Juan P. Hernández-Ortiz

Dynamics of confined suspensions of swimming particles

Low Reynolds number direct simulations of large populations of hydrodynamically interacting swimming particles confined between planar walls are performed. The results of simulations are compared with a theory that describes dilute suspensions of swimmers. The theory yields scalings with concentration for diffusivities and velocity fluctuations as well as a prediction of the fluid velocity spatial autocorrelation function. Even for uncorrelated swimmers, the theory predicts anticorrelations between nearby fluid elements that correspond to vortex-like swirling motions in the fluid with length scale set by the size of a swimmer and the slit height. Very similar results arise from the full simulations indicating either that correlated motion of the swimmers is not significant at the concentrations considered or that the fluid phase autocorrelation is not a sensitive measure of the correlated motion. This result is in stark contrast with results from unconfined systems, for which the fluid autocorrelation captures large-scale collective fluid structures. The additional length scale (screening length) introduced by the confinement seems to prevent these large-scale structures from forming.

Liquid-crystal-mediated self-assembly at nanodroplet interfaces

Technological applications of liquid crystals have generally relied on control of molecular orientation at a surface or an interface. Such control has been achieved through topography, chemistry and the adsorption of monolayers or surfactants. The role of the substrate or interface has been to impart order over visible length scales and to confine the liquid crystal in a device. Here, we report results from a computational study of a liquid-crystal-based system in which the opposite is true: the liquid crystal is used to impart order on the interfacial arrangement of a surfactant. Recent experiments on macroscopic interfaces have hinted that an interfacial coupling between bulk liquid crystal and surfactant can lead to a two-dimensional phase separation of the surfactant at the interface, but have not had the resolution to measure the structure of the resulting phases. To enhance that coupling, we consider the limit of nanodroplets, the interfaces of which are decorated with surfactant molecules that promote local perpendicular orientation of mesogens within the droplet. In the absence of surfactant, mesogens at the interface are all parallel to that interface. As the droplet is cooled, the mesogens undergo a transition from a disordered (isotropic) to an ordered (nematic or smectic) liquid-crystal phase. As this happens, mesogens within the droplet cause a transition of the surfactant at the interface, which forms new ordered nanophases with morphologies dependent on surfactant concentration. Such nanophases are reminiscent of those encountered in block copolymers, and include circular, striped and worm-like patterns.

Liquid Crystal Mediated Interactions Between Nanoparticles in a Nematic Phase

A continuum theory is used to study the interactions between nanoparticles suspended in nematic liquid crystals. The free energy functional that describes the system is minimized using an Euler-Lagrange approach and an unsymmetric radial basis function method. It is shown that nanoparticle liquid-crystal mediated interactions can be controlled over a large range of magnitudes through changes of the anchoring energy and the particle diameter. The results presented in this work serve to reconcile past discrepancies between theoretical predictions and experimental observations, and suggest intriguing possibilities for directed nanoparticle self-assembly in liquid crystalline media.

Morphological transitions in liquid crystal nanodroplets

A continuum theory is used to study ordering in liquid crystal nanodroplets. The free energy functional that describes the system is minimized using an Euler–Lagrange approach and an unsymmetric radial basis function method. The equilibrium morphology in nanodroplets is shown to represent a delicate balance between bulk and surface contributions; when the radius of the droplet reaches a critical value, that balance is altered and the droplet undergoes a transition. By controlling the anchoring conditions at the droplets surface, one can control the radius where the transition occurs and even prepare metastable droplets where small perturbations can trigger a morphological transition. The results of the theory are shown to be consistent with recent experimental observations on monodisperse nematic liquid crystal nanodroplets.

Pair collisions of fluid-filled elastic capsules in shear flow: Effects of membrane properties and polymer additives

The dynamics and pair collisions of fluid-filled elastic capsules during Couette flow in Newtonian fluids and dilute solutions of high-molecular weight (drag-reducing) polymers are investigated via direct simulation. Capsule membranes are modeled using either a neo-Hookean constitutive model or a model introduced by Skalak et al. [“Strain energy function of red blood-cell membranes,” Biophys. J. 13, 245 (1973)], which includes an energy penalty for area changes. This model was developed to capture the elastic properties of red blood cells. Polymer molecules are modeled as bead-spring trimers with finitely extensible nonlinearly elastic springs; parameters were chosen to loosely approximate 4000 kDa poly(ethylene oxide). Simulations are performed with a novel Stokes flow formulation of the immersed boundary method for the capsules, combined with Brownian dynamics for the polymer molecules. The results for isolated capsules in shear indicate that at the very low concentrations considered here, polymers have...

Flow induced deformation of defects around nanoparticles and nanodroplets suspended in liquid crystals

A three-dimensional molecular theory is used to describe the effect of flow on the defects that arise around nanoparticles and nanodroplets suspended in a nematic liquid crystal. It is observed that flow displaces the Saturn ring line defect that forms around a nanoparticle at equilibrium in the upstream direction; it is eventually closed by the flow and becomes a Hedgehog point defect. In contrast, the Saturn ring that forms around a nanodroplet is slightly displaced in the downstream direction. Experimental measurements of defects around nanoparticles have not been reported in the literature. In the absence of experiments, the validity of theoretical predictions is assessed through a direct comparison to results of many-body molecular dynamics simulations of a coarse grain liquid crystal model. Theoretical predictions and molecular simulations are in quantitative agreement, thereby lending credibility to the predictions presented in this work and suggesting that flow can be used to manipulate defect structure and aggregation of nanoparticles in nematic liquid crystals.

Hydrodynamic effects on the translocation rate of a polymer through a pore.

The translocation of large DNA molecules through narrow pores has been examined in the context of multiscale simulations that include a full coupling of fluctuating hydrodynamic interactions, boundary effects, and molecular conformation. The actual rate constants for this process are determined for the first time, and it is shown that hydrodynamic interactions can lead to translocation rates that vary by multiple orders of magnitude when molecular weights are only changed by a factor of 10, in stark contrast to predictions from widely used free draining calculations.

Liquid crystal nanodroplets, and the balance between bulk and interfacial interactions

Molecular dynamics simulations of a coarse grain model are used to explore the morphology of thermotropic liquid crystal nanodroplets. The characteristic length of the droplets is such that different contributions to the energy, including interfacial and bulk-like terms, have comparable magnitudes. Depending on the relative strength of such contributions, a wide variety of mesophases can be identified. These range from a completely disordered isotropic phase at elevated temperatures, to ordered radial and smectic phases at low temperatures. Bipolar, uniaxial and axial phases are also observed. Our results suggest that according to the ratio between perpendicular and planar anchoring strengths, an isotropic–radial transition may occur through several intermediate phases. In contrast, a direct bipolar–radial transition is never observed. Our results are summarized in the form of a generic phase diagram for spherical nanodroplets as a function of anchoring strength. The diagram exhibits a number of common features with phase transitions that have been observed in experiments with larger, micron-sized droplets. Perhaps more importantly, it serves to emphasize the balance that exists in nanodroplets between surface and bulk interactions, droplet size and temperature, and how that balance influences the behavior of the system.

Modeling flows of confined nematic liquid crystals

The flow of nematic liquid crystals in tightly confined systems was simulated using a molecular theory and an unsymmetric radial basis function collocation approach. When a nematic liquid crystal is subjected to a cavity flow, we find that moderate flows facilitate the relaxation of the system to the stable defect configuration observed in the absence of flow. Under more extreme flow conditions, e.g., an Ericksen number Er=20, flows can alter the steady-state defect structure observed in the cavity. The proposed numerical method was also used to examine defect annihilation in a thin liquid crystal film. The flows that arise from shear stresses within the system result in a higher velocity for s = +1∕2 defect than for the defect of opposing charge. This higher velocity can be attributed to reactive stresses within the deformed liquid crystal, which result in a net flow that favors the motion of one defect. These two examples serve to illustrate the usefulness of radial basis functions methods in the context of liquid crystal dynamics both at and beyond equilibrium.

Dipole-induced self-assembly of helical β-peptides

In this work, the interactions between beta-peptides are investigated for helix-forming peptides using molecular simulation. The role of electrostatic interactions in the self-assembly of these peptides is studied by calculating the dipole moment of various 14-helical beta-peptides using molecular dynamics simulations. The stability of a beta-peptide that is known to form a liquid crystalline phase is determined by calculating the potential of mean force using the expanded ensemble density of states method. This peptide is found to form a mechanically stable 14-helix in an implicit solvent model. The interaction between two of these peptides is examined by calculating the potential of mean force between the two peptides in implicit solvent. The peptides are shown to favorably associate in an end-to-end manner, driven largely by dipolar interactions. In order to understand the possible structures that form when many peptides interact in solution, a coarse-grained model is developed. Brownian dynamics simulations of the coarse-grained model at intermediate concentrations (1-50 mM) are performed, and the aggregation behavior is understood by calculating the diffusivity and the radial distribution function. An analysis of the resultant structures reveals that the coarse-grained model of the peptide leads to the formation of spherical clusters.