Determination of core and hydrodynamic size distributions of CoFe2O4 nanoparticle suspensions using ac susceptibility measurements

Abstract

The complex susceptibility was measured on CoFe2O4 nanoparticle suspensions in the frequency range between 1 kHz and 1 MHz for different values of a superimposed static magnetic field. The maximum in the imaginary part χ″ of the ac susceptibility shifts to higher frequencies with increasing static magnetic field. The shift is theoretically modeled utilizing the magnetic field dependence of the Brownian relaxation time constant and assuming a distribution of hydrodynamic particle sizes. The mean hydrodynamic size as determined from the maximum of χ″ in zero field and the mean core size as obtained from the shift of the χ″ peak with static field agree very well with the data from transmission electron microscopy and dynamic light scattering measurements, respectively. The results indicate that both core and hydrodynamic size distributions can be determined from measurements on nanoparticle suspensions proposed that magnetic dipole-dipole interactions are negligible.

Effective particle magnetic moment of multi-core particles

“…By using different AC susceptibility models based on Debye relations for multi-core and single-core particles integrated over a size distribution (log-normal distribution) considering both Brownian and Néel relaxation behavior [12][13][14][15] and fitting the AC susceptibility data to these models, we are able to determine the particle and nanocrystal (core) size of the particle systems. The determined particle size from the AC susceptibility analysis is largely dependent on the surrounding liquid (that is the viscosity of the carrier liquid) while the determined nanocrystal (core) size is largely dependent on the nanocrystal intrinsic magnetic anisotropy.…”

“…The DynoMag system [12] was utilized between 1 Hz and 500 kHz, a lab high frequency AC susceptometer [13] was used in the frequency range between 10 kHz and 10 MHz and an additional lab high frequency susceptometer up to 1 MHz [14]. Measurements were carried out at 300 K.…”

Self-consistent magnetic properties of magnetite tracers optimized for magnetic particle imaging measured by ac susceptometry, magnetorelaxometry and magnetic particle spectroscopy

“…In contrast to the model discussed below, the authors only consider a distribution of core diameters assuming a constant organic shell thickness. The ACS spectra discussed here were recorded with our 1 MHz ac susceptometer having a field amplitude of 95 μT/μ 0 [13] and Fig. 2 shows the measured real and imaginary parts as a function of frequency.…”

Debye-Based Frequency-Domain Magnetization Model for Magnetic Nanoparticles in Magnetic Particle Spectroscopy

“…An established technique for studying the magnetization dynamics of a nanoparticle sample is the ac susceptometry (ACS) [12]. In ACS, the sample is exposed to an alternating field with small amplitude (typical 1 mT) sweeping frequency through the spectrum (from a few hertz to several megahertz).…”