Dipolar Hard Sphere Fluid Research Articles

Second virial coefficient for the dipolar hard sphere fluid

The dipolar hard sphere fluid is a useful model for a polar fluid. Some years ago, the second virial coefficient, B(2), of this fluid was obtained as a series expansion in the inverse temperature or (dipole strength) by Keesom. Little work on this problem seems to have been done since that time. Using a result of Chan and Henderson for the spherical average of the Boltzmann factor of this fluid, more complete results are obtained for B(2). The more complete results are more negative than the Keesom series, as one would expect, but his expansion is remarkably accurate. This method can be used to obtain the second virial coefficient of the dipolar Lennard-Jones (Stockmayer) or dipolar Yukawa fluids.

Magnetization of multicomponent ferrofluids

The solution of the mean spherical approximation (MSA) integral equation for isotropicmulticomponent dipolar hard sphere fluids without external fields is used to construct adensity functional theory (DFT), which includes external fields, in order to obtain ananalytical expression for the external field dependence of the magnetization of ferrofluidicmixtures. This DFT is based on a second-order Taylor series expansion of the free energydensity functional of the anisotropic system around the corresponding isotropic MSAreference system. The ensuing results for the magnetic properties are in quantitativeagreement with our canonical ensemble Monte Carlo simulation data presented here.

Patching up dipoles: can dipolar particles be viewed as patchy colloids?

We investigate whether the liquid–vapour phase transition of strongly dipolar fluids can be understood using a model of patchy colloids. These consist of hard spherical particles with three short-ranged attractive sites (patches) on their surfaces. Two of the patches are of type A and one is of type B. Patches A on a particle may bond either to a patch A or to a patch B on another particle. Formation of an AA (AB) bond lowers the energy by ε AA (ε AB ). In the limit , this patchy model exhibits condensation driven by AB-bonds (Y-junctions). Y-junctions are also present in low-density, strongly dipolar fluids, and have been conjectured to play a key role in determining their critical behaviour. We map the dipolar Yukawa hard-sphere (DYHS) fluid onto this 2A + 1B patchy model by requiring that the latter reproduce the correct DYHS critical point as a function of the isotropic interaction strength εY. This is achieved for sensible values of ε AB and the bond volumes. Results for the internal energy and the particle coordination number are in qualitative agreement with simulations of DYHSs. Finally, by taking the limit , we arrive at a new estimate for the critical point of the dipolar hard-sphere fluid, which agrees with extrapolations from simulation.

Some simple results for the properties of polar fluids

The author's lecture notes concerning the correlation functions and the thermodynamics of a simple polar fluid are summarized. The emphasis is on the dipolar hard sphere fluid and the mean spherical approximation and on the relation of these results to the Clausius-Mossotti and Onsager formulae for the dielectric constant. Previous excerpts from these lecture notes, Condens. Matter Phys., 2009, 12, 127; ibid., 2010, 13, 13002, have contained results that were not widely known. It is hoped that this third, and likely final, excerpt will prove equally helpful by gathering several results together and making these more widely available and recording a few new results.

Nonadditivity of orientational interactions and perturbation theory for dipole hard spheres

The procedure of approximate summation is applied to a series of many-body perturbation theory for the internal energy of a dipolar hard sphere (DHS) fluid to produce an expression similar to the mean field approximation in the Widom-Rowlinson penetrable sphere model, which is well consistent with the experiment at moderate or high densities. Similar results are obtained from the hindered rotation model generalized for arbitrary density. The critical parameters ρc, Pc and Tc of both models are consistent with the data of machine experiments and are close to the parameters of the percolation transition in the DHS system.

Second virial coefficients of dipolar hard spheres

An asymptotic formula is reported for the second virial coefficientB2 of a dipolar hard-sphere (DHS) fluid, in zero external field, for strongly coupled dipolarinteractions. This simple formula, together with the one for the weak-couplingB2,provides an accurate prediction of the second virial coefficient for a wide range of dipole moments,including those that are experimentally accessible in magnetite ferrofluids. The weak-couplingB2 also yields an estimate of the magnetic moment minimally needed for isotropic gas–liquidphase-separation, if any, in the DHS fluid.

The structure of strongly dipolar hard sphere fluids with extended dipoles by Monte Carlo simulations

We have investigated the structural change of dipolar hard sphere fluid while we change the dipole from an idealised point dipole (pDHS fluid) to a physically more realistic extended dipole (eDHS fluid) by increasing the distance d of the two point charges ±q while keeping the dipole moment μ = qd fixed. We discuss our results on the basis of the first- and second-rank orientational order parameters, angular distribution functions, chain-length distributions, and snapshots. At a low density, we have found chain formation with longer chains as the distance d is increased. At a high density, we have found phase transition from an orientationally ordered ferroelectric nematic phase (at low d) into an isotropic liquid containing chains (at large d).

Electrostatic fluctuations in cavities within polar liquids and thermodynamics of polar solvation

We present the results of numerical simulations of the fluctuations of the electrostatic potential and electric field inside cavities created in the fluid of dipolar hard spheres. We found that the thermodynamics of polar solvation changes dramatically when the cavity size becomes about 4-5 times larger than the size of the liquid particle. The range of small cavities can be reasonably understood within the framework of current solvation models. On the contrary, the regime of large cavities is characterized by a significant softening of the cavity interface resulting in a decay of the fluctuation variances with the cavity size much faster than anticipated by both the continuum electrostatics and microscopic theories. For instance, the variance of the electrostatic potential at the cavity center decays with the cavity radius R0 approximately as 1R{0};{4-6} instead of the 1R{0} scaling expected from the standard electrostatics. Our results suggest that cores of nonpolar molecular assemblies in polar liquids lose solvation strength much faster than is traditionally anticipated.

Model energy landscapes of low-temperature fluids: Dipolar hard spheres

An analytical model of non-Gaussian energy landscape of low-temperature fluids is developed based on the thermodynamics of the fluid of dipolar hard spheres. The entire excitation profile of the liquid, from the high-temperature liquid to the point of ideal-glass transition, has been obtained from Monte Carlo simulations. The fluid of dipolar hard spheres loses stability close to the point of ideal-glass transition transforming via a first-order transition into a columnar liquid phase of dipolar chains locally arranged in a body-centered-tetragonal order. Significant non-Gaussianity of the energy landscape is responsible for narrowing of the distribution of potential energies and energies of inherent structures with decreasing temperature. We suggest that the proposed functionality of the enumeration function is widely applicable to both polar and nonpolar low-temperature liquids.

The dielectric virial expansion and the models of dipolar hard-sphere fluid

The virial expansion technique to determine the dielectric constant epsilon of dipolar hard-sphere fluid is developed. It is shown that the formalism allows to bring into agreement the results of Debye's, Onsager's, and Langevin's to the problem. The third virial coefficient of epsilon is considered as a series over dipolar parameter lambda=m(2)d(3)kT. The terms up to O(lambda(11)) are calculated analytically providing a correct description of the third virial coefficient for small and intermediate values of lambda (0<or=lambda<or=4). The results of the dielectric virial series are compared with the Monte Carlo data for epsilon found by Matyushov and Ladanyi [J. Chem. Phys. 110, 994 (1999)]. The theory is in agreement with simulations only at small values of lambda<or=2. At higher polarities, the virial series diverges. Realization of the renormalization procedure permits to enlarge the range of applicability of the virial series. In this way, the new expression for the dielectric constant as a function of two dipolar parameters, lambda and y=4 pi nm(2)9kT, has been found explicitly. The expression gives a perfect upper bound of the dielectric constant and is more reliable for determination of epsilon than the previously known ones.

Orientational order in high density dipolar hard sphere fluids

Taking advantage of recent estimates, by one of us, of the critical temperature of the isotropic-ferroelectric transition of high density dipolar hard spheres, we performed new Monte Carlo simulations in the close vicinity of these estimates and applied histogram reweighting methods to obtain refined values of the critical temperatures from the crossing of the fourth-order cumulant for different system sizes. The ferroelectric line is determined in the density range rho*=0.80-0.95, and the onset of columnar ordering is located.

Relative Permittivity of Polar Liquids. Comparison of Theory, Experiment, and Simulation

A molecular-based second-order perturbation theory is applied to calculate the relative permittivity of polar liquids. Our basic model is the dipolar hard sphere fluid. The main purpose of this work is to propose various approaches to take into account the molecular polarizability. In the continuum approach, we apply the Kirkwood-Fröhlich equation and use the high-frequency relative permittivity. The Kirkwood g-factor representing molecular correlations is calculated by a perturbation theory. In the molecular approach, the molecular polarizability is built into the model on the molecular level (the polarizable dipolar hard sphere fluid). To calculate the relative permittivity of this system, an equation obtained from a renormalization procedure is used. In both approaches, we apply a series expansion for the relative permittivity and show that these series expansions give results in better agreement with simulation data than the original equations. After testing our theoretical equations against our own Monte Carlo simulation results, we compare the results obtained from our theoretical equations and simulations to experimental data for amines, ethers, and halogenated, sulfur, and hydroxy compounds. We propose a procedure to calculate potential parameters (hard sphere diameter, reduced polarizability, and reduced dipole moment) from experimental data such as the permanent dipole moment, refractive index, density, and temperature. We show that for compounds of low relative permittivity the polarizable dipolar hard sphere (PDHS) model and the continuum approach give reasonable results. For nonassociative liquids of higher relative permittivity, the PDHS model overestimates experimental data due to unsatisfactory representation of the shape of the molecules. In the case of associative liquids, the PDHS model works well, and in some cases it underestimates the experimental values due to the unsatisfactory treatment of electrostatic interactions.

Dielectric constant of the polarizable dipolar hard sphere fluid studied by Monte Carlo simulation and theories

A systematic Monte Carlo (MC) simulation and perturbation theoretical (PT) study is reported for the dielectric constant of the polarizable dipolar hard sphere (PDHS) fluid. We take the polarizability of the molecules into account in two different ways. In a continuum approach we place the permanent dipole of the molecule into a sphere of dielectric constant ∞ in the spirit of Onsager. The high frequency dielectric constant ∞ is calculated from the Clausius-Mosotti relation, while the dielectric constant of the polarizable fluid is obtained from the Kirkwood-Frohlich equation. In the molecular approach, the polarizability is built into the model on the molecular level, which makes the interactions nonpairwise additive. Here we use Wertheim’s renormalized PT method to calculate the induced dipole moment, while the dielectric constant is calculated from our recently introduced formula [22]. We also apply a series expansion for the dielectric constant both in the continuum and the molecular approach. These series expansions ensure a better agreement with simulation results. The agreement between our MC data and the PT results in the molecular approach is excellent for low to moderate dipole moments and polarizabilities. At stronger dipolar interactions ergodicity problems and anizotropic behaviour appear where simulation results become uncertain and the theoretical approach becomes invalid.

Spontaneous orientational ordering in magnetic fluids

The problem of spontaneous orientational order in dipolar hard sphere fluid is studied on the basis of the BBGKY equation self-consistent solution. This self-consistent approach is used in the density functional method and proves to be equivalent to the mean field theory. In the framework of dipole–dipole interaction second order perturbation model the following effect is discovered: the self-consistent density functional approach leads to the spontaneous “ferrimagnetic’’ state of the magnetic fluid induced by the dipole–dipole interaction.

Long-range order of dipolar fluids

The general theory of the isotropic–ferromagnetic transition of dipolar hard sphere fluids is considered on the base of the formalism of the direct correlation function. The equation of the Lovett–Mou–Buff–Gubbins type, described the one-particle orientational distribution, is generalized on a case of long-range interparticle potential and ellipsoidal sample shape. The exact criterion of the isotropic–ferromagnetic transition is found as a result of bifurcation analysis. It is shown that the formalism reduces to all known approximations in partial cases. A new expression for the susceptibility is obtained analytically within the framework of the generalized mean-spherical approximation. It is demonstrated that the susceptibility diverges at appropriate values of short-range correlations. In this way, the decisive role of short-range correlations outside the core in the transition appearance is established whereas the long-range correlations are found to be of secondary importance. The qualitative estimations show that the short-range pair correlations in dipolar fluids are most likely antiferromagnetic in character so as the transition to ferromagnetic liquid becomes questionable.

Susceptibility measurements on afractionated aggregate-free ferrofluid

The concentration dependence of the susceptibility ofaggregate-free ferrofluids was investigated. The ferrofluidsconsisted of oleic-acid-grafted magnetite particles incyclohexane. One of the samples contained strongly interactingparticles (interaction strength of approximately 5kT). Qualitatively, the measurements are in agreementwith theoretical predictions on dipolar hard-sphere fluids:dipolar interactions raise the susceptibility above the ideal(Langevin) susceptibility, and when plotted as a function ofthe Langevin (ideal) susceptibility, the measurements on thetwo samples are very similar. Quantitatively, theoreticalpredictions overestimate the experimental susceptibilities athigher ferrofluid concentrations.

Microscopic dynamics of molecular liquids and glasses: role of orientations and translation-rotation coupling.

We investigate the dynamics of a fluid of dipolar hard spheres in its liquid and glassy phases, with emphasis on the microscopic time or frequency regime. This system shows rather different glass transition scenarios related to its rich equilibrium behavior, which ranges from a simple hard sphere fluid to long range ferroelectric orientational order. In the liquid phase close to the ideal glass transition line and in the glassy regime a medium range orientational order occurs leading to a softening of an orientational mode. To investigate the role of this mode we use the molecular mode-coupling equations to calculate the spectra straight phi"lm(q,omega) and chi"lm(q,omega). In the center of mass spectra straight phi"00(q,omega) and chi"00(q,omega) we found, besides a high frequency peak at omega(hf), a peak at omega(op), about one decade below omega(hf) x omega(op) has almost no q dependence and exhibits an "isotope" effect omega(op) proportional to I(-1/2), with I the moment of inertia. We give evidence that the existence of this peak is related to the occurrence of medium range orientational order. It is shown that some of these features also exist for schematic mode coupling models.

Fluids of strongly interacting dipoles: Monte Carlo sampling using Tsallis statistics

Monte Carlo simulations of dipolar hard-sphere fluids in a generalized ensemble based on the physical realisation of Tsallis probabilities are reported. The new algorithm leads to a significantly better sampling than the standard Monte Carlo method. At very low densities, when the dipolar system is characterized by the presence of polymeric chains of head-to-tail aligned dipoles, simulations with q>1 may exhibit a better convergence to equilibrium. The improved sampling can be explained by the use in the generalized ensemble of an effective dipolar potential with a q-dependent anisotropy.

Comparison of perturbation theory and mean spherical approximation for polar fluids and ion–dipole mixtures based on molecular simulation data

A comprehensive study on various internal energies, pressures and chemical potentials for the pure dipolar hard sphere fluids, pure Stockmayer fluids, the Lennard–Jones and Stockmayer mixtures, the Stockmayer and Stockmayer mixtures and the ion–dipole mixtures is reported based on the perturbation theory (PT) and mean spherical approximation (MSA). Compared with the results of molecular simulations, it is shown that the PT is superior to MSA in most cases.

Comment on "Algebraic perturbation theory for polar fluids: A model for the dielectric constant"

Kalikmanov [Phys. Rev. E 59, 4085 (1999)] proposed a perturbation theory method to calculate the dielectric constant of dipolar hard sphere fluids using an infinitely long cylindrical container to avoid the depolarization. We demonstrate that while the method is very helpful, his theory appears to be incomplete because of the incorrect calculation of the corresponding three-body integrals. It is shown that with the correct consideration of these terms the theory is consistent with the results of earlier work in low-density limit, and at high densities the method yields the equation of Tani et al. [Mol. Phys. 48, 863 (1983)] for the dipolar hard sphere fluid dielectric constant.