Integral equation theory for dipolar hard sphere fluids with fluctuating orientational order

Static structure of active Brownian hard disks

We explore the changes in static structure of a two-dimensional system of active Brownian particles (ABP) with hard-disk interactions, using event-driven Brownian dynamics simulations. In particular, the effect of the self-propulsion velocity and the rotational diffusivity on the orientationally-averaged fluid structure factor is discussed. Typically activity increases structural ordering and generates a structure factor peak at zero wave vector which is a precursor of motility-induced phase separation. Our results provide reference data to test future statistical theories for the fluid structure of active Brownian systems. This manuscript was submitted for the special issue of the Journal of Physics: Condensed Matter associated with the Liquid Matter Conference 2017.

Size effect and stability of polarized fluid phases

The existence of a ferroelectric fluid phase for systems of 1000-2000 dipolar hard or soft spheres is well established by numerical simulations. Theoretical approaches proposed to determine the stability of such a phase are either in qualitative agreement with the simulation results or disagree with them. Experimental results for systems of molecules or particles with large electric or magnetic dipole moments are also inconclusive. As a contribution to the question of existence and stability of a fluid ferroelectric phase this simulation work considers system sizes of the order of 10 000 particles, thus an order of magnitude larger than those used in previous studies. It shows that although ferroelectricity is not affected by an increase of system size, different spatial arrangements of the dipolar hard spheres in such a phase are possible whose free energies seem to differ only marginally.

Phase behavior of an amphiphilic fluid

We invoke mean-field density functional theory (DFT) to investigate the phase behavior of an amphiphilic fluid composed of a hard-sphere core plus a superimposed anisometric Lennard-Jones perturbation. The orientation dependence of the interactions consists of a contribution analogous to the interaction potential between a pair of "spins" in the classical, three-dimensional Heisenberg fluid and another one reminiscent of the interaction between (electric or magnetic) point dipoles. At fixed orientation both contributions are short-range in nature decaying as r-6 (r being the separation between the centers of mass of a pair of amphiphiles). Based upon two mean-field-like approximations for the pair correlation function that differ in the degree of sophistication we derive expressions for the phase boundaries between various isotropic and polar phases that we solve numerically by the Newton-Raphson method. For sufficiently strong coupling between the Heisenberg "spins" both mean-field approximations generate three topologically different and generic types of phase diagrams that are observed in agreement with earlier work [see, for example, Tavares et al., Phys. Rev. E 52, 1915 (1995)]. Whereas the dipolar contribution alone is incapable of stabilizing polar phases on account of its short-range nature it is nevertheless important for details of the phase diagram such as location of the gas-isotropic liquid critical point, triple, and tricritical points. By tuning the dipolar coupling constant suitably one may, in fact, switch between topologically different phase diagrams. Employing also Monte Carlo simulations in the isothermal-isobaric ensemble the general topology of the DFT phase diagrams is confirmed.

Thermodynamics of ferrofluids in applied magnetic fields

The thermodynamic properties of ferrofluids in applied magnetic fields are examined using theory and computer simulation. The dipolar hard sphere model is used. The second and third virial coefficients (B(2) and B(3)) are evaluated as functions of the dipolar coupling constant λ, and the Langevin parameter α. The formula for B(3) for a system in an applied field is different from that in the zero-field case, and a derivation is presented. The formulas are compared to results from Mayer-sampling calculations, and the trends with increasing λ and α are examined. Very good agreement between theory and computation is demonstrated for the realistic values λ≤2. The analytical formulas for the virial coefficients are incorporated in to various forms of virial expansion, designed to minimize the effects of truncation. The theoretical results for the equation of state are compared against results from Monte Carlo simulations. In all cases, the so-called logarithmic free energy theory is seen to be superior. In this theory, the virial expansion of the Helmholtz free energy is re-summed in to a logarithmic function. Its success is due to the approximate representation of high-order terms in the virial expansion, while retaining the exact low-concentration behavior. The theory also yields the magnetization, and a comparison with simulation results and a competing modified mean-field theory shows excellent agreement. Finally, the putative field-dependent critical parameters for the condensation transition are obtained and compared against existing simulation results for the Stockmayer fluid. Dipolar hard spheres do not undergo the transition, but the presence of isotropic attractions, as in the Stockmayer fluid, gives rise to condensation even in zero field. A comparison of the relative changes in critical parameters with increasing field strength shows excellent agreement between theory and simulation, showing that the theoretical treatment of the dipolar interactions is robust.

Isotropic-polar phase transitions in an amphiphilic fluid: density functional theory versus computer simulations

We investigate the critical line separating isotropic from polar phases in an amphiphilic bulk fluid by means of density functional theory (DFT) and Monte Carlo (MC) simulations in the isothermal-isobaric ensemble. The intermolecular interactions are described by a Lennard-Jones potential in which the attractive contribution is modified by an orientation-dependent function. The latter consists of two terms: The first one has the orientation dependence of a classical three-dimensional Heisenberg interaction, whereas, the second one has the orientation dependence of a classical dipole-dipole interaction. However, both contributions are short range. Employing DFT together with a modified mean-field (MMF) approximation for the orientation-dependent pair correlation function, we derive an analytical expression for the critical line separating isotropic from polar liquidlike phases. In parallel MC simulations, we locate the line of critical points through an analysis of Binder's second-order cumulant of the polar-order parameter. Comparison with DFT shows that the dipolelike contribution is irrelevant for the isotropic-polar phase transition. As far as the Heisenberg contribution is concerned, the MC data are in semiquantitative agreement with the DFT predictions for sufficiently strong coupling between molecular orientations. For weaker coupling, the variation in the ratio of critical density and temperature ρ(c)/T(c) with the Heisenberg coupling constant ε(H) is underestimated by the MMF treatment. The MC results suggest that this is because ρ(c) increases with decreasing ε(H) such that the assumption on which the MMF approach rests becomes less applicable in the weaker-coupling limit.

Role of dipole elongation in orientationally ordered liquids

A recent study shows that the dipole elongation in the extended dipole model plays a significant role in the phase transitions of liquid crystal phases. In this paper, molecular dynamics (MD) simulations were performed for the dipole model with different distances between the two charges keeping the total dipole moment the same. The potential energy consists of the Lennard-Jones potential and the site-site electrostatic contribution of partial charges. Detailed analyses were made with respect to the average order parameters (P(1)) and (P(2)) as functions of density along with other thermodynamic properties. When the reduced dipole elongations are 0.16 and 0.32, respectively, it is shown that the chainlike structures in the low density regime, liquid phases with columnar and smectic orders, and solid phases are formed; the phase with nematic order is not present anymore. At 0.64, the phases with antiferroelectric order were favored. The transition is found at the reduced elongation 0.55. It shows that the phase transitions are quite sensitive to the molecular charge distribution; this simple system could exhibit rather rich phase behaviors, which represents a significant advance in identifying molecular and state parameters of the future ferroelectric liquids.

Pair correlation functions and a free energy functional for the nematic phase

In this paper we have presented the calculation of pair correlation functions in a nematic phase for a model of spherical particles with the long-range anisotropic interaction from the mean spherical approximation (MSA) and the Percus-Yevick (PY) integral equation theories. The results found from the MSA theory have been compared with those found analytically by Holovko and Sokolovska [J. Mol. Liq. 82, 161 (1999)]. A free energy functional which involves both the symmetry conserving and symmetry broken parts of the direct pair correlation function has been used to study the properties of the nematic phase. We have also examined the possibility of constructing a free energy functional with the direct pair correlation function which includes only the principal order parameter of the ordered phase and found that the resulting functional gives results that are in good agreement with the original functional. The isotropic-nematic transition has been located using the grand thermodynamic potential. The PY theory has been found to give a nematic phase with pair correlation function harmonic coefficients having all the desired features. In a nematic phase the harmonic coefficient of the total pair correlation function h(x1,x2) connected with the correlations of the director transverse fluctuations should develop a long-range tail. This feature has been found in both the MSA and PY theories.

Pair correlation functions in nematics: Free-energy functional and isotropic-nematic transition

We develop a free-energy functional for an inhomogeneous system that contains both symmetry conserved and symmetry broken parts of the direct pair correlation function. These correlation functions are found by solving the Ornstein-Zernike equation with the Percus-Yevick closure relation. The method developed here gives the pair correlation functions in the ordered phase with features that agree well with the results found by computer simulations. The theory predicts accurately the isotropic-nematic transition in a system of anisotropic molecules and can be extended to study other ordered phases such as smectics and crystalline solids.

Ordering in linear multipolar colloids driven by an external field

An approach to describe a linear multipolar colloid driven by an external field is developed by considering a colloid which in absence of the field is low structured and its coupling potential is axially symmetric. The equilibrium correlation of one component of the orientation tensor, self and collective, is computed up to linear order in density, which can be measured in an appropriate light scattering experiment. The self-correlation is written in terms of the second and fourth order parameters. All the equilibrium quantities are computed up to two-body level. This is done by assuming that the two-body equilibrium density function is given by the Boltzmann distribution, whereas the one-body density function is computed as solution of the equilibrium N-body Smoluchowski equation in the absence of hydrodynamic interactions. These observables, self and collective, as well as the second and fourth order parameters are able to describe when the colloid would evolve to an orientationally ordered phase. Explicit results for the dipole and quadrupole moments are reported. These results predict a different alignment with the external field for each moment. A relationship is provided between second and fourth order parameters, predicting the critical value of the external field in which the colloid goes into an axially symmetric phase.

Theory of solvation in polar nematics

We develop a linear response theory of solvation of ionic and dipolar solutes in anisotropic, axially symmetric polar solvents. The theory is applied to solvation in polar nematic liquid crystals. The formal theory constructs the solvation response function from projections of the solvent dipolar susceptibility on rotational invariants. These projections are obtained from Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist both in the isotropic and nematic phases. Based on the properties of the solvent susceptibility from simulations and the formal solution, we have obtained a formula for the solvation free energy which incorporates the experimentally available properties of nematics and the length of correlation between the dipoles in the liquid crystal. The theory provides a quantitative framework for analyzing the steady-state and time-resolved optical spectra and makes several experimentally testable predictions. The equilibrium free energy of solvation, anisotropic in the nematic phase, is given by a quadratic function of cosine of the angle between the solute dipole and the solvent nematic director. The sign of solvation anisotropy is determined by the sign of dielectric anisotropy of the solvent: solvation anisotropy is negative in solvents with positive dielectric anisotropy and vice versa. The solvation free energy is discontinuous at the point of isotropic-nematic phase transition. The amplitude of this discontinuity is strongly affected by the size of the solute becoming less pronounced for larger solutes. The discontinuity itself and the magnitude of the splitting of the solvation free energy in the nematic phase are mostly affected by microscopic dipolar correlations in the nematic solvent. Illustrative calculations are presented for the equilibrium Stokes shift and the Stokes shift time correlation function of coumarin-153 in 4-n-pentyl-4'-cyanobiphenyl and 4,4-n-heptyl-cyanopiphenyl solvents as a function of temperature in both the nematic and isotropic phases.

Pair formation and global ordering of strongly interacting ferrocolloid mixtures: an integral equation study

Using the reference hypernetted chain (RHNC) integral equation theory and an accompanying stability analysis we investigate the structural and phase behaviors of model bidisperse ferrocolloids based on correlations of the homogeneous isotropic high-temperature phase. Our model consists of two species of dipolar hard spheres (DHSs) which dipole moments are proportional to the particle volume. At small packing fractions our results indicate the onset of chain formation, where the (more strongly coupled) A species behaves essentially as a one-component DHS fluid in a background of B particles. At high packing fractions, on the other hand, the RHNC theory indicates the appearance of isotropic-to-ferromagnetic transitions (volume ratios close to one) and demixing transitions (smaller volume ratios). However, contrary with the related case of monodisperse DHS mixtures previously studied by us [Phys. Rev. E 70, 031201 (2004)], none of the present bidisperse systems exhibit demixing within the isotropic phase, rather we observe coupled ferromagnetic/demixing phase transitions.

Colloid-induced structure in liquid crystal media

The structural perturbations induced by colloidal particles immersed in a model nematic subjected to an external field are calculated employing integral equation methods. Maps of the density-orientational distribution about a colloidal particle are obtained, and these provide a microscopic picture of the colloid's nematic coat. We focus on colloidal particles that favor homeotropic anchoring, but planar anchoring cases are also considered. The range and structure of the nematic coat is shown to be significantly influenced by the nature of the anchoring, the size of the colloidal particle, the range and strength of the colloid-nematogen interaction, and the external field strength. All of these factors are discussed.