The OMC experiment is based on light scattering at superparamagnetic microparticles. In an external mag-netic field, these particles become magnetized and interact with each other and with the field. Two particles that have encountered and formed a magnetic dimer will follow the rotation of a rotating magnetic field. The light scattering at the rotating dimers is used to determine the number of dimers in solution. The method for this measurement is explained in this section.
3.2. MEASURING DIMER CONCENTRATIONS CHAPTER 3. THE OPTOMAGNETIC CLUSTER EXPERIMENT
The rotating dimers in the solution are illuminated with a laser and scatter light in all directions. The photo-detector measures the intensity of the scattered light at 90°. The intensity of the scattered light depends on the orientation of the dimers and fluctuates over time while the dimers are rotating, see Fig. 3.2a.
When the magnetic field is off, all the dimers have a random orientation, due to the Brownian motion and rotation. The signal of the scattering is then noisy due to particles and clusters that move in and outside the focus volume of the laser. When the (rotating) magnetic field is turned on, the particles and the dimers align with the magnetic field and start rotating. A particle rotates because it has a magnetic anisotropy axis, which aligns with the magnetic field. A dimer rotates due to its magnetic shape anisotropy, as explained in section 1.4. The intensity of the light scattering at a rotating particle does not oscillate in time, due to its spherical symmetry. So only the scattering at clusters contributes to the oscillation of the scattered light. The contribution of each dimer is assumed to be equal, because all dimers rotate in sync, parallel to the field. Thus, the magnitude of the oscillation increases linearly with the number of dimers that are present in the focus volume of the laser.
Fig. 3.2a shows the signal that is measured with the photo detector at a scattering angle of 90°, around the time when the magnetic field is turned on for 0.6 seconds. Initially the field is off, so the photo detector measures only random scatter events, resulting in a noisy baseline. After switching the field on, a clear oscillating signal appears, resulting from scattering at the rotating dimers. The rotating frequency of the magnetic field is 5 Hz, which corresponds to a period of 0.2 seconds. The oscillating signal repeats after each half period. When the magnetic field is turned off, the dimers are not forced to be aligned anymore. The dimers will become randomly oriented and the oscillation relaxes to the original noisy baseline.
3.2.2 Quantifying dimer concentration with Fourier amplitude
In order to get the amplitude of the oscillating signal, and thus to get a quantification for the dimer concentra-tion, the Fourier transformation is taken from the scattering signal. Fig. 3.2b shows the Fourier transformation of Fig. 3.2a, of the period when the magnetic field is turned on. The x-axis of this graph shows the frequency
3.2. MEASURING DIMER CONCENTRATIONS CHAPTER 3. THE OPTOMAGNETIC CLUSTER EXPERIMENT
(a) (b)
Fig. 3.2: Example of a result from OMC experiments. (a) A scattering signal and the magnetic field strength plotted against the time. The magnetic field is switched on for 0.6 seconds. When the field is switched on the scattering signal changes from noise to a clear oscillating signal. The magnetic field rotates with a frequency of 5 Hz, so 1 period correspond to 0.2 seconds, which is indicated by the arrow. When the magnetic field is turned of, the scattering signal relaxes back to the original noisy signal. The insert shows a zoom of the signal that is marked with the blue square. Above the signal the possible dimer orientation is depicted, which changes in time. One period corresponds to a full rotation of a dimer. The signal is repeated after half a rotation due to the symmetry of a dimer, so the scattering signal oscillates at two times the rotation frequency.
(b)The Fourier transformation of the signal from figure (a). The absolute Fourier amplitude is plotted as a function of the frequency component relative to the rotation frequency fr = 5 Hz. The |A2f| peak and the
|A4f| peak corresponds to an oscillation of 10 Hz and 20 Hz respectively. The Fourier spectrum only has peaks at the even frequencies, because the scattering signal oscillates at two times the rotation frequency.
components of the signal normalized on the rotation frequency of the field (fr = 5 Hz). Due to the symmetry of the rotating dimers, the signal has only frequency components that are multiplications of 2 times the ro-tation frequency (2fr, 4fr, 6fr...). Therefore the Fourier amplitude has only peaks at the even numbers. The height of these peaks corresponds to the main amplitude of the oscillating signal. In this project, the|A2f| and the|A4f| peak from the Fourier spectrum are used for the quantification of the dimer concentration.
Quantifying the dimer concentration with an OMC experiment is only accurate when the height of the |A2f|-or |A4f|-peak is linearly prop|A2f|-ortional to the number of dimers in solution. The relation between the height of the peak and the amount of dimers is tested by measuring the scattering signal at different dimer concen-trations.
For this measurement, samples with different dimer concentrations are prepared by diluting the stock solution of magnetic particles. It is estimated that about 10 % of the particles in the stock solution is part of a dimer. By diluting the stock solution, the particle and also the dimer concentration is decreased. The scattering signal of these diluted samples is measured with the setup of the OMC experiments at a scatter angle of 90° using a rotating magnetic field of 4 mT at 5 Hz.
Fig. 3.3 shows the height of the Fourier amplitude (|A4f|) against the particle concentration, the data is fitted linearly. Under the assumption that the dimer concentration is linear proportional to the particle concentra-tion, it can be concluded that the |A4f| is linear with the dimer concentration.