The investigation of frequency response for the magnetic nanoparticulate assembly induced by time-varied magnetic field
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The field-induced assembly of γ-Fe2O3 nanoparticles under alternating magnetic field of different frequency was investigated. It was found that the assembly was dependent upon the difference between colloidal relaxation time and field period. The same experiments on DMSA-coated γ-Fe2O3 nanoparticles exhibited that the relaxation time may be mainly determined by the magnetic size rather than the physical size. Our results may be valuable for the knowledge of dynamic assembly of colloidal particles.
Keywordsmagnetic field dynamic assembly pattern formation magnetic nanoparticles
With the expanding application of magnetic nanoparticles in cellular culture-matrix and tissue engineering, the interaction between nanomaterials and cells is becoming a central issue [1, 2]. The assembly of magnetic nanoparticles will play an important role in the issue because the colloidal behavior can be greatly affected by the assembled morphology. Very recently, the time-varied (alternating) magnetic field got reported to be capable of inducing the assembly of iron oxide nanoparticles. It was discovered that Fe3O4 nanoparticles can form the fibrous assemblies in the presence of 80-KHz or 50-Hz alternating magnetic field [3, 4]. The results also showed that the mechanism of colloidal assembly induced by the alternating magnetic field is essentially different from that induced by the static magnetic field, which may result from the variety in time domain. Thus, the frequency response of colloidal assembly directed by time-varied magnetic field is imperative to study. However, there has been little report on this topic.
In this paper, the experimental results of γ-Fe2O3 nanoparticulate assembly induced by alternating magnetic field of different frequency were presented. In the colloidal assembly induced by alternating magnetic field, the attractive force may arise from the interaction between two anti-parallel magnetic moments because the field is perpendicular to the assembly plane. Here, the strength of magnetic interaction is dependent upon the angle between two moment vectors. Now that the magnetic moments vary with external field during the assembly process, the frequency of external field may directly affect the magnetic interaction. Moreover, the nanoparticles often aggregate into clusters in aqueous suspension so that the state of magnetic coupling between nanoparticles is also vital for the magnetic interaction. In our experiments, two types of nanoparticles are employed to demonstrate the influence of magnetic coupling between nanoparticles on the field-directed assembly: bare γ-Fe2O3 nanoparticles and DMSA (meso-2,3-dimercaptosuccinic acid, HOOC-CH(SH)-CH(SH)-COOH)-coated γ-Fe2O3 nanoparticles.
Results and discussion
where τB is the Brownian relaxation time, η is the basic liquid viscosity, r is the hydrodynamic radius of the cluster, k is the Boltzmann's constant, and T is the absolute temperature  When the average relaxation time of clusters in colloidal suspension is above the period of external field, the reversal of magnetic moments cannot keep up with the variety of external field, resulting in the occurrence of the anti-parallel magnetic moments to generate the attractive interaction. Based on Equation 1, the relaxation time for 285 nm clusters is 72 ms. Because even the period of 1 kHz field (1 ms) is much below the relaxation time (72 ms), the bare γ-Fe2O3 nanoparticles can form the one-dimensional assemblies under any kilohertz-ranged alternating magnetic field. Moreover, with the frequency increasing, the magnetic relaxation time of cluster is more and more above the period of external field (The relaxation time is constant while the period of field is the reciprocal of frequency). Then, the magnetic moments of cluster have greater possibility to be perfectly anti-parallel (the angle between two moments is 180°) so that the magnetic interaction between clusters is stronger to overwhelm the disturbances.
According to the abovementioned analysis, when the frequency of external field is low enough, the field will be incapable of inducing the assembly of magnetic nanoparticles. Here, the variety of magnetic moments can keep up with the variety of external field so that the magnetic moments are always parallel, leading to the repulsive interaction. In our experiments, when the frequency of alternating magnetic field was 20 Hz, the visible fibrous assemblies nearly disappeared (Figure 2g). The period of 20-Hz field was 50 ms which has been analogous to the relaxation time. The morphological images of 50 and 100 Hz induced assembly were shown in Additional file 1 (Figure S2). The fibrous assemblies remain able to form. Thus, the assembly mechanism lies in the attractive interaction between anti-parallel magnetic moments, which arises from the incoherent magnetic relaxation of colloidal clusters with respect to the oscillation of field.
In summary, we demonstrated the frequency response of γ-Fe2O3 colloidal assembly induced by time-varied magnetic field. The higher frequency favors the formation of fibrous assemblies. The assembly mechanism lies in the difference between the magnetic relaxation time and the field period. It was also preliminarily exhibited that the nanoparticulate assembly induced by alternating magnetic field may be essentially dependent upon the magnetic size rather than the physical size. The work may deepen the knowledge of field-mediated colloidal assembly and widen the technological means for the formation of colloidal patterns.
The synthesis process of bare γ-Fe2O3 nanoparticles and DMSA-coated γ-Fe2O3 nanoparticles
The synthesis of bare γ-Fe2O3 nanoparticles
The 25% (w/w) N(CH3)4OH was slowly added into the mixture of Fe2+ and Fe3+ (molar ratio is 1:2) until the pH reached 13. Then, the reaction continued for 1 h to obtain the black colloidal particles (Fe3O4). Then, the air was pumped into the reaction system under the 95°C water bathing after the pH was adjusted to 3. Finally, the reaction system was kept for 3 h to oxidize Fe3O4 colloidal particles into γ-Fe2O3 particles. During the whole reaction, the vigorous stirring was needed.
The modification of DMSA
The pH and concentration of abovementioned solution were adjusted to 2.7 and 2 mg/ml, respectively. Then, the DMSA molecules were added into the system to react for 5 h. During the whole reaction, the vigorous stirring was needed. Finally, the impurity was removed by dialysis and centrifugation.
This work is supported by grants from the National Natural Science Foundation of China (NSFC, 20903021, 60725101, 81001412) and the National Basic Research Program of China (2011CB933503). This work also belongs to the US-China International S&T Cooperation Project (2009DFA31990).
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