Self-assembly-driven nematization

Dilute suspensions of Janus rods: the role of bond and shape anisotropy

Nanometer-sized clusters are often targeted due to their potential applications as nanoreactors or storage/delivery devices. One route to assemble and stabilize finite structures consists of imparting directional bonding patterns between the nanoparticles. When only a portion of the particle surface is able to form an inter-particle bond, finite-size aggregates such as micelles and vesicles may form. Building on this approach, we combine particle shape anisotropy with the directionality of the bonding patterns and investigate the combined effect of particle elongation and surface patchiness on the low density assembly scenario. To this aim, we study the assembly of tip-functionalised Janus hard spherocylinders by means of Monte Carlo simulations. By exploring the effects of changing the interaction strength and range at different packing fractions, we highlight the role played by shape and bond anisotropy on the emerging aggregates (micelles, vesicles, elongated micelles, and lamellae). We observe that shape anisotropy plays a crucial role in suppressing phases that are typical to spherical Janus nanoparticles and that a careful tuning of the interaction parameters allows promoting the formation of spherical micelles. These finite-size spherical clusters composed of elongated particles might offer more interstitials and larger surface areas than those offered by micelles of spherical or almost-spherical units, thus enhancing their storage and catalytic properties.

In silico study of DNA mononucleotide self-assembly

Recent experiments have demonstrated the self-assembly and long-range ordering of concentrated aqueous solutions of DNA and RNA mononucleotides. These are found to form Watson-Crick pairs that stack into columns that become spatially organized into a columnar liquid-crystalline phase. In this work, we numerically investigate this phase behavior by adopting an extremely coarse-grained model in which nucleotides are represented as semi-disk-like polyhedra decorated with attractive (patchy) sites that mimic the stacking and pairing interactions. We carry out Monte Carlo simulations of these patchy polyhedra by adapting algorithms borrowed from computer graphics. This model reproduces the features of the experimental phase behavior, which essentially depends on the combination of pairing and stacking interactions.

Structural and dynamical equilibrium properties of hard board-like particles in parallel confinement

We performed Monte Carlo and dynamic Monte Carlo simulations to model the diffusion of monodispersed suspensions composed of impenetrable cuboidal particles, specifically hard board-like particles (HBPs), in the presence of parallel hard walls. The impact of the walls was investigated by adjusting the size of the simulation box while maintaining constant packing fractions, fixed at η = 0.150, for systems consisting of HBPs with prolate, dual-shaped, and oblate geometries. We observed that increasing the distance between the walls led to the recovery of an isotropic bulk phase, while local particle organization near the walls remained stable. Due to their shape, oblate HBPs exhibit more efficient anchoring at wall surfaces compared to prolate shapes. The formation of nematic-like particle assemblies near the walls, confirmed by theoretical calculations based on density functional theory, significantly influenced local particle dynamics. This effect was particularly pronounced to the extent that a modest portion of cuboids near the walls tended to diffuse exclusively in planes parallel to the confinement, even more efficiently than observed in the bulk regions.

On the role of polydispersity on the phase diagram of colloidal rods

The rich and complex phase diagram typical of anisotropic biological or synthetic nanoparticles, has brought a great deal of interest over the equilibrium phase behaviour of non-spherical colloids. Amongst the class of anisotropic nanoparticles, hard spherocylindrical colloids have been, over the years, extensively studied because of their optical properties, for their rich phase diagrams, and their important industrial applications, as model particles for biological systems (viruses), or for example as potential drug carriers having the ability of surviving the attacks of the immune systems. As real anisotropic nanoparticles are often polydisperse in size and/or in shape, unveiling the effect of such a perturbation over their equilibrium phase diagram is of paramount importance. This work focuses on the effects of polydispersity over the full equilibrium phase diagram of hard spherocylindrical colloids (HSCs). Previous studies showed that a polydispersity in L alters the equilibrium phase diagram of HSCs. With this work we determine, both theoretically as well as computationally, the effects due to a generic polydispersity, namely in D, in L and, in both ones, on the equilibrium phase diagram and introduce a viable theoretical generalisation of the Onsager theory that allows us to get some insight into the observed phase behaviour.

Self-Assembly of All-DNA Rods with Controlled Patchiness

Double-stranded DNA (dsDNA) fragments exhibit noncovalent attractive interactions between their tips. It is still unclear how DNA liquid crystal self-assembly is affected by such blunt-end attractions. It is demonstrated that stiff dsDNA fragments with moderate aspect ratio can specifically self-assemble in concentrated aqueous solutions into different types of smectic mesophases on the basis of selectively screening of blunt-end DNA stacking interactions. To this end, this type of attractions are engineered at the molecular level by constructing DNA duplexes where the attractions between one or both ends are screened by short hairpin caps. All-DNA bilayer and monolayer smectic-A type of phases, as well as a columnar phase, can be stabilized by controlling attractions strength. The results imply that the so far elusive smectic-A in DNA rod-like liquid crystals is a thermodynamically stable phase. The existence of the bilayer smectic phase is confirmed by Monte-Carlo simulations of hard cylinders decorated with one attractive terminal site. This work demonstrates that DNA blunt-ends behave as well-defined monovalent attractive patches whose strength and position can be potentially precisely tuned, highlighting unique opportunities concerning the stabilization of nonconventional DNA-based lyotropic liquid crystal phases assembled by all-DNA patchy particles with arbitrary geometry and composition.

Second-virial theory for shape-persistent living polymers templated by disks

Living polymers composed of noncovalently bonded building blocks with weak backbone flexibility may self-assemble into thermoresponsive lyotropic liquid crystals. We demonstrate that the reversible polymer assembly and phase behavior can be controlled by the addition of (nonadsorbing) rigid colloidal disks which act as an entropic reorienting "template" onto the supramolecular polymers. Using a particle-based second-virial theory that correlates the various entropies associated with the polymers and disks, we demonstrate that small fractions of discotic additives promote the formation of a polymer nematic phase. At larger disk concentrations, however, the phase is disrupted by collective disk alignment in favor of a discotic nematic fluid in which the polymers are dispersed antinematically. We show that the antinematic arrangement of the polymers generates a nonexponential molecular-weight distribution and stimulates the formation of oligomeric species. At sufficient concentrations the disks facilitate a liquid-liquid phase separation which can be brought into simultaneously coexistence with the two fractionated nematic phases, providing evidence for a four-fluid coexistence in reversible shape-dissimilar hard-core mixtures without cohesive interparticle forces. We stipulate the conditions under which such a phenomenon could be found in experiment.

Liquid crystal ordering of nucleic acids

Several analytical calculations and computer simulations propose that cylindrical monodispersive rods having an aspect ratio (ratio of length to diameter) greater than 4 can exhibit liquid crystal (LC) ordering. But, recent experiments demonstrated the signature of LC ordering in systems of 4- to 20-base pair (bp) long nucleic acids (NAs) that do not satisfy the shape anisotropy criterion. Mechanisms of end-to-end adhesion and stacking have been proposed to explain this phenomenon. In this study, using all-atom molecular dynamics (MD) simulation, we explicitly verify the end-to-end stacking of double-stranded RNA (dsRNA) and demonstrate the LC ordering at the microscopic level. Using umbrella sampling (US) calculation, we quantify the potential of mean force (PMF) between two dsRNAs for various reaction coordinates (RCs) and compare our results with previously reported PMFs for double-stranded DNA (dsDNA). The PMF profiles demonstrate the anisotropic nature of inter-NA interaction. We find that, like dsDNA, dsRNA also prefers to stack on top of each other while repelling sideways, leading to the formation of supra-molecular-columns that undergo LC ordering at high NA volume fraction (φ). We also demonstrate and quantify the nematic ordering of the RNAs using several hundred nanosecond-long MD simulations that remain almost invariant for different initial configurations and under different external physiological conditions.

Free energy of conformational isomers: The case of gapped DNA duplexes

Liquid-crystalline phases in all-DNA systems have been extensively studied in the past and although nematic, cholesteric and columnar mesophases have been observed, the smectic phase remained elusive. Recently, it has been found evidence of a smectic-A ordering in an all-DNA system, where the constituent particles, which are gapped DNA duplexes, resemble chain-sticks. It has been argued that in the smectic-A phase these DNA chain-sticks should be folded as a means to suppress aggregate polydispersity and excluded volume. Nevertheless, if initial crystalline configurations are prepared in silico with gapped DNA duplexes either fully unfolded or fully folded by carrying out computer simulations one can end up with two different phases having at the same concentration and temperature the majority of gapped DNA duplexes either folded or unfolded. This result suggests that these two phases have a small free energy difference, since no transition is observed from one to the other within the simulation time span. In the present manuscript, we assess which of these two phases is thermodynamically stable through a suitable protocol based on thermodynamic integration. Our method is rather general and it can be used to discriminate stable states from metastable ones of comparable free energy.

Nematic liquid crystals of bifunctional patchy spheres

Anisotropic interactions can bring about the formation, through self-assembly, of semi-flexible chains, which in turn can give rise to nematic phases for suitable temperatures and concentrations. A minimalist model constituted of hard cylinders decorated with attractive sites has been already extensively studied numerically. Simulation data shows that a theoretical approach recently proposed is able to properly capture the physical properties of these self-assembly-driven liquid crystals. Here, we investigated a simpler model constituted of bifunctional Kern-Frenkel hard spheres which does not possess steric anisotropy but which can undergo a istropic-nematic transition as a result of their self-assembly into semi-flexible chains. For this model we compare an accurate numerical estimate of isotropic-nematic phase boundaries with theoretical predictions. The theoretical treatment, originally proposed for cylinder-like particles, has been greatly simplified and its predictions are in good agreement with numerical results. Finally, we also assess a crucial, and not obvious, hypothesis used in the theory, i.e. the ability of the Onsager trial function to properly model particle orientation in the presence of aggregation, that has not been properly checked yet.

Backbone-free duplex-stacked monomer nucleic acids exhibiting Watson-Crick selectivity

The columnar liquid crystal phases reported here are physical associations of the smallest molecular species to self-assemble into the duplex base-paired stacked columnar double-helical structures of nucleic acids. These assemblies of monomers can provide starting states capable of partitioning appropriate molecules from solution with a high degree of selectivity, acting as pathways for the prebiotic appearance of molecular selection, self-assembly, and, ultimately, of the sequence-directed assembly of polymers.

We demonstrate that nucleic acid (NA) mononucleotide triphosphates (dNTPs and rNTPs), at sufficiently high concentration and low temperature in aqueous solution, can exhibit a phase transition in which chromonic columnar liquid crystal ordering spontaneously appears. Remarkably, this polymer-free state exhibits, in a self-assembly of NA monomers, the key structural elements of biological nucleic acids, including: long-ranged duplex stacking of base pairs, complementarity-dependent partitioning of molecules, and Watson–Crick selectivity, such that, among all solutions of adenosine, cytosine, guanine, and thymine NTPs and their binary mixtures, duplex columnar ordering is most stable in the A-T and C-G combinations.

How to simulate patchy particles⋆

Patchy particles is the name given to a large class of systems of mesoscopic particles characterized by a repulsive core and a discrete number of short-range and highly directional interaction sites. Numerical simulations have contributed significantly to our understanding of the behaviour of patchy particles, but, although simple in principle, advanced simulation techniques are often required to sample the low temperatures and long time-scales associated with their self-assembly behaviour. In this work we review the most popular simulation techniques that have been used to study patchy particles, with a special focus on Monte Carlo methods. We cover many of the tools required to simulate patchy systems, from interaction potentials to biased moves, cluster moves, and free-energy methods. The review is complemented by an educationally oriented Monte Carlo computer code that implements all the techniques described in the text to simulate a well-known tetrahedral patchy particle model.

Speeding up Monte Carlo simulation of patchy hard cylinders

The hard cylinder model decorated with attractive patches proved to be very useful recently in studying physical properties of several colloidal systems. Phase diagram, elastic constants and cholesteric properties obtained from computer simulations based on a simple hard cylinder model have been all successfully and quantitatively compared to experimental results. Key to these simulations is an efficient algorithm to check the overlap between hard cylinders. Here, we propose two algorithms to check the hard cylinder overlap and we assess their efficiency through a comparison with an existing method available in the literature and with the well-established algorithm for simulating hard spherocylinders. In addition, we discuss a couple of optimizations for performing computer simulations of patchy anisotropic particles and we estimate the speed-up which they can provide in the case of patchy hard cylinders.

Understanding the origin of liquid crystal ordering of ultrashort double-stranded DNA

Recent experiments have shown that short double-stranded DNA (dsDNA) fragments having six- to 20-base pairs exhibit various liquid crystalline phases. This violates the condition of minimum molecular shape anisotropy that analytical theories demand for liquid crystalline ordering. It has been hypothesized that the liquid crystalline ordering is the result of end-to-end stacking of dsDNA to form long supramolecular columns which satisfy the shape anisotropy criterion necessary for ordering. To probe the thermodynamic feasibility of this process, we perform molecular dynamics simulations on ultrashort (four base pair long) dsDNA fragments, quantify the strong end-to-end attraction between them, and demonstrate that the nematic ordering of the self-assembled stacked columns is retained for a large range of temperature and salt concentration.

Smectic phase in suspensions of gapped DNA duplexes

Smectic ordering in aqueous solutions of monodisperse stiff double-stranded DNA fragments is known not to occur, despite the fact that these systems exhibit both chiral nematic and columnar mesophases. Here, we show, unambiguously, that a smectic-A type of phase is formed by increasing the DNA's flexibility through the introduction of an unpaired single-stranded DNA spacer in the middle of each duplex. This is unusual for a lyotropic system, where flexibility typically destabilizes the smectic phase. We also report on simulations suggesting that the gapped duplexes (resembling chain-sticks) attain a folded conformation in the smectic layers, and argue that this layer structure, which we designate as smectic-fA phase, is thermodynamically stabilized by both entropic and energetic contributions to the system's free energy. Our results demonstrate that DNA as a building block offers an exquisitely tunable means to engineer a potentially rich assortment of lyotropic liquid crystals.

Hierarchical Propagation of Chirality through Reversible Polymerization: The Cholesteric Phase of DNA Oligomers

Unveiling the subtle rules that control the buildup of macroscopic chirality starting from chiral molecular elements is a challenge for theory and computations. In this context, a remarkable phenomenon is the formation of helically twisted nematic (cholesteric) phases, with pitch in the micrometer range, driven by self-assembly of relatively small chiral species into supramolecular semiflexible polymers. We have developed a theoretical framework to connect the cholesteric organization to the shape and chirality of the constituents, described with molecular detail, in this kind of system. The theory has been tested against new accurate measurements for solutions of short DNA duplexes. We show that the cholesteric organization is determined by steric repulsion between duplexes, and we identify distinctive features of linear self-assembly in the temperature and concentration dependence of the pitch.

Nematic phase characterisation of the self-assembling sphere-cylinders based on the theoretically calculated RDFs

We put forward a theoretical framework to calculate pair distribution functions in the nematic liquid crystals formed by sphere-cylinders that self-assemble in linear chain structures. For a nematically ordered system, one can distinguish between the spatial correlations in the plane perpendicular to the crystalline axis, and in the direction parallel to the latter. Following this separation, we show that the RDFs in the parallel case can be described using a superposition of a chain model and Onsager distribution, whereas the RDFs in the perpendicular case turn out to be that of the soft disks. Based on this concept, we show how the spatial correlations in the system are influenced by the nematic order parameter. We conclude that even if the nematic ordering is high in the system, the imperfection of the crystal is strongly reflected in the pair distributions.

Self-assembly of mesogenic bent-core DNA nanoduplexes

Short cylinder-like DNA duplexes, comprising 6 to 20 base pairs, self-assemble into semi-flexible chains, due to coaxial stacking interactions between their blunt ends. The mutual alignment of these chains gives rise to macroscopically orientationally ordered liquid crystal phases. Interestingly, experiments show that the isotropic-nematic phase boundary is sequence-dependent. We perform all-atom simulations of several sequences to gain insights into the structural properties of the duplex and correlate the resulting geometric properties with the observed location of the isotropic-nematic phase boundary. We identify in the duplex bending the key parameter for explaining the sequence dependence, suggesting that DNA duplexes can be assimilated to bent-core mesogens. We also develop a coarse-grained model for the different DNA duplexes to evaluate in detail how bending affects the persistence length and excluded volume of the aggregates. This information is fed into a recently developed formalism to predict the isotropic-nematic phase boundary for bent-core mesogens. The theoretical results agree with the experimental observations.