Patterned Magnetic Structures for Micro-/Nanoparticle and Cell Manipulation

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy

in the Graduate School of The Ohio State University

Gregory Butler Vieira

Graduate Program in Physics

The Ohio State University

2012

Dissertation Committee:

Professor Ratnasingham Sooryakumar, Advisor

Professor Gregory Lafyatis

Professor David Stroud

Professor Fengyuan Yang

Gregory Butler Vieira

2012

Abstract

Remote manipulation of fluid-borne magnetic particles on a surface is useful to probe, assemble, and sort microscale and nanoscale objects. By patterning magnetic structures in shapes designed to exploit local heterogeneities in thin film magnetization, we have demonstrated effective trapping mechanisms for superparamagnetic micro- and nanoparticles. The features necessary for trapping are shown to arise at domain walls or indentations in microscale and smaller magnetic wires, at the periphery of magnetized disks, and at corners of magnetized triangles.

Weak (<150 Oe) in- and out-of-plane external magnetic fields modify the energy landscape of the trapped particles, allowing for the objects to be remotely maneuvered along selected routes across the surface. The mechanism is multiplexed, allowing for simultaneous manipulation of many trapped particles, and their motion is directed using a handheld user interface. Particles are able to be transported over hundreds of micrometers with velocities of upwards of 200 μm/s and average forces of up to hundreds of picoNewtons.

The magnetic fields, their spatial distribution, and resulting forces are estimated by modeling magnetization of the patterned structures using micromagnetic simulation or by approximating the traps as point sources of fields. The quality of these models and their relevance for describing particle manipulation under the experimental conditions is discussed. ii

The applicability of these techniques is demonstrated for various biological, biomolecular, and nanoscale systems. Binding of magnetic particles to cells allows for guided cell transport. Composite micelle nanostructures, only tens of nm across, are simultaneously trapped and maneuvered magnetically and tracked fluorescently, despite their small size. The implications for use of this technology in lab-on-chip devices are discussed.

iii

Dedication

To my parents: Mr. Allen Thomas Vieira and Mrs. Priscilla Fay Butler.

Thanks for inspiring my interest in science. I hope it’s okay I didn’t go into your fields.

Acknowledgments

It would not be fitting to write this dissertation without including acknowledgement of all the assistance, advice, guidance, and general good-natured camaraderie from those who have been a part of my graduate experience and life for the last six plus years. First and foremost, I would like to thank my advisor, Dr. R.

Sooryakumar, for trusting me with what turned out to be a wonderful idea for a project and for providing the means and encouraging the action that were necessary for its implementation.

I would like to thank my advisory committee, Professor Gregory Lafyatis,

Professor David Stroud, and Professor Fengyuan Yang, for help and guidance, and for sitting through and being supporting during year after year of annual reviews. Dr.

Lafyatis, it was a pleasure collaborating with you. Dr. Stroud, it was a joy being in your quantum mechanics class. Dr. Yang, thank you for some very good experimental advice that was very necessary for our work (not to mention a few samples your group made for us).

Next, my group members are the ones who made all of this possible. Tom

Henighan and Aaron Chen, you were in Soory’s group with me back when our lab was not equipped for this type of research; thanks for building up the systems that made these

v experiments possible, not to mention doing great science in the meantime. Marci

Howdyshell, Mike Prikockis, Atul Bharde, Dan Giglio, Eric Suchyta, Tom Byvank,

Anand Harvind, Sam Stuard, Gilbert Bustamante, Bavi Sadayappan, Manjari Randeria,

Mudd Hussain, Amanda Krasowski, Paul Zivick, and Yang Li, it’s been a pleasure working with you on these projects, and I have a lot of optimism both for the direction of the research, as well as the future endeavors of every one of you. Wei Zhou, Sheldon

Bailey, and Jon Zizka, it was great being in the same group and getting to know you, even though we studied vastly different systems; and thanks for putting up with hearing about our projects for so long at group meeting.

The success of this work is only possible because of the brilliance, hard work, and helpfulness of our collaborators. I am eternally indebted (not legally binding) to Adam

Hauser, Jeremy Lucy, and Brian Peters in Dr. Yang’s group for growing countless samples for us, not to mention Josh Zhao for teaching me just about everything I needed to know about sample fabrication. I see great things from our collaboration with

Professor Jessica O. Winter in Chemical Engineering, and it’s been a joy working with those in her group: Gang Ruan, Dhananjay Thakur, Kalpesh Mahajan, and C. Jenny

Dorcena, as well as our collaborators at Sandia National Labs, George Bachand and

Nathan Bouxsein. Many group members in the group of Professor L. James Lee were instrumental in our work, including Pouyan Boukany, Daniel Gallego-Perez, Xi Zhao,

Yun Wu, Kwang-Joo Kwak, and in particular, Bo Yu for providing means for reducing non-specific binding, without which much of this research would not have been possible.

Also, thanks to: Andrew Morss in Dr. Lafyatis’s group for exciting collaboration with

vi optical tweezers; Rustin Shenkman, Jie Xu, and Brandon Miller in Professor Jeffrey

Chalmers’s group for providing labeled cells on an impressively regular basis; and Woo-

Jin Chang in Professor Rashid Bashir’s group at UIUC, HyunChul Jung and Hyeongnam

Kim in Professor Wu Lu’s group and Veysi Malkoc and Daniel Gallego-Perez in

Professor Derek Hansford’s group for some very well-made microfluidic devices.

Also, I am grateful to Dr. Lee for the opportunities with regard to leadership positions in Ohio State’s Nanoscale Science and Engineering Center (NSEC) and the

Council for Nanoscience Graduate Students (CONGS). Thanks so much to Jeremiah

Schley, Tony Duong, Xi Zhao, Marci Howdyshell, Edwin Lee, and many other CONGS members for all of your help making and keeping this organization active. Also, CONGS and other NSEC activities wouldn’t have been possible without guidance of Professor

Sherwin Singer, as well as additional assistance from Layla Mohmmad-Ali, Prem Rose

Kumar, Theresa Gordon, and Karim Jackson.

Graduate school would not have been the same without the many friends who made every day better. Julia Young, Elena Chung, and Isham Khan, thanks for being a

Maryland presence all the way out in Ohio. Dave Gohlke, Ivana, Becky, and Heather

Rosenblatt, and Jeff Stevens, thanks for coming out to all those ultimate Frisbee games.

Adam Hauser, Patrick Truitt, Alex Mooney, Jenn Holt, Justin North, Rakesh Tiwari,

Mike Fellinger, Mike Boss, Mike Hinton, Bill Schneider, Hayes Merritt, Nick Harmon,

Dave Massey, James and Veronica Stapleton, Ben and Bryanne Dundee, Chris and

Nicole Roedig, Mehul Dixit, John Draskovic, Kevin Driver, and anyone I might have forgotten, thanks for being my friends. And I can’t forget everyone who taught me how

vii great of a music town Columbus is: Travis Bunner, Will Fleeter, and everyone else who’s ever been in The Glance, Craig James, Matt Montaw, Jesse and Brian Maxwell, Jon

Keylor, Fred Haertel, Leone Batte, Ken Pardee, Mary Miller, Dawn Lepere, Jeff Starns,

Joy Hall, Ron and Savannah Freeman, and of course the legendary Billy Zenn.

Catherine Sundt, thank you so much for being there for me these last five years, and for your love, support, and excellent ability to edit the written word.

And finally, to my family, who mean the world to me. To my aunts Carolyn

Vieira and Bonnie Poli, Uncles Kelly Butler and David Vieira, to my sister Scotty Vieira, to Gustavo Lemos and Elisabeth Oliveras, and to my parents Penny Butler and Allen

Vieira, thank you for being there when I’ve needed you.

This work was supported in part by the U.S. Army Research Office under

Contract W911NF-10-1-053 and in part by the National Science Foundation under grant

EEC-0914790.

viii

Vita

June 2002 ...... Montgomery Blair High School, Silver Spring, MD

May 2006 ...... B.S. Physics, University of Maryland, College Park

2006 – 2009...... Graduate Research and Teaching Associate, The Ohio

State University

June 2009 ...... M.S. Physics, The Ohio State University

2009 – 2011...... Graduate Research Fellow, The Ohio State University

2011 – 2012...... Presidential Fellow, The Ohio State University

2012 ...... Graduate Research and Teaching Associate, The Ohio

State University

Publications

Vieira, G., Henighan, T., Chen, A., Hauser, A.J., Yang, F.Y., Chalmers, J.J., and Sooryakumar, R., Magnetic Wire Traps and Programmable Manipulation of Biological Cells. Physical Review Letters, 103, 128101 (2009).

Ruan, G., Vieira, G., Henighan, T., Chen, T., Thakur, D., Sooryakumar, R., and Winter, J.O., Simultaneous Magnetic Manipulation and Fluorescent Tracking of Multiple Individual Hybrid Nanostructures. Nano Letters, 10, 2220-2224 (2010).

Henighan, T. Chen, A., Vieira, G., Hauser, A.J., Yang, F.Y., Chalmers, J.J., and Sooryakumar, R., Manipulation of Magnetically Labeled and Unlabeled Cells with Mobile Magnetic Traps.” Biophysical Journal, 98, 412-417 (2010).

Henighan, T., Giglio, D., Chen, A., Vieira, G., and Sooryakumar, R., Patterned magnetic traps for magnetophoretic assembly and actuation of microrotor pumps. Applied Physics Letters, 98, 103505 (2011).

Chen, A., Vieira, G., Henighan, T., Howdyshell, M., North, J.A., Hauser, A.J., Yang, F.Y., Poirier, M.G., Jayaprakash, C., and Sooryakumar, R., “Regulating Brownian Fluctuations with Tunable Microscopic Magnetic Traps.” Physical Review Letters, 107, 087206 (2011).

Vieira, G. Chen, A., Henighan, T., Lucy, J., Yang, F.Y., and Sooryakumar, R., “Transport of magnetic microparticles via tunable stationary magnetic traps in patterned wires” Physical Review B, 85, 174440 (2012).

Chen, A., Byvank, T., Vieira, G. B., and Sooryakumar, R., “Magnetic Microstructures for Control of Brownian Motion and Microparticle Transport” Accepted by IEEE Trans. Magn., Oct. 2012.

Mahajan, K.D., Vieira, G.B., Ruan, G., Miller, B.L., Lustberg, M.B., Chalmers, J.J., Sooryakumar, R., Winter, J.O., “A MagDot-Nanoconveyor Assay Detects and Isolates Molecular Biomarkers” Accepted by AIChE: Chem. Eng. Prog., Nov. 2012.

Fields of Study

Major Field: Physics

Table of Contents

Abstract ...... ii

Dedication ...... iv

Acknowledgments...... v

Vita ...... ix

Publications ...... ix

Fields of Study ...... x

Table of Contents ...... xi

List of Tables ...... xv

List of Figures ...... xvi

Chapter 1: Introduction ...... 1

1.1 Current Force Probe Technologies ...... 3

1.1.1 Optical Tweezers ...... 3

1.1.2 Atomic Force Microscopy ...... 5

1.1.3 Magnetic Tweezers ...... 5

1.2 Magnetism in Thin Films ...... 6 xi

1.3 Surface-Based Magnetic Traps ...... 9

1.4 Superparamagnetic Particle Response in a Magnetic Field ...... 12

Chapter 2: Experimental Procedures ...... 15

2.1 Device Fabrication ...... 15

2.2 Prevention of Surface Adhesion ...... 17

2.2.1 Surfactants...... 18

2.2.2 Surface Modifications ...... 18

2.3 Electromagnet and Solenoid Platform for Manipulation ...... 19

2.4 Magneto-Optic Kerr Imaging ...... 21

Chapter 3: Patterned Wire Traps for Particle and Cell Trapping and Transport ...... 23

3.1 Zigzag Wires ...... 24

3.1.1 Particle Transport via External Fields ...... 27

3.1.2 Cell Transport ...... 34

3.1.3 Wire Traps on Alternative Substrates ...... 38

3.2 Straight Notched Wire Traps...... 39

3.3 Wire Trap Calculations ...... 44

3.4 Integrated Optical-Magnetic Tweezers for Cell Manipulation ...... 48

3.5 Summary of Wire-Based Techniques ...... 51

Chapter 4: Discrete Patterned Magnetic Elements for Particle and Cell Transport ...... 53

4.1 Disk Trap Profiles and Tunability ...... 54 xii

4.2 Cell Manipulation on Disk Arrays ...... 57

4.2.1 Labeled Cells ...... 57

4.2.2 Label-Free Manipulation ...... 59

4.2.3 Instantaneous Labeling ...... 59

4.3 Characterization of Particle Transport Speed on Disk Arrays ...... 61

4.4 Triangular Elements for Particle Trapping and Manipulation ...... 64

4.5 Disk Array Applications...... 68

Chapter 5: Composite Nanoparticle Trapping ...... 71

5.1 Formation of Hybrid Magnetic Quantum Dot Particles ...... 73

5.2 Characterization of Nanocontainers ...... 75

5.3 Nanocontainer Manipulation ...... 77

5.4 Blinking Quantum Dots in Heterostructures ...... 81

5.5 Calculations of Magnetic Fields and Forces on Nano-Containers ...... 82

5.6 Trapping Force Estimate and Tunability with Out-of-Plane Fields ...... 83

5.7 Device Attributes...... 85

Chapter 6: Micromagnetic Models and Field Calculation Methods ...... 88

6.1 Micromagnetic Modeling ...... 88

6.2 Field Calculation Methods ...... 89

6.2.1 Point Charge/Point Dipole Model for Field Calculation ...... 89

6.2.2 Dipole and Charge Distribution Model for Field Calculation ...... 90 xiii

Chapter 7: Conclusions and Future Work ...... 92

Appendix: Mathematica Code for Calculating Fields from Domain Wall ...... 96

References ...... 101

xiv

List of Tables

Table 1: Saturation magnetization values and exchange constants for permalloy31 and iron-cobalt32–34. Note that the OOMMF User’s guide31 indicates “the material parameter values provided … should not be taken as standard reference values for these materials. These values are only approximate.” ...... 9

List of Figures

Figure 1: Established micro and nanomanipulation techniques: Optical tweezers, atomic force microscope (AFM) manipulation, and magnetic tweezers. (a) Ray tracing diagram of a focused laser incident on a spherical dielectric particle, indicating optical tweezers apply force (FA) toward the focal point of the laser. “A”s indicate refracted rays and “R”s indicate reflected rays (schematic from Ashkin et al. 198616). (b) Cartoon of AFM cantilever tip (red) obtaining an image of a carbon nanotubes (yellow), contacting the surface (blue), and bending the nanotube (picture from IBM research website20). (c) Schematic of magnetic tweezers using a magnetic pole piece, applying an upward force to a superparamagnetic particle (schematic from Gosse et al. 200221)...... 4

Figure 2: Mapping crosstie domain walls in permalloy thin films using the Bitter technique. (Image from Garrood et al. 1962.36) Magnetic nanoparticles and nanoparticle aggregates are attracted to domain walls in the thin film. Inset shows schematic of magnetization profile in a crosstie domain wall for comparison. (Schematic from McCord et al. 200938.) ...... 9

Figure 3: I – Magnetic particles are trapped at domain walls in a garnet film. A particle at a domain wall tip can be maneuvered in two dimensions by application of strong external fields, in turn repositioning the domain walls. (Image modified from Helseth et al. 2003.40) II – Five μm-diameter cobalt disks, coupled with weak external rotating out-of- plane magnetic fields, maneuver a 1 μm particle rightward along the disk array. The disk magnetizations are fixed for the applied fields, as the particle manipulation is a result of the changing energy landscape created by the rotating field. (Image from Yellen et al. 2007.41) III – Patterned permalloy microstructures are used to transport magnetic particles using rotating in-plane magnetic fields. Devices enabled by teardrop and saw-tooth structures (images from Conroy et al. 200842), as well as oval shaped structures (image from Gunnarsson et al. 200543), exploit changing magnetization and in particular enhanced stray fields that occur at sharp edges of microstructures...... 11

Figure 4: Schematic45 illustrating magnetic moment (m) versus applied field (H) for a superparamagnetic particle. At low fields, m varies approximately linearly with H, while at high fields, m saturates asymptotically...... 13

Figure 5: Single-layer and two-layer resist procedure. (a) Resists are spin coated onto device, and patterned regions are exposed, either with e-beams or UV light. (b) Device is

xvi developed, removing exposed region of resist. (c) Desired material is sputtered onto device. (d) Excess resist and sacrificial material is chemically lifted off, leaving patterned structures. Two layer resist helps prevent occurrence of “fences”. (e) Atomic force microscopy profiles of patterned disks (left) with and (right) without fences. Resist thickness used is generally ~100s of nm, while deposited material thickness is generally ~10s of nm. (Sloping in right side of part (e) due to slight angle of sample.) ...... 16

Figure 6: (a) Schematic and (b) photograph of setup for applying magnetic fields. Four electromagnets apply in-plane fields and solenoid coil (z-coil) applies an out-of-plane field. (c) Schematic of configuration of computer-controlled power supply, microscope with camera and magnets, and video game controller as a user interface. “Joystick” image from Microsoft Xbox website52...... 20

Figure 7: Schematic45 of the magneto-optical Kerr effect (MOKE) setup for imaging magnetic domains. Polarized white light is incident through half of the rear aperture of an objective lens so that light is obliquely incident on the surface of interest. The resulting polarized component of reflected light increases or decreases by an amount proportional to the sample magnetization. The analyzer transmits only the desired polarization of reflected light to the CCD camera, and the MOKE signal is processed digitally. The result is a grayscale image which coincides with sample magnetization...... 22

Figure 8: (a) Schematic of a rectangular zigzag wire with a head-to-head (HH) domain wall (DW) at the vertex, associated ﬁeld HDW, and a trapped magnetic particle (gray circle). (b) Array of zigzag wires patterned on platform with perpendicular (Hz) and in- plane (H//) magnetic fields. Sketch in (a) is an enlarged view of the dotted circle around a vertex55...... 25

Figure 9: (a) Magnetic configuration of a head-to-head (HH) domain wall in a 1-μm- wide, 40-nm-thick zigzag Co0.5Fe0.5 wire as derived from micromagnetic OOMMF simulation, after relaxation from a uniform +y initial magnetization. (b) A magnetic force microscopy image of a Co0.5Fe0.5 zigzag wire showing alternating bright and dark HH and tail-to-tail (TT) domain walls at vertices. (c) A grayscale MOKE image. Bright and dark contrast shows the alternating magnetization component (Mx) of adjacent arms in zigzag wire. (d) A dark field image of Co0.5Fe0.5 zigzag wire showing 2.8-μm magnetic particles trapped at vertices. Vertex-to-vertex separation is 16 μm in all images45...... 26

Figure 10: Calculated field gradient, force, and energy profiles from a 1000 nm-wide domain wall localized on a 40 nm-thick, 1 μm-wide Co0.5Fe0.5 wire. (a) Magnetic field gradients above the wire based on point charge (solid line) model and micromagnetic simulation (dashed line) increase rapidly above 104 T/m as distance z to the domain wall decreases. (b) Variation of axial force Fz determined from point charge model on a magnetic bead (volume susceptibility, χ = 0.85) lying 1.42 μm above domain wall with external field Hz. (c)-(f) Potential energy profiles transform from attractive (c)-(e) to max repulsive (f) by changing Hz further negative. Calculated maximum force Fx along length of wire shows its tunability with Hz. Note for distances z > 1300 nm relevant to xvii this study, the magnetic energies are not sensitive to the precise magnetization profiles within the domain wall55...... 28

Figure 11: (a) Orientation of a zigzag wire, magnetization M (open arrows), and external H//, Hz fields. (b)-(f) Variation of magnetic potential energy within point charge model with distance d from the HH vertex along the wire. Orientations of H// and Hz are indicated. Inset photographs show close correlation between locations of a microsphere with a diameter of 2.8 μm on the wire and the calculated local energy minimum position55...... 30

Figure 12: Left column: Calculated potential energy landscapes of zigzag wire, where brighter shades in grayscale background image indicate lower potential energy (i.e. trap). Right column: Images of 2.8-μm-diameter magnetic particles trapped at corresponding vertices and subseq-uently maneuvered in response to changing fields Hxy and Hz. (a) and (b) In the absence of an external field, both HH and TT domain walls are traps for the superparamagnetic particles. The scale bars represent 10 microns. (c) The combination of Hz = 120 Oe and Hxy = 25 Oe fields render some vertices to remain as traps while others transform to repulsive sites. (d), (f), (h), and (j) Two magnetic particles manipulated from one wire to the next and back based on the magnetic field sequence indicated by white arrows in (c), (e), (g), and (i), respectively. Inverting the magnetic field sequence reverses the direction of particle transport. Energy minima associated with secondary traps, only present under external fields, are too weak to be evident in the grayscale energy landscapes45...... 31

Figure 13: Characteristics of secondary potential energy minima45. (a) Schematic of locations of secondary minima, indicated by black dots, for a particle near an HH domain wall in the presence of Hxy = 50 Oe and Hz = 120 Oe. Each dot corresponds to the calculated potential minimum for field directions defined by the nearest black arrows, indicating that the direction of Hxy dictates the particle trajectory. (b) Potential energy landscapes for Hz = 120 Oe and various Hxy values showing that the depth and width of secondary traps is tunable by changing the magnitude of Hxy...... 33

Figure 14: (a) Sequential applications of planar (H//) and perpendicular (Hz) fields transport (indicated by dots) four labeled T-lymphocyte cells along a zigzag wire on a Si platform. The cells (dashed circles in top panel) are conjugated to 1 μm magnetic spheres. (b) Trajectory (white dots) of a single T-lymphocyte cell away from the wires and its controlled return to a neighboring vertex on the same wire. The arrows (and dashed circle in first panel) identify the cell. (d) Simultaneous back and forth transport of five fluid- borne T cells between zigzag wire (1), (2), and (3). Dots identify trajectory of five cells55...... 35

Figure 15: (a) Magnetically-labeled T-lymphocyte cells lined up at top of an array of zigzag wires. (b) - (d) Cells are remotely moved downward along the wire tracks until most cells are aligned at the bottom edge of the wire array. All movements achieved through remotely-controlled sequences of changing external magnetic fields...... 37 xviii

Figure 16: (a) 8 μm superparamagnetic microspheres trapped at head-to-head and tail-to- tail domain walls in Co0.5Fe0.5 zigzag wires patterned onto a Mylar film. (b)-(g) A single microsphere transported along a wire by a controlled sequence of changing external magnetic fields. (Vertex-to-vertex distance is 16 μm in all images.)60...... 38

Figure 17: Simulated magnetization profile for varying initial magnetizations in notched Co0.5Fe0.5 wires. (a) Initial magnetization M0 perpendicular to the wire results in a tail-to- tail domain wall. (b) - (c) Slight variation in M0 from perpendicular does not result in well-formed domain wall, and instead results in near-uniform horizontal magnetization. (d) Even for horizontal initial magnetization, the resulting magnetization is locally non- uniform near the notch to follow the contours of the wire edge. Bottom panel defines the angle of initial magnetization and the blue-white-red color scheme...... 40

Figure 18: (a) Schematic of magnetization configuration in a notched straight Co0.5Fe0.5 wire after relaxation from a momentary uniform +x initial magnetization. (b) A bright field image of Co0.5Fe0.5 wires showing 2.8 μm magnetic particles trapped at notches. (c) Magnetic force microscope image of a notched Co0.5Fe0.5 straight wire shows dark/light spots to left/right of each notch. The MFM image has been blurred using a standard Gaussian blurring technique. Scale bars in (b) and (c): 10 μm45...... 42

Figure 19: (a) Schematic of magnetization configuration of a notched wire. (b)–(g) A 4.5- μm-diameter magnetic particle transported from left to right by sequencing the out-of- plane (Hz) and in-plane (Hxy) external magnetic fields as indicated by white arrows on right. Paired under each image is the calculated magnetic energy landscape along the wire. Particle positions correlate well with local energy minima. Reversing sequence of magnetic fields reverses the direction of particle motion. Notch-to-notch distance is 10 μm in all images45...... 43

45 Figure 20: Fields, field gradients, and forces from Co0.5Fe0.5 zigzag and notched wires . (a),(b) Magnetic fields and (c),(d) field gradients as a function of height z directly above a domain wall in a zigzag or notch wire. Calculations based on the point charge/dipole, dipole distribution, and charge distribution models reveal localized fields (> 100 Oe) and large gradients (> 104 T/m) in the immediate vicinity of the traps. (e),(f) Calculated forces as a function of z on a 2.8 μm-diameter magnetic particle with susceptibility χ = 0.85 for zigzag and notch wire traps...... 45

Figure 21: Left Column: Calculated field and field gradient 1.4 μm above the vertex of a 1 μm zigzag wire, and subsequent force on a particle of magnetic susceptibility 0.85 for varying wire thicknesses. Right Column: Same, but for a fixed 40 nm-thick wire, varying wire widths...... 46

xix point is maneuvered away from the bead/wire, but the cell is held in place adjacent to the bead, presumably by antibody binding...... 49

Figure 23: Laser focal point (green dot) at power of ~600 mW traverses across a zigzag Co0.5Fe0.5 wire, ablating a region of wire, indicated by the white arrow, and dislodging a nearby particle, denoted by the black arrow. Vertex-to-vertex distance is 16 μm...... 50

Figure 24: Micromagnetic simulation of the magnetization of a 40 nm-thick, 5 μm-wide magnetic disk in the presence of an in-plane, 50 Oe field...... 53

Figure 25: Calculated energy and force profiles for a permalloy disk 5 μm in diameter and 40 mm thick, magnetized with an in-plane field Hxy = 50 Oe and perpendicular field 64 Hz = +50 Oe . (a)-(c) Potential energy (P.E.) profiles of a 2.8-mm magnetic particle (χ = 0.85) and contour plot of the energy profile in the xy-plane. The trap strengths are tunable with Hz. (d)-(f) Images of a microsphere moved along the periphery of the disk. Arrows indicate orientation of in-plane field Hxy...... 55

Figure 26: (a) Fz, the z-component of the force, on a 2.8-mm magnetic particle with Hx = 50 Oe and Hz = 0. With Hz = 0, the two traps (A and B) are formed at opposite ends of the disk along the x-axis. The lack of complete symmetry of the energy profile of traps A and B arises from the magnetization of the disk being not perfectly symmetric in the OOMMF simulation. (b) Potential energy profiles of traps A and B for Hz = 0. (c) The attractive force from trap A decreases with increasing Hz, with the reverse response for trap B64...... 56

Figure 27: (a) Sequential applications of planar and perpendicular fields transport a labeled T-lymphocyte cell on a Si platform along the periphery of a 10 μm-diameter disk before hopping to a neighboring disk. The initial position of the cell (double circle) is shown and the trajectory of the cell is indicated by connected lines at discrete intervals. (b) Simultaneous transport of four labeled fluid-borne T-cells traveling from top to bottom and then to the right in unison along the platform. Lines identify trajectories of the four cells. (c) Six unlabeled leukemia cells (left, solid circles) being sequentially manipulated by a single microsphere to create a hexagonal lattice (right, dashed circles). The magnetic disks are 5 μm in diameter. (d) Two magnetic microspheres navigating a single leukemia cell on the surface from initial position (double circle) to final location (dashed circle). (e) Several microspheres surrounding and guiding the motion of a single unlabeled leukemia cell. Successive center positions of remotely controlled movement of the cell in solution are shown by solid lines. White arrows indicate direction of travel of the cells64...... 58

Figure 28: (a) An array of 10 μm-diameter permalloy disks on a silicon surface. (b) In the presence of an in-plane field, magnetic beads deposited on the platform are attracted to trapping sites on peripheries of disks. (c) Jurkat cells, introduced at t = 0, attach upon contact to beads with antiCD3 antibody, observed at t ≈ 10 s. (d) Cells are maneuvered around disks by rotating in-plane magnetic field. (e) Cells are transported downward xx across disk array by sequence of rotating in-plane field and switching out-of-plane field. Note that labeled cells trail motion of maneuvered particles. (f) After t ≈ 60 s, excess cell labeling occurs, creating particle-cell aggregates. (Note that (a) – (e) are one location, ) 60

Figure 29: Linear speed of magnetic particle across 40 nm thick permalloy disks array as function of transport frequency. Transport frequency defined as f = 1/(tr+tw) where tr is time allotted for 180 degree in-plane field rotation and tw is time allotted for out-of-plane field switch. Particle transport on Mylar shows a maximum linear speed of 150 μm/s at a critical frequency of 10.0 Hz; on Au surface (deposited on Si), 140 μm/s at 9.1 Hz; on 60 SiO2 surface (deposited on Si), 122 μm/s at 9.1 Hz; on glass surface, 94 μm/s at 6.7 Hz ...... 62

Figure 30: Linear speed of magnetic particle along Mylar surface as function of transport frequency. Maximum linear speed obtained with 40 nm permalloy disks was 150 μm/s at a critical frequency of 10 Hz; with 84 nm disks, 157 μm/s at 11.1 Hz; with 84 nm disks and an applied surface treatment (Sigmacote), 225 μm/s at 16.7 Hz60...... 63

Figure 31: (a) Micromagnetic simulation of the tip of a 60 nm-thick permalloy triangle of side length 6 μm in the presence of a 100 Oe magnetic field. (b) Calculated magnetic field and (c) field gradient based on micromagnetic simulations for locations above triangle vertex or disk (6 μm diameter) periphery. (d) Calculated force for 0.5 μm diameter superparamagnetic particle of magnetic susceptibility 0.85. Fields, gradients, and forces are significantly higher for the sharp point of the triangle...... 65

Figure 32: Particles manipulated in opposing directions simultaneously by permalloy triangle structures in a rotating magnetic field (field direction indicated by white arrow). The direction of transport is defined by the orientation of the triangles. (Mark in center of each image is a blemish on the surface and is irrelevant to the experiment.) ...... 67

Figure 33: Schematic of the nano-conveyor belt technology61. Nano-conveyor belt arrays can transport multiple individual nanocontainers simultaneously with external control and real-time tracking. Nanocontainers can encapsulate various nanospecies. Here we show encapsulation of quantum dots, which permit long-term tracking with high sensitivity (down to the single nanocontainer level) and magnetic nanoparticles, which permit nanocontainer motion. Nanoconveyors are composed of microfabricated magnetic patterns coupled with electromagnets. The encapsulated magnetic nanoparticles allow nanocontainers to be magnetically manipulated by nanoconveyors...... 72

Figure 34: Nanocontainers consisting of quantum dots61 (QDs) and superparamagnetic iron oxide nanoparticles (SPIONs): (a) schematic; (b) TEM with negative staining, scale bar = 50 nm; (c) confirmation of co-encapsulation of QDs and SPIONs in nanocontainers. Nanocontainer accumulation (left) in the presence of a magnet and (right) with no magnet. HMQDs fluorescence was observed using a handheld UV lamp (λem = 605 nm); (d) co-encapsulation of nanorods and nanospheres, scale bar = 50 nm...... 74

xxi

Figure 35: (a) Schematic of the magnetic nanoconveyor platform, where label (1) identifies the viewing/tracking microscope, (2) the two pairs of orthogonal miniature tuning electromagnets to create in-plane magnetic fields Hx, Hy, and (3) the coil to create the out-of-plane magnetic field Hz. (b) Superimposed differential interference contrast (DIC)/fluorescence microscopy image of ferromagnetic disks patterned on a silicon substrate and the diffraction limited fluorescent nanocontainers. Scale bar: 2 µm. (c) Disk magnetization in the presence of in-plane field Hx, Hy. (d) Superposed DIC/fluorescence microscopy image of zigzag wires patterned on a silicon surface with three fluorescent nanocontainers trapped at vertices. (e) Direction of magnetization within the zigzag wires after application of a momentary in-plane magnetic field of 1000 Oe. Head-to-head (HH) or tail-to-tail (TT) domain walls are formed at each vertex61...... 76

Figure 36: (a)-(c) Combined fluorescent image of a nano-container aggregate superposed onto a brightfield image of a 12.5 micron-diameter permalloy disk. The aggregate tracks the periphery of the disk, and the position of the aggregate on the disk tracks with the direction of the applied in-plane magnetic field. Frames shown at (a) 0, (b) 1, and (c) 2.5 seconds. (d)-(g) Two nanocontainer aggregates, (1) and (2), manipulated across an array of 4 μm disks by changing external magnetic fields. Note that during transport across adjacent disks, aggregate (2) leaves the field of view of the disks and is no longer trapped (g). This is due to Brownian fluctuations in the fluid61...... 78

Figure 37: Magnetic manipulation and fluorescent tracking of HMQD-filled nanocontainers collected using DIC/fluorescence microscopy61. Red and blue arrows label individual HMQD-filled nanocontainers that are in flow to the left. The nanocontainers are trapped and released from the zigzag wire platform in response to altering the external magnetic field (Hz) at ~10, 20, and 30 s. Note that at 30 s the Hz change caused the nanocontainer labeled with the red arrow to move out of view. Blinking of encapsulated HMQDs is displayed in frame 2 (red arrow) and frame 10 (blue arrow). Blinking is a probable indicator of single nanocontainers. Scale bar (black) 6 µm...... 80

Figure 38: Calculations of (A) magnetic field and (B) field gradient from the vertex of a 380 nm-wide, 40 nm-thick Fe0.5Co0.5 wire. (C) Forces from this vertex on a typical nano- container61...... 83

Figure 39: Average force on large (~500 nm), low magnetic volume, nano-container aggregates trapped at a zigzag wire vertex, demonstrating tunability with out-of-plane field Hz. Force is calculated by tracking particle positions...... 84

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Chapter 1: Introduction

The ability to precisely localize, sort, arrange, and apply tunable forces to micro- and nanoscale objects is valuable for a variety of scientific fields. The associated tools, resulting from physics principles such as magnetism and light-matter interactions, have proven vital in recent advances in many fields such as biophysics1,2, microfluidics3,4, and biomedical diagnostics5–7. For example, magnetic and optical traps are used for assembly of composite structures of multiple magnetic8 and semiconductor9 nanowires.

Additionally, commercially available cell sorting devices use magnetic field gradients to selectively sort circulating tumor cells in heterogeneous blood cell populations based on magnetic nanoparticle binding, with the intention of detecting various types of cancers in humans10,11. Furthermore, magnetic and optical force probes are used to determine DNA structural response under controlled biochemical conditions12,13 as well as to investigate nanomotor motility mechanisms on molecular filaments such as microtubules14.

This thesis describes a manipulation and force probe technology based on the use of highly localized magnetic field gradients at specified locations of patterned ferromagnetic structures. These new technologies allow for the trapping and manipulation of microspheres, magnetically-labeled cells, or hybrid magnetic/fluorescent nanoparticle micelle structures on designed arrays. By combining these platforms with externally controlled weak (0-150 Oe) fields, such magnetic and magnetically-labeled 1 objects are transported in parallel across surfaces with programmable directed forces that are gentle enough to not produce damage to the cargoes.

The central aspects of this thesis are demonstrated by trapping and remotely manipulating objects on a patterned surface. The two dimensionality of the platform eases lithographic creation of the trapping structures, scale-up to prototypes, and real- time observation with a standard reflective microscope. With symmetries and architecture determined by present nanoscale fabrication techniques, trap arrays with large aerial density can be created and integrated into microfluidic devices. The highlights of this thesis are (1) several distinct patterned magnetic structures used for particle trapping, (2) multiplexed manipulation of magnetic particles via programmable changing magnetic fields (3) application of these structures for biological cell and magnetic/fluorescent micelle heterostructure manipulation, and (4) calculations of fields, gradients and forces attained by these patterned structures.

The remaining sections of Chapter 1 discuss current manipulation and force probe techniques, magnetism in thin films, established magnetic surface trap technologies, and magnetic response to superparamagnetic particles in external fields. Chapter 2 details several experimental techniques used in this study, including photo- and e-beam lithography, methods for prevention of surface adhesion, the electromagnet and solenoid platform using for particle manipulation, and magneto-optic Kerr imaging. Chapter 3 and

Chapter 4 illustrate wire platforms and disk arrays, respectively, and demonstrate their use for particle/cell trapping and transport. Chapter 5 details the use of these techniques to trap and manipulate composite micelle nanoparticles. Chapter 6 discusses

2 micromagnetic modeling and methods used for calculating fields from the patterned magnetic structures. Finally, Chapter 7 will conclude the thesis and provide opportunities for future work.

1.1 Current Force Probe Technologies

Several established techniques are commonly used when controlled application of forces to micro- or nanoscale objects is necessary. This section will discuss three techniques: optical tweezers, atomic force microscopy (AFM) manipulation, and magnetic tweezers. Each offers distinct advantages and disadvantages based on the physical mechanisms underlying the techniques being utilized.

1.1.1 Optical Tweezers

Optical tweezers were developed in the 1970s and 1980s as a method for trapping nanometer to micrometer-sized dielectric particles15,16. Laser light with a Gaussian intensity profile, incident on a dielectric sphere, is refracted such that momentum is transferred to the particle, applying a force toward the focal point of the laser as indicated in Figure 1(a). The resulting trap applies forces proportional in magnitude to the displacement from the trap center (for small displacements), much like an ideal spring.

Soon after their initial development, Ashkin and Dziedzic showed that optical tweezers could be used to trap cells and viruses17 without attaching a peripheral particle, and Block used the technology to probe stepping properties of kinesin motors on microtubule tracks14. Polarized laser light can offer rotational control, in addition to positional control, over birefringent particles (which have different refractive indices depending on lattice

3 direction). For example, an optical torque wrench can apply a torque to crystalline quartz particles for DNA twisting applications18.

While advantageous because of their ability for precise, three dimensional control, lack of need for labeling, and avoidance of direct contact with the specimen, optical tweezers are generally used to manipulate individual, or at most a few, entities.

Sophisticated optics, however, can create optical lattices by which multiplexed manipulation of dozens of particles simultaneously is possible, allowing for light-based sorting of heterogeneous cell and particle solutions19. However, optical lattice techniques offer significantly lower trap strengths than conventional optical tweezers.

1.1.2 Atomic Force Microscopy

Cantilever tips, often used for atomic force microscopy, can also be used to push and assemble particles22, individual molecules such as DNA23 or carbon nanotubes24,25, and biological entities26,27 on a surface. The cantilever tip location is controlled by piezoelectric elements, and hence this technique offers very precise (~nm) positional control. However, the tip must be in extremely close proximity with the object being probed (as seen in Figure 1(b)), and simultaneous experiments are not possible without creating a complex, multi-tipped apparatus.

1.1.3 Magnetic Tweezers

The first published use of magnetic tweezers for biological applications was by

Crick and Hughes in 1950 to stretch and twist living cells using magnetic particles and large permanent magnets to determine the cells’ elastic properties28. Generally, “magnetic tweezers” refers to any device that applies forces or torques to superparamagnetic or ferromagnetic particles via applied magnetic fields and field gradients, for example the apparatus shown in Figure 1(c). Often the source of the fields and gradients is a macroscopic permanent magnet, where the field/gradient is tuned by adjusting the distance to the magnet, though electromagnets or pole pieces can offer additional control21. Magnetic tweezer devices are technologically simple and can apply forces to many particles simultaneously, allowing for the possibility of elaborate multiplexed experimental setups29. However, for studying biological or other non-magnetic entities, it is necessary to attach magnetic particles to the objects being investigated. Furthermore,

5 additional means (generally particle tracking and image analysis) are needed to quantify the force acting on a particle12 because the forces vary greatly with particle location.

A subset of magnetic tweezers is comprised of devices based on magnetic thin films. The films either contain inhomogeneous magnetic domain configurations arising from their composition or are patterned, resulting in strong stray fields and field gradients at particular locations. These stray fields trap magnetic particles, as is discussed in

Section 1.3. The energetic considerations and interactions that govern thin film magnetization and domain structure will be briefly discussed in the following section.

1.2 Magnetism in Thin Films

Domains of uniform magnetization form in ferromagnetic thin films (below the

Curie temperature) without the necessity of an externally applied magnetic field. These domains arise from, and their characteristics are dictated by, several quantum mechanical, magnetostatic, and anisotropic considerations. Here we discuss the energy terms associated four of these considerations: exchange energy, crystalline anisotropy, Zeeman energy, and magnetostatic energy30. The total energy E, is defined as

E = Eexch + Eanis + EZeeman + Emag. (1) and is minimized for a given system.

The exchange energy, Eexch, is the underlying principle behind ferromagnetism and is associated with the tendency of neighboring spins to align in a ferromagnet as a result of the quantum mechanical exchange interaction. As such, any change in orientation of neighboring spins is energetically unfavorable. For a material with

6 magnetization M = Mx xˆ + My yˆ + Mz zˆ , the exchange energy density within a ferromagnetic sample is

A 2 2 2 Eexch = ( M x  M y  M z ) (2) 2 M S where A is the exchange constant in J/m and MS is the saturation magnetization of the material, each parameter being dependent on the material. In typical soft magnetic materials such as permalloy (which is commonly used in devices when a high magnetic moment and easy magnetization reversal is needed), the exchange constant is on the order of 10-11 J/m, and the saturation magnetization is on the order of 1 Tesla.

Crystalline anisotropy, which result from spin-orbit coupling, dictates that magnetization will preferentially align in specific directions relative to the atomic lattice.

For example, in a cubic lattice (with lattice directions along x, y, and z), the energy density contribution is

K1 2 2 2 2 2 2 Eanis = (M x M y  M y M z  M z M x ) (3) 2 M S

3 where K1 is the magnetocrystalline constant in J/m . For a positive K1, the easy

(preferred) axes of magnetization are the x-, y-, and z-axes and the hard axes are the

<1,±1,±1> directions, while for a negative K1, the opposite is true. Crystalline anisotropy has strong effects in magnetic garnet films and monocrystalline cobalt, for example.

However, the thin films studied for this thesis are polycrystalline and hence any effects from crystalline anisotropy are ignored.

The Zeeman energy contribution is the energy associated with the magnetic material and an applied field, H. For permalloy, 1 kOe is sufficient to overwhelm the 7 other energetic contributions and fully magnetize a sample in the direction of the applied field, while a few Oe is not. The energy density contribution is

EZeeman =  0M  H .

The last energetic contribution that is discussed here which dictates the domain structure in a magnetic thin film is the magnetostatic energy (also known as the demagnetizing energy). The magnetostatic energy is a result of dipole-dipole interactions throughout a magnetic sample. The result of the magnetostatic interaction on a ferromagnet is to minimize the effective magnetic charge (locations of nonzero divergence of magnetization) throughout the volume and surface of the material. The energy density associated with magnetostatic energy is calculated by

  0  r  r' 3 r  r' 2  Emag = M(r)    M(r') d r'  nˆ  M(r') d r' (4) 8 V 3 S 3   r  r' r  r'  where the first integral is calculated over the material volume and the second integral is calculated over the material surface. One result of the demagnetizing field is to engender shape anisotropy. Magnetization will preferentially point in the plane of a thin film, along the direction of a wire, and parallel to pattern walls to avoid effective magnetic charge buildup on the material surface.

Table 1 gives approximate values for saturation magnetization and exchange constants for permalloy and cobalt iron, the two magnetic materials relevant for this thesis.

Saturation Magnetization, Exchange Constant, A Material Ms (Oe, A/m) (J/m)

4 5 -12 Permalloy (Ni~0.8Fe~0.2) 1.08  10 , 8.6  10 13 x 10

4 5 -12 Iron Cobalt (Fe0.5Co0.5) ~2  10 , 16  10 14 x 10 Table 1: Saturation magnetization values and exchange constants for permalloy31 and iron-cobalt32–34. Note that the OOMMF User’s guide31 indicates “the material parameter values provided … should not be taken as standard reference values for these materials. These values are only approximate.”

1.3 Surface-Based Magnetic Traps

The interaction between magnetization inhomogeneities on surfaces and magnetic particles has been known since the 1930s, when Frances Bitter used fluid-borne iron oxide particles to map the locations of irregularities of magnetic flux (i.e. stray fields) on ferromagnetic surfaces35, as seen in Figure 2.

The microscopic patterns would respond to application of and changes in applied magnetic fields and were independent of grain boundary locations, suggesting they were mimicking domain wall patterns. This technique for domain characterization, known as the Bitter technique, has been improved upon36 and is still occasionally used37, however, modern domain characterization methods such as magneto-optic Kerr microscopy and magnetic force microscopy has made the Bitter technique unnecessary.

Nonetheless, the stray field/fluid-borne particle interaction has recently been exploited as a technique to trap and manipulate particles. It has been shown that commercially available superparamagnetic particles, micro-scale polystyrene particles encapsulating iron oxide nanoparticles, attract to two-dimensional domain walls in bismuth-substituted ferrite garnet films39,40. The domain walls can be mobilized by application of strong external fields, dragging the particles along. Additional control is exploited by creating a domain wall tip, as seen in Figure 3-I, allowing for precision movement of the magnetic particles in two dimensions.

Patterned magnetic entities have been utilized for similar purposes. Yellen et al. showed that patterned micro-scale disk arrays could be used to trap and maneuver magnetic particles and magnetically-labeled cells41. The disks, 5 μm in diameter, made of cobalt and having a fixed, in-plane magnetization, would create a spatially periodic energy landscape for a magnetic particle. A rotating, out-of-plane, weak (<100 Oe) magnetic field would alter this energy landscape, resulting in controlled manipulation of particles, as seen in Figure 3-II.

In additional to patterns with fixed magnetization, patterned structures with variable magnetization have been used to trap and transport particles controllably along the surface. In general, if the magnetization of an isolated patterned magnetic structure is rotated, a particle will be rotated about the periphery of the structure. However, because of shape anisotropy of the magnetic material, the resulting stray fields at sharp edges are larger than the stray fields at smoother edges, and hence the attractive magnetic force on a particle will also increase. This effect can be utilized to hop particles from one location to another with a continuously-rotating in-plane magnetic field as the driving mechanism.

Such an approach has been utilized by Conroy et al. in teardrop- and saw tooth-shaped structures, and by Gunnarsson et al. in carefully designed oval arrays43, as seen in Figure

3-III.

1.4 Superparamagnetic Particle Response in a Magnetic Field

The magnetic force on a superparamagnetic particle results from both a nonzero magnetic field, which magnetizes the particle, as well as a field gradient which applies a force. The magnetization of a superparamagnetic particle increases linearly for low fields and asymptotically approaches a saturation magnetization at high fields, as is schematically illustrated in Figure 4. For the Fe3O4 nanoparticles that make up the magnetic microspheres used for the research in this thesis, saturation occurs at fields greater than a few kOe, and the range of external fields used in this study (≤ 150 Oe) is contained within the linear region near the origin of Figure 444. Far from saturation, in

12 this linear response region, the magnetic moment m of a superparamagnetic particle in a field H can be approximated as m = χmVH (5) where χm and V are the particle susceptibility and volume respectively.

The equation for the force on a generic point-like paramagnetic object is

F  0 (m)H (6)

46 where µ0 is the magnetic permeability in free space . Combined with (5), this gives the force as a function of the magnetic field H and constants

F  0 mV(H)H (7)

Given the vector identity47

(ab)  (a)b  (b)a a(b) b(a) (8)

13 and equating a = b = H yields

(H2 )  2(H)H  H(H) (9) where the final term is necessarily zero in the absence of free currents. Combining (7) and (9) gives an equation for the force on a particle far from saturation41.

1 2 F  2 0 mV(H ) (10)

From the force energy relation F = −U, the corresponding energy is found to be

1 2 U   2 0 mVH (11) which shows that the energy minimum, and hence trapping location, occurs at locations of highest field magnitude, H. This is generally true as long as M increases monotonically with H.

Chapter 2: Experimental Procedures

2.1 Device Fabrication

The micro- or nano-scale magnetic wires and disks discussed in this thesis were patterned using electron-beam lithography (EBL) or photolithography (PL). Either technique was suitable for devices with feature sizes greater than ~1 μm.

Photolithography is less time consuming and less costly, provided an appropriate photomask is available, so PL is preferred whenever many samples needed to be made simultaneously. In addition, e-beam patterning on glass substrates causes slowly- dissipating pockets of charge to accumulate, deflecting the electron beam and hindering precise patterning. However, for wires with sub-micron features, such as the wires described in Chapter 5, EBL was necessary. In addition, because patterns made by EBL are controlled by a computer program and not a mask, it allows for more versatility in defining patterned features.

A two-layer positive resist procedure [Figure 5] was used to minimize the occurrence of “fences” [Figure 5(d) and (e), left side], unwanted material protruding from pattern edges caused by deposited material forming along sidewalls of the resist. The undercut in the lift-off resist and the overhang in the top resist which form during development [Figure 5(b)], prevent fences by blocking access of deposited material to resist sidewalls. Undercuts can be increased by employing longer resist development

15 times or shorter bake times48. Height profiles of patterned permalloy disks, investigated with atomic force microscopy, show the presence or absence of fences [Figure 5(e)].

Figure 5: Single-layer and two-layer resist procedure. (a) Resists are spin coated onto device, and patterned regions are exposed, either with e-beams or UV light. (b) Device is developed, removing exposed region of resist. (c) Desired material is sputtered onto device. (d) Excess resist and sacrificial material is chemically lifted off, leaving patterned structures. Two layer resist helps prevent occurrence of “fences”. (e) Atomic force microscopy profiles of patterned disks (left) with and (right) without fences. Resist thickness used is generally ~100s of nm, while deposited material thickness is generally ~10s of nm. (Sloping in right side of part (e) due to slight angle of sample.) 16

For e-beam lithography, two layers of e-beam resist (methylmethacrylate and polymethyl methacrylate) were spin-coated at 4500 rpm and each layer was baked at 180 oC for 60 s. Wire or disk patterns were exposed at 280 μC/cm2 using a scanning electron microscope (FEI, Hillsboro, OR, USA) and developed using 1:2 methyl isobutyl ketone : isopropyl alcohol.

For photolithography, a two-layer photoresist procedure was used. LOR3B and

S1813 (MicroChem Corp., Newton, MA, USA) were spin-coated at 3000 rpm and baked at 180 oC and 110 oC, respectively. Patterns were exposed using a contact mask process and developed with 2.5% tetramethylammonium hydroxide developer for 45 s.

The magnetic materials, either Co0.5Fe0.5 for wires or Ni0.8Fe0.2 (permalloy) for disks, were deposited onto the patterned resists on the substrates by magnetron sputtering.

For disk patterns on glass or Mylar substrates, a 1.5 nm titanium layer was deposited prior to permalloy to promote adhesion to the substrate. Excess magnetic material was lifted off by submerging the substrate in 50 oC acetone (for e-beam lithography) or N-

Methyl-2-pyrrolidone remover (for photolithography). (Cobalt iron was used for wires because its higher coercivity allowed the wires to maintain their domain structure in small magnetic fields as discussed in Chapter 3. For disks, a magnetically softer material, such as permalloy, was necessary to allow for easy rotation of disk magnetization.)

2.2 Prevention of Surface Adhesion

Micro- or nano-scale particles or cells adhere easily to surfaces, restricting ease of manipulation. This is exacerbated by surface-based traps, which pull cells toward the

17 surface and further promote sticking. Several techniques were used to prevent unwanted surface adhesion.

2.2.1 Surfactants

When manipulating particles alone in water or buffer, a small amount of surfactant was added to the solution to prevent adhesion. Specifically, nearly 0% of particles with a –COOH (i.e. carboxyl) surface modification are mobile on surface traps when diluted in water or buffer alone. However, upon adding 0.05 - 0.1% by volume

Triton X-100 surfactant (Dow Chemical, Midland, MI, USA), nearly 100% of particles are mobile.

Note that, when the Triton X-100 concentration was increased to 1% by volume, carboxyl particles were again rendered immobile. Additionally, this technique (at 0.05 -

0.1%) failed for particles with antibodies, such as antiCD3 or antiCD20, conjugated to the particle surface. Furthermore, this surfactant is often used to make eukaryotic cell membranes permeable49 or to solubilize membrane proteins50, so a different adhesion prevention technique would be necessary for labeled cell manipulation.

2.2.2 Surface Modifications

Polyethylene glycol (PEG) molecules can be functionalized with thiol (–SH) groups to promote bonding of PEG to gold surfaces. Creation of these PEG monolayers is known to resist nonspecific protein adsorption and to be hydrophilic51. Devices meant for labeled cell manipulation were coated with 20-40 nm Au by magnetron sputtering.

Usually a 1 nm permalloy, titanium, or chromium seed layer was necessary to ensure quality gold-substrate binding. (Note that 1 nm of permalloy is too little to nucleate

18 ferromagnetic domains; the seed layer had no effect on the magnetic traps.) The gold surface is cleaned by UV ozone treatment for ~10 min and submerged in a 1 mM PEG-

SH solution (molecular weight 5000, Laysan Bio, Arab, Alabama, USA) in ethyl alcohol for at least 1 hr, allowing the PEG monolayer to form. The surface is then rinsed in ethyl alcohol and deionized water and dried with an air or nitrogen hose. The successful enactment of the surface treatment is verified by water droplet contact angle. Instead of

PEG-SH, triethylene glycol mono-11-mercaptoundecyl ether could be used following the same procedure and yielding the same results.

2.3 Electromagnet and Solenoid Platform for Manipulation

Controlled manipulation of micro- and nanoscale entities on a patterned sample was actualized by applying magnetic fields via the two pairs of electromagnets and solenoid coil seen in Figure 6(a) and (b). Opposite pole steel core electromagnets (OP-

2025, Magnetech Corp., Novi, MI) were selected to maximize field output at large distances (~4 cm) from the electromagnet face, allowing for in-plane fields of up to about

100 Oe. A machine-wound solenoid (i.e. z-coil) consisting of a few hundred turns of 1 mm-diameter copper wire is placed between the electromagnets with its longitudinal axis perpendicular to the sample. The sample is positioned at the center of the solenoid to maximize the field from the z-coil and to minimize field gradients from both the electromagnets and the z-coil. The z-coil would allow for fields of ~150 Oe.

In this thesis, the in-plane fields from the electromagnets are denoted as either H// or Hxy, and the out-of-plane fields from the z-coil are denoted as Hz.

The configuration allowed for use under a reflective microscope, provided an objective lens could fit above the sample, inside the z-coil. The system is equipped with

10x, 20x, and 40x objectives with large (>2 mm) working distances as well as 63x and

100x oil immersion lenses for fluorescent and other low light applications.

The magnetic fields are controlled and modified by connecting the solenoid and each electromagnet to independent current channels of DC bipolar operational power supplies/amplifiers (Kepco BOP 20-10ML for solenoid, Kepco BOP 20-10ML4886 for electromagnets, Flushing, NY). There are also alternative configurations that we use which do not use bipolar power supplies and instead incorporate relay switches to reverse currents/magnetic fields. The power supplies (and relay switches, if necessary) are controlled by routines programmed in LabView software (National Instruments, Austin,

TX). The routines control the power supplies’ current (as opposed to voltage) output to maintain the desired field output despite increased resistance in the electromagnets or z- coil due to Joule heating. Real-time, user-specified, functionality of the LabView routine is allowed using a video game controller interface, as seen in Figure 6(c). The game controller interface has both direct field control (i.e. field direction mimicking joystick direction) and automated field routines (i.e. field rotation at a user-specified frequency) programmed to respond to various controller inputs.

2.4 Magneto-Optic Kerr Imaging

The Magneto-Optic Kerr Effect (MOKE) is used to image domains in magnetic materials. The MOKE system in our lab was built and operated by group member Aaron

Chen with my assistance. To obtain the MOKE signal from, for example, the Mx component of the in-plane magnetization M = Mx xˆ + My yˆ , y-polarized white light is incident through half of the rear aperture of an objective lens whose central axis is along zˆ so that p-polarized light is obliquely incident on the wire surface (i.e. yz-plane of

21 incidence; see Figure 7 for a schematic of the MOKE setup). The resulting p-polarized component of the reflected light increases or decreases (depending on the direction of Mx) by an amount proportional to Mx due to the transverse MOKE. The analyzer, placed before a CCD camera, transmits only p-polarized reflected light. The image recorded when the medium is magnetized in one direction is subtracted digitally from that recorded with the magnetization in the opposite direction and the resulting spectrum amplified 100-fold. The result is a grayscale image where white-gray-black corresponds to an Mx value that is positive-zero-negative. A similar approach can be implemented to

53 monitor the My component .

Chapter 3: Patterned Wire Traps for Particle and Cell Trapping and Transport

In this chapter, we present results associated with magnetic wire devices used to trap and transport miniature (<10 μm) magnetic particles along programmed routes. The wires are of rectangular cross section patterned onto a surface by standard lithography techniques. Two types of engineered surfaces are discussed for the purpose of creating traps. First, we investigate a technique of using stationary domain walls (DWs) in patterned zigzag wires with regular turns (vertices) for trapping particles. Second, a particle trapping technique based on straight wires with periodic indentations (notches) is studied. In particular, by selecting a high-shape anisotropy design for the notched or zigzag wire and a particular ferromagnetic material (Co0.5Fe0.5), our investigation focuses on conditions where the wire magnetization is substantially unchanged and the DW does not leave the immediate vicinity of the trapping site for low (<100 Oe) external magnetic fields. For the low external fields (~100 Oe) used in this study, the highly localized, large field gradients (>104 T/m) and associated forces arising from the stationary DWs enable individual fluid-borne magnetic particles in the 10 nm to 10 μm range to be steered across the platform in a controlled manner.

The magnetization profiles at the wire vertices and notches are evaluated via micromagnetic simulation (Object Oriented MicroMagnetic Framework, or OOMMF, discussed in more detail in Chapter 6), magneto-optical Kerr effect (MOKE) microscopy, and magnetic force microscopy (MFM). In calculating the forces from the two distinct 23 wire patterns, the net magnetic field and its spatial distribution are determined either as resulting from the micromagnetic magnetization distribution of the wire or by approximating the domain wall/notch as a point charge/point dipole. We consider the applicability of these models to particle manipulation under the experimental conditions reported in this chapter.

The accompanying changes to the energy landscape across the entire platform and the corresponding attractive and repulsive directed forces offer advantages over approaches that rely on properties of mobile magnetization. These benefits include the ability to (a) maneuver and transport particles away from the ferromagnetic wire conduits

(in addition to transporting particles along the wire), (b) generate the required directed forces for transport along specific surface trajectories through weak external fields

(< 150Oe) produced by inexpensive miniature electromagnets, (c) weaken or strengthen the trapping potential to control Brownian fluctuations54 that become more pronounced with diminishing particle size, and (d) multiplex trapping and transport of particle ensembles across a surface, thereby enabling efficient outcomes related to transfer and conveyor applications. In addition, since in this approach the wire magnetization is stationary, the transport mechanism is not encumbered by domain wall pinning at topographic imperfections or defects that could hinder magnetization dynamics.

3.1 Zigzag Wires

Figure 8 illustrates key aspects of the zigzag wire platform: a set of zigzag

Fe0.5Co0.5 wires with stationary domain walls (DWs) located at wire turns [Figure 8(a)]

24 patterned onto a silicon substrate [Figure 8(b)]. Head-to-head (HH) and tail-to-tail (TT) domain walls [Figure 8(a)] are created at neighboring vertices by a momentary in-plane external field (~1 kOe). Upon removing the field, alternating domains form in adjacent segments of the zigzag wire. The localized trapping fields at the wire vertices are evident upon dispensing a solution of Dynabeads M-280 magnetic microspheres (Invitrogen,

Carlsbad, CA, USA) on the platform. The spheres are attracted to and trapped only at the

HH and TT domain walls.

Figure 9(a) shows results of the micromagnetic simulation (see section 6.1) of the equilibrium domain wall structure at the vertex for a 1 μm-wide, 40 nm-thick zigzag wire. The magnetization in the wire arms is found to transition from pointing up-right to up-left. Because of the relatively large width of the wire (compared to ~100 nm-wide wires containing transverse or vortex domain walls), the domain wall cannot be classified as purely transverse or vortex type, but instead consists of multiple transition regions. 25

Figure 9(b) shows an MFM image of light and dark spots at alternating vertices that correspond to HH and TT domain walls, respectively. Figure 9(c) illustrates a magneto-optical Kerr image where the different magnetization orientations within

26 alternate zigzag arms lead to the interchanging bright and dark MOKE signals for the Mx magnetization component. Figure 9(d) shows a dark field image of 2.8-μm diameter magnetic spheres trapped at domain walls at the vertices of the Co0.5Fe0.5 wires.

Note that, for Co0.5Fe0.5 wires, a magnetic field of 5 kOe was used in the MOKE system to attain oppositely magnetized images for image subtraction (see Chapter 2.4).

However, when significantly weaker fields, up to a few hundred Oe, were used, the

MOKE image contrasts would not appear. This feature indicates that a few hundred Oe fields are too weak to remagnetize the Co0.5Fe0.5 wires in this geometry. The lack of such a MOKE contrast suggests that for our experimental conditions (external fields ≤ 150

Oe), the wire magnetization would remain substantially unchanged during particle transport. In contrast, for similar wire-based devices made of permalloy, fields on the order of a few hundreds of Oe were sufficient to significantly remagnetize the wires56–58.

As discussed in Chapter 6, the magnetic fields, gradients, and forces associated with the wires can be calculated either by assuming a point charge at the wire vertex or by modeling the discretized magnetization of the wire.

3.1.1 Particle Transport via External Fields

Figure 10 reveals noteworthy characteristics of an individual trap and its response to external fields. (i) The z-component of the field gradient above the DW rapidly increases beyond 104 T/m in magnitude as the wire surface is approached from above

[Figure 10(a)]. Such high, spatially confined gradients offer a means to manipulate ferromagnetic nanoparticles, despite their low volume magnetization, ranging in size from a few nanometers to 30 nm with pN size forces.

Figure 10: Calculated field gradient, force, and energy profiles from a 1000 nm-wide domain wall localized on a 40 nm-thick, 1 μm-wide Co0.5Fe0.5 wire. (a) Magnetic field gradients above the wire based on point charge (solid line) model and micromagnetic simulation (dashed line) increase rapidly above 104 T/m as distance z to the domain wall decreases. (b) Variation of axial force Fz determined from point charge model on a magnetic bead (volume susceptibility, χ = 0.85) lying 1.42 μm above domain wall with external field Hz. (c)-(f) Potential energy profiles transform from attractive (c)-(e) to max repulsive (f) by changing Hz further negative. Calculated maximum force Fx along length of wire shows its tunability with Hz. Note for distances z > 1300 nm relevant to this study, the magnetic energies are not sensitive to the precise magnetization profiles within the domain wall55.

As shown in Figure 10(a), both a point charge-based and a micromagnetic-based model yield similar calculations for field gradients at a height of 1.4 μm (radius of a standard microsphere) above the wall, showing our results are essentially independent of the wall model at such heights. (ii) A weak perpendicular external field Hz (~50 Oe) can augment or diminish the fields near HH and TT walls and thereby tune traps attractive or repulsive - thus targeted objects can be manipulated at tunable distances from the wall

[Figure 10(b) - (f)]. (iii) The magnitude of Fz is tunable to hundreds of picoNewtons

[Figure 10(b)], larger than the ~20 pN limit for 2.8 μm diameter particles widely used in

59 magnetic tweezers . (iv) In the absence of H// and Hz, HDW localizes individual particles at wire vertices [Figure 10(c)].

The mechanism for tuning trap strengths and rendering vertices repulsive results from the realignment of the particle dipole moments by external fields. External fields used in this study are too weak to significantly remagnetize the wire patterns. However, a trapped particle, already magnetized by the local fields from the wire, can be further magnetized by externally applied fields so that its magnetic moment is strengthened in the direction of the local stray fields, creating a stronger trap as seen in Figure 10(d).

Similarly, if the external field direction is switched, the particle can be magnetized counter to the local stray field, rendering the location repulsive as seen in Figure 10(f).

Applying and systematically changing in-plane and out-of-plane fields allows for programmable means of applying tunable forces and directing particle motion as specified locations along and near patterned structures are switched from attractive to repulsive.

Figure 11 highlights the forward motion of a particle by showing how it is assisted by inverting the energy landscape along the wire. The applicable structure and field geometries are shown in Figure 11(a). Figure 11(b)-(f) are calculated magnetic energy profiles for a 2.8 μm-diameter bead in the presence of HDW, Hz, and H//. In Figure

11(b), the energy minimum is centered above the HH vertex. Upon reversing Hz (while

H// remains unchanged), the HH trap at the origin transforms to a repulsive site while 30 moving the energy minimum towards the neighboring TT vertex. The local energy minimum is guided, as shown in Figure 11(d), towards the TT site by reversing H//. Upon alternating the sequence of Hz and H// fields, the particle reaches the TT trap at an average speed of 20 μm/s. Insets in Figure 11(b)–(f) show photographs of the microsphere and their direct correspondence to the mobile energy minimum.

Figure 12: Left column: Calculated potential energy landscapes of zigzag wire, where brighter shades in grayscale background image indicate lower potential energy (i.e. trap). Right column: Images of 2.8-μm- diameter magnetic particles trapped at corresponding vertices and subseq- uently maneuvered in response to changing fields Hxy and Hz. (a) and (b) In the absence of an external field, both HH and TT domain walls are traps for the superparamagnetic particles. The scale bars represent 10 microns. (c) The combination of Hz = 120 Oe and Hxy = 25 Oe fields render some vertices to remain as traps while others transform to repulsive sites. (d), (f), (h), and (j) Two magnetic particles manipulated from one wire to the next and back based on the magnetic field sequence indicated by white arrows in (c), (e), (g), and (i), respectively. Inverting the magnetic field sequence reverses the direction of particle transport. Energy minima associated with secondary traps, only present under external fields, are too weak to be evident in the grayscale energy landscapes45.

Figure 12 presents the calculated grayscale potential energy landscapes (left column) associated with a 2.8 μm-diameter microparticle in the presence of this Co0.5Fe0.5 wire, as well as images related to corresponding experimental particle manipulation (right column). The calculated potential energy landscapes are based on point charge approximations of the vertices. Figure 12(a) shows calculated potential energy landscapes of the trapping platform with the brighter shade representing lower energy. As indicated

[Figure 12(a)], in the absence of an external field, low energy sites (i.e. traps) arise at both HH and TT domain walls [Figure 12 (b)] for superparamagnetic microparticles.

Application of an external field Hz = 120 Oe directed perpendicular to the platform plane creates repulsive centers (dark spots) at alternating vertices evident in

Figure 12(c), (e), (g), and (i). An in-plane field Hx, Hy creates a secondary trap away from the wire, displaced a few microns from these repulsive centers, where the line connecting the vertex (domain wall) and this secondary trap is parallel to the direction of the net in- plane field Hxy = Hx xˆ + Hy yˆ . Note that due to the shallowness of the secondary traps, they are not directly visible in the grayscale energy landscape plots of Figure 12. The occurrence of the secondary trap and its response to external fields are however more clearly illustrated in Figure 13. The location of the secondary trap thus specifies the direction in which the particle is steered from the vertex [Figure 13(a), Hxy = 50 Oe

(black arrows) and Hz = 120 Oe (circles with enclosed “X”s)]. In the absence of an in- plane applied field, the secondary minimum does not exist. The characteristics of the secondary trap (depth, width, and location) are tunable by the external in-plane field. For example, using the point charge model discussed in Chapter 6, Figure 13(b) illustrates the

32 secondary trap for Hz = 120 Oe and Hxy = 25 Oe, 50 Oe, and 75 Oe, that respectively lead to increasing trap depth and decreasing trap width. This correlation between field strength and trap features is consistent with observed particle manipulation results. For instance, for manipulation over long distances (>10 micron) shown in Figure 12, a weak, in-plane

ﬁeld Hxy = 25 Oe was used to weaken the deep confining potential (ΔU >> kBT) and ensure that the particle could be maneuvered along the platform plane to an adjacent vertex.

In Figure 12(c) (Hz = 120 Oe and Hxy = 25 Oe), the point charge model reveals traps at HH walls (white spots) and repulsive sites at TT domain walls (dark spots).

Correspondingly, magnetic particles are trapped only at HH domain walls [Figure 12(d)].

Upon reversing Hz, the HH domain walls become repulsive [Figure 12(e)], and the trapped particles are steered to secondary traps upward and to the right of the vertices

[Figure 12(f)] to be captured by the TT domain wall [Figure 12(h)]. Reorienting Hx, Hy

[Figure 12(g)] redirects the particles in preparation for transport to a new set of vertices.

Once again, reversing the direction of Hz switches traps and repulsive centers [Figure

12(i)], and the particles are transported down and to the right to be trapped at HH domain walls [Figure 12(j)]. The general rightward trajectory of particle movement is dictated by the sequence in which the external fields are applied. Inverting the sequence reverses the particle trajectory.

3.1.2 Cell Transport

Figure 14 shows transporting examples of T-lymphocyte cells. Previously separated T cells (CD3 positive) from human blood6 were labeled with 1 μm anti-CD3- conjugated microspheres. Figure 14(a) shows the movement of several T-lymphocyte cells above the wire by a sequence of alternating 60 Oe H// and Hz fields. Guided by the wire, the remotely directed forces move these cells with an average speed of 20 μm/sec from one vertex to the next and beyond by the same set of steps detailed for Figure 11.

The trajectory can be reversed by reordering the sequence of the H// and Hz fields.

Figure 14(b) illustrates a T-lymphocyte cell transported away from a wire and returning further along the same wire. Depending on the domain wall (HH or TT), the route and directional forces are regulated by orienting H// (60 Oe) parallel or antiparallel to the desired planar direction of movement on the platform. Moreover, although the

34 influence of HDW diminishes from the wires and Brownian motion of the microspheres becomes clearly noticeable, the fluid-borne microsphere or cell can be held suspended away from the vertex for tens of minutes.

Recording ≡ of the particle using tracking software provides a direct

2 −1 measure of the trap stiffness (~2kBT ) at temperature T. For example, the average rms fluctuation ½ of a 2.8 μm sphere over 2 min was reduced from 2.25 μm when the sphere is far from the trap to 0.54 μm at a distance of 5 μm from the vertex for Hz = H// =

20 Oe. This reduction confirms that the experimentally determined 2.8  10−2 pN/μm stiffness of a trap located 5 μm from the wire vertex has an observable effect in suppressing Brownian fluctuations through non-contact confinement of fluid-borne microparticles.

Figure 14(d) illustrates the correlated motion of five T-lymphocyte cells from adjacent vertices on one wire to those on the neighboring wire and their return to the first, each shifted one vertex. Reversing Hz transforms an attractive HH wall on one wire repulsive while the cells are transported to an attractive TT trap on the neighboring wire, much like for particles in Figure 12. With in-plane trajectories controlled by H//, multiple cells or particles are maneuvered in unison between vertices on separated wires at an average speed of ~10 μm/s.

Figure 15 demonstrates additional versatility of this manipulation technique. After a solution of magnetically-labeled T-lymphocyte cells is introduced onto the substrate, 12 cells are maneuvered to the top of the wire array. (Five are temporarily immobilized.)

The result, an assembled horizontal line of cells, is seen in Figure 15(a). Using the same sequence of alternating external fields illustrated in Figure 14(a), the cells are then maneuvered downward along the wire tracks [Figure 15(b,c)] until 15 of 17 cells are aligned at the bottom edge of the wire array [Figure 15(d)]. This technique shows both

36 how a large number of cells can be manipulated simultaneously and how those cells can be assembled into designed patterns. Note some cells temporarily adhere to and detach from the surface, resulting in slight non-uniformity of their motion.

3.1.3 Wire Traps on Alternative Substrates

In addition to rigid silicon substrates, microscopic devices for particle trapping and transport were fabricated onto Mylar, a polystyrene film. Shown in Figure 16,

Co0.5Fe0.5 zigzag wires were patterned onto a 100 μm-thick Mylar film using the photolithography process described in Section 2.1. The wire array was magnetized to create alternating head-to-head and tail-to-tail domain walls at adjacent vertices. Each domain wall type acts as a trap for magnetic particles [Figure 16(a)], similar to previously mentioned silicon-based devices. By applying a sequence of varying fields (detailed earlier in this chapter), we demonstrate controlled motion of 8 μm magnetic particles along a wire as seen in Figure 16(b)-(g).

The flexible and transparent properties of Mylar films have several advantages over rigid materials. The polymeric nature of Mylar and its general bio-compatible 38 characteristics offer the potential for in-vivo adaption of the magnetic transport technology presented. Moreover, the magnetically patterned Mylar film can be easily cut into replaceable strips of required dimensions that could be readily inserted into pre- existing microfluidic platforms. Integration of such low-cost, thin transparent flexible templates with micro- and nano-scale measurement devices offers optical access, real time tracking with regular or inverted microscopes, and convenience of remotely directed transport without delicate electrode configurations.

3.2 Straight Notched Wire Traps

Straight wires with periodic notches patterned along its length on alternate edges were investigated. Results of several OOMMF simulations, each representing a different initial wire magnetization, are shown in Figure 17. The simulations apply to a 1 μm-wide,

40 nm-thick straight Co0.5Fe0.5 wire with a single notch on one edge that extends inward by a length equal to one third of the width.

The initial constant magnetization, M0, used in the micromagnetic simulations is used to mimic the effect of placing the device in a constant saturating field before the magnetization is allowed to relax at zero applied field. (See section 6.1 for more information about micromagnetic simulations.) Simulations suggest that for notched wires, the direction of initial magnetization (or saturating field) plays a critical role in the final wire magnetization. For example, for an initial magnetization which is perfectly perpendicular to the wire [θ = 90.0°, Figure 17(a)], the simulation results in a domain wall structure at the notch (in this case, a TT domain wall). However, if the angle differs

39 from perpendicular by 0.1° [θ = 89.9°, Figure 17(b)], the DW is not as well formed. The micromagnetic results for M0 which is 0.2° off perpendicular [θ = 89.8°, Figure 17(c)] do not differ greatly from the results of magnetizing wire along the direction of the wire [θ =

0.0°, Figure 17(d)].

Because of the experimental difficulty in producing consistent domain walls implied by the micromagnetic simulations in Figure 17, we focused on notched wires with magnetization mostly in the direction of the wires as in Figure 17(d).

Similar to the case of zigzag wires, the straight wire was momentarily magnetized by a 5 kOe field, however, in this instance in the +x direction, resulting in a mostly uniform magnetization along the length of the straight wire [Figure 18(a)]. The magnetization realigns at the notch to contour with the wire edge, creating regions of changing magnetization, which coincide with locations of particle traps. Figure 18(b) shows two 2.8 μm-diameter magnetic particles trapped at notches in straight Co0.5Fe0.5 wires. Magnetic force microscopy imaging [Figure 18(c)] shows dark/light spots to the left/right of each notch, indicating that the magnetic configuration in the immediate vicinity of the notch is consistent with approximating each notch as a magnetic dipole

(see Section 6.2.1), which gives the repulsive/attractive energy contour in Figure 19.

In the absence of external fields, a particle is trapped in the vicinity of a notch.

Under the application of ~100 Oe fields, trapping locations can be moved (despite the magnetization profile remaining substantially unchanged). Figure 19 shows a 4.5 μm- diameter particle tracking the location of the calculated local potential minima for the prescribed external field orientation when it is steered from left to right along the wire by sequencing the external fields. As with the zigzag wires, when the order of field applications is reversed, the particle is transported in the opposite direction.

3.3 Wire Trap Calculations

Figure 20(a) and (b) illustrate the calculated magnetic field as a function of height z directly above the center of a vertex or notch. The thick, dotted, and thin lines representing the point charge/dipole, dipole distribution, and charge distribution models respectively, yield similar results for heights in the range ~2 μm  z  ~10 μm. As explained in Section 6.2.1, the point source models do not take into account the specific microscopic magnetization configuration, but rather approximate the profile by a monopole-like point charge qm or a point dipole md. This approximation accounts for the deviations evident for z < 2 m in the point source-derived field values from those based on the more realistic dipole- and charge- distribution models.

In comparing near-source (z < 500 nm) magnetic fields from domain wall (zigzag) traps and notch traps, they are calculated to be within an order of magnitude of each other. However, as dipole fields, the notch field decreases significantly faster (~1/r3) than the domain wall fields (1/r2). The corresponding field gradients (d|B|/dz) above the vertex/notch are illustrated in Figure 20(c) and (d). Field gradients from domain wall

(zigzag) traps are found to rise well above 104 T/m for z < 1000 nm. This is an important characteristic for trapping and manipulating low volume magnetic particles (<100 nm in diameter) which are susceptible to fluid drag forces and Brownian motion61. Figure 20(e) and (f) show the vertical component of the force (Fz) on a 2.8 m-diameter particle (χm =

0.85) as a function of height z above the vertex/notch. The plot shows that, when localized at the domain wall (z = 1.4 μm), the trapping force is several hundred picoNewtons (pN), while the forces associated with notch traps are significantly lower at

44 a few pN. As comparison, a stationary 2.8-μm diameter particle in 100 m/s fluid flow experiences a drag force of about 2 pN, while a DNA molecule, tethered to a magnetic particle and fully extended by magnetic tweezers, results in a recoil force that ranges between 0 - 20 pN.12

Similarly, fields, gradients, and forces were investigated for varying patterned wire thicknesses and widths. The vertex of a zigzag wire was simulated using micromagnetic software, and fields were calculated using the charge distribution model.

The left column of Figure 21 illustrates the dependence of fields, gradients, and forces on zigzag wire thickness. Fields and gradients are calculated 1.4 μm (the radius of a standard-sized bead) above the vertex of a 1 μm-wide Co0.5Fe0.5 zigzag wire. The force on a 2.8 μm-diameter bead of magnetic susceptibility 0.85 was also calculated. For wire thicknesses much less than the particle size, fields and gradients increase linearly with wire thickness, and the force increases as the square of the wire thickness. (Slight deviation from linear in field and gradient calculations occurs because wire thickness begins to approach the length scale of the magnetic bead.)

As seen in the right column of Figure 21, fields, gradients, and forces were calculated for a similar system, however for varying wire widths and a constant wire thickness of 40 nm. (All other parameters were identical.) The relation between these quantities and wire width is not as direct as for wire thickness, but the model does suggest an optimal wire width of about 1 μm for maximizing trapping forces (specific for a 2.8 μm-diameter bead). Nonetheless, the wire thickness is the more relevant parameter when calibrating trapping forces in patterned magnetic traps.

We note that the robustness of this experimental ferromagnetic wire-based manipulation scheme will depend on the stability of the magnetic properties of the fabricated wires. For example oxidation of the metal or repeated use of the platform could lead to changes in the magnetic characteristics of the wire. In particular, if the saturation magnetization were modified by a multiplicative factor  then, while the field and field gradient would be altered by the same factor, the magnetic force would change

2 by a factor  of the original value. Thus a 10% degradation in Ms for example would

47 lead to a more substantial 19% reduction in the trapping force Fz. Experiments based on observing particle trapping in the presence of controlled fluid flow, tracking particle fluctuations while at trapping locations, and stretching DNA with well-known force extension curves (now a metrology standard62) while in the vicinity of traps could be used to verify the calculated forces.

3.4 Integrated Optical-Magnetic Tweezers for Cell Manipulation

The feasibility of using a wire-based magnetic platform in conjunction with optical tweezers was tested for the purpose of demonstrating control over cell-antibody binding. Co0.5Fe0.5 wires 2 μm wide and 40 nm thick were patterned onto a glass cover slip, approximately 0.1 mm thick, using e-beam lithography. A transparent substrate is necessary to allow transmission of the laser used for the optical trap.

The optical tweezer apparatus, operated by Andrew Morss in the group of

Professor Greg Lafyatis, consists of an inverted microscope, a ~100 – 1,500 milliwatt infrared laser, and a 100x oil immersion objective lens. A cell is held in an optical trap and is able to be maneuvered with respect to the surface. Because of the limited space availability atop and around the objective lens, no external fields were applied.

Figure 22 shows three magnetic particles, each conjugated with antiCD20 antibodies, trapped near the endpoint of a Co0.5Fe0.5 wire. (The additional magnetic particle, several micrometers from the wire, is adhered to the surface.) The wire, magnetized primarily parallel to the segment of the wire, experiences an abrupt change in magnetization near the endpoint of the wire such that the magnetization near the

48 boundary edge of the wire is parallel to the boundary edge. This region, like a domain wall or notch, contains a strong effective magnetic charge and hence acts as a trap even in the absence of an applied field.

Figure 22: First row: Via optical trap, a Raji cell is brought in contact with an antiCD20- conjugated magnetic particle trapped at the endpoint of a Co0.5Fe0.5 wire. Green dot denotes approximate location of laser focal point/optical trap. Second row: The focal point is maneuvered away from the bead/wire, but the cell is held in place adjacent to the bead, presumably by antibody binding.

A Raji cell is brought near one of the trapped particles (Figure 22, top row) by the optical trap. Upon contact, the cell binds to the magnetic particle. Upon moving the focal point (green dot) downward, the force adhering the cell to the bead is greater than the optical force pulling the cell, and the cell remains near the magnetic trap (Figure 22, 49 bottom row). A subsequent attempt to remove the cell via optical tweezer dislodges the cell from the magnetic particle and the cell is mobile, indicating that the cell/bead binding force is comparable to the optical trapping force. Note that the failure to remove the cell does not necessarily imply that the optical trap is weaker than the magnetic trap, and that the dislodging of the cell from the particle does not imply that the magnetic trapping is stronger than the antibody binding. We suspect that the magnetic particle’s adherence to the surface is partially due to magnetic trapping and partially due to chemical adhesion between the particle and the surface.

For this experiment, the laser output power was 1500 mW. At the sample, the power had been reduced to approximately 600 mW due to losses in the optics. A laser at this power focused onto the patterned metal structure will ablate the local region of the metal as shown in Figure 23. This effect creates local heating and turbulence which eliminates control of particles or cells, creating difficulty for an integrated optical- magnetic tweezer experiment under the present conditions.

If the optical tweezer and magnetic trapping forces are known, this experimental scenario could be used for quantitative studies of antibody binding forces by pulling apart composite structures bound together by antibodies. Possibilities for the constituents of the composite structures include cells and magnetic particles as described above or magnetic and polystyrene synthetic particles conjugated with the necessary antibody-antigen combinations. Similarly, by using DNA as a tether between two particles, the length of an optically stretched DNA molecule would indicate the force holding a particle in place62.

By eliminating non-specific surface adhesion, this method would indicate the magnetic force on the particle.

3.5 Summary of Wire-Based Techniques

In this chapter we have demonstrated a technique for trapping magnetic particles and magnetically-labeled cells at microscopic vertices and notches in patterned wires with the ability to remotely manipulate them through weak external magnetic fields.

Unlike many other approaches where the particle transport is restricted to conduits along which the DW motion occurs, in the present study, the magnetic domain walls and profiles associated with the wires remain essentially stationary as the particles are maneuvered across the platform along trajectories that are not restricted to the wires. The calculation results detailed in this chapter provide qualitative explanations of some of the more subtle characteristics, such as the ability to (i) steer particles with weak external fields (< 150 Oe) away from the wires or along them in predetermined directions, (ii) localize the fluid-borne particles within a trap for extended time periods (tens of

51 minutes), and (iii) provide rapid particle transit times that are limited only by protocols that modulate the external fields and the fluid environment.

While the magnetic fields and their gradients emanating from the miniature surface profiles play a central role in steering the particles across a surface, use of standard optical or e-beam lithography methods allow for large numbers of traps to be fabricated on a single device. Furthermore, since the weak external magnetic fields necessary for manipulation generally do not interfere with chemical or biological interactions, this approach has the potential for wide ranging applications. These features thus lend themselves to be integrated into microfluidic devices for biological cell55,56,63 and microparticle sorters, as well as next-generation biomedical devices. For instance, we envision scale up for transporting ~106 magnetic particles on a single centimeter-sized platform. Moreover, by conjugating magnetic particles to a biological cell, these tethered entities could be steered to a location-specific stimulus for eventual interrogation. The potential for large-scale multiplex operation would also offer this technique as an attractive approach for rapid sequential analysis operations that do not rely on ensemble averaging.

Chapter 4: Discrete Patterned Magnetic Elements for Particle and Cell Transport

We also employ reprogrammable magnetization profiles created through lithographically patterned discrete ferromagnetic disks as a template for producing highly localized trapping fields. Underpinning this technique, which was developed and carried out in close collaboration with group members Thomas Henighan and Aaron Chen, are patterned permalloy disks, which in a weak in-plane field (|B| ≈ 50 Oe) will be magnetized generally in the direction of the field [Figure 24].

Figure 24: Micromagnetic simulation of the magnetization of a 40 nm-thick, 5 μm-wide magnetic disk in the presence of an in-plane, 50 Oe field.

The resulting magnetic field gradients, occurring primarily on opposite edges of the disk periphery, enable directed forces to be applied to (1) non-biological magnetic microspheres, (2) immunomagnetically labeled biological cells, and (3) magnetic microspheres that act as magnetically actuated miniature force-transmitting probes to navigate fluid-borne unlabeled cells with micrometer precision. The principal features of

53 this study are demonstrated by remotely transporting and arranging multiple or individual

T-lymphocyte and leukemia cells using joystick-controlled programmed routines. The forces are shown to transport particles with speeds up to 225 μm/s across a platform to predetermined sites.

4.1 Disk Trap Profiles and Tunability

Figure 25 and Figure 26 illustrate the calculated energy, trapping fields, and forces associated with a magnetic microparticle trapped by a permalloy disk 5 μm in diameter and 40 nm thick. The disk magnetization is approximated by micromagnetic simulation as seen in Figure 24, and the resulting traps are demonstrated for different external fields Hx and Hy, as well as their tunability with Hz. Figure 25(a)-(c) shows the potential energy profiles for different in-plane field directions for Hz = 50 Oe. The sharp potential energy minimum moves along the outer disk periphery tracking synchronously with the direction of the in-plane field. Figure 25(d)-(f), shows images of a magnetic microsphere trapped and transported along with the energy minimum around the disk.

With Hz = 0 [Figure 26(a)], two traps, A and B, are located near diametrically opposite ends parallel to the in-plane field Hx. Figure 26(a) and (b), show that these two traps are approximately symmetric for Hz = 0. The lack of complete symmetry of the energy profile of traps A and B arises from the magnetization of the disk being not perfectly symmetric in the OOMMF simulation. The introduction of an axial field, Hz

(+50 Oe), directed upward from the substrate, renders trap B more attractive, at the same

54 time weakening trap A [Figure 26(c)]. Reversing Hz (–50 Oe) inverts the character of traps A and B [Figure 26(c)], which illustrates the tunability of trapping forces.

4.2 Cell Manipulation on Disk Arrays

4.2.1 Labeled Cells

Figure 27(a) and (b) show transporting examples of labeled T-lymphocyte cells.

The directional forces are regulated by the clockwise or counterclockwise rotation in 90° steps of the in-plane field (60 Oe) and timed reversal of Hz. The tethered cells are made to hop from one disk to the next by reversing Hz, creating an attractive trapping center on the targeted disk, and the trajectory is reversed by reordering the sequence of the planar

(Hx, Hy) and Hz fields. The controlled navigation of single [Figure 27(a)] and multiple

[Figure 27(b)] tethered T-lymphocyte cells traveling at an average speed of 20 μm/s illustrates the labeled cell following the magnetic potential well (as in Figure 25) as it is manipulated along the surface.

The Reynolds number, Re, is a dimensionless quantity which dictates the deterioration a fluid will have on an object traveling through it. A higher Re implies more impact on the object, for example, by fluid-induced shedding on the object surface. The particle Reynolds number is given by Re = VL/ν, where V is the object velocity, L is the characteristic length scale, (in this case, the cell diameter), and ν is the kinematic viscosity of the fluid (~1 mm2/s for water). Re for a cell (12 μm in diameter) traveling at

20 μm/s is ~2.4  10-4. The effect of the resulting hydrodynamic forces arising from the induced movement of cells is negligible. For example, Gregoriades et al. demonstrated that it took flow through a flow contraction with a corresponding Reynolds number of

323 to remove Chinese hamster ovary cells attached to 200 μm microcarriers65. Later,

Mollet et al. experimentally demonstrated that flow through a 225-mm contraction at 21.7

57 m/s, corresponding to a Reynolds number of 8146, was required before detectable damage to suspended Chinese hamster ovary cells is observed66.

4.2.2 Label-Free Manipulation

Figure 27 (c)-(e) illustrates the manipulation of living leukemia cells without attachment of a magnetic microsphere. This feature overcomes a limitation of standard magnetic tweezer-based cell manipulation schemes – namely, attachment of magnetic beads that may affect the cells’ intrinsic properties. Figure 27(c) shows six leukemia cells sequentially maneuvered by a microsphere into a hexagonal pattern on the surface. To have greater regulation of the cell movement, Figure 27(d) illustrates two magnetic spheres acting as a pair of handles to navigate a cell in a controlled manner. Figure 27(e) illustrates several microspheres around a leukemia cell, which is then navigated by the multiple spheres. Direct measurements of the microsphere speed show the transmitted forces that overcome drag on the cells to be on the order of several tens of picoNewtons.

4.2.3 Instantaneous Labeling

It was shown that on the magnetic disk platform, cell labeling can occur in situ in timescales on the order of a few seconds, assisted by particle manipulation on disk arrays.

This is demonstrated for the case of Jurkat cells and antiCD3-conjugated particles. Jurkat cells are grown from a cultured leukemia cell line and express the CD3 antigen. An array of 10 μm diameter Permalloy disks [Figure 28(a)] is magnetized by a 60 Oe external magnetic field prior to depositing a solution of 2.8 μm magnetic microspheres conjugated with anti-CD3 [Figure 28(b), dark dots]. The spheres, in saline solution, are trapped at the periphery of the disks. When Jurkat cells [Figure 28(c), gray circles] are introduced, they rapidly conjugate upon contact with the magnetic particles (within 10 seconds).

Figure 28: (a) An array of 10 μm-diameter permalloy disks on a silicon surface. (b) In the presence of an in-plane field, magnetic beads deposited on the platform are attracted to trapping sites on peripheries of disks. (c) Jurkat cells, introduced at t = 0, attach upon contact to beads with antiCD3 antibody, observed at t ≈ 10 s. (d) Cells are maneuvered around disks by rotating in-plane magnetic field. (e) Cells are transported downward across disk array by sequence of rotating in-plane field and switching out-of-plane field. Note that labeled cells trail motion of maneuvered particles. (f) After t ≈ 60 s, excess cell labeling occurs, creating particle-cell aggregates. (Note that (a) – (e) are one location, )

Programmable in-plane external fields maneuver the magnetic traps around the disks [Figure 28(d)], thereby moving the particles and labeled cells around the periphery.

Cells can be further manipulated across the disk array [Figure 28(e)]. Note that for cells labeled with single particles, the particle is manipulated by the magnetic traps, and the cells follow behind the particles, restrained by fluid drag. The user utilized the manipulation procedure to collide magnetic particles with unlabeled cells to promote labeling. After ~60 s, excess cell labeling occurred, resulting in large particle-cell

60 aggregates. Particles at different locations on these aggregates can experience competing forces from different disks in the array, resulting in hindered cell manipulation.

4.3 Characterization of Particle Transport Speed on Disk Arrays

Magnetic particles were transported across disk arrays to investigate response velocities at various transport frequencies (defined in the following paragraph). Transport frequency experiments were performed in our lab by group member Tom Byvank. Past a critical frequency, the mobile trap is transported at too high a velocity, and fluid drag prevents the particle from staying synchronized with the trap. This critical velocity gives an indication of the magnetic force associated with the magnetic traps. Transport was investigated with –COOH (i.e. carboxyl) modified 8 μm-diameter superparamagnetic microspheres (UMC4N/10150, Bangs Laboratories, Inc., Fishers, IN, USA), diluted in

0.1% Triton X-100 (Dow Chemical, Midland, MI, USA) detergent to prevent surface adhesion.

The transport frequency is calculated based on two experimental parameters, rotation time and hopping time, denoted by tr and tw, respectively. Here tr is the total time for the 180 degree rotation of the in-plane field. The out-of-plane field is switched a time period tw/2 after rotation is completed. The protocol waits another tw/2 before repeating the rotation sequence. The linear speed of particle motion, determined by averaging the speed over dozens of disks, was controlled by the transport frequency, calculated as f =

1/(tr+tw).

A limiting factor for the maximum transport speed is the rotation time tr. For too small tr, the particle stalls because hydrodynamic drag inhibits the magnetically driven motion along the disk periphery. Furthermore, even with uninterrupted field rotation

(tw = 0), when the out-of-plane field is switched, for a sufficiently slow field rotation, the particle can reach the nearest trap on the adjacent disk before the trap leaves the local vicinity. However, if the field rotation is too fast (tr too small), the particle is likely to remain on the original disk thereby stalling its motion. For a given transport frequency, the rotation time tr was chosen to optimize the average velocity. For example, (1) tr = 0.1 s and tw = 0.01 s and (2) tr = 0.01 s and tw = 0.1 s, would both result in f ≈ 9.1 Hz.

However, since rotation is the limiting component of transport, scenario (1) permitted a faster linear speed than scenario (2) which is more prone to stalling.

As plotted in Figure 29, particle transport was investigated on multiple substrate materials. Each data series represented the same disk array structure: 40 nm permalloy disks of 10 μm diameter with 5 μm spacing between disks. The particle speed increases linearly in f with a slope of ~15 μm/s/Hz, which closely corresponds to the center-to- center spacing of the disks (15 μm). Beyond the critical frequency of about 10 Hz, the linear speed decreases steadily until the particle completely stalls at f ≈ 25 Hz. Maximum particle transport speeds were approximately equal for Mylar, SiO2 on Si, and Au on

Cr/SiO2/Si, with Mylar giving a slightly larger speed (150 μm/s), while that on glass was significantly lower (94 μm/s).

Particle transport was also investigated on disk arrays of 84 nm height (in addition to 40 nm), providing more magnetic material and correspondingly, larger magnetic 63 forces. Additionally, applying a hydrophobic surface treatment (Sigmacote; Sigma-

Aldrich, St. Louis, MO, USA) was observed to improve the transport. The same transport frequency and corresponding rotation and hopping times were used as for the untreated surface. As depicted in Figure 30, the critical frequency and maximum speed of particle transport on untreated 84 nm thick disks increases modestly from 10 to 11.1 Hz and 150 to 157 μm/s when compared to the 40 nm disks on Mylar. Application of the surface treatment leads to a larger improvement for 84 nm disks, shifting the critical frequency to

16.7 Hz and linear speed to 225 μm/s. These responses indicate that optimizing the surface chemistry to minimize adhesion has a more significant role in increasing transport speed than modest increases to the magnetic force.

The hydrodynamic drag force on an 8 μm diameter particle rotating around a 10

μm diameter disk with tr = 0.1 s is 12 pN, whereas rotation with tr = 0.01 s corresponds to

67 a force of 120 pN as given by Stokes’ Law Fd = 6πηRv where η is the fluid’s dynamic viscosity, R the particle radius, and v the particle speed. At the velocity at which the particle motion stalls, the hydrodynamic drag force equals the magnetic manipulation force. We find that a fluid drag force of approximately 100 pN is required to overcome the magnetic manipulation force along the periphery of the disk.

4.4 Triangular Elements for Particle Trapping and Manipulation

Trapping strength from a patterned magnetic entity differs depending on the shape of the patterned structure. For example, a pattern with a sharp point will contain a very large, localized effective magnetic charge due to constriction of the magnetization, as

64 seen in Figure 31(a). The result is a significantly higher magnetic field and field gradient originating from the sharp point than from a smooth edge, for example in a perfectly round magnetic disk.

To illustrate this, we model a 60 nm-thick permalloy equilateral triangle with a side of length 6 μm in an in-plane 100 Oe magnetic field and compare it to a 6 μm- diameter disk of the same thickness composition, and applied field. The simulated magnetization vector plot is shown for the tip of the structure in Figure 31(a). (The magnetization structure for a disk would be similar to that shown in Figure 24.)

Based on calculations utilizing the micromagnetic simulations, the magnetic fields and field gradients are significantly higher above the vertex of the triangle than for a smoother edge associated with a similarly-sized disk (Figure 31(b) and (c)). Similarly, the force on a particle would also be higher at a sharp point; Figure 31(d) shows the calculated comparison between forces on a 0.5 μm-diameter particle from a triangle point and a disk periphery.

This augmented trapping force is exploited to transport particles on a surface without the assistance of an out-of-plane magnetic field. Similar to several previously reported techniques which utilize magnetic teardrop, saw-tooth42, and oval43 structures, the location selectivity allowed by the pattern shape has the added benefit of simultaneous multidirectional control by the process detailed below.

A magnetic particle trapped at a triangle vertex while in an in-plane field will experience a strong attractive force. Upon rotating the field 180 degrees, the particle will either traverse the perimeter of the triangle or hop from vertex to vertex until the new trapping location will be on a flat edge. This trap would be weak compared to a vertex trap. However, an adjacent triangle with a nearby vertex will be preferentially attractive,

66 and the particle will hop to the adjacent triangle. By continuing to rotate the field, the process will continue and the particle will hop to subsequent disks.

Figure 32 demonstrates this capability. Superparamagnetic particles of diameter 4

μm are transported both left and right, simultaneously, along two rows of triangles by rotating a 100 Oe in-plane field. (It should be noted that the out-of-plane field was necessarily off, as such a field forbids hopping to an adjacent triangle, prohibiting long- distance transport.) The direction of motion imparted on the particles is dictated by the orientation of the triangle rows; transport occurs opposite the direction that the triangles point.

This technique for particle transport has several possible advantages over the disk hopping mechanisms detailed earlier. First, out-of-plane fields are often difficult to incorporate into microscope setups because of physical restrictions due to, for example, locations of objective lenses. Secondly, the multidirectional transport afforded by this technique allows for automated loading and unloading of cargo carried by magnetic particles; one could foresee a conveyor belt mechanism where the only necessary input was a rotating magnetic field. This manipulation scheme is similar to techniques demonstrated by Conroy et al42. and Gunnarsson et al43. The main difference is the shape of the patterned structure.

4.5 Disk Array Applications

Discrete patterned element-based platforms may find applications related to propulsion and navigation of objects in aqueous environments. Common micromanipulation approaches based on optical tweezers, or atomic force cantilevers, are not suitable for work at long ranges, as they require proximity to a microscope objective

68 or an atomic force microscope tip, whereas the magnetic microspheres on the platform are readily controlled from a distance through external fields. In addition to untethered cells, the magnetic spheres can also push inert entities and act as local delivery agents to targeted sites on surfaces for realizing functional microelectromechanical systems. For instance, it should be possible to assemble dielectric microspheres to create two- dimensional photonic band lattices68.

Development of microfabricated magnetic traps and their tunability by external programmable fields makes it possible to readily integrate them into microfluidic devices69,70. For example, embedded micro-disk arrays in one or multiple microfluidic channels can capture and transport magnetically labeled species in the sample flowing perpendicular to the array channels. The magnetic arrays can be initialized with programmed routines (as in Figure 27(a) and (b)) to move a labeled species to a different cross-channel, where it can be chemically detached and detected. The ability to manipulate multiple objects at the individual cell level coupled within existing microfluidic technology could form the basis for realizing low cost, lab-on-a-chip analytical tools for detection of living microorganisms.

Our current design allows for transport of one given functional marker at a time.

In the case of sorting a heterogeneous cell population, this would be achieved with different markers (magnetic particles) targeting different cells in a sequential approach that can be readily integrated into a chip. Alternatively, we can use a ‘‘cocktail’’ of antibodies that target several specific markers on the cell surface simultaneously and move different targeted cells at once. It is envisioned that this technique will be used

69 primarily on cells that are either grown in suspension or previously suspended by some method. The suspended cells can come from blood, digested tissue, or cell culture.

In addition to the simplicity, reliability, and tunability of the traps, there are other advantages of the planar platform. These include ease of standard lithography fabrication, a single focal plane that allows for real-time image acquisition of the cells in a parallel manner that is greatly increased compared to point or line scanning, and ready scale up to high array densities, enabling concurrent measurement of single-particle and ensemble average responses. In addition, the array of magnetic disks can be fabricated on other biocompatible platforms, such as glass microscope slides or Mylar, thus providing low- cost platforms for manipulating cells. Moreover, the remotely-controlled external fields allow for manipulation of cells by programmed routines that will not require dynamic refocusing or out-of-focus calibrations.

Chapter 5: Composite Nanoparticle Trapping

The ability to simultaneously control multiple individual nanostructures is the cornerstone of bottom-up assembly strategies, with possible applications that range from video displays to therapeutics that can diagnose, treat, and monitor disease71,72. The small size of nanostructures provides two significant challenges in controlled transport of multiple nanostructures: (1) separate large external fields may be required to manipulate each particle73–75, and (2) it is difficult to track the motion of structures below 200 nm using traditional optical microscopy. Here, we describe a “nano-conveyor-belt” platform technology for simultaneous manipulation and optical tracking of multiple nanostructures. This technology is based on two key components. Polymeric micelle nanocontainers (~35 nm) encapsulating separate quantum dots (QDs) and iron oxide nanoparticles (i.e., hybrid magnetic quantum dots, HMQDs76) permit magnetic manipulation with simultaneous fluorescent observation, and patterned magnetic nano-conveyor arrays provide the tunable, high magnetic field gradients needed for controlled particle motion55,64. This nano-conveyor belt technology, which permits simultaneous observation and control of nanostructure movement, will open new avenues in nanofabrication, nanofluidics, biomechanics, drug delivery, magnetic actuation, and molecular detection.

Two critical features in controlled motion of nanomaterials are: (1) providing a sufficient force for movement and (2) providing a visualization scheme to track that motion. In collaboration with Professor Jessica O. Winter’s group in the William G. 71

Lowrie Department of Chemical and Biomolecular Engineering at The Ohio State

University, we have overcome these challenges with two enabling technologies: nanocontainers and nanoconveyors. Nanocontainers consist of polymeric micelles encapsulating HMQDs, which permit particle motion via magnetic fields and observation of that motion via fluorescence microscopy. Nanoconveyors are composed of patterned magnetic nanowires or disks with three orthogonal and addressable weak magnetic fields.

Nanocontainer motion is controlled by nanoconveyors, which propagate containers along the length of the conveyor belt or enable, on-demand, capture and release of the containers in a flow stream [Figure 33].

Nanocontainers are composed of ~35 nm polymeric micelles with a hydrophobic core, into which hydrophobic nanostructures can be incorporated. To provide both manipulation and observation properties, Dr. Winter’s group has encapsulated superparamagnetic iron oxide nanoparticles (SPIONs) and semiconductor quantum dots

(QDs) within this core to yield HMQDs. Manipulation of magnetic micro- and nanoparticles containing iron oxide has been demonstrated with magnetic bead force application77 and magnetic tweezers techniques78. However, in situ manipulation and tracking of single sub-100-nm magnetic nanoparticles has not yet been demonstrated, primarily because of difficulties in observing their motion and their controlled manipulation79–81. Conversely, because of their strong fluorescence and resistance to photo bleaching, QDs have been used for long-term single particle tracking82 and optical imaging83, demonstrating superiority to traditional fluorescent dyes, which experience photo bleaching and photo degradation over time84. However, in these technologies QDs play only passive roles. Their positioning and motion cannot be controlled by investigators85–88. The combination of SPIONs and QDs within a nanocontainer provides a mechanism for investigator controlled nanoparticle manipulation with long-term optical tracking capability.

5.1 Formation of Hybrid Magnetic Quantum Dot Particles

Nanocontainers encapsulating HMQDs [Figure 34(a)] were created by Dr.

Winter’s group by utilizing interfacial instability89. Amphiphilic block copolymers were initially dissolved in an organic, water-immiscible solvent (e.g., chloroform), and were

73 later dispersed in aqueous solution, yielding water-soluble micelles with hydrophobic cores. QDs and SPIONs with hydrophobic surfaces were incorporated into the hydrophobic cores by addition to the initial, organic phase. The numbers of QDs and

SPIONs in each micelle were controlled by the molecular structure of the polymer employed and the quantities of polymer, QDs, and SPIONs used.

5.2 Characterization of Nanocontainers

Transmission electron microscopy (TEM) with negative staining, carried out by

Dr .Winter’s group, was used to observe nanocontainer morphology [Figure 34(b)]. QDs and SPIONs (both electron dense) are evident as dark spherical spots within the core of the white, hydrophilic nanocontainer. The diameter of the QD and SPION-filled nanocontainer is ~35 nm, substantially smaller than the smallest particles to have been previously magnetically manipulated and simultaneously imaged (i.e., ~100 nm)81,90.

Because SPIONs and QDs (with similar size and shape) cannot be distinguished by TEM imaging, centrifugation in the presence of a magnet was performed to confirm incorporation of both nanoparticles into the nanocontainer. In the presence of a magnet, nanocontainers encapsulating HMQDs were attracted to the bottom of a centrifuge tube and could be observed by a hand-held ultraviolet lamp (λem = 605 nm) [Figure 34(c), left].

In contrast, in the absence of a permanent magnet, nanocontainer accumulation was not observed [Figure 34(c), right].

Micellar nanocontainers composed of amphiphilic block copolymers are a remarkably versatile encapsulation technology. Multiple individual nanoparticles (>10 as seen in Figure 34(b)) can be enclosed within the micelle core. In contrast, lipid-PEG micelles76 have been reported to encapsulate as little as one nanoparticle76,91. This most likely results from the shorter hydrophobic segment of lipid-PEGs compared to those of amphiphilic block copolymers, which yield a hydrophobic core of only 8 nm vs. 20 nm for amphiphilic block copolymers. Also, for lipid-PEG micelles, core size can be dramatically affected by the encapsulated nanospecies. Sailor et al.76 reported that adding

75 rod-shaped and spherical nanocrystals to the oil phase created a new lipid-PEG micelle structure several times larger than empty micelles and encapsulating both types of nanocrystals. The larger core appears to be produced as a result of interactions between the lipid-PEG molecules and the nanocrystals enclosed, suggesting that the range of nanomaterials that can be encapsulated with this method is limited. In contrast, block copolymer micelles can theoretically encapsulate any hydrophobic nanomaterial smaller than the micelle core (e.g., carbon nanotubes, gold nanoparticles92).

In addition to the spherical QDs and SPIONs that form the HMQDs studied here,

Dr. Winter’s group has also shown co-encapsulation of QD rods and magnetic nanospheres [Figure 34(d)], demonstrating the broad applicability of this approach.

5.3 Nanocontainer Manipulation

The patterned magnetic wire and disk platforms discussed in Chapters 3 and 4 were used to trap and manipulate nanocontainers. The very high field gradients present at the periphery of each magnetized disk or at each zigzag vertex are sufficient to trap

HMQD nanocontainers as shown in panels (b) and (d) in Figure 35, despite their low volume magnetization. For example, the magnetic field gradient above a magnetic domain wall located at a vertex of a single 380 nm wide, 40 nm thick Fe0.5Co0.5 zigzag wire (see Figure 38), as used in the present work, is ~3 × 105 T/m at a height of 40 nm above the platform. Assuming that an average nanocontainer encapsulates ~10 SPIONs

[Figure 34(b)] each with a magnetic susceptibility of 1.3,93 this field gradient will generate forces on the order of 0.01 pN to a nanocontainer. As evident from our observations, these forces are sufficient to overcome thermal fluctuations in fluid and trap a single or an aggregate of a few nanocontainer(s). In addition to this feature, the nanoconveyor platform can easily manipulate multiple nanocontainers simultaneously, in contrast to other technologies (i.e., AFM, optical tweezers, and magnetic tweezers)73–75.

The nanocontainers (and even aggregates thereof) are sub-100 nm in diameter, suggesting necessary experimental considerations for viewing or controlling the particles.

First, because they are smaller than the diffraction limit, fluorescence is necessary to

77 visualize HMQDs. Fluorescent imaging was performed using a 100x oil immersion objective, 100 W mercury lamp, excitation wavelength λex = 488 nm, long-pass filter, and an Olympus DP70 CCD camera. Second, because of their small size and hence small volume magnetization, single HMQDs were especially difficult to capture. Disk arrays were used to manipulate HMQD aggregates, which have higher total magnetization, but the significantly higher fields and gradients associated with patterned nanowires were necessary to capture single (or few) HMQDs.

As with micron-scale particles, nanocontainers can be manipulated in fluid around the periphery of a disk by rotating the in-plane magnetic field Hxy, which tracks synchronously with the sharp potential energy minimum, as seen for a HMQD aggregate in Figure 36(a)-(c). Further, inverting the out-of-plane field Hz allows nanocontainers to jump to adjacent disks; reversing this sequence returns the nanocontainers to the original disks. By combining rotation with disk-to-disk motion, nanocontainers can be manipulated in investigator-selected directions, as seen for two aggregates in Figure

36(d)-(g). Note that the smaller aggregate leaves the field of view of the disks and is no longer trapped due to Brownian fluctuations in the fluid.

For the wire-based platform, switching the direction of Hz moves nanocontainers between vertices (head-to-head (HH) to tail-to-tail (TT) vertices, or vice versa) permitting migration in the xy-plane. As shown in Figure 37, the platform can also trap and release nanoparticles in a flow stream. As discussed in Chapter 3, while an upward oriented Hz of

~100 Oe enhances the field originating from the HH magnetic domain walls, this field weakens trapping forces linked to TT vertices (a downward oriented Hz has the opposite effect). It should be noted that Hz is sufficiently low (<100 Oe) to not affect the structure of magnetic domains. Corresponding to Figure 37, at approximately 10, 20, and 30 s, the direction of Hz was alternated to move HMQD-filled nanocontainers between vertices.

Generally, the nanocontainers moved between HH and TT vertices with rare exceptions.

The direction of motion in both the wire and disk systems is determined by the underlying micro-/nano-pattern and the investigator-controlled magnetic fields. For example, using the disk system, motion from disk-to-disk can be achieved in virtually

79 any xy-direction, and traps can be located anywhere on a disk’s periphery; however, for the wire system, motion is confined primarily to vertex locations. Additionally, it should be noted that manipulation of each nanoparticle is coordinated; that is, all particles are moved in the same direction, which can be altered by adjustment of underlying magnetic fields.

5.4 Blinking Quantum Dots in Heterostructures

The unique fluorescent properties of constituent QDs permitted imaging and tracking of HMQD-filled nanocontainers for at least several hours and confirmation of sub-100-nm size. Because the diameter of a single nanocontainer (~35 nm) is smaller than the diffraction limit of optical microscopy (200-300 nm), nanocontainers in fluorescence images appear as solid spherical spots with size determined by the diffraction limit [Figure 37]. However, “blinking” exhibited by some nanocontainers

[Figure 37, frames 2 and 10], indicates sub-100-nm nanocomposites. Blinking is a characteristic property of single quantum dots, resulting in the intermittent loss of fluorescence signal88. Because blinking is a stochastic process, small aggregates of quantum dots (i.e., one to four particles) exhibit this behavior94, whereas in larger aggregates (i.e., greater than four particles), blinking of adjacent QDs is out of phase resulting in a continuous fluorescence signal [Figure 36]. Using four QDs encapsulated in separate, yet aggregated, nanocontainers as the upper limit for aggregate particle size (an unlikely scenario), the largest blinking nanocomposite composed of fluorescent micelles would be ~70 nm (noting the spherical shape of the particle), which is smaller than that of previously imaged 100 nm magnetic nanoparticle composites81. The possibility that fluorescent micelles aggregate with either empty micelles or micelles containing only magnetic nanoparticles, increasing particle size above 100 nm, was also considered; however, using rough probability calculations it can be shown that this is extremely unlikely. All of the blinking, composite nanoparticles observed in this experiment (more than 10) were capable of being manipulated using nanoconveyor arrays. If we assume

81 that the probability of aggregation is 1/3, (based on the experimentally observed ratio of blinking to non-blinking micelles), then the probability of all 10 particles consisting of aggregated micelles is (1/3)10 or 0.0017%. Even if a larger probability of aggregation is assumed, the probability would need to be >63% before there is even a 1% chance of all

10 particles manipulated consisting of aggregated micelles. This is extremely unlikely given our experimental observations and the antiadhesive PEG component of the micelles.

5.5 Calculations of Magnetic Fields and Forces on Nano-Containers

The magnetization profile of a 380 nm-wide, 40 nm-thick zigzag Fe0.5Co0.5 wire, the same as the zigzag wire used in this study, was derived from the Object-Oriented

Micromagnetic Framework (OOMMF) program31. The resulting magnetic fields and field gradients were calculated from simulations and plotted as a function of height above the domain wall (Figure 38 A-B). The force, F, on a nano-container with 10 encapsulated six-nanometer-diameter Fe3O4 nanoparticles, in the absence of an external magnetic field,

1  2 was calculated using F  2 N0 V z (H ), where N = 10 is the number of encapsulated

Fe3O4 nanoparticles, μ0 is the permeability of free space, χ = 1.3 is the magnetic susceptibility of the nanoparticles, V is the volume of each encapsulated nanoparticle, and

H is the calculated magnetic field. The results are illustrated in Figure 38.

Figure 38: Calculations of (A) magnetic field and (B) field gradient from the vertex of a 380 nm-wide, 40 nm-thick Fe0.5Co0.5 wire. (C) Forces from this vertex on a typical nano- container61.

5.6 Trapping Force Estimate and Tunability with Out-of-Plane Fields

To estimate the trapping force on the nano-containers, the trajectories of particle aggregates at wire vertices were tracked. The particular aggregates used for this purpose were sufficiently large (~500 nm) that they were visible and trackable by brightfield microscopy. Additionally, the magnetic volume (fraction of magnetic material per volume) in these nano-container aggregates was small, allowing their trapping to be less and their fluctuations to be easily resolvable. 83

By the equipartition theorem, in two dimensions, assuming a radially symmetric harmonic potential of spring constant k, the trap strength can be related to the ambient temperature, kBT by

2 2 k(+) = kBT (12) where x and y are the particle coordinates with respect to the average position, and denotes the average of a quantity Q. The average force on a trapped particle is estimated as

2 2 ½ Fave = k = k<(x +y ) >. (13)

The force was calculated for five out-of-plane applied fields Hz to indicate the increase in trap strength with field.

0.0140

0.0120

0.0100

0.0080

0.0060

Average Force (pN) 0.0040

0.0020

0.0000 0 25 50 75 100

H z (Oe)

The data in Figure 39 should be considered approximate and likely a lower bound.

The trapped sub-diffraction limit-sized particles observed under fluorescence, for example in Figure 37, experienced significantly less fluctuation under the same conditions than the aggregates used to generate Figure 39, and therefore their position fluctuations are not easily resolvable under 100x magnification. In addition to having a higher magnetic volume fraction, the magnetic material in the smaller particles is concentrated very close to the wire, hence experiencing a comparatively large force.

Figure 39 experimentally demonstrates the tunability of the trap strength offered by the out-of-plane field Hz, similar to the calculated force tunability shown in Figure

10(b). Similarly, for a negative (oppositely-directed) out-of-plane field, the trap strength weakens until the applied field strength is high enough to render the trap repulsive.

5.7 Device Attributes

We have demonstrated simultaneous magnetic manipulation and fluorescent tracking of sub-100-nm nanocomposites using the nano-conveyor-belt platform, a first step toward externally controlled nanoassembly of multiple particles. This technology is extremely versatile. The disk or wire arrays can be designed and engineered to have different dimensions than those presented here without much effect on trapping ability.

Because of their simple design, nanocontainers can encapsulate a wide range of nanomaterials, including quantum dots and rods and magnetic nanoparticles. Apart from the internalized materials, nanocontainer surfaces could be easily modified with selected

85 chemical moieties or biomolecules through traditional approaches (e.g., using amphiphilic polymers with –COOH or –NH2 end groups) for further targeting. The entire nanoconveyor system is small, portable, readily integrated into microfluidic devices, and easily mounted on a reflective fluorescent microscope [Figure 35].

Non-specific binding to the nanoconveyor platform, which could be a significant issue because of the high surface area-to-volume ratio of nanoparticles, is prevented by two unique features of the design. The external surface of the nanocontainers is composed of polyethylene glycol and the nanoconveyor surface is coated with triethylene glycol mono-11-mercaptoundecyl ether. These antiadhesive coatings permit reversible trapping of nanocontainers in the presence of applied external fields.

Finally, the nanoconveyor array technology is based on patterned magnetic nanowires or disks, whose sizes, shapes, and spacing can be controlled lithographically to create specific device structures. Taken together, this technology allows user control of the materials, nanocontainer surfaces, and conveyor belt design.

Given the versatility of this technology, the nanoconveyor belt platform could substantially impact a number of fields. For example, in micro-/nanofluidics, sub-100-nm nanostructures could be transported by magnetic manipulation with their individual trajectories being monitored by fluorescence95. Complex nanostructures could be assembled magnetically with color-coded QDs labeling the individual components71.

Therapeutic nanoparticles could be magnetically targeted to sub-cellular locations with nanometer precision, overcoming barriers of intracellular transport96. Mechanical

86 properties of single biomolecules in the cytoplasm or nucleoplasm of living cells could be probed by examining their force-movement relationships97.

Chapter 6: Micromagnetic Models and Field Calculation Methods

6.1 Micromagnetic Modeling

To model the magnetic forces on a superparamagnetic particle, we considered the magnetization profiles of the patterned structures. Computer simulations based on the 2D version of the Object-Oriented Micromagnetic Framework31 (OOMMF) program yielded the micromagnetic structure associated with the wires and disks, as seen in Figure 9(a),

Figure 17, and Figure 24.

For Co0.5Fe0.5 wires, vector maps of these magnetic configurations were generated using a cell size of 20 nm × 20 nm × (height =) 40 nm, saturation magnetization of 2 T, exchange constant 1.5 × 10−11 J/m, and no external field. An initial, spatially uniform magnetization along the +y or +x direction (for 40-nm-thick, 1-μm-wide zigzag or notch wires, respectively) was allowed to relax to yield equilibrium magnetization configurations.

For permalloy disks, OOMMF simulations were generated using the same cell size, a saturation magnetization of 1.08 T, an exchange constant of 1.3 × 10−11 J/m, and a constant in-plane magnetic field of 50 Oe to magnetize the disks.

Because the thin films in both cases are polycrystalline with grain sizes on the order of 10s of nm, the crystalline anisotropy constant was set to zero. The resulting vector data provides the spatially dependent magnetization M(x,y,z) with the

88 magnetization remaining largely in plane for the modest out-of-plane fields (Hz < 150

Oe) used in this study.

6.2 Field Calculation Methods

We estimate the fields arising from a given patterned configuration using approaches based on (i) effective point charges/dipoles (ii) dipole distributions and (iii) magnetic charge distributions. The corresponding fields, field gradients, and forces are calculated at center of the spherical particle utilizing the OOMMF-derived equilibrium magnetization configuration.

6.2.1 Point Charge/Point Dipole Model for Field Calculation

This model describes magnetic fields as arising from a point source, either an effective point charge qm (i.e. monopole-like) or a point dipole. An effective point charge is given by

qm   M(x, y, z) nˆdA (14) S where M(x,y,z) is the spatially-dependent magnetization of the wire, nˆ an outwardly directed normal to the surface. In the case of a domain wall, qm = 2Mswt, where Ms, w, and t are respectively the saturation magnetization, width, and thickness of the wire. The magnetic field at location r from this effective charge at the origin is

q r H(r)  m . (15) 4 r 3

In the case of the notches, the total effective charge is zero, and the notch can be approximated as a point dipole. The magnetic field at a distance r from a dipole moment md is given by

1 H(r)  [3(m rˆ)rˆ  m ] . (16) 4r3 d d

While the point charge (qm) was calculated based on geometrical considerations,

-14 2 the point dipole md associated with the notch traps was calculated to be 1.2 x 10 Am by fitting the fields from the point dipole model at large z (> 2 m) to those derived from dipole and charge distribution models. In comparison, a typical superparamagnetic bead 1

μm in diameter in a 100 Oe magnetic field has a magnetic moment of ~10-15 Am2.

Either point source model works best for r >> w (wire width). Closer to the domain wall or notch, the precise magnetization profile is needed for a more realistic calculation of the magnetic field in the immediate vicinity of the wire. The following approaches provide a better description of the field profile close to the trap.

6.2.2 Dipole and Charge Distribution Model for Field Calculation

The OOMMF simulations yield the magnetization profile as a 2D grid of magnetized cells. A cell located at (x,y,z) is characterized by a magnetic dipole of moment md(x,y,z) = M(x,y,z)VC, where VC is the volume of the cells. While each dipole can, in general, orient in any direction in three dimensions, in the present case, the magnetization is primarily confined to the xy-plane of the ultra thin, 40 nm-thick wire.

Summing the fields originating from all of the dipoles [Equation (16)] provides the resulting magnetic field and its spatial distribution.

The magnetic field from the domain wall can also be determined from the

47 magnetic charge density ρm given by ρm = M(x,y,z) where the divergence is evaluated numerically based on the OOMMF cell magnetizations. The collection of magnetic charges associated with each cell qm = ρmVC, and the resulting field as calculated by

Equation (15) yields the net field from the domain wall. This method is advantageous in that ρm only arises where M(x,y,z) is nonzero (i.e. at the domain wall), thereby rendering this approach computationally far less intensive than summation of the fields from each dipole.

Chapter 7: Conclusions and Future Work

We have demonstrated a mechanism for trapping, transporting, and probing micro- and nanoscale objects by means of utilizing patterned magnetic structures. The two-dimensionality of the trap platform enables (i) trapping and transport along a single focal plane for real-time optical observation of single or multiple biological or inert particles, (ii) standard lithography of patterned structures, (iii) easy manipulation by programmed routines via remotely-controlled external fields produced by miniature electromagnets, and (iv) ease of integration into microfluidic devices. Traditional magnetic tweezers operate in a mode where the motion is perpendicular to the viewing plane, requiring dynamic refocusing or out-of-focus calibrations12,98. Further, standard nanoscale lithography allows carefully positioned, ultrahigh field gradients (> 104 T/m) to be applied to nanometer sized magnetic particles which have only limited interference with cell activity.

The resulting forces thus offer promising intracellular directed force probe applications78,99. For instance, forces greater than 1 pN on 25–50 nm-sized iron oxide particles will enable non-contact planar manipulation of these ultra small particles within a cell. Similarly, larger particles could be used as external probes of cells, serving the purpose of investigating their mechanical properties which in some cases act as indicators of disease100.

There is also potential for single cell measurements to investigate statistical distributions that would otherwise be obscured by ensemble averaging. Examples of manipulating multiple cells, shown in several instances in this dissertation, support the scale-up to simultaneously perform the experiment on thousands of identical samples. A typical experiment would be to monitor the response of a large number of samples (e.g.,

~105 cells on a 1 cm  1 cm platform) to the same stimulus in real time, for example, to measure the consequence of time-resolved optical illumination using a charge-coupled device. Subsequent analysis would produce statistically valid data not only for the ensemble average response but also its individual fluctuation spectrum.

Another application of the high array density is their incorporation into microfluidic analytic devices to detect small concentration of one species in the midst of other species. An embedded patterned magnetic trap array in one microfluidic channel can pick off the magnetically labeled species in the sample flowing in a channel perpendicular to the array channel. This basic idea can be integrated into existing microfluidic technology as the basis for a new family of on-chip analytic tools with biomedical applications. For example, simply by isolating and counting labeled cells, we target cell surface receptors which are indicators of disease, for example on circulating tumor cells101,102. Acting as a detection technique for rare cells in blood, magnetically sorting cells would indicate to doctors the level of a cancer patient’s improvement during treatment at intervals shorter than is allowed by current techniques. The separation technique could be coupled with miniature magnetic resonance systems or micro-Hall

93 detectors for additional detection efficiency and immediate specimen information gathering in point-of-care clinical diagnostic systems103,104.

Beyond cell separation, the precise location control afforded by our techniques allows for the possibility of an automated nanofactory for analyzing and probing many individual cells. After separation from a heterogeneous population, a transport method can move the conjugated species to, for example, a separate cross channel where it can be chemically detached, a nanochannel where it can be injected with precise concentrations of genetic material105, or a patterned electrode for cell lysing and constituent analysis106.

In addition, a device could be engineered for magnetically-actuated, position controlled catalysis, where the presence or absence of magnetic particles surface-coated with appropriate enzymes could promote chemical catalysis in locations and at types chosen by an operator.

Our devices could be used for assembly of large numbers of nanoscale objects that could not be assembled by conventional means. For example, by tuning particle separations, one could envision creating a microwave or infrared photonic crystal in fluid.

Additionally, assembling magnetically-conjugated microtubules on a surface would allow for the creation of a transit system for kinesin nanomotors that could be remotely modifiable by applied magnetic field. Nanomotor pathways, and hence the pathways of the motor cargo, could be guided by remote means.

In conclusion, remotely controlled directed forces from patterned magnetic micro- and nanostructures enable the transport of fluid borne individual or multiple particles, cells, or nanocontainer hybrids at speeds up to hundreds of microns per second on a

94 surface-based platform. Central to this study are the simple methods necessary to create highly-confined field gradients with nanoscale position and to alter the magnetic energy landscape by remote means. In addition to the convenience of optical microscope observation and advantage of suppressing randomizing thermal fluctuations of fluid- borne objects, development of such mobile magnetic traps will provide real-time analysis of living cells and many other systems through direct manipulation that offers much more accurate selection than data-averaging over a large population.

Appendix: Mathematica Code for Calculating Fields from Domain Wall

100

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