Effects of interactions on magnetization relaxation dynamics in ferrofluids

Superparamagnetic effects in the linear magnetic response of polydisperse ensembles of nanoparticles suspended in a fluid

Within a kinetic theory, the linear magnetic response of uniaxial single-domain particles suspended in a fluid is analyzed. The main qualitatively different types of frequency dependence of the longitudinal dynamic magnetic susceptibility of such particles are described. It is shown that superparamagnetic (related to orientation thermal fluctuations of the magnetic moment inside a particle) peculiarities of the response of a particle to a probing magnetic field are not fully determined by the ratio of anisotropy energy to thermal energy when a stationary bias field is applied. For a case where the indicated ratio is much greater than one, a simple approximate expression for the dynamic magnetic susceptibility of a particle is proposed. The developed approach is extended to polydisperse suspensions of noninteracting uniaxial nanoparticles. It is shown that polydispersity does not vanish away specific superparamagnetic features in the dynamic magnetic response of such systems. Quantitative estimates of the corresponding effects are performed in different frequency ranges of the applied field. It is demonstrated that under certain restrictions on the disperse composition of a suspension, the internal diffusion of the magnetic moment can lead to a splitting of the absorption spectrum of the system. The significant role of the bias field is revealed. In particular, it can cause an additional absorption maximum provided the particle-size distribution meets the outlined condition. Also, it enables one to assess how important it is to take into account superparamagnetism of particles: the effect of the biasing is stronger for particles with smaller anisotropy and thereby more pronounced superparamagnetic properties. A qualitative agreement of some of the inferences with the experimental data is briefly discussed.

Field- and concentration-dependent relaxation of magnetic nanoparticles and optimality conditions for magnetic fluid hyperthermia

The field-dependent relaxation dynamics of suspended magnetic nanoparticles continues to present a fascinating topic of basic science that at the same time is highly relevant for several technological and biomedical applications. Renewed interest in the intriguing behavior of magnetic nanoparticles in response to external fields has at least in parts be driven by rapid advances in magnetic fluid hyperthermia research. Although a wealth of experimental, theoretical, and simulation studies have been performed in this field in recent years, several contradictory findings have so far prevented the emergence of a consistent picture. Here, we present a dynamic mean-field theory together with comprehensive computer simulations of a microscopic model system to systematically discuss the influence of several key parameters on the relaxation dynamics, such as steric and dipolar interactions, the external magnetic field strength and frequency, as well as the ratio of Brownian and Néel relaxation time. We also discuss the specific and intrinsic loss power as measures of the efficiency of magnetic fluid heating and discuss optimality conditions in terms of fluid and field parameters. Our results are helpful to reconcile contradictory findings in the literature and provide an important step towards a more consistent understanding. In addition, our findings also help to select experimental conditions that optimize magnetic fluid heating applications.

Correlating the Dipolar Interactions Induced Magneto-Viscoelasticity and Thermal Conductivity Enhancements in Nanomagnetic Fluids

The effective thermal management of electronic system holds the key to maximize their performance. The recent miniaturization trends require a cooling system with high heat flux capacity, localized cooling, and active control. Nanomagnetic fluids (NMFs) based cooling systems have the ability to meet the current demand of the cooling system for the miniaturized electronic system. However, the thermal characteristics of NMFs have a long way to go before the internal mechanisms are well understood. This review mainly focuses on the three aspects to establish a correlation between the thermal and rheological properties of the NMFs. First, the background, stability, and factors affecting the properties of the NMFs are discussed. Second, the ferrohydrodynamic equations are introduced for the NMFs to explain the rheological behavior and relaxation mechanism. Finally, different theoretical and experimental models are summarized that explain the thermal characteristics of the NMFs. Thermal characteristics of the NMFs are significantly affected by the morphology and composition of the magnetic nanoparticles (MNPs) in NMFs as well as the type of carrier liquids and surface functionalization that also influences the rheological properties. Thus, understanding the correlation between the thermal characteristics of the NMFs and rheological properties helps develop cooling systems with improved performance.

Magnetization relaxation dynamics in polydisperse ferrofluids

When a ferrofluid is magnetized in a strong magnetic field, and then the field is switched off, the magnetization decays from its saturation value to zero. The dynamics of this process are controlled by the rotations of the constituent magnetic nanoparticles, and for the Brownian mechanism, the respective rotation times are strongly influenced by the particle size and the magnetic dipole-dipole interactions between the particles. In this work, the effects of polydispersity and interactions on the magnetic relaxation are studied using a combination of analytical theory and Brownian dynamics simulations. The theory is based on the Fokker-Planck-Brown equation for Brownian rotation and includes a self-consistent, mean-field treatment of the dipole-dipole interactions. The most interesting predictions from the theory are that, at short times, the relaxation of each particle type is equal to its intrinsic Brownian rotation time, while at long times, each particle type has the same effective relaxation time, which is longer than any of the individual Brownian rotation times. Noninteracting particles, though, always relax at a rate controlled only by the Brownian rotation times. This illustrates the importance of including the effects of polydispersity and interactions when analyzing the results from magnetic relaxometry experiments on real ferrofluids, which are rarely monodisperse.

Dynamical effective field model for interacting ferrofluids: II. The proper relaxation time and effects of dynamic correlations

The recently proposed dynamical effective field model (DEFM) is quantitatively accurate for ferrofluid dynamics. It is derived in paper I within the framework of dynamical density functional theory (DDFT) along with a phenomenological description of nonadiabatic effects. However, it remains to clarify how the characteristic rotational relaxation time of a dressed particle, denoted byτ_r, is quantitatively related to that of a bare particle, denoted byτr0. By building macro-micro connections via two different routes, I reveal that under some gentle assumptionsτ_rcan be identified with the mean time characterizing long-time rotational self-diffusion. I further introduce two simple but useful integrated correlation factors, describing the effects of quasi-static (adiabatic) and dynamic (nonadiabatic) inter-particle correlations, respectively. In terms of both the dynamic magnetic susceptibility is expressed in an illuminating and elegant form. Remarkably, it shows that the macro-micro connection is established via two successive steps: a dynamical coarse-graining with nonadiabatic effects accounted for by the dynamic factor, followed by equilibrium ensemble averaging captured by the static factor. By analyzing data from Brownian dynamics simulations on monodisperse interacting ferrofluids, I findτr/τr0is, somehow unexpectedly, insensitive to changes of particle volume fraction. A physical picture is proposed to explain it. Furthermore, an empirical formula is proposed to characterize the dependence ofτr/τr0on dipole-dipole interaction strength. The DEFM supplemented with this formula leads to parameter-free predictions in good agreement with results from Brownian dynamics simulations. The theoretical developments presented in this paper may have important consequences to studies of ferrofluid dynamics in particular and other systems modeled by DDFTs in general.

How chains and rings affect the dynamic magnetic susceptibility of a highly clustered ferrofluid

The dynamic magnetic susceptibility, χ(ω), of a model ferrofluid at a very low concentration (volume fraction, approximately 0.05%), and with a range of dipolar coupling constants (1≤λ≤8), is examined using Brownian dynamics simulations. With increasing λ, the structural motifs in the system change from unclustered particles, through chains, to rings. This gives rise to a nonmonotonic dependence of the static susceptibility χ(0) on λ and qualitative changes to the frequency spectrum. The behavior of χ(0) is already understood, and the simulation results are compared to an existing theory. The single-particle rotational dynamics are characterized by the Brownian time, τ_{B}, which depends on the particle size, carrier-liquid viscosity, and temperature. With λ≤5.5, the imaginary part of the spectrum, χ^{''}(ω), shows a single peak near ω∼τ_{B}^{-1}, characteristic of single particles. With λ≥5.75, the spectrum is dominated by the low-frequency response of chains. With λ≥7, new features appear at high frequency, which correspond to intracluster motions of dipoles within chains and rings. The peak frequency corresponding to these intracluster motions can be computed accurately using a simple theory.

Magnetoimpedance Thin Film Sensor for Detecting of Stray Fields of Magnetic Particles in Blood Vessel

Multilayered [FeNi (100 nm)/Cu (3 nm)]₅/Cu (500 nm)/[Cu (3 nm)/[FeNi (100 nm)]₅ structures were used as sensitive elements of the magnetoimpedance (MI) sensor prototype for model experiments of the detection of magnetic particles in blood vessel. Non-ferromagnetic cylindrical polymer rod with a small magnetic inclusion was used as a sample mimicking thrombus in a blood vessel. The polymer rod was made of epoxy resin with an inclusion of an epoxy composite containing 30% weight fraction of commercial magnetite microparticles. The position of the magnetic inclusion mimicking thrombus in the blood vessel was detected by the measurements of the stray magnetic fields of microparticles using MI element. Changes of the MI ratio in the presence of composite can be characterized by the shift and the decrease of the maximum value of the MI. We were able to detect the position of the magnetic composite sample mimicking thrombus in blood vessels. Comsol modeling was successfully used for the analysis of the obtained experimental results and the understanding of the origin the MI sensitivity in proposed configuration. We describe possible applications of studied configuration of MI detection for biomedical applications in the field of thrombus state evaluation and therapy.