Hard Spherocylinders Research Articles

Dimerizing hard spherocylinders in porous media

This research focuses on the unique phase behavior of non-spherical patchy colloids in porous environments. Based on the theory of scaled particle (SPT), methods have been refined and applied to analyze the thermodynamic properties of non-spherical patchy particles in a disordered porous medium. Utilizing the associative theory of liquids in conjunction with SPT, we investigated the impact of associative interactions and connections between the functional nodes of particles on the formation of the nematic phase. Calculations of orientational and spatial distributions were conducted, which helped to understand the phase behavior of particles during the transition from isotropic to nematic phase under the spatial constraints imposed by the disordered matrix of the porous medium.

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.

Equation of State of Charged Rod Dispersions.

We study the accuracy of the theory of Stroobants, Lekkerkerker, and Odijk [Macromolecules 1986, 19, 2232-2238], called SLO theory, to describe the thermodynamic properties of an isotropic fluid of charged rods. By incorporation of the effective diameter of the rods according to SLO theory into scaled particle theory (SPT), we obtain an expression for the rod concentration-dependent free volume fraction and the osmotic pressure of a collection of charged hard spherocylinders. The results are compared to Monte Carlo simulations. We find close agreement between the simulation results and the SLO-SPT predictions for not too large values of the Debye length and for high rod charge densities. The deviations increase with rod density, particularly at concentrations above which isotropic-nematic phase transitions are expected.

Dense Disordered Jammed Packings of Hard Spherocylinders with a Low Aspect Ratio: A Characterization of Their Structure.

This work numerically investigates dense disordered (maximally random) jammed packings of hard spherocylinders of cylinder length L and diameter D by focusing on L/D ∈ [0,2]. It is within this interval that one expects that the packing fraction of these dense disordered jammed packings ϕMRJhsc attains a maximum. This work confirms the form of the graph ϕMRJhsc versus L/D: here, comparably to certain previous investigations, it is found that the maximal ϕMRJhsc = 0.721 ± 0.001 occurs at L/D = 0.45 ± 0.05. Furthermore, this work meticulously characterizes the structure of these dense disordered jammed packings via the special pair-correlation function of the interparticle distance scaled by the contact distance and the ensuing analysis of the statistics of the hard spherocylinders in contact: here, distinctly from all previous investigations, it is found that the dense disordered jammed packings of hard spherocylinders with 0.45 ≲ L/D ≤ 2 are isostatic.

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.

Thermodynamic perturbation theory coefficients for hard spherocylinders and cylinders

Thermodynamic perturbation theories are indispensable in the development of equations of state based on Statistical Mechanics. Recently, a new statistical thermodynamic model has been proposed in which molecules are represented as cylindrically symmetric hard bodies (ellipsoids of revolution, spherocylinders, and cylinders) interacting with identical neighboring molecules through a spherically symmetric square-well potential. This novel equation of state embeds at least two approximations to the Onsager’s second virial theory: one restrains the equation of state to systems with an isotropic (disordered) orientation distribution, while the other decouples the translational and orientational degrees of freedom, being only valid at low densities. Using canonical Monte Carlo simulations, we investigated the feasibility of such approximations by determining the uniaxial nematic order parameter of the systems and calculating the first- and second-order perturbation coefficients of the high-temperature series expansion (HTSE) of the Helmholtz free energy. Our results indicate that both approximations are reasonable for a certain range of packing fractions and molecular anisotropies. We have also calculated the full Helmholtz free energy of the perturbed system, which can be used for determining high-order perturbation terms to improve the predictive capability of the equation of state.

Fluid-fluid phase behaviour in the explicit hard spherocylinder solvent ionic model confined in a disordered porous medium

We propose a theoretical approach that takes into account the effects of a disordered porous confinement on the liquid–liquid phase behavior of the ionic solution modelled by the restricted primitive model with an explicit consideration of the neutral hard spherocylinder solvent. The theory is based on a combination of two approaches: the scale particle theory for the description of the reference system represented by a mixture of hard spheres and hard spherocylinders confined in a disordered hard-sphere matrix and the associative mean-spherical approximation for taking into account Coulomb interactions between ions. Alternatively, the mean spherical approximation is applied for the description of the ionic subsystem for comparison. For the considered solvent explicit model in a matrix, analytical expressions for pressure, free energy and partial chemical potentials are derived for the first time. Using these expressions, the liquid–liquid phase transition is studied, where one phase is enriched with ions and another one – with solvent particles. In the solvent-rich phase, the isotropic-nematic phase transition is observed due to the orientational ordering of the spherocylinder solvent particles at different porosities of a matrix. The effects of the matrix confinement and of the solvent particle elongation on the liquid–liquid and isotropic-nematric phase transitions are studied at different pressures. The role of association phenomena appearing between positively and negatively charged ions in phase behavior of the considered ionic solutions under confinement is discussed.

Multiphase Coexistences in Rod-Polymer Mixtures.

Using recently derived analytical equations of state for hard rod dispersions, we predict the phase behavior of athermal rod–polymer mixtures with free volume theory. The rods are modeled as hard spherocylinders, while the nonadsorbing polymer chains are described as penetrable hard spheres. It is demonstrated that all of the different types of phase states that are stable for pure colloidal rod dispersions can coexist with any combination of these phases if polymers are added, depending on the concentrations, rod aspect ratio, and polymer–rod size ratio. This includes novel two-, three-, and four-phase coexistences and isostructural coexistences between dilute and concentrated phases of the same kind, even for the more ordered (liquid) crystal phases. This work provides insight into the conditions at which particular multiphase coexistences are expected for well-defined model colloidal rod–polymer mixtures. We provide a quantitative map detailing the various types of isostructural coexistences, which confirms an early qualitative hypothesis by Bolhuis et al. (J. Chem. Phys.107, 19971551).

Protein-polymer mixtures in the colloid limit: Aggregation, sedimentation, and crystallization.

While proteins have been treated as particles with a spherically symmetric interaction, of course in reality, the situation is rather more complex. A simple step toward higher complexity is to treat the proteins as non-spherical particles and that is the approach we pursue here. We investigate the phase behavior of the enhanced green fluorescent protein (eGFP) under the addition of a non-adsorbing polymer, polyethylene glycol. From small angle x-ray scattering, we infer that the eGFP undergoes dimerization and we treat the dimers as spherocylinders with aspect ratio L/D - 1 = 1.05. Despite the complex nature of the proteins, we find that the phase behavior is similar to that of hard spherocylinders with an ideal polymer depletant, exhibiting aggregation and, in a small region of the phase diagram, crystallization. By comparing our measurements of the onset of aggregation with predictions for hard colloids and ideal polymers [S. V. Savenko and M. Dijkstra, J. Chem. Phys. 124, 234902 (2006) and Lo Verso et al., Phys. Rev. E 73, 061407 (2006)], we find good agreement, which suggests that the behavior of the eGFP is consistent with that of hard spherocylinders and ideal polymers.

Phase separation in mixed suspensions of bacteria and nonadsorbing polymers.

The shapes of bacteria can vary widely; they may, for instance, be spherical, rod-like, string-like, or curved. In general, bacilli are highly anisotropic. For research and (bio)technological purposes, it can be useful to concentrate bacteria, which is possible by adding nonadsorbing polymers. The induced phase separation originates from a polymer-mediated depletion interaction, first understood by Asakura and Oosawa. Here, it is shown that free volume theory (FVT) can semi-quantitatively describe the phase transitions observed when adding sodium polystyrene sulfonate polymers to E. coli bacteria [Schwarz-Linek et al., Soft Matter 6, 4540 (2010)] at high ionic strength. The E. coli bacteria are described as short, hard spherocylinders. FVT predicts that the phase transitions of the mixtures result from a fluid-ABC crystal solid phase coexistence of a hard spherocylinder-polymer mixture.

Rheology and structure of suspensions of spherocylinders via Brownian dynamics simulations

Brownian dynamics simulations were employed to investigate the rheological properties and structure of suspensions of rigid spherocylinders, as a model for rodlike colloids. The spherocylinders interacted only through a soft repulsive force that mimicked a hard spherocylinder interaction. The translational and rotational diffusivities of hard spherocylinder suspensions were reproduced. Liquid crystalline phases, including isotropic, nematic, and smectic and solid phases were identified using orientational and hexatic order parameters and pair distribution functions. Typical flow curves observed experimentally for rodlike colloidal suspensions were reproduced in the simulations, with two shear thinning regions that bracketed a viscosity plateau at intermediate Péclet numbers. The transient rheology and structure of suspensions that were nematic at rest exhibited a variety of behaviors that depended on the Péclet number and concentration. Systemwide domains that aligned in and kayaked about the vorticity direction, domains that rotated coherently locally, and layered domains were observed. Oscillations in the order parameter, viscosity, and the first and second normal stress differences were associated with changes in the structure.

Algebraic equations of state for the liquid crystalline phase behavior of hard rods.

Based on simplifications of previous numerical calculations [H. Graf and H. Löwen, Phys. Rev. E 59, 1932 (1999)1063-651X10.1103/PhysRevE.59.1932], we propose algebraic free energy expressions for the smectic-A liquid crystal phase and the crystal phases of hard spherocylinders. Quantitative agreement with simulations is found for the resulting equations of state. The free energy expressions can be used to straightforwardly compute the full phase behavior for all aspect ratios and to provide a suitable benchmark for exploring how attractive interrod interactions mediate the phase stability through perturbation approaches such as free-volume or van der Waals theory.

Ordering, clustering, and wetting of hard rods in extreme confinement

This work builds the phase diagrams of hard spherocylinders for aspect ratios of 8, 10 and 16 in the quasi-two-dimensional regime. The fact that these phase diagrams share similar characteristics allows for the construction of a master phase diagram. Besides delimiting the isotropic, nematic, and solid phases, particular attention is paid to the wetting behavior of the particles on the confining walls.

On generalization of Van der Waals approach for isotropic-nematic fluid phase equilibria of anisotropic fluids in disordered porous medium

A generalized Van der Waals approach is developed for anisotropic fluids in disordered porous media. As the reference system a hard spherocylinder fluid in a disordered porous medium is considered and described in the framework of the scaled particle theory with the Carnahan-Starling and Parsons-Lee corrections. The attractive part of interaction is treated in the framework of the mean field approximation in which due to orientational dependence of the excluded volume of two spherocylinders, a coupling between attractive and repulsive contributions is found. We focus on spherocylinder fluids with sufficiently long particle lengths for which the nematic-nematic transition was established. It is shown that these two nematic phases have different densities and are characterized by different orientational ordering. Strong influence of the type of interparticle attraction on the phase behaviour of anisotropic fluids in disordered porous media is established. Three simple models for this purpose are considered, namely a model with the Lennard-Jones anisotropic attraction, a model with modified Lennard-Jones attraction and a model with anisotropic square-well potential. For all considered models, the phase diagram shifts to the region of lower densities and lower temperatures as the porosity decreases.

Critical properties of binary mixtures of hydrocarbons for linear hard sphere models of molecules based on ISPT, Nezbeda and Boublik equations of state, and the chain equation of state of R J Sadus

The predicted results of virial coefficients from different equations of state of hard body fluids such as linearly tangent hard spheres, hard ellipsoidals or hard spherocylinders have been used to calculate the values of nonsphericity factor and the van der Waals parameters. The parameters of these equations of state testify the predicted critical properties satisfactorily. The improved accuracy of the predicted results has been observed by incorporating the chain concept with the shape of the molecules of binary mixtures of hydrocarbons.

Biaxial, Twist-bend, and Splay-bend Nematic Phases of Banana-shaped Particles Revealed by Lifting the “Smectic Blanket”

We perform an extensive computational study on the phase behavior of hard banana-shaped particles, and show that biaxial, twist-bend, and splay-bend nematic phases are metastable with respect to a smectic phase for a system of hard bent spherocylinders. However, if the smectic phase is destabilized-either by polydispersity in the particle length or by curvature in the particle shape-stable biaxial, twist-bend, and splay-bend nematic phases are obtained. This provides a unified and consistent picture on the subtle role of particle shape on the phase behavior of bent rods.

Phase behavior of hard C_{2h}-symmetric particle systems.

Using Monte Carlo numerical simulation, this work sketches the phase diagram of systems of certain hard C_{2h}-symmetric particles, formed by gluing two aligned and displaced hard spherocylinders with a cylindrical-length-to-diameter ratio realistically, if viewed not only from the lyotropic colloidal liquid-crystal side but also from the thermotropic low-molecular-mass liquid-crystal side, equal to 5, as a function of the displacement. Several distinctive phases are observed, such as a nonperiodic smectic-B-like phase, a nonperiodic smectic-H-like phase, a smectic-C phase, and a short-layer-spacing uniaxial smectic-A phase but no biaxial nematic phase.

Fluid-fluid phase behaviour in the explicit solvent ionic model: Hard spherocylinder solvent molecules

We study a fluid-fluid phase transition of the explicit solvent model represented as a mixture of the restricted primitive model (RPM) of ionic fluid and neutral hard spherocylinders (HSC). To this end, we combine two theoretical approaches, i.e., the scale particle theory (SPT) and the associative mean spherical approximation (AMSA). Whereas the SPT is sufficient to provide a rather good description of a reference system taking into account hard-core interactions, the AMSA is known to be efficient in treating the Coulomb interactions between the ions. Alternatively, we also use the mean spherical approximation (MSA) for comparison. We restrict our attention to the HSC with aspect ratios L2/σ2 = 5 and 10, when the diameter of RPM particles is set to σ1 = σ2. We find the conditions at which the fluid-fluid phase transition is accompanied by the isotropic-nematic phase transition occurring in the solvent component. Furthermore, the effect of asphericity of solvent molecules on the fluid-fluid phase transition is studied by considering an “equivalent” mixture in which the HSC particles are replaced by hard spheres (HS) of the same volume. We discuss an importance of accounting for the association effects which appear between oppositely charged ions.

Simulation study of the electrical tunneling network conductivity of suspensions of hard spherocylinders

Using Monte Carlo simulations, we investigate the electrical conductivity of networks of hard rods as a function of the volume fraction for two tunneling conductance models. For a simple, orientationally independent tunneling model, we observe non-monotonic behaviour of the bulk conductivity as a function of volume fraction at the isotropic-nematic transition. However, this effect is lost if one allows for anisotropic tunneling. We also compute the mesh number of the Kirchhoff network, which turns out to be a simple alternative to the computationally expensive conductivity of large systems in order to get a qualitative estimate.

Isotropic-nematic transition of self-propelled rods in three dimensions.

Using overdamped Brownian dynamics simulations we investigate the isotropic-nematic (IN) transition of self-propelled rods in three spatial dimensions. For two well-known model systems (Gay-Berne potential and hard spherocylinders) we find that turning on activity moves to higher densities the phase boundary separating an isotropic phase from a (nonpolar) nematic phase. This active IN phase boundary is distinct from the boundary between isotropic and polar-cluster states previously reported in two-dimensional simulation studies and, unlike the latter, is not sensitive to the system size. We thus identify a generic feature of anisotropic active particles in three dimensions.