Sublimation of isolated toric focal conic domains on micro-patterned surfaces.

Toric focal conic domains (TFCDs) in smectic liquid crystals exhibit distinct topological characteristics, featuring torus-shaped molecular alignment patterns with rotational symmetry around a central core. TFCDs have attracted much interest due to their unique topological structures and properties, enabling not only fundamental studies but also potential applications in liquid crystal (LC)-based devices. Here, we investigated the precise spatial control of the arrangement of TFCDs using micropatterns and sublimation of TFCDs to estimate the energy states of the torus-like structures. Through simulations, we observed that the arrangement of TFCDs strongly depends on the shape of the topographies of underlying substrates. To accurately estimate the energetic effects of non-zero eccentricity and evaluate their thermodynamic stability, we propose a geometric model. Our findings provide valuable insights into the behavior of smectic LCs, offering opportunities for developing novel LC-based devices with precise control over their topological properties.

Phase-field model for a weakly compressible soft layered material: morphological transitions on smectic-isotropic interfaces.

A coupled phase-field and hydrodynamic model is introduced to describe a two-phase, weakly compressible smectic (layered phase) in contact with an isotropic fluid of different density. A non-conserved smectic order parameter is coupled to a conserved mass density in order to accommodate non-solenoidal flows near the smectic-isotropic boundary arising from density contrast between the two phases. The model aims to describe morphological transitions in smectic thin films under heat treatment, in which arrays of focal conic defects evolve into conical pyramids and concentric rings through curvature dependent evaporation of smectic layers. The model leads to an extended thermodynamic relation at a curved surface that includes its Gaussian curvature, non-classical stresses at the boundary and flows arising from density gradients. The temporal evolution given by the model conserves the overall mass of the liquid crystal while still allowing for the modulated smectic structure to grow or shrink. A numerical solution of the governing equations reveals that pyramidal domains are sculpted at the center of focal conics upon a temperature increase, which display tangential flows at their surface. Other cases investigated include the possible coalescence of two cylindrical stacks of smectic layers, formation of droplets, and the interactions between focal conic domains through flow.

Role of Gaussian curvature on local equilibrium and dynamics of smectic-isotropic interfaces.

Recent research on interfacial instabilities of smectic films has shown unexpected morphologies that are not fully explained by classical local equilibrium thermodynamics. Annealing focal conic domains can lead to conical pyramids, changing the sign of the Gaussian curvature and exposing smectic layers at the interface. In order to explore the role of the Gaussian curvature on the stability and evolution of the film-vapor interface, we introduce a phase-field model of a smectic-isotropic system as a first step in the study. Through asymptotic analysis of the model, we generalize the classical condition of local equilibrium, the Gibbs-Thomson equation, to include contributions from surface bending and torsion and a dependence on the layer orientation at the interface. A full numerical solution of the phase-field model is then used to study the evolution of focal conic structures in smectic domains in contact with the isotropic phase via local evaporation and condensation of smectic layers. As in experiments, numerical solutions show that pyramidal structures emerge near the center of the focal conic owing to evaporation of adjacent smectic planes and to their orientation relative to the interface. Near the center of the focal conic domain, a correct description of the motion of the interface requires the additional curvature terms obtained in the asymptotic analysis, thus clarifying the limitations in modeling motion of hyperbolic surfaces solely driven by mean curvature.

Surfactant effects on droplet dynamics and deposition patterns: a lattice gas model.

A coarse-grained lattice gas model is developed to study pattern forming processes in drying drops containing surfactant. By performing Monte Carlo simulations of the model, the coupled dynamics of surfactant and liquid evaporation and the resulting oscillatory dynamics at the contact line are elucidated. We show that the coupled drop dynamics and the resulting final deposition patterns can be altered by adsorption kinetics. For slow adsorption rates, surfactant molecules recirculate along with colloidal particles and the area covered by the surfactant on the surface grows from the contact line as the initial concentration of the surfactant increases. This leads to coffee-ring patterns with wide rim areas upon drying or to multi-ring patterns depending on the surfactant concentration. For fast adsorption rates, a surfactant skin covers the entire surface area during the early phase of evaporation. This suppresses the coffee ring effect, and uniform patterns are obtained independent of surfactant concentration. The results suggest that the distribution of surfactant on the surface is critical in determining final deposition patterns and that understanding of the skin-forming process of the surfactant on the surface can help in manipulating the delicate pattern forming process of particles in evaporating drops.

Instability deposit patterns in an evaporating droplet.

The characteristics of several patterns left after the evaporation of a particle-laden liquid droplet are investigated by using a coarse-grained lattice model. The model includes both evaporative convection and the Brownian motion of weakly interacting particles. The model is implemented by using a Monte Carlo method to investigate the different deposit patterns near the contact line. It was found that different deposit patterns form depending on the interplay between the convective transport and the deposition of interacting particles. The patterns were analyzed by varying the ratio of the convective forces to the interaction forces as well as the size and the number of particles. It was also found that the ring-like patterns are formed when the convective potential dominates the interactions of particles, whereas either wave-like or island-like patterns form in the opposite case. Finally, the average thickness of the wave-like patterns is mainly determined by evaporation rates.

Temperature-dependent formation of dendrimer islands from ring structures.

Previously unobserved high surface mobility and phase transformation phenomena in condensed, micron-scale dendrimer structures are documented using atomic force microscopy. Stratified dendrimer rings (a unique morphology resulting from microdroplet evaporation of dendrimer-alcohol solutions on mica) undergo dramatic temperature, time, and dendrimer-generation-dependent morphological changes associated with large-scale molecular rearrangements and partial melting. These transformations produce ring structures consisting of a highly stable first monolayer of the scalloped structure in equilibrium with spherical cap shaped dendrimer islands that form at the center of each pre-existing scallop (creating a "pearl necklace" structure). A generation-dependent critical temperature for dendrimer melting is determined. As-evaporated structures can be stabilized against thermally driven rearrangements by holding them at room temperature before annealing. Analysis of the dendrimer island shapes reveals a dependence of island contact angle on contact line curvature (island size) that varies systematically with dendrimer generation. A negative line tension, tau, is deduced in these systems. The morphological transformations in this system indicate the potential for creating complex, dendrimer-based multilevel structures and macroscopic-scale arrays using, for example, droplet-on-demand or dip pen nanolithography techniques, coupled with appropriate annealing and stabilizing treatments.

Dendrimer pattern formation in evaporating drops.

The redistribution of organic solutes during drop evaporation is a nanoscale self-assembly process with relevance to technologies ranging from inkjet printing of organic displays to synthesis of biosmart interfaces for sensing and screening. We have used solutions of dendrimer molecules with incrementally varying terminal site chemistry to explore whether the condensed dendrimer patterns resulting from microdroplet evaporation sensitively depend on, and are characteristic of, the surface chemistry of the solute molecules. This hypothesis has been experimentally confirmed by comparing the behavior of microdroplets of G4, G4-25%C12, and G4-50%C12 dendrimers dissolved in pentanol and deposited on mica substrates. For the dilute concentration studied here, the presence of periodically 'scalloped' dendrimer rings is ubiquitous. The instability wavelength of the scalloped rings is found to be proportional to the width of the ring, similar to observations of the rim instability in dewetting holes. The effect of dendrimer surface chemistry is obvious in the detailed structure of the self-assembled rings. G4 rings are diffuse and disordered with no evidence for layered growth. G4-25%C12 exhibits highly ordered ring structures and the onset of monomolecular terracing. G4-50%C12 exhibits highly periodic scallops and very distinct monomolecular height terraced growth of the rings with flat terraces and sharply defined steps. On the basis of these results, it is likely that the morphology of condensed molecule-based ring patterns formed by evaporation of microdroplets on surfaces can be used as a 'fingerprint' to identify, for example, solute molecule surface chemistry and concentration and function as a sensor for a variety of biochemical events.