Vapour–liquid phase transition of dipolar particles

Percolation transition and bimodal density distribution in hydrogen fluoride

Hydrogen-bond networks in associating fluids can be extremely robust and characterize the topological properties of the liquid phase, as in the case of water, over its whole domain of stability and beyond. Here, we report on molecular dynamics simulations of hydrogen fluoride (HF), one of the strongest hydrogen-bonding molecules. HF has more limited connectivity than water but can still create long, dynamic chains, setting it apart from most other small molecular liquids. Our simulation results provide robust evidence of a second-order percolation transition of HF's hydrogen bond network occurring below the critical point. This behavior is remarkable as it underlines the presence of two different cohesive mechanisms in liquid HF, one at low temperatures characterized by a spanning network of long, entangled hydrogen-bonded polymers, as opposed to short oligomers bound by the dispersion interaction above the percolation threshold. This second-order phase transition underlines the presence of marked structural heterogeneity in the fluid, which we found in the form of two liquid populations with distinct local densities.

Chain Formation and Phase Separation in Ferrofluids: The Influence on Viscous Properties

Ferrofluids have attracted considerable interest from researchers and engineers due to their rich set of unique physical properties that are valuable for many industrial and biomedical applications. Many phenomena and features of ferrofluids' behavior are determined by internal structural transformations in the ensembles of particles, which occur due to the magnetic interaction between the particles. An applied magnetic field induces formations, such as linear chains and bulk columns, that become elongated along the field. In turn, these structures dramatically change the rheological and other physical properties of these fluids. A deep and clear understanding of the main features and laws of the transformations is necessary for the understanding and explanation of the macroscopic properties and behavior of ferrofluids. In this paper, we present an overview of experimental and theoretical works on the internal transformations in these systems, as well as on the effect of the internal structures on the rheological effects in the fluids.

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.

Modified mean-field theory of the magnetic properties of concentrated, high-susceptibility, polydisperse ferrofluids

The effects of particle-size polydispersity on the magnetostatic properties of concentrated ferrofluids are studied using theory and computer simulation. The second-order modified mean-field (MMF2) theory of Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)1063-651X10.1103/PhysRevE.64.041405] has been extended by calculating additional terms of higher order in the dipolar coupling constant in the expansions of the initial magnetic susceptibility and the magnetization curve. The theoretical predictions have been tested rigorously against results from Monte Carlo simulations of model monodisperse, bidisperse, and highly polydisperse ferrofluids. Comparisons have been made between systems with the same Langevin susceptibility and the same saturation magnetization. In all cases, the new theoretical magnetization curve shows better agreement with simulation data than does the MMF2 theory. As for the initial susceptibility, MMF2 theory is most accurate for the monodisperse model, while the new theory works best for polydisperse systems with a significant proportion of large particles. These results are important for the analysis and characterization of recently synthesized polydisperse ferrofluids with record-breaking values of the initial magnetic susceptibility.

Charge ordering and scattering pre-peaks in ionic liquids and alcohols

The structural properties of ionic liquids and alcohols are viewed under the charge ordering process as a common basis to explain the peculiarity of their radiation scattering properties, namely the presence, or absence, of a scattering pre-peak.

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.

From solutions to molecular emulsions

Concentration fluctuations play an important role in the statistical description of the stability of liquids, particularly in the neighborhood of phase transitions. Classical thermodynamics is blind to fluctuations, and statistical thermodynamics is required to fully understand quantities such as the isothermal compressibility or heat capacity, by linking them to fluctuations of appropriate statistical microscopic quantities and showing that they are response functions. This is illustrated by the seminal Kirkwood–Buff theory of solutions. However, the existence of micro-heterogeneous structures, particularly in aqueous mixtures, which leads to large Kirkwood–Buff integrals, suggest that micro-heterogeneity is a form of concentration fluctuation. This interpretation becomes difficult to accept when extrapolated to larger micro-heterogeneous structures such as micellar aggregates in micro-emulsions. By analyzing how different methods, experimental, computer experiments and theoretical approaches deal with the underlying duality behind these two physical manifestations, we put in evidence the need to reconsider the description of liquids by incorporating the description of emergent “objects”, such as the micro-heterogeneous structures from a molecular point of view. On this path, the concept of “molecular emulsion” allows to describe in a unified way all type of disordered liquids, from solutions to the organized liquids of soft matter.

Phase separation and self-assembly in a fluid of Mickey Mouse particles

Recent developments in the synthesis of colloidal particles allow for control over shape and inter-particle interaction. One example, among others, is the so-called "Mickey Mouse" (MM) particle for which the self-assembly properties have been previously studied yielding a stable cluster phase together with elongated, tube-like structures. Here, we investigate under which conditions a fluid of Mickey Mouse particles can yield phase separation and how the self-assembly behaviour affects the gas-liquid coexistence. We vary the distance between the repulsive and the attractive lobes (bond length), and the interaction range, and follow the evolution of the gas-liquid (GL) coexistence curve. We find that upon increasing the bond length distance the binodal line shifts to lower temperatures, and that the interaction range controls the transition between phase separation and self-assembly of clusters. Upon further reduction of the interaction range and temperature, the clusters assume an increasingly ordered tube-like shape, ultimately matching the one previously reported in literature. These results are of interest when designing particle shape and particle-particle interaction for self-assembly processes.

A simplified representation of anisotropic charge distributions within proteins

Effective coarse-grained representations of protein-protein interaction potentials are vital in the modeling of large scale systems. We develop a method to fit an arbitrary number of effective charges to approximate the electrostatic potential of a protein at a given pH in an ionic solution. We find that the effective charges can reproduce an input potential calculated from a high resolution Poisson-Boltzmann calculation. Since the effective charges used in this model are not constrained to the locations of the original charged groups, the extra degrees of freedom allows us to reproduce the field anisotropy with fewer charges. The fitting procedure uses a number of approximations in the charge magnitudes, initial conditions, and multipoles to speed convergence. The most significant gains are found by fitting the multipole moments of the effective charge potential to the moments of the original field. We show that the Yukawa potential is not only sufficient as a pairwise summation in reproducing the potential, but comes naturally from the linearized expansion of the Poisson-Boltzmann equation. We compute interaction energies and find excellent agreement to the original potential. From the effective charge model we compute the electrostatic contribution to the second virial coefficient.

Self-assembly in chains, rings, and branches: a single component system with two critical points

We study the interplay between phase separation and self-assembly in chains, rings, and branched structures in a model of particles with dissimilar patches. We extend Wertheim's first order perturbation theory to include the effects of ring formation and to theoretically investigate the thermodynamics of the model. We find a peculiar shape for the vapor-liquid coexistence, featuring reentrant behavior in both phases and two critical points, despite the single-component nature of the system. The emergence of the lower critical point is caused by the self-assembly of rings taking place in the vapor, generating a phase with lower energy and lower entropy than the liquid. Monte Carlo simulations of the same model fully support these unconventional theoretical predictions.

Slow relaxation in structure-forming ferrofluids

We study the behavior of colloidal magnetic fluids at low density for various dipolar interaction strengths by performing extensive Langevin dynamics simulations with model parameters that mimic cobalt-based ferrofluids used in experiments. Our study mainly focuses on the structural and dynamical properties of dipolar fluids and the influence of structural changes on their dynamics. Drastic changes from chainlike to networklike structures in the absence of an external magnetic field are observed. This crossover plays an important role in the slowing down of dynamics that is reflected in various dynamical properties including the tracer diffusion and the viscosity and also in the structural relaxation.

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.

Nonmonotonic magnetic susceptibility of dipolar hard-spheres at low temperature and density

We investigate, via numerical simulations, mean field, and density functional theories, the magnetic response of a dipolar hard sphere fluid at low temperatures and densities, in the region of strong association. The proposed parameter-free theory is able to capture both the density and temperature dependence of the ring-chain equilibrium and the contribution to the susceptibility of a chain of generic length. The theory predicts a nonmonotonic temperature dependence of the initial (zero field) magnetic susceptibility, arising from the competition between magnetically inert particle rings and magnetically active chains. Monte Carlo simulation results closely agree with the theoretical findings.

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.

Theory and simulation of anisotropic pair correlations in ferrofluids in magnetic fields

Anisotropic pair correlations in ferrofluids exposed to magnetic fields are studied using a combination of statistical-mechanical theory and computer simulations. A simple dipolar hard-sphere model of the magnetic colloidal particles is studied in detail. A virial-expansion theory is constructed for the pair distribution function (PDF) which depends not only on the length of the pair separation vector, but also on its orientation with respect to the field. A detailed comparison is made between the theoretical predictions and accurate simulation data, and it is found that the theory works well for realistic values of the dipolar coupling constant (λ = 1), volume fraction (φ ≤ 0.1), and magnetic field strength. The structure factor is computed for wavevectors either parallel or perpendicular to the field. The comparison between theory and simulation is generally very good with realistic ferrofluid parameters. For both the PDF and the structure factor, there are some deviations between theory and simulation at uncommonly high dipolar coupling constants, and with very strong magnetic fields. In particular, the theory is less successful at predicting the behavior of the structure factors at very low wavevectors, and perpendicular Gaussian density fluctuations arising from strongly correlated pairs of magnetic particles. Overall, though, the theory provides reliable predictions for the nature and degree of pair correlations in ferrofluids in magnetic fields, and hence should be of use in the design of functional magnetic materials.

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.

Phase diagrams of particles with dissimilar patches: X-junctions and Y-junctions

We use Wertheim's first-order perturbation theory to investigate the phase behaviour and the structure of coexisting fluid phases for a model of patchy particles with dissimilar patches (two patches of type A and f(B) patches of type B). A patch of type α = {A,B} can bond to a patch of type β = {A,B} in a volume v(αβ), thereby decreasing the internal energy by ϵ(αβ). We analyse the range of model parameters where AB bonds, or Y-junctions, are energetically disfavoured (ϵ(AB) < ϵ(AA)/2) but entropically favoured (v(AB) ≫ v(αα)), and BB bonds, or X-junctions, are energetically favoured (ϵ(BB) > 0). We show that, for low values of ϵ(BB)/ϵ(AA), the phase diagram has three different regions: (i) close to the critical temperature a low-density liquid composed of long chains and rich in Y-junctions coexists with a vapour of chains; (ii) at intermediate temperatures there is coexistence between a vapour of short chains and a liquid of very long chains with X- and Y-junctions; (iii) at low temperatures an ideal gas coexists with a high-density liquid with all possible AA and BB bonds formed. It is also shown that in region (i) the liquid binodal is reentrant (its density decreases with decreasing temperature) for the lower values of ϵ(BB)/ϵ(AA). The existence of these three regions is a consequence of the competition between the formation of X- and Y-junctions: X-junctions are energetically favoured and thus dominate at low temperatures, whereas Y-junctions are entropically favoured and dominate at higher temperatures.

Nonequilibrium condensation and coarsening of field-driven dipolar colloids

In colloidal suspensions, self-organization processes can be easily fueled by external fields. Here we consider monolayers of particles with permanent dipole moments that are driven by rotating external fields. In recent experiments, it has been shown that the particles in such systems self-organize into two-dimensional clusters. Here we report results from a computer simulation study of these pattern forming systems. Specifically, we employ Langevin dynamics simulations, Brownian dynamics simulations that include hydrodynamic interactions, and Wang-Landau Monte Carlo simulations of soft spheres interacting via dipolar potentials. We investigate at which field strengths and frequencies clusters form and explore the influence of hydrodynamic interactions. We also examine the phase behavior of the equilibrium system resulting from a time average of the colloidal interactions in the rotating field. In this way we demonstrate that the clustering described in the driven system arises from a first-order phase transition between a vapor and a condensed phase.

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.

Reentrant phase diagram of network fluids

We introduce a microscopic model for particles with dissimilar patches which displays an unconventional "pinched" phase diagram, similar to the one predicted by Tlusty and Safran in the context of dipolar fluids [Science 290, 1328 (2000)]. The model-based on two types of patch interactions, which account, respectively, for chaining and branching of the self-assembled networks-is studied both numerically via Monte Carlo simulations and theoretically via first-order perturbation theory. The dense phase is rich in junctions, while the less-dense phase is rich in chain ends. The model provides a reference system for a deep understanding of the competition between condensation and self-assembly into equilibrium-polymer chains.

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.

Dipolar sticky hard spheres within the Percus-Yevick approximation plus orientational linearization

We consider a strongly idealized model for polar fluids, which consists of spherical particles, having, in addition to a hard-core repulsion, a "surface dipolar" interaction, acting only when particles are exactly at contact. A fully analytic solution of the molecular Orstein-Zernike equation is found for this potential, within the Percus-Yevick approximation complemented by a linearization of the angular dependence on molecular orientations (Percus-Yevick closure with orientational linearization). Numerical results are also presented in a detailed analysis about the local orientational structure. From the pair correlation function g(1,2), we first derive the best orientations of a test particle which explores the space around an arbitrary reference molecule. Then some local and global order parameters, related to the polarization induced by the reference particle, are also calculated. The local structure of this model with only short-ranged anisotropic interactions turns out to be, at least within the chosen approximation, qualitatively different from that of hard spheres with fully long-ranged dipolar potentials.

Local orientational ordering in fluids of spherical molecules with dipolarlike anisotropic adhesion

We discuss some interesting physical features stemming from our previous analytical study of a simple model of a fluid with dipolarlike interactions of very short range in addition to the usual isotropic Baxter potential for adhesive spheres. While the isotropic part is found to rule the global structural and thermodynamical equilibrium properties of the fluid, the weaker anisotropic part gives rise to an interesting short-range local ordering of nearly spherical condensation clusters, containing short portions of chains having nose-to-tail parallel alignment, which runs antiparallel to adjacent similar chains.

Dipolar particles in an external field: Molecular dynamics simulation and mean field theory

Using molecular dynamics computer simulation we compute gas-liquid phase coexistence curves for the Stockmayer fluid in an external electric field. We observe a field-induced shift of the critical temperature DeltaTc. The sign of DeltaTc depends on whether the potential or the surface charge density is held constant assuming that the dielectric material fills the space between capacitor plates. Our own as well as previous literature data for DeltaTc are compared to and interpreted in terms of a simple mean field theory. Despite considerable errors in the simulation results, we find consistency between the simulation results obtained by different groups including our own and the mean field description. The latter ties the sign of DeltaTc to the outside constraints via the electric field dependence of the orientation part of the mean field free energy.

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.

Criticality of colloids with distinct interaction patches: the limits of linear chains, hyperbranched polymers, and dimers

We use a simple model of associating fluids which consists of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type A and one is of type B; the bonding interactions between each pair of spots have strengths epsilon(AA), epsilon(BB), and epsilon(AB). The theory is applied over the whole range of bonding strengths and the results are interpreted in terms of the equilibrium cluster structures of the phases. In addition to our numerical results, we derive asymptotic expansions for the free energy in the limits for which there is no liquid-vapor critical point: linear chains (epsilon(AA) not equal to 0, epsilon(AB)=epsilon(BB)=0) , hyperbranched polymers (epsilon(AB) not equal to 0, epsilon(AA)=epsilon(B)=0) , and dimers (epsilon(BB) not equal to 0, epsilon(AA)=epsilon(AB)=0) . These expansions also allow us to calculate the structure of the critical fluid by perturbing around the above limits, yielding three different types of condensation: of linear chains (AA clusters connected by a few AB or BB bonds); of hyperbranched polymers (AB clusters connected by AA bonds); or of dimers (BB clusters connected by AA bonds). Interestingly, there is no critical point when in(AA) vanishes despite the fact that AA bonds alone cannot drive condensation.