute limit and the particles are not too elongated. The procedure allows to construct a continuum-medium model in which correlations between the particles are introduced through an effective volume fraction. We have tested the procedure using spheres, ellipsoids, cylinders, dumbells, and other complex shapes. In the case of hard spherical particles, our expression improves considerably previous models like the widely used Krieger-Dougherty relation. The final expressions obtained for the viscosity scale with the effective volume fraction and show remarkable agreement with experiments and numerical simulations at a large variety of situations.

The rheology of hard sphere suspensions at arbitrary volume fractions: An improved differential viscosity model.

We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method where correlations between the spheres are introduced through an effective volume fraction. In contrast to other differential methods, the introduction of the effective volume fraction as the integration variable implicitly considers interactions between the spheres of the same recursive stage. The final expression for the viscosity scales with this effective volume fraction, which allows constructing a master curve that contains all the experimental situations considered. The agreement of our expression for the viscosity with experiments at low- and high-shear rates and in the high-frequency limit is remarkable for all volume fractions.

Electrorheological response and orientational bistability of a homogeneously aligned nematic capillary.

We consider a homogeneously aligned nematic liquid crystal confined in the region between two rotating coaxial cylinders. We study the nematic's director and velocity profiles induced by the imposed Couette flow and an applied radial electric field. We present calculations for the specific flow-aligning nematic liquid crystal 4(')-n-pentyl-4-cyanobiphenyl and numerically solve a hydrodynamic model assuming hard anchoring and nonslip boundary conditions. We calculate a phase diagram in the parameter space showing a region where there exist multiple equilibrium solutions for the nematic's configuration and a region where there exists only one stationary solution. We also study the rheology of the system by calculating the apparent viscosity and the first normal stress difference. We find that the competition between the Couette flow and the electric field gives rise to an interesting non-Newtonian response which switches its behavior from shear thickening to shear thinning by exceeding a critical field.

Electrorheological effect and directional non-Newtonian behavior in a nematic capillary subjected to a pressure gradient.

We consider a capillary consisting of two coaxial cylinders whose core is filled with a nematic liquid crystal (LC) subjected to the simultaneous action of both a pressure gradient applied parallel to the axis of the cylinders and a radial low frequency electric field. We find the configuration of the director of the nematic, initially with an escaped-like configuration, for the flow aligning LC 4'-n-pentyl-4-cyanobiphenyl (5CB) by assuming hard anchoring hybrid boundary conditions. Also, we obtain the velocity profile parametrized by the electric field and the pressure gradient for nonslip boundary conditions. Finally, we calculate exactly the effective viscosity, the first normal stress difference, and the dragging forces on the cylinders. The results show an important electrorheological effect and a directional non-Newtonian response with regions of flow thinning and thickening.