Phase diagram of hard colloidal platelets: a theoretical account

We construct the complete liquid crystal phase diagram of hard plate-like cylinders for variable aspect ratio using Onsager's second virial theory and employing the Parsons–Lee decoupling approximation to account for higher-body interactions in the isotropic and nematic fluid phases. The stability of the solid (columnar) state at high packing fraction is included by invoking a simple equation of state based on a Lennard–Jones–Devonshire cell model which has proven to be quantitatively reliable over a large range of packing fractions. By employing an asymptotic analysis based on the Gaussian approximation we are able to show that the nematic–columnar transition is universal and independent of particle shape. The predicted phase diagram is in qualitative agreement with simulation results.     

Demixing and nematic behaviour of oblate hard spherocylinders and hard spheres mixtures: Monte Carlo simulation and Parsons–Lee theory

Parsons–Lee approach is formulated for the isotropic–nematic transition in a binary mixture of oblate hard spherocylinders and hard spheres. Results for the phase coexistence and for the equation of state in both phases for fluids with different relative size and composition ranges are presented. The predicted behaviour is in agreement with Monte Carlo simulations in a qualitative fashion. The study serves to provide a rational view of how to control key aspects of the behaviour of these binary nematogenic colloidal systems. This behaviour can be tuned with an appropriate choice of the relative size and molar fractions of the depleting particles. In general, the mixture of discotic and spherical particles is stable against demixing up to very high packing fractions. We explore in detail the narrow geometrical range where demixing is predicted to be possible in the isotropic phase. The influence of molecular crowding effects on the stability of the mixture when spherical molecules are added to a system of discotic colloids is also studied.     

Demixed and ordered phases in hard-rod mixtures

We analyse demixing and ordering transitions in systems of hard cylindrical particles. The second virial approximation of Onsager and a bifurcation analysis, as introduced by Koda and Kimura, are used to evaluate the free energies, pressures, and density distribution functions in mixtures of equally long but differently wide cylinders. The spatial density distribution along the one relevant coordinate is of particular importance as it provides more detailed information concerning the nature of the phase transition than the bare bifurcation diagnosis. Detailed results are given for the nematic–nematic spinodal and the nematic–smectic transitions. Allowing for the absence of an isotropic phase, our results are in good qualitative agreement with those for freely orienting rods reported previously, and indicate a complex sequence of phase diagrams as the diameter dissimilarity of the two components is increased, with upper and lower critical points bounding nematic and smectic demixing regions. However, experimental results on colloidal rods show that nematic demixing occurs at a diameter ratio much smaller than ours or those for freely rotating fluids, indicating that Onsager-type theories may be insufficient to reproduce this phenomenon in a quantitative manner and, consequently, that more sophisticated approaches, presumably incorporating particle flexibility and additional interactions, are required.     

The Effect of Sphere Size on the Phase Behaviors in the Rod and Sphere Mixture System

The addition of polysaccharides, such as chondroitin sulfate (Chs), to the aqueous suspension of tobacco mosaic virus (TMV) results in the TMV aggregation at very dilute TMV concentration compared with the addition of polyethylene oxide (PEO). The Chs chain has a semirigid nature, whereas the PEO has a flexible nature. In this study, we investigated the effect of the size of spherical polymer coils on the phase behaviors in the mixtures of rods and spheres using Monte Carlo simulations. As a model for TMV, we used the spherocylinder particle. The Chs and PEO chains were simplified to spherical particles having different sizes. With the addition of large spherical particles, the system changed from miscible phase to isotropic–isotropic phase separation and then isotropic–nematic phase separation states, whereas with the addition of small spherical particles, the system transformed from miscible isotropic phase to miscible nematic phase. We found that the sphere size had an important influence on the phase behaviors in the mixtures of rods and spheres.     

External field induced tricritical phenomenon in the isotropicnematic phase transition of hard non-spherical particle systems

The effect of static external field is studied on the isotropic–nematic phase transition of a system of hard non-spherical particles (rods or platelets) with negative anisotropic polarizability (susceptabilities). On the basis of Onsager theory, the phase coexistence curve is calculated numerically without any approximation. It is found that a weakly ordered nematic phase (uniaxial planar) is in coexistence with a highly ordered biaxial nematic phase which ends at a tricritical point. In the limit of infinite field strength, the orientations of the particles are confined in a plane perpendicular to the field and continuous isotropic–nematic phase transition takes place.     

Molar volume for mixtures of methane with krypton,argon, ethane and carbon monoxide using the ISM equation of state

In this paper, an analytical equation of state (EoS) proposed by Ihm–Song–Mason (ISM) was employed to calculate the molar volume of mixtures of methane with krypton, argon, ethane and carbon monoxide. The best available pair interaction potential energy has been used to evaluate the second virial coefficients required by the ISM EoS. The calculated values of second virial coefficients were applied to the ISM EOS to predict the molar volumes for the above mentioned mixtures. Agreement with the experiment is excellent for all systems.     

The equation of state of a system of hard spherocylinders

Using the Monte Carlo method, we have computed the equation of state of a system of hard spherocylinders (cylinders with a hemisphere at each end), of length-to-breadth ratio equal to 3, in the isotropic liquid phase. We obtain a pressure slightly smaller than that predicted by the scaled-particle theory (SPT). The SPT predicts a liquid to nematic transition when the density is increased; we have observed that the isotropic liquid phase is stable up to densities significantly higher than the SPT transition density. Using the free-volume theory, we have also determined the behaviour of the pressure at very high densities, for any value of the length-to-breadth ratio γ. Moreover, we have shown that the packing fraction (number density times the volume of one spherocylinder) corresponding to the beginning of the fusion of the solid is an increasing function of γ.     

Square-well fluid based decoupling approximation for system of hard non-spherical particles with spherical square-wells

A new theory based on the virial equation has been developed to study a system of hard non-spherical particles embedded into square-wells. The theory relies on a mapping of the pair correlation function of the system of interest onto that of spherical square-wells. This is a generalization of the Parsons—Lee theory of pure hard convex bodies. Comparisons show that this theory is superior to previous theories and incorporates them into a common framework. Competition between the excluded volume effect of repulsive forces and the condensation effect of attractive forces has been demonstrated. We have found three types of phase diagrams, among which one exhibits a nematic—nematic phase transition.     

A new method to obtain the Carnahan–Starling equation and its generalization

We obtain the Carnahan–Starling equation for a system of hard spheres using the Euler method of accelerated series convergence. For this purpose, the virial series is transformed into a new series with coefficients that differ slightly from each other, even when considering the eleven currently known virial coefficients. The method of accelerated convergence was applied to this series; it allowed us to obtain the Carnahan–Starling equation. In this work, this equation is derived for the first time using the method of accelerated convergence. It is generalized to accurately reproduce all of the known virial coefficients and the asymptotic behavior of the free energy at high densities. This also makes it possible to describe a metastable region with a high degree of accuracy and to obtain the equation of state for a homogeneous system of hard spheres with the accuracy of a computer experiment.     

Critical properties of non-spherical molecule fluids from the virial expansion

Critical constants of pure fluids (as important reference data in constructing vapour-liquid phase diagrams and basic input of various estimation methods) were determined for systems of non-spherical Kihara molecules; values of the critical temperature, density, compression factor and pressure of fluids composed of prolate and oblate molecules were evaluated from the fourth-order virial expansion. The second and third virial coefficients of the Kihara molecules were determined by applying the recently proposed method in which the effect of molecular core geometry and functional dependence of a pair interaction on the surface-surface distance are factorized and the former contribution determined from a formula for the corresponding hard convex body virial coefficient. The virial expansion for non-spherical Kihara molecules is applied to determine the critical constants of n-alkanes (methane to octane) and cyclic hydrocarbons (cyclopentane, cyclohexane, benzene and naphthalene); a fair agreement with experimental data was found.     

Depletion-induced biaxial nematic states of boardlike particles

With the aim of investigating the stability conditions of biaxial nematic liquid crystals, we study the effect of adding a non-adsorbing ideal depletant on the phase behavior of colloidal hard boardlike particles. We take into account the presence of the depletant by introducing an effective depletion attraction between a pair of boardlike particles. At fixed depletant fugacity, the stable liquid-crystal phase is determined through a mean-field theory with restricted orientations. Interestingly, we predict that for slightly elongated boardlike particles a critical depletant density exists, where the system undergoes a direct transition from an isotropic liquid to a biaxial nematic phase. As a consequence, by tuning the depletant density, an easy experimental control parameter, one can stabilize states of high biaxial nematic order even when these states are unstable for pure systems of boardlike particles.     

An equation of state for hard convex body chains

The thermodynamic perturbation theory of hard sphere chains is generalized to derive an equation of state for hard convex body chains. The hard convex body chain equation of state contains two parameters that are related directly and rigorously to the geometry of the hard convex body. The compressibility factors and second virial coefficients of chains composed of prolate spherocylinders, oblate spherocylinders and doublecones are calculated and compared with hard sphere chain calculations. The comparison indicates that the nature of the hard convex body has a profound influence on the properties of the chain.     

Detecting columnar deformations in a supermesogenic octapode by proton NMR relaxometry

We used proton ( ¹H nuclear magnetic relaxation (NMR) dispersions to study the molecular dynamics in the isotropic phase and mesophases (nematic and columnar hexagonal) of a supermesogenic octapode formed by laterally connecting calamitic mesogens to an inorganic silsesquioxane cube through flexible spacers. The dispersions of the spin-lattice relaxation time (T₁) are interpreted through relaxation mechanisms used for the study of molecular dynamics in low-molar-mass liquid crystals but adapted to the case of liquid crystalline supermolecules. At high frequencies (above 10MHz) the behaviour of the T₁ with the Larmor frequency is similar for all phases and is ascribed to local reorientations and/or rotations. At intermediate and low frequencies (below 10MHz) our results show notable differences in the T₁ behaviour with respect to the mesophases. The nematic (N) and isotropic (Iso) phases’ low-frequency results are similar and are interpreted for both phases in terms of order director fluctuations (ODF), revealing that even in the isotropic phase local nematic order is detected by proton NMR relaxometry. Local nematic order in the Iso phase is interpreted in terms of the presence of nematic cybotactic clusters induced by the interdigitation of mesogens that is promoted by the silsesquioxane octapode molecular structure. In the columnar hexagonal (Col _h phase, the T₁ dispersions show that elastic columnar deformations (ECD) dominate the nuclear magnetic relaxation below 10MHz. This result shows that the columnar packing of the octapode clearly restricts the collective fluctuations of the mesogenic units inspite of their local nematic order.     

Charge ordering induces a smectic phase in oblate ionic liquid crystals

We report a computer simulation study of an electroneutral mixture of oppositely charged oblate ellipsoids of revolution with aspect ratio A=1/3. In contrast with hard or soft repulsive ellipsoids, which are purely nematic, this system exhibits a smectic-A phase in which charges of equal sign are counterintuitively packed in layers perpendicular to the nematic director.     

Hard body fluids again: Virial coefficients and equations of state

The table of the virial coefficientsB ₂ throughB ₄ of all hard body fluid models considered so far has been completed by calculating the missing coefficients. Applicability of these coefficients to predicting the thermodynamic behaviour of dense hard body fluids is assessed and certain discrepancies in the data for oblate spherocylinders are found. It is shown that by combining the Padé approximant with an appropriate analytic expression an accurate 3-parameter equation of state results.     

Systems of oblate molecules. Monte Carlo study

Monte Carlo (MC) simulations were performed for systems of hard oblate spherocylinders with breadth-to-height ratios φ = 0.5–3.5 and packing fractions y = 0.25–0.45 and for Kihara oblate molecule systems of φ = 1 at reduced temperatures T* = 0.75 and 1.0 and y = 0.05–0.45. The compression factors and the dependence of the average correlation functions on the shortest surface-to-surface distance were determined for the case of hard oblate spherocylinders and the compression factors, residual internal energies and average correlation functions for the case of the generalized Kihara molecule systems. In addition, values of the third virial coefficient of the hard oblate spherocylinders were evaluated in the range of φ = 1–3. Results of the MC simulations for the hard oblate spherocylinders compare well with the available data in the literature and theoretical values; thermodynamic functions of the Kihara molecule systems were determined from the second-order perturbation theory. They agree well with our MC values at lower densities and higher reduced temperatures.     

Biphasic Dielectrophoresis of Isotropic Pocket Carriers Containing Quantum Dots (QDs) in Nematic Medium and Fabrication of QD Cluster Array with Matrix Emission of Point Light Sources

Unusual physical properties of an anisotropic liquid crystal (LC) medium, such as topological defects, elastic interaction with particles, and nonlinear electrophoresis, are ingeniously utilized to handle nanoparticles. Here, a new approach to manipulate quantum dots (QDs) using volume‐tunable and electrically movable isotropic pocket carriers in a nematic medium is demonstrated. This method is based on multiple mechanisms: spontaneous formation of QD flocs in LCs, sharp solubility contrast of QDs in nematic and isotropic phases, and biphasic dielectrophoresis in isotropic–nematic mixture. By thermally and electrically controlling the isotropic pockets containing QDs, an array of hierarchical QD clusters with the arbitrarily controllable size and location is fabricated. The phase boundary pressure squeezes the QD flocs to adhere to each other and on the substrate. The QD cluster array can be transferred to a flexible substrate, and can serve as a point light source array for display and image acquisition applications.     

Tilted and helical columnar phases for an axially symmetric discoidal system

We report novel phase behavior for a system of disclike ellipsoidal particles interacting via a pair potential. We identify a structural phase transition between two hexagonal columnar phases, both tilted, induced by spatial ordering of the tilt about the columnar axis and positional correlations between neighboring columns upon cooling. The local minima of the potential energy surface support irregular helical arrangements of the discoids about the columnar axis for the high-temperature hexagonal columnar phase, and a tilted arrangement for both phases. Our study demonstrates that dispersion-repulsion forces corresponding to oblate ellipsoids are sufficient to produce a columnar phase that is tilted and helical.     

External magnetic field-dependent tricritical points of uniaxial-to-biaxial nematic transition

External magnetic field-dependent behavior of tricritical points of uniaxial–biaxial nematic phase transition in a mixture of prolate and oblate molecules has been studied using the Landau phenomenological theory. Topological classification of phase diagrams in the field-temperature coordinates is performed using a sixth-order term in order parameter tensor. For both prolate and oblate molecules, the tricritical order parameters corresponding to the uniaxial–biaxial increase with the intensity of the external magnetic field. Field-induced paranematic phase has only been reported for prolate molecules, but for oblate molecules, field-induced splitting of the order parameter has been reported.     

On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

Modifications to the traditional Onsager theory for modeling isotropic–nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee–Parsons resummation term. The Lee–Parsons resummation term uses the Carnahan–Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager’s original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee–Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equation of state.