The non-linear magnetisation response. So the SD-nonSPM possibility is left untreated.
The non-linear magnetisation response
The non-linear magnetisation response
Coercivity weighted Langevin magnetisation: A new approach to interpret superparamagnetic and nonsuperparamagnetic behaviour in single domain magnetic nanoparticles
“Coercivity weighted Langevin magnetisation: A new approach tointerpret superparamagnetic and nonsuperparamagnetic behaviour insingle domain magnetic nanoparticles” Dhanesh Rajana and Jukka Lekkalab a,b Department of Automation Science and Engineering, Tampere University of Technology, Finland
Presentation OutlineIntroductionA few words on… Coercivity weighted Langevin magnetisation: A new approach tointerpret superparamagnetic and nonsuperparamagnetic behaviourin single domain magnetic nanoparticlesMotivation for this workResultsHow is it useful ?
-- Ferromagnetism MR - remanence MS - saturation magnetisation susceptibility, χ = M H M - magnetisation (A/m) Hc - coercivity H - applied field (A/m)
-- Ferromagnetism-- Paramagnetism MS - saturation magnetisation susceptibility, χ = M H M - magnetisation (A/m) H - applied field (A/m)
-- Ferromagnetism-- Paramagnetism-- Superparamagnetism (SPM) MS - saturation magnetisation χ SPM χ PM Super-paramagnetism (SPM) M - magnetisation (A/m) >> H - applied field (A/m)
-- Superparamagnetism (SPM) MS - saturation magnetisation MR (remanence ) =0 χ SPM χ PM Super-paramagnetism (SPM) M - magnetisation (A/m) >> H - applied field (A/m) Langevin approach
-- Superparamagnetism (SPM)-- A few application areas.. Functionalised particles , Drug delivery and gene transfection Separation: Cell, DNA, protein, RNA fishing As contrast agent in MRI (magnetic resonance imaging ) & (MRA) magnetic resonance angiography Ferrofluid (magnetic fluid) & Sensors Hyperthermia treatment MPI (magnetic particle imaging) Tomographic imaging using the nonlinear response of magnetic particles, Nature 435, Bernhard Gleich & Jürgen Weizenecker
-- Motivation (1/2)When, What factors actually determine SPM behaviour Magnetic particle imaging using a ﬁeld free line J. Weizenecker, B. Gleich and J. Borgert, J. Phys. D: Appl. Phys. 41 Magnetisation response spectroscopy of SD superparamagnetic nanoparticles for MPI S.Biederer, T Knopp et al. J. Phys. D: Appl. Phys. 42 SPM Tomographic imaging using the nonlinear response of magnetic particles B. Gleich & J.Weizenecker, Nature Letter 435, 1214-1217
-- Motivation (2/2)When, What factors actually determine SPM behaviour SPM particles are SD particles but not all SD particles are SPM particles The SPM behaviour depends on a few parameters including material type, temperature, time period & magneto crystalline anisotropy There can be remanence and coercivity in SD regime (= can act like ferromagnetic) Limitation of classical Langevin equations:- Langevin approach Its applicability is limited to pure SD-SPM behaviour; Lacks parameters to predict remanence and coercivity in SD regime. To solve this issue, we propose a new model by modifying the classical Langevin equations.
-- Results KA dSD = 72 µ 0 Ms 2 6kbT dSPM = 2 3 K [Check the article references] Single domain critical diameter dSD, superparamagnetic diameter dSPM as a function of temperature for magnetite and maghemite particles Table 1: Anisotropy and crystalline parameters defining SD and SPM critical diameters at 300K
-- Results 1 kbT τ m 2 Hc = Hco 1 − ln KV τ O ÷÷ where 1/τm is measurement frequency.1/τo is attempt frequency characteristicto material Coercivity as a function of particle diameter a) at different temperatures and b) at different field frequencies. The zero coercivity corresponds to the superparamagnetic transition which is clearly a function of temperature (blocking temperature) and measurement frequency.
-- Results 1 1 ωτ eff 1 MAC = φ Ms coth(α eff cos ωt ) − ÷+ coth(α eff sin ωt ) − ÷ 1 + ω τ eff 2 2 α eff cos ω t ÷ 1 + ω 2τ eff 2 α eff sin ω t ÷ πµ Msd 3 (H x ± Hc ) α eff = 0 6k T b The magnetisation plots for a) SD magnetite and b) SD maghemite particles at different temperatures. Two diameters 10% above and below the critical d SPM are considered. (For computations, f = 10Hz, particle concentration = 0.1mmol/L, suspension medium = distilled water)
-- Results 1 α χ DC = φ Ms − eff ( coth 2 (α eff ) − 1) α eff Heff Heff φ Ms 1 α χ= − eff ( coth 2 (α eff ) − 1) 1 + w2τ eff 2 α eff Heff Heff wτφ Ms 1 α eff χ = 1 + w2τ eff − ( coth 2 (α eff ) − 1) The χʹ and χ” plots for SD- SPM and SD- nonSPM particles for α eff Heff Heff 2 magnetite and maghemite at different frequencies. The cusp observed in experimental χʹ versus T plots χʹ versus T curve for magnetite for a given SPM diameter
-- Conclusions The new model 1) Combines steady / time varying magnetisation dynamics and considers all known factors affecting the SPM state 2) Directly calculates coercivity compensated magnetisations and susceptibilities. 3) Covers full spectrum of SD diameters 4) Defines the switching between SPM and non-SPM (= can act like ferromagnetic) states more accurately. Direct calculation of coercivity weighted magnetisation and susceptibility would be helpful in biomedical areas where magnetic particles have been used for eg. calculating magnetisation dependent voltage, magnetisation dependent polarisation, magneto optic effect etc. Further work: Next stage : inclusion of ‘log normal diameter distribution’ of particles to accommodate polydispersity, and validation experiments.
For more details please check the conference article... Thank you ! Questions ??