Tailoring the phase diagram of discotic mesogens.

The computational modelling of discotic molecules is a central topic in colloid science that is key for the smart design of a broad range of modern functional materials. This work lays out a versatile interaction model capable of exposing the rich mesogenic behaviour of discotics. A single coarse-grained spheroplatelet core framework is employed to generate a variety of pair interaction anisotropy classes, favouring specific relative orientations of the particles (stacked, side-side, crossed, T-shaped). This paves the way for the systematic tailoring of the discotic liquid phase diagram. Monte Carlo simulations are performed for an ensemble of case studies to illustrate the correlation between the topology of the interaction and the formation of stable nematic, smectic and columnar phases, as well as of less common cubatic, uniaxial and biaxial columnar domains.

Coadsorption of Counterionic Colloids at Fluid Interfaces: A Coarse-Grained Simulation Study of Gibbs Monolayers.

Monolayers of oppositely charged colloids form versatile self-organizing substrates, with a recognized potential to tailor functional interfaces. In this study, a coarse-grained Monte Carlo simulation approach is laid out to assess the structural properties of Gibbs monolayers, in which one of the counterionic species is partially soluble. It is shown that the composition of this type of monolayer varies in a nontrivial way with surface coverage, as a result of a subtle competition between steric and attractive forces. In the regime of weak electrostatic interactions, the monolayer is depleted of soluble colloids as the surface coverage is increased. At sufficiently strong interactions, the incorporation of soluble colloids is favored at high surface coverage, leading to a re-entrant-type behavior in the expansion/compression isotherms. Strong electrostatic interactions also favor the clustering of the colloids, leading to a range of aggregated configurations, qualitatively resembling those obtained in previous experimental studies. At sufficiently high surface coverage, the clusters collapse into a gel-like percolated mesoscopic structure and eventually into a square crystal lattice configuration. Such interfacial structures are in good agreement with the ones observed in the few experimental investigations available for these systems, showing that the simple methodology introduced in this study provides a valuable predictive framework to anticipate the landscape of interfacial structures that may be produced with oppositely charged colloids, through the modulation of pair interactions and thermodynamical conditions.

Self-assembly of freely-rotating polydisperse cuboids: unveiling the boundaries of the biaxial nematic phase.

Colloidal cuboids have the potential to self-assemble into biaxial liquid crystal phases, which exhibit two independent optical axes. Over the last few decades, several theoretical works have predicted the existence of a wide region of the phase diagram where the biaxial nematic phase would be stable, but imposed rather strong constraints on the particle rotational degrees of freedom. In this work, we use molecular simulation to investigate the impact of size dispersity on the phase behaviour of freely-rotating hard cuboids, here modelled as self-dual-shaped nanoboards. This peculiar anisotropy, exactly in between the oblate and prolate geometry, has been proposed as the most appropriate to promote phase biaxiality. We observe that size dispersity radically changes the phase behaviour of monodisperse systems and leads to the formation of an elusive biaxial nematic phase, being found in a large region of the packing fraction vs. polydispersity phase diagram. Although our results confirm the tendencies reported in past experimental observations on colloidal dispersions of slightly prolate goethite particles, they cannot reproduce the direct isotropic-to-biaxial nematic phase transition observed in these experiments.

Correction: Directional-dependent pockets drive columnar-columnar coexistence.

Correction for 'Directional-dependent pockets drive columnar-columnar coexistence' by Álvaro González García et al., Soft Matter, 2020, DOI: 10.1039/d0sm00802h.

Directional-dependent pockets drive columnar-columnar coexistence.

The rational design of materials requires a fundamental understanding of the mechanisms driving their self-assembly. This may be particularly challenging in highly dense and shape-asymmetric systems. Here we show how the addition of tiny non-adsorbing spheres (depletants) to a dense system of hard disc-like particles (discotics) leads to coexistence between two distinct, highly dense (liquid)-crystalline columnar phases. This coexistence emerges due to the directional-dependent free-volume pockets for depletants. Theoretical results are confirmed by simulations explicitly accounting for the binary mixture of interest. We define the stability limits of this columnar-columnar coexistence and quantify the directional-dependent depletant partitioning.

Biaxial nematics of hard cuboids in an external field.

By computer simulation, we model the phase behaviour of colloidal suspensions of board-like particles under the effect of an external field and assess the still disputed occurrence of the biaxial nematic (NB) liquid crystal phase. The external field promotes the rearrangement of the initial isotropic (I) or uniaxial nematic (NU) phase and the formation of the NB phase. In particular, very weak field strengths are sufficient to spark a direct I-NB or NU-NB phase transition at the self-dual shape, where prolate and oblate particle geometries fuse into one. By contrast, forming the NB phase at any other geometry requires stronger fields and thus reduces the energy efficiency of the phase transformation. Our simulation results show that self-dual shaped board-like particles with moderate anisotropy are able to form NB liquid crystals under the effect of a surprisingly weak external stimulus and suggest a path to exploit low-energy uniaxial-to-biaxial order switching.

Brownian dynamics simulations of oblate and prolate colloidal particles in nematic liquid crystals.

It is well known that understanding the transport properties of liquid crystals is crucial to optimize their performance in a number of technological applications. In this work, we analyze the effect of shape anisotropy on the diffusion of rodlike and disklike particles by Brownian dynamics simulations. To this end, we compare the dynamics of prolate and oblate nematic fluids incorporating particles with the same infinite-dilution translational or rotational diffusion coefficients. Under these conditions, which are benchmarked against the standard case of identical aspect ratios, we observe that prolate particles display faster dynamics than oblate particles at short and long time scales. Nevertheless, when compared at identical infinite-dilution translational diffusion coefficients, oblate particles are faster than their prolate counterparts at short-to-intermediate time scales, which extend over almost three time decades. Both oblate and prolate particles exhibit an anisotropic diffusion with respect to the orientation of the nematic director. More specifically, prolate particles show a fast diffusion in the direction parallel to the nematic director, while their diffusion in the direction perpendicular to it is slower. By contrast, the diffusion of oblate particles is faster in the plane perpendicular to the nematic director. Finally, in the light of our recent study on the long-time Gaussian and Fickian diffusion in nematic systems, we map the decay of the autocorrelation functions and their fluctuations over the time scales of our simulations to ponder the existence of mobile clusters of particles and the occurrence of collective motion.

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

Colloids have a striking relevance in a wide spectrum of industrial formulations, spanning from personal care products to protective paints. Their behaviour can be easily influenced by extremely weak forces, which disturb their thermodynamic equilibrium and dramatically determine their performance. Motivated by the impact of colloidal dispersions in fundamental science and formulation engineering, we have designed an efficient Dynamic Monte Carlo (DMC) approach to mimic their out-of-equilibrium dynamics. Our recent theory, which provided a rigorous method to reproduce the Brownian motion of colloids by MC simulations, is here generalised to reproduce the Brownian motion of colloidal particles during transitory unsteady states, when their thermodynamic equilibrium is significantly modified. To this end, we investigate monodisperse and bidisperse rod-like particles in the isotropic phase and apply an external field that forces their reorientation along a common direction and induces an isotropic-to-nematic phase transition. We also study the behaviour of the system once the external field is removed. Our simulations are in excellent quantitative agreement with Brownian Dynamics simulations when the DMC results are rescaled with a time-dependent acceptance ratio, which depends on the strength of the applied field.

Phase behaviour of hard board-like particles.

We examine the phase behaviour of colloidal suspensions of hard board-like particles (HBPs) as a function of their shape anisotropy, and observe a fascinating spectrum of nematic, smectic, and columnar liquid-crystalline phases, whose formation is entirely driven by excluded volume effects. We map out the phase diagram of short and long HBPs by gradually modifying their shape from prolate to oblate and investigate the long-range order of the resulting morphologies along the phase directors and perpendicularly to them. The intrinsic biaxial nature of these particles promotes the formation of translationally ordered biaxial phases, but does not show solid evidence that it would, per se, promote the formation of the biaxial nematic phase. Our simulations shed light on the controversial existence of the discotic smectic phase, whose layers are as thick as the minor particle dimension, which is stable in a relatively large portion of our phase diagrams. Additionally, we modify the Onsager theory to describe the isotropic-nematic phase transition of freely rotating biaxial particles as a function of the particle width, and find a relatively strong first-order signature, in excellent agreement with our simulations. In an attempt to shed light on the elusive formation of the biaxial nematic phase, we apply this theory to predict the uniaxial-biaxial nematic phase transition and confirm, again in agreement with simulations, the prevailing stability of the translationally ordered smectic phase over the orientationally ordered biaxial nematic phase.

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.

Insight into the Viscoelasticity of Self-Assembling Smectic Liquid Crystals of Colloidal Rods from Active Microrheology Simulations.

The rheology of colloidal suspensions is of utmost importance in a wide variety of interdisciplinary applications in formulation technology, determining equally interesting questions in fundamental science. This is especially intriguing when colloids exhibit a degree of long-range positional or orientational ordering, as in liquid crystals (LCs) of elongated particles. Along with standard methods, microrheology (MR) has emerged in recent years as a tool to assess the mechanical properties of materials at the microscopic level. In particular, by active MR one can infer the viscoelastic response of a soft material from the dynamics of a tracer particle being dragged through it by external forces. Although considerable efforts have been made to study the diffusion of guest particles in LCs, little is known about the combined effect of tracer size and directionality of the dragging force on the system's viscoelastic response. By dynamic Monte Carlo simulations, we apply active MR to investigate the viscoelasticity of self-assembling smectic (Sm) LCs consisting of rodlike particles. In particular, we track the motion of a spherical tracer whose size is varied within a range of values matching the system's characteristic length scales and being dragged by constant forces that are parallel, perpendicular, or at 45° to the nematic director. Our results reveal a uniform value of the effective friction coefficient as probed by the tracer at small and large forces, whereas a nonlinear, force-thinning regime is observed at intermediate forces. However, at relatively weak forces the effective friction is strongly determined by correlations between the tracer size and the structure of the host fluid. Moreover, we also show that external forces forming an angle with the nematic director provide additional details that cannot be simply inferred from the mere analysis of parallel and perpendicular forces. Our results highlight the fundamental interplay between tracer size and force direction in assessing the MR of Sm LC fluids.

Computer simulation study of nutrient-driven bacterial biofilm stratification.

Here, employing computer simulation tools, we present a study on the development of a bacterial biofilm from a single starter cell on a flat inert surface overlaid by an aqueous solution containing nutrients. In our simulations, surface colonization involves an initial stage of two-dimensional cell proliferation to eventually transition to three-dimensional growth leading to the formation of biofilm colonies with characteristic three-dimensional semi-ellipsoids shapes. Thus, we have introduced the influence of the nutrient concentration on bacterial growth, and calculated the cell growth rate as a function of nutrient uptake, which in turn depends on local nutrient concentration in the vicinity of each bacterial cell. Our results show that the combination of cell growth and nutrient uptake and diffusion leads to the formation of stratified colonies containing an inner core in which nutrients are depleted and cells cannot grow or divide, surrounded by an outer, shallow crust in which cells have access to nutrients from the bulk medium and continue growing. This phenomenon is more apparent at high uptake rates that enable fast nutrient depletion. Our simulations also predict that the shape and internal structure of the biofilm are largely conditioned by the balance between nutrient diffusion and uptake.

Experimental evidence of the relevance of orientational correlations in photoinduced bimolecular reactions in solution.

A major problem in the extraction of the reaction probability in bimolecular processes is the disentanglement from the influence of molecular diffusion. One of the strategies to overcome it makes use of reactive solvents in which the reactants do not need to diffuse to encounter each other. However, most of our quantitative understanding of chemical reactions in solution between free partners is based on the assumption that they can be approximated by spheres because rotation averages their mutual orientations. This condition may not be fulfilled when the reaction takes place on time scales faster than that of molecular reorientation. In this work, the fluorescence quenching of two very similar polyaromatic hydrocarbons with different electric dipole moments is measured. The concentration of a liquid electron-donating quencher is varied from very dilute solutions to pure quencher solutions. In both cases, the thermodynamics of the reactions are very similar and, according to the Marcus expression, the kinetics are expected to proceed at similar rates. However, one of them is 10 times faster in the pure quencher solution. This difference starts at relatively low quencher concentrations. An explanation based on the fluorophore-solvent dipole-dipole interaction and the consequent orientational solvent structure is provided. The orientational correlation between fluorophore and quencher is calculated by means of computer simulations. Important differences depending on the fluorophore dipole moment are found. The kinetics can be explained quantitatively with a reaction-diffusion model that incorporates the effects of the presence of the dipole moment and the rotational diffusion, only in the highest quencher concentration case, but not in dilute solutions, most likely due to fundamental limitations of the kinetic theory.

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.

Microrheology of colloidal suspensions via dynamic Monte Carlo simulations.

Understanding the rheology of colloidal suspensions is crucial in the formulation of a wide selection of industry-relevant products, such as paints, foods and inks. To characterise the viscoelastic behaviour of these soft materials, one can analyse the microscopic dynamics of colloidal tracers diffusing through the host fluid and generating local deformations and stresses. This technique, referred to as microrheology, links the bulk rheology of fluids to the microscopic dynamics at the particle scale. If tracers are subjected to external forces, rather than freely diffusing, it is called active microrheology. Motivated by the impact of microrheology in providing information on local structure in complex systems such as colloidal glasses, active matter or biological systems, we have extended the dynamic Monte Carlo (DMC) technique to investigate active microrheology in colloidal suspensions. The original DMC theoretical framework, able to accurately describe the Brownian dynamics of colloids at equilibrium, is here reconsidered and expanded to describe the effects of an external force pulling a tracer embedded in isotropic colloidal suspensions at different densities. To this end, we studied the dynamics of a spherical tracer dragged by a constant external force through a bath of spherical and rod-like particles of comparable size. We could extract valuable details on its effective friction coefficient, being constant at small and large values of the external force, but otherwise displaying a nonlinear behaviour that indicates the occurrence of a force-thinning regime. Our DMC simulation results are in excellent quantitative agreement with past Langevin dynamics simulations and theoretical works for the bath of spherical colloids. The bath of rod-like particles is studied in the isotropic phase, and displays an example where DMC is more convenient than Brownian or Langevin dynamics, in this case, in dealing with particle rotation.

Phase behavior of hard colloidal platelets using free energy calculations.

We investigate the phase behavior of a model for colloidal hard platelets and rigid discotic molecules: oblate hard spherocylinders (OHSC). We perform free energy calculations using Monte Carlo simulations to map out the phase diagram as a function of the aspect ratio L∕D of the particles. The phase diagram displays a stable isotropic phase, a nematic liquid crystal phase for L∕D≤0.12, a columnar phase for L∕D≲0.3, a tilted crystal phase for L≲0.45, and an aligned crystal phase for L∕D≳0.45. We compare the results to the known phase diagram of hard cut spheres. Thin cut spheres are almost cylinder-shaped, while the interactions between real discotic mesogens and colloidal platelets are more consistent with the toroidal rims of the OHSC. Since the shapes of the OHSC and the cut spheres are otherwise similar, the phase diagrams of the two types of particles are quite akin. However, the tilted crystal phase for OHSC, which is of a crystal type that is frequently found in experiments on disklike molecules, has not been found for hard cut spheres. Furthermore, although we have found a cubatic phase, it was shown to be definitely unstable, whereas the stability of the cubatic phase of cut spheres is still disputed. Finally, we also show that the phase boundaries differ significantly from those for cut spheres. These are remarkable consequences of a subtle change in particle shape, which show that for a detailed comparison with the phase behavior of experimental particles, the OHSC should be used as a model particle.

Polymer-induced microcolony compaction in early biofilms: A computer simulation study.

Microscopic organisms, such as bacteria, have the ability of colonizing surfaces and developing biofilms that can determine diseases and infections. Most bacteria secrete a significant amount of extracellular polymer substances that are relevant for biofilm stabilization and growth. In this work, we apply computer simulation and perform experiments to investigate the impact of polymer size and concentration on early biofilm formation and growth. We observe as bacterial cells formed loose, disorganized clusters whenever the effect of diffusion exceeded that of cell growth and division. Addition of model polymeric molecules induced particle self-assembly and aggregation to form compact clusters in a polymer size- and concentration-dependent fashion. We also find that large polymer size or concentration lead to the development of intriguing stripe-like and dendritic colonies. The results obtained by Brownian dynamic simulation closely resemble the morphologies that we experimentally observe in biofilms of a Pseudomonas Putida strain with added polymers. The analysis of the Brownian dynamic simulation results suggests the existence of a threshold polymer concentration that distinguishes between two growth regimes. Below this threshold, the main force driving polymer-induced compaction is the hindrance of bacterial cell diffusion, while collective effects play a minor role. Above this threshold, especially for large polymers, polymer-induced compaction is a collective phenomenon driven by depletion forces. Well above this concentration threshold, severely limited diffusion drives the formation of filaments and dendritic colonies.

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.

Internal and free energy in a pair of like-charged colloids: Monte Carlo simulations.

The effective interaction between two colloidal particles in a bath of monovalent co- and counterions is studied by means of lattice Monte Carlo simulations with the primitive model. The internal electrostatic energy as a function of the colloid distance is studied fixing the position of the colloids. The free energy of the whole system is obtained introducing a bias parabolic potential, that allows us to sample efficiently small separations between the colloidal particles. For small charges, both the internal and free energy increase when the colloids approach each other, resulting in an effective repulsion driven by the electrostatic repulsion. When the colloidal charge is large enough, on the other hand, the colloid-ion coupling is strong enough to form double layers. The internal energy in this case decreases upon approaching the colloids because more ions enter the double layer. This attractive contribution to the interaction between the colloids is stronger for larger charges and larger ionic concentrations. However, the total free energy increases due to the loss of ionic entropy, and resulting finally in a repulsive interaction potential driven by the entropic contributions. The loss of ionic entropy can be almost quantitatively reproduced with the ideal contribution, the same level of approximation as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The overall behavior is captured by the DLVO theory qualitatively, and a comparison is made with the functional form predicted by the theory, showing moderate agreement.

Dynamics of hard colloidal cuboids in nematic liquid crystals.

We perform dynamic Monte Carlo simulations to investigate the equilibrium dynamics of hard board-like colloidal particles in oblate and prolate nematic liquid crystals. In particular, we characterize the particles' diffusion along the nematic director and perpendicularly to it, and observe a structural relaxation decay that strongly depends on the particle anisotropy. To assess the Gaussianity of their dynamics and eventual occurrence of collective motion, we calculate two- and four-point correlation functions that incorporate the instantaneous values of the diffusion coefficients parallel and perpendicular to the nematic director. Our simulation results highlight the occurrence of Fickian and Gaussian dynamics at short and long times, locate the minimum diffusivity at the self-dual shape, the particle geometry that would preferentially stabilise biaxial nematics, and exclude the existence of dynamically correlated particles.