Magnetic Microlassos for Reversible Cargo Capture, Transport, and

Mar 20, 2017 - ... Colorado School of Mines, Golden, Colorado 80401, United States ... microbots must be able to load and unload contents on command w...
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Magnetic Microlassos for Reversible Cargo Capture, Transport, and Release Tao Yang, Tonguc O. Tasci, Keith B. Neeves, Ning Wu,* and David W. M. Marr* Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, Colorado 80401, United States S Supporting Information *

ABSTRACT: Microbot propulsion has seen increasing interest in recent years as artificial methods that overcome the well-established reversible and challenging nature of microscale fluid mechanics. While controlled movement is an important feature of microbot action, many envisioned applications also involve cargo transport where microbots must be able to load and unload contents on command while tolerating complex solution chemistry. Here we introduce a physical method that uses flexible and linked superparamagnetic colloidal chains, which can form closed rings or “lassos” in the presence of a planar rotating magnetic field. By adding an additional AC magnetic field along the direction perpendicular to the substrate, we can orient the lasso at a tilted camber angle. We show that these magnetic lassos can roll at substantial velocities, with precise spatial control by manipulating both field strength and phase lag. Moreover, the lasso can curl around and capture cargo tightly and transport it based on a wheel-type mechanism. At the targeted destination, cargo is easily released upon field removal and the lasso can be readily reused. Since the entire process is physically controlled with no chemistry for attachment or disengagement involved, our system can potentially be used for transporting diverse types of cargo under different solution conditions.

1. INTRODUCTION

2. EXPERIMENTAL SECTION

There is increased interest in microbot propulsion mechanisms that overcome the well-established reversible and challenging nature of microscale fluid mechanics.1 These include swimming techniques that employ external fields such as electric,2 magnetic,3−5 and optical fields6,7 to mimic the beating or rotation of helically shaped flagella, and chemically powered approaches that propel colloidal particles via catalytic reactions, such as those that use hydrogen peroxide.8−11 We recently reported an approach powered by rotating magnetic fields that instead takes advantage of readily available surfaces to translate colloidal wheels rapidly with precisely defined direction.12 While this controlled movement is an important feature of microbot action, many envisioned applications13 also involve cargo transport where microbots load and unload contents on command within a variety of solution chemistries. Chains and filaments that mimic biologic swimmers2,5,14 can capture and transport cargo such as polymeric beads or cells. A limitation of this approach is that cargo binding and unbinding typically requires delicate but often irreversible approaches based on chemical modification15 of either motor or cargo surfaces. These modifications can cause cargo damage or limit the range of potential application.6,16 A physical approach that can reversibly load and unload cargo is therefore highly desirable. Here, we fabricate chains of superparamagnetic colloids and use them to lasso model cargo, translate it to a desired destination, and then unwrap for cargo delivery all without the need for chemical attachment15 or disengagement.

2.1. Materials. Because they can be manipulated with rotating magnetic fields17,18 and have well-characterized magnetic properties,19 Dynabeads M-450 epoxy (4.5 μm in diameter, Thermo Fisher Scientific Inc.) were used. Sodium dodecyl sulfate (SDS) and polyvinylpyrrolidone (PVP, Mw = 1 300 000) were purchased from Sigma-Aldrich Co. LLC. and used as received. Hollow glass beads were obtained from Polyscience, Inc. (Cat. No. 19823−5). Before use, beads were washed with deionized water three times by centrifugation at 500 rpm for 5 min. Both supernatant and any cracked glass beads were removed. 2.2. Fabrication of Flexibly Linked Magnetic Chains. To create flexible chains of magnetic beads, we mixed 20 μL of diluted (2 mg/mL) epoxy-functionalized Dynabeads M-450 solution with 200 μL 1 wt % PVP aqueous solution in a vial. As illustrated in Figure S1, vials were placed in an oil bath maintained at a constant temperature (75 °C). We then applied a one-dimensional (1D) DC magnetic field (∼20 mT) in the vertical direction. The magnetic fields were produced by air-cored copper solenoid coils of 50 mm inner diameter, 51 mm length, and 400 turns with current capacity of 3.5 A. Amplifiers (Behringer EP2000) were used to generate current signals. Matlab (Mathworks, Inc.) combined with an output card (National Instruments, NI-9263) was used to control current output. In-time signal monitoring was achieved via data card (National Instruments, NIUSB-6009) and gaussmeter (VGM Gaussmeter, Alphalab, Inc.). After the field was turned on, magnetic particles formed linear chains aligned parallel with the field. Entanglement of adsorbed PVP between adjacent particles enabled linkage with the aid of modest heating

© XXXX American Chemical Society

Received: February 1, 2017 Revised: March 12, 2017 Published: March 20, 2017 A

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When we apply a 2D rotating magnetic field, Bx = B0 cos(ωMt) x̂ and By = B0 sin(ωMt)ŷ, flexible chains of length L roll up and curl into a closed ring, or “lasso”, of radius R (Figure 1a and SI Movie S1). In this, chains initially bend into an “S″

(Figure S1c). After 0.5 h, the solution was gradually cooled to room temperature and the magnetic field removed. Excess PVP was then removed via centrifugation and replaced with a 2 wt % SDS solution. 2.3. Lasso Formation and Cargo Transport. Once linear chains were formed, we applied a two-dimensional (2D) circularly rotating magnetic field in the x-y plane by running programmed currents through two pairs of orthogonal air-core Helmholtz coils. Fields in the x and y directions, Bx = B0 cos(ωMt) x̂ and By = B0 sin(ωMt)ŷ (where ωM = 2πf M is the angular frequency of the field and f M is the field frequency) were set to identical amplitudes but differing phase angle of π/2. The frequency of the rotating magnetic field f M was fixed at 50 Hz unless otherwise stated. For lasso translation, we applied an additional AC magnetic field in the z-direction, Bz = Bz cos(ωMt + ϕz) ẑ. The camber angle θc was controlled by the ratio of B0 to Bz, θc = arc tan(B0/Bz) and the lasso rolling direction was manipulated by phase lag ϕz. For all propulsion experiments, total magnetic field strength was kept at 3.3 mT, while θc was changed from 79° to 32°, or equivalently, B0/Bz was varied from 0.62 to 5.14. Instantaneous magnetic fields were monitored indirectly by measuring coil currents using Matlab (Mathworks, Inc.). Lasso propulsion was captured at a frame rate of 50 fps with a CCD camera (Epix, Inc., SV643M) mounted on a microscope (Carl Zeiss, Axioplan 2). Instantaneous velocities were then obtained by calculating displacement over a time interval of Δt = 0.04 s. Lasso rotational frequency was determined via Fourier transform of the instantaneous velocities. We used hollow glass beads with a broad size distribution as model cargo.

Figure 1. Deformation of flexible magnetic chains into lassos under a circularly rotating magnetic field in the x−y plane. (a) Typical formation dynamics from a chain in solution as seen in Figure S1. (b) Lasso radius R* scales with magnetic field B0−2/3. Scale bar: 12.5 μm.

shape and rotate in the same field direction where we see that, with small variations in local flexural rigidity along the chain, the more flexible end curls first and then touches the main chain body. As a result and for a typical lasso, L is longer than 2πR because of the additional tail that attaches to the primary ring. With subsequent chain rotation and addition of hydrodynamic forces, the entire structure collapses until a steady-state loop is formed which rotates continuously. Although previous work has shown that linked and unlinked colloidal chains can form stable rods23 or S-like configurations,23−29 closed rings have not been demonstrated under a rotating magnetic field. The deformation of a flexible chain into a lasso can be understood as the result of minimization of the summed elastic and magnetic energies in which both chain flexural rigidity EI and field strength B0 are governing parameters. Under a rotating magnetic field with frequencies f M > 20 Hz, it has been shown that the pair interaction between particles is essentially isotropic,30 depending only on separation r as

3. RESULTS AND DISCUSSION 3.1. Lasso Formation under 2D Circularly Rotating Magnetic Field. To achieve this, we first fabricate linear chains of magnetic beads that are flexibly connected via polymeric linkages. We apply a 1D DC magnetic field (∼20 mT) along the direction of gravity to a suspension of superparamagnetic latex beads (diameter 2a = 4.5 μm) that assemble into linear chains aligned with the field due to induced dipolar interactions (Figure S1). The suspension also contains concentrated highmolecular-weight (Mw = 1 300 000) polyvinylpyrrolidone (PVP), which adsorbs onto the particle surface. As the magnetic field brings particles close to each other, the entanglement of PVP between adjacent particles irreversibly links them so that chains remain intact even upon removal of the field.20 Typical magnetic chains as fabricated are shown in Figure S1b. The flexural rigidity EI, (where E is the Young’s modulus and I = πa4/4 is the moment of inertia) of fabricated chains was probed by first aligning a chain with a DC field along the x-axis and then removing it to quickly apply another field along the orthogonal y-axis. Flexible chains then bend into a U-shape (SI Figure S2a) due to the competition between elastic and magnetic energies.11,21 The measured separation between U-chain arms, 2R, scales with EI1/2 and is inversely proportional to the field strength22 B0 (see details in SI), as confirmed in SI Figure S2b. From the slopes, we determined the flexural rigidities of chains as summarized in Table 1. We note that these values are 1−3 orders of magnitude smaller than chains linked by bis-biotin-poly(ethylene glycol)23 with the high flexibility attributed to the high molecular weight of PVP.

UM(r ) = −αp2 /8πμ0 r 3

where p = 4πa χμ0B0/3 is the induced magnetic dipole moment of a particle, χ is the volumetric susceptibility, and μ0 is the vacuum permeability. The coefficient α is a function of both susceptibility χ and particle separation r. Based on this, one can conclude that a chain coiled into a spiral where all beads are packed closely is of minimum magnetic energy; however, the elastic energy penalty for a fully coiled chain is enormous. Therefore, the lasso structure we observe in Figure 1a results from a balance: chains coil in a tight ring to have a long zippered tail but do so with a penalty from the bending energy. To quantify, we first calculate the magnetic energy of a lasso of radius R by separating into two parts, the energy of a closed ring and the energy between the zippering tail and the ring. If we only consider nearest neighbor contributions, the former is

Table 1. Flexural Rigidity (×10−24 J·m) of Chains Determined Using a 1D DC Field to Bend into a “U”-Shape and a 2D Rotational Field Forming a Closed Ring

EI (U-shape) EI (Closed ring)

10-mer

11-mer

13-mer

5.00 ± 0.86 5.85 ± 0.41

7.38 ± 1.46 6.99 ± 0.97

3.42 ± 0.58 3.73 ± 0.25

(1)

3

Uring = U0N = U02πR /2a = πU0R /a

(2)

where U0 is the magnetic energy between two particles in contact, U0 = UM (r = 2a) and N is the number of particles in a ring. The latter can be modeled as the magnetic energy between two closely staggered chains of length L − 2πR B

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Langmuir Utail =

4NU0 2U0 (L − 2πR ) = (L − 2πR ) 2aN a

(3)

where 4NU0 is the magnetic energy between staggered chains of length 2aN. The coefficient 4 arises because each bead along the chain has four nearest neighbors. The elastic energy of a lasso is UE =

∫0

L

1 ⎛⎜ 1 ⎞⎟2 EIL EI ds = ⎝ ⎠ 2 2 2R2

(4)

where s is the arc length along the chain, an equation that simplifies here with constant lasso radius R. To facilitate the scaling analysis, we assume, when integrating eq 4, that both the primary loop and the tail segment have the same radius of curvature, justified because the tail is relatively short and both radii are a few times larger than the individual particle size. Combining eqs 2−4, we obtain the total energy of a lasso as U=

U0 EIL (2L − 3πR ) + a 2R2

(5)

Clearly, the magnetic energy decreases (since U0 is negative) and the elastic energy increases with decreasing radius R, with an energy minimum at some intermediate value R* ⎛ 12LEI ⎞1/3 ⎟ (aχB0 )−2/3 R * = ⎜⎜ 2⎟ αμ π ⎝ 0 ⎠

(6)

Equation 6 indicates that the radius of a stable lasso scales with the −2/3 power of the field strength and the 1/3 power of the flexural rigidity. For a fixed chain length, therefore, a stronger magnetic field or higher flexibility will yield smaller lassos. To demonstrate this, we measure the radii of lassos at different field strengths and note that these lassos are assembled from the same chains bent into U-shapes under a 1D DC magnetic field in SI Figure S2. As shown in Figure 1b, we find a linear relationship between R* and B0−2/3, consistent with eq 6. The flexural rigidity EI from the slopes of these lines average within 10% of those obtained by measuring the separation between arms when the same chains are bent into U-shape under a DC field, validating our energetic model (Table 1). 3.2. Lasso Propulsion under 3D Magnetic Field. As expected from our previous studies,12 rotating lassos do not translate if the applied field is within the x−y plane. To reorient the field relative to the substrate and break symmetry, we apply an additional AC magnetic field along the z-direction.12 As shown schematically in Figure 2a, the resulting 3D field can be expressed as

Figure 2. Lasso translation under a 3D magnetic field. (a) Force balance on a translating magnetic lasso. The inset indicates the applied magnetic field. (b) Instantaneous velocity of the center of mass for a 16-mer (B0 = 3.3 mT, Bz = 2.6 mT, and θc = 51.4°). Red circles, blue diamonds, and pink squares represent characteristic velocities Vmax, Vshoulder, and Vmin. Insets show the corresponding lasso orientations. Red arrows indicate the part of a lasso that is adjacent to the wall. (c) Average rolling velocity of magnetic lassos scales with angular rotation rate ω, lasso radius R*, and camber angle θc.

note that, as the contact area between lasso and wall decreases, the instantaneous velocity also becomes smaller while Vshoulder is close to the average translation velocity (Vavg). To model chain translation, we recognize that, at steady state, forces due to wall-induced friction Ff and translational fluid drag Fd must balance (Figure 2a). Following our previous work,12 we define the wet frictional force as

B = B0 cos(ωM t )x ̂ + B0 sin(ωM t )y ̂ + Bz cos(ωM t + ϕz)z ̂ (7)

Upon field application, we observe that lassos spin in the plane at a camber angle θc relative to the surface normal, where θc = arctan (B0/Bz)(Figure 2a). As they orient off the substrate surface, lassos translate due to friction with the substrate acting like a rolling hoop. The lasso translation direction can be controlled by the phase lag ϕz as illustrated in Movie S2. Based on image processing, we identify the lasso center of mass and measure its instantaneous velocity during translation (Figure 2b) where the velocity is not constant over a full period. Three characteristic velocities, Vmax, Vshoulder, and Vmin arise because of lasso asymmetry. As shown in Figure 2b, these velocities correspond to different lasso orientations when the overlapping lasso tail, lasso body, or the tail tip is adjacent to the wall. We

Fj = μk M = μ*V *M

(8)

where μk is the wet friction coefficient, proportional to the fluid velocity (V*) between lasso and substrate,12,31 μk = μ*V* = μ* ωR*, and M the load, the gravitational force projected on the field plane. The friction force is therefore Ff = μ*ωR *Nmg cos θc

(9)

where ω is the angular frequency of the lasso, N is the number of particles in the lasso, and mg is the weight of a single particle. The fluid drag of a ring in the direction of travel is proportional to its circumference32 and translational velocity V, and, if we neglect wall effects, can be expressed as C

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Figure 3. Cargo capture and transport with magnetic lassos. (a) Cargo-loading dynamics. (b) Cargo of different diameters can be loaded by the same lasso: (i) 1.8 μm, (ii) 7.0 μm, and (iii) 13.2 μm. (c) The ratio of degree of slip for loaded and unloaded lassos γ with relative size of cargo to lasso (Rc/Na). The dashed line represents eq 11. (d) Measured minimum θc for different size ratios. The regime above the dashed line shows stable entrapment and transport of cargo. Scale bars: 12.5 μm.

Fd = 4πηaNV

V L / ωL 1 =γ= 3R V /ω 1 + 2Nac

(10)

where η is the fluid viscosity. Equating eqs 9 and 10 yields a simple scaling law that suggests the average lasso propulsion speed V is proportional to the product of its angular rotation rate ω, lasso radius R*, and cosine of camber angle θc, V ∝ ωR* cos θc. To test this, we measure the translation speeds of lassos of different sizes under a variety of field conditions. As shown in Figure 2c, the model is a good qualitative fit with a maximum velocity achieved of approximately 20 μm/s. 3.3. Cargo Capture, Transport, and Release. While the rotation of the lasso leads to well controlled translation, lasso structure provides the opportunity for cargo loading. As shown in Figure 3a and Movie S3, one can load cargo with a lasso approaching the target and opening under a low magnetic field strength B0 and high θc. To capture cargo, the 2D rotating field B0 is gradually increased making the chain recurl to tighten around the target. Since the lasso radius can be tuned via field strength, a wide size range of cargos can be loaded by a given lasso. As shown in Figure 3b, for a 16-mer lasso whose largest diameter is ∼13.6 μm under a weak field of 3.3 mT, we have successfully loaded cargo ranging from 1.8 to 13.2 μm (Figure 3b). When the cargo size is significantly smaller than the lasso, it is more convenient to apply a weak field in the x−y direction and a strong one in the z-direction. As it approaches the cargo, the z-field can be removed allowing the lasso to fall in place (Movie S3), stably trapping cargo within the vortex generated by rotation. Under three-dimensional (3D) magnetic fields, loaded lassos roll similarly to unloaded ones. Figure S3 shows the instantaneous velocity of the lasso center of mass loaded with 7.0 μm cargo where we observe similar characteristic velocities, VLmax, VLshoulder, and VLmin. However, the rotation frequency of loaded lassos becomes 2-fold smaller and the average velocity approximately half that of unloaded lassos due to additional hydrodynamic drag. To model the impact of cargo on lasso transport, we follow our previously developed force balance but incorporate the additional hydrodynamic drag due to cargo leading to an average rolling velocity given by eq S7. Since the loaded and unloaded lassos have different rotational frequency ω, we compare the ratio of V to ω for both lassos

(11)

where VL (V) and ωL (ω) are the average translation velocity and rotation frequency of loaded (unloaded) lassos, respectively, and Rc is the cargo radius. Here, γ represents the ratio of the degree of slip for loaded and unloaded lassos since both have the same radius. Equation 11 predicts that loaded lassos have a higher degree of slip and roll more slowly as cargo size increases. This is confirmed by our experimental results shown in Figure 3c where, for a lasso loaded with cargo of comparable size, Rc/R ∼ 1, we observe a γ decrease of ∼20%. Although the rolling velocity of loaded lassos can be increased by lowering θc, there exists a minimum camber angle below which lassos can no longer carry cargo. This minimum θc is predicted by the geometric constraint illustrated in the Figure 3d inset, where cosθc must be equal to or greater than the size ratio of cargo to lasso Rc/R. A measurement of the minimum θc for different size ratios in Figure 3d shows good qualitative agreement with this simple prediction. Because the magnetic field is applied over a relatively large sample area, all magnetic chains within the sample volume experience the same rotating field. As a result, samples with many chains could function in a highly parallel fashion; however, each chain would mimic other chains in rotation and direction. Although manipulating individual microlassos simultaneously is beyond the scope of this work, other recent studies have demonstrated that such control in similar systems is indeed possible.33 In addition, alternative imaging techniques are feasible, as X-ray34 and MRI35 show significant contrast with the superparamagnetic particles used to create our chains. Loaded lassos can be used to transport cargo with precise directional control by reorienting the field rotation axis via the phase lag ϕz between the x−y rotating field and the field in the z-direction. Because redirection is immediate, we have implemented control via preprogrammed translation as well as via joystick and, as shown in Figure 4a and Movie S4, the cargo pathway can be precisely directed. Once the loaded lasso reaches its destination, the magnetic field can be removed, dipole interactions vanish, elastic energy dominates, and the chain relaxes to release cargo. With this reset, the same lasso D

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Reversible cargo loading and unloading (MPG)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail:[email protected]. ORCID

Ning Wu: 0000-0002-2167-3621 David W. M. Marr: 0000-0002-6820-761X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS T.Y., N.W., and D.W.M.M. acknowledge financial support from National Aeronautics and Space Administration (Grant No. NNX13AQ54G). T.O.T., K.B.N., and D.W.M.M. also acknowledge support from the NIH (R21NS082933).

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Figure 4. Precise control of cargo transport with magnetic lassos. (a) Transport of a loaded cargo in an “M” trajectory. (b) Reversible unloading and loading of cargo. Scale bars: 12.5 μm.

can be used for transporting other cargo as shown in Figure 4b and Movie S5. Compared with previous approaches,6,15,16 the reversibility in cargo loading and unloading represents a significant advantage.

4. CONCLUSION In conclusion, we have demonstrated that superparamagnetic microlassos can achieve reversible cargo capture, transport, and release under a 3D AC magnetic field. Lassos are fabricated by aligning magnetic beads into linear chains under a 1D DC magnetic field and locked in place with polyvinylpyrrolidone. By further applying a planar x−y rotating field, lassos curl around cargo capturing them. In the presence of an additional orthogonal AC magnetic field, loaded lassos translate with precise spatial control. Both propulsion velocity and direction can be varied with simple manipulation of the applied field. At the targeted destination, cargo is readily released by lowering field strength or reversing field rotation unfolding the lasso. Since the entire process is physically controlled with no chemical attachment/detachment required, this approach has the potential for transporting a wide range of cargo under different solution conditions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.7b00357. Bending of a linked chain into "U"-shape under a DC magnetic field; force balance on a loaded lasso; fabrication of flexibly linked magnetic chains; instantaneous velocity of the center of mass for a 16-mer lasso (PDF) Dynamic formation of a 19-mer lasso under a rotating magnetic field (MPG) Translation of an unloaded lasso under a 3D magnetic field manipulated via joystick (MPG) Two different methods of cargo loading (MPG) Control of loaded lasso trajectory (MPG) E

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DOI: 10.1021/acs.langmuir.7b00357 Langmuir XXXX, XXX, XXX−XXX