Fluid Of Hard Ellipsoids Research Articles

The Three-Body Direct Correlation Function of Hard Sphere and Hard Ellipsoid Fluids

In previous work, the direct correlation functions of hard spheres and hard ellipsoidal fluids were calculated. In the present work, using Marko variational method and Pynn–Wulf approximation, the three-body direct correlation function of hard ellipsoid fluid is calculated. In these calculations, the triplet direct correlation function of hard spheres is required. The new expressions for the direct correlation function of hard spheres and hard ellipsoids and triplet correlation of hard spheres, introduced by Muller and coworker, are used. The Fourier transform of new triplet direct correlation of hard sphere fluid is compared with the simulation data. As mentioned in previous work, the expansion coefficients of two-body correlations of hard ellipsoids (components of three-body correlations) are fairly in agreement with the Monte Carlo simulation and the other theories. The Fourier transform of new triplet direct correlation of hard spheres and hard ellipsoid fluids is calculated. These Fourier transforms can be used for calculation of triplet structure factor of hard spheres and hard ellipsoid fluids. The Fourier transforms of triplet correlation of hard ellipsoids with elongations $$x = 1.50,\,\,1.20,\,\,1.10$$ as limited cases are compared with exact result of hard spheres of unit diameter. There is qualitative agreement between hard ellipsoids and hard spheres results of triplet correlations.

Confinement Induced Ordering in Fluid of Hard Ellipsoids

The ordering configurations of a fluid of anisotropic ellipsoids under the confinement of two apposing impenetrable walls are studied by Monte Carlo simulations. The excess adsorption of the fluid on the walls with respect to the aspect ratio has a maximum at the critical aspect ratio of 2.9 in high-density ellipsoid fluids, indicating an orientational ordering in the adjacent region of the walls, which is confirmed by probing into the density configurations and the orientational order parameter in the adjacent region of the walls for varying aspect ratios. In addition, the orientational order parameter in the bulk fluid at the same density is calculated, and it indicates an isotropic state as the bulk density is still below the bulk isotropic-to-nematic transition. Therefore, it can be concluded that the anisotropic ordering near the walls in the ellipsoid fluid that exhibits isotropic in the bulk is induced by the confinement effect of the walls.

Isotropic-Nematic Transition of Hard Ellipsoid Fluids

We numerically study the thermodynamic properties of a hard ellipsoid fluid by mainly focusing on its phase transition from an isotropic phase into a nematic phase (i.e. isotropic—nematic phase transition). To improve the accuracy, precision, and efficiency of our computations, we attempt to employ the Wang—Landau NPT Monte Carlo algorithm in our simulations to calculate the function p(V) that gives the probability of arriving at the threshold density of the isotropic—nematic transition. Our results directly reveal that the nematic fluid phase, which is characterized by an ordered direction rather than an ordered configuration, appears and coexists with the isotropic phase when the aspect ratio α of the ellipsoid is located in a relatively narrow range of α = 2.0–2.25, and it becomes dominant and is fully established when α ≥ αcut = 2.25. We find that our estimated αcut is significantly lower than previously reported values of around 2.75. This prediction is further confirmed by the calculations of both the fluid reduced density and pressure of coexistence which show that the pressure grows up as the density increases and the probability function p(V) exhibits double peaks when the pressure enters the coexistence region. Based on these consistent results we are able to conclude that when α ≥ 2.25 an ellipsoid fluid can fully display the nematic behavior. This study will place a useful and tight theoretical constraint on investigations of the isotropic—nematic phase transition in the future.

Solvation force in hard ellipsoid fluids with HNW interaction

In present work, using density functional theory and extended restricted orientation model, the one particle density of hard Gaussian overlap fluid near the colloid walls is calculated. The hard needle–wall interaction between molecules and colloids are considered. Using non-linear equation, proposed by Grimson–Rickyazen, the solvation force of hard ellipsoidal molecular fluid with hard Gaussian overlap interaction is calculated. We could not find the exact or simulation results for comparison. The results in the case k = 2.0 are compared with the solvation force of one-dimensional hard rod fluids. The results are corresponded, qualitatively.

Universal pattern for the distribution of relaxation times in the isotropic phase of liquid crystallinen-cyanobiphenyls

A universal pattern emerging from the analysis of the distribution of relaxation times in the isotropic phase of liquid crystalline n-alkylcyanobiphenyls (nCB) from 4CB to 14CB is presented. The increase of the length of nCB molecules causes the high-frequency (short-time) branch of the primary relaxation loss curve to approach the form epsilon(f>fpeak) approximately omega(-n), with n-->1/2 in frequency (omega=2pif) or approximately sqrt[t] in time on cooling toward the isotropic-mesophase "clearing" phase-transition temperature (TC). Recently, such behavior was suggested as a hypothetical universal pattern for diverse glass forming organic liquids on approaching the glass temperature [A. I. Nielsen, T. Christensen, B. Jakobsen, K. Niss, N. B. Olsen, R. Richert, and J. C. Dyre, J. Chem. Phys. 130, 154508 (2009)]. The isotropic phase of rodlike liquid crystalline compounds is considered to be an important experimental model system for studying glassy dynamics since it constitutes a link with the model fluid of hard ellipsoids of revolution.

Fluids of hard natural and Gaussian ellipsoids: A comparative study by integral equation theories

The hard Gaussian overlap (HGO) model for ellipsoids is compared to the hard ellipsoid of revolution (HER) model, in the isotropic fluid phase and within the framework of the Percus-Yevick (PY) and hypernetted chain (HNC) integral equation theories. The former model is often used in place of the latter in many approximate theories. Since the HGO model slightly overestimates the contact distance when the two ellipsoids are perpendicular to each other, it leads to small differences in the Mayer function of the two models, but nearly none in the integrals of these functions and particularly for the second virial coefficients. However, it leads to notable differences in the pair correlation functions, as obtained by the Percus-Yevick and the hypernetted chain theories, especially at high densities. The prediction of the stability of the isotropic phase with respect to orientational order, at high densities, is notably influenced by these small differences. Both theories predict that, for same aspect ratios, the HGO model overestimates the ordering, when compared to the HER model. This explains why the PY approximation predicts ordering for the HGO model with aspect ratio of 1:3, while it does not for the HER model, in accordance with the very first integral equation results obtained for this system, and at variance with many opposite claims from subsequent publications that used the HGO model in place of the HER model.

Structure of hard ellipsoids: The Gaussian overlap model

The equilibrium properties of isotropic fluids composed of hard ellipsoids of revolution represented by a Gaussian overlap model are studied using the integral equation theories. The Percus–Yevick and the hypernetted-chain integral equations have been devised for calculating the angular pair-correlation function for fluids of hard ellipsoids of a revolution. This model is computationally simple and shears some similarities with the widely used hard ellipsoids. The methods used involve an expansion of angle-dependent functions appearing in the integral equations in terms of spherical harmonics and the harmonic coefficients are obtained by an iterative algorithm. We have considered all the terms of harmonic coefficients which involve l indices up to less than or equal to 6. The numerical accuracy of the results depends on the number of spherical harmonic coefficients considered for each orientation-dependent functions. Ellipsoids with length-to-width ratios of 2.0 and 3.0 are considered and the harmonic coefficients are compared with the molecular-dynamics results for prolate ellipsoids. We find that both the Percus–Yevick and hypernetted-chain theories are in reasonable agreement with the computer simulation results. The pressure obtained from the virial and compressibility routes of these fluids have also been compared with the computer simulation results which shows that these integral equations are thermodynamically inconsistent.

Dynamical precursor of nematic order in a dense fluid of hard ellipsoids of revolution.

We investigate hard ellipsoids of revolution in a parameter regime where no long range nematic order is present but already finite-size domains are formed which show orientational order. Domain formation leads to a substantial slowing down of a collective rotational mode which separates well from the usual microscopic frequency regime. A dynamic coupling of this particular mode into all other modes provides a general mechanism which explains an excess peak in spectra of molecular fluids. Using molecular dynamics simulation on up to 4096 particles and on solving the molecular mode coupling equation we investigate dynamic properties of the peak and prove its orientational origin.

The isotropic–nematic transition in hard Gaussian overlap fluids

We report a study of the isotropic–nematic (I–N) transition in fluids of molecules interacting through the hard Gaussian overlap (HGO) model. This model is computationally simple and shears some similarities with the widely used hard ellipsoid (HE) fluid. The I–N coexistence properties of HGO fluids have been accurately determined by combining different simulation techniques, including thermodynamic integration and Gibbs–Duhem integration for various molecular elongations, κ, in the range 3⩽κ⩽10. The accuracy of the Gibbs–Duhem integration scheme has been independently assessed by locating the I–N transition using the Gibbs-ensemble simulation technique for the largest elongation considered here (κ=10). The simulation results are analyzed within the context of the simplest version of the decoupling approximation as introduced by Parsons and Lee. The agreement between theoretical predictions and simulation data might be considered satisfactory, particularly for large nonsphericities. A comparison with the simulation results for the I–N properties of HE fluids shows that there exist large quantitative differences between HGO and HE fluids in this region, and this is ascribed to the larger volume excluded by a pair of HGO molecules compared to that of HE. In the light of the results presented here, approximating the distance of closest approach, or the excluded volume in the HE model by the corresponding expressions borrowed from the Gaussian overlap approximation—as is implemented in some theoretical descriptions of the HE fluid—does not seem to be appropriate.

Integral equation theory for molecular fluids: effect of quadrupolar interactions

The Percus–Yevick (PY) and the hypernetted chain (HNC) integral equations have been solved for fluids of hard ellipsoids of a revolution represented by a hard Gaussian overlap model and for fluids of quadrupolar hard Gaussian overlap model. The structural and thermodynamic properties of the isotropic phase are discussed in detail. Ellipsoids with length-to-width ratios of 1.792, 3.0, 4.0 and 5.0 are considered and results are reported for different densities and quadrupole moments. It is shown that both the HNC and PY theories are in reasonable agreement with the computer simulation results.

Fluids of hard ellipsoids: Phase diagram including a nematic instability from Percus-Yevick theory.

An important aspect of molecular fluids is the relation between orientation and translation parts of the two-particle correlations. Especially, a detailed knowledge of the influence of orientation correlations is needed to explain and calculate in detail the occurrence of a nematic phase. The simplest model system that shows both orientation and translation correlations is a system of hard ellipsoids. We investigate an isotropic fluid formed of hard ellipsoids with the Percus-Yevick theory. Solving the Percus-Yevick equations self-consistently and accurately in the high density regime gives, contrary to previous works, a clear criterion for a nematic instability. We calculate in detail the equilibrium phase diagram for a fluid of hard ellipsoids of revolution. Our results compare well with Monte Carlo simulations and density-functional theory.

Mode coupling theory for molecular liquids: What can we learn from a system of hard ellipsoids?

Molecular fluids show rich and complicated dynamics close to the glass transition. Some of these observations are related to the fact that translational and orientational degrees of freedom couple in nontrivial ways. A model system which can serve as a paradigm to understand these couplings is a system of hard ellipsoids of revolution. To test this we compare at the ideal glass transition the static molecular correlators of a linear A-B Lennard-Jones molecule obtained from a molecular dynamics simulation with a selected fluid of hard ellipsoids for which the static correlators have been obtained using Percus-Yevick theory. We also demonstrate that the critical non-ergodicity parameters obtained from molecular mode coupling theory for both systems show a remarkable similarity at the glass transition, provided the aspect ratio is chosen properly. Therefore we conclude that a system of hard ellipsoids can indeed be used to understand part of the essential behaviour of such a simple molecular system like the A-B Lennard-Jones molecules in the vicinity of the ideal glass transition.

A model for the study of the structure of hard molecular fluids

A model previously introduced to study the structure and thermodynamics of fluids of anisotropic molecules with orientations restricted to certain discrete directions is generalized and used to study normal molecular fluids in which the molecules can rotate freely. The basis is an ansatz for the direct correlation function which depends on the geometry of two molecules. The method leads to the Percus—Yevick solution for hard spheres and to Onsager's solution in the limit of long needles. In this paper it is applied to fluids comprising hard spherocylinders and to fluids of hard ellipsoids.

A model for the study of the structure of hard molecular fluids

A model previously introduced to study the structure and thermodynamics of fluids of anisotropic molecules with orientations restricted to certain discrete directions is generalized and used to study normal molecular fluids in which the molecules can rotate freely. The basis is an ansatz for the direct correlation function which depends on the geometry of two molecules. The method leads to the Percus—Yevick solution for hard spheres and to Onsager's solution in the limit of long needles. In this paper it is applied to fluids comprising hard spherocylinders and to fluids of hard ellipsoids.

Phase diagram of the hard biaxial ellipsoid fluid

The phase diagram of fluids of hard biaxial ellipsoids with c/a=10 and b/a∈{1,10}, where a, b, and c are the semi-axes, has been studied using computer simulation. Four homogeneous phases are in evidence: isotropic (I), nematic (N+), discotic (N−) and biaxial (B). First-order isotropic-nematic and isotropic-discotic coexistence lines have been traced out using Gibbs–Duhem integration of the coexistence pressure with respect to the molecular biaxiality. We conclude that the isotropic-nematic transition is greatly weakened by a modest degree of molecular biaxiality, in agreement with several recent theories. The I–N+ and I–N− lines meet two second-order nematic-biaxial and discotic-biaxial lines at the Landau bicritical point. This point is predicted to occur at around the self-dual particle shape, b/a=c/a, and so extensive simulations have been performed at and around this point. Very sluggish behaviour is expected in this region of the phase diagram and so long simulations were required. An estimate of the location of the Landau bicritical point is reported. We also highlight the asymmetry of the phase diagram about b/a=c/a, where the ellipsoid is neither prolate nor oblate.

A model of molecular fluids: a three-parameter direct correlation function

A previous two-parameter model of a molecular fluid is extended to three parameters and applied to a fluid of hard ellipsoids with restricted orientations. The direct correlation function of the fluid is written as a linear combination of three basic functions derived from the geometry of two molecules and the coefficients determined from algebraic equations also satisfied by the Percus–Yevick (PY) solution of the problem. The theory yields the PY solution and PY equation of state in the special case of hard spheres. For ellipsoids the equation of state agrees better with the results of computer simulation than the two-parameter version although the discrepancy increases with increasing anisotropy of the molecules. According to the model the fluid makes a transition to a nematic state although the predicted densities at which the transition takes place are too low.

The isotropic–nematic phase transition in uniaxial hard ellipsoid fluids: Coexistence data and the approach to the Onsager limit

The isotropic–nematic (I-N) phase transition in hard ellipsoid fluids has been studied by computer simulation, using the Gibbs–Duhem integration technique introduced by Kofke; and theoretically, using Onsager theory and the Parsons–Lee improvement. In the simulations, the I-N coexistence line is mapped out in the P–x plane, where P is the pressure and x is the elongation, by numerically integrating a Clapeyron-like first-order differential equation, using constant-pressure simulation data for the two coexisting phases. The elongation range 5≤x≤20 has been studied, using independent starting points provided by chemical potential calculations and thermodynamic integration of the equation of state at x=5,20, plus a direct Gibbs ensemble simulation at x=20. The Onsager–Parsons–Lee theory has been applied to the I-N phase transition for aspect ratios up to x=1000, affording an accurate investigation of the approach to the Onsager limit for this model. This involved the numerical computation of the orientation-dependent second virial coefficient in a way that avoids expansions in Legendre polynomials, so as to be accurate at high elongation. Over the elongation range studied here, agreement between simulation and the Parsons–Lee theory is good.

Stability of the nematic phase for the hard ellipsoid fluid

Abstract Monte Carlo and molecular dynamics techniques are used for the computer simulation of the stability of the nematic phase of hard ellipsoids of revolution with axial ratio 3, for system sizes in the range N = 108–576. It is concluded that the phase is not, as had been suggested previously, rendered unstable by increasing the number of particles in this range. The difficulties in making accurate estimates of the positions of both the nematic-isotropic and nematic-solid transitions are emphasized.

Stability of the nematic phase for the hard ellipsoid fluid

Abstract Monte Carlo and molecular dynamics techniques are used for the computer simulation of the stability of the nematic phase of hard ellipsoids of revolution with axial ratio 3, for system sizes in the range N = 108–576. It is concluded that the phase is not, as had been suggested previously, rendered unstable by increasing the number of particles in this range. The difficulties in making accurate estimates of the positions of both the nematic-isotropic and nematic-solid transitions are emphasized.

Stability of the nematic phase for the hard ellipsoid fluid

Stability of the nematic phase for the hard ellipsoid fluid