Colloidal particles in liquid crystal films and at interfaces

This mini-review discusses the recent contribution of theoretical and computational physics as well as experimental efforts to the understanding of the behavior of colloidal particles in confined geometries and at liquid crystalline interfaces. Theoretical approaches used to study trapping, long- and short-range interactions, and assembly of solid particles and liquid inclusions are outlined. As an example, an interaction of a spherical colloidal particle with a nematic-isotropic interface and a pair interaction potential between two colloids at this interface are obtained by minimizing the Landau-de Gennes free energy functional using the finite-element method with adaptive meshes.Comment: 22 pages, 10 figure

Binary Mixtures of Locally Coupled Mobile Oscillators

We study synchronization dynamics in binary mixtures of locally coupled Kuramoto oscillators which perform Brownian motion in a two-dimensional box. We introduce two models, where in model $\cal I$ there are two type of oscillators, say $\cal A$ and $\cal B$, and any two similar oscillators tend to synchronize their phases, while any two dissimilar ones tend to be out of phase. In model $\cal J$, in contrast, the oscillators in subpopulation $\cal A$ behave as in model $\cal I$, while the oscillators in subpopulation $\cal B$ tend to be out of phase with all the others. In the real space all the oscillators in both models interact via a soft-core repulsive potential. Both subpopulations of model $\cal I$ and subpopulation $\cal A$ of model $\cal J$, by their own, exhibit a phase coherent attractor in a certain region of model parameters. The approach to the attractor, after an initial transient regime, is exponential with some characteristic synchronization time scale $\tau$. Numerical analysis reveals that the attractors of the two subpopulations survive within model $\cal I$, regardless of the composition of the mixture $\phi$ and the strength of the cross-population negative coupling constant $H$, and that $\tau$ sensitively depends on $\phi$, $H$ and the packing fraction. In particular, the ability of the oscillators to move and exchange neighbours can significantly decrease $\tau$. In contrast, model $\cal J$ predicts suppression of the synchronized state in subpopulation $\cal A$ and emergence of the coherent attractor in the "contrarians" subpopulation $\cal B$ for strong and weak cross-population coupling, respectively.Comment: 11 pages, 10 figure

Enhanced diffusivity in microscopically reversible active matter

Physics of self-propelled objects at the nanoscale is a rapidly developing research field where recent experiments focused on motion of individual catalytic enzymes. Contrary to the experimental advancements, theoretical understanding of possible self-propulsion mechanisms at these scales is limited. A particularly puzzling question concerns origins of reportedly high diffusivities of the individual enzymes. Here we start with the fundamental principle of microscopic reversibility (MR) of chemical reactions powering the self-propulsion and demonstrate that MR can lead to increase of the particle mobility and of short- and long-time diffusion coefficients as compared to dynamics where MR is neglected. Moreover, the diffusion coefficients can be enhanced by a constant external force. We propose a way to use these effects in experimental investigations of active propulsion mechanisms at the nanoscale. Our results can shed new light on interpretation of the measured diffusivities and help to test and to evaluate relevance of MR for the active motion of individual nanoswimmers.Comment: SM included as an ancillary fil

Recovering superhydrophobicity in nanoscale and macroscale surface textures

Here, we investigate complete drying of hydrophobic cavities in order to elucidate its dependence on the size of confinement, its geometry, and the degree of hydrophobicity. Two complementary theoretical approaches are adopted: a macroscopic one based on classical capillarity and a microscopic classical density functional theory. This combination allows us to pinpoint unique drying mechanisms at the nanoscale and to clearly differentiate them from the mechanisms operational at the macroscale. Nanoscale hydrophobic cavities allow the thermodynamic destabilization of the confined liquid phase over an unexpectedly broad range of conditions, including pressures as large as 10 MPa and contact angles close to 90°. On the other hand, for cavities on the micron scale, such destabilization occurs only for much larger contact angles and close to liquid-vapor coexistence. These scale-dependent drying mechanisms are used to propose design criteria for hierarchical superhydrophobic surfaces capable of spontaneous self recovery over a broad range of operating conditions. In particular, we detail the requirements under which it is possible to realize perpetual superhydrophobicity at positive pressures on surfaces with micron-sized textures by exploiting drying, facilitated by nanoscale coatings. Concerning the issue of superhydrophobicity, these findings indicate a promising direction both for surface fabrication and for the experimental characterization of perpetual surperhydrophobicity. From a more basic perspective, the present results have an echo on a wealth of biological problems in which hydrophobic confinement induces drying, such as in protein folding, molecular recognition, and hydrophobic gating

Perpetual superhydrophobicity

A liquid droplet placed on a geometrically textured surface may take on a “suspended” state, in which the liquid wets only the top of the surface structure, while the remaining geometrical features are occupied by vapor. This superhydrophobic Cassie–Baxter state is characterized by its composite interface which is intrinsically fragile and, if subjected to certain external perturbations, may collapse into the fully wet, so-called Wenzel state. Restoring the superhydrophobic Cassie–Baxter state requires a supply of free energy to the system in order to again nucleate the vapor. Here, we use microscopic classical density functional theory in order to study the Cassie–Baxter to Wenzel and the reverse transition in widely spaced, parallel arrays of rectangular nanogrooves patterned on a hydrophobic flat surface. We demonstrate that if the width of the grooves falls below a threshold value of ca. 7 nm, which depends on the surface chemistry, the Wenzel state becomes thermodynamically unstable even at very large positive pressures, thus realizing a “perpetual” superhydrophobic Cassie–Baxter state by passive means. Building upon this finding, we demonstrate that hierarchical structures can achieve perpetual superhydrophobicity even for micron-sized geometrical textures

Dispersions of ellipsoidal particles in a nematic liquid crystal

Colloidal particles dispersed in a partially ordered medium, such as a liquid crystal (LC) phase, disturb its alignment and are subject to elastic forces. These forces are long-ranged, anisotropic and tunable through temperature or external fields, making them a valuable asset to control colloidal assembly. The latter is very sensitive to the particle geometry since it alters the interactions between the colloids. We here present a detailed numerical analysis of the energetics of elongated objects, namely prolate ellipsoids, immersed in a nematic host. The results, complemented with qualitative experiments, reveal novel LC configurations with peculiar topological properties around the ellipsoids, depending on their aspect ratio and the boundary conditions imposed on the nematic order parameter. The latter also determine the preferred orientation of ellipsoids in the nematic field, because of elastic torques, as well as the morphology of particles aggregates.Comment: 31 pages, 11 figure

Colloidal interactions and unusual crystallization versus de-mixing of elastic multipoles formed by gold mesoflowers

Colloidal interactions in nematic liquid crystals can be described as interactions between elastic multipoles that depend on particle shape, topology, chirality, boundary conditions and induced topological defects. Here, we describe a nematic colloidal system consisting of mesostructures of gold capable of inducing elastic multipoles of different order. Elastic monopoles are formed by relatively large asymmetric mesoflower particles, for which gravity and elastic torque balancing yields monopole-type interactions. High-order multipoles are instead formed by smaller mesoflowers with a myriad of shapes corresponding to multipoles of different orders, consistent with our computer simulations based on free energy minimization. We reveal unexpected many-body interactions in this colloidal system, ranging from de-mixing of elastic monopoles to a zoo of unusual colloidal crystals formed by high-order multipoles like hexadecapoles. Our findings show that gold mesoflowers may serve as a designer toolkit for engineering colloidal interaction and self-assembly, potentially exceeding that in atomic and molecular systems

Chiral liquid crystal colloids

Colloidal particles disturb the alignment of rod-like molecules of liquid crystals, giving rise to long-range interactions that minimize the free energy of distorted regions. Particle shape and topology are known to guide this self-assembly process. However, how chirality of colloidal inclusions affects these long-range interactions is unclear. Here we study the effects of distortions caused by chiral springs and helices on the colloidal self-organization in a nematic liquid crystal using laser tweezers, particle tracking and optical imaging. We show that chirality of colloidal particles interacts with the nematic elasticity to predefine chiral or racemic colloidal superstructures in nematic colloids. These findings are consistent with numerical modelling based on the minimization of Landau-de Gennes free energy. Our study uncovers the role of chirality in defining the mesoscopic order of liquid crystal colloids, suggesting that this feature may be a potential tool to modulate the global orientated self-organization of these systems

Mechanochemical active ratchet

Abstract Self-propelled nanoparticles moving through liquids offer the possibility of creating advanced applications where such nanoswimmers can operate as artificial molecular-sized motors. Achieving control over the motion of nanoswimmers is a crucial aspect for their reliable functioning. While the directionality of micron-sized swimmers can be controlled with great precision, steering nano-sized active particles poses a real challenge. One of the reasons is the existence of large fluctuations of active velocity at the nanoscale. Here, we describe a mechanism that, in the presence of a ratchet potential, transforms these fluctuations into a net current of active nanoparticles. We demonstrate the effect using a generic model of self-propulsion powered by chemical reactions. The net motion along the easy direction of the ratchet potential arises from the coupling of chemical and mechanical processes and is triggered by a constant, transverse to the ratchet, force. The current magnitude sensitively depends on the amplitude and the periodicity of the ratchet potential and the strength of the transverse force. Our results highlight the importance of thermodynamically consistent modeling of chemical reactions in active matter at the nanoscale and suggest new ways of controlling dynamics in such systems