Series expansions for the magnetisation of a solid superparamagnetic system of non-interacting particles with anisotropy

The implant assisted magnetic targeted drug delivery system of Avilés, Ebner and Ritter is considered both experimentally (in vitro) and theoretically. The results of a 2D mathematical model are compared with 3D experimental results for a magnetizable wire stent. In this experiment a ferromagnetic, coiled wire stent is implanted to aid collection of particles which consist of single domain magnetic nanoparticles (radius ≈ 10 nm). In order to model the agglomeration of particles known to occur in this system, the magnetic dipole-dipole and hy- A c c e p t e d m a n u s c r i p t PACS: 47.63.mh, 87.85.gf

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“…Thus, the average projection of m the moment in the direction of B total can be calculated from the Langevin function [6,8,22,23,24]…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Many particle magnetic dipole–dipole and hydrodynamic interactions in magnetizable stent assisted magnetic drug targeting

Cregg

Murphy

Mardinoğlu

et al. 2010

Journal of Magnetism and Magnetic Materials

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“…Finally, a third approach to the problem of describing the ZFC magnetization data of superparamagnetic-based material systems has been proposed by Cregg and Bessais [8]. In this approach the magnetization of a superparamagnetic system is given by M(β,α,= ) = M s <cosω> = M s (∂Z/∂β)/Z, with α = KV/k B T, β = HM s V/k B T, where K is the anisotropy constant, H is the applied magnetic field, M s is the saturation magnetization and V is the volume of the particle (see Fig.…”

Section: Discussionmentioning

confidence: 99%

Magnetic investigation of iron-nitride-based magnetic fluid

et al. 2007

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Transmission electron microscopy (TEM), Mössbauer spectroscopy and magnetization measurements were used in the present study to investigate a non-aqueous ironnitride-based magnetic fluid (MF) sample containing about 2×10 16 particle/cm 3 . The TEM micrographs indicated spherical-shaped iron nitride nanoparticles with an average diameter of 12.3 nm and diameter dispersity of 0.14. The 77 K Mössbauer spectrum of the frozen MF sample indicated the presence of about 95% of the γ′-Fe 4 N phase, with a residual 5% of the ɛ-Fe 4 N phase. The temperature dependence of the magnetization was investigated under zero-field-cooled (ZFC) condition, in the temperature range of 4 to 165 K. The ZFCdata were curve-fitted using a new approach that takes into account the particle size distribution and the temperature dependence of the magnetocrystalline anisotropy, making the description of the experimental situation more realistic.

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“…where the functions i n (x) are the modified spherical Bessel functions of the first kind [13][14][15] as given in appendix A. Noting the orthogonality properties of the Legendre polynomials given by (A.5) this reduces to a single series…”

Section: The Partition Function For the Two-spin Casementioning

confidence: 99%

“…where the functions i n (x) are the modified spherical Bessel functions of the first kind [13][14][15] …”

Section: Appendix a Equations For Reduction Of The Integralsmentioning

confidence: 99%

Partition functions of classical Heisenberg spin chains with arbitrary and different exchange

Cregg¹,

García‐Palacios²,

Svedlindh³

2008

J. Phys. A: Math. Theor.

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The classical Heisenberg model has been effective in modelling exchange interactions in molecular magnets. In this model, the partition function is important as it allows the calculation of the magnetization and susceptibility. For an ensemble of N-spin sites, this typically involves integrals in 2N dimensions. Here, for two-, three-and four-spin nearest neighbour open linear Heisenberg chains these integrals are reduced to sums of known functions, using a result due to Gegenbauer. For the case of the three-and four-spin chains, the sums are equivalent in form to the results of Joyce. The general result for an N-spin chain is also obtained.

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Series expansions for the magnetisation of a solid superparamagnetic system of non-interacting particles with anisotropy

Cited by 29 publications

References 7 publications

Many particle magnetic dipole–dipole and hydrodynamic interactions in magnetizable stent assisted magnetic drug targeting

Many particle magnetic dipole–dipole and hydrodynamic interactions in magnetizable stent assisted magnetic drug targeting

Magnetic investigation of iron-nitride-based magnetic fluid

Partition functions of classical Heisenberg spin chains with arbitrary and different exchange

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