The Effective Field Method in the Orientational Kinetics of Magnetic Fluids and Liquid Crystals

Raǐkher, Yu. L.; Shliomis, M. I.

doi:10.1002/9780470141465.ch8

Cited by 143 publications

(104 citation statements)

References 48 publications

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“…In the presence of a strong polarizing field, H (i.e. larger than the anisotropy field), the theoretically predicted effective value of the uniaxial magnetocrystalline anisotropy field, as measured by magnetic resonance, is given by [1], [2]: …”

Section: Introductionmentioning

confidence: 99%

An experimental study of the dynamic properties of nanoparticle colloids with identical magnetization but different particle size

Fannin

Marin

Raj

et al. 2012

Journal of Magnetism and Magnetic Materials

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Section: Introductionmentioning

confidence: 99%

An experimental study of the dynamic properties of nanoparticle colloids with identical magnetization but different particle size

Fannin

Marin

Raj

et al. 2012

Journal of Magnetism and Magnetic Materials

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“…In strong H t with respect to k B T (k B is the Boltzmann's constant and T is the temperature), the perpendicular susceptibility, χ ⊥ (ω,H) can be expressed in its LandauLifshitz form [3,4]:…”

Section: Introductionmentioning

confidence: 99%

“…The parallel or longitudinal susceptibility component, χ || (ω,H) can be described by the Debye equation [3,5], with ( )…”

Section: Introductionmentioning

confidence: 99%

“…There are two relaxation times which influence the magnetic relaxation in magnetic fluids: i) the Brownian relaxation time, τ B , which is determined by the rotation of particles in the carrier liquid [3], and ii) the Néel relaxation time, τ N , correlated to the rotation of the magnetic moment of particles, by overcoming the energy barrier within the particles [3].…”

Section: Introductionmentioning

confidence: 99%

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The resonance decay function method in the determination of the pre-factor of the Néel relaxation time of single-domain nanoparticles

Fannin

Marin

Couper

2011

Journal of Magnetism and Magnetic Materials

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In its simple form, the relaxation time of the Néel relaxation process of the magnetic moment of single-domain particles is given by τ N = τ 0N exp(σ), σ being the ratio of the anisotropy energy to thermal energy. The pre-factor, τ 0N , is normally given a value of 10 -9 s, but values ranging from 10 -8 to 10 -12 s have been reported in literature. Here, by means of the field and frequency dependence of the complex magnetic susceptibility, χ(ω,H)= χ'(ω,H)-i χ''(ω,H), of a magnetic fluid sample, in the MHz -GHz range, in conjunction with the determination of the sample decay function, b(t), the pre-factor τ 0N is determined. b(t) is readily obtained through the inverse Fourier transformation relationship which exists between b(t) and χ'' (ω).

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“…The field is free to be slightly different than the applied field. 31,32 The advantages of the effective field model are the simpler more intuitive form and the ease of implementation relative to the stochastic or FPE methods. It is clear that the model describes an exponential decay when the applied field is zero, and when the effective field is equal to the actual field, the mean magnetization does not change.…”

Section: Truncating the Moment Equationmentioning

confidence: 99%

Comparisons of characteristic timescales and approximate models for Brownian magnetic nanoparticle rotations

Reeves

Weaver

2015

Journal of Applied Physics

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Magnetic nanoparticles are promising tools for a host of therapeutic and diagnostic medical applications. The dynamics of rotating magnetic nanoparticles in applied magnetic fields depend strongly on the type and strength of the field applied. There are two possible rotation mechanisms and the decision for the dominant mechanism is often made by comparing the equilibrium relaxation times. This is a problem when particles are driven with high-amplitude fields because they are not necessarily at equilibrium at all. Instead, it is more appropriate to consider the "characteristic timescales" that arise in various applied fields. Approximate forms for the characteristic time of Brownian particle rotations do exist and we show agreement between several analytical and phenomenological-fit models to simulated data from a stochastic Langevin equation approach. We also compare several approximate models with solutions of the Fokker-Planck equation to determine their range of validity for general fields and relaxation times. The effective field model is an excellent approximation, while the linear response solution is only useful for very low fields and frequencies for realistic Brownian particle rotations. V C 2015 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4922858] I. DESCRIBING DRIVEN NANOPARTICLE ROTATIONSIn many magnetic nanoparticle (MNP) applications like biosensing, 1-7 hyperthermia, 8,9 and magnetic particle imaging, 10-13 nanoparticles are driven to rotate by oscillating magnetic fields.14 Understanding the resulting magnetic particle dynamics is important to advance these applications. A typical way to discuss the dynamics is through the timescales of the nanoparticle rotations. [15][16][17] In particular, we often consider the relaxation time: the timescale for a sample of particles to return to equilibrium after some perturbation (e.g., alignment with a field). Conventional magnetic particles are understood to have two rotational mechanisms. The entire particle can rotate as a rigid body by Brownian rotations, 18 and the particle's magnetic moment can also rotate internally due to restructuring of electronic states in N eel rotation. 19,20 The equilibrium relaxation time is different for each mechanism and depends on many parameters. 21,22 However, because most applications involve magnetically excited particles, it is more important to examine non-equilibrium timescales determining the speed of movements in varying driving fields-these timescales can be very different from the relaxation time. One only needs to imagine that in a stronger field, the particles will align faster to see why this is true. We will hence refer to those non-equilibrium timescales as the "characteristic times" of the rotations.In reality, the possibility for N eel rotations complicates the matter and it is important to understand which mechanism is dominant for chosen nanoparticles. 23,24 This is an open problem because these processes will in general not be decoupled. If the processes did truly happen independently (in parallel)...

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The Effective Field Method in the Orientational Kinetics of Magnetic Fluids and Liquid Crystals

Cited by 143 publications

References 48 publications

An experimental study of the dynamic properties of nanoparticle colloids with identical magnetization but different particle size

An experimental study of the dynamic properties of nanoparticle colloids with identical magnetization but different particle size

The resonance decay function method in the determination of the pre-factor of the Néel relaxation time of single-domain nanoparticles

Comparisons of characteristic timescales and approximate models for Brownian magnetic nanoparticle rotations

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