Dipolar Fluids Research Articles

Effect of elastic constants of liquid crystals in their electro-optical properties

Recently following the success of the density functional theory (DFT) in obtaining the structure and thermodynamics of homogeneous and inhomogeneous classical systems such as simple fluids, dipolar fluid and binary hard spheres, this theory was also applied to obtain the density profile of a molecular fluid in between hard planar walls by Kalpaxis and Rickayzen. In the theory of molecular fluids, the direct correlation function (DCF) can be used to calculate the equation of state, free energy, phase transition, elastic constants, etc. It is well known that the hard core molecular models play an important role in understanding complex liquids such as liquid crystals. In this paper, a classical fluid of nonspherical molecules is studied. The required homogeneous (DCF) is obtained by solving Orenstein–Zernike (OZ) integral equation numerically. Some of the molecules in the liquid crystals have a sphere shape and this kind of molecular fluid is considered here. The DCF sphere of the molecular fluid is calculated and it will be shown that the results are in good agreement with the pervious works and the results of computer simulation. Finally the electro-optical properties of ellipsoid liquid crystal using DCF of these molecules are calculated.

Global Existence of Weak Solutions to a Higher-Order Parabolic System

In this paper, we study the coupling of the non-Newtonian Navier–Stokes equation and the oil–water–surfactant equation which stand for a model of a multi-phase incompressible dipolar viscous non-Newtonian fluid under shear. Based on Galerkin approximation and Simon’s compactness results, we obtain the existence and uniqueness of weak solutions of the system.

Effect of the surface charge distribution on the fluid phase behavior of charged colloids and proteins.

A generic but simple model is presented to evaluate the effect of the heterogeneous surface charge distribution of proteins and zwitterionic nanoparticles on their thermodynamic phase behavior. By considering surface charges as continuous "patches," the rich set of surface patterns that is embedded in proteins and charged patchy particles can readily be described. This model is used to study the fluid phase separation of charged particles where the screening length is of the same order of magnitude as the particle size. In particular, two types of charged particles are studied: dipolar fluids and protein-like fluids. The former represents the simplest case of zwitterionic particles, whose charge distribution can be described by their dipole moment. The latter system corresponds to molecules/particles with complex surface charge arrangements such as those found in biomolecules. The results for both systems suggest a relation between the critical region, the strength of the interparticle interactions, and the arrangement of charged patches, where the critical temperature is strongly correlated to the magnitude of the dipole moment. Additionally, competition between attractive and repulsive charge-charge interactions seems to be related to the formation of fluctuating clusters in the dilute phase of dipolar fluids, as well as to the broadening of the binodal curve in protein-like fluids. Finally, a variety of self-assembled architectures are detected for dipolar fluids upon small changes to the charge distribution, providing the groundwork for studying the self-assembly of charged patchy particles.

Theory of model electrolyte solutions: Assessing the short- and long-ranged contributions by molecular simulations

In this work, we conduct a comprehensive simulation study on Helmholtz energies for non-primitive model electrolyte solutions in order to assess fluid theories. Simulation data is obtained with two different methods. Using a new thermodynamic integration path, we calculate Helmholtz energy contributions arising from damped, short-ranged electrostatic pair potentials. The division of the potential into a damped, short-ranged and a long-ranged part using a complementary error function corresponds to the division of a standard Ewald sum. Additionally, we applied a standard thermodynamic integration method to obtain the full electrostatic contribution to the Helmholtz energy. We evaluate the analytical long-range contribution developed by Rodgers and Weeks [J. M. Rodgers and J. D. Weeks, J. Chem. Phys. 131, 244108 (2009)] and find excellent agreement to our simulation data for any damping parameter α*≥1.5 for liquid-like densities. Further, the simulation data is compared to a third order perturbation theory we recently presented. By analyzing the theory against results of molecular simulations we were able to introduce refinements to our theory, such as a rearranged Padé approximation. We show, however, that third order perturbation theory, despite these improvements, is only reliable for strongly damped potentials (α*<1) for ion-dipole as well as for purely dipolar fluids. This study shows that a perturbation theory of third order is insufficient for such systems.

Polarisation of polar dumbbell fluids in thermal gradients: the importance of the treatment of electrostatic interactions

ABSTRACTWe use non-equilibrium molecular dynamics simulations to study dipolar dumbbell fluids in a thermal gradient. We study the relative orientation of size asymmetric molecules with respect to the thermal gradient, and the sensitivity of the orientation to whether the Wolf method or Ewald summation is employed to compute the electrostatic interactions. For these systems, we find that the Wolf method overestimates the degree of molecular orientation. We also present new data on fluids with very small dipole moments which give novel insight into how the molecular asymmetry influences the polarisation response in the thermal gradient.

Real space electrostatics for multipoles. III. Dielectric properties.

In Papers I and II, we developed new shifted potential, gradient shifted force, and Taylor shifted force real-space methods for multipole interactions in condensed phase simulations. Here, we discuss the dielectric properties of fluids that emerge from simulations using these methods. Most electrostatic methods (including the Ewald sum) require correction to the conducting boundary fluctuation formula for the static dielectric constants, and we discuss the derivation of these corrections for the new real space methods. For quadrupolar fluids, the analogous material property is the quadrupolar susceptibility. As in the dipolar case, the fluctuation formula for the quadrupolar susceptibility has corrections that depend on the electrostatic method being utilized. One of the most important effects measured by both the static dielectric and quadrupolar susceptibility is the ability to screen charges embedded in the fluid. We use potentials of mean force between solvated ions to discuss how geometric factors can lead to distance-dependent screening in both quadrupolar and dipolar fluids.

Corresponding-states behavior of a dipolar model fluid with variable dispersion interactions and its relevance to the anomalies of hydrogen fluoride.

More than two decades ago, the elusiveness of a liquid-vapor equilibrium and a corresponding critical point in simulations of the supposedly simple model of dipolar hard spheres came as a surprise to many liquid matter theorists. van Leeuwen and Smit [Phys. Rev. Lett. 71, 3991 (1993)] showed that a minimum of attractive dispersion interactions among the dipolar particles may be needed to observe regular fluid behavior. Here, we adopt their approach and use an only slightly modified model, in which the original point dipole is replaced by a dipole moment produced by charges that are separated in space, to study the influence of dispersion interactions of variable strength on the coexistence and interfacial properties of a polar fluid. The thermophysical properties are discussed in terms of Guggenheim's corresponding-states approach. In this way, the coexistence curve, the critical compressibility factor, the surface tension, Guggenheim's ratio, and modifications of Guldberg's and Trouton's rules (related to the vapor pressure and the enthalpy of vaporization) are analyzed. As the importance of dispersion is decreased, a crossover from simple-fluid behavior to that characteristic of strongly dipolar systems takes place; for some properties, this transition is monotonic, but for others it occurs non-monotonically. For strongly dipolar systems, the reduced surface tension is very low, whereas Guggenheim's ratio and Guldberg's ratio are found to be high. The critical compressibility factor is smaller, and the coexistence curve is wider and more skewed than for simple fluids. For very weak dispersion, liquid-vapor equilibrium is still observable, but the interfacial tension is extremely low and may, eventually, vanish marking the end of the existence of a liquid phase. We discuss the implications of our findings for real fluids, in particular, for hydrogen fluoride.

Fourth and fifth virial coefficients and thermodynamic properties of the dipolar hard sphere fluids in zero external magnetic field

Analytical expressions of the fourth and the fifth virial coefficients for the dipole hard sphere fluid in zero external magnetic field are obtained on the basis of numerical results of Mayer-sampling calculations. The virial coefficients are incorporated in to the so-called logarithmic free energy (LFE) theory [E.A. Elfimova, A.O. Ivanov, P.J. Camp, Phys. Rev. E, 86, 021126 (2012)]. In this theory, the virial expansion of the Helmholtz free energy is re-summed into a logarithmic function. The argument of the logarithm is a polynomial expansion in density with coefficients chosen to give the first few terms in the conventional virial expansion. The theoretical predictions of the thermodynamic functions based on the LFE theory that accounts five virial coefficients are compared critically with published results from Monte Carlo simulations, conventional virial expansion, and known theory based on Padé approximation [G.S. Rushbrooke, G. Stell, J.S. Hoye, Mol. Phys., 26, 1199 (1973)]. It is shown that the LFE theory accurately captures computer simulation results for dipolar coupling constant λ ≤ 4, even at the highest value of the particle volume fraction φ ≲ 0.5, and outperforms thermodynamic theories mentioned above.

Sedimentation equilibria in polydisperse ferrofluids: critical comparisons between experiment, theory, and computer simulation.

The sedimentation equilibrium of dipolar particles in a ferrofluid is studied using experiment, theory, and computer simulation. A theory of the particle-concentration profile in a dipolar hard-sphere fluid is developed, based on the local-density approximation and accurate expressions from a recently introduced logarithmic free energy approach. The theory is tested critically against Monte Carlo simulation results for monodisperse and bidisperse dipolar hard-sphere fluids in homogeneous gravitational fields. In the monodisperse case, the theory is very accurate over broad ranges of gravitational field strength, volume fraction, and dipolar coupling constant. In the bidisperse case, with realistic dipolar coupling constants and compositions, the theory is excellent at low volume fraction, but is slightly inaccurate at high volume fraction in that it does not capture a maximum in the small-particle concentration profile seen in simulations. Possible reasons for this are put forward. Experimental measurements of the magnetic-susceptibility profile in a real ferrofluid are then analysed using the theory. The concentration profile is linked to the susceptibility profile using the second-order modified mean-field theory. It is shown that the experimental results are not consistent with the sample being monodisperse. By introducing polydispersity in the simplest possible way, namely by assuming the system is a binary mixture, almost perfect agreement between theory and experiment is achieved.

Long-range correction for dipolar fluids at planar interfaces

A slab-based long-range correction for dipolar interactions in molecular dynamics simulation of systems with a planar geometry is presented and applied to simulate vapour–liquid interfaces. The present approach is validated with respect to the saturated liquid density and the surface tension of the Stockmayer fluid and a molecular model for ethylene oxide. The simulation results exhibit no dependence on the cut-off radius for radii down to 1 nm, proving that the long-range correction accurately captures the influence of the dipole moment on the intermolecular interaction energies and forces as well as the virial and the surface tension.

Simulations of dipolar fluids using effective many-body isotropic interactions.

The partition function of a system with pairwise-additive anisotropic dipole-dipole interactions is equal to that of a hypothetical system with many-body isotropic interactions [G. Stell, Phys. Rev. Lett. 32, 286 (1974)]. The effective many-body interactions contain n-body contributions of all orders. Each contribution is known as an expansion in terms of the particle-particle distances r, and the coefficients are temperature dependent. The leading-order two-body term is the familiar -r(-6) attraction, and the leading-order three-body term is equivalent to the Axilrod-Teller interaction. In this work, a fluid of particles with the leading-order two-body and three-body interactions is compared to an equivalent dipolar soft-sphere fluid. Molecular simulations are used to determine the conditions under which the effective many-body interactions reproduce the fluid-phase structures of the dipolar system. The effective many-body interaction works well at moderately high temperatures but fails at low temperatures where particle chaining is expected to occur. It is shown that an adjustment of the coefficients of the two-body and three-body terms leads to a good description of the structure of the dipolar fluid even in the chaining regime, due primarily to the ground-state linear configuration of the three-body Axilrod-Teller interaction. The vapor-liquid phase diagrams of systems with different Axilrod-Teller contributions are determined. As the strength of the three-body interaction is increased, the critical temperature and density both decrease and disappear completely above a threshold strength, where chaining eventually suppresses the condensation transition.

Monte Carlo simulations of the two-dimensional dipolar fluid

We study a two-dimensional fluid of dipolar hard disks by Monte Carlo simulations in a square with periodic boundary conditions and on the surface of a sphere. The theory of the dielectric constant and the asymptotic behaviour of the equilibrium pair correlation function in the fluid phase are derived for both geometries. After having established the equivalence of the two methods we study the stability of the liquid phase in the canonical ensemble. We give evidence of a phase made of living polymers at low temperatures and provide a tentative phase diagram.

Static dielectric properties of dense ionic fluids.

The static dielectric properties of dense ionic fluids, e.g., room temperature ionic liquids (RTILs) and inorganic fused salts, are investigated on different length scales by means of grandcanonical Monte Carlo simulations. A generally applicable scheme is developed which allows one to approximately decompose the electric susceptibility of dense ionic fluids into the orientation and the distortion polarization contribution. It is shown that at long range, the well-known plasma-like perfect screening behavior occurs, which corresponds to a diverging distortion susceptibility, whereas at short range, orientation polarization dominates, which coincides with that of a dipolar fluid of attached cation-anion pairs. This observation suggests that the recently debated interpretation of RTILs as dilute electrolyte solutions might not be simply a yes-no-question but it might depend on the considered length scale.

Thermodynamics of dipolar square-well fluids

The thermodynamic properties of a dipolar square-well fluid in zero external magnetic field are studied using theory and simulations. The theory is based on the virial expansion of the Helmholtz free energy. The second and third virial coefficients are calculated as functions of the dimensionless temperature T*, the reduced dipolar interaction parameter μ, and the potential well width λ. The formulas are compared to results from Mayer-sampling calculations. The analytical expressions for the virial coefficients are incorporated in to various forms of virial expansion for the Helmholtz free energy and the equation of state. Thermodynamic functions are tested against results from Monte Carlo simulations for subcritical vapor–liquid transition parameters T*≥5 and 10.5; μ≤4; λ≤2 over the range of the particle volume fraction φ≤0.4. Finally, predictions of the critical parameters for the condensation transition are obtained on the basis of the virial expansion of the Helmholtz free energy and compared with computer-simulation results and the theories available in the literature. Although the critical parameter values formally lie beyond the applicability of the theory developed in this work they fall in the range of values previously obtained by other methods. Accurate theoretical prediction of the critical parameters for dipolar square-well fluids remains as a challenge.

Tuning the smooth particle mesh Ewald sum: application on ionic solutions and dipolar fluids.

Numerical properties of the smooth particle mesh Ewald (SPME) sum [U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen, J. Chem. Phys. 103, 8577 (1995)] have been investigated by molecular dynamics simulation of ionic solutions and dipolar fluids. Scaling dependence of execution time on the number of particles at optimal performance have been determined and compared with the corresponding data of the standard Ewald (SE) sum. For both types of systems and over the range from N = 10(3) to 10(5) particles, the SPME sum displays a sub O(N ln N) complexity, whereas the SE sum possesses an O(N(3/2)) complexity. The breakeven of the simulation times appears at O(10(3)) particles, and the SPME sum is ≈20 times faster than the SE sum at 10(5) particles. Furthermore, energy truncation error and the energy and force execution time of the reciprocal space evaluation as function of the number of particles and the convergence parameters of the SPME sum have been determined for both types of systems containing up to 10(6) particles.

Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles.

A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.

Dynamic mesoscale model of dipolar fluids via fluctuating hydrodynamics.

Fluctuating hydrodynamics (FHD) is a general framework of mesoscopic modeling and simulation based on conservational laws and constitutive equations of linear and nonlinear responses. However, explicit representation of electrical forces in FHD has yet to appear. In this work, we devised an Ansatz for the dynamics of dipole moment densities that is linked with the Poisson equation of the electrical potential ϕ in coupling to the other equations of FHD. The resulting ϕ-FHD equations then serve as a platform for integrating the essential forces, including electrostatics in addition to hydrodynamics, pressure-volume equation of state, surface tension, and solvent-particle interactions that govern the emergent behaviors of molecular systems at an intermediate scale. This unique merit of ϕ-FHD is illustrated by showing that the water dielectric function and ion hydration free energies in homogeneous and heterogenous systems can be captured accurately via the mesoscopic simulation. Furthermore, we show that the field variables of ϕ-FHD can be mapped from the trajectory of an all-atom molecular dynamics simulation such that model development and parametrization can be based on the information obtained at a finer-grained scale. With the aforementioned multiscale capabilities and a spatial resolution as high as 5 Å, the ϕ-FHD equations represent a useful semi-explicit solvent model for the modeling and simulation of complex systems, such as biomolecular machines and nanofluidics.

Low-temperature magnetic susceptibility of concentrated ferrofluids: The influence of polydispersity

In this paper we address the question of theoretical explanation of extremely high low-temperature initial magnetic susceptibility of concentrated ferrofluids . These laboratory synthesized samples [A.F. Pshenichnikov, A.V. Lebedev, J. Chem. Phys. 121(11) (2004) 5455; Colloid J. 67(2) (2005) 189] demonstrated the record-breaking values χ ~ 120 – 150 at temperatures ~ 230–240 K. The existing models predict such high susceptibility only under the assumption of unreasonably large dipolar coupling constant, which is out of the range of applicability. Here we calculate the second virial contribution to susceptibility for polydisperse ferrofluid, modeled by the dipolar hard sphere fluid. In the resulting expression there exists the parameter, which plays a part of dipolar coupling constant and which is defined in a form of double averaging of high powers of particle sizes over the granulometric distribution. For real particle size distribution this effective parameter at least twice exceeds the commonly defined polydisperse dipolar coupling constant. We show that the low-temperature magnetic susceptibility of the record-breaking ferrofluids could be explained theoretically on the basis of the first terms of the polydisperse second virial contribution in combination with the second-order modified mean field model. • Record-breaking magnetic susceptibility of ferrofluids at low temperatures. • Second virial contribution to magnetic susceptibility of polydisperse ferrofluids. • Interparticle dipole correlations are more pronounced in dense ferrofluids. • Presented model describes the ferrofluid susceptibility χ ~ 120 at temperature 240 K.

Nonlocal and nonlinear electrostatics of a dipolar Coulomb fluid

We study a model Coulomb fluid consisting of dipolar solvent molecules of finite extent which generalizes the point-like dipolar Poisson–Boltzmann model (DPB) previously introduced by Coalson and Duncan (1996 J. Phys. Chem. 100 2612) and Abrashkin et al (2007 Phys. Rev. Lett. 99 077801). We formulate a nonlocal Poisson–Boltzmann equation (NLPB) and study both linear and nonlinear dielectric response in this model for the case of a single plane geometry. Our results shed light on the relevance of nonlocal versus nonlinear effects in continuum models of material electrostatics.

Quantum hexatic order in two-dimensional dipolar and charged fluids

Recent advances in cold atom experimentation suggest that studies of quantum two-dimensional melting of dipolar molecules, with dipoles aligned perpendicular to ordering plane, may be on the horizon. An intriguing aspect of this problem is that two-dimensional classical aligned dipoles (already studied in great detail in soft matter experiments on magnetic colloids) are known to melt via a two-stage process, with an intermediate hexatic phase separating the usual crystal and isotropic fluid phases. We estimate here the effect of quantum fluctuations on this hexatic phase, for both dipolar systems and charged Wigner crystals. Our approximate phase diagrams rely on a pair of Lindemann criteria, suitably adapted to deal with the effects of thermal fluctuations in two dimensions. As part of our analysis, we determine the phonon spectra of quantum particles on a triangular lattice interacting with repulsive $1/{r}^{3}$ and $1/r$ potentials. A large softening of the transverse and longitudinal phonon frequencies, due to both lattice effects and quantum fluctuations, plays a significant role in our analysis. The hexatic phase is predicted to survive down to very low temperatures.