Computer simulations of the structure of colloidal ferrofluids

Pair correlations of the easy magnetisation axes of superparamagnetic nanoparticles in a ferrofluid/ferrocomposite

The widespread use of magnetic nanoparticles in modern technologies and medical applications highlights the need for reliable theoretical models that can predict their physical properties. The pair correlation function of two randomly selected superparamagnetic nanoparticles in a ferrofluid/ferrocomposite is studied to depict the joint probability density of the easy magnetisation axes across the planes of parameters of major importance; these are the interaction of ferroparticles with an external magnetic field, the energy of magnetic anisotropy inside the superparamagnetic nanoparticle, and the interparticle magnetic dipole-dipole interaction. Assuming the rotational symmetry of the system, we come to the conclusion that the pair correlations of interest are dependent only on the polar angles, determining the inclinations of the ferroparticle easy axes from the direction of an external magnetic field. The dimer configuration, where two ferroparticles are in close contact along a magnetic field with their easy magnetisation axes aligned, is the most probable. This configuration becomes more pronounced with increasing anisotropy energy, dipolar coupling constant, and external magnetic field.

Structure and dynamics in suspensions of magnetic platelets

In this research, we employ Brownian dynamics simulations, density functional theory, and mean-field theory to explore the profound influence of shape anisotropy of magnetic nanoplatelets on suspension magnetic response. Each platelet is modelled as an oblate cylinder with a longitudinal point dipole, with an emphasis on strong dipolar interactions conducive to self-assembly. We investigate static structural and magnetic properties, characterising the system through pair distribution function, static structure factor, and cluster-size distribution. The findings demonstrate that shape-specific interactions and clustering lead to significant changes in reorientational relaxation times. Under zero field, distinctive modes in the dynamic magnetic susceptibility identify individual particles and particle clusters. In the presence of an applied field, the characteristic relaxation time of clusters increases, while that of single particles decreases. This research provides insights into the intricate interplay between shape anisotropy, clustering, and magnetic response in platelet suspensions, offering valuable perspectives for recent experimental observations.

Multiparametric modulation of magnetic transduction for biomolecular sensing in liquids

The recent COVID19 pandemic has remarkably boosted the research on in vitro diagnosis assays to detect biomarkers in biological fluids. Specificity and sensitivity are mandatory for diagnostic kits aiming to reach clinical stages. Whilst the modulation of sensitivity can significantly improve the detection of biomarkers in liquids, this has been scarcely explored. Here, we report on the proof of concept and parametrization of a novel biosensing methodology based on the changes of AC magnetic hysteresis areas observed for magnetic nanoparticles following biomolecular recognition in liquids. Several parameters are shown to significantly modulate the transducing capacity of magnetic nanoparticles to detect analytes dispersed in saline buffer at concentrations of clinical relevance. Magnetic nanoparticles were bio-conjugated with an engineered recognition peptide as a receptor. Analytes are engineered tetratricopeptide binding domains fused to the fluorescent protein whose dimerization state allows mono- or divalent variants. Our results unveil that the number of receptors per particle, analyte valency and concentration, nanoparticle composition and concentration, and field conditions play a key role in the formation of assemblies driven by biomolecular recognition. Consequently, all these parameters modulate the nanoparticle transduction capacity. Our study provides essential insights into the potential of AC magnetometry for customizing biomarker detection in liquids.

Energy dissipation of rigid dipoles in a viscous fluid under the action of a time-periodic field: The influence of thermal bath and dipole interaction

Ferrofluid heating by an external alternating field is studied based on the rigid dipole model, where the magnetization of each particle in a fluid is supposed to be firmly fixed in the crystal lattice. Equations of motion, employing Newton's second law for rotational motion, the condition of rigid body rotation, and the assumption that the friction torque is proportional to angular velocity are used. This oversimplification permits us to expand the model easily: to take into account the thermal noise and interparticle interaction that allows us to estimate from unified positions the role of thermal activation and dipole interaction in the heating process. Our studies are conducted in three stages. The exact expressions for the average power loss of a single particle are obtained within the dynamical approximation. Then, in the stochastic case, the power loss of a single particle is estimated analytically using the Fokker-Planck equation and numerically using the effective Langevin equation. Finally, the power loss for the particle ensemble is obtained using the molecular dynamics method. Here, the local dipole fields are calculated approximately based on the Barnes-Hut algorithm. The revealed trends in the behavior of both a single particle and the particle ensemble suggest the way of choosing the conditions for obtaining the maximum heating efficiency. The competitiveness character of the interparticle interaction and thermal noise is investigated in detail. Two situations, when the thermal noise rectifies the power loss reduction caused by the interaction, are described. The first of them is related to the complete destruction of dense clusters at high noise intensity. The second one originates from the rare switching of the particles in clusters due to thermal activation, when the noise intensity is relatively weak. In this way, the constructive role of noise appears in the system.

Compressibility of ferrofluids: Towards a better understanding of structural properties

This paper addresses a computational method aimed at obtaining the isothermal compressibility of ferrofluids by means of molecular dynamics (MD) simulations. We model ferrofluids as a system of dipolar soft spheres and carry out MD simulations in the NPT ensemble. The obtained isothermal compressibility computed via volume fluctuations provides us with a strong evidence that dipolar interactions lead to a higher compressibility of dipolar soft sphere systems: the stronger the dipolar interactions, the bigger is the deviation of the compressibility from the one of a system with no dipoles. Furthermore, we use the isothermal compressibility to calculate the structure factor of ferrofluids at low values of wave vectors, i.e. in the range where it is difficult to predict its behaviour because of a problem with accounting for long-range particle correlations that give the main contribution to the structure factor in this range. Our approach based on the interpolation of the structure factor and the computed isothermal compressibility allows us to obtain the smooth structure factor in the range of low wave vectors and the reliable fractal dimension of the clusters formed in the system.

Polymer architecture of magnetic gels: a review

In this review article, we provide an introduction to ferrogels, i.e. polymeric gels with embedded magnetic particles. Due to the interplay between magnetic and elastic properties of these materials, they are promising candidates for engineering and biomedical applications such as actuation and controlled drug release. Particular emphasis will be put on the polymer architecture of magnetic gels since it controls the degrees of freedom of the magnetic particles in the gel, and it is important for the particle-polymer coupling determining the mechanisms available for the gel deformation in magnetic fields. We report on the different polymer architectures that have been realized so far, and provide an overview of synthesis strategies and experimental techniques for the characterization of these materials. We further focus on theoretical and simulational studies carried out on magnetic gels, and highlight their contributions towards understanding the influence of the gels' polymer architecture.

Hyperuniformity and its generalizations

Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystal and liquid: They are like perfect crystals in the way they suppress large-scale density fluctuations and yet are like liquids or glasses in that they are statistically isotropic with no Bragg peaks. These exotic states of matter play a vital role in a number of problems across the physical, mathematical as well as biological sciences and, because they are endowed with novel physical properties, have technological importance. Given the fundamental as well as practical importance of disordered hyperuniform systems elucidated thus far, it is natural to explore the generalizations of the hyperuniformity notion and its consequences. In this paper, we substantially broaden the hyperuniformity concept along four different directions. This includes generalizations to treat fluctuations in the interfacial area (one of the Minkowski functionals) in heterogeneous media and surface-area driven evolving microstructures, random scalar fields, divergence-free random vector fields, and statistically anisotropic many-particle systems and two-phase media. In all cases, the relevant mathematical underpinnings are formulated and illustrative calculations are provided. Interfacial-area fluctuations play a major role in characterizing the microstructure of two-phase systems (e.g., fluid-saturated porous media), physical properties that intimately depend on the geometry of the interface, and evolving two-phase microstructures that depend on interfacial energies (e.g., spinodal decomposition). In the instances of random vector fields and statistically anisotropic structures, we show that the standard definition of hyperuniformity must be generalized such that it accounts for the dependence of the relevant spectral functions on the direction in which the origin in Fourier space is approached (nonanalyticities at the origin). Using this analysis, we place some well-known energy spectra from the theory of isotropic turbulence in the context of this generalization of hyperuniformity. Among other results, we show that there exist many-particle ground-state configurations in which directional hyperuniformity imparts exotic anisotropic physical properties (e.g., elastic, optical, and acoustic characteristics) to these states of matter. Such tunability could have technological relevance for manipulating light and sound waves in ways heretofore not thought possible. We show that disordered many-particle systems that respond to external fields (e.g., magnetic and electric fields) are a natural class of materials to look for directional hyperuniformity. The generalizations of hyperuniformity introduced here provide theoreticians and experimentalists new avenues to understand a very broad range of phenomena across a variety of fields through the hyperuniformity "lens."

Self-Assembly of Crystalline Structures of Magnetic Core-Shell Nanoparticles for Fabrication of Nanostructured Materials

A theoretical study is presented of the template-assisted formation of crystalline superstructures of magnetic-dielectric core-shell particles. The templates produce highly localized gradient fields and a corresponding magnetic force that guides the assembly with nanoscale precision in particle placement. The process is studied using two distinct and complementary computational models that predict the dynamics and energy of the particles, respectively. Both mono- and polydisperse colloids are studied, and the analysis demonstrates for the first time that although the particles self-assemble into ordered crystalline superstructures, the particle formation is not unique. There is a Brownian motion-induced degeneracy in the process wherein various distinct, energetically comparable crystalline structures can form for a given template geometry. The models predict the formation of hexagonal close packed (HCP) and face centered cubic (FCC) structures as well as mixed phase structures due to in-plane stacking disorders, which is consistent with experimental observations. The polydisperse particle structures are less uniform than the monodisperse particle structures because of the irregular packing of different-sized particles. A comparison of self-assembly using soft- and hard-magnetic templates is also presented, the former being magnetized in a uniform field. This analysis shows that soft-magnetic templates enable an order-of-magnitude more rapid assembly and much higher spatial resolution in particle placement than their hard-magnetic counterparts. The self-assembly method discussed is versatile and broadly applies to arbitrary template geometries and multilayered and multifunctional mono- and polydisperse core-shell particles that have at least one magnetic component. As such, the method holds potential for the bottom-up fabrication of functional nanostructured materials for a broad range of applications. This work provides unprecedented insight into the assembly process, especially with respect to the viability and potential fundamental limitations of realizing structure-dependent material properties for applications.

Template-assisted nano-patterning of magnetic core-shell particles in gradient fields

A method is proposed for controlling the assembly of colloidal magnetic core-shell nanoparticles into patterned monolayer structures with nanoscale feature resolution. The method is based on magnetic field-directed self-assembly that is enhanced using soft-magnetic template elements. The elements are embedded in a nonmagnetic substrate and magnetized using a uniform bias field. A key feature of this approach is the combined use of a uniform field with induced gradient-fields produced by the template elements. This enables the customization of a force field with localized regions of attractive and repulsive magnetic forces that provide extraordinary control of particle motion during assembly. The method is demonstrated using a computational model that simulates the assembly process taking into account magnetic and hydrodynamic forces including interparticle interactions, Brownian diffusion, van der Waals force and effects of surfactants. The analysis shows that extended geometric patterns of particles can be assembled with nanoscale resolution, beyond that of the template elements, within milliseconds. This is achieved by tailoring key parameters including the template geometry to produce a force field that focuses the particles into prescribed patterns; the thickness of the dielectric particle shell to control the magnetic dipole-dipole force upon contact and the particle volume fraction to suppress undesired aggregation during assembly. The proposed method broadly applies to arbitrary template geometries and multi-layered core-shell particles with at least one magnetic component. It can enable the self-assembly of complex patterns of nanoparticles and open up opportunities for the scalable fabrication of multifunctional nanostructured materials for a broad range of applications.

Direct observations of field-induced assemblies in magnetite ferrofluids

Evolution of microstructures in magnetite-based ferrofluids with weak dipolar moments (particle size ≤ 10 nm) is studied with an emphasis on examining the effects of particle concentration (ϕ) and magnetic field strength (H) on the structures. Nanoparticles are dispersed in water at three different concentrations, ϕ = 0.15%, 0.48%, and 0.59% (w/v) [g/ml%] and exposed to uniform magnetic fields in the range of H = 0.05-0.42 T. Cryogenic transmission electron microscopy is employed to provide in-situ observations of the field-induced assemblies in such systems. As the magnetic field increases, the Brownian colloids are observed to form randomly distributed chains aligned in the field direction, followed by head-to-tail chain aggregation and then lateral aggregation of chains termed as zippering. By increasing the field in low concentration samples, the number of chains increases, though their length does not change dramatically. Increasing concentration increases the length of the linear particle assemblies in the presence of a fixed external magnetic field. Thickening of the chains due to zippering is observed at relatively high fields. Through a systematic variation of concentration and magnetic field strength, this study shows that both magnetic field strength and change in concentration can strongly influence formation of microstructures even in weak dipolar systems. Additionally, the results of two commonly used support films on electron microscopy grids, continuous carbon and holey carbon films, are compared. Holey carbon film allows us to create local regions of high concentrations that further assist the development of field-induced assemblies. The experimental observations provide a validation of the zippering effect and can be utilized in the development of models for thermophysical properties such as thermal conductivity.

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.

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.

Oscillatory-like relaxation behavior of light transmitted through ferrofluids

An oscillatory-like relaxation process in which there are two valleys in the T-t curve is observed when light is transmitted through binary ferrofluids composed of both ferrimagnetic CoFe(2)O(4) nanoparticles and paramagnetic p-MgFe(2)O(4) nanoparticles in the presence of a high magnetic field and through pure (single) CoFe(2)O(4) ferrofluids in a low magnetic field. This relaxation behavior is explained using a model of a bidispersed system based on both chained and unchained particles. In such a bidispersed system, the variation of the transmitted light results mainly from the motion of the chains, with the polarized unchained particles' gas producing the modulation effect. The oscillatory-like relaxation phenomenon depends on the features of both the chained and unchained particle systems. If either the particle volume fraction of chained particles or of unchained particles is very low, or the degree of polarization of the unchained particles gas is very weak, a simple nonlinear relaxation process, giving only a valley in the T-t curve, will appear for the transmitted light. For pure CoFe(2)O(4) ferrofluids, the number of chained and unchained particles does not remain constant under different values of the magnetic field. According to the analysis of the relaxation behavior of transmitted light, it is known that binary ferrofluids based on strong magnetic CoFe(2)O(4) particles and weak magnetic p-MgFe(2)O(4) particles can be much closer to the theoretical bidispersed system than single ferrofluids containing only strong magnetic particles.

Behavior of bulky ferrofluids in the diluted low-coupling regime: theory and simulation

A theoretical formalism to predict the structure factors observed in dipolar soft-sphere fluids based on a virial expansion of the radial distribution function is presented. The theory is able to account for cases with and without externally applied magnetic fields. A thorough comparison of the theoretical results to molecular-dynamics simulations shows a good agreement between theory and numerical simulations when the fraction of particles involved in clustering is low; i.e., the dipolar coupling parameter is lambda less, similar 2, and the volume fraction is phi less, similar 0.25. When magnetic fields are applied to the system, special attention is paid to the study of the anisotropy of the structure factor. The theory reasonably accounts for the structure factors when the Langevin parameter is smaller than 5.

Polydispersity Influence upon Magnetic Properties of Aggregated Ferrofluids

In the present paper we compare the static magnetic properties of a bidisperse ferrofluid obtained via computer simulations with the predictions of the theoretical chain model. At weak fields, the computer simulations showed a strong dependence of the magnetization on the concentration of large particles. When the latter is small the magnetization behavior is close to the one given by the modified mean field approach, but at higher concentrations of large particles the initial susceptibility increases significantly. This increase cannot be described in terms of the modified mean field model for the homogeneous system. A new theoretical approach for the description of the static magnetic properties of a bidisperse ferrofluid was developed. The theoretical predictions are in good agreement with the results of a recent computer simulation study.

Magnetic-field-induced optical anisotropy in ferrofluids: a time-dependent light-scattering investigation

We report an experimental investigation of time dependent anisotropic light scattering by an aqueous suspension of tetramethyl ammonium hydroxide coated Fe3O4 nanoparticles (approximately 6 nm) under the ON-OFF transient of an external dc magnetic field. The study employs the synchronized recording and measurement of the two magnetic-field-induced light-scattering patterns produced by two identical orthogonal He-Ne laser beams passing through the ferrofluid sample and propagating parallel and perpendicular to the applied field, respectively. From these patterns, we extract the time dependence of the induced optical anisotropy, which provides a measure of the characteristic time scale and kinematic response for field-induced structure formation in the sample. We propose that the time evolution of the scattering patterns, which is very fast at short times and significantly slower at long times, can be explained using a model based on a two-stage chain formation and coarsening processes.

Magnetic properties of polydisperse ferrofluids: a critical comparison between experiment, theory, and computer simulation

Experimental magnetization curves for a polydisperse ferrofluid at various concentrations are examined using analytical theories and computer simulations with the aim of establishing a robust method for obtaining the magnetic-core diameter distribution function p(x). Theoretical expressions are fitted to the experimental data to yield the parameters of p(x). It is shown that the majority of available theories yield results that depend strongly on the ferrofluid concentration, even though the magnetic composition should be fixed. The sole exception is the second-order modified mean-field (MMF2) theory of Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)] which yields consistent results over the full experimental range of ferrofluid concentration. To check for consistency, extensive molecular dynamics and Monte Carlo simulations are performed on systems with discretized versions of p(x) corresponding as closely as possible to that of the real ferrofluid. Essentially perfect agreement between experiment, theory, and computer simulation is demonstrated. In addition, the MMF2 theory provides excellent predictions for the initial susceptibility measured in simulations.

Dynamics of magnetic-field-induced clustering in ionic ferrofluids from Raman scattering

Using Raman spectroscopy, the authors have investigated the aggregation/disgregation of magnetic nanoparticles in dense ionic ferrofluids (IFF) into clusters due to the action of an inhomogeneous external magnetic field. Evidence for changes in particle density and/or effective cluster size were obtained from the variation of the Raman intensity in a time window from 10 s to 10 min for magnetic fields up to 350 mT and at a temperature of 28 degrees C. Clustering sets in already at very low fields (>15 mT) and the IFF samples exhibit a clear hysteresis in the Raman spectra after releasing the magnetic field, which lasts for many hours at room temperature. The authors determined the characteristic times of the two competing processes, that of field-induced cluster formation and, at room temperature, that of thermal-activated dissociation, to range from 100 to 150 s.

Viscoelasticity of suspensions of magnetic particles in a polymer: Effect of confinement and external field

We study the suspensions of magnetic particles, the precursor state of magnetic gels and elastomers. We use magnetic particles with a permanent magnetization which is high enough to overcome thermal energy and low enough to guarantee a long live time of the sample. These particles form a space-filling structure at very low volume fractions (approximately 0.5 vol %), which modifies the viscoelastic response of the matrix significantly. In confined geometry the particles form clusters of a size that depends on the sample thickness. Even small external fields induce a strong anisotropy in the mechanical and optical properties of the suspension. The action of the applied magnetic field induces a gel-like response in one direction but leaves the other directions liquidlike. The viscosity is a very sensitive mechanical test for the anisotropy of the material. Light scattering data confirm our mechanical results.

What Tunes the Structural Anisotropy of Magnetic Fluids under a Magnetic Field?

In the present study, the structure of monophasic ionic magnetic fluids under a static magnetic field is explored. In these aqueous electrostatically stabilized ferrofluids, we vary both the isotropic interparticle interactions and the anisotropic dipolar magnetic interaction by tuning the ionic strength and the size of the nanoparticles. Small angle neutron scattering measurements carried out on nanoparticles dispersed in light water exhibit miscellaneous 2D nuclear patterns under a magnetic field with various q-dependent anisotropies. In this nondeuterated solvent where the magnetic scattering is negligible, this anisotropy originates from an anisotropy of the structure of the dispersions. Both the low q region and the peak of the structure factor can be anisotropic. On the scale of the interparticle distance, the structure is better defined in the direction perpendicular to the field. In the thermodynamic limit (q-->0), the model previously described in ref 10 matches the data without any fitting parameters: the interparticle interaction is more repulsive in the direction parallel to the magnetic field. At low q, the amplitude of the anisotropy of the pattern is governed by the ratio of two interaction parameters: the reduced parameter of the anisotropic magnetic dipolar interaction, gamma/Phi, over the isotropic interaction parameter, , in zero field, which is proportional to the second virial coefficient.

Brownian dynamics investigation of magnetization and birefringence relaxations in ferrofluids

Brownian dynamics simulations are used to investigate the dynamics of orientational properties of real charge-stabilized ferrofluids, i.e. stable colloidal dispersions of magnetic nanoparticles. The relaxation times of the magnetization and of the birefringence, data accessible by experimental techniques, have been computed at several volume fractions. Besides, the effect of hydrodynamic interactions has been investigated. Equilibrium simulations without field are found to be inadequate to determine the aforementioned relaxation times for the systems under study, the dipolar interaction being too weak. Thus a nonequilibrium simulation procedure that mimics the experimental operating mode has been developed. After equilibrium simulations under a magnetic field, both birefringence and magnetization decays are recorded once the field is suppressed. Birefringence and magnetization decays are markedly impeded as the volume fraction increases, whereas they are barely enhanced when the intensity of the initial magnetic field is increased at a fixed volume fraction. Eventually, hydrodynamic interactions exhibit a slight but systematic lengthening of the relaxation times.