Tunable structures of mixtures of magnetic particles in liquid-crystalline matrices

Directed assembly of small binary clusters of magnetizable ellipsoids

We report the effect of shape anisotropy and material properties on the directed assembly of binary suspensions composed of magnetizable ellipsoids. In a Monte Carlo simulation, we implement the ellipsoid-dipole model to calculate the pairwise dipolar interaction energy as a function of position and orientation. The analysis explores dilute suspensions of paramagnetic and diamagnetic ellipsoids with different aspect ratios in a superparamagnetic medium. We analyze the local order of binary structures as a function of particle aspect ratio, medium permeability, and dipolar interaction strength. Our results show that local order and symmetry are tunable under the influence of a uniform magnetic field when one component of the structure is dilute with respect to the other. The simulation results match previously reported experiments on the directed assembly of binary suspension of spheres. Additionally, we report the conditions on particle aspect ratios and medium properties for various structures with rotational symmetries, as well as open and enclosed structures under the influence of a uniform magnetic field.

Liquid-crystal composites of carbon nanotubes in a magnetic field: Bridging continuum theory and a molecular-statistical approach

We propose an approach combining the continuum theory and molecular-statistical approach for a suspension of carbon nanotubes based on a negative diamagnetic anisotropy liquid crystal. Using the continuum theory, we show that in the case of an infinite sample in suspension it is possible to observe peculiar magnetic Fréedericksz-like transitions between three nematic phases: planar, angular, and homeotropic with different mutual orientations of liquid-crystal and nanotube directors. The transition fields between these phases are found analytically as functions of material parameters of the continuum theory. To account for the effects associated with temperature changes, we propose a molecular-statistical approach that allows obtaining the equations of orientational state for the orientation angles of the main axes of the nematic order, i.e., the liquid-crystal and carbon-nanotube directors in a similar form as was obtained within the continuum theory. Thus, it is possible to relate the parameters of the continuum theory, such as the surface-energy density of a coupling between molecules and nanotubes, to the parameters of the molecular-statistical model and the order parameters of the liquid crystal and carbon nanotubes. This approach allows determining the temperature dependencies of the threshold fields of transitions between different nematic phases, which is impossible in the framework of the continuum theory. In the framework of the molecular-statistical approach we predict the existence of an additional direct transition between the planar and homeotropic nematic phases of the suspension, which cannot be described based on the continuum theory. As the main results, the magneto-orientational response of the liquid-crystal composite is studied and a possible biaxial orientational ordering of the nanotubes in the magnetic field is shown.

Multifunctionality by dispersion of magnetic nanoparticles in anisotropic matrices

Interactions between magnetic nanoparticles and an anisotropic environment give rise to a variety of new magneto-optical, rheological and mechanical phenomena. This opens new avenues for developing novel multifunctional materials. In the course of this project, we investigated three types of anisotropic systems: dispersions of shape-anisotropic nanocrystals, magnetically doped molecular and colloidal liquid crystals, and organoferrogels. They were investigated by means of magneto-optical observations and by a magneto-mechanical torsion pendulum method.

Field-induced anti-nematic and biaxial ordering in binary mixtures of discotic mesogens and spherical magnetic nanoparticles

Using computer simulations we explore the equilibrium structure and response to external stimuli of complex magnetic hybrids consisting of magnetic particles in discotic liquid crystalline matrices. We show that the anisotropy of the liquid crystalline matrix (either in the nematic or in the columnar phase) promotes the collective orientational ordering of self-assembled magnetic particles. Upon applying an external homogeneous magnetic field in an otherwise isotropic state, the magnetic particles self-assemble into linear-rodlike-chains. At the same time structural changes occur in the matrix. The matrix transforms from an isotropic to a non-conventional anti-nematic state in which the symmetry axis of the discs is, on average, perpendicular to the magnetic field. In addition, a stable biaxial nematic state is found upon applying an external field to an otherwise uniaxial discotic nematic state. These observed morphologies constitute an appealing alternative to binary mixtures of rigid rod-disc system and indicate that non-trivial biaxial ordering can be obtained in the presence of a uniaxial external stimulus.

Structure and rheology of soft hybrid systems of magnetic nanoparticles in liquid-crystalline matrices: results from particle-resolved computer simulations

Hybrid mixtures composed of magnetic nanoparticles (MNP) in liquid crystalline (LC) matrices are a fascinating class of soft materials with intriguing physical properties and a wide range of potential applications, e.g., as stimuli-responsive and adaptive materials. Already in the absence of an external stimulus, these systems can display various types of orientationally disordered and ordered phases, which are enriched by self-assembled structures formed by the MNPs. In the presence of external fields, one typically observes highly nonlinear macroscopic behavior. However, an understanding of the structure and dynamics of such systems on the particle level has, so far, remained elusive. In the present paper we review recent computer simulation studies targeting the structure, equilibrium dynamics and rheology of LC-MNP systems, in which the particle sizes of the two components are comparable. As a numerically tractable model system we consider mixtures of soft spherical or elongated particles with a permanent magnetic dipole moment and ellipsoidal non-magnetic particles interacting via a Gay-Berne potential. We address, first, equilibrium aspects such as structural organization and self-assembly (cluster formation) of the MNPs in dependence of the orientational state of the matrix, the role of the size ratio, the impact of an external magnetic field, and the translational and orientational diffusion of the two components. Second, we discuss the non-equilibrium dynamics of LC-MNP mixtures under planar shear flow, considering both, spherical and non-spherical MNPs. Our results contribute to a detailed understanding of these intriguing hybrid materials, and they may serve as a guide for future experiments.

Scaling law of Brownian rotation in dense hard-rod suspensions

Self-diffusion in dense rod suspensions are subject to strong geometric constraints because of steric interactions. This topological effect is essentially anisotropic when rods are nematically aligned with their neighbors, raising considerable challenges in understanding and analyzing their impacts on the bulk physical properties. Via a classical Doi-Onsager kinetic model with the Maier-Saupe potential, we characterize the long-time rotational Brownian diffusivity for dense suspensions of hard rods of finite aspect ratios, based on quadratic orientation autocorrelation functions. Furthermore, we show that the computed nonmonotonic scalings of the diffusivity as a function of volume fraction can be accurately predicted by an alternative tube model in the nematic phase.

Steady-state rheology and structure of soft hybrid mixtures of liquid crystals and magnetic nanoparticles

Using non-equilibrium molecular dynamics simulations, we study the rheology of a model hybrid mixture of liquid crystals (LCs) and dipolar soft spheres (DSS) representing magnetic nanoparticles. The bulk isotropic LC-DSS mixture is sheared with different shear rates using Lees-Edwards periodic boundary conditions. The steady-state rheological properties and the effect of the shear on the microstructure of the mixture are studied for different strengths of the dipolar coupling, λ, among the DSS. We find that at large shear rates, the mixture shows a shear-thinning behavior for all considered values of λ. At low and intermediate values of λ, a crossover from Newtonian to non-Newtonian behavior is observed as the rate of applied shear is increased. In contrast, for large values of λ, such a crossover is not observed within the range of shear rates considered. Also, the extent of the non-Newtonian regime increases as λ is increased. These features can be understood via the shear-induced changes of the microstructure. In particular, the LCs display a shear-induced isotropic-to-nematic transition at large shear rates with a shear-rate dependent degree of nematic ordering. The DSS show a shear-induced nematic ordering only for large values of λ, where the particles self-assemble into chains. Moreover, at large λ and low shear rates, our simulations indicate that the DSS form ferromagnetic domains.

Anomalous transport of magnetic colloids in a liquid crystal-magnetic colloid mixture

We report an extensive molecular dynamics study on the translational dynamics of a hybrid system composed of dipolar soft spheres (DSS), representing ferromagnetic particles, suspended in a liquid crystal (LC) matrix. We observe that the LC matrix strongly modifies the dynamics of the DSS. In the isotropic regime, the DSS show a crossover from subdiffusive to normal diffusive behavior at long times, with an increase of the subdiffusive regime as the dipolar coupling strength is increased. In the nematic regime, the LC matrix, due to the collective reorientation of LC particles, imposes a cylindrical confinement on the DSS chains. This leads to a diffusive dynamics of DSS along the nematic director and a subdiffusive dynamics (with an exponent of ∼0.5) in the perpendicular direction. The confinement provided by the LC matrix is also reflected by the oscillatory behavior of the components of the velocity autocorrelation function of the DSS in the nematic phase.

Phase diagrams of mixtures of dipolar rods and discs

Self-assembly of binary mixtures that contain anisotropic, interacting colloidal particles have been proposed as a way to create new, multi-functional materials. We simulate binary mixtures of dipolar rods and dipolar discs in two-dimensions using discontinuous molecular dynamics to determine how the assembled structures of these mixtures differ from those seen in single component systems. Two different binary mixtures are investigated: a mixture of an equal number of dipolar rods and dipolar discs ("equal number"), and a mixture where the area fraction of dipolar rods is equal to the area fraction of dipolar discs ("equal area"). Phase boundaries between fluid, string-fluid, and "gel" phases are calculated and compared to the phase boundaries of the pure components. Looking deeper at the underlying structure of the mixture reveals a complex interplay between the rods and discs and the formation of states where the two components are in different phases. The mixtures exhibit phases where both rods and discs are in the fluid phase, where rods form a string-fluid while discs remain in the fluid phase, a rod string-fluid coexisting with a disc string-fluid, a "gel" that consists primarily of rods while the discs form either a fluid or string-fluid phase, and a "gel" that contains both rods and discs. Our results give insight into the general assembly pathway of binary mixtures, and how complex aggregates can be created by varying the mixture composition, strength of interaction between the two components, and the temperature. By manipulating the properties of one of the components it should be possible to fabricate bifunctional, thermally responsive self-assembled materials.

Tunable dynamic moduli of magnetic elastomers: from characterization by x-ray micro-computed tomography to mesoscopic modeling

Ferrogels and magnetorheological elastomers are composite materials obtained by embedding magnetic particles of mesoscopic size in a crosslinked polymeric matrix. They combine the reversible elastic deformability of polymeric materials with the high responsivity of ferrofluids to external magnetic fields. These materials stand out, for example, for significant magnetostriction as well as a pronounced increase of the elastic moduli in the presence of external magnetic fields. By means of x-ray micro-computed tomography, the position and size of each magnetic particle can be measured with a high degree of accuracy. We here use data extracted from real magnetoelastic samples as input for coarse-grained dipole-spring modeling and calculations to investigate internal restructuring, stiffening, and changes in the normal modes spectrum. More precisely, we assign to each particle a dipole moment proportional to its volume and set a randomized network of springs between them that mimics the behavior of the polymeric elastic matrix. Extending our previously developed methods, we compute the resulting structural changes in the systems as well as the frequency-dependent elastic moduli when magnetic interactions are turned on. Particularly, with increasing magnetization, we observe the formation of chain-like aggregates. Interestingly, the static elastic moduli can first show a slight decrease with growing amplitude of the magnetic interactions, before a pronounced increase appears upon the chain formation. The change of the dynamic moduli with increasing magnetization depends on the frequency and can even feature nonmonotonic behavior. Overall, we demonstrate how theory and experiments can complement each other to learn more about the dynamic behavior of this interesting class of materials.

Orientational order and translational dynamics of magnetic particle assemblies in liquid crystals

Implementing extensive molecular dynamics simulations we explore the organization of magnetic particle assemblies (clusters) in a uniaxial liquid crystalline matrix comprised of rodlike particles. The magnetic particles are modelled as soft dipolar spheres with diameter significantly smaller than the width of the rods. Depending on the dipolar strength coupling the magnetic particles arrange into head-to-tail configurations forming various types of clusters including rings (closed loops) and chains. In turn, the liquid crystalline matrix induces long range orientational ordering to these structures and promotes their diffusion along the director of the phase. Different translational dynamics are exhibited as the liquid crystalline matrix transforms either from isotropic to nematic or from nematic to smectic state. This is caused due to different collective motion of the magnetic particles into various clusters in the anisotropic environments. Our results offer a physical insight for understanding both the structure and dynamics of magnetic particle assemblies in liquid crystalline matrices.

Colloidal Suspensions of Rodlike Nanocrystals and Magnetic Spheres under an External Magnetic Stimulus: Experiment and Molecular Dynamics Simulation

Using experiments and molecular dynamics simulations, we explore magnetic field-induced phase transformations in suspensions of nonmagnetic rodlike and magnetic sphere-shaped particles. We experimentally demonstrate that an external uniform magnetic field causes the formation of small, stable clusters of magnetic particles that, in turn, induce and control the orientational order of the nonmagnetic subphase. Optical birefringence was studied as a function of the magnetic field and the volume fractions of each particle type. Steric transfer of the orientational order was investigated by molecular dynamics (MD) simulations; the results are in qualitative agreement with the experimental observations. By reproducing the general experimental trends, the MD simulation offers a cohesive bottom-up interpretation of the physical behavior of such systems, and it can also be regarded as a guide for further experimental research.

GPU-Accelerated Molecular Dynamics Simulation to Study Liquid Crystal Phase Transition Using Coarse-Grained Gay-Berne Anisotropic Potential

Gay-Berne (GB) potential is regarded as an accurate model in the simulation of anisotropic particles, especially for liquid crystal (LC) mesogens. However, its computational complexity leads to an extremely time-consuming process for large systems. Here, we developed a GPU-accelerated molecular dynamics (MD) simulation with coarse-grained GB potential implemented in GALAMOST package to investigate the LC phase transitions for mesogens in small molecules, main-chain or side-chain polymers. For identical mesogens in three different molecules, on cooling from fully isotropic melts, the small molecules form a single-domain smectic-B phase, while the main-chain LC polymers prefer a single-domain nematic phase as a result of connective restraints in neighboring mesogens. The phase transition of side-chain LC polymers undergoes a two-step process: nucleation of nematic islands and formation of multi-domain nematic texture. The particular behavior originates in the fact that the rotational orientation of the mesogenes is hindered by the polymer backbones. Both the global distribution and the local orientation of mesogens are critical for the phase transition of anisotropic particles. Furthermore, compared with the MD simulation in LAMMPS, our GPU-accelerated code is about 4 times faster than the GPU version of LAMMPS and at least 200 times faster than the CPU version of LAMMPS. This study clearly shows that GPU-accelerated MD simulation with GB potential in GALAMOST can efficiently handle systems with anisotropic particles and interactions, and accurately explore phase differences originated from molecular structures.

Superelastic stress–strain behavior in ferrogels with different types of magneto-elastic coupling

Anisotropic ferrogels and magnetorheological elastomers allow for reversible tunability of their markedly nonlinear stress–strain properties.

Spontaneous ordering of magnetic particles in liquid crystals: From chains to biaxial lamellae

Using Monte Carlo computer simulations we explore the self-assembly and ordering behavior of a hybrid, soft magnetic system consisting of small magnetic nanospheres in a liquid-crystalline (LC) matrix. Inspired by recent experiments with colloidal rod matrices, we focus on conditions where the sphere and rod diameters are comparable. Already in the absence of a magnetic field, the nematic ordering of the LC can stabilize the formation of magnetic chains along the nematic or smectic director, yielding a state with local (yet no macroscopic) magnetic order. The chains, in turn, increase the overall nematic order, reflecting the complex interplay of the structure formation of the two components. When increasing the sphere diameter, the spontaneous uniaxial ordering is replaced by biaxial lamellar morphologies characterized by alternating layers of rods and magnetic chains oriented perpendicular to the rod's director. These ordering scenarios at zero field suggest a complex response of the resulting hybrid to external stimuli, such as magnetic fields and shear forces.