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Manipulating mimicked magnetosome chains produced Using superparamagnetic microbeads in a confined space
Microelectronic Engineering 153 (2016) 37–42
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Manipulating mimicked magnetosome chains produced Using superparamagnetic microbeads in a confined space Yan-Hom Li a,⁎, Ting-Yu Su b, Tien-Li Chang c, Ya-Wei Lee a,⁎ a b c
Department of Mechanical and Aerospace Engineering, Chung Cheng Institute of Technology, National Defense University, Taoyuan, 335, Taiwan Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, 300, Taiwan Department of Mechatronic Engineering, National Taiwan Normal University, Taipei, 300, Taiwan
a r t i c l e
i n f o
Article history: Received 18 October 2015 Received in revised form 19 January 2016 Accepted 19 January 2016 Available online 21 January 2016 Keywords: Superparamagnetic microbead Confined spaces Oscillating field Magnetosomes Magnetotactic bacteria
a b s t r a c t In this study, we investigated the dynamics of microchains containing superparamagnetic microbeads under the influence of oscillating magnetic fields in a confined space. The behavior of constrained microchains was investigated experimentally. Chains in confined spaces were first formed using a static directional field or a permanent magnet and then manipulated using an additional dynamical perpendicular field. An oscillating chain in a confined space can be designed to mimic magnetosome chains synthesized by magnetotactic bacteria, which have been exploited recently for various applications in biological and medical sciences. The effects of crucial parameters, such as the lengths of particle chains and sizes of confined spaces, were thoroughly analyzed to observe the distinct behavior and investigate the dynamics of the constrained chains. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Electromagnetic systems, magnetic microrobots, and microswimmers have recently attracted considerable attention because of their potential applications in mini-invasive or noninvasive treatments [1–4]. Based on biomimetic principles, interventional microrobots have been developed for reducing both the damage caused to the human body during an operation and the operation time. Bacterial magnetosomes synthesized by magnetotactic bacteria (MTB) have provided an opportunity to enhance the efficiency of magnetic hyperthermia, an innovative and noninvasive therapy [5–9]. Over the past decade, several studies have elucidated the possible factors involved in the formation of magnetosome membranes and the biomineralization of magnetic minerals [10–12]. Although MTB are ubiquitous and abundant in freshwater and marine habitat sediments, isolating and cultivating MTB are difficult because of their fastidious growth characteristics [13]. Therefore, research in this area has proceeded slowly. Moreover, magnetosome formation is a complex process that involves several discrete steps [14,15]. An investigation of magnetosomes extracted from MTB for treating tumors suggested that magnetosome chains are more efficient than individual magnetosomes in inhibiting cancer cell proliferation under an external magnetic field [9]. Therefore, a stable mechanism for manipulating magnetic nanoparticles in relatively ⁎ Corresponding authors. E-mail addresses: [email protected] (Y.-H. Li), [email protected] (Y.-W. Lee).
http://dx.doi.org/10.1016/j.mee.2016.01.020 0167-9317/© 2016 Elsevier B.V. All rights reserved.
small confined spaces might provide potential applications in the use of medical hyperthermia. The behavior of particle chains manipulated using either a rotating [16–18] or an oscillating [19–21] field in an infinite space has been discussed in detail. However, manipulation of magnetic nanoparticle chains in a small confined space has not been studied in detail. In this study, we devised a method for producing magnetosome-like chains of dispersed and clustered magnetic microbeads in a relatively small confined space that might mimic the behavior of these types of particles when injected in a tumor and then subjected to an external magnetic field. Magnetic particles dispersed in solution are ideal model systems to study their behavior under the influences of magnetic forces and induced hydrodynamic drags. In general, more than 75% of beads are dispersed as single particles, with the remainder aggregated in groups of two or more [22] because of the lack of steric repulsion generated by a surfactant. The particle groups are difficult to manipulate under the applied field, and the elimination of the particles results in increased cost for further application. To improve the dispersibility and redispersibility of magnetic particles, innovative methods for preparing monodispersed magnetic nanoparticles and microparticles have drawn considerable attention recently [23–26]. Moreover, the redispersibility of ironbased magnetorheological fluids was studied by adding various additives [27]. In the present study, we demonstrated a simple method for redispersing the particle group in a small confined space. The redispersed magnetic microbeads could be reaggregated to form a
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Y.-H. Li et al. / Microelectronic Engineering 153 (2016) 37–42
Fig. 1. Schematic representation of the (a) overall experimental setup, (b) top view of the placement of the four coils, and (c) distribution of the field strengths measured at the center of the four coils by using a Gauss/Tesla meter. The strengths of the static unidirectional and perpendicular fields are Hd = 24.15 Oe and Hp = 42.03 Oe, respectively. The black dashed and dotted line represents the overall oscillating field.
linear chain that oscillates with the dynamical field. The behavior of the constrained chain and the synchronicity of the phase angle trajectory between the oscillating magnetic particle chain and the
external field were elucidated. In addition, the effects of control parameters, such as the field configuration and chain length, were analyzed.
Fig. 2. Sequential images of the chaining of seven dispersed beads by applying an external field comprising a static directional field (Hd) and oscillating field (Hp) with strengths of Hd = 18.15 Oe and Hp = 11.44 Oe, respectively.
Y.-H. Li et al. / Microelectronic Engineering 153 (2016) 37–42
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Fig. 3. Images of the redispersion and aggregation of the five clustered microparticles. A permanent magnet was used to manipulate the particles' dispersion and chaining behavior in a confined spherical space.
2. Materials and methods 2.1. Magnetic microbeads manipulated using an external magnetic field in a confined space Superparamagnetic particles comprising iron oxide magnetite embedded in polystyrene microspheres were used to create linear chains. To observe and manipulate the particles simply and conveniently, microbeads with diameter d = 4.5 μm, susceptibility χ = 1.6, and without magnetic hysteresis or remanence were employed. The superparamagnetic property of these particles implies that they are magnetized under an external field and completely demagnetized when the field is removed. The microsized magnetic particles were dispersed and suspended in 500 μL of distilled water containing sodium dodecyl sulfate surfactants at 0.4% by weight. The viscosity of this mixing solvent was measured at ηs = 1.75 cp. This solvent, containing magnetic particles, was injected into highly viscous silicon oil to form a confined spherical space. The motions of the chains oscillating in the solvent fluid were recorded using an optical microscope connected to a digital camera (Silicon Video 643C),
whose maximum shooting rate was 200 frames/s. Representative snapshot images are described in the following sections for identifying the distinct behavior of the constrained particle chains exposed to an external magnetic field.
2.2. Field configuration Fig. 1 schematically illustrates the experimental configuration. To create a magnetosome-like chain oscillating in a finite spherical area, two magnetic fields were employed. The chain was first aligned with a homogeneous static field Hd, and a dynamical sinusoidal field Hy with a maximum amplitude Hp and an adjustable frequency f; that is, Hv = Hp sin(2πft), which were then applied in a direction perpendicular to Hd. These two fields have comparable amplitudes, resulting in an overall oscillating field H0 = Hdi + Hvj, where i and j are unit vectors in the directional and perpendicular axes, respectively. Under this field configuration, the phase angle trajectory (θ) of the external field is expressed as θ(t) = tan−1[(Hp/Hd)sin(2πft)], which is associated with an amplitude of θAmax = tan−1(Hp/Hd).
Fig. 4. (a) Trajectories of the phase angle (θ) of the external field and chains consisting of four, seven, and eight particles, and (b) evolutions of the phase angle lag (△θL) of chains comprising different numbers of particles. All chains oscillate under a field configuration of Hd = 18.15 Oe and Hp = 11.44 Oe, and f = 1 Hz.
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Y.-H. Li et al. / Microelectronic Engineering 153 (2016) 37–42
Fig. 5. (a) Phase trajectories and (b) phase lags of the P7 chain in confined and free spaces under field strengths of Hd = 18.15 Oe and Hp = 11.44 Oe, and (c) and (d) depict images of the constrained and unbound P7 chains, respectively.
3. Results and discussion
particles is subjected to an external field, it experiences a magnetic torque (Mm) and an opposing viscous torque (Mv) expressed as [28]
3.1. Particle aggregation Fig. 2 shows sequential images of chaining the initially dispersed magnetic particles subjected to static directional and dynamical perpendicular fields. When the microbeads were suspended in an aqueous sphere in the absence of an applied field, the particles were randomly scattered. Once an external field was applied, the particles were polarized, generating linear multiparticle chains along the direction of the field. As shown in Fig. 2, the particles aggregated to form two short chains on switching in the static directional field (Fig. 2 (a)–(f)), and then formed a single longer chain after the oscillating field was applied (Fig. 2 (g)–(i)). Conversely, when the particles were initially clustered because of the lack of steric repulsion generated using a surfactant, it was difficult to form a linear chain by applying the unidirectional static field in the infinite space. This study demonstrated a simple methodology for redispersing the clustered particles and reconstructing a linear chain in a restricted space by using a permanent magnet. Fig. 3 shows sequential images of the redispersion of five clustered particles and the restructuring of a linear chain in the aqueous sphere. 3.2. Effects of the chain length The behavior of a magnetic chain, which is defined as a dimensionless Mason number (Mn), is dominated by the competition between magnetic forces and induced hydrodynamic drags. When a chain comprising N
Mm ¼
! 2 2 μ 0 μ r 3 m N sinð2ΔθL Þ 4π 2ð2aÞ3
ð1Þ
Mv ¼
4 2N2 ηω Nπa3 ln ðN=2Þ 3
ð2Þ
Mn ¼
32ηω * 2 : μ 0 χ 2 H
ð3Þ
Here, μ0 and μr are the vacuum permeability and relative permeabil! ity of the solvent, respectively; m is the dipole moment of a magnetic particle; a is the radius; △θL is the instantaneous phase angle lag between the field and the chain; and η and Ω are the solvent fluid viscosity and angular speed of the chain, respectively. The deviation in the actual phase angle trajectory of an oscillating chain from the external field is crucial for effectively manipulating the microchain [20]. A longer chain generally induces stronger drags under the same field condition, thus leading to a higher phase angle lag (time delay) between the external field and the chain. Fig. 4 shows the evolutions of the phase angle trajectories of constrained chains composed of several particles subjected to identical field strengths of 18.15 Oe and 11.44 Oe for Hd and Hp, respectively, and f = 1 Hz (or
Fig. 6. Images of the P5 chain in a (a) considerably small space, (b) confined space, and (c) free space. (d) Oscillating trajectories of the external field and P5 chains in three spaces with various sizes. (e) Evolutions of the phase angle lag (△θL) of the three P5 chains. All chains oscillate under the field configuration of Hd = 18.15 Oe, Hp = 11.44 Oe, and f = 1 Hz.
Y.-H. Li et al. / Microelectronic Engineering 153 (2016) 37–42
41
Fig. 7. Stable and unstable images of the P16 chain subjected to the identical field configuration of Hd = 18.15 Oe and Hp = 11.44 Oe in a (a) free space and (b) confined space.
period P = 1 s) within one and a half periods (1.5 P). Because of the lower induced drag, a higher oscillating amplitude is observed for the shorter chain. In addition, the shorter chain oscillates more synchronically with the external field, leading to insignificant phase lags.
leads to an excessive Mn. Because the stable dynamical chains can yield efficient treatment of tumors by using magnetic hyperthermia [6], ruptures of such chains must be prevented in biological and medical applications.
3.3. Effects of the confined space
4. Conclusions
This study investigated the effects of a confined space on the behavior of oscillating chains. Fig. 5 demonstrates the trajectories of the phase angle of an unbound and constrained chain comprising seven particles (denoted as a P7 chain) under identical field strengths of Hd = 18.15 Oe, Hp = 11.44 Oe, and f = 1 Hz. The amplitude of the constrained chain is almost equal to the amplitude of the unbound chain, except near the initial unstable oscillating period. This remarkable feature indicates that the inertial force of such a short chain leads to a higher amplitude compared with that of the field, and reduces the effects of the drag when the oscillating chains reach maximum oscillating trajectories. However, because of the stronger hydrodynamic drag in the restricted area, the phase lag is slightly higher for the constrained chain, prompting a question regarding how different sizes of a confined space affect the motions of the chains. Fig. 6 shows that the chains comprising five particles remain stable in restricted spaces of two sizes and an infinite space. Using a markedly smaller confined space leads to considerably more phase angle lags, although the size does not affect the maximum oscillating amplitudes of the chains because of the excessive inertial force, which is in agreement with the phenomenon illustrated in Fig. 5.
In this study, we investigated the motions of micromagnetic particle chains subjected to a uniform external field in a confined space. Dispersed particles can aggregate to form a single chain under an applied external field comprising static directional and dynamical oscillating fields. Conversely, clustered particles were manipulable to redisperse them and construct a single linear chain by using a permanent magnet. These quickly synthesized devices can mimic magnetosome chains, which are extracted with difficulty from MTB. A dynamical chain in a confined space sustains stronger induced drag than that in an infinite space, and a narrower space causes a substantially stronger drag, leading to a considerable phase lag between the field and the chain. In addition, a fracture of the chain in a confined space confirms that the stronger induced drag acted on the constrained chain, suggesting that the magnetosome-like chain is more unstable when manipulated in a confined space. We plan to quantitatively determine a criterion for manipulating stabile constrained chains for potential biological and medical applications.
3.4. Instability of the chain in a confined space Previous studies have reported that rupturing failures of the chains are primarily caused by the external field strength or chain length, which causes stronger induced drags when oscillating with the field [20,21]. In this section, we discuss the effect of the confined space on the stability of oscillating chains. Fig. 7 depicts stable and unstable images of a 16-particle (P16) chain subjected to identical field conditions in free and confined spaces, respectively. The governing parameter of such a dynamical chain is the dimensionless Mason number (Mn), as shown in (3), which determines the ratio of the hydrodynamic drag to magnetic attraction. When the Mn exceeds a certain critical value because of a stronger drag or weaker magnetic attraction, the structure ruptures. Fig. 7(a) shows a stable chain bent into an S-shape in the presence of field strengths Hd = 18.15 Oe and Hp = 11.44 Oe. Despite the length of the chains being considerably longer than those reported in previous studies and a stronger drag being induced, the structure of the P16 chain remains stable without rupture because of the moderate Mn. However, a structural rupture near the center of the chain is evident for a chain with the same length subjected to an identical field configuration in a confined space. As shown in Fig. 7(b), the P16 chain ruptures with a single break at nearly t = 2P/3, similar to the pattern reported in a previous study [21]. The oscillating orientation begins in a clockwise direction in this scenario, which is opposite to the scenarios depicted in Fig. 7(a). According to the distinct result of the P16 chain in the restricted space, the rupture is attributed to the stronger drag, which
Acknowledgments The authors thank the Ministry of Science and Technology of the Republic of China (Taiwan) for financially supporting this study through Grant MOST 104-2221-E-606-009 and MOST 104-2218-E-606-001. References [1] Y.S. Zhou, Y.X. Quan, K. Yoshinaka, K. Ikeuchi, Proc. Inst. Mech. Eng. H 215 (2001) 215–220. [2] R. Dreyfus, J. Baudry, M. Roper, M. Fermigier, H. Stone, J. Bibette, Nature 437 (2005) 862. [3] F. Ullrich, C. Bergeles, J. Pokki, O. Ergeneman, S. Erni, G. Chatzipirpiridis, S. Pané, C. Framme, B.J. Nelson, Invest. Ophthalmol. Vis. Sci. 54 (2013) 2853–2863. [4] B.J. Nelson, I.K. Kaliakatsos, J.J. Abbott, Annu. Rev. Biomed. Eng. 12 (2010) 55–85. [5] L. Yan, S. Zhang, P. Chen, H. Liu, H. Yin, H. Li, Microbiol. Res. 167 (2012) 507–519. [6] E. Alphandéry, F. Guyot, I. Chebbi, Int. J. Pharm. 434 (2012) 444–452. [7] S.E. Greene, K. Arash, Curr. Opin. Cell Biol. 24 (4) (2012) 490–495. [8] Z. Oestreicher, C. Valverde-Tercedor, L. Chen, C. Jimenez-Lopez, D.A. Bazylinski, N.N. Casillas-Ituarte, S.K. Lower, B.H. Lower, Micron 43 (2012) 1331–1335. [9] C. Jogler, S. Dirk, Annu. Rev. Microbiol. 63 (2009) 501–521. [10] S. Dirk, J. Mol. Microbiol. Biotechnol. 1 (1999) 79–86. [11] S. Dirk, FEMS Microbiol. Rev. 32 (2008) 654–672. [12] X. Wang, L. Liang, Bioelectromagnetics 30 (2009) 313–321. [13] A. Postec, N. Tapia, A. Bernadac, M. Joseph, S. Davidson, L.F. Wu, B. Ollivier, N. Pradel, Microb. Ecol. 63 (2012) 1–11. [14] D.A. Bazylinski, S. Schubbe, Adv. Appl. Microbiol. 62 (2007) 21–62. [15] S. Dirk, Int. Microbiol. 5 (2002) 209–214. [16] S. Melle, G. Fuller, M. Rubio, Phys. Rev. E 61 (2000) 4111–4117. [17] S. Melle, O. Calderon, G. Fuller, M. Rubio, J. Colloid Interface Sci. 247 (2002) 200. [18] S. Melle, O. Calderon, M. Rubio, G. Fuller, J. Non-Newtonian Fluid Mech. 102 (2002) 135–148. [19] Y.H. Li, S.T. Sheu, J.M. Pai, C.Y. Chen, J. Appl. Phys. 111 (2012) 07A924. [20] Y.H. Li, C.Y. Chen, S.T. Sheu, J.M. Pai, Microfluid. Nanofluid. 13 (2012) 579–588. [21] H.C. Lin, Y.H. Li, C.Y. Chen, Microfluid. Nanofluid. 17 (2014) 73–84.
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[22] D. Dressman, H. Yan, G. Traverso, K.W. Kinzler, B. Vogelstein, Proc. Natl. Acad. Sci. 100 (2003) 8817–8822. [23] L.P. Ramirez, K. Landfester, Macromol. Chem. Phys. 204 (2003) 22–31. [24] S. Laurent, D. Forge, M. Port, A. Roch, C. Robic, L. Vander Elst, R.N. Muller, Chem. Rev. 110 (2009) 2574.
[25] Y.W. Lee, T.L. Chang, Microelectron. Eng. 111 (2013) (2013) 58–63. [26] N.G. Bastús, F. MerkoçI, J. Piella, V. Puntes, Chem. Mater. 26 (2014) 2836–2846. [27] M.T. López-López, A. Zugaldía, F. González-Caballero, J.D.G. Durán, J. Rheol. 50 (2006) 543–560 (1978-present). [28] S.L. Biswal, A.P. Gast, Phys. Rev. E 69 (2004) 041406.
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Manipulating mimicked magnetosome chains produced Using superparamagnetic microbeads in a confined space Yan-Hom Li a,⁎, Ting-Yu Su b, Tien-Li Chang c, Ya-Wei Lee a,⁎ a b c
Department of Mechanical and Aerospace Engineering, Chung Cheng Institute of Technology, National Defense University, Taoyuan, 335, Taiwan Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, 300, Taiwan Department of Mechatronic Engineering, National Taiwan Normal University, Taipei, 300, Taiwan
a r t i c l e
i n f o
Article history: Received 18 October 2015 Received in revised form 19 January 2016 Accepted 19 January 2016 Available online 21 January 2016 Keywords: Superparamagnetic microbead Confined spaces Oscillating field Magnetosomes Magnetotactic bacteria
a b s t r a c t In this study, we investigated the dynamics of microchains containing superparamagnetic microbeads under the influence of oscillating magnetic fields in a confined space. The behavior of constrained microchains was investigated experimentally. Chains in confined spaces were first formed using a static directional field or a permanent magnet and then manipulated using an additional dynamical perpendicular field. An oscillating chain in a confined space can be designed to mimic magnetosome chains synthesized by magnetotactic bacteria, which have been exploited recently for various applications in biological and medical sciences. The effects of crucial parameters, such as the lengths of particle chains and sizes of confined spaces, were thoroughly analyzed to observe the distinct behavior and investigate the dynamics of the constrained chains. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Electromagnetic systems, magnetic microrobots, and microswimmers have recently attracted considerable attention because of their potential applications in mini-invasive or noninvasive treatments [1–4]. Based on biomimetic principles, interventional microrobots have been developed for reducing both the damage caused to the human body during an operation and the operation time. Bacterial magnetosomes synthesized by magnetotactic bacteria (MTB) have provided an opportunity to enhance the efficiency of magnetic hyperthermia, an innovative and noninvasive therapy [5–9]. Over the past decade, several studies have elucidated the possible factors involved in the formation of magnetosome membranes and the biomineralization of magnetic minerals [10–12]. Although MTB are ubiquitous and abundant in freshwater and marine habitat sediments, isolating and cultivating MTB are difficult because of their fastidious growth characteristics [13]. Therefore, research in this area has proceeded slowly. Moreover, magnetosome formation is a complex process that involves several discrete steps [14,15]. An investigation of magnetosomes extracted from MTB for treating tumors suggested that magnetosome chains are more efficient than individual magnetosomes in inhibiting cancer cell proliferation under an external magnetic field [9]. Therefore, a stable mechanism for manipulating magnetic nanoparticles in relatively ⁎ Corresponding authors. E-mail addresses: [email protected] (Y.-H. Li), [email protected] (Y.-W. Lee).
http://dx.doi.org/10.1016/j.mee.2016.01.020 0167-9317/© 2016 Elsevier B.V. All rights reserved.
small confined spaces might provide potential applications in the use of medical hyperthermia. The behavior of particle chains manipulated using either a rotating [16–18] or an oscillating [19–21] field in an infinite space has been discussed in detail. However, manipulation of magnetic nanoparticle chains in a small confined space has not been studied in detail. In this study, we devised a method for producing magnetosome-like chains of dispersed and clustered magnetic microbeads in a relatively small confined space that might mimic the behavior of these types of particles when injected in a tumor and then subjected to an external magnetic field. Magnetic particles dispersed in solution are ideal model systems to study their behavior under the influences of magnetic forces and induced hydrodynamic drags. In general, more than 75% of beads are dispersed as single particles, with the remainder aggregated in groups of two or more [22] because of the lack of steric repulsion generated by a surfactant. The particle groups are difficult to manipulate under the applied field, and the elimination of the particles results in increased cost for further application. To improve the dispersibility and redispersibility of magnetic particles, innovative methods for preparing monodispersed magnetic nanoparticles and microparticles have drawn considerable attention recently [23–26]. Moreover, the redispersibility of ironbased magnetorheological fluids was studied by adding various additives [27]. In the present study, we demonstrated a simple method for redispersing the particle group in a small confined space. The redispersed magnetic microbeads could be reaggregated to form a
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Y.-H. Li et al. / Microelectronic Engineering 153 (2016) 37–42
Fig. 1. Schematic representation of the (a) overall experimental setup, (b) top view of the placement of the four coils, and (c) distribution of the field strengths measured at the center of the four coils by using a Gauss/Tesla meter. The strengths of the static unidirectional and perpendicular fields are Hd = 24.15 Oe and Hp = 42.03 Oe, respectively. The black dashed and dotted line represents the overall oscillating field.
linear chain that oscillates with the dynamical field. The behavior of the constrained chain and the synchronicity of the phase angle trajectory between the oscillating magnetic particle chain and the
external field were elucidated. In addition, the effects of control parameters, such as the field configuration and chain length, were analyzed.
Fig. 2. Sequential images of the chaining of seven dispersed beads by applying an external field comprising a static directional field (Hd) and oscillating field (Hp) with strengths of Hd = 18.15 Oe and Hp = 11.44 Oe, respectively.
Y.-H. Li et al. / Microelectronic Engineering 153 (2016) 37–42
39
Fig. 3. Images of the redispersion and aggregation of the five clustered microparticles. A permanent magnet was used to manipulate the particles' dispersion and chaining behavior in a confined spherical space.
2. Materials and methods 2.1. Magnetic microbeads manipulated using an external magnetic field in a confined space Superparamagnetic particles comprising iron oxide magnetite embedded in polystyrene microspheres were used to create linear chains. To observe and manipulate the particles simply and conveniently, microbeads with diameter d = 4.5 μm, susceptibility χ = 1.6, and without magnetic hysteresis or remanence were employed. The superparamagnetic property of these particles implies that they are magnetized under an external field and completely demagnetized when the field is removed. The microsized magnetic particles were dispersed and suspended in 500 μL of distilled water containing sodium dodecyl sulfate surfactants at 0.4% by weight. The viscosity of this mixing solvent was measured at ηs = 1.75 cp. This solvent, containing magnetic particles, was injected into highly viscous silicon oil to form a confined spherical space. The motions of the chains oscillating in the solvent fluid were recorded using an optical microscope connected to a digital camera (Silicon Video 643C),
whose maximum shooting rate was 200 frames/s. Representative snapshot images are described in the following sections for identifying the distinct behavior of the constrained particle chains exposed to an external magnetic field.
2.2. Field configuration Fig. 1 schematically illustrates the experimental configuration. To create a magnetosome-like chain oscillating in a finite spherical area, two magnetic fields were employed. The chain was first aligned with a homogeneous static field Hd, and a dynamical sinusoidal field Hy with a maximum amplitude Hp and an adjustable frequency f; that is, Hv = Hp sin(2πft), which were then applied in a direction perpendicular to Hd. These two fields have comparable amplitudes, resulting in an overall oscillating field H0 = Hdi + Hvj, where i and j are unit vectors in the directional and perpendicular axes, respectively. Under this field configuration, the phase angle trajectory (θ) of the external field is expressed as θ(t) = tan−1[(Hp/Hd)sin(2πft)], which is associated with an amplitude of θAmax = tan−1(Hp/Hd).
Fig. 4. (a) Trajectories of the phase angle (θ) of the external field and chains consisting of four, seven, and eight particles, and (b) evolutions of the phase angle lag (△θL) of chains comprising different numbers of particles. All chains oscillate under a field configuration of Hd = 18.15 Oe and Hp = 11.44 Oe, and f = 1 Hz.
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Y.-H. Li et al. / Microelectronic Engineering 153 (2016) 37–42
Fig. 5. (a) Phase trajectories and (b) phase lags of the P7 chain in confined and free spaces under field strengths of Hd = 18.15 Oe and Hp = 11.44 Oe, and (c) and (d) depict images of the constrained and unbound P7 chains, respectively.
3. Results and discussion
particles is subjected to an external field, it experiences a magnetic torque (Mm) and an opposing viscous torque (Mv) expressed as [28]
3.1. Particle aggregation Fig. 2 shows sequential images of chaining the initially dispersed magnetic particles subjected to static directional and dynamical perpendicular fields. When the microbeads were suspended in an aqueous sphere in the absence of an applied field, the particles were randomly scattered. Once an external field was applied, the particles were polarized, generating linear multiparticle chains along the direction of the field. As shown in Fig. 2, the particles aggregated to form two short chains on switching in the static directional field (Fig. 2 (a)–(f)), and then formed a single longer chain after the oscillating field was applied (Fig. 2 (g)–(i)). Conversely, when the particles were initially clustered because of the lack of steric repulsion generated using a surfactant, it was difficult to form a linear chain by applying the unidirectional static field in the infinite space. This study demonstrated a simple methodology for redispersing the clustered particles and reconstructing a linear chain in a restricted space by using a permanent magnet. Fig. 3 shows sequential images of the redispersion of five clustered particles and the restructuring of a linear chain in the aqueous sphere. 3.2. Effects of the chain length The behavior of a magnetic chain, which is defined as a dimensionless Mason number (Mn), is dominated by the competition between magnetic forces and induced hydrodynamic drags. When a chain comprising N
Mm ¼
! 2 2 μ 0 μ r 3 m N sinð2ΔθL Þ 4π 2ð2aÞ3
ð1Þ
Mv ¼
4 2N2 ηω Nπa3 ln ðN=2Þ 3
ð2Þ
Mn ¼
32ηω * 2 : μ 0 χ 2 H
ð3Þ
Here, μ0 and μr are the vacuum permeability and relative permeabil! ity of the solvent, respectively; m is the dipole moment of a magnetic particle; a is the radius; △θL is the instantaneous phase angle lag between the field and the chain; and η and Ω are the solvent fluid viscosity and angular speed of the chain, respectively. The deviation in the actual phase angle trajectory of an oscillating chain from the external field is crucial for effectively manipulating the microchain [20]. A longer chain generally induces stronger drags under the same field condition, thus leading to a higher phase angle lag (time delay) between the external field and the chain. Fig. 4 shows the evolutions of the phase angle trajectories of constrained chains composed of several particles subjected to identical field strengths of 18.15 Oe and 11.44 Oe for Hd and Hp, respectively, and f = 1 Hz (or
Fig. 6. Images of the P5 chain in a (a) considerably small space, (b) confined space, and (c) free space. (d) Oscillating trajectories of the external field and P5 chains in three spaces with various sizes. (e) Evolutions of the phase angle lag (△θL) of the three P5 chains. All chains oscillate under the field configuration of Hd = 18.15 Oe, Hp = 11.44 Oe, and f = 1 Hz.
Y.-H. Li et al. / Microelectronic Engineering 153 (2016) 37–42
41
Fig. 7. Stable and unstable images of the P16 chain subjected to the identical field configuration of Hd = 18.15 Oe and Hp = 11.44 Oe in a (a) free space and (b) confined space.
period P = 1 s) within one and a half periods (1.5 P). Because of the lower induced drag, a higher oscillating amplitude is observed for the shorter chain. In addition, the shorter chain oscillates more synchronically with the external field, leading to insignificant phase lags.
leads to an excessive Mn. Because the stable dynamical chains can yield efficient treatment of tumors by using magnetic hyperthermia [6], ruptures of such chains must be prevented in biological and medical applications.
3.3. Effects of the confined space
4. Conclusions
This study investigated the effects of a confined space on the behavior of oscillating chains. Fig. 5 demonstrates the trajectories of the phase angle of an unbound and constrained chain comprising seven particles (denoted as a P7 chain) under identical field strengths of Hd = 18.15 Oe, Hp = 11.44 Oe, and f = 1 Hz. The amplitude of the constrained chain is almost equal to the amplitude of the unbound chain, except near the initial unstable oscillating period. This remarkable feature indicates that the inertial force of such a short chain leads to a higher amplitude compared with that of the field, and reduces the effects of the drag when the oscillating chains reach maximum oscillating trajectories. However, because of the stronger hydrodynamic drag in the restricted area, the phase lag is slightly higher for the constrained chain, prompting a question regarding how different sizes of a confined space affect the motions of the chains. Fig. 6 shows that the chains comprising five particles remain stable in restricted spaces of two sizes and an infinite space. Using a markedly smaller confined space leads to considerably more phase angle lags, although the size does not affect the maximum oscillating amplitudes of the chains because of the excessive inertial force, which is in agreement with the phenomenon illustrated in Fig. 5.
In this study, we investigated the motions of micromagnetic particle chains subjected to a uniform external field in a confined space. Dispersed particles can aggregate to form a single chain under an applied external field comprising static directional and dynamical oscillating fields. Conversely, clustered particles were manipulable to redisperse them and construct a single linear chain by using a permanent magnet. These quickly synthesized devices can mimic magnetosome chains, which are extracted with difficulty from MTB. A dynamical chain in a confined space sustains stronger induced drag than that in an infinite space, and a narrower space causes a substantially stronger drag, leading to a considerable phase lag between the field and the chain. In addition, a fracture of the chain in a confined space confirms that the stronger induced drag acted on the constrained chain, suggesting that the magnetosome-like chain is more unstable when manipulated in a confined space. We plan to quantitatively determine a criterion for manipulating stabile constrained chains for potential biological and medical applications.
3.4. Instability of the chain in a confined space Previous studies have reported that rupturing failures of the chains are primarily caused by the external field strength or chain length, which causes stronger induced drags when oscillating with the field [20,21]. In this section, we discuss the effect of the confined space on the stability of oscillating chains. Fig. 7 depicts stable and unstable images of a 16-particle (P16) chain subjected to identical field conditions in free and confined spaces, respectively. The governing parameter of such a dynamical chain is the dimensionless Mason number (Mn), as shown in (3), which determines the ratio of the hydrodynamic drag to magnetic attraction. When the Mn exceeds a certain critical value because of a stronger drag or weaker magnetic attraction, the structure ruptures. Fig. 7(a) shows a stable chain bent into an S-shape in the presence of field strengths Hd = 18.15 Oe and Hp = 11.44 Oe. Despite the length of the chains being considerably longer than those reported in previous studies and a stronger drag being induced, the structure of the P16 chain remains stable without rupture because of the moderate Mn. However, a structural rupture near the center of the chain is evident for a chain with the same length subjected to an identical field configuration in a confined space. As shown in Fig. 7(b), the P16 chain ruptures with a single break at nearly t = 2P/3, similar to the pattern reported in a previous study [21]. The oscillating orientation begins in a clockwise direction in this scenario, which is opposite to the scenarios depicted in Fig. 7(a). According to the distinct result of the P16 chain in the restricted space, the rupture is attributed to the stronger drag, which
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