Demixing in binary mixtures of apolar and dipolar hard spheres

Free energy calculations for rings and chains formed by dipolar hard spheres

We employ a method based on Monte Carlo grand-canonical simulations to precisely calculate partition functions of non-interacting chains and rings formed by dipolar hard spheres (DHS) at low temperature. The extended low temperature region offered by such cluster calculations, compared to what had been previously achieved with standard simulations, opens up the possibility of exploring a part of the DHS phase diagram which was inaccessible before. The reported results offer the unique opportunity of verifying well-established theoretical models based on the ideal gas of cluster approximation in order to clarify their range of validity. They also provide the basis for future studies in which cluster-cluster interactions will be included.

Phase Behavior of Magnetic Nanocolloids of Different Sizes Suspended in an Apolar Solvent

We employ classical density functional theory (DFT) to investigate the phase behavior and composition of binary mixtures; each compound consists of hard spheres of different sizes with superimposed dispersion attraction. In addition to the dispersion attraction, molecules of one component carry an additional three-dimensional magnetic "spin" where the orientation-dependent spin-spin interaction is accounted for by the Heisenberg model. We are treating the excess free energy using a modified mean-field approximation (second virial coefficient) for the orientation-dependent pair correlation function. Depending on the concentration of the magnetic particles, the strength of the spin-spin coupling, and the size ratio of the particles, the model predicts the formation of ordered (polar) phases in addition to the more conventional gas and isotropic liquid phases. Key features of our model are a particle-size dependent shift of the gas-liquid critical point (critical temperature and density) and a change in the width of the phase diagram. In the near-critical region, the latter can be analyzed quantitativly in terms of an effective critical exponent β_eff that may differ from the classical critical exponent [Formula: see text]; the classical value is attained in the immediate vicinity of the critical point as it must. The deviation between β_eff and β can be linked to nontrivial composition effects along the phase boundaries.

Condensation, demixing, and orientational ordering of magnetic colloidal suspensions

In this work we study the phase behavior of magnetic particles suspended in a simple nonmagnetic solvent. Magnetic particles are modelled as spherical particles carrying a three-dimensional, classical Heisenberg spin, whereas solvent molecules are treated as spherically symmetric Lennard-Jones particles. The binary mixture of magnetic particles and solvent is studied within the framework of classical density functional theory (DFT). Within DFT pair correlations are treated at the modified mean-field level at which they are approximated by orientation dependent Mayer f functions. In the absence of an external magnetic field four generic types of phase diagrams are observed depending on the concentration of magnetic particles. In this case we observe liquid-liquid phase coexistence between an orientationally ordered (polarized) and a disordered phase characterized by slightly different concentrations of magnetic particles. Liquid-liquid phase coexistence is suppressed by an external field and vanishes completely if the strength of the field is sufficiently large.

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.

Phase coexistence for charged soft dumbbell and ionic soft sphere systems via molecular dynamics simulation

Gas-liquid critical parameters of charged soft dumbbells (CSDs) as function of the site-to-site separation on the dumbbells, d, obtained on the basis of molecular dynamics computer simulation are presented. A mean field theoretical description is developed, which explains the results at small and large d, respectively. We note that in the limit d→0 the CSD system exhibits gas-liquid phase separation solely driven by repulsion and dipole-dipole interaction. If the dumbbell bond is eliminated the CSD system becomes similar to the restricted primitive model of ionic fluids with hard core repulsion replaced by soft repulsion. We obtain the gas-liquid critical parameters for this model and discuss their relation to the CSD system.

Thermodynamics of dipolar hard spheres with low-to-intermediate coupling constants

The thermodynamic properties of the dipolar hard-sphere fluid are studied using theory and simulation. A new theory is derived using a convenient mathematical approximation for the Helmholtz free energy relative to that for the hard-sphere fluid. The approximation is designed to give the correct low-density virial expansion. New theoretical and numerical results for the fourth virial coefficient are given. Predictions of thermodynamic functions for dipolar coupling constants λ=1 and 2 show excellent agreement with simulation results, even at the highest value of the particle volume fraction φ. For higher values of λ, there are deviations at high volume fractions, but the correct low-density behavior is retained. The theory is compared critically against the established thermodynamic perturbation theory; it gives significant improvements at low densities and is more convenient in terms of the required numerics. Dipolar hard spheres provide a basic model for ferrofluids, and the theory is accurate for typical experimental parameters λ </~ 2 and φ </~ 0.1. This is demonstrated explicitly by fitting osmotic equations of state for real ferrofluids measured recently by analytical centrifugation.

No evidence of gas-liquid coexistence in dipolar hard spheres

We report accurate calculations of the particle density of states in the dipolar hard-sphere fluid. Implementing efficient and tailored Monte Carlo algorithms, we are able to explore, in equilibrium, the low temperature region where a phase separation between a dilute gas of chain ends and a high-density liquid of chain junctions has been predicted to occur. Our data clearly show that the density of states remains always single peaked, definitively excluding the possibility of critical phenomena in the investigated temperature and density region. The analysis of the low temperature configurations shows that at low densities particles preferentially self-assemble into closed rings, strongly suppressing the chain ends concentration.

Gas-liquid coexistence in a system of dipolar soft spheres

The existence of gas-liquid coexistence in dipolar fluids with no other contribution to attractive interaction than dipole-dipole interaction is a basic and open question in the theory of fluids. Here we compute the gas-liquid critical point in a system of dipolar soft spheres subject to an external electric field using molecular dynamics computer simulation. Tracking the critical point as the field strength is approaching zero we find the following limiting values: T(c)=0.063 and ρ(c)=0.0033 (dipole moment μ=1). These values are confirmed by independent simulation at zero field strength.

Binary mixture adsorbed in a slit pore: Field-induced population inversion near the bulk instability

The recently proposed method for modulating through an external field the composition of a binary fluid mixture adsorbed in a slit pore is discussed. The population inversion near the bulk (demixing) instability is first analyzed in the case of a symmetric mixture of nonadditive hard spheres, without field. It is next investigated for a mixture comprising dipolar particles subject to an external field. The influence of several factors on the adsorption curves including bulk composition, pore width, field direction, polarizability versus permanent dipoles, and temperature on this field induced population inversion is shown by Monte Carlo simulation.

Tracking gas-liquid coexistence in fluids of charged soft dumbbells

The existence of gas-liquid coexistence in dipolar fluids with no other contribution to attractive interaction than dipole-dipole interaction is a basic and open question in the theory of fluids. Recent Monte Carlo work by Camp and co-workers indicates that a fluid of charged hard dumbbells does exhibit gas-liquid (g-l) coexistence. This system has the potential to answer the above fundamental question because the charge-to-charge separation, d , on the dumbbells may be reduced to, at least in principle, yield the dipolar fluid limit. Using the molecular-dynamics technique we present simulation results for the g-l critical point of charged soft dumbbells at fixed dipole moment as function of d . We do find a g-l critical point at finite temperature even at the smallest d value (10;{-4}) . Reversible aggregation appears to play less a role than in related model systems as d becomes small. Consequently attempts to interpret the simulation results using either an extension of Flory's lattice theory for polymer systems, which includes reversible assembly of monomers into chains, or the defect model for reversible networks proposed by Tlusty and Safran are not successful. The overall best qualitative interpretation of the critical parameters is obtained by considering the dumbbells as dipoles immersed in a continuum dielectric.

Phase behavior of the hard-sphere Maier-Saupe fluid under spatial confinement

The Maier-Saupe hard-sphere fluid is one of the simplest models that accounts for the isotropic-nematic transition characteristic of liquid crystal phases. At low temperatures the model is known to present a gas-liquid-like transition with a large difference between the densities of the coexistence phases, whereas at higher temperature the transition becomes a weak first-order transition resembling the typical order-disorder (nematic-isotropic) phase change of liquid crystals. Spatial dimensionality directly conditions the character of the orientational phase change (i.e., the high temperature transition), that goes from a first-order transition in the purely three-dimensional case, to a Berezinskii-Kosterlitz-Thouless-like continuous transition which occurs when the three dimensional Maier-Saupe spins are constrained to lie on a plane. In the latter instance, the ordered phase is not endowed with true long-range order. In this work we investigate how the continuous transition transforms into a true first-order phase change, by analyzing the phase behavior of a system of three dimensional Maier-Saupe hard spheres confined between two parallel plates, with separations ranging from the quasi-two-dimensional regime to the bulk three-dimensional limit. Our results indicate that spatial confinement in one direction induces the change from first order to a continuous transition with a corresponding decrease of the transition temperatures. As to the gas-liquid transition, the estimated "critical" temperatures and densities also decrease as the fluid is confined, in agreement with previous results for other simple systems.

A cluster algorithm for Monte Carlo simulation at constant pressure

We propose an efficient algorithm to sample the volume in Monte Carlo simulations in the isobaric-isothermal ensemble. The method is designed to be applied in the simulation of hard-core models at high density. The algorithm is based in the generation of clusters of particles. At the volume change step, the distances between pairs of particles belonging to the same cluster do not change. This is done by rescaling the positions of the center of mass of each cluster instead of the position of each individual particle. We have tested the performance of the algorithm by simulating fluid and solid phases of hard spheres, finding that in both cases the algorithm is much more efficient than the standard procedure. Moreover, the efficiency of the method measured in terms of correlation "time" does not depend on the system size in contrast with the standard method, in which the sampling becomes rapidly inefficient as the system size increases. We have used the procedure to compute with high precision the equation of state of the face-centered-cubic phase of the hard sphere system for different system sizes. Using these results we have estimated the equation of state at the thermodynamic limit. The results are compared to different equations of state proposed in literature.