The use of functionalised magnetic particles in suspension is of current interest in nanotechnology and especially in biological related research and biotechnological applications. In this project obtaining the hysteresis loops of magnetic particles in liquid suspension is investigated. For instance, magnetic measurements taken in a DC Magnetic Property Measurement System (MPMS-SQUID sensor) of ferromagnetic beads (surface-functionalized NH2, mean diameter 4.32 μm) prepared in three conditions: dry, suspended in sucrose solution and in suspension after functionalization with fluorophore can be obtained. For this purpose, special small containers (1.3 cm long) made of non magnetic plastic are being designed to hold the beads in liquid. Partial results indicate that the bead's remnant magnetization is half of the value at maximum applied field in all cases. However, due to the additional degrees of rotational freedom, beads suspended in a liquid do not present coercivity.
As an example Fig. 1 shows the hysteresis loops of the NH2 beads (4.32μm mean diameter) in suspension. In all cases the corresponding dry measurements under the same conditions are also shown for comparison. The magnetization axes are normalized with respect to the maximum magnetizations. The scattered points are noise caused by the motion of the beads. This noise is much less when the temperature decreases. As in the dry case the coercivity increases as the temperature decreases, however saturation is reached at around 4kOe. At this point it is assumed that most of the beads are aligned with the external field and then the diamagnetic behaviour of the sample holder is observed. As in the dry case, the remnant moment was nearly half the maximum magnetization achieved at 4kOe. Figures 1 (a) and (b) show the hysteresis loops measured from beads suspended in the sucrose solution. The maximum applied field this time was 15kOe. The measurements were taken at five different temperatures (a) 285K and (b) 200K, 150K, 100K and 50K. When the beads reach their maximum saturation (around 4KOe) and their magnetic moment remains constant, the diamagnetic behaviour of the plastic sample holder is notorious, giving and downward trend in the plots. Figures 1 (c) and (d) present the hysteresis loops of TAMRA functionalized beads suspended in Phosphate Buffered Saline (PBS) solution. The maximum applied field was 4kOe and the temperatures were 285K (e), 250K and 200K (f). The behaviour of the magnetization is the same as in the previous case
Fig 1. Hysteresis loops of ferromagnetic beads in suspension at different temperatures. Hysteresis loops for the dry case is also plotted in each case for comparison. Note that near room temperature (285K) no coercivity appears
In general, from Fig 1 it is noticeable that near room temperature (285K) there is no coercive field; this means that the magnetic moments of the suspended beads abruptly switch to align with the applied field when it reverses. In addition, it can be observed that, at room temperature, in the suspended case, there is a remnant magnetization in each sample; at this point some of the beads are in suspension and still aligned in the direction of the previous magnetic field. In each case this remnant magnetization is nearly half of the maximum magnetization value which is similar to the dry case. The M-H loop of the sample containing suspended beads can be understood as follows: Since the beads are suspended in a liquid medium they have more degrees of freedom (translation and rotation) than their dried packed counterparts. When the external field reverses direction, the suspended beads physically rotate to align to it. This is essentially a reversible process and hence the M-H loop exhibits very little hysteresis and zero coercivity. In the dry sample this is not possible for the beads to physically rotate since all the beads are packed or are stuck together and reorientation of the bead's magnetic domains is necessary. When the applied field switches the beads back to the opposite direction, it would be expected that the external field would align all the beads and hence the magnetization would easily become constant. However complete saturation has not been reached at 4kOe, probably because there is some sedimentation leading to beads become immobilized and unable rotate so that they behave as in the dry case; the viscosity of the medium plays a role in this case too. Moreover since it is expected the sucrose solution starts freezing from nearly 273K, downwards that temperature the noise decreases and the coercivity increases. The noise in the suspended bead samples is caused by motion of the beads in suspension (Brownian motion is not applicable here because the beads are bigger than 1micrometer in diameter). The beads are not completely static because the sample holder is in continuous vertical movement, and hence the exact position of the beads in the SQUID equipment varies. Moreover, in equilibrium, the gravitational force, FG, of a particular bead is equal to the buoyancy force, FB. The magnetophoretical force, FM, generated during application of the magnetic field over the ferromagnetic bead is compensated by the drag force (FD). The diagram of forces acting over a single bead of the sample at any arbitrary time is represented in Fig. 2. When H changes value in the MPMS, it is not uniform and FM appears and the beads move slightly over the applied field direction, resulting in a change of the exact position of the bead in the SQUID detection and hence the noise is produced. The vertical movement of the bead due to this change of H causes FD. This force tries to minimize the bead displacement. As the beads accelerate, the drag force increases, causing a decrease in the acceleration. Eventually a force balance is achieved when the acceleration is zero and the maximum or terminal relative velocity is reached or when H becomes constant in the MPMS equipment. At this point not all the beads return to their original position.
In addition of the above mentioned forces, dipole-dipole interactions exist between neighboring beads. However, these interactions are always attractive and relatively short-ranged; they decay with inter-particle distances as ~l -3, where l is the distance between the beads. Due to these forces some beads are stuck to others, forming groups. This reduces the beads degrees of freedom and the samples remnant magnetization because these groups will favour flux closure. As the temperature decreases the liquid medium freezes and the degree of freedom for the beads become limited. Therefore, switching must again occur via the reorientation of magnetic domains rather than physical rotation, leading to a non-zero coercivity. This field is expected to be nearly the same as in the dry case when the sample is completely frozen.
Fig 2. Representation of the acting forces over a bead. The MPMS takes some seconds increasing or decreasing H, FM appears during that time interval
For further reading about this project:
Luis De Los Santos V., Justin Llandro, Dongwook Lee, Thanos Mitrelias, Justin J. Palfreyman, Thomas J. Hayward, Jos Cooper, J.A.C. Bland, Crispin H.W. Barnes, Juan Arroyo C., Martin Lees, "Magnetic measurements of suspended functionalised ferromagnetic beads under DC applied fields", Journal of Magnetism and Magnetic Materials 321 (2009) 2129-2134.