Theory of structural transformations in ferrofluids: chains and "gas-liquid" phase transitions

The relevance of curvature-induced quadrupolar interactions in dipolar chain aggregation

The aggregation of dipolar chains driven by thermal fluctuations in an external strong (electric or magnetic) field is investigated theoretically. We discover a new simple electrostatic mechanism that rationalizes the counter-intuitive lateral coalescence of dipolar chains. There, we first demonstrate that two bent dipolar chains can either attract or repel each other depending if they possess similar or opposite curvatures, respectively. Upon bending, dipolar chains become the siege of polarization-induced local charges that in turn lead to quadrupolar couplings. This striking feature is then exploited to understand our conducted Monte Carlo simulations at finite temperature where thermal fluctuations cause local curvatures in the formed dipolar chains. The related quadrupolar attractive mode with correlated chain-curvatures is clearly identified in the simulation snapshots. Our findings shed new light on a longstanding problem in soft matter and related areas.

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.

Thermal and rheological properties of magnetic nanofluids: Recent advances and future directions

Technological advancement and miniaturization of electronic gadgets fueled intense research on nanofluids as potential candidates for cooling applications as a substitute to conventional heat transfer fluids. Among nanofluids, magnetic nanofluids, traditionally known as ferrofluids have attracted a lot of attention owing to their magnetic field tunable thermal conductivity and rheological properties due to the aggregation of the magnetic nanoparticles into chains or columns in the presence of the magnetic field. The field-induced aggregates act as low resistance pathways thereby improving thermal transport substantially. Recent studies show that ferrofluids with smaller size and narrow size distribution display significant enhancement in thermal conductivity in the presence of a magnetic field with negligible viscosity enhancement, which is ideal for effective thermal management of electronic devices, especially in miniature electronic devices. On the contrary, highly polydisperse ferrofluids containing large aggregates, show modest enhancement in thermal conductivity in the presence of a magnetic field and a huge enhancement in viscosity. The most recent studies show that magnetic field ramp rate has a profound effect on aggregation kinetics and thermal and rheological properties. The viscosity enhancement under an external stimulus impedes their practical use in electronics cooling, which warrants the need to attain a high thermal conductivity to viscosity ratio, under a modest magnetic field. Though there are several reviews on heat transfer in nanofluids and hybrid nanofluids, a comprehensive review on fundamental understanding of field-induced thermal and rheological properties in magnetic fluids is missing in the literature. This review provides a pedagogical description of the fundamental understanding of field-induced thermal and rheological properties in magnetic fluids, with the necessary background, key concepts, definitions, mechanisms, theoretical models, experimental protocols, and design of experiments. Many important case studies are presented along with the experimental design aspects. The review also provides a summary of important experimental studies with key findings, along with the key challenges and future research directions. The review is an ideal material for experimentalists and theoreticians practicing in the field of magnetic fluids, and also serves as an excellent reference for freshers who indent to begin research on this topic.

The role of structural anisotropy in the magnetooptical response of an organoferrogel with mobile magnetic nanoparticles

We investigate the structure and the magnetooptical response of isotropic and anisotropic fibrillous organoferrogels with mobile magnetic nanoparticles (MNPs). We demonstrate that the presence of the gel network restricts the magnetooptical response of the ferrogel. Even though the ferrogel exhibits no magnetic hysteresis, an optical hysteresis has been found. This suggests that the magnetooptical response is primarily determined by the dynamics of self-assembly of the MNPs into shape-anisotropic agglomerates. Furthermore, we show that the optical anisotropy of the system can be fine-tuned by varying the concentration of the gelator and the MNPs, respectively. The optical response in structurally anisotropic gels becomes orientation-dependent, revealing an intricate interplay between the gel mesh and the MNPs.

Study of the thixotropic behaviors of ferrofluids

The thixotropic behaviors of ferrofluid samples of different particle concentration were studied using different measurement methods, including the three interval thixotropic test and the hysteresis loop test. The experimental results demonstrated that ferrofluids exhibit significant thixotropic behaviors and the microstructural evolution in ferrofluids behind the macroscopic rheological mechanics is discussed. The influence of magnetic field strength, particle concentration and temperature on the thixotropy of ferrofluids was also analyzed. Microscopic ferrofluid theory was adopted to study the thixotropic behaviors of ferrofluids under different shearing conditions, indicating that different thixotropic behaviors of ferrofluids can be induced by the presence and evolution of different kinds of microstructures, such as linear chain-like and dense drop-like structures. Furthermore, a phenomenal thixotropic model was employed to analyze the experimental results, indicating that a more specific model for ferrofluids is needed. These findings contribute to a better understanding of the microscopic mechanism of the complex rheological behaviors of ferrofluids.

Kinetics of doublet formation in bicomponent magnetic suspensions: The role of the magnetic permeability anisotropy

Micron-sized particles (microbeads) dispersed in a suspension of magnetic nanoparticles, i.e., ferrofluids, can be assembled into different types of structures upon application of an external magnetic field. This paper is devoted to theoretical modeling of a relative motion of a pair of microbeads (either soft ferromagnetic or diamagnetic) in the ferrofluid under the action of applied uniform magnetic field which induces magnetic moments in the microbeads making them attracting to each other. The model is based on a point-dipole approximation for the magnetic interactions between microbeads mediated by the ferrofluid; however, the ferrofluid is considered to possess an anisotropic magnetic permeability thanks to field-induced structuring of its nanoparticles. The model is tested against experimental results and shows generally better agreement with experiments than the model considering isotropic magnetic permeability of ferrofluids. The results could be useful for understanding kinetics of aggregation of microbeads suspended in a ferrofluid. From a broader perspective, the present study is believed to contribute to a general understanding of particle behaviors in anisotropic media.

Self-assembly and rheology of dipolar colloids in simple shear studied using multi-particle collision dynamics

Magnetic nanoparticles in a colloidal solution self-assemble in various aligned structures, which has a profound influence on the flow behavior. However, the precise role of the microstructure in the development of the rheological response has not been reliably quantified. We investigate the self-assembly of dipolar colloids in simple shear using hybrid molecular dynamics and multi-particle collision dynamics simulations with explicit coarse-grained hydrodynamics, conduct simulated rheometric studies and apply micromechanical models to produce master curves, showing evidence of the universality of the structural behavior governed by the competition between the bonding (dipolar) and erosive (thermal and/or hydrodynamic) stresses. The simulations display viscosity changes across several orders of magnitude in fair quantitative agreement with various literature sources, substantiating the universality of the approach, which seems to apply generally across vastly different length scales and a broad range of physical systems.

Microfluidic separation of magnetic nanoparticles on an ordered array of magnetized micropillars

Microfluidic separation of magnetic particles is based on their capture by magnetized microcollectors while the suspending fluid flows past the microcollectors inside a microchannel. Separation of nanoparticles is often challenging because of strong Brownian motion. Low capture efficiency of nanoparticles limits their applications in bioanalysis. However, at some conditions, magnetic nanoparticles may undergo field-induced aggregation that amplifies the magnetic attractive force proportionally to the aggregate volume and considerably increases nanoparticle capture efficiency. In this paper, we have demonstrated the role of such aggregation on an efficient capture of magnetic nanoparticles (about 80 nm in diameter) in a microfluidic channel equipped with a nickel micropillar array. This array was magnetized by an external uniform magnetic field, of intensity as low as 6-10 kA/m, and experiments were carried out at flow rates ranging between 0.3 and 30 μL/min. Nanoparticle capture is shown to be mostly governed by the Mason number Ma, while the dipolar coupling parameter α does not exhibit a clear effect in the studied range, 1.4 < α < 4.5. The capture efficiency Λ shows a strongly decreasing Mason number behavior, Λ∝Ma^{-1.78} within the range 32 ≤ Ma ≤ 3250. We have proposed a simple theoretical model which considers destructible nanoparticle chains and gives the scaling behavior, Λ∝Ma^{-1.7}, close to the experimental findings.

Characterization, nanoparticle self-organization, and Monte Carlo simulation of magnetoliposomes

In this work we have developed and implement a new approach for the study of magnetoliposomes using Monte Carlo simulations. Our model is based on interaction among nanoparticles considering magnetic dipolar, van der Waals, ionic-steric, and Zeeman interaction potentials. The ionic interaction between nanoparticles and the lipid bilayer is represented by an ionic repulsion electrical surface potential that depends on the nanoparticle-lipid bilayer distance and the concentration of ions in the solution. A direct comparison among transmission electron microscopy, vibrating sample magnetometer, dynamic light scattering, nanoparticle tracking analysis, and experimentally derived static magnetic birefringence and simulation data allow us to validate our implementation. Our simulations suggest that confinement plays an important role in aggregate formation.

Chain formation and aging process in biocompatible polydisperse ferrofluids: experimental investigation and Monte Carlo simulations

We review the use of Monte Carlo simulations in the description of magnetic nanoparticles dispersed in a liquid carrier. Our main focus is the use of theory and simulation as tools for the description of the properties of ferrofluids. In particular, we report on the influence of polydispersity and short-range interaction on the self-organization of nanoparticles. Such contributions are shown to be extremely important for systems characterized by particles with diameters smaller than 10nm. A new 3D polydisperse Monte Carlo implementation for biocompatible magnetic colloids is proposed. As an example, theoretical and simulation results for an ionic-surfacted ferrofluid dispersed in a NaCl solution are directly compared to experimental data (transmission electron microscopy - TEM, magneto-transmissivity, and electron magnetic resonance - EMR). Our combined theoretical and experimental results suggest that during the aging process two possible mechanisms are likely to be observed: the nanoparticle's grafting decreases due to aggregate formation and the Hamaker constant increases due to oxidation. In addition, we also briefly discuss theoretical agglomerate formation models and compare them to experimental data.

Haloing in bimodal magnetic colloids: the role of field-induced phase separation

If a suspension of magnetic micrometer-sized and nanosized particles is subjected to a homogeneous magnetic field, the nanoparticles are attracted to the microparticles and form thick anisotropic halos (clouds) around them. Such clouds can hinder the approach of microparticles and result in effective repulsion between them [M. T. López-López, A. Yu. Zubarev, and G. Bossis, Soft Matter 6, 4346 (2010)]. In this paper, we present detailed experimental and theoretical studies of nanoparticle concentration profiles and of the equilibrium shapes of nanoparticle clouds around a single magnetized microsphere, taking into account interactions between nanoparticles. We show that at a strong enough magnetic field, the ensemble of nanoparticles experiences a gas-liquid phase transition such that a dense liquid phase is condensed around the magnetic poles of a microsphere while a dilute gas phase occupies the rest of the suspension volume. Nanoparticle accumulation around a microsphere is governed by two dimensionless parameters--the initial nanoparticle concentration (φ(0)) and the magnetic-to-thermal energy ratio (α)--and the three accumulation regimes are mapped onto a α-φ(0) phase diagram. Our local thermodynamic equilibrium approach gives a semiquantitative agreement with the experiments on the equilibrium shapes of nanoparticle clouds. The results of this work could be useful for the development of the bimodal magnetorheological fluids and of the magnetic separation technologies used in bioanalysis and water purification systems.

Field-induced columnar transition of biocompatible magnetic colloids: An aging study by magnetotransmissivity

The field dependence of the optical transmission of tartrate-coated and polyaspartate-coated magnetite-based aqueous colloids was studied. The colloidal stock samples were diluted to prepare a series of samples containing different particle volume fractions ranging from 0.17% up to 1.52% and measured at distinct times after preparation (1, 30, 120, 240, and 1460 days). We show that the magneto-transmissivity behavior is mainly described by the rotation of linear chains, at the low-field range, whereas the analysis of the data provided the measurement of the average chain length. Results also reveal that the optical transmissivity has a minimum at a particular critical field, whose origin is related to the onset of columns of chains built from isolated particle chains, i.e., due to a columnar phase transition. We found the critical field reducing as the particle volume fraction increases and as the sample's aging time increases. To investigate the origin of this phenomenon we used phase condensation models and Mie's theory applied to a chain of spheres and to an infinite cylinder. Possible implications for magnetophotonic colloidal-based devices and biomedical applications were discussed.

Magnetic measurements on frozen ferrofluids as a method for estimating the magnetoviscous effect

Magnetic measurements on frozen ferrofluids with and without significant structure formation in an applied magnetic field have been performed. The results of these investigations were compared with the magnetic field dependent rheological properties for two different kinds of ferrofluids. Magnetic experiments performed similarly to conventional field cooled-field warming magnetic tests show the contribution of magnetic domain blocking and structure reorganization to the rheology of ferrofluids. Our efforts have shown the possibility of giving an estimate of the magnetoviscous effect by considering the temperature dependence of the magnetization of a frozen sample.

Adhesion properties of chain-forming ferrofluids

Denser and highly magnetized ferrofluids exhibit several non-Newtonian behaviors attributed to the formation of magnetic particle chains. We investigate the rheological and adhesive properties during tensile deformation of a confined chain-forming ferrofluid subjected to a radial magnetic field. Both the magnetoviscous contribution to the viscosity and the adhesive force are derived analytically. The response of the system to changes in the length of the chains is examined under zero and nonzero shear circumstances. Our results indicate that the existence of chains has a significant impact on the adhesive strength as well as on the viscosity of the ferrofluid, allowing it to display both shear-thinning and shear-thickening regimes. These findings open up the possibility of monitoring complex rheological responses of such fluids with the assistance of applied magnetic fields, allowing a more accurate assessment of their adhesive properties.

Condensation phase transitions in ferrofluids

Experiments show that under suitable conditions magnetic particles in ferrofluids and other polar suspensions undergo condensation phase transitions and form dense liquidlike or solidlike phases. The problem of fundamental features and scenarios of the phase transitions is one of the central problems of the physics of these systems. This work deals with the theoretical study of scenarios of condensation phase transitions in ferrofluids, consisting of identical magnetic particles. Our results show that, unlike the classical condensation phase transitions, the appearance of the linear chains precedes the magnetic particle bulk condensation. The effect of the chains on the diagrams of the equilibrium phase transitions is studied.

Rheological properties of magnetic suspensions

We present results of a theoretical study of the magnetorheological viscosity η of a suspension versus the applied magnetic field H and shear rate [Formula: see text]. It is supposed that the macroscopic rheological effects are provided by linear chain-like aggregates. Unlike in traditional models, the natural statistical distribution of the chains over the number of particles in them is taken into account. The results obtained explain important features of the rheological η versus [Formula: see text] law, which has been detected in experiments but qualitatively contradicts known theories of rheological properties of magnetic suspensions.

Hydrodynamic theory of polydisperse chain-forming ferrofluids

The larger magnetic particles in ferrofluids are known to form chains, causing the fluid to display non-Newtonian behavior. In this paper, a generalization of the familiar ferrofluid dynamics by Shliomis is shown capable of realistically accounting for these fluids. The modification consists of identifying the relaxing magnetization as that of the chain-forming particles, while accounting for the free magnetic particles by dissipative terms in the Maxwell equations.

Computer simulations of the structure of colloidal ferrofluids

The structure of a ferrofluid under the influence of an external magnetic field is expected to become anisotropic due to the alignment of the dipoles into the direction of the external field, and subsequently to the formation of particle chains due to the attractive head to tail orientations of the ferrofluid particles. Knowledge about the structure of a colloidal ferrofluid can be inferred from scattering data via the measurement of structure factors. We have used molecular-dynamics simulations to investigate the structure of both monodispersed and polydispersed ferrofluids. The results for the isotropic structure factor for monodispersed samples are similar to previous data by Camp and Patey that were obtained using an alternative Monte Carlo simulation technique, but in a different parameter region. Here we look in addition at bidispersed samples and compute the anisotropic structure factor by projecting the q vector onto the XY and XZ planes separately, when the magnetic field was applied along the z axis. We observe that the XY-plane structure factor as well as the pair distribution functions are quite different from those obtained for the XZ plane. Further, the two-dimensional structure factor patterns are investigated for both monodispersed and bidispersed samples under different conditions. In addition, we look at the scaling exponents of structure factors. Our results should be of value to interpret scattering data on ferrofluids obtained under the influence of an external field.

Structure formation in electromagnetically driven granular media

We report structure formation in submonolayers of magnetic microparticles subjected to periodic electrostatic and magnetic excitations. Depending on the excitation parameters, we observe the formation of a rich variety of structures: clusters, rings, chains, and networks. The dynamics and shapes of the structures are strongly dependent on the amplitude and frequency of the external magnetic field. We find that for pure ac magnetic driving the low-frequency magnetic excitation favors compact clusters, whereas high frequency driving favors chains and netlike structures. An abrupt phase transition from chains to a network phase was observed for a high density of particles.

Magnetic Soret effect: application of the ferrofluid dynamics theory

The ferrofluid dynamics theory is applied to thermodiffusive problems in magnetic fluids in the presence of magnetic fields. The analytical form for the magnetic part of the chemical potential and the most general expression of the mass flux are given. By applying these results to experiments, global Soret coefficients in agreement with measurements are determined. An estimate for a hitherto unknown transport coefficient is also made.

Structural properties of charge-stabilized ferrofluids under a magnetic field: A Brownian dynamics study

We present Brownian dynamics simulations of real charge-stabilized ferrofluids, which are stable colloidal dispersions of magnetic nanoparticles, with and without the presence of an external magnetic field. The colloidal suspensions are treated as collections of monodisperse spherical particles, bearing point dipoles at their centers and undergoing translational and rotational Brownian motions. The overall repulsive isotropic interactions between particles, governed by electrostatic repulsions, are taken into account by a one-component effective pair interaction potential. The potential parameters are fitted in order that computed structure factors are close to the experimental ones. Two samples of ferrofluid differing by the particle diameter and consequently by the intensity of the magnetic interaction are considered here. The magnetization and birefringence curves are computed: a deviation from the ideal Langevin behaviors is observed if the dipolar moment of particles is sufficiently large. Structure factors are also computed from simulations with and without an applied magnetic field H: the microstructure of the repulsive ferrofluid becomes anisotropic under H. Even our simple modeling of the suspension allows us to account for the main experimental features: an increase of the peak intensity is observed in the direction perpendicular to the field whereas the peak intensity decreases in the direction parallel to the field.

Statistical analysis of two-dimensional cluster structures composed of ferromagnetic particles based on a flexible chain model

We investigate two-dimensional cluster structures composed of ferromagnetic colloidal particles, based on a flexible chain model, by the configurational-bias Monte Carlo method. We clarify the dependence of the probabilities of the creation of different types of clusters on the dipole-dipole interactive energy and the cluster size.

Structural transformations in ferrofluids

We present results of theoretical study of internal structural transformations in magnetic liquids consisting of identical spherical magnetic particles suspended in a carrier liquid. As the results show, when the dimensionless characteristic energy of magnetic interaction epsilon between particles is less than a certain critical value epsilon('), the system of particles is in spatially homogeneous state with linear chainlike aggregates. When epsilon exceeds epsilon('), bulk droplike aggregates, consisting of large number of particles, can occur in this system. The critical parameter epsilon(') decreases when external magnetic field increases. This means that, in accordance with all known experiments, magnetic field stimulates the phase separation. Our estimates of epsilon(') are in agreement with magnitudes of the parameter of interaction between particles in typical ferrofluids where these phase transitions have been observed experimentally. Analysis shows that the bulk dense structures can occur provided that the total number N of particles in the system exceeds a threshold value N', which is about a thousand by order of magnitude. We think that this result explains why the bulk dense clusters, observed in many real experiments, have never been observed in three-dimensional computer simulations of ferrofluids-the total number of particles in these simulations was too small to provide the formation of bulk structures.

Structure and magnetic properties of polydisperse ferrofluids: a molecular dynamics study

We study by Langevin molecular dynamics simulations systematically the influence of polydispersity in the particle size, and subsequently in the dipole moment, on the physical properties of ferrofluids. The polydispersity is in a first approximation modeled by a bidisperse system that consists of small and large particles at different ratios of their volume fractions. In the first part of our investigations the total volume fraction of the system is fixed, and the volume fraction phiL of the large particles is varied. The initial susceptibility chi and magnetization curve of the systems show a strong dependence on the value of phiL. With the increase of phiL, the magnetization M of the system has a much faster increment at weak fields, and thus leads to a larger chi. We performed a cluster analysis that indicates that this is due to the aggregation of the large particles in the systems. The average size of these clusters increases with increasing phiL. In the second part of our investigations, we fixed the volume fraction of the large particles, and increased the volume fraction phiS of the small particles in order to study their influence on the chain formation of the large ones. We found that the average aggregate size formed by large particles decreases when phiS is increased, demonstrating a significant effect of the small particles on the structural properties of the system. A topological analysis of the structure reveals that the majority of the small particles remain nonaggregated. Only a small number of them are attracted to the ends of the chains formed by large particles.