Crystal structures and freezing of dipolar fluids

Topological structures, spontaneous symmetry breaking and energy spectra in dipole hexagonal lattices

The interplay between the special triangular/hexagonal two dimensional lattice and the long range dipole-dipole interaction gives rise to topological defects, specifically the vortex, formed by a particular arrangement of the interacting classic dipoles. The nature of such vortices has been traditionally explained on the basis of numerical evidence. Here we propose the emerging formation of vortices as the natural minimum energy configuration of interacting (in-plane) two-dimensional dipoles based on the mechanism of spontaneous symmetry breaking. As opposed to the quantal case, where spin textures such as skyrmions or bimerons occur due to non-linearities in their Hamiltonian, it is still possible to witness classic topological structures due only to the nature of the dipole-dipole force. We shall present other (new) topological structures for the in-plane honeycomb lattice, as well as for two-dimensional out-of-plane dipoles. These structures will prove to be essential in the minimum energy configurations for three-dimensional simple hexagonal and hexagonal-closed-packed structures, whose energies in the bulk are obtained for the first time.

Minimum and maximum energy for crystals of magnetic dipoles

Properties of many magnetic materials consisting of dipoles depend crucially on the nature of the dipole-dipole interaction. In the present work, we study systems of magnetic dipoles where the dipoles are arranged on various types of one-dimensional, two-dimensional and three-dimensional lattices. It is assumed that we are in the regime of strong dipole moments where a classical treatment is possible. We combine a new classical numerical approach in conjuncture with an ansatz for an energy decomposition method to study the energy stability of various magnetic configurations at zero temperature for systems of dipoles ranging from small to an infinite number of particles. A careful analysis of the data in the bulk limit allows us to identify very accurate minimum and maximum energy bounds as well as ground state configurations corresponding to various types of lattices. The results suggest stabilization of a particularly interesting ground state configuration consisting of three embedded spirals for the case of a two-dimensional hexagonal lattice.

Magnetic dimer at a surface: Influence of gravity and external magnetic fields

The interaction of two dipolar hard spheres near a surface and under the influence of gravity and external perpendicular magnetic fields is investigated theoretically. The full ground-state phase diagram as a function of gravity and magnetic field strengths is established. A dimer (i.e., two touching beads) can only exist when the gravity and magnetic field strengths are simultaneously not too large. Thereby, upon increasing the magnetic field strength, three dimeric states emerge: a lying state (dimer axis parallel to the substrate), an inclined state (intermediate state between the lying and standing ones) and a standing state (dimer axis normal to the substrate). It is found that the orientation angles of the dimer axis and the dipole moment in the newly discovered inclined phase are related by a strikingly simple Snell-Descartes-like law. We argue that our findings can be experimentally verified in colloidal and granular systems.

Self-assembly of Pseudo-Dipolar Nanoparticles at Low Densities and Strong Coupling

Nanocolloids having directional interactions are highly relevant for designing new self-assembled materials easy to control. In this article we report stochastic dynamics simulations of finite-size pseudo-dipolar colloids immersed in an implicit dielectric solvent using a realistic continuous description of the quasi-hard Coulombic interaction. We investigate structural and dynamical properties near the low-temperature and highly-diluted limits. This system self-assembles in a rich variety of string-like configurations, depicting three clearly distinguishable regimes with decreasing temperature: fluid, composed by isolated colloids; string-fluid, a gas of short string-like clusters; and string-gel, a percolated network. By structural characterization using radial distribution functions and cluster properties, we calculate the state diagram, verifying the presence of string-fluid regime. Regarding the string-gel regime, we show that the antiparallel alignment of the network chains arises as a novel self-assembly mechanism when the characteristic interaction energy exceeds the thermal energy in two orders of magnitude, u_d/k_BT ≈ 100. This is associated to relevant structural modifications in the network connectivity and porosity. Furthermore, our results give insights about the dynamically-arrested nature of the string-gel regime, where we show that the slow relaxation takes place in minuscule energy steps that reflect local rearrangements of the network.

Self-organization into ferroelectric and antiferroelectric crystals via the interplay between particle shape and dipolar interaction

Ferroelectricity and antiferroelectricity are widely seen in various types of condensed matter and are of technological significance not only due to their electrical switchability but also due to intriguing cross-coupling effects such as electro-mechanical and electro-caloric effects. The control of the two types of dipolar order has practically been made by changing the ionic radius of a constituent atom or externally applying strain for inorganic crystals and by changing the shape of a molecule for organic crystals. However, the basic physical principle behind such controllability involving crystal-lattice organization is still unknown. On the basis of a physical picture that a competition of dipolar order with another type of order is essential to understand this phenomenon, here we develop a simple model system composed of spheroid-like particles with a permanent dipole, which may capture an essence of this important structural transition in organic systems. In this model, we reveal that energetic frustration between the two types of anisotropic interactions, dipolar and steric interactions, is a key to control not only the phase transition but also the coupling between polarization and strain. Our finding provides a fundamental physical principle for self-organization to a crystal with desired dipolar order and realization of large electro-mechanical effects.

Mean-field density functional theory of a nanoconfined classical, three-dimensional Heisenberg fluid. II. The interplay between molecular packing and orientational order

As in Paper I of this series of papers [S. M. Cattes et al., J. Chem. Phys. 144, 194704 (2016)], we study a Heisenberg fluid confined to a nanoscopic slit pore with smooth walls. The pore walls can either energetically discriminate specific orientations of the molecules next to them or are indifferent to molecular orientations. Unlike in Paper I, we employ a version of classical density functional theory that allows us to explicitly account for the stratification of the fluid (i.e., the formation of molecular layers) as a consequence of the symmetry-breaking presence of the pore walls. We treat this stratification within the White Bear version (Mark I) of fundamental measure theory. Thus, in this work, we focus on the interplay between local packing of the molecules and orientational features. In particular, we demonstrate why a critical end point can only exist if the pore walls are not energetically discriminating specific molecular orientations. We analyze in detail the positional and orientational order of the confined fluid and show that reorienting molecules across the pore space can be a two-dimensional process. Last but not least, we propose an algorithm based upon a series expansion of Bessel functions of the first kind with which we can solve certain types of integrals in a very efficient manner.

Ground state of dipolar hard spheres confined in channels

We investigate the ground state of a classical two-dimensional system of hard-sphere dipoles confined between two hard walls. Using lattice sum minimization techniques we reveal that at fixed wall separations, a first-order transition from a vacuum to a straight one-dimensional chain of dipoles occurs upon increasing the density. Further increase in the density yields the stability of an undulated chain as well as nontrivial buckling structures. We explore the close-packed configurations of dipoles in detail, and we find that, in general, the densest packings of dipoles possess complex magnetizations along the principal axis of the slit. Our predictions serve as a guideline for experiments with granular dipolar and magnetic colloidal suspensions confined in slitlike channel geometry.

Dipolar Crystals: The Crucial Role of the Clinohexagonal Prism Phase

We report a new phase called clinohexagonal prism (CHP) that accounts for all the ground states of dipolar hard spheres prepared at any density. This phase merely consists of an oblique prismatic lattice with a hexagonal base. Our calculations show that at intermediate densities, a special close packed body-centered orthorhombic phase coincides with the CHP phase in the ground state for a wide density window. In the high packing regime, i.e., in the vicinity of the density of the hexagonal close packed phase, it is a limiting case of the CHP phase with vanishing obliquity that emerges. These findings provide a unified and clarified view of the solid-solid transitions occurring at zero temperature in dipolar systems and should be relevant in other related molecular or soft matter systems governed by anisotropic (and possibly isotropic) soft potentials.

Ferroelectric glass of spheroidal dipoles with impurities: polar nanoregions, response to applied electric field, and ergodicity breakdown

Using molecular dynamics simulation, we study dipolar glass in crystals composed of slightly spheroidal, polar particles and spherical, apolar impurities between metal walls. We present physical pictures of ferroelectric glass, which have been observed in relaxors, mixed crystals (such as KCN _x KBr_1-x ), and polymers. Our systems undergo a diffuse transition in a wide temperature range, where we visualize polar nanoregions (PNRs) surrounded by impurities. In our simulation, the impurities form clusters and their space distribution is heterogeneous. The polarization fluctuations are enhanced at relatively high T depending on the size of the dipole moment. They then form frozen PNRs as T is further lowered into the nonergodic regime. As a result, the dielectric permittivity exhibits the characteristic features of relaxor ferroelectrics. We also examine nonlinear response to cyclic applied electric field and nonergodic response to cyclic temperature changes (ZFC/FC), where the polarization and the strain change collectively and heterogeneously. We also study antiferroelectric glass arising from molecular shape asymmetry. We use an Ewald scheme of calculating the dipolar interaction in applied electric field.

A simulation study of the electrostriction effects in dielectric elastomer composites containing polarizable inclusions with different spatial distributions

Controlled actuation of electroactive polymers with embedded high dielectric nanoparticles is theoretically analyzed.

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 transitions and ordering of confined dipolar fluids

We apply a modified mean-field density functional theory to determine the phase behavior of Stockmayer fluids in slit-like pores formed by two walls with identical substrate potentials. Based on the Carnahan-Starling equation of state, a fundamental-measure theory is employed to incorporate the effects of short-ranged hard-sphere-like correlations while the long-ranged contributions to the fluid interaction potential are treated perturbatively. The liquid-vapor, ferromagnetic-liquid-vapor, and ferromagnetic-liquid-isotropic-liquid first-order phase separations are investigated. The local orientational structure of the anisotropic and inhomogeneous ferromagnetic liquid phase is also studied. We discuss how the phase diagrams are shifted and distorted upon varying the pore width.

Importance of depletion interactions for structure and dynamics of ferrofluids

The influence of attractive depletion forces on the structure and dynamics of ferrofluids is studied by computer simulations. In the presence of a magnetic field, we find that sufficiently strong depletion forces lead to an assembly of particle chains into columnar structures with hexagonal ordering inside the columns. In a planar shear flow, this ordering is destroyed, leading to strong shear thinning behavior. A pronounced anisotropy of the shear viscosity is observed. The viscosity is found to be largest when the magnetic field is oriented in the gradient direction of the flow.

Phase diagram for stimulus-responsive materials containing dipolar colloidal particles

Dipolar colloidal particles self-assemble into a rich variety of microstructures ranging from co-crystals of unusual symmetry, to open networks (gels) of cross-linked chains of particles. We use molecular dynamics computer simulation to explore the self-assembly, structure, crystallization and/or gelation of systems of colloid particles with permanent dipole moments immersed in a high-dielectric solvent. Particle-particle interactions are modeled with a discontinuous potential. The phase diagram in the temperature-packing fraction plane is calculated. Several types of phases are found in our simulations: ordered phases including face-centered-cubic, hexagonal-close-packed, and body-centered-tetragonal at high packing fractions, and fluid, string-fluid, and gel phases at low packing fractions. The very low volume fraction gel phases and the well-ordered crystal phases are promising for advanced materials applications.

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.

Dipolar structures in magnetite ferrofluids studied with small-angle neutron scattering with and without applied magnetic field

Field-induced structure formation in a ferrofluid with well-defined magnetite nanoparticles with a permanent magnetic dipole moment was studied with small-angle neutron scattering (SANS) as a function of the magnetic interactions. The interactions were tuned by adjusting the size of the well-defined, single-magnetic-domain magnetite (Fe3O4) particles and by applying an external magnetic field. For decreasing particle dipole moments, the data show a progressive distortion of the hexagonal symmetry, resulting from the formation of magnetic sheets. The SANS data show qualitative agreement with recent cryogenic transmission electron microscopy results obtained in 2D [Klokkenburg, Phys. Rev. Lett. 97, 185702 (2006)] on the same ferrofluids.

A molecular-dynamics simulation study on the dependence of Lennard-Jones gas-liquid phase diagram on the long-range part of the interactions

The particle-transfer molecular-dynamics technique is adopted to construct the Lennard-Jones fluid gas-liquid phase diagram. Detailed study of the dependence of the simulation results on the system size and the cutoff distance is performed to test the validity of the simulation technique. Both the traditional cutoff plus long-range correction (CPC) and Ewald summation methods are used in the simulations to calculate the interactions. In the intermediate range of temperatures, the results with the Ewald summation method are almost the same as those with the CPC method. However, in the range close to the critical point, the results with the CPC method deviate from those with the Ewald summation. Compared with the results obtained via the Ewald summation in a smaller system, simply increasing the system size in the CPC scheme may not give better results.

Phase behavior of dipolar hard and soft spheres

We study the phase behavior of hard and soft spheres with a fixed dipole moment using Monte Carlo simulations. The spheres interact via a pair potential that is a sum of a hard-core Yukawa (or screened-Coulomb) repulsion and a dipole-dipole interaction. The system can be used to model colloids in an external electric or magnetic field. Two cases are considered: (i) colloids without charge (or dipolar hard spheres) and (ii) colloids with charge (or dipolar soft spheres). The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres shows, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and is in agreement with the experimental phase diagram [Nature (London) 421, 513 (2003)]. In both cases, the fluid phase is inhomogeneous but we find no evidence of a gas-liquid phase separation. The validity of the dipole approximation is verified by a multipole moment expansion.

Predicting equilibrium structures in freezing processes

We propose genetic algorithms as a new tool that is able to predict all possible solid candidate structures into which a simple fluid can freeze. In contrast to the conventional approach where the equilibrium structures of the solid phases are chosen from a preselected set of candidates, genetic algorithms perform a parameter-free, unbiased, and unrestricted search in the entire search space, i.e., among all possible candidate structures. We apply the algorithm to recalculate the zero-temperature phase diagrams of neutral star polymers and of charged microgels over a large density range. The power of genetic algorithms and their advantages over conventional approaches is demonstrated by the fact that new and unexpected equilibrium structures for the solid phases are discovered. Improvements of the algorithm that lead to a more rapid convergence are proposed and the role of various parameters of the method is critically assessed.

Paraelectric and ferroelectric order in two-state dipolar fluids

Monte Carlo simulations are used to examine the cooperative creation of a polar state in fluids of two-state particles with nonzero dipole in the excited state. With lowering temperature such systems undergo a second-order transition from nonpolar to polar, paraelectric phase. The transition is accompanied by a dielectric anomaly of polarization susceptibility increasing by three orders of magnitude. The paraelectric phase is then followed by a formation of a nematic ferroelectric which further freezes into a fcc ferroelectric crystal by a first-order transition. A mean-field model of phase transitions is discussed.

Phase diagram of dipolar hard and soft spheres: manipulation of colloidal crystal structures by an external field

Phase diagrams of hard and soft spheres with a fixed dipole moment are determined by calculating the Helmholtz free energy using simulations. The pair potential is given by a dipole-dipole interaction plus a hard-core and a repulsive Yukawa potential for soft spheres. Our system models colloids in an external electric or magnetic field, with hard spheres corresponding to uncharged and soft spheres to charged colloids. The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres exhibits, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and it agrees well with the experimental phase diagram [Nature (London) 421, 513 (2003)]. Our results show that bulk hcp, bct, and bco crystals can be realized experimentally by applying an external field.

Crystal structures of two-dimensional magnetic colloids in tilted external magnetic fields

The stability of different crystal lattices of two-dimensional superparamagnetic suspensions that are confined to a planar liquid-gas interface and exposed to a tilted external magnetic field is studied theoretically by lattice sum minimizations. The magnetic field induces magnetic dipoles onto the colloidal particles along its direction, whose strength can be controlled by the amplitude of the external field. The mutual interaction between the colloids is governed by dipole-dipole forces and a short-ranged repulsion having its physical origin at the presence of the colloidal cores. If the direction of the magnetic field is perpendicular to the liquid-gas interface, there is a purely repulsive interaction leading to stable triangular crystals. By tilting the external field, the interaction becomes anisotropic and a mutual attraction appears upon a threshold tilt angle. We have calculated the full phase diagram at zero temperature varying the tilt angle, the colloidal density, and the strength of the magnetic field. Apart from the triangular lattice we find a variety of stable crystal lattices including rectangular, oblique, chainlike oblique, and rhombic structures. We also present the accurate derivation of the Hamiltonian of two polarizable particles of finite arbitrary geometries in external magnetic and electric fields.

Field-induced pseudocrystalline ordering in concentrated ferrofluids

Concentrated surfactant stabilized cobalt ferrofluids up to 6 vol % Co have been studied by small-angle scattering using polarized neutrons and synchrotron x rays. The combination of these techniques allowed the magnetic and nuclear form factors to be reliably separated from the structure factors. Above 1 vol % Co, inter particle interactions are induced by an applied external magnetic field that gives rise to pseudocrystalline ordering of cobalt core-shell particles. Particles are arranged in hexagonal planes, with the magnetic moments aligned parallel to the [110] direction. Two types of equivalent textures were found to be present simultaneously, corresponding to a stacking of the hexagonal planes in horizontal and vertical direction. The in-plane nearest-neighbor distance is almost independent of the concentration and temperatures, whereas the distance between the neighboring planes, c, strongly varies from sample to sample. In addition, segments of chains of particles with parallel moments are aligned along the magnetic field and frozen-in when the carrier liquid is solidified. The field induced pseudocrystalline lamellar hexagonal particle arrangement, observed experimentally in colloidal magnetic liquids, confirms predictions from molecular-dynamics and Monte Carlo simulations.