Left or right cholesterics? A matter of helix handedness and curliness

We have investigated the relationship between the morphology of helical particles and the features of the cholesteric (N$^\ast$) phase that they form. Using an Onsager-like theory, applied to systems of hard helices, we show that the cholesteric handedness and pitch depend on both the pitch and the curliness of the particles. The theory leads to the definition of pseudoscalars that correlate the helical features of the phase to the chirality of the excluded volume of the constituent particles

Cholesteric and screw-like nematic phases in systems of helical particles

Recent numerical simulations of hard helical particle systems unveiled the existence of a novel chiral nematic phase, termed screw-like, characterised by the helical organization of the particle C2 symmetry axes round the nematic director with periodicity equal to the particle pitch. This phase forms at high density and can follow a less dense uniform nematic phase, with relative occurrence of the two phases depending on the helix morphology. Since these numerical simulations were conducted under three-dimensional periodic boundary conditions, two questions could remain open. First, the real nature of the lower density nematic phase, expected to be cholesteric. Second, the influence that the latter, once allowed to form, may have on the existence and stability of the screw-like nematic phase. To address these questions, we have performed Monte Carlo and molecular dynamics numerical simulations of helical particle systems confined between two parallel repulsive walls. We have found that the removal of the periodicity constraint along one direction allows a relatively-long-pitch cholesteric phase to form, in lieu of the uniform nematic phase, with helical axis perpendicular to the walls while the existence and stability of the screw-like nematic phase are not appreciably affected by this change of boundary conditions

From rods to helices: evidence of a screw-like nematic phase

Evidence of a special chiral nematic phase is provided using numerical simulation and Onsager theory for systems of hard helical particles. This phase appears at the high density end of the nematic phase, when helices are well aligned, and is characterized by the C$_2$ symmetry axes of the helices spiraling around the nematic director with periodicity equal to the particle pitch. This coupling between translational and rotational degrees of freedom allows a more efficient packing and hence an increase of translational entropy. Suitable order parameters and correlation functions are introduced to identify this screw-like phase, whose main features are then studied as a function of radius and pitch of the helical particles. Our study highlights the physical mechanism underlying a similar ordering observed in colloidal helical flagella [E. Barry et al. \textit{Phys. Rev. Lett.} \textbf{96}, 018305 (2006)] and raises the question of whether it could be observed in other helical particle systems, such as DNA, at sufficiently high densities.Comment: List of authors correcte

Hybrid Particle-Field Molecular Dynamics Under Constant Pressure

Hybrid particle-field methods are computationally efficient approaches for modelling soft matter systems. So far applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field interactions to represent systems coupled to constant external pressure. First, we show that the commonly used particle-field energy functional can be modified to model and parameterize the isotropic contributions to the pressure tensor without interfering with the microscopic forces on the particles. Second, we employ a square gradient particle-field interaction term to model non-isotropic contributions to the pressure tensor, such as in surface tension phenomena. This formulation is implemented within the hybrid particle-field molecular dynamics approach and is tested on a series of model systems. Simulations of a homogeneous water box demonstrate that it is possible to parameterize the equation of state to reproduce any target density for a given external pressure. Moreover, the same parameterization is transferable to systems of similar coarse-grained mapping resolution. Finally, we evaluate the feasibility of the proposed approach on coarse-grained models of phospholipids, finding that the term between water and the lipid hydrocarbon tails is alone sufficient to reproduce the experimental area per lipid in constant-pressure simulations, and to produce a qualitatively correct lateral pressure profile.Comment: 24 pages, 7 figure

Unconventional Liquid Crystal Phases of Helical Particles

Helical particles are ubiquitous in nature. Many natural and synthetic biomolecules like polynucleotides and polypeptides; colloidal suspensions like filamentous (fd) virus and helical flagella and certain organic molecules are found in helical shape. Despite their abundance in nature, understanding of the phase behaviour of helical particles is poor. These helical molecules have a well known propensity to form liquid crystal phases. The chirality in the helical shapes influence their liquid crystal organization. Experimental results of the liquid crystal phases shown by these molecules are often compared to those of rods, neglecting the effect of helical shape on phase behaviour. We have undertaken an extensive investigation of the phase diagram of hard helical particles using Monte Carlo simulations. We provide evidence of new chiral phases exhibiting screw-like order. This new chiral phase is different to the cholesteric phase and is characterized by the C2 symmetry axes of helices spiralling around the nematic director with periodicity equal to the particle pitch. We have used Isobaric Monte Carlo simulations to obtain a full phase diagram of helical particles. A rich polymorphism is observed exhibiting a special screw-like nematic and a number of screw-like smectic phases. The effect of helical shape on the phase diagram is studied by considering different shapes of helix obtained by tuning the helical parameters like radius and pitch. We found a remarkable change in the phase behaviour with the change in the shape of helix. Dense packing structures of different helical shapes are found by implementing Isopointal set Structural Search Method (ISSM). The physical mechanism underlying the liquid crystal order observed in helical flagella is explained. Finally, some results are shown discussing the relation between the pitch and the handedness of cholesteric phase and the shape of the helix

Chiral self-assembly of helical particles

The shape of the building blocks plays a crucial role in directing self-assembly towards desired architectures. Out of the many different shapes, the helix has a unique position. Helical structures are ubiquitous in nature and a helical shape is exhibited by the most important biopolymers like polynucleotides, polypeptides and polysaccharides as well as by cellular organelles like flagella. Helical particles can self-assemble into chiral superstructures, which may have a variety of applications, e.g. as photonic (meta)materials. However, a clear and definite understanding of these structures has not been entirely achieved yet. We have recently undertaken an extensive investigation on the phase behaviour of hard helical particles, using numerical simulations and classical density functional theory. Here we present a detailed study of the phase diagram of hard helices as a function of their morphology. This includes a variety of liquid-crystal phases, with different degrees of orientational and positional ordering. We show how, by tuning the helix parameters, it is possible to control the organization of the system. Starting from slender helices, whose phase behaviour is similar to that of rodlike particles, an increase in curliness leads to the onset of azimuthal correlations between the particles and the formation of phases specific to helices. These phases feature a new kind of screw order, of which there is experimental evidence in colloidal suspensions of helical flagella.G. C. thanks the Government of Spain for the award of a Ramón y Cajal research fellowship and the financial support under the grant FIS2013-47350-C5-1-R. This work was also supported by MIUR PRIN-COFIN2010-2011 (contract 2010LKE4CC)

Chiral self-assembly of helical particles

The shape of the building blocks plays a crucial role in directing self-assembly towards desired architectures. Out of the many different shapes, the helix has a unique position. Helical structures are ubiquitous in nature and a helical shape is exhibited by the most important biopolymers like polynucleotides, polypeptides and polysaccharides as well as by cellular organelles like flagella. Helical particles can self-assemble into chiral superstructures, which may have a variety of applications, e.g. as photonic (meta)materials. However, a clear and definite understanding of these structures has not been entirely achieved yet. We have recently undertaken an extensive investigation on the phase behaviour of hard helical particles, using numerical simulations and classical density functional theory. Here we present a detailed study of the phase diagram of hard helices as a function of their morphology. This includes a variety of liquid-crystal phases, with different degrees of orientational and positional ordering. We show how, by tuning the helix parameters, it is possible to control the organization of the system. Starting from slender helices, whose phase behaviour is similar to that of rodlike particles, an increase in curliness leads to the onset of azimuthal correlations between the particles and the formation of phases specific to helices. These phases feature a new kind of screw order, of which there is experimental evidence in colloidal suspensions of helical flagella

Self-Assembly of α-Tocopherol Transfer Protein Nanoparticles – a Patchy-Protein Model

We describe the mechanism of self-aggregation of α-tocopherol transfer protein into a spherical nano-cage employing by Monte Carlo simulations. The protein is modelled by a patchy coarse-grained representation, where the protein-protein interfaces, determined in the past by x-ray diffraction, are represented by simplified two-body interaction potentials. Our results show that the oligomerization kinetics proceeds in two steps, with the formation of meta-stable trimeric units, and the subsequent assembly into the spherical aggregates. Data are in agreement with experimental observations regarding the prevalence of different aggregation states at specific ambient conditions. Finally, our results indicate a route for the experimental stabilization of the trimer, crucial for the understanding of the physiological role of such aggregates in vitamin E body trafficking.</p

Self-assembly of alpha-tocopherol transfer protein nanoparticles: a patchy-protein model

We describe the mechanism of self-aggregation of α-tocopherol transfer protein into a spherical nanocage employing Monte Carlo simulations. The protein is modeled by a patchy coarse-grained representation, where the protein–protein interfaces, determined in the past by X-ray diffraction, are represented by simplified two-body interaction potentials. Our results show that the oligomerization kinetics proceeds in two steps, with the formation of metastable trimeric units and the subsequent assembly into the spherical aggregates. Data are in agreement with experimental observations regarding the prevalence of different aggregation states at specific ambient conditions. Finally, our results indicate a route for the experimental stabilization of the trimer, crucial for the understanding of the physiological role of such aggregates in vitamin E body trafficking