Liquid crystal phase diagram of soft repulsive rods and its mapping on the hard repulsive reference fluid

Two-temperature activity induces liquid-crystal phases inaccessible in equilibrium

In equilibrium hard-rod fluids, and in effective hard-rod descriptions of anisotropic soft-particle systems, the transition from the isotropic (I) phase to the nematic phase (N) is observed above the rod aspect ratio L/D=3.70 as predicted by Onsager. We examine the fate of this criterion in a molecular dynamics study of a system of soft repulsive spherocylinders rendered active by coupling half the particles to a heat bath at a higher temperature than that imposed on the other half. We show that the system phase-separates and self-organizes into various liquid-crystalline phases that are not observed in equilibrium for the respective aspect ratios. In particular, we find a nematic phase for L/D=3 and a smectic phase for L/D=2 above a critical activity.

Packing and emergence of the ordering of rods in a spherical monolayer

Spatially ordered systems confined to surfaces such as spheres exhibit interesting topological structures because of curvature induced frustration in orientational and translational order. The study of these structures is important for investigating the interplay between the geometry, topology, and elasticity, and for their potential applications in materials science, such as engineering directionally binding particles. In this work, we numerically simulate a spherical monolayer of soft repulsive spherocylinders (SRSs) and study the packing of rods and their ordering transition as a function of the packing fraction. In the model that we study, the centers of mass of the spherocylinders (situated at their geometric centers) are constrained to move on a spherical surface. The spherocylinders are free to rotate about any axis that passes through their respective centers of mass. We show that, up to moderate packing fractions, a two dimensional liquid crystalline phase is formed whose orientational ordering increases continuously with increasing density. This monolayer of orientationally ordered SRS particles at medium densities resembles a hedgehog-long axes of the SRS particles are aligned along the local normal to the sphere. At higher packing fractions, the system undergoes a transition to the solid phase, which is riddled with topological point defects (disclinations) and grain boundaries that divide the whole surface into several domains.

Influence of homeostatic mechanisms of bacterial growth and division on structural properties of microcolonies: A computer simulation study

Bacterial growth and division generally occur by the process known as binary fission, in which the cells grow polarly until they divide into two daughter cells. Although this process is affected by factors that introduce stochastic variability in both growth rate and daughter cell length, the fact is that the size distribution in growing bacteria remains stable over time. This suggests the existence of homeostatic mechanisms that contribute to maintaining a stable size distribution. Those known as sizer and adder stand out among these mechanisms whose relevance is not entirely determined. In this work, computer simulations using an agent-based model are used to study the effect of these homeostatic mechanisms on the geometrical and structural properties of the developing microcolonies, focusing on the early stages of its development. Also, we examine the effect of linear or exponential dependence with the time of cellular growth on these properties. From our study, we deduce that these mechanisms do not have a noticeable impact on the properties studied, which could be due to the importance that stochastic factors play in the cell division and growth process. In addition, we discuss how competition between cell growth and diffusion is a key aspect in explaining the structure and geometry of developing bacterial microcolonies. The results of the study will help to clarify which processes and parameters should be considered relevant when designing simulation models.

Group formation and collective motion of colloidal rods with an activity triggered by visual perception

We investigate the formation of cohesive groups and the collective diffusion of colloidal spherocylinders with a motility driven by a simple visual perception model. For this, we perform Brownian dynamics simulations without hydrodynamic interactions. The visual perception is based on sight cones attached to the spherocylinders and perception functions quantifying the visual stimuli. If the perception function of a particle reaches a predefined threshold, an active component is added to its motion. We find that, in addition to the opening angle of the cone of sight, the aspect ratio of the particles plays an important role for the formation of cohesive groups. If the elongation of the particles is increased, the maximum angle for which the rods organize themselves into such groups decreases distinctly. After a system forms a cohesive group, it performs a diffusive motion, which can be quantified by an effective diffusion coefficient. For increasing aspect ratios, the spatial expansion of the cohesive groups and the effective diffusion coefficient of the collective motion increase, while the number of active group members decreases. We also find that a larger particle number, a smaller propulsion velocity of the group members, and a smaller threshold for the visual stimulus increase the maximum opening angle for which cohesive groups form. Based on our results, we expect anisotropic particles to be of great relevance for the adjustability of visual perception-dependent motility.

Long-time relaxation dynamics in nematic and smectic liquid crystals of soft repulsive colloidal rods

Understanding the relaxation dynamics of colloidal suspensions is crucial to identifying the elements that influence the mobility of their constituents, assessing their macroscopic response across the relevant time and length scales, and thus disclosing the fundamentals underpinning their exploitation in formulation engineering. In this work, we specifically assess the impact of long-ranged ordering on the relaxation dynamics of suspensions of soft repulsive rodlike particles, which are able to self-organize into nematic and smectic liquid-crystalline phases. Rods are modeled as soft repulsive spherocylinders with a length-to-diameter ratio L^{★}=5, interacting via the truncated and shifted Kihara potential. By performing dynamic Monte Carlo simulations, we analyze the effect of translational and orientational order on the diffusion of the rods along the relevant directions imposed by the morphology of the background phases. To provide a clear picture of the resulting dynamics, we assess its dependence on temperature, which can dramatically determine the response time of the system relaxation and the self-diffusion coefficients of the rods. The computation of the van Hove correlation functions allows us to identify the existence of rods that diffuse significantly faster than the average and whose concentration can be accurately adjusted by a suitable choice of temperature.

Heating leads to liquid-crystal and crystalline order in a two-temperature active fluid of rods

We report phase separation and liquid-crystal ordering induced by scalar activity in a system of soft repulsive spherocylinders (SRSs) of shape anisotropy L/D=5 using molecular dynamics (MD) simulations. Activity is introduced by increasing the temperature of half of the SRSs (labeled hot) while maintaining the temperature of the other half constant at a lower value (labeled cold). The difference between the two temperatures scaled by the lower temperature provides a measure of the activity. Starting from different equilibrium initial phases, we find that activity leads to segregation of the hot and cold particles. Activity also drives the cold particles through a phase transition to a more ordered state and the hot particles to a state of less order compared to the initial equilibrium state. The cold components of a homogeneous isotropic structure acquire nematic and, at higher activity, crystalline order. Similarly, the cold zone of a nematic initial state undergoes smectic and crystal ordering above a critical value of activity while the hot component turns isotropic. We find that the hot particles occupy a larger volume and exert an extra kinetic pressure, confining, compressing, and provoking an ordering transition of the cold-particle domains.

Quantitative Relationships Between Growth, Differentiation, and Shape That Control Drosophila Eye Development and Its Variation

The size of organs is critical for their function and often a defining trait of a species. Still, how organs reach a species-specific size or how this size varies during evolution are problems not yet solved. Here, we have investigated the conditions that ensure growth termination, variation of final size and the stability of the process for developmental systems that grow and differentiate simultaneously. Specifically, we present a theoretical model for the development of the Drosophila eye, a system where a wave of differentiation sweeps across a growing primordium. This model, which describes the system in a simplified form, predicts universal relationships linking final eye size and developmental time to a single parameter which integrates genetically-controlled variables, the rates of cell proliferation and differentiation, with geometrical factors. We find that the predictions of the theoretical model show good agreement with previously published experimental results. We also develop a new computational model that recapitulates the process more realistically and find concordance between this model and theory as well, but only when the primordium is circular. However, when the primordium is elliptical both models show discrepancies. We explain this difference by the mechanical interactions between cells, an aspect that is not included in the theoretical model. Globally, our work defines the quantitative relationships between rates of growth and differentiation and organ primordium size that ensure growth termination (and, thereby, specify final eye size) and determine the duration of the process; identifies geometrical dependencies of both size and developmental time; and uncovers potential instabilities of the system which might constraint developmental strategies to evolve eyes of different size.

Self-Assembly of Patchy Colloidal Rods into Photonic Crystals Robust to Stacking Faults

Diamond-structured colloidal photonic crystals are much sought-after for their applications in visible light management because of their ability to support a complete photonic band gap (PBG). However, their realization via self-assembly pathways is a long-standing challenge. This challenge is rooted in three fundamental problems: the design of building blocks that assemble into diamond-like structures, the sensitivity of the PBG to stacking faults, and ensuring that the PBG opens at an experimentally attainable refractive index. Here we address these problems simultaneously using a multipronged computational approach. We use reverse engineering to establish the design principles for the rod-connected diamond structure (RCD), the so-called "champion" photonic crystal. We devise two distinct self-assembly routes for designer triblock patchy colloidal rods, both proceeding via tetrahedral clusters to yield a mixed phase of cubic and hexagonal polymorphs closely related to RCD. We use Monte Carlo simulations to show how these routes avoid a metastable amorphous phase. Finally, we show that both the polymorphs support spectrally overlapping PBGs. Importantly, randomly stacked hybrids of these polymorphs also display PBGs, thus circumventing the requirement of polymorph selection in a scalable fabrication method.

Dynamic Monte Carlo simulations of inhomogeneous colloidal suspensions

The dynamic Monte Carlo (DMC) method is an established molecular simulation technique for the analysis of the dynamics in colloidal suspensions. An excellent alternative to Brownian dynamics or molecular dynamics simulation, DMC is applicable to systems of spherical and/or anisotropic particles and to equilibrium or out-of-equilibrium processes. In this work, we present a theoretical and methodological framework to extend DMC to the study of heterogeneous systems, where the presence of an interface between coexisting phases introduces an additional element of complexity in determining the dynamic properties. In particular, we simulate a Lennard-Jones fluid at the liquid-vapor equilibrium and determine the diffusion coefficients in the bulk of each phase and across the interface. To test the validity of our DMC results, we also perform Brownian Dynamics simulations and unveil an excellent quantitative agreement between the two simulation techniques.

Computer simulation study of early bacterial biofilm development

Most bacteria form organized sessile communities, known as biofilms. Their ubiquity and relevance have stimulated the development of efficient mathematical models able to predict biofilm evolution and characteristics at different conditions. Here we present a study of the early stages of bacterial biofilm formation modeled by means of individual cell-based computer simulation. Simulation showed that clusters with different degrees of internal and orientational order were formed as a function of the aspect ratio of the individual particles and the relation between the diffusion and growth rates. Analysis of microscope images of early biofilm formation by the Gram-negative bacterium Pseudomonas putida at varying diffusion rates revealed a good qualitative agreement with the simulation results. Our model is a good predictor of microcolony morphology during early biofilm development, showing that the competition between diffusion and growth rates is a key aspect in the formation of stable biofilm microcolonies.

Dynamic Monte Carlo algorithm for out-of-equilibrium processes in colloidal dispersions

Field-induced isotropic-to-nematic phase transition of colloidal rods studied with Dynamic Monte Carlo simulations.

Equivalence of Brownian dynamics and dynamic Monte Carlo simulations in multicomponent colloidal suspensions

We propose a simple but powerful theoretical framework to quantitatively compare Brownian dynamics (BD) and dynamic Monte Carlo (DMC) simulations of multicomponent colloidal suspensions. By extending our previous study focusing on monodisperse systems of rodlike colloids, here we generalize the formalism described there to multicomponent colloidal mixtures and validate it by investigating the dynamics in isotropic and liquid crystalline phases containing spherical and rodlike particles. In order to investigate the dynamics of multicomponent colloidal systems by DMC simulations, it is key to determine the elementary time step of each species and establish a unique timescale. This is crucial to consistently study the dynamics of colloidal particles with different geometry. By analyzing the mean-square displacement, the orientation autocorrelation functions, and the self part of the van Hove correlation functions, we show that DMC simulation is a very convenient and reliable technique to describe the stochastic dynamics of any multicomponent colloidal system. Our theoretical formalism can be easily extended to any colloidal system containing size and/or shape polydisperse particles.

Transport of spherical colloids in layered phases of binary mixtures with rod-like particles

The transport properties of colloids in anisotropic media constitute a general problem of fundamental interest in experimental sciences, with a broad range of technological applications. This work investigates the transport of soft spherical colloids in binary mixtures with rod-like particles by means of Monte Carlo and Brownian Dynamics simulations. Layered phases are considered, that range from smectic phases to lamellar phases, depending on the molar fraction of the spherical particles. The investigation serves to characterize the distinct features of transport within layers versus those of transport across neighboring layers, both of which are neatly differentiated. The insertion of particles into layers and the diffusion across them occur at a smaller rate than the intralayer diffusion modulated by the formation of transitory cages in its initial stages. Collective events, in which two or more colloids diffuse across layers in a concerted way, are described as a non-negligible process in these fluids.