Kinetic pathways for the isotropic-nematic phase transition in a system of colloidal hard rods: a simulation study

Diffusionless rotator-crystal transitions in colloidal truncated cubes

Upon osmotic compression, rotationally symmetric faceted colloidal particles can form translationally ordered, orientationally disordered rotator mesophases. This study explores the mechanism of rotator-to-crystal phase transitions where orientational order is gained in a translationally ordered phase, using rotator-phase forming truncated cubes as a testbed. Monte Carlo simulations were conducted for two selected truncations (s), one for s = 0.527 where the rotator and crystal lattices are dissimilar and one for s = 0.572 where the two phases have identical lattices. These differences set the stage for a qualitative difference in their rotator-crystal transitions, highlighting the effect of lattice distortion on phase transition kinetics. Our simulations reveal that significant lattice deviatoric effects could hinder the rotator-to-crystal transition and favor arrangements of lower packing fraction instead. Indeed, upon compression, it is found that for s = 0.527, the rotator phase does not spontaneously transition into the stable, densely packed crystal due to the high lattice strains involved but instead transitions into a metastable solid phase to be colloquially referred to as "orientational salt" for short, which has a similar lattice as the rotator phase and exhibits two distinct particle orientations having substitutional order, alternating regularly throughout the system. This study paves the way for further analysis of diffusionless transformations in nanoparticle systems and how lattice-distortion could influence crystallization kinetics.

Nematic-isotropic phase transitions in thin slabs of liquid crystals with topological defect arrays

We study the nematic-to-isotropic phase transitions in thin slabs of nematic liquid crystals with photopatterned director fields of topological defect arrays at constant heating rates and show that the transition kinetics is significantly impacted by both the heating rate and the topological strengths of these defects. Specifically, with ±1/2 defect arrays, the isotropic domains emerge from the defect cores when the heating rate is high, while from random places when the heating rate is low. With ±1 defect arrays, the isotropic domains always emerge from the defect cores regardless of the heating rate. Furthermore, the isotropic domains show significant movements at slow heating rates, and the total area of the isotropic domains grows with the temperature T following a simple power law (T - T')γ, where the exponent γ is approximately 1 in most cases and is 2/3 for the ±1 defect arrays at low heating rates when the isotropic domains are pinned on the defect cores. We attribute this phenomenon to an interplay between the surface tension and bulk free energy.

Engineering the Thermodynamic Stability and Metastability of Mesophases of Colloidal Bipyramids through Shape Entropy

We report several types of entropy-driven phase transition behaviors in hard bipyramid systems using Monte Carlo simulations. Bipyramidal nanoparticle shapes are synthesizable from gold and silver, with sizes ranging from tens to hundreds of nanometers. We report numerous colloidal crystalline phases with varying symmetries and complexities as the bipyramid aspect ratio and base polygon are varied. Some bipyramids are mesogenic and undergo either monotropic or enantiotropic phase transitions. We show that such mesophase behavior can be modulated by tuning the bipyramid aspect ratio. In addition, we report stepwise kinetic crystallization and melting pathways that occur via an intermediate mesophase as the system gains or loses order in successive stages. Our results demonstrate that complex phase transition behavior involving mesophases can be driven by entropy alone. Importantly, our results can guide the synthesis of bipyramid shapes able to assemble target structures and can be used to engineer the kinetic pathways to and from those structures to involve or avoid mesophases.

Disentangling kinetics from thermodynamics in heterogeneous colloidal systems

In Nucleation and Growth, the process by which most heterogeneous systems form, thermodynamics sets the asymptotic boundaries toward which the system must evolve, while kinetics tries to cope with it by imposing the transport rates. In all heterogeneous colloidal systems observed in nature, composition, shape, structure and physical properties result from the trade-off between thermodynamics and kinetics. Here we show, by carefully selecting colloidal systems and controlling phase separation in microfluidic devices, that it becomes possible to disentangle kinetics effects from thermodynamics. Using amyloids and nanocellulose filamentous colloids, we demonstrate that decoupling kinetics from thermodynamics in the phase separation process unveils new physical phenomena, such as orders of magnitude shorter timescales, a wider phase diagram, and structures that are not observable via conventional liquid-liquid phase separation. Our approach enables on-demand fabrication of multicomponent heterogeneous liquid crystals, enhancing their potential, and introducing original fundamental and technological directions in multicomponent structured fluids.

Multistep nucleation of anisotropic molecules

Phase transition of anisotropic materials is ubiquitously observed in physics, biology, materials science, and engineering. Nevertheless, how anisotropy of constituent molecules affects the phase transition dynamics is still poorly understood. Here we investigate numerically the phase transition of a simple model system composed of anisotropic molecules, and report on our discovery of multistep nucleation of nuclei with layered positional ordering (smectic ordering), from a fluid-like nematic phase with orientational order only (no positional order). A trinity of molecular dynamics simulation, machine learning, and molecular cluster analysis yielding free energy landscapes unambiguously demonstrates the dynamics of multistep nucleation process involving characteristic metastable clusters that precede supercritical smectic nuclei and cannot be accounted for by the classical nucleation theory. Our work suggests that molecules of simple shape can exhibit rich and complex nucleation processes, and our numerical approach will provide deeper understanding of phase transitions and resulting structures in anisotropic materials such as biological systems and functional materials.

Revealing Polymerization Kinetics with Colloidal Dipatch Particles

Limited-valency colloidal particles can self-assemble into polymeric structures analogous to molecules. While their structural equilibrium properties have attracted wide attention, insight into their dynamics has proven challenging. Here, we investigate the polymerization dynamics of semiflexible polymers in 2D by direct observation of assembling divalent particles, bonded by critical Casimir forces. The reversible critical Casimir force creates living polymerization conditions with tunable chain dissociation, association, and bending rigidity. We find that unlike dilute polymers that show exponential size distributions in excellent agreement with Flory theory, concentrated samples exhibit arrest of rotational and translational diffusion due to a continuous isotropic-to-nematic transition in 2D, slowing down the growth kinetics. These effects are circumvented by the addition of higher-valency particles, cross linking the polymers into networks. Our results connecting polymer flexibility, polymer interactions, and the peculiar isotropic-nematic transition in 2D offer insight into the polymerization processes of synthetic two-dimensional polymers and biopolymers at membranes and interfaces.

Crystal nucleation in colloidal rod suspensions: The effect of depletant size

In order to better control the assembly of nanorods, knowledge of the pathways by which they form ordered structures is desirable. In this paper, we characterize crystal nucleation in suspensions of spherocylindrical rods with aspect ratio L/D = 2.3 in the presence of both small and large polymer depletants. Using a combination of Langevin dynamics and Monte Carlo simulations, together with biased sampling techniques, we show that the preferred pathway always involves the formation of monolayer assemblies irrespective of the volume fraction of the initial isotropic phase and the diameter of the depletants. This includes the previously neglected case of nucleation from the colloidal liquid phase and shows that the presence of depletion attraction can alter nucleation pathways even when the initial phase is dense.

An Artificial Neural Network Reveals the Nucleation Mechanism of a Binary Colloidal AB13 Crystal

Colloidal suspensions of two species have the ability to form binary crystals under certain conditions. The hunt for these functional materials and the countless investigations on their formation process are justified by the plethora of synergetic and collective properties these binary superlattices show. Among the many crystal structures observed over the past decades, the highly exotic colloidal icosahedral AB₁₃ crystal was predicted to be stable in binary hard-sphere mixtures nearly 30 years ago, yet the kinetic pathway of how homogeneous nucleation occurs in this system is still unknown. Here we investigate binary nucleation of the AB₁₃ crystal from a binary fluid phase of nearly hard spheres. We calculate the nucleation barrier and nucleation rate as a function of supersaturation and draw a comparison with nucleation of single-component and other binary crystals. To follow the nucleation process, we employ a neural network to identify the AB₁₃ phase from the binary fluid phase and the competing fcc crystal with single-particle resolution and significant accuracy in the case of bulk phases. We show that AB₁₃ crystal nucleation proceeds via a coassembly process where large spheres and icosahedral small-sphere clusters simultaneously attach to the nucleus. Our results lend strong support for a classical pathway that is well-described by classical nucleation theory, even though the binary fluid phase is highly structured and exhibits local regions of high bond orientational order.

Crystallization of semiflexible polymers in melts and solutions

We studied the crystallization of semiflexible polymer chains in melts and poor-solvent solutions with different concentrations using dissipative particle dynamics (DPD) computer simulation techniques. We used the coarse-grained polymer model to reveal the general principles and microscopic scenario of crystallization in such systems at large time and length scales. It covers both primary and secondary nucleation as well as crystallites' merging. The parameters of the DPD model were chosen appropriately to reproduce the entanglements of polymer chains. We started from an initial homogeneous disordered solution of Gaussian chains and observed the initial stages of crystallization process caused in our model by orientational ordering of polymer chains and polymer-solvent phase separation. We found that the overall crystalline fraction at the end of the crystallization process decreases with the increasing polymer volume fraction while the steady-state crystallization speed at later stages does not depend on the polymer volume fraction. The average crystallite size has a maximal value in the systems with a polymer volume fraction from 0.7 to 0.95. In our model, these polymer concentrations represent an optimal value in the sense of balance between the amount of polymer material available to increase the crystallite size and chain entanglements, that prevent crystallites' growth and merging. On large time scales, our model allows us to observe lamellar thickening linear in logarithmic time scale.

Shear driven vorticity aligned flocs in a suspension of attractive rigid rods

A combination of rheology, optical microscopy and computer simulations was used to investigate the microstructural changes of a semi-dilute suspension of attractive rigid rods in an imposed shear flow. The aim is to understand the relation of the microstructure with the viscoelastic response, and the yielding and flow behaviour in different shear regimes of gels built from rodlike colloids. A semi-dilute suspension of micron sized, rodlike silica particles suspended in 11 M CsCl salt solution was used as a model system for attractive rods' gel. Upon application of steady shear the gel microstructure rearranges in different states and exhibits flow instabilities depending on shear rate, attraction strength, volume fraction and geometrical confinement. At low rod volume fractions, the suspension forms large, vorticity aligned, particle rich flocs that roll in the flow-vorticity plane, an effect that is due to an interplay between hydrodynamic interactions and geometrical confinement as suggested by computer simulations. Experimental data allow the creation of a state diagram, as a function of volume fraction and shear rates, identifying regimes of stable (or unstable) floc formation and of homogeneous gel or broken clusters. The transition is related to dimensionless Mason number, defined as the ratio of shear forces to interparticle attractive force.

Translational and rotational critical-like behaviors in the glass transition of colloidal ellipsoid monolayers

Critical-like behaviors have been found in translational degrees of freedom near the glass transition of spherical particle systems mainly with local polycrystalline structures, but it is not clear if criticality exists in more general glassy systems composed of nonspherical particles without crystalline structures. Here, through experiments and simulations, we show critical-like behaviors in both translational and rotational degrees of freedom in monolayers of monodisperse colloidal ellipsoids in the absence of crystalline orders. We find rich features of the Ising-like criticality in structure and slow dynamics at the ideal glass transition point ϕ₀, showing the thermodynamic nature of glass transition at ϕ₀ A dynamic criticality is found at the mode-coupling critical point ϕ_c for the fast-moving clusters whose critical exponents increase linearly with fragility, reflecting a dynamic glass transition. These results cast light on the glass transition and explain the mystery that the dynamic correlation lengths diverge at two different temperatures.

Short and Soft: Multidomain Organization, Tunable Dynamics, and Jamming in Suspensions of Grafted Colloidal Cylinders with a Small Aspect Ratio

The yet virtually unexplored class of soft colloidal rods with a small aspect ratio is investigated and shown to exhibit a very rich phase and dynamic behavior, spanning from liquid to nearly melt state. Instead of the nematic order, these short and soft nanocylinders alter their organization with increasing concentration from isotropic liquid with random orientation to small domains with preferred local orientation and eventually a multidomain arrangement with a local orientational order. The latter gives rise to a kinetically suppressed state akin to structural glass with detectable terminal relaxation, which, on further increasing concentration, reveals features of hexagonally packed order as in ordered block copolymers. The respective dynamic response comprises four regimes, all above the overlapping concentration of 0.02 g/mL:(I) from 0.03 to 0.1 g/mol, the system undergoes a liquid-to-solidlike transition with a structural relaxation time that grows by 4 orders of magnitude. (II) From 0.1 to 0.2 g/mL, a dramatic slowing-down is observed and is accompanied by an evolution from isotropic to a multidomain structure. (III) Between 0.2 and 0.6 g/mol, the suspensions exhibit signatures of shell interpenetration and jamming, with the colloidal plateau modulus depending linearly on concentration. (IV) At 0.74 g/mL, in the densely jammed state, the viscoelastic signature of hexagonally packed cylinders from microphase-separated block copolymers is detected. These properties set short and soft nanocylinders apart from long colloidal rods (with a large aspect ratio) and provide insights for fundamentally understanding the physics in this intermediate soft colloidal regime and for tailoring the flow properties of nonspherical soft colloids.

A versatile simulation method for studying phase behavior and dynamics in colloidal rod and rod-polymer suspensions

Here, we present an implicit-solvent model for dynamic simulations of hard-rod and rod-polymer suspensions. Individual rods are represented by a rigid linear chain consisting of overlapping spheres which interact through a pseudohard-core potential based on the cut-and-shifted Mie (generalized Lennard-Jones) potential with exponents (50, 49). In the rod-polymer suspensions, the polymers are modeled as freely interpenetrable spheres with respect to each other, while there is the pseudohard-core repulsion between the polymer and rod spheres. Dynamic simulations with this model are carried out with a dissipative particle dynamics (DPD) thermostat-each sphere is put in a larger DPD sphere and thus interacts with others via additional pairwise frictional and random forces-which captures the effects of Brownian forces due to the solvent while conserving local momentum. The phase behavior of these models, obtained from continuous compression and expansion simulations, reproduces previous predictions based on theoretical calculations and Monte Carlo simulations. Our method is suited to study dynamic processes in these suspensions, including nucleation and self-assembly, and can be readily extended to colloidal particles of different shapes and chemistry.

Plastic Crystal-to-Crystal Transition of Janus Particles under Shear

Colloidal Janus spheres in the bulk typically spontaneously assemble into plastic crystalline phases, while particle orientations exhibit glasslike dynamics without long-range order. Through Brownian dynamics simulations, we demonstrate that shear can trigger a phase transition from an isotropic crystal with orientational disorder to an orientationally ordered crystal with lamellae along the shear direction. This nonequilibrium transition is accompanied with the orientational ordering following a nucleation and growth mechanism. By performing a phenomenological extension of free energy analysis, we reveal that the nucleation originates from the orientation fluctuations induced by shear. The growth of the orientationally crystalline cluster is examined to be disklike, captured by developing a lattice model with memoryless state functions. These findings bring new insights into the mechanisms for the ordering transition of anisotropic particles at nonequilibrium states.

Nucleation of pseudo hard-spheres and dumbbells at moderate metastability: appearance of A15 Frank–Kasper phase at intermediate elongations

Crystal nucleation of repulsive hard-dumbbells from the sphere to the two tangent spheres limit is investigated at moderately high metastability by brute-force molecular dynamics simulations.

How Implementation of Entropy in Driving Structural Ordering of Nanoparticles Relates to Assembly Kinetics: Insight into Reaction-Induced Interfacial Assembly of Janus Nanoparticles

The ability to understand and exploit entropic contributions to ordering transition is of essential importance in the design of self-assembling systems with well-controlled structures. However, much less is known about the role of assembly kinetics in entropy-driven phase behaviors. Here, by combining computer simulations and theoretical analysis, we report that the implementation of entropy in driving phase transition significantly depends on the kinetic process in the reaction-induced self-assembly of newly designed nanoparticle systems. In particular, such systems comprise binary Janus nanoparticles at the fluid-fluid interface and undergo phase transition driven by entropy and controlled by the polymerization reaction initiated from the surfaces of just one component of nanoparticles. Our simulations demonstrate that the competition between the reaction rate and the diffusive dynamics of nanoparticles governs the implementation of entropy in driving the phase transition from randomly mixed phase to intercalated phase in these interfacial nanoparticle mixtures, which thereby results in diverse kinetic pathways. At low reaction rates, the transition exhibits abrupt jump in the mixing parameter, in a similar way to first-order, equilibrium phase transition. Increasing the reaction rate diminishes the jumps until the transitions become continuous, behaving as a second-order-like phase transition, where a critical exponent, characterizing the transition, can be identified. We finally develop an analytical model of the blob theory of polymer chains to complement the simulation results and reveal essential scaling laws of the entropy-driven phase behaviors. In effect, our results allow for further opportunities to amplify the entropic contributions to the materials design via kinetic control.

A Shape-Induced Orientation Phase within 3D Nanocrystal Solids

When nanocrystals self assemble into ordered superstructures they form functional solids that may inherit the electronical properties of the single nanocrystals. To what extent these properties are enhanced depends on the positional and orientational order of the nanocrystals within the superstructure. Here, the formation of micrometer-sized free-standing supercrystals of faceted 20 nm Bi nanocrystals is investigated. The self-assembly process, induced by nonsolvent into solvent diffusion, is probed in situ by synchrotron X-ray scattering. The diffusion-gradient is identified as the critical parameter for controlling the supercrystal-structure as well as the alignment of the supercrystals with respect to the substrate. Monte Carlo simulations confirm the positional order of the nanocrystals within these superstructures and reveal a unique orientation phase: the nanocrystal shape, determined by the atomic Bi crystal structure, induces a total of 6 global orientations based on facet-to-facet alignment. This parallel alignment of facets is a prerequisite for optimized electronic and optical properties within designed nanocrystal solids.

Stimuli-responsive hydroxyapatite liquid crystal with macroscopically controllable ordering and magneto-optical functions

Liquid crystals are mostly formed by self-assembly of organic molecules. In contrast, inorganic materials available as liquid crystals are limited. Here we report the development of liquid-crystalline (LC) hydroxyapatite (HAp), which is an environmentally friendly and biocompatible biomineral. Its alignment behavior, magneto-optical properties, and atomic-scale structures are described. We successfully induce LC properties into aqueous colloidal dispersions of rod-shaped HAp by controlling the morphology of the material using acidic macromolecules. These LC HAp nanorod materials are macroscopically oriented in response to external magnetic fields and mechanical forces. We achieve magnetic modulation of the optical transmission by dynamic control of the LC order. Atomic-scale observations using transmission electron microscopy show the self-organized inorganic/organic hybrid structures of mesogenic nanorods. HAp liquid crystals have potential as bio-friendly functional materials because of their facile preparation, the bio-friendliness of HAp, and the stimuli-responsive properties of these colloidal ordered fluids.

Stochastic kinetics reveal imperative role of anisotropic interfacial tension to determine morphology and evolution of nucleated droplets in nematogenic films

For isotropic fluids, classical nucleation theory predicts the nucleation rate, barrier height and critical droplet size by ac- counting for the competition between bulk energy and interfacial tension. The nucleation process in liquid crystals is less understood. We numerically investigate nucleation in monolayered nematogenic films using a mesoscopic framework, in par- ticular, we study the morphology and kinetic pathway in spontaneous formation and growth of droplets of the stable phase in the metastable background. The parameter κ that quantifies the anisotropic elastic energy plays a central role in determining the geometric structure of the droplets. Noncircular nematic droplets with homogeneous director orientation are nucleated in a background of supercooled isotropic phase for small κ. For large κ, noncircular droplets with integer topological charge, accompanied by a biaxial ring at the outer surface, are nucleated. The isotropic droplet shape in a superheated nematic background is found to depend on κ in a similar way. Identical growth laws are found in the two cases, although an unusual two-stage mechanism is observed in the nucleation of isotropic droplets. Temporal distributions of successive events indi- cate the relevance of long-ranged elasticity-mediated interactions within the isotropic domains. Implications for a theoretical description of nucleation in anisotropic fluids are discussed.

Seeding approach to crystal nucleation

We present a study of homogeneous crystal nucleation from metastable fluids via the seeding technique for four different systems: mW water, Tosi-Fumi NaCl, Lennard-Jones, and Hard Spheres. Combining simulations of spherical crystal seeds embedded in the metastable fluid with classical nucleation theory, we are able to successfully describe the nucleation rate for all systems in a wide range of metastability. The crystal-fluid interfacial free energy extrapolated to coexistence conditions is also in good agreement with direct calculations of such parameter. Our results show that seeding is a powerful technique to investigate crystal nucleation.

Entropy-driven formation of chiral nematic phases by computer simulations

Predicting the macroscopic chiral behaviour of liquid crystals from the microscopic chirality of the particles is highly non-trivial, even when the chiral interactions are purely entropic in nature. Here we introduce a novel chiral hard-particle model, namely particles with a twisted polyhedral shape and obtain a stable fully entropy-driven cholesteric phase by computer simulations. By slightly modifying the triangular base of the particle, we are able to switch from a left-handed prolate (calamitic) to a right-handed oblate (discotic) cholesteric phase using the same right-handed twisted particle model. Furthermore, we show that not only prolate and oblate chiral nematic phases, but also other novel entropy-driven phases, namely chiral blue phases, chiral nematic phases featuring both twist and splay deformations, chiral biaxial nematic phases with one of the axes twisted, can be obtained by varying particle biaxiality and chirality. Our results allow to identify general guidelines for the stabilization of these phases.

Lattice mold technique for the calculation of crystal nucleation rates

We present a new simulation method for the calculation of crystal nucleation rates by computer simulation. The method is based on the use of molds to induce crystallization in state points where nucleation is a rare event. The mold is a cluster of potential energy wells placed in the lattice positions of the solid. The method has two distinct steps. In the first one the probability per unit volume of forming a sub-critical crystal cluster in the fluid is computed by means of thermodynamic integration. The thermodynamic route consists in gradually switching on an attractive interaction between the wells and the fluid particles. In the second step, the frequency with which such cluster becomes post-critical is computed in Molecular Dynamics simulations with the mold switched on. We validate our method with a continuous version of the hard sphere potential and with the sodium chloride Tosi–Fumi model. In all studied state points we obtain a good agreement with literature data obtained from other rare event simulation techniques. Our method is quite suitable for the study of both crystal nucleation of arbitrarily complex structures and the competition between different polymorphs in the nucleation stage.

Phase behavior of Janus colloids determined by sedimentation equilibrium

We investigate the phase behavior of short-range interacting isotropic particles and single-patch Janus particles via simulations of sedimentation equilibrium, which allows for a rapid assessment of the equation of state and phase behavior directly from simulation. The methodology is tested against results by traditional methods and is found to yield good agreement for isotropic interactions. The method is then used to study single-patch Janus particles with different interaction strengths and patch sizes with particle area coverage greater than ∼0.63. Our results show an interplay between translational and orientational order. We observe a lamellar phase, a fluid phase and a rotator close-packed structure. The lamellar phase is shown to have a different range of stability than previously observed in simulation studies for systems of similar and longer-ranged interactions.

Supramolecular nature of the nematic-nematic phase transitions of hard boardlike molecules

The phase behavior of hard boardlike biaxial particles of relative dimensions close to the clamitic to discotic crossover is explored by means of Monte Carlo molecular simulations. Transitions between two distinct biaxial nematic phases as well as transitions from a biaxial nematic to a uniaxial Sm-A phase are obtained. The formation of anisotropic supramolecular assemblies is demonstrated and is quantified by means of rotationally invariant pair correlation functions.

Phase ordering kinetics in uniaxial nematic liquid crystals with second- and fourth-rank interactions

We present comprehensive results of the Monte Carlo (MC) simulations of the phase ordering dynamics in d = 2 nematic liquid crystals. We study a system of size N (2)(N = 512) with molecules confined to a 512×512 square lattice and report the results for two LC Hamiltonians: generalized Lebwohl-Lasher (GLL) model and r(-6) dependent anisotropic dispersion interaction potential. In these Hamiltonians a fourth-rank Legendre polynomial P4 interaction term is added to the usual second-rank P2 term. We find that in both the cases the presence of the P4 interaction term significantly influences the nematic domains morphology. Our numerical data show a diffusive growth law with a logarithmic correction: L(t) ∼ (t/ln t)(1/2).

Simulations of nematic homopolymer melts using particle-based models with interactions expressed through collective variables

We develop a hybrid Monte Carlo approach for modelling nematic liquid crystals of homopolymer melts. The polymer architecture is described with a discrete worm-like chain model. A quadratic density functional accounts for the limited compressibility of the liquid, while an additional quadratic functional of the local orientation tensor of the segments captures the nematic ordering. The approach can efficiently address large systems parametrized according to volumetric and conformational properties, representative of real polymeric materials. The results of the simulations regarding the influence of the molecular weight on the isotropic-nematic transition are compared to predictions from a Landau-de Gennes free energy expansion. The formation of the nematic phase is addressed within Rouse-like dynamics, realized using the current model.

Isotropic-nematic phase transition in the Lebwohl-Lasher model from density of states simulations

Density of states Monte Carlo simulations have been performed to study the isotropic-nematic (IN) transition of the Lebwohl-Lasher model for liquid crystals. The IN transition temperature was calculated as a function of system size using expanded ensemble density of states simulations with histogram reweighting. The IN temperature for infinite system size was obtained by extrapolation of three independent measures. A subsequent analysis of the kinetics in the model showed that the transition occurs via spinodal decomposition through aggregation of clusters of liquid crystal molecules.

Frustration of the isotropic-columnar phase transition of colloidal hard platelets by a transient cubatic phase

Using simulations and theory, we show that the cubatic phase is metastable for three model hard platelets. The locally favored structures of perpendicular particle stacks in the fluid prevent the formation of the columnar phase through geometric frustration resulting in vitrification. Also, we find a direct link between structure and dynamic heterogeneities in the cooperative rotation of particle stacks, which is crucial for the devitrification process. Finally, we show that the lifetime of the glassy cubatic phase can be tuned by surprisingly small differences in particle shape.

Tactoids of plate-like particles: size, shape, and director field

We studied, by means of polarized light microscopy, the shape and director field of nematic tactoids as a function of their size in dispersions of colloidal gibbsite platelets in polar and apolar solvents. Because of the homeotropic anchoring of the platelets to the interface, we found large tactoids to be spherical with a radial director field, whereas small tactoids turn out to have an oblate shape and a homogeneous director field, in accordance with theoretical predictions. The transition from a radial to a homogeneous director field seems to proceed via two different routes depending in our case on the solvent. In one route, the what presumably is a hedgehog point defect in the center of the tactoid transforms into a ring defect with a radius that presumably goes to infinity with decreasing drop size. In the other route, the hedgehog defect is displaced from the center to the edge of the tactoid, where it becomes virtual again going to infinity with decreasing drop size. Furthermore, quantitative analysis of the tactoid properties provides us with useful information on the ratio of the splay elastic constant and the anchoring strength and the ratio of the anchoring strength and the surface tension.

Glassy dynamics, spinodal fluctuations, and the kinetic limit of nucleation in suspensions of colloidal hard rods

Using simulations we identify three dynamic regimes in supersaturated isotropic fluid states of short hard rods: (i) for moderate supersaturations, we observe nucleation of multilayered crystalline clusters; (ii) at higher supersaturation, we find nucleation of small crystallites which arrange into long-lived locally favored structures that get kinetically arrested; and (iii) at even higher supersaturation, the dynamic arrest is due to the conventional cage-trapping glass transition. For longer rods we find that the formation of the (stable) smectic phase out of a supersaturated isotropic state is strongly suppressed by an isotropic-nematic spinodal instability that causes huge spinodal-like orientation fluctuations with nematic clusters diverging in size. Our results show that glassy dynamics and spinodal instabilities set kinetic limits to nucleation in highly supersaturated hard-rod fluids.

Supersaturated dispersions of rodlike viruses with added attraction

The kinetics of isotropic-nematic (I-N) and nematic-isotropic (N-I) phase transitions in dispersions of rodlike fd viruses are studied. Concentration quenches were applied using pressure jumps in combination with polarization microscopy, birefringence, and turbidity measurements. The full biphasic region could be accessed, resulting in the construction of an experimental analog of the bifurcation diagram. The N-I spinodal points for dispersions of rods with varying concentrations of depletion agent (dextran) were obtained from orientation quenches using cessation of shear flow in combination with small-angle light scattering. We found that the location of the N-I spinodal point is independent of the attraction, which was confirmed by theory. Surprisingly, the experiments showed that also the absolute induction time, the critical nucleus, and the growth rate are insensitive of the attraction if the concentration is scaled to the distance to the phase boundaries.

Do multilayer crystals nucleate in suspensions of colloidal rods?

We study the isotropic-to-crystal transformation in a mixture of colloidal hard rods and nonabsorbing polymer using computer simulations. We determine the height of the nucleation barrier and find that the critical cluster consists of a single crystalline layer growing laterally for all polymer fugacities considered. At lower supersaturation, the free energy of a single hexagonally packed layer increases monotonically with size, while the nucleation barrier of a second crystalline layer is extremely high. Hence, the nucleation of multilayer crystals is never observed. Multilayer crystals form only in the spinodal decomposition regime, either where, in an intermediate stage, single crystalline membranes coalesce into multilayer clusters or where, at higher polymer fugacity, smaller clusters of rods stack on top of each other to form long filaments. Eventually, these transient structures evolve into a thermodynamically stable bulk crystal phase.

Capillary rise of an isotropic-nematic fluid interface: surface tension and anchoring versus elasticity

A theoretical study is presented on the shape of the interface between coexisting isotropic and nematic phases in contact with a solid vertical wall. The interface profile is determined by a competition between three surface tensions, two anchoring strengths, gravity, and the Frank elastic constants of the director field. In the weak-anchoring limit, the director field is rigid and uniform, and we find the capillary rise height to depend nontrivially on the orientation of the director field relative to the solid-fluid interface. For strong surface anchoring, the director field adjusts to the preferred homeotropic or planar anchoring at the solid-liquid and liquid-liquid interfaces. The shape of the interfacial profile is now a function of the balance between the surface energy and the splay and bend elastic deformation energies. Interestingly, for both weak and strong anchoring the profile decays nonmonotonically albeit only very weakly so. We compare our theory with recent capillary rise experiments on coexisting isotropic and nematic phases of colloidal platelets [van der Beek et al. Phys. Rev. Lett. 2006, 97, 087801] and are able to extract from the experimental data the surface tension and the anchoring strength.

Numerical method of lines for the relaxational dynamics of nematic liquid crystals

We propose an efficient numerical scheme, based on the method of lines, for solving the Landau-de Gennes equations describing the relaxational dynamics of nematic liquid crystals. Our method is computationally easy to implement, balancing requirements of efficiency and accuracy. We benchmark our method through the study of the following problems: the isotropic-nematic interface, growth of nematic droplets in the isotropic phase, and the kinetics of coarsening following a quench into the nematic phase. Our results, obtained through solutions of the full coarse-grained equations of motion with no approximations, provide a stringent test of the de Gennes ansatz for the isotropic-nematic interface, illustrate the anisotropic character of droplets in the nucleation regime, and validate dynamical scaling in the coarsening regime.

Isotropic-to-nematic nucleation in suspensions of colloidal rods

Using computer simulations, we study the isotropic-to-nematic nucleation in a fluid of colloidal hard rods as well as in a mixture of colloidal rods and non-adsorbing polymer. In order to follow the transformation of the system from the isotropic to the nematic phase, we use a new cluster criterion that enables us to distinguish the nematic clusters from the isotropic fluid phase. Applying this criterion in Monte Carlo simulations, we find two different regimes depending on the supersaturation. At low supersaturation we find nucleation and growth, while at higher supersaturation spinodal decomposition is observed. We determine the height of the nucleation barrier, and we study the structure as well as the shape of the nematic clusters. We discuss our simulation results in the light of classical nucleation theory.