arXiv subjects

Szabolcs Varga

Publications and source records attributed to Szabolcs Varga.

30 records · Page 2Linked to original sources

arXiv2015

Phase behaviour and correlations of parallel hard squares: From highly confined to bulk systems

We study a fluid of two-dimensional parallel hard squares in bulk and under confinement in channels, with the aim of evaluating the performance of Fundamental-Measure Theory (FMT). To this purpose, we first analyse the phase behaviour of the bulk system using FMT and Percus-Yevick theory, and compare the results with MD and MC simulations. In a second step, we study the confined system and check the results against those obtained from Transfer Matrix Method and from our own Monte Carlo simulations. Squares are confined to channels with parallel walls at angles of 0$^{\circ}$ or 45$^{\circ}$ relative to the diagonals of the parallel hard squares, respectively, which allows for an assessment of the effect of the external-potential symmetry on the fluid structural properties. In general FMT overestimates bulk correlations, predicting the existence of a columnar phase (absent in simulations) prior to crystallisation. The equation of state predicted by FMT compares well with simulations, although the PY approach with the virial route is better in some range of packing fractions. The FMT is highly accurate for the structure and correlations of the confined fluid due to the dimensional crossover property fulfilled by the theory. Both density profiles and equations of state of the confined system are accurately predicted by the theory. The highly non-uniform pair correlations inside the channel are also very well described by FMT.

cond-mat.soft↗

arXiv2015

Effect of orientational restriction on monolayers of hard ellipsoids

The effect of out-of-plane orientational freedom on the orientational ordering properties of a monolayer of hard ellipsoids is studied using Parsons-Lee scaling approach and replica exchange Monte Carlo computer simulation. Prolate and oblate ellipsoids exhibit very different ordering properties, namely, the axes of revolution of prolate particles tend to lean out, while those of oblate ones prefer to lean into the confining plane. The driving mechanism of this is that the particles try to maximize the available free area on the confining surface, which can be achieved by minimizing the cross section areas of the particles with the plane. In the lack out-of-plane orientational freedom the monolayer of prolate particles is identical to a two-dimensional hard ellipse system, which undergoes an isotropic-nematic ordering transition with increasing density. With gradually switching on the out-of-plane orientational freedom the prolate particles lean out from the confining plane and a destabilisation of the in-plane isotropic-nematic phase transition is observed. The system of oblate particles behaves oppositely to that of prolates. It corresponds to a two-dimensional system of hard disks in the lack of out-of-plane freedom, while it behaves similar to that of hard ellipses in the freely rotating case.

cond-mat.soft↗

arXiv2015

Beyond the single-file fluid limit using transfer matrix method: Exact results for confined parallel hard squares

We extend the transfer matrix method of one-dimensional hard core fluids placed between confining walls for that case where the particles can pass each other and at most two layers can form. We derive an eigenvalue equation for a quasi-one-dimensional system of hard squares confined between two parallel walls, where the pore width is between $σ$ and $3σ$ ( $σ$ is the side length of the square). The exact equation of state and the nearest neighbour distribution functions show three different structures: a fluid phase with one layer, a fluid phase with two layers and a solid-like structure where the fluid layers are strongly correlated. The structural transition between differently ordered fluids develops continuously with increasing density, i.e. no thermodynamic phase transition occurs. The high density structure of the system consists of clusters with two layers which are broken with particles staying in the middle of the pore.

cond-mat.stat-mech↗

arXiv2015

A heuristic rule for classification of classical fluids: Master curves for Mie, Yukawa and square-well potentials

A shift of the vapor-liquid coexistence curves by the critical value of the reduced second virial coefficient yields striking data collapses to define master curves. This is observed for the Mie, Yukawa and square-well fluids of different attractive ranges. This modification of the extended corresponding-states law of Noro and Frenkel strongly improves the outcomes from the van der Waals principle. Moreover, this shifted extended principle makes the master curves from Mie and Yukawa potentials to be one on top of the other. The square-well potential forms two well defined master curves, each one corresponding to different effective critical exponents.

cond-mat.stat-mech↗

arXiv2014

Effect of shape biaxiality on the phase behavior of colloidal liquid-crystal monolayers

We extend our previous work on monolayers of uniaxial particles [J. Chem. Phys. 140, 204906 (2014)] to study the effect of particle biaxiality on the phase behavior of liquid-crystal monolayers. Particles are modelled as board-like hard bodies with three different edge lengths $σ_1\geqσ_2\geqσ_3$, and use is made of the restricted-orientation approximation (Zwanzig model). A density-functional formalism based on the fundamental-measure theory is used to calculate phase diagrams for a wide range of values of the largest aspect ratio ($κ_1=σ_1/σ_3\in[1,100]$). We find that particle biaxiality in general destabilizes the biaxial nematic phase already present in monolayers of uniaxial particles. While plate-like particles exhibit strong biaxial ordering, rod-like ones with $κ_1>21.34$ exhibit reentrant uniaxial and biaxial phases. As particle geometry is changed from uniaxial- to increasingly biaxial-rod-like, the region of biaxiality is reduced, eventually ending in a critical-end point. For $κ_1>60$, a density gap opens up in which the biaxial nematic phase is stable for any particle biaxiality. Regions of the phase diagram where packing-fraction inversion occurs (i.e. packing fraction is a decreasing function of density) are found. Our results are compared with the recent experimental studies on nematic phases of magnetic nanorods.

cond-mat.soft↗

arXiv2013

Hard rods in a cylindrical pore: the nematic-to-smectic phase transition

The effect of cylindrical confinement on the phase behaviour of a system of parallel hard rods is studied using Onsager's second virial theory. The hard rods are represented as hard cylinders of diameter $D$ and length $L$, while the cylindrical pore is infinite with diameter $W$. The interaction between the wall and the rods is hard repulsive, and it is assumed that molecules are parallel to the surface of the pore (planar anchoring). In very narrow pores ($D 100 D$, results for bulk and confined fluids agree well due to the short range effect of the wall ($\sim 3-4D$).

cond-mat.soft↗

arXiv2011

Biaxial nematic phases in fluids of hard board-like particles

We use density-functional theory, of the fundamental-measure type, to study the relative stability of the biaxial nematic phase, with respect to non-uniform phases such as smectic and columnar, in fluids made of hard board-like particles with sizes $σ_1>σ_2>σ_3$. A restricted-orientation (Zwanzig) approximation is adopted. Varying the ratio $κ_1=σ_1/σ_2$ while keeping $κ_2=σ_2/σ_3$, we predict phase diagrams for various values of $κ_2$ which include all the uniform phases: isotropic, uniaxial rod- and plate-like nematics, and biaxial nematic. In addition, spinodal instabilities of the uniform phases with respect to fluctuations of the smectic, columnar and plastic-solid type, are obtained. In agreement with recent experiments, we find that the biaxial nematic phase begins to be stable for $κ_2\simeq 2.5$. Also, as predicted by previous theories and simulations on biaxial hard particles, we obtain a region of biaxility centred on $κ_1\approxκ_2$ which widens as $κ_2$ increases. For $κ_2\agt 5$ the region $κ_2\approxκ_1$ of the packing-fraction vs. $κ_1$ phase diagrams exhibits interesting topologies which change qualitatively with $κ_2$. We have found that an increasing biaxial shape anisotropy favours the formation of the biaxial nematic phase. Our study is the first to apply FMT theory to biaxial particles and, therefore, it goes beyond the second-order virial approximation. Our prediction that the phase diagram must be asymmetric is a genuine result of the present approach, which is not accounted for by previous studies based on second-order theories.

cond-mat.soft↗

arXiv2011

Towards understanding the ordering behavior of hard needles: New analytical solutions in one dimension

We re-examine the ordering behavior of a one-dimensional fluid of freely rotating hard needles, where the centers of mass of the particles are restricted to a line. Analytical equations are obtained for the equation of state, order parameter and orientational correlation functions using the transfer-matrix method if some simplifying assumptions are applied for either the orientational freedom or the contact distance between two needles. The two-state Zwanzig model accounts for the orientational ordering, but it produces unphysical pressure at high densities and there is no orientational correlation. The four-state Zwanzig model gives reasonable results for orientational correlation function, but the pressure is still poorly represented at high densities. In the continuum limit, apart from the orientational correlation length it is managed to reproduce all relevant bulk properties of the hard needles using an approximate formula for the contact distance. The results show that the orientational correlation length diverges at zero and infinite pressures. The high density behavior of needles is not resolved.

cond-mat.stat-mech↗

arXiv2010

Competition between capillarity, layering and biaxiality in a confined liquid crystal

The effect of confinement on the phase behaviour and structure of fluids made of biaxial hard particles (cuboids) is examined theoretically by means of Onsager second-order virial theory in the limit where the long particle axes are frozen in a mutually parallel configuration. Confinement is induced by two parallel planar hard walls (slit-pore geometry), with particle long axes perpendicular to the walls (perfect homeotropic anchoring). In bulk, a continuous nematic-to-smectic transition takes place, while shape anisotropy in the (rectangular) particle cross section induces biaxial ordering. As a consequence, four bulk phases, uniaxial and biaxial nematic and smectic phases, can be stabilised as the cross-sectional aspect ratio is varied. On confining the fluid, the nematic-to-smectic transition is suppressed, and either uniaxial or biaxial phases, separated by a continuous trasition, can be present. Smectic ordering develops continuously from the walls for increasing particle concentration (in agreement with the supression of nematic-smectic second order transition at confinement), but first-order layering transitions, involving structures with n and n+1 layers, arise in the confined fluid at high concentration. Competition between layering and uniaxial-biaxial ordering leads to three different types of layering transitions, at which the two coexisting structures can be both uniaxial, one uniaxial and another biaxial, or both biaxial. Also, the interplay between molecular biaxiality and wall interactions is very subtle: while the hard wall disfavours the formation of the biaxial phase, biaxiality is against the layering transitions, as we have shown by comparing the confined phase behaviour of cylinders and cuboids. The predictive power of Onsager theory is checked and confirmed by performing some calculations based on fundamental-measure theory.

cond-mat.soft↗

arXiv2008

Biaxial nematic and smectic phases of parallel particles with different cross sections

We have calculated the phase diagrams of one--component fluids made of five types of biaxial particles differing in their cross sections. The orientation of the principal particle axis is fixed in space, while the second axis is allowed to freely rotate. We have constructed a free-energy density functional based on fundamental--measure theory to study the relative stability of nematic and smectic phases with uniaxial, biaxial and tetratic symmetries. Minimization of the density functional allows us to study the phase behavior of the biaxial particles as a function of the cross-section geometry. For low values of the aspect ratio of the particle cross section, we obtain smectic phases with tetratic symmetry, although metastable with respect to the crystal, as our MC simulation study indicates. For large particle aspect ratios and in analogy with previous work [Phys. Chem. Chem. Phys. 5, 3700 (2003)], we have found a four--phase point where four spinodals, corresponding to phase transitions between phases with different symmetries, meet together. The location of this point is quite sensitive to particle cross section, which suggests that optimizing the particle geometry could be a useful criterion in the design of colloidal particles that can exhibit an increased stability of the biaxial nematic phase with respect to other competing phases with spatial order.

cond-mat.soft↗

arXiv2007

Smectic ordering in athermal systems of rod-like triblock copolymers

The phase behavior of the system of parallel rigid triblock copolymers is examined using the second-virial density functional theory. The triblock particle consists of two identical infinitely thin hard rods of finite lengths on the opposite ends of one central hard cylinder with nonzero length and diameter. Stability analyses and free energy calculations show that the system of parallel particles can form not only uniform nematic and smectic A phases, but a smectic-C phase too. The stability and structure of the tilted structure is controlled by only the diameter and the length of the central cylinder segment. Interestingly, the diameter effects only the layer tilting and the periodicity, but not the packing fraction of the nematic to smectic-C transition. For all values of cylinder length the usual smectic-A and smectic-C transitions compete with each other and no nematic-columnar transition is observed. At low and high cylinder length the smectic-A phase is stabilized first, while the smectic C is the most stable for intermediate length values.

cond-mat.soft↗

arXiv2004

Nematic phase transitions in mixtures of thin and thick colloidal rods

We present the first experimental measurements of the isotropic and nematic phases of mixtures of thin, charged semiflexible fd virus, and thick, fd-PEG created by covalently grafting poly-(ethylene glycol) to the the surface of fd, rods. The fd-PEG is sterically stabilized and its phase behavior is independent of ionic strength. The fd is charged. Therefore, by varying the ionic strength of a mixture of fd and fd-PEG, only the effective diameter of the bare fd rods changes, subsequently varying the effective diameter ratio (d=D_fd-PEG/D_fd) from 3.7 to 1. In solution, binary mixtures of fd and fd-PEG are shown to exhibit isotropic-nematic, isotropic-nematic-nematic and nematic-nematic coexisting phases with increasing concentration. We measure the binary phase diagrams as a function of composition, total concentration, and ionic strength. We find a lower critical point in the nematic-nematic coexistence region which has not been observed previously. These experimental results resolve a controversy in the literature concerning the evolution of the nematic-nematic phase separation with concentration. The experimental results are qualitatively described by a rescaled Onsager-type theory for the phase behavior of binary rod mixtures.

cond-mat.soft↗