Characterization

The measurement of the alternating field (or ac-) susceptibility is a method established for years for the characterization of magnetic nanoparticles as well as for the realization of homogeneousgenerbinding assays . A mostly cylindrical coil generates a sinusoidal excitation magnetic field whose amplitude is small enough to be in the linear range of the magnetization characteristic of the magnetic nanoparticles. This contains two antiserially connected detection coils whose signal is measured with a lock-in amplifier. If there is no sample in either of the two detection coils and the setup is perfectly aligned, the signals induced in the two detection coils compensate each other, so that the resulting signal is zero. If a sample containing magnetic nanoparticles is positioned in one of the two detection coils, a resulting voltage is measured, which can be divided with the lock-in amplifier into a contribution U_x, which is in phase with the excitation magnetic field, and a contribution U_y, which is phase-shifted by 90°. From these, the real χ' and the imaginary part χ'' of the ac susceptibility can be determined.

For the characterisation of magnetic nanoparticles as well as for the realisation of binding assays, a frequency sweep is generally performed at a constant amplitude of the excitation field. The spectra of the real and imaginary parts are generally interpreted within the framework of the Debye model. Figure 2 shows the dependence on the frequency. The imaginary part has its maximum at ωt = 1, so that the mean time constant of the nanoparticles can be determined directly from the position of the maximum.

ACS superstructures with the following parameters are available at the Institute:

LF-ACS: 10 Hz - 10 kHz, ac field amplitude: 560 µT

HF-ACS: 200 Hz - 1 MHz, ac field amplitude: 95 µT

Fluxgate-based ACS: 0.1 Hz - 9 kHz, ac field amplitudes: up to 9 mT, additionally dc magnetic fields up to 9 mT can be applied parallel or perpendicular to the ac field.

All ACS systems were calibrated with Dy2O3 powder samples so that the susceptibility can be measured absolutely.

The basic sequence of an MRX measurement is shown in the picture on the right. Without an external magnetic field, the superparamagnetic nanoparticles show no measurable magnetic signal. If an external magnetic field Hmag is applied, the magnetic nanoparticles align themselves and the sample shows a measurable magnetic signal. If the magnetic field is switched off again, the magnetic signal of the nanoparticles drops back to zero. This so-called relaxation of the magnetic signal depends on the size of the nanoparticles. If the nanoparticle is in a liquid, it can rotate as a whole. This process is known as Brown relaxation and is characterised by the Brown time constant tB. Large nanoparticles rotate slowly, while small ones rotate quickly. However, if the nanoparticle cannot rotate, e.g. by embedding it in a sugar matrix or by binding it to a surface or a large target, the internal magnetisation of superparamagnetic particles can flip back and forth. This process is called Néel relaxation. The associated time constant tN depends exponentially on the volume of the magnetic particle core. If both mechanisms are possible, the one with the shorter time constant dominates. The accessible range of time constants is limited by the switch-off time of the magnetisation field and the bandwidth of the sensors.

Measurement parameters: Time window: 300 µs - several seconds, pulse amplitudes: up to 2 mT

As part of a BMBF-funded joint project, we have developed a compact magnetic nanoparticle analyser based on the magnetic relaxometry principle (image below).

In addition to the switched and alternating magnetic field, the rotating magnetic field represents another possibility for the magnetic manipulation of magnetic nanoparticles (MNP), which are dissolved in an aqueous medium and relax according to Brown. Here, the magnetic torque between the rotating magnetic field and the magnetization of the magnetic nanoparticles causes a rotational movement of the particles, which has the frequency of the rotating magnetic field. In the alternating magnetic field, however, the MNP change their orientation according to their magnetic moment and the applied magnetic field in time with the selected frequency without entering a defined rotational movement. The rotational movement of the MNP or the magnetic moment has a phase difference φ to the rotating magnetic field (Figure 1 ), which is mainly caused by the rotational friction between the particle envelope and the medium. The absolute phase angle φ also depends on the frequency and field strength of the rotating magnetic field and on the parameters (temperature, viscosity, charge) of the medium. Thus, by determining the phase angle between the rotating magnetic field and the magnetization of the magnetic nanoparticles, a statement can be made about the ratio of magnetic core to particle shell if the temperature and viscosity of the medium are kept constant. In contrast to the alternating magnetic field, the rotating magnetic field is generated by a 2-axis Helmholtz coil system (Figure 1 ).

The principle dependence of the phase angle φ on the frequency and field strength of the rotating magnetic field is illustrated in Figure 2 using the example of an aqueous suspension of iron oxide particles with a hydrodynamic diameter (particle including shell) of 120 nm. It can be clearly seen that an increasing frequency causes an increase in the phase angle, whereas a higher field strength reduces the phase angle. In the case of the alternating magnetic field, a phase angle for the fundamental frequency of the manipulating magnetic field can be determined analogue to the rotating magnetic field, which has a significantly lower dependence on the field strength in comparison. This becomes clear from the smaller spread of the blue curves (ACF) in Figure 2.

Measurement parameters: Frequency: 0.1 Hz - 9 kHz, field amplitude: up to 9 mT, temperatures: room temperature up to 70°C