Evaluation of the Initial SPS Formation

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described as being somewhat equivalent to the formation of crystal nuclei from monomers in a solution. There is a certain inhibiting threshold (in this case more kinetic than thermodynamic) that needs to be overcome. Once a nucleus is formed, it can grow rapidly until there is no more material in the vicinity that can be incorporated into the agglomerate. With further study, the system could possibly be used as a scaled-up model system for the formation of crystal nuclei.

In general, the rate of formation of larger SPS can best be seen from the development of agglomerates of one or two beads¹. Thus, in the following sections, the figures show the development of the ratio of beads present as single beads and two-bead-agglomerates compared to the total number of beads.

Influence of the Rotation Frequency

According to the results of the experiments (presented in Figure 4.3), the rotation frequency has no significant influence on the rate with which SPS form. The differences between the four curves can be explained through statistical variations. This is supported by the fact that there appears to be no trend for different frequencies and the resulting ratio. Note, however, that although the initial rate of formation is obviously not affected, the shape of the resulting SPS is: Figure 4.2 shows two images taken at 160 s seconds at rotation frequencies of 60 rpm and 60000 rpm. It can clearly be seen that at low rotation frequencies the SPS form chains, while higher frequencies cause a reformation into cluster structures. Therefore, although the formation rate does not differ, the final SPS size and shape will.

1 Agglomerates of two beads were included as the initial sample in the absence of a magnetic field already contained up to 10 % of agglomerates of two beads. This was caused by unspecific attractive forces between the beads that could not be completely cancelled by Tween 20. The use of carboxylic acid coated beads would have solved this problem, but as the M-280 beads are not available with this functionalization and the MyOne beads would have been too small to resolve them optically, the use of M-280 SA beads presented the best available compromise.

0 20 40 60 80 100 120 140 160 0

0.2 0.4 0.6 0.8 1

Time t / s

RatioofSPSwithXbeads

1&2 beads/SPS 3&4 beads/SPS 5&6 beads/SPS 7&8 beads/SPS 9&≥10 beads/SPS

Figure 4.1: Formation dynamics of SPS structures under the influence of a rotating magnetic field. SPS consisting ofX beads (see legend) form and are incorporated into larger SPS. The experiment was performed with a bead concentration of 100 µg mL⁻¹, a magnetic field strength of 90 Oe and a rotation frequency of 600 rpm.

Figure 4.2: Microscopy image of the SPS shapes after 160 s at a rotation frequency of 60 rpm (left) and 60000 rpm (right). It can clearly be seen that at low rotation frequencies, the SPS remain in the chain formation.

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0 20 40 60 80 100 120 140 160

0 0.2 0.4 0.6 0.8 1

Time t / s

RatioofSPSwith1&2beads ^{60 rpm}

600 rpm 6000 rpm 60000 rpm

Figure 4.3: Influence of the rotation frequency on the SPS formation rate.

The y-axis gives the ratio of beads that are present as single beads or 2-beads-SPS compared to the overall number of beads. The data was collected at a magnetic field strength of 90 Oe and a concentration of 50 µg mL⁻¹.

Influence of the Field Strength

A higher field strength induces a larger magnetic moment in the super-paramagnetic beads, which in turn leads to an increase in the attractive forces between the particles (see section 2.2 for details). Thus, a higher field strength should favor the rate of SPS formation. This is reflected in the results of the experiment, presented in Figure 4.4. The higher the magnetic field strength, the faster beads form into SPS. However, the influence is not as strong as would be expected when considering that according to equations 2.15 and 2.16, the length Lof an SPS chain is proportional to the field strength H. When the field strength is doubled (from 63 Oe to 117 Oe), the final ratio at 160 s only decreases from 30 % to 22 %¹. However, equations 2.15 and 2.16 apply to SPS structures that are already

1 The results from the 36 Oe curve were not used for this comparison as the starting SPS composition differs strongly from the rest of the experiments, with only 78 % of the beads present as single beads or 2-bead-agglomerates.

formed and where interactions take place between adjacent beads. In this experiment, beads interact over a distance (single beads are attracted by other beads or SPS). As the magnetic stray field decays rapidly with the distance between the beads, it doesn’t surprise that the influence of H is weaker than when considering the interactions between adjacent beads.

Thus, although a trend is visible, it can be said that the field strength does not have a strong influence on the SPS formation dynamics.

Influence of the Bead Concentration

Compared to the magnetic field strength, the concentration of beads in the dispersion has a stronger influence on the SPS formation rate. As can be seen from Figure 4.5, doubling the concentration (from 50 µg mL⁻¹ to 100 µg mL⁻¹) decreases the final ratio after 160 s from 61 % to 11 %. The complete set of curves shows a general trend for a faster formation at high concentrations, which doesn’t surprise as a higher concentration means a lower interbead distance, thus increasing the chance that two magnetized

0 20 40 60 80 100 120 140 160

0 0.2 0.4 0.6 0.8 1

Time t / s

RatioofSPSwith1&2beads

36 Oe 63 Oe 90 Oe 117 Oe

Figure 4.4: Influence of the magnetic field strength on the SPS formation rate. The y-axis gives the ratio of beads that are present as single beads or 2-beads-SPS compared to the overall number of beads. The data was collected at a rotation frequency of 600 rpm and a concentration of 50 µg mL⁻¹.

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beads attract each other and agglomerate.

It is noteworthy that below a concentration of 20 µg mL⁻¹ no noticeable SPS formation takes place within the 160 s. This shows that there is a lower threshold for SPS formation, below which SPS formation can be prevented. To evaluate this threshold for microfluidic applications and use it to prevent unwanted agglomeration, however, the experiment would have to be repeated measuring the SPS formation in the liquid volume, not on the glass surface.