Utilizing Advanced Field Functions to Drive the Assembly and Disassembly of Magnetic

Particles

A Dissertation Presented

By

Rasam Soheilian

to

The Department of Mechanical and Industrial Engineering

In partial fulfillment of the requirements

for the degree of

Doctor of Philosophy

in the field of

Mechanical Engineering

Northeastern University

Boston, Massachusetts

2017

Copyright (©) 2017 by Rasam Soheilian

All rights reserved. Reproduction in whole or in part in any form requires the prior written permission of Rasam Soheilian or designated representative.

III

ABSTRACT

Directed assembly of particle suspensions in massively parallel formats, such as with magnetic

fields, has application in rheological control, smart drug delivery, and active colloidal devices from

optical materials to microfluidics. At the heart of these applications lies a control optimization

problem for driving the assembly and dissolution of highly monodisperse particle clusters. This

control problem quickly becomes complex when considering high-order magnetic interactions,

near-field and far-field hydrodynamics, Brownian motion, and advanced magnetic field functions

characterized by three-axes of incoherent, oscillating magnitudes. In this work, theoretical,

numerical, and experimental approaches have been investigated in parallel to study the assembly

behavior of particle suspensions in presence of advanced magnetic field functions. Applying such

magnetic fields to suspensions of magnetic particles enables unprecedented control over the

assembly of particle clusters. These findings were leveraged within the field of magnetic drug

targeting for possible treatment of pancreatic cancer. Specifically, a novel five-step drug delivery

scheme was developed in which drug-laden magnetic nanoparticles (coated with rosette nanotubes

and small interfering RNA) can be (1) self-assembled in a carrier fluid, (2) transported to the tumor

site with continuous fields and field gradients; (3) driven to penetrate through the porous fibrotic

tissue encapsulating a pancreatic tumor with advanced field functions; (4) get endocytosed within

tumor cells; (5) and effectively deliver small interfering RNA to disrupt the translation of

messenger RNA to silence genes critical to cancer proliferation. In this case, it is shown, both in-

situ and in-vitro, that the suggested system can lead to a higher drug delivery efficiency in

comparison with current existing techniques.

IV

Contents

List of Figures ............................................................................................................................... VI

List of Tables .............................................................................................................................. XIII

Acknowledgement ..................................................................................................................... XIV

1. Introduction ..................................................................................................................................1

1.1 Magnetic Field Functions .......................................................................................................1

1.2 Magnetic Transport ................................................................................................................3

1.3 In-situ and In-vitro magnetic targeting ..................................................................................5

1.4 Magneto-Rheology, Micro-mixing, and Tunable Optical Applications ...............................8

2. Theory ........................................................................................................................................12

2.1 Magnetic Properties .............................................................................................................12

2.2 Magnetic Interactions ...........................................................................................................14

2.3 Hydrodynamics ....................................................................................................................16

2.4 Brownian Motion .................................................................................................................20

2.5 Sterics Model ........................................................................................................................21

2.6 Magnetic Field Gradients .....................................................................................................22

2.7 Numerical Scheme ...............................................................................................................22

3. Numerical and Experimental Platforms .....................................................................................24

3.1 Numerical Platform .............................................................................................................24

3.2 Experimental Platform ........................................................................................................24

V

4. Assembly and Disassembly of Microparticles Under Rotating Magnetic Fields ......................28

5. Assembly and Disassembly of Microparticles Under Advanced Magnetic Field Functions ....42

5.1 Advanced Two Dimensional Field Functions .....................................................................42

5.2 Three Dimensional Field Functions ....................................................................................43

5.2.1 Incoherent 3D Magnetic Fields ...................................................................................45

5.2.2 Particle Response to Incoherent Fields: Two-Body Case ...........................................45

5.2.3 Particle Response to Incoherent Fields: Eight-Body Case .........................................50

6. Assembly and Transport of Magnetic Nanoparticles In Presence of Static Magnetic Fields ....58

6.1 Magnetics Interactions ........................................................................................................59

6.2 Hydrodynamics Interactions ...............................................................................................62

7. Improving in-vitro Magnetic Targeting with Advanced Field Functions ..................................65

7.1 Identification of Potential Applications for Advanced Drug Targeting ..............................67

7.2 Assembly of Magnetic Carriers for Magnetic Targeting ....................................................68

7.3 Magnetic Transport of Magnetic Carriers ............................................................................71

7.4 Penetration of Magnetic Carriers through Porous Tissue ....................................................71

7.5 Endocytosis of Magnetic Carriers ........................................................................................75

7.6 Delivery of Cargo from Magnetic Carriers ..........................................................................76

8. Conclusions and Future Work ..................................................................................................78

9. References .................................................................................................................................81

VI

List of Figures

Figure 1.1) a) General behavior of paramagnetic particle chains at different frequencies.

Transitional behavior from one dimensional chain to fragmented sections to clusters. b)

Superparamagnetic microparticles aligned into chains and subjected to rotational fields exhibit a

transient chain shape below the critical frequency due to hydrodynamic drag on the particles. c)

Particle chains have been studied extensively and have been used as surface walkers. d) Larger

assemblies of paramagnetic particles have been used to create “magnetic carpets” capable of

transporting cargo. ...........................................................................................................................4

Figure 1.2) Concentration of drug-laden magnetic nanoparticles in tumor sites can be enhanced

with dynamic magnetic fields and gradients. a) Simple magnetic fields and gradients lead to linear

aggregation that prevents nanoparticles from entering the pores between tumor cells and

densifying within the tumor tissue. b) Instead, certain dynamic fields similarly concentrate the

magnetic nanoparticles at target sites while altogether avoiding aggregation of nanoparticles, thus

maximizing the efficiency and effectiveness of drug delivery. .....................................................6

Figure 1.3) a) Assembly of Saturn rings by using paramagnetic and non-magnetic particles while

submerged in ferrofluid. b) Hierarchical assemblies can be achieved by using different types of

particles and volume fractions. c) Using electrostatics to assemble oppositely charged particles has

given rise to new structures. ..........................................................................................................11

Figure 2.1) Typical Hysteresis curve for a) ferromagnetic materials and b) paramagnetic material

where Mp denotes the particle magnetization and Ms denotes the saturation magnetization. .......13

Figure 3.1) SEM image of 2.8 µm particles (M-280 Streptavidin Dynabeads). ............................25

Figure 3.2) Schematic of the magnetic field setup in a rotating magnetic field case. ...................26

VII

Figure 4.1) Geometry of two magnetic particles in a rotating magnetic field. ..............................29

Figure 4.2) Phase lag is a function of the applied frequency. Below the critical frequency this phase

lag is found to be constant in numerical simulations (dots) and fits well with predictions from Eq.

4.1 (solid line). ...............................................................................................................................31

Figure 4.3) Simulation results for 2a=2.29 μm, =0.163, η=2.5 mPa s for a) 0.1 Hz and b) 2 Hz

( 1.87 ). c) Normalized separations, , are plotted over time for different rotational

frequencies. d) There is a non-linear response in the average separation for a specific viscosity

of 2.5 mPa s. e) A phase diagram can be attained for the average de-aggregation separation between

two particles across rotational frequencies and viscosities. This compares well with Equation 4.1

(red line). .......................................................................................................................................33

Figure 4.4) Aggregated pairs of 2.29 μm particles were subjected to 100 Oe rotating magnetic

fields at a) 0.1 Hz and b) 2 Hz. c) Below the critical frequency for this system ( =1.87 Hz), the

particles remain in an aggregated state. d) Above the critical frequency, many separation events

are observed. Numerical simulations agree well with experimental results. .................................34

Figure 4.5) a) The maximum normalized separation, δ , and b) the frequency of those separation

events between two particles under a rotating magnetic field is plotted. Phase lag is a function of

the applied frequency. Red lines are just visual guides. ................................................................34

Figure 4.6) a) Rigid body behavior at Mn=0.7659, b) Periodic behavior at Mn=1.1489, and c)

Transient chaotic behavior at Mn=4.7871. ....................................................................................36

Figure 4.7) a) Rigid body behavior at Mn=1.01, b) Periodic behavior at Mn= 1.76, and c) Transient

chaotic behavior at Mn= 1.92. .......................................................................................................38

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Figure 4.8) Unstable molecule observed at Mn=1.92 which collapses into a cluster after a very

short time. ......................................................................................................................................38

Figure 4.9) a) Experimental magnetostatic energy, FFT of experimental data, and FFT of

simulations for the periodic regime. b) Experimental magnetostatic energy, FFT of experimental

data, and FFT of simulations for the chaotic regime. Note that magnetostatic energy has been

normalized by the magnetostatic energy of two particles in contact. ............................................40

Figure 4.10) Linear behavior of log of survival probability vs. number of field rotations. At this

specific mason number, 66% of the chains collapse into a cluster after approximately 8 field

rotations..........................................................................................................................................41

Figure 5.1) a) Shows functions that have been used for the field setup. b) Separation events

obtained numerically (2a=2.29 μm, =0.163, η=2.5 mPa s). .......................................................43

Figure 5.2) Phase diagram for mean separation between a particle pair when subjected to

incoherent 3D magnetic fields for different field ratios, a) 1, b) 0.5, c) 2.

Simulations were done at 0.01 Hz increments and considering 120 seconds real time interaction

between particles. ...........................................................................................................................46

Figure 5.3) Phase diagram shown for different initial conditions where α is representing both θ and

φ in spherical coordinates. .............................................................................................................46

Figure 5.4) a) Discrete Fourier Transform (DFT) and separation profile are shown for a)

1.058, 1.209. b) 1.511, 2.116. c) 1.722, 1.511. d)

1.813, 1.058. e) 1.964, 0.226. Note that ,, . ........49

IX

Figure 5.5) Numerical simulations depicting a) Formation of Singlets at A=1, 1.322, and

0.952 and b) Formation of Dimers at A=1, 0.476, and 0.634. Experiments

depicting c) Formation of Singlets (I) at A=2, 0.74, and 1.057 and formation of

Dimers (II) at A=2, 0.453, and 0.767 d) Approximate distance of Dimers from each

other calculated by recording xy positions. ...................................................................................51

Figure 5.6) Non-Brownian, simulated probability of a cluster having a given size ( 1 8).

Statistics of cluster size are reported throughout 2000 seconds of simulated time from an original

8 particle chain subjected to 3D fields across different and . Specific frequency

combinations (marked i-vi) lead to interesting responses including the formation of stable

monomers (ii), dimers (i), and quadramers (iii). ............................................................................53

Figure 5.7) Numerical simulations depicting a) Formation of Quadramers at A=1, 1.957,

and 2.221 with better stability and b) Formation of unstable Quadramers at A=1,

1.957, and 1.904. c) Approximate distance of Quadramers from each other calculated by

recording xy positions where the unstable Quadramers were obtained at A=1, 1.036, and

1.244 (red line) and Quadramers with better stability were obtained with modified field

function at A= 1.5, 1.642, and 1.747. ........................................................................54

Figure 5.8) Formation of a) Stable trimer/pentamer pair at 1.75, 1.90 and b) Unstable

trimer/pentamer pair at 2.17, 2.22. ............................................................................55

X

Figure 5.9) Numerical simulations done without and with Brownian motion to study the effects of

temperature where a, b) Shows formation of Singlets at A=1, 1.322, and 0.952. c, d)

Shows formation of Dimers at A=1, 0.476, and 0.634. e, f) shows formation of

Quadramers at A=1, 1.957, and 1.904 and g, h) Shows formation of Quadramers at

A=1, 1.957, and 2.221 with better stability.. .............................................................56

Figure 5.10) Probability of achieving either quadramers or a trimer/pentamer pair presented for 3

different cases. ...............................................................................................................................57

Figure 6.1) a) magnetic moment saturation shown for different susceptibilities by increasing the

number of particles. b) Polynomial trend observed for different chain sizes by increasing the

magnetization of particles. c) Ratio of increase in magnetic moment in a Brownian case over a

zero temperature case defined as 1 / 1 . d) Ratio of magnetostatic

energy over thermal energy for cases presented in c. d) Effects of Brownian motion presented by

reducing the size of particles for a chain of N=10 where the field is held constant at 10 Gauss. d)

Snapshots of N=10 chain for different sizes at χ=2.1 and H=10 Gauss.. ......................................60

Figure 6.2) a) Mobility of chains presented for three different models and experiments. Brownian

dynamics simulations presented where b) is depicting initial position of chains at t=0 s and c)

shows the distance (δ) traveled by chains after 5 seconds. ...........................................................63

Figure 7.1) Generic schematic of the proposed five step process for magnetic drug targeting. ....65

Figure 7.2) Detailed description of the proposed five step process where coated MNPs are guided

by utilizing high field gradients. By reaching the tumor site, transport mode is triggered where

dynamic magnetic fields are used for disaggregation and then endocytosis of particles is observed

XI

where eventually the designed complex degrades and siRNA acts to silent the cancerous genes.

........................................................................................................................................................66

Figure 7.3) Proposed clinical studies for magnetic targeting techniques by other groups and this

work. Main challenges with conventional methods used are listed in the figure .........................68

Figure 7.4) a) Schematic of the layer by layer assembly where both b) hydrodynamic diameter and

c) Zeta potential measurements have been done to verify the LbL assembly. TEM images of

nanoparticles d) before and e) after RNT coating can be seen. .....................................................69

Figure 7.5) Experimental dark-field micrographs of 150 nm magnetic particles under rotating

fields of a) 0.1 Hz frequency and b) 2.5 Hz frequency. c) significant aggregation in 150 nm

magnetic nanoparticles under static fields after 2 minutes. The magnetic field gradient was 60

Oe/cm and the applied magnetic field was 165 Oe. d) Dynamic fields studied here immediately

de-aggregate nanoparticles while maintaining 165 Oe and 60 Oe/cm ..........................................72

Figure 7.6) a, d) Schematics depicting how gradient and dipolar forces can affect the sytem under

constant and rotating magneti fields where by applying constant magnetic fields, particles

aggregate at the edges (b, c) and by initiating the dynamic magnetic field, disaggregation is

triggered and nanoparticles diffuse through the membrane (d, e). Relative concentartion

measurements for these field condition is presented in section g. .................................................73

Figure 7.7) a) Untreated Panc-1 pancreatic cancer cells. b) Treated cancer cells with siRNA only.

c) Treated cancer cells with MNP+RNT+siRNA. Note that blue areas are the nucleus and the

orange areas are the siRNA. ...........................................................................................................76

Figure 7.8) Viability of cells evaluated under different conditions.. .............................................77

XII

Figure 8.1) a) Schematics of how these formed structures can change either transmission or

absorption peaks of infrared light going through the suspension. b) Schematics of suggested

approaches for assembling these structures. .................................................................................80

XIII

List of Tables

Table 1) List of FDA approved Iron based particles for clinical studies .........................................7

XIV

Acknowledgement

First and foremost, I would like to thank my advisor Professor Randall Erb. His guidance, support,

and creativity, bring about most of the results I have reported here and he deserves a significant

credit for that.

I would like to thank my dissertation committee for their support and help in the past four years.

Professor Craig Maloney has been a perceptive collaborator in this work, He and his student

Hamed Abdi have been a great help with the theoretical side of stuff that I am presenting here.

Professor Hicham Fenniri has been a visionary collaborator, he and his student Karlo Delos Reyes

helped a lot with developing and testing of the magnetic drug targeting system. Professor Yongmin

Liu has been a great teacher, he and his student Kan Yao have helped me significantly in order to

be able to use reported particle assemblies in this work for an optical system. This work with them

is still in the initial stages and I hope to see this work continued by future students.

I would like to thank my lab mates at Directed Assembly of Particles and Suspensions (DAPS)

Lab. Always grateful for their help and support. Specifically, I would like to mention Joshua

Martin, Chunzhou Pan, Jessica Faust, and Anvesh Gurijala, the people I have had the chance to

not only collaborate with, but also learn a lot from, their visionary has been a great help for

advancing in the work I have been doing in the past four years. Additionally, I like to thank

Jonathan Sander, who taught me a lot about the important factors to consider for experiments

presented in this work.

Last but not least, I like to thank my family, their support and help throughout my life has been

the greatest gift for me and I am grateful for that.

1

1. Introduction

The interaction of magnetic particles (positive dipolar colloids) in the presence of various types of

external magnetic fields has recently attracted attention due to potential applications in drug

delivery, optics, structural materials, and magneto-rheology. This heed rises from the fact that

magnetic fields can apply the highest forces and torques possible to particle suspensions in

comparison with other available colloidal forces1. Furthermore, magnetic fields allow for the

remote control of particle suspensions with high resolution whereas other existing methods (i.e.

electric fields, ultrasonic waves, optical manipulation, etc) either need a specific environment for

manipulation or have low resolutions and are weak.

Despite the aforementioned advantages of magnetic manipulation, the main drawback in this

technique is the need for using magnetic materials in particle suspensions which hinders the

utilization of magnetic fields for specific applications that demand manipulation of nonmagnetic

particles. In order to overcome this barrier, researchers have developed magnetic carrier fluids that

allow for manipulation of nonmagnetic particles. This technique is known as negative

magnetophoresis in the scientific community. In this dissertation, we focus on assembly and

disassembly of magnetic particles for specific applications in drug delivery and optics in which

magnetic manipulation shows unprecedented capabilities.

1.1 Magnetic Field Functions

The simplest magnetic field that can be used to manipulate magnetic colloidal suspensions is a

constant magnetic field. This type of magnetic field has been heavily implemented for studying

different phenomena such as aggregation kinetics2-5, particle assembly6, and drug delivery7,8. It is

known that aggregates and linear chains of magnetic particles can be formed by applying constant

2

magnetic fields. The formation of these 1D structures has been thoroughly studied and it is depicted

that there is a power law dependence between mean chain size and time2-5. In addition, it is also

depicted that by applying constant magnetic fields, various phases such as face-centered-cubic

(fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) can be seen in assembly

of hard magnetic spheres6. Finally, static magnetic fields have also been used for guiding drug

laden magnetic nanoparticles in vivo in order to treat cancer cells locally7,8.

In recent years there has been a growing trend toward using more complicated magnetic fields

such as biaxial, and triaxial magnetic fields to assemble particle suspensions. The most common

biaxial magnetic field that has been utilized in studies to this date is a homogeneous rotating

magnetic field and much work has gone into describing the behavior of magnetically chained

particles in presence of such a field9-16. In these studies mixing processes9-11,14, chain

behavior12,13,15,16, and crystal formation17-19 by applying rotating magnetic fields have been

discussed. These studies have led to development of products like magnetic Micro and Nano stir

bars for mixing of small samples in life sciences and lab-on-a-chip technologies1. Moving beyond

biaxial fields, some recent efforts have been focused on utilization of triaxial magnetic fields to

study different aspects of pattern formation20, and colloidal phases21. Furthermore, it has been

demonstrated that formation of structural materials22 and vigorous mixing of fluids by inducing

vorticities23 can be achieved. For example, composite particle sheets that have unique thermal

properties have been built through utilizing such magnetic fields. Since the design space for triaxial

magnetic fields is vast and unique types of magnetic fields can be developed for studying different

phenomena in particle suspensions, these fields are an appealing subject for exploration.

Despite all the progress made, there is still a need for improvement in magnetic manipulation

techniques with regards to different applications (e.g. assembly of particles for tunable optical

3

systems, and magnetic field deigns for drug delivery purposes). In this work, we intend to address

and resolve the current existing issues by designing and utilizing various types of biaxial and

triaxial magnetic fields in order to gain control over the assembly of particle suspensions. In the

following sections, the need for such developments in different fields is discussed in great detail.

1.2 Magnetic Transport

Transport is one of the main applications of magnetics and it has potential applications in

microfluidic manipulation and micro-robotics. Isolated particles do not translate in the presence of

low gradient constant magnetic fields. In order to induce locomotion with magnetic fields,

asymmetry is required. There are two ways to create this asymmetry. In the first case, field

asymmetries (i.e. magnetic field gradients) can be used to create a magnetic driving force. In the

second way geometric asymmetries can be coupled to dynamic magnetic fields to induce motion.

For example, magnetic surface walkers can be used as a simple approach to induce locomotion.

Simple assemblies of magnetic particles in a liquid can “tumble” along a surface when subjected

to a rotating magnetic field24-26. The tumbling method of magnetic locomotion depends on the

hydrodynamic interaction between the particles, friction and a nearby wall. Non-slip conditions at

the surface of a rotating particle assembly and at the surface of a static wall create high shear in

the solvent layer between the assembly and the surface27-30. Because of this slipping between fluid

layers, magnetic walkers generally show reduced translation motion relative to their rotational

speed. As magnetic walkers are rotated faster, the assemblies tend to push away from the wall to

minimize this increased shear energy, further decreasing the relative translational velocity

compared to the field rotation rate. Sing et al.24 used non-crosslinked chains of paramagnetic

microparticles as surface walkers that translated with a velocity of about 12 µm/sec when rotated

at 30 Hz. These colloidal assemblies were used to create flow near a substrate and transport large

4

Figure 1.1) a) General behavior of paramagnetic particle chains at different frequencies.

Transitional behavior from one dimensional chain to fragmented sections to clusters. b)

Superparamagnetic microparticles aligned into chains and subjected to rotational fields exhibit a

transient chain shape below the critical frequency due to hydrodynamic drag on the particles31. c)

Particle chains have been studied extensively and have been used as surface walkers24. d) Larger

assemblies of paramagnetic particles have been used to create “magnetic carpets” capable of

transporting cargo32.

5

vesicles (Figure 1.1c). In addition, 2D colloidal crystals of microparticles stable under a rotating

magnetic field can be used as a “magnetic carpet” to transport cargo (Figure 1.1d).32 Each

microparticle that makes up the carpet has a slight magnetic anisotropy that experiences magnetic

torque under a rotating field and drives independent rotation of the particles. These particles can

roll along the surface staying connected to each other through magnetic dipole interactions. If

cargo is somehow placed on top of these assemblies, the cargo can be delivered to a point along

the surface and then can be delivered upon removal of the field when the carpet dissociates due to

Brownian motion. The average propulsion speed of the carpet increases with the number of

particles but seems to saturate with 300 particles around 6.5 µm/s.32

In this section, detailed analysis on effects of magnetics and hydrodynamics interactions are given

for mobility of chained magnetic particles in presence of high field gradients. Furthermore, Effects

of Brownian motion are also studied to an extent where suggestions for overcoming thermal

fluctuations are presented.

1.3 In-situ and In-vitro magnetic targeting

Despite decades of effort developing more effective diagnostic and therapeutic tools, cancer

remains the cause of almost 30% of all deaths each year33. While traditional chemotherapies have

shown some efficacy against cancer, their broad distribution throughout the body and associated

toxic side-effects limit dosing to sub-therapeutic concentrations of drug in the cancer (neoplastic)

tissue34. Recent developments in nanomedicine with receptor targeting and further understanding

of the leaky vasculature properties of tumors has significantly improved targeting. Still, the percent

of injected dose (% ID/g tissue) that distributes into the tumor is generally below ten percent35,36.

It has been shown that magnetic targeting could be applied with magnetic nanoparticles (MNPs)

to greatly improve delivery of drugs to tumors8. These methods, however, have so far used simple

6

static magnetic fields and gradients to concentrate the MNPs at the tumor site. Under these static

fields, magnetic particles, even those as small as 150 nm in diameter, have been observed to

agglomerate after only a few minutes7. This agglomeration hinders the extravasation of

nanoparticles from the tumor vessels, which have pore cutoff sizes less than 600 - 800 nm37,38, and

would greatly limit their mobility deep into a tumor tissue.

Figure 1.2) Concentration of drug-laden magnetic nanoparticles in tumor sites can be enhanced

with dynamic magnetic fields and gradients. a) Simple magnetic fields and gradients lead to linear

aggregation that prevents nanoparticles from entering the pores between tumor cells and

densifying within the tumor tissue. b) Instead, certain dynamic fields similarly concentrate the

magnetic nanoparticles at target sites while altogether avoiding aggregation of nanoparticles, thus

maximizing the efficiency and effectiveness of drug delivery39.

As mentioned previously, the break-up of magnetically chained particles under simple rotating

magnetic fields has been heavily investigated9-16 and may be utilized to both concentrate the drug-

laden magnetic nanoparticles within a tumor and enable extravasation through the leaky

7

vasculature by preventing particle aggregation. As we find in this work, however, MNP

aggregation occurs rapidly, even in the presence of Brownian motion, and the average aggregate

size quickly surpasses the typical pore size of leaky tumor vasculature in the presence of static

magnetic fields (Figure 1.2).

Table 1) List of FDA approved Iron based particles for clinical studies40.

Finally, it should be mentioned that clinical studies of the suggested method here rely on using

FDA approved Iron based particles. Over the past few decades, a number of products based on

Iron oxide particles have been developed for imaging and drug delivery purposes in clinical studies

(Table 1) but it is noticed that there is no specific product available in the market for magnetic

targeting studies. Moreover, some of the products developed are discontinued and no longer

available in the market for clinical trials. This can be due to specific biological, technological, and

study design related challenges that these products face upon entering the clinical trial stage40. For

example, from the technological view point, scaling up these products for clinical usage is a main

8

challenge that should be addressed. Also, it is known that particles have to be passive to proteins

in order to avoid binding and accumulation at off target sites. On the other hand, more specific

studies need to be designed at clinical stages to investigate the effects of control parameters on

delivery mechanism.

1.4 Magneto-Rheology, Micro-mixing, and Tunable Optical Applications

Utilizing Magnetorheological fluids in controllable devices is one of other main applications of

magnetics. In these systems, fluid has the ability to change its behavior from a linear viscous fluid

to a linear elastic solid when exposed to external magnetic fields. These fluids can be used as

vibration dampers41,42, suspension systems, and controllers of seismic vibrations41. Understanding

the behavior of particle suspensions in presence of dynamic magnetic fields can lead to new

interesting observations from the magnetorheological point of view.

In another context, it is known that mixing is important for life science and lab-on-a-chip

technologies that usually deal with small droplets. In these cases typical magnetic stir bars cannot

be used because of their size. Also, at these small fluid volumes, Reynolds number is significantly

low and the fluid experiences laminar flow. Mixing in laminar flow is based on pure diffusion and

is very slow as well. In order to overcome this limitation microscopic mixing with magnetic

particles can be utilized. In this case a dynamic magnetic field is applied to induce oscillatory

motion within particle suspensions. As with magnetic stir bars, a simple, homogeneous rotating

magnetic field can induce mixing. Under a magnetic field, paramagnetic particles will become

magnetized and nearby particles will be attracted in-line with the applied field and will be driven

to form an effective chain or rod in one dimension. Within the rod, the particles have a strong

attraction to each other, giving this stir bar some amount of structural integrity. To make this chain

permanent, chemical cross-linking can additionally be used. If the field is then slowly rotated, the

9

chain will rotate and effectively stir the local surrounding fluid. Unless the chain is crosslinked,

removing the field will quickly disperse the paramagnetic particles due to Brownian motion.

Non-crosslinked paramagnetic particle chains are reconfigurable and can be constructed on the

spot within microfluidic networks. As it was mentioned earlier, the rotational dynamics of non-

crosslinked12-14,31 paramagnetic particle chains have been thoroughly studied and it is suggested

that such systems can be used for micro-mixing. The physical response of non-crosslinked particle

chains under rotating magnetic fields is deceivingly complex. In the simplest classification, there

exists a critical frequency where the chain can no longer keep up with the rotating field and breaks

apart transiently into smaller sections (Figure 1.1a)12,13,16,43. This critical frequency can be

approximated through a simple torque or force balance. However, even rotating below the critical

frequency creates a “transient chain shape” because of increased hydrodynamic drag the particles

on the outside of the chain experience at their higher velocities. In most cases, an anti-symmetric

S shape configuration is formed (Figure 1.1b).31 Furthermore, micro-mixing can also be achieved

by using oscillating magnetic fields where it has been shown that chained paramagnetic colloids

experience structural instabilities44,45. In this section, both experiments and simulations have been

done to study the nonlinear behavior of particle suspensions in great detail while being exposed to

advanced field functions. More specifically, a four particle chain is investigated in the presence of

a rotating magnetic field and a step has been taken toward explaining the physics behind the

transitional behavior of the chain.

Finally, magnetic manipulation can also be used for assembling complex structures via remote

control46-48. These complex structures are of interest since they can allow researchers to build meta-

materials with unique optical properties49. There are two main approaches for magnetic assembly

of colloidal particles. In the first approach, paramagnetic colloids (or nonmagnetic colloids

10

suspended in ferrofluid), are used above a magnetic substrate with a known pattern and by applying

magnetic fields particles can be trapped and assembled to form a variety of structures such as

honeycombs50-53. It is also possible to utilize this technique to form uniform monolayers of Dimers

(two particle assemblies) and Trimes (triangular assembly of three particles)50. In the second

approach, both paramagnetic and diamagnetic colloids are mixed with ferrofluid and by varying

the applied magnetic field and also using different particle sizes in the solution, many different

types of colloidal crystals can be formed46,47 (Figure 1.3a, b). In this approach the inter-particle

forces and also volume fraction of the particles used, play an important role in uniform spacing of

the structures obtained. Similar complex structures can also be assembled via using electrical

manipulation54,55 (Figure 1.3c).

Despite all the advantages of the aforementioned techniques, there are some issues that need to be

addressed. In the magnetic substrate approach issues with re-configurability rise and system is only

able to switch from the state that particles are not assembled to a state that particles are assembled

based on the known magnetic pattern. Assembling structures in a re-configurable way where

switching from one type of assembly to another can be achieved by just changing the magnetic

field characteristics is a topic that deserves further research in the field of optics. In addition,

although the ferrofluid approach is capable of achieving complex structures for optical

measurements, using ferrofluid as a background fluid can change the absorption or transmission

peaks of the assembled structures and this adds some complexity to our optical measurements. In

order to take a step toward addressing these challenges, three dimensional magnetic fields are

designed that are capable of manipulating the assembly of magnetic colloids suspension. This

technique can help with magnifying the measured optical signal and also enabling the use of a

wider area for optical measurements.

11

Figure 1.3) a) Assembly of Saturn rings by using paramagnetic and non-magnetic particles while

submerged in ferrofluid46. b) Hierarchical assemblies can be achieved by using different types of

particles and volume fractions47. c) Using electrostatics to assemble oppositely charged particles

has given rise to new structures54.

12

2. Theory

In this section, models that have been used to characterize the behavior of magnetic colloids are

discussed.

2.1 Magnetic Properties

Magnetic materials are categorized into five different classes based on their magnetization. These

categories are referred to as ferromagnetism, ferrimagnetism, paramagnetism, diamagnetism, and

antiferromagnetism56,57. Ferromagnetic materials are types of materials that respond to applied

fields and gain parallel alignment of moments. Furthermore, Ferromagnetic materials retain a

magnetization upon removal of the applied magnetic field. Ferrimagnetic materials are types of

materials that are composed of two magnetic sublattices where although, some of the ions have

their moments aligned in an antiparallel arrangement, the moments do not completely cancel out

each other and a net magnetization remains even after removing the applied field. It is observed

that above a critical field strength, both class of materials will reach a level of magnetization that

is known as saturation magnetization (Ms). In addition hysteresis (history dependent

magnetization) is one of the other concepts that is seen in ferromagnetic and ferrimagnetic

materials depicted in Figure 2.1a.

It has to be mentioned that both ferromagnetic and ferrimagnetic materials are sensitive to

temperature. Specifically when ferromagnetic materials are heated above Curie temperature, the

spin-spin coupling in these materials can no longer overcome the thermal fluctuation energy and

they exhibit an almost linear behavior with no hysteresis which is referred to as paramagnetism

(Figure 2.1b). Paramagnetic materials still respond to applied magnetic fields but they do not have

the ability to retain their magnetization upon removal of the field.

13

Diamagnetic materials are another type of magnetic materials that can be found in nature. In

presence of magnetic fields, these materials show a magnetization in the opposite direction of the

applied magnetic fields. As a result, these materials are going to be repelled by the applied

magnetic fields. Diamagnetic materials also lose their magnetization upon removal of the field

similar to what have been seen in paramagnetic materials. Finally, antiferromagnetic materials are

types of materials that show no net magnetization in presence of magnetic fields and this is due to

the fact that the arrangement of moments in the magnetic sublattices is such that they cancel out

each other.

There is a new type of magnetic material that has been developed lately and is referred to as

superparamagnetic material. Superparamagnetic materials are basically ferromagnetic materials

that are small in size (e.g. 15nm). These materials do not show any remanence in the absence of

applied magnetic fields but have the capability to exhibit tremendous magnetic responses in

presence of applied magnetic fields.

Figure 2.1) Typical Hysteresis curve for a) ferromagnetic materials and b) paramagnetic material

where Mp denotes the particle magnetization and Ms denotes the saturation magnetization58.

14

In this work, microparticles that are filled with superparamagnetic materials have been used for

magnetic assembly. One of the major discussions that has been arisen around superparamagnetic

microparticles is the fact that these particles can experience torque and studies have been done to

show the origin of this torque. It has been suggested that this torque arises from the magnetic

anisotropy of the particle which is due to aggregation of the superparamagnetic materials inside

the shell of the microparticle59,60. These torque effects are minimal and can be neglected for

intended studies in this work.

2.2 Magnetic Interactions

It is known that the magnetic field around a single magnetic colloid can resemble the magnetic

field of a dipole under certain conditions. The magnetic dipole expression is the simplest

expression that can be considered for describing the magnetic interactions between a pair of

magnetic dipoles. Results obtained by this equation can qualitatively explain the observed

phenomena in experiments but it needs to be mentioned that this expression fails to give accurate

descriptions when particles are near contact or high magnetic field strengths and high susceptibility

particles are being used. The main reasons for this inaccuracy are that interacting particles affect

each other’s magnetic moment due to generated local field and furthermore this model is not

capable of capturing the multipolar effects. Below the magnetostatic energy between two

interacting dipoles can be seen61

4

3 . . 2.1

Where and denote magnetic moments of particle i and j. is the pair separation vector. By

taking the derivative of this expression we can get to the magnetic force expression shown below

15

3 0

4 5 . . .5 . .

2 2.2

If a low magnetic field strength and/or a low particle susceptibility is used, magnetic moment of

the particle can be slaved to the applied magnetic field and in addition multipolar effects can be

neglected (this model is known as Dipolar Model). As a result, m can be described by

2.3

Where x is the magnetic susceptibility of the particle. is the external magnetic field applied

and is the volume of the particle.

As it was mentioned previously the dipolar model doesn’t account for the effects that particles

have on each other’s magnetic moments. Hence, a new model called Mutual Dipolar Model62 is

suggested to be used when dealing with particles that have relatively high susceptibilities. In this

model a correction term is added to the magnetic moment expression and can be described as

43

3 . . 4

2.4

In order to solve for m either iterative methods that are less computationally expensive can be used

or a system of linear equations can be formed and magnetic moments can be found by taking the

inversion of the coefficients matrix with computational cost being part of the solution.

Recently, there have been efforts toward refining the mutual dipolar model so that it can resemble

the profile obtained by the exact solution of the Laplace’s equation63,64 but in this work the original

derivation by Zhang and Widom62 is used since at length scales of interest the difference between

refined models and the original model is negligible.

16

Finally, it should be mentioned that the mutual dipolar model is going to become singular at a

certain susceptibility for magnetic particles. In such cases using quasi analytic models is no longer

justified and full solution of Laplace’s equation, by satisfying initial conditions and boundary

conditions, should be used coupled with calculation of Maxwell stress tensors for each particle65.

2.3 Hydrodynamics

Similar to magnetics interaction, there are different approaches that can be taken into account for

studying hydrodynamics interactions of particles. The simplest possible analytic expression for

drag around a sphere at low Reynolds numbers is Stokes drag. In order to derive the Stokes drag

expression, Navier-Stokes equation for an incompressible fluid should be first written

. 2.5

Where is the mass density of the fluid, u is the velocity field, p is the pressure, is the viscosity

and f is representing the external body forces.

By assuming a low Reynolds number and also scouting a stationary solution the Navier-Stokes

equation can be reduced to

2.6

There are two boundary conditions that are imposed on the solution of this equation. First, no-slip

condition on the surface of the sphere and second, it is considered that there is a uniform flow with

speed U far from the sphere.

In order to obtain the drag expression around a sphere, pressure should be determined. After

obtaining the pressure expression and calculating stress tensors, the component of the stress tensor

17

in the direction of the uniform flow far from the sphere can be chosen and by integrating this

component over the surface of the sphere we can get to the analytic expression for Stokes drag

force

6 2.7

A key assumption of Stokes Law is that there are no nearby particles to affect the fluid flow pattern,

which would not be true for the situations considered here. None-the-less, the Stokes drag

expression is employed to describe the hydrodynamics in parts of this thesis and depending on the

problem that it is being used for, results obtained can qualitatively match the experimental data.

In order to account for the effects of particles on each other, hydrodynamics interactions known as

Stokesian Dynamics are considered. In this case, in order to obtain an expression for the motion

of a particle in flow, Faxen Laws for spheres are used66

61

16

2.8

Ω Ω8

12

2.9

203

1110

2.10

Where ’ denotes the disturbance velocity field caused by other particles in the suspension,

denotes the velocity of the impressed flow, is the strain rate of the disturbance flow, is

strain rate of the flow, and Ω is the vorticity of the flow.

18

Detailed explanation about the derivation of expressions for hydrodynamics interactions and also

their computational cost can be found in other works66-68 as it is not the purpose of this thesis but

in summary by solving equations 2.8-2.10 for each particle, a grand mobility matrix (M) can be

formed which translates the velocities, angular velocities, and rate of strains to forces, torques, and

stresslets. This grand mobility matrix for two particles can be formed as below66

Ω ΩΩ Ω

. 2.11

α and β denote two different particles. Analytical expressions for calculating the mobility

coefficients can be used based on Durlofsky, Brady, and Bossis’ paper66

, ,

, ,

2 ,

32

13

13

12

4

12

,

2.12

19

Where the scalar function are given as below

1,32

1

1,34

12

0,34

34 ,

34

34 ,

38

0,94

185

0,65

0, 98

910 ,

92

545

910 ,

94

365

910 ,

95

Mobility matrix can be expanded for higher number of particles based on pair-wise additivity.

Also, it should be noted that this model is only considering the long range interactions and is

neglecting the lubrication effects between particles. In order to incorporate these interactions, the

grand resistance matrix is formed where

2.14

2.13

20

In this case, R denotes the grand resistance matrix, is the inverse of the mobility matrix and

is the two body lubrication matrix developed based on Jeffrey and Onishi’s derivations for

nearly touching spheres67. It should be mentioned that this lubrication matrix also accounts for

long range interactions that are already described by . As a result, the two body reflected

interactions that are already included in should be subtracted. In order to do so, a two body

resistance matrix based on the inversion of the two body mobility matrix is developed ( ).

Finally, notice that for computing these singular lubrication terms, the surface-surface separation

of particles is set at 10 when overlap occurs69. Furthermore, the stresslet terms are not

considered in this model since there is no significant shear contribution in the system.

2.4 Brownian Motion

Brownian motion is basically the random motion of particles in a fluid suspension and it rises from

the collisions that atoms or molecules of the background fluid have with the particle. Contributions

of Brownian motion may be significant for some cases that are considered in this work. As a result,

a Brownian force expression needs to be added to equation of motion. Incorporation of Brownian

motion depends on whether Stokes drag or hydrodynamics interactions are implemented in the

simulation. If Stokes drag is the hydrodynamics considered for simulations then a simple Brownian

force equation can be implemented as below

2 ∆⁄ 2.14

Where kB is Boltzmann’s constant, T is the temperature (K), ∆ is the time step of the simulation, is a

random number generated based on a normal distribution, and /6 is Einstein’s diffusion

coefficient in reference to an isolated particle.

21

Calculation of Brownian forces while considering hydrodynamics interactions is going to be based on

forming the grand resistance matrix (R) based on a FT model which means terms related to forces and

torques are considered. In order to obtain the grand resistance matrix, it is needed to take the inversion of

the grand mobility matrix when all coefficients in equation 2.11 are calculated. The obtained resistance

matrix is no longer based on pair-wise interaction and it represents a multibody interacting system. In this

case, Brownian force expression can be written as below70,71

2 ∆⁄ 2.15

Where L is a lower triangular matrix that is found by Cholesky decomposition of the positive definite matrix

RFU. RFU is part of the resistance matrix that relates the forces to velocities.

2.5 Sterics Model

One necessary force that has to be implemented in order to prevent particles from overlapping is

the sterics model. In this thesis two different types of sterics are used which are very

computationally efficient. The first model used is a simple Hookean spring described as

2 20 2

2.16

Where denotes the stiffness of the spring, r is the pair separation magnitude and a is the radius

of the particle. To obtain an appropriate value for the stiffness of the spring, the summation of the

magnetostatic and spring energy is minimized based on a certain overlap.

The second model used is a sterics exponential model called the excluded-volume force which is

considered for simulation of hard spheres13,15,72

22

23

4 2 2.17

Where is vacuum permeability, a is the radius of the particle, m denotes the magnetic moment

of particle i, r is the center to center distance. Suggested value used for ε is 30 which can be

modified based on different inputs13.

2.6 Magnetic Field Gradients

Studying aggregation kinetics and mobility of particles are of interest in this thesis. In these

systems usually high gradient systems are used to guide particles from a low to a high density field

position. To account for this force in the numerical scheme a magnetic gradient force is used that

ignores the magnetization in-homogeneities across the body of the particle

. 2.18

Where is the vacuum permeability, m is the magnetic moment, and H is the applied magnetic

field.

2.7 Numerical Scheme

To complement the obtained analytic expression, a numerical simulation has been developed to

observe particle interactions using particle simulation dynamics modeled with a Matlab code. The

force balance was used to determine the instantaneous velocity of the particles at each time step of

the simulation according to the following Langevin equation:

(2.19)

23

For microparticle simulations, the inertial term can be neglected allowing magnetics,

hydrodynamics, sterics, and Brownian equations combined to solve for the instantaneous particle

velocity, . A simulation run involves calculating the new position of a particle at each time step

according to forward Euler method

, , z, , , z, ∆ , , z, ∆ (2.20)

By considering Brownian dynamics with Hydrodynamics interactions70,73-76 the position of the

particles can be updated in the following form based on the pre stated assumptions in this thesis

, , z, , , z, ∆ ∆ ∆ 2.21

Here, represents the position of the particle in space as a function of time, and R denotes the

resistance matrix that relates velocities to forces. Note that the second term in eq. 2.21, known as

the spatial gradient of the resistance matrix, is expensive to be computed explicitly. In this case, a

method suggested by Banchio and Brady77, based on Fixman’s78 midpoint algorithm, is used in

order to avoid these expensive computations.

24

3. Numerical and Experimental Platforms

3.1 Numerical Platform

Equations mentioned in the theory section were solved by using Matlab. This program is very

efficient for simulating dilute concentrations of dipolar colloids in non-confined space. Major

drawbacks related to this program are high computational time for simulation of nanoparticles with

inertia and also the inability to model high volume fractions of particles that are interacting with

walls placed at the boundary. In order to be able to visualize the interactions of the magnetic

particles, positions of all beads were saved in a text file that was then read by a visualization

software called Ovito.

3.2 Experimental Platform

Magnetic Particles: Four different synthesized and commercial magnetic micro- and nano-

particles were employed in this thesis including dilute suspensions of 2.8 µm M-270 Carboxylic

Acid Dynabeads (Invitrogen, 0.512), dilute suspensions of 2.29 μm fluorescent magnetic

polystyrene particles (Corpuscular, 0.163), 130 nm PEG-coated (PEG 300) iron oxide

nanoparticles (Micromod, 1.76), and 150 nm PEG-coated iron oxide nanoparticles

(synthesized, 4.36). The 150 nm nanoparticles were synthesized according to literature79.

Briefly, fluidMAG-D starch-coated iron oxide nanoparticles (chemicell GmbH, Germany) were

crosslinked with epichlorohydrin and then reacted with ammonium hydroxide to produce an

aminated magnetic nanoparticle (MNP). The aminated MNP was then reacted with Methoxyl

polyethylene glycol succinimidyl ester (mPEG-NHS) to obtain the PEGylated magnetic

nanoparticles. Analysis of the particles using a Zetasizer Nano ZS (Malvern ,Worcestershire, UK)

dynamic light scattering instrument yielded an average intensity-based hydrodynamic diameter of

25

144 ± 18 nm and a zeta potential of 37.4 ± 1.7 mV. The sizing of the 2.29 µm was verified with

scanning electron microscopy. The magnetic susceptibilities indicated above were determined

using a MPMS-XL superconducting quantum interference device magnetometer (Quantum Design

Inc., San Diego, CA).The particles were initially in aqueous suspensions and were added

volumetrically to glycerol-water solutions for in-situ testing.

Figure 3.1) SEM image of 2.8 µm particles (M-280 Streptavidin Dynabeads).

Magnetic Field Setup: Magnetic fields were applied either with computer-controlled solenoids

(low gradient) or a motorized permanent magnet (high gradient). For the case of the low gradient

field, two 4 inch diameter iron-core solenoids are positioned in the x direction and the y direction.

The solenoids are fed with current from two 20-5M Bipolar Operational Amplifiers (Kepco)

controlled with a LabView program. For high-gradient systems, a motorized 2 inch by 2 inch

square rare-earth magnet magnetized through the 0.5 inch thickness (K&J Magnetics) and also a

cylindrical magnet with height and radius of 1 in magnetized through the radius (K&J Magnetics)

26

were used. Magnetic fields generated were measured using 425 gaussmeter (Lake Shore

Cryotronics Inc., OH, USA).

Figure 3.2) Schematic of the magnetic field setup in a rotating magnetic field case.

Visualization and Analysis: Optical microscopy (custom column-mounted Nikon, Zyla Andor

sCMOS camera) was utilized to study the behavior of particle chains in real time while suspended

in a fluid cell with a thickness of ~500 . Particle chains away from the surface of the substrate

were studied for this work in order to avoid surface interactions. Low exposure times were used to

track particles over time and videos were recorded with 10-20 ms time steps. Particle tracking was

done by using the image analysis software Fiji. Obtained positions were used as an input in a

MATLAB code where by assuming uniform magnetic susceptibility for the particles,

magnetostatic energy was obtained. It should be mentioned that visualization of 150 nm particles

was made possible by using a dark-field attachment (MVI Darklite).

In-situ and In-vitro Penetration Studies: For In-situ penetration studies, a capillary system was

designed that exhibited a scaffold barrier in the middle of the capillary. The capillary was

constructed from polypropylene tubing sealed with epoxy to contain Teflon scaffolding that has 2

27

μm pores. The Teflon scaffolding was removed from a PTFE filter (Catalog # SF200T,

Environmental Express). 10 μl of MNPs suspension with a concentration of 1.12 mg/ml was

injected in the input port of the capillary system while applying either dynamic or static magnetic

fields. After 1 hour, the output port was entirely collected to analyze the amount of penetrated

MNPs. Analysis of penetration was conducted with intensity measurements (measured with image

analysis using ImageJ). Panc-1 pancreatic cancer cells (ATCC) were cultured in Dulbecco's

Modified Eagle's Medium (DMEM, Gibco) supplemented with 10% fetal bovine serum (Gibco)

in a humidified 5% CO2 environment. Prior to treatment, Panc-1 cells were transferred to a white,

96-well plate (Fisher) at 10,000 cells/well and allowed to attach overnight. Also, for in-situ studies,

Iron oxide nanoparticles (IONP) were diluted into DI water at concentration of 0.5 mg/ml and the

penetrated liquid was collected after 1 hour, using either a no magnetic field, a constant magnetic

field or a rotating magnetic field. Ultraviolet-visible spectroscopy was used to obtain the

concentration of the Iron oxide nanoparticles.

28

4. Assembly and Disassembly of Microparticles Under Rotating Magnetic

Fields

As it was mentioned previously, dipolar interaction between magnetic particles in a static magnetic

field leads to formation of chains parallel to the external field. The continuously changing energy

landscape of dynamic magnetic fields, on the other hand, prevents magnetic particles from

reaching an equilibrium state of aggregation. These dynamics are dictated by viscous drags that

need to be taken into account. In general, there exist two regimes: 1) the phase-locked regime,

where the orientation between adjacent particles remains fixed relative to the coordinate axis of

the changing external field; and 2) the phase-slip regime where the orientation between adjacent

particles can no longer keep up with the changing external field and the particles are, therefore,

forced to cycle between attractive and repulsive configurations. These repulsive configurations

represent separation events where magnetic particles are driven apart from each other.

Treating the magnetic particles as simple dipoles represents a simplification in this system. As the

separation between two particles approaches contact, full multi-pole expansions of the fields will

provide maximum accuracy. Such accuracy is required when attempting to model particles with

high susceptibilities or in strong fields. Here, we are well below these thresholds and therefore

proceed with simple dipole approximations. The variables are further defined in Figure 4.1.

The dipolar force works to keep the magnetic particles chained in line with the instantaneous applied field.

As the field precesses, the dipole forces work to rotate the chain so that particles remain phase-locked. The

motion of the particles, however, generates a drag force similar to a Stokes force on a particle in flow. The

well-known Stokes equation can be used to express the drag force on a particle in this case in order

to be able to calculate the phase lag and critical frequency.

29

Figure 4.1) Geometry of two magnetic particles in a rotating magnetic field.

Two chained particles in line with the applied field experience zero angular force. As the field

begins to rotate at a radial frequency of 2 , the angular magnetic force grows with a growing

until the angular magnetic force balances with the counteracting Stokes force. Here, the

radial velocity of the particles ( ~2 ) is used in Stokes equation to provide a calculation for

the required for the particles to stay in the phase-locked condition ( and

2 ) as:

Phase-Locked Regime: 144 ⁄ (4.1)

There are no solutions for Equation 4.1 when 144 ⁄ 1 and this condition represents

the bifurcation for when the system is driven into the phase-slip regime. Thus, the boundary

between these two regimes exists at a critical frequency, , as follows:

144⁄ (4.2)

The angular magnetic force experiences a maximum when = π/4. If the phase lag gets driven

beyond this point (i.e. ) , the two particles will continue to phase slip since the angular

magnetic force begins to reduce. Once the particles slip beyond the first magic angle

30

0.3 , the particles enter a repulsive configuration and the particles are driven to disassemble have

a separation event. As the particles separate, the phase lag continues to slip until it reaches the

second magic angle 0.7 , and the particles again have moved into an attractive

configuration and re-assemble. We believe that such separation events can be exploited to allow

magnetic particles to penetrate porous media during magnetic targeting. It is interesting to note

that is not a function of the particle radius, . The accuracy of this expression is therefore

questionable when Brownian motion starts to play a significant role in the particle dynamics.

Smaller particles will be subjected to higher random forces that would eventually work to drive

them apart when they are rotating under fields slightly below the critical frequency. Thus, these

smaller particles should experience a higher average separation relative to their radii as compared

to larger particles.

To understand magnetic particle responses to rotating fields, numerical predictions were conducted

using the approach detailed in the theory section. In each case a range of frequencies was tested

and the simulation results were analyzed. In this case, an example of simulation results for two

2.29 μm particle assemblies above and below the critical frequency calculated according to

Equation 4.2 is shown in Figure 4.3a,b for a fluidic environment of η =2.5 mPa s. Below the critical

frequency, the angular magnetic forces work to rotate the chains with the rotating field but are

counteracted by the viscous forces working against this reorientation. This force balance develops

the expected phase lag predicted by Equation 4.1 (Figure 4.2).

31

Figure 4.2) Phase lag is a function of the applied frequency. Below the critical frequency this phase

lag is found to be constant in numerical simulations (dots) and fits well with predictions from Eq.

4.1 (solid line).

As the rotational frequency of the applied field is increased beyond the critical frequency, the

viscous forces drive the particles into the phase-slip regime. Once the particles rotate beyond the

magic angle, the interaction of their moments induces repulsive interactions, creating a separation

). Tracking of the separation between these simulated particles normalized to the particle radius,

/ , is shown in Figure 4.3c for frequencies below (0.1 Hz), near (2 Hz), and well above

(5 Hz). The average separation was tracked for a range of frequencies and is shown in Figure

4.3d, demonstrating the non-linear dynamics of the response to the oscillating field by this particle

pair. At higher frequencies, separation events are more frequent, but less significant. At the critical

frequency, separation events are the largest but occur less frequently. Thus, maximum separation

of the magnetic particles occurs in the region slightly above the critical frequency, where the

32

separation events are both significant and somewhat frequent. This realization highlights the

importance of properly characterizing the experimental system in each case to maximize dis-

aggregation.

These simulations were carried out across the design space of frequency and viscosity to compare

the numerically observed critical frequency with the analytic value derived from Eq. 4.2. As shown

in Figure 4.3e, the analytic theory (red line) and the numerical prediction are determined to nicely

agree with each other.

The numerical simulation and the analytic model were then compared against experimental

observations of several different two particle assemblies in a η =2.5 mPa s carrier fluid. Figure 4.4

shows 2.29 μm particles oscillating in a rotating magnetic field. Below the critical frequency (

0.1 , Figure 4.4a), the two particles are able to stay aggregated and rotate with the applied field.

Above the critical frequency ( 1.87 , Figure 4.4b), separation events were observed during

field application. The separation between the two particles was tracked in both cases and closely

matched the numerical predictions that incorporate Brownian motion (Figure 4.4c,d).

33

Figure 4.3) Simulation results for 2a=2.29 μm, =0.163, η=2.5 mPa s for a) 0.1 Hz and b) 2 Hz

( 1.87 ). c) Normalized separations, , are plotted over time for different rotational

frequencies. d) There is a non-linear response in the average separation for a specific viscosity

of 2.5 mPa s. e) A phase diagram can be attained for the average de-aggregation separation between

two particles across rotational frequencies and viscosities. This compares well with Equation 4.1

(red line).

34

Figure 4.4) Aggregated pairs of 2.29 μm particles were subjected to 100 Oe rotating magnetic

fields at a) 0.1 Hz and b) 2 Hz. c) Below the critical frequency for this system ( =1.87 Hz), the

particles remain in an aggregated state. d) Above the critical frequency, many separation events

are observed. Numerical simulations agree well with experimental results.

Figure 4.5) a) The maximum normalized separation, δ , and b) the frequency of those separation

events between two particles under a rotating magnetic field is plotted. Phase lag is a function of

the applied frequency. Red lines are just visual guides.

35

Studying two particle assemblies for a wide range of frequencies above the critical frequency

shows that although the pair separation magnitude between the two particles goes down as

frequency of the field is increased but the ratio of slipping (separation) frequency to field frequency

is eventually going to reach 2 (Figure 4.5a,b).

Moving beyond two particles assemblies, we start looking into effects of number of particles (N)

on chain dynamics. In this case, in collaboration with Hamed Abdi and Craig Maloney, the

dynamics of four particle chains in presence of rotating magnetic fields was studied. Prior to

beginning the discussion on dynamics of a four particle chain, it is required to introduce one major

concept (known as Mason number) that is used for describing the behavior of bead chains in the

presence of rotating magnetic fields. Mason number is basically a dimensionless number that is

described by the ratio of hydrodynamics to magnetics forces11,15,31,72. In this work, the derivation

of Gao et al.13 is used for mason number which also captures the effects of number of particles

present in the chain

161 ln 2

2.4 4.3

Where N is the number of particles, is the angular velocity of the magnetic field applied, is

the viscosity of the fluid, x is the susceptibility of the particle, and H0 is the strength of the applied

magnetic field.

36

Figure 4.6) a) Rigid body behavior at Mn=0.7659, b) Do-Si-Do motion (periodic behavior) at

Mn=1.1489, and c) Transient chaotic behavior leading to formation of c) molecules and d) clusters

at Mn=4.7871.

It is known that as the number of particles is increased in the chain, the critical frequency goes

down. This can be explained by the increased drag presented in the structure. In this work, detailed

simulations depicted that in a four particle system, there exist three different regimes (equivalent

to stating that system goes under two transitions). These transitions are labeled as first and second

critical frequency in this work. Below the first critical frequency, the chain acts as a rigid rod and

basically a rigid body motion is observed (Figure 4.6a). Above the first and below the second

critical frequency, a type of periodic motion is observed in which the bead chain breaks in the

middle and there are two rotating dimers that depict stick-slip events similar to American square

dancing (labeled as Do-Si-Do in this work, Figure 4.6b). Above the second critical frequency,

37

system shows a very complex behavior that has been characterized as transient chaos in our work.

Transient chaos means that a dynamical system depicts a non-periodic/complex behavior for a

number of field rotations before collapsing into a periodic orbit that can either be a close packed

quadramer or a novel colloidal molecule (Figure 4.6c,d). In order to characterize this regime in the

system, a tangent dynamics model was developed by our collaborators and then Largest Lyapunov

Exponent (LLE) was calculated. LLE is basically the parameter that shows whether a system is

depicting a chaotic behavior or not. In a simple explanation, positive LLE means that system is

experiencing chaotic behavior and zero or negative LLE implies that system is non-chaotic.

These three different regimes have also been observed in experiments with two minor differences

that show up at and also (Figure 4.7a, b, c and Figure 4.8). For

, although periodic motion is still observed but unlike the simulation case the stick-slip events

between two dimers are not observed and there is only one particle that detaches and rejoins the

chain periodically (Figure 4.7b). It is believed that this difference lies in the non-uniform magnetic

susceptibility and non-uniform size of the particles. For , formation of molecules has been

observed experimentally for a very short time (before collapsing into a cluster, Figure 4.8). It is

believed that three major factors can contribute to this issue. With two of them already stated, it is

found that the third factor is related to contributions of Brownian motion. In this case, our

collaborators have seen that even the slight existence of temperature (meaning low / , where

is the magnetostatic energy of two particles in contact that are aligned in the field direction) can

make formation of molecules rare.

38

Figure 4.7) a) Rigid body behavior at Mn=1.01, b) Periodic behavior at Mn= 1.76, and c) Transient

chaotic behavior at Mn= 1.92.

Figure 4.8) Unstable molecule observed at Mn=1.92 which collapses into a cluster after a very

short time.

39

As it was mentioned earlier, LLE is a measure for quantifying whether a system is behaving chaotic

or not. Calculating LLE for experimental data is very challenging mainly due to the existing noise

in measurements. In this work, in order to qualitatively characterize these different behaviors, Fast

Fourier Transform (FFT) of the magnetostatic energy was taken. Computing magnetostatic energy

was possible by recording the positions of each particle within the chain over time. Moreover, we

assume nominal contact among particles and use dipole approximation to calculate the magnetic

moment. Time difference between the initiation of the field and recording the positions of the

particles is ±20 ms which introduces some error but doesn’t change the overall behavior. Once the

magnetostatic energy is obtained, Fast Fourier analysis can be performed to characterize the

aforementioned differences. It is known that when a system experiences a periodic motion,

multiple peaks on DFT plot that are integer ratios of each other should rise. Also, in chaotic

systems, it is expected to see a very noisy DFT plot that doesn’t show a major peak in the system.

Our statements have been confirmed by both experiments and simulations in figure 4.9a and b.

Finally, when a system is experiencing chaos, its escape time to a periodic state can be affected by

modifying the initial condition. In this case, our collaborators found that for a specific mason

number, there exists an exponential behavior for survival probability vs. the number of field

rotations. In other words, transition rates necessary for reaching periodic orbits can be described

as a Poisson process. This method can be used to find the probability of forming clusters or

molecules at a specific mason number based on the number of field rotations. In order to verify

this observation experimentally, a specific mason number was chosen and escape rates of 14 chains

over the period of 1 minute were obtained (Figure 4.10). Notice that the plot does not start from

zero due to the fact that out of the fourteen cases studied experimentally, one did not collapse into

40

Figure 4.9) a) Experimental magnetostatic energy, FFT of experimental data, and FFT of

simulations for the periodic regime. b) Experimental magnetostatic energy, FFT of experimental

data, and FFT of simulations for the chaotic regime. Note that magnetostatic energy has been

normalized by the magnetostatic energy of two particles in contact (PE0).

41

Figure 4.10) Fraction of trajectories in chaotic and non-chaotic states for high Ma limit in

experiments. Notice that we only observe escape into clusters.

a cluster over the time period of recording. As a result, the survival probability in the plot starts

from 13/14 and goes to 1 /14. By obtaining the slope of this plot, it can be concluded that

approximately after 8 field rotations 63% of the chains have collapsed into a cluster (Figure 4.10).

This can be clarified by equation below

log 4.4

Where represents the slope and represents the number of field rotations.

42

5. Assembly and Disassembly of Microparticles Under Advanced Magnetic

Field Functions

Though simple rotating field functions are effective in disaggregating magnetic particles from each

other, more complex field functions have the possibility of enhancing and also enabling smart

assembly of particle suspensions. The design space of advanced field functions is very large. To

highlight this we first show a few examples of 2D field functions that lead to higher than the

rotating field function at the critical frequency and then a designed 3D magnetic field is presented

that is capable of both disaggregating and smart assembly of particle suspensions.

5.1 Advanced Two Dimensional Field Functions

In general, higher is expected to coincide with more isolated particles in the concentration zone

though this is dependent upon local packing fraction of the particles. Here two types of 2D

magnetic fields that can lead to higher separation events between two particles are presented. First,

a stepped function is considered (the red line in Figure 5.1a) where the field switches directly from

100 Oe in the x direction to 100 Oe in the y direction at a frequency of 0.5 Hz. Applying this

magnetic field to the numerical simulation shows very large disaggregation (high δ) compared to

the standard rotating magnetic field function and also the pulsed rotating field function.

Similarly, another advanced field function of a pulsed rotating field with a rotational frequency of

and pulse frequency of 1 Hz was simulated (green line in Figure 5.1a). This field function

gives a relatively higher average separation compared to the rotating field. In this setup the time

interval that field is off should not be large since there is a chance of losing the concentration of

the particles. By tuning the applied dynamic fields, particles can stay disaggregated for significant

43

longer times compared to the static fields currently used, while concurrently maintain a strong

magnetic field gradient.

Figure 5.1) a) Shows functions that have been used for the field setup. b) Separation events

obtained numerically (2a=2.29 μm, =0.163, η=2.5 mPa s).

5.2 Three Dimensional Field Functions

In another context, it is known that directed assembly techniques of particle suspensions represent

an exciting approach for the development of reconfigurable optical fluids that can bend, adsorb, or

accentuate light. As two optical particles come together, they create local enhancement to the

44

electromagnetic fields. Magnetic fields allow for the remote control of particle assembly in a

massively parallel format in bulk fluid. However, linear magnetic fields offer very little tunability

for the resultant assemblies. For example, a linear field will provide a time-dependent chain

aggregation of magnetic particles3,80. Instead, 2D rotating fields allow for enhanced tunability,

creating planar assemblies17,18,81. By expanding the applied magnetic field functions into the third

dimensions, a significantly large design space for particle assemblies can be realized.

New particle control opportunities have recently been reported using three-dimensional, transient

magnetic fields that can be defined as coherent where the x, y, and z field components are in phase

with each other. A balanced triaxial field, is capable of forming unique types of particle clusters

such as metastable decorated fused rings and decorated polyhedrons22. 3D magnetic fields have

also shown potential applications in generation of potent noncontact flows where strong mixing

and ballistic droplet motion can be observed in the fluid23,82.

In this section, we discuss numerical, and experimental investigations that have been done to study

the assembly behavior of magnetic particles in presence of incoherent 3D magnetic fields. It is

depicted both numerically and experimentally that applying such incoherent 3D magnetic fields to

suspensions of magnetic particles enables unprecedented control over the assembly of particle

clusters. Gaining additional order and tunability by changing the applied 3D magnetic fields from

coherent to incoherent is dramatic and surprising. Incoherent magnetic fields can assemble

monodisperse particle clusters in bulk fluid and exhibiting long term stability. Such ordered

clusters can either serve as well-defined colloidal building blocks for bottom-up manufacturing or

as tunable components in optical or rheological particle suspensions.

45

5.2.1 Incoherent 3D Magnetic Fields

The 3D magnetic field considered in this paper is the superposition of two coherent field

components that generate a rotating field in the x-y plane at while an incoherent field

component generates oscillations in the z direction at (Equation 5.1).

sin cos cos (5.1)

Here is the magnitude of the x-y magnetic field and is set to a constant value of 8 mT throughout

this work. In addition, A is the ratio between the magnitudes of the z magnetic field relative to the

x-y field.

5.2.2 Particle Response to Incoherent Fields: Two-Body Case

The response of two paramagnetic particles to incoherent fields is poorly understood and is

investigated here. Two paramagnetic particles in an incoherent field from Equation 1 show a

surprisingly rich and complex behavior that exhibits regions of stability, multiple critical

frequencies, and some chaos-like behavior. This two-body phase diagram shown for 1 in

Figure 5.2 is plotted in terms of the average displacement between the particle surfaces, , and

shows parabolic and linear boundaries among five distinct regions in the phase space (Regions I

to VI). The frequency is normalized by the critical frequency of a 2D rotating field case, . The

validity of the presented phase diagram has been tested for four different initial conditions and no

significant changes were observed (see Figure 5.3). This phase diagram represents 20340

independent numerical simulations run and analyzed for 120s of experimental time to provide

sufficient temporal characterization to be comparable with experimental observations. It is noted

that long-term observation of chaos-like regimes in coherent 2D fields have been observed to

46

Figure 5.2) Phase diagram for mean separation between a particle pair when subjected to

incoherent 3D magnetic fields for different field ratios, a) 1, b) 0.5, c) 2.

Simulations were done at 0.01 Hz increments and considering 120 seconds real time interaction

between particles.

Figure 5.3) Phase diagram shown for different initial conditions where α is representing both θ and

φ in spherical coordinates.

47

eventually transition to stable clusters and similar behavior in these incoherent 3D fields is an open

question.

Region I represents the rigid body regime where the field precesses sufficiently slow to allow the

two particles to rotate with a phase lag as a connected dimer. The phase lag varies due to the

changing magnitude of the magnetic field which also leads to nanoscale compression and

relaxation of the dimer. This nanoscale oscillation is shown for one such dimer (

1.06 , 1.21 ) in Figure 5.4a where both the instantaneous displacement ( ) and the

Discrete Fourier Transform (DFT) of are presented. The peak frequency of the DFT plot

corresponds to the frequency of the out-of-plane field. Regions II-VI comprise the separation

regime divided from Region I by a parabolic function that represents a changing critical frequency.

This parabolic function approaches both at low and high . At low , the z-field dynamics

are significantly slower than the in-plane dynamics and, during the long periods when 0, the

dimer will exhibit separation events according to x-y fields. At high , the z-field dynamics are

significantly faster than the particle dynamics and the dimer does not significantly deflect from the

in-plane orientation at 1 and the system begins to converge with the coherent 2D rotating field

case. For moderate , the field dynamics are better matched with the limits of the dimer dynamics

and a synergetic region of stability exists in the ‘nose’ of the parabolic region. In this region, the

magnitude of the z-field contributes to keeping the particles together while the frequency of the z-

field is not too high that the particles can’t respond.

As and are increased, at least five different regions develop that depict clear micron scale

separations between particles. Similar to the rotating magnetic field case where maximum

48

separation between particles is observed at , Regions III, and IV depict a region with high

mean separation right after the region characterized with nanoscale compression and relaxation.

In Region II, the dimers undergo complex periodic and aperiodic, separation events. Figure 5.4b

shows an example of an aperiodic separation profile. There is a clear, but poorly understood,

texturing of in this region.

Region III, is characterized by a mixture of periodic and aperiodic separation profiles similar to

Region II. Figure 5.4c depicts the nature of one aperiodic dimer seen in this region where no clear

peaks in the DFT plot are observed. In some cases, particles greatly separate ( 3 ) resulting in

very weak magnetic interactions between particles, an observation that is comparable to a

disaggregated state.

In Region IV, simple slipping events similar to a 2D rotating magnetic field case are observed as

shown in Figure 5.4d The slipping events occur as Hz goes to zero giving rise to DFT peaks at

integer factors of . As increases, the maximum separation between particles decreases.

Regions V and VI are very similar and are characterized by ≪ . In both, the average

separation gets larger with increasing as the x-y contribution smears out into a time-averaged

force along the x-y plane leaving the slowly oscillating Z-field as a purely repulsive contribution

to the assembly driving larger separations. Figure 5.4e displays a typical separation profile in this

region. The maximum peak in the DFT plot is associated with by a factor of 2. This can be

explained by monitoring the strength of the out of plane field (Hz) where it is noticed that as Hz

weakens, slipping events appear. Movies for all cases are available in SI (see Supplementary

Videos 1-5).

The phase diagrams have also been considered for 0.5 and 2 as shown in Figure 2b and

c. The regions in the phase diagrams evolve with different field ratios. As → 0, the system

49

Figure 5.4) Discrete Fourier Transform (DFT) and separation profile are shown for a)

1.058, 1.209. b) 1.511, 2.116. c) 1.722, 1.511. d)

1.813, 1.058. e) 1.964, 0.226. Note that ,, .

converges with the coherent 2D rotating field case. This convergence is observed in the flattening

of the nose of the phase-locked regime from 2 → 1 → 0.5. Meanwhile as ≫ 1, the z field

begins to dominate manipulating the energy landscape. At 2, large separation events are

observed at high and low even leading to separation events that reach up to 7 times the

50

radius of the particle. Such separations reduce the magnetic interactions to energy levels well

below to justify the claim that these particles are completely disaggregated. This subset of our

results appears consistent with prior work by van Reenen et al.83 in which similar 3D field

functions have been coupled to magnetic field gradients and were reported to entirely dis-aggregate

colloidal clusters.

5.2.3 Particle Response to Incoherent Fields: Eight-Body Case

Though the two-body case is already rich with phases and phenomena, the interesting application

space of these field-driven particle assemblies lie in even denser suspensions. To move a little

closer to dense particle suspensions, the eight-body case was also considered in this work.

Specifically, chains of eight particles were subjected to magnetic fields both numerically and

experimentally to test if incoherent magnetic fields could drive the assembly of coherent particle

clusters. Our numerical simulations have shown that at 1, a variety of eight particle structures

can be formed by changing fxy and fz. For example, at specific frequencies shown in Figure 5.5a-b,

eight-body chains break into monodisperse fragments, such as in the form of monomers or dimers,

respectively. This fragmentations can be observed by tracking the evolution of the magnetostatic

energy from the initial eight-body chained state to the final fragmented state over long simulation

times as shown in Figure 5.5a-b. The ability to produce four stable, coherent dimer assemblies

from incoherent magnetic fields is quite surprising to us. We conducted experimental

investigations in this frequency area to verify the observed phenomena in simulations. We

discovered that controlled monomers and dimers could indeed be experimentally produced as

shown in Figure 5.5c. Interestingly, to find very stable monomers and dimers, the strength of the

out of plane field (Hz) was increased to provide a field anisotropy of 2. These deviations

between experiment and theory are attributed to the simplifications in the hydrodynamic and

51

magnetic numerical model coupled with the dispersity of the experimental particles in both size

and susceptibility. Still, these regions of the phase space can reliably produce monomers or dimers

throughout a suspension. In the experimental example of the formed dimers, the x-y positions of

the center of mass for each dimer are tracked over time in Figure 5.5d. As it can be seen, the

separation of the dimers is quite stable with a slight tendency to drive the dimers further apart,

further enhancing the stability of these assemblies and indicating that these dimers are no longer

strongly interacting with one another in this incoherent field.

Figure 5.5) Numerical simulations depicting a) Formation of Singlets at A=1, 1.322, and

0.952 and b) Formation of Dimers at A=1, 0.476, and 0.634. Experiments

depicting c) Formation of Singlets (I) at A=2, 0.74, and 1.057 and formation of

Dimers (II) at A=2, 0.453, and 0.767 d) Approximate distance of Dimers from each

other calculated by recording xy positions.

52

To achieve a more comprehensive understanding of the eight-body system, simulations were done

for a wide range of frequencies and resulting particle assemblies were analyzed to identify the

fraction of different types of assembly lifetimes formed over the course of the simulated time. As

shown in Figure 5.6, the phase transitions in the system aren’t as clear as in the two-body case, but

clearly disparate behaviors can be observed in different regions of the phase space. Specifically,

six notable points have been identified in Figure 5.6 by asterisks that highlight these different

regimes. Point i depicts formation of coherent dimers where a chain of eight particles will

dissociate into four dimers that are stable and non-interacting (Figure 5.5b). Similarly, Point ii

shows an incoherent field regime that produces non-interactive monomers (Figure 5.5a).

Increasing the frequency of both fields further induces unique assemblies in the eight-body system.

Point iii depicts cluster formation of two quadramers that exhibit long term stability (Figure 5.7a).

Surprisingly, this island of stability occurs at higher frequencies than the stable dimers. Naively,

we would have expected the bigger assemblies to only be stable when the fields are oscillating

with slower dynamics. Still, slightly away from this region at Point iv these quadramers initially

form but exhibit short term stability and collapse into sheet-like crystal structures to minimize their

energy (Figure 5.7b) similar to structures reported previously19,84. Similarly, there are cases where

formation of a trimer and a pentamer is preferred and show long or short term stability (Points v

and vi, see figure 5.8a,b).

Similar to the cases of the monomers and dimers, experiments were conducted to verify the

existence of these higher order structures. Formation of unstable quadramers and an unstable

trimer/pentamer pair was achieved at the 1 condition (Figure 5.7c). Exploring around the

phase space experimentally could not produce convincing islands of stability for trimers,

quadramers or pentamers. Therefore, to stabilize these higher order assemblies, we devised a slight

53

modification to the out of plane magnetic field that further drove the system into incoherency by

adding a second oscillating term to as follows:

cos 22.22

cos 4 5.2

This additional oscillating term was found to sufficiently frustrate the system such that the eight

particles never collapsed into the sheet-like crystalline state over the course of experiments. Using

this modified function, we identified an experimental condition that produced stable quadramers

for long time periods with 1.5, shown in Figure 5.7c. Though complex, the phase space for

the eight-body case is also rich and filled with island of stability in which coherent particle

assemblies can be produce from incoherent magnetic fields.

Figure 5.6) Non-Brownian, simulated probability of a cluster having a given size ( 1 8).

Statistics of cluster size are reported throughout 2000 seconds of simulated time from an original

8 particle chain subjected to 3D fields across different and . Specific frequency

combinations (marked i-vi) lead to interesting responses including the formation of stable

monomers (ii), dimers (i), and quadramers (iii).

54

Finally, specific eight-body simulations were repeated with Brownian motion to study finite

temperature effects on the stability of formed particle clusters. Figure 5.9 shows side-by-side

comparisons between non-Brownian (right) and Brownian (left) simulations at frequencies that

result in interesting cluster formations (i.e. monomers, dimers, quadramers). Initial results suggest

Figure 5.7) Numerical simulations depicting a) Formation of Quadramers at A=1, 1.957,

and 2.221 with better stability and b) Formation of unstable Quadramers at A=1,

1.957, and 1.904. c) Approximate distance of Quadramers from each other calculated by

recording xy positions where the unstable Quadramers were obtained at A=1, 1.036, and

1.244 (red line) and Quadramers with better stability were obtained with modified field

function at A= 1.5, 1.642, and 1.747.

55

Figure 5.8) Formation of a) Stable trimer/pentamer pair at 1.75, 1.90 and b) Unstable

trimer/pentamer pair at 2.17, 2.22.

that inclusion of Brownian motion could play a significant role in the stability of formed structures

even at small temperatures / ~10 . This role can be either to add destability or,

surprisingly, stability to formed particle clusters. For some cases, and due to the stochastic nature

of Brownian motion, longer transition times are needed to form the assemblies (e.g. formation of

quadramers in Figure 5.9 f compared to Figure 5.9 e). In some case, finite temperature effects lead

to insignificant changes in outcomes as shown for the formation of dimers in figures 5.9c, d.

However, in other cases, finite temperature effects could in fact lead to stabilizing formed clusters,

such as in the formation of quadramers in Figure 5.9f. Here, the stochastic nature of Brownian

motion seemed to help avoid the collapse of two neighboring quadramers into sheetlike structures.

Interestingly, in this case, the addition of Brownian motion to the simulation leads sometimes to

stable quadramer pairs and sometimes to stable trimer/pentamer pairs (figure 5.10).

56

Figure 5.9) Numerical simulations done without and with Brownian motion to study the effects of

temperature where a, b) Shows formation of Singlets at A=1, 1.322, and 0.952. c, d)

Shows formation of Dimers at A=1, 0.476, and 0.634. e, f) shows formation of

Quadramers at A=1, 1.957, and 1.904 and g, h) Shows formation of Quadramers at

A=1, 1.957, and 2.221 with better stability.

57

Figure 5.10) Probability of achieving either quadramers or a trimer/pentamer pair presented for 3 different cases.

58

6. Assembly and Transport of Magnetic particles in Presence of Static

Magnetic Fields

Mobilizing rods and chained particles has shown potential applications in fields such as magnetic

targeting. In these techniques, particles are used either as carriers or vortex inducers in the fluid

for delivery purposes. In such cases, detailed investigations on hydrodynamics interactions of

particles in proximity of walls are essential in order to understand how these mechanisms work.

Early studies on this topic were focused on mobility of single spheres in proximity of a planar wall

where drag coefficient modifications are suggested for both cases of perpendicular and parallel

movement of the sphere85 but as it can be imagined such modifications are not promising when a

chain of particles is considered. As a result, slender body theory86 has been suggested to

approximate the chain mobility in cases where the length of the chain is much longer than the

diameter of the particle. In this case, a good estimation for both the friction coefficient and the

sedimentation velocity can be attained. Notice that this model is based on considering the chain as

a prolate ellipsoid and is not capturing the particle-particle interactions. In general, such

simplifications show less accuracy in calculating the velocity of chained particles.

Development of more accurate hydrodynamics models66,67 has made it possible to consider

particle-particle interactions when dealing with such systems. In these models, the hydrodynamics

interactions can be broken into two parts of far field (FF) and near field (NF) interactions. The

dominant many body interactions can be captured by FF interactions but this model still lacks the

effects of lubrication. By adding the NF interactions, where the focus is on shearing, squeezing,

pumping, and twisting motions between particles, this issue can be resolved.

59

In this section, we focus on studying the mobility of chained magnetic particles in proximity of a

hard planar wall. This study is broken into two sections where we first discuss the effects of

magnetics interactions by considering both the simple dipolar model (DM) and the more complex

mutual dipolar model (MDM). In section two, we consider hydrodynamics interactions where both

FF and NF interactions have been incorporated based on a Force-Torque Stokesian dynamics

model. Also, wall interactions have been accounted for to an extent. Finally, we consider the

effects of thermal fluctuations in our system by doing Brownian dynamics simulations. Moreover,

In order to verify the obtained results, experiments have also been done.

Although results presented in this section are based on using microparticles for both experiments

and simulation, we believe that similar trends should also be seen with nanoparticles. Furthermore,

simulating microparticles is less computationally expensive compared to nanoparticles where both

very small time steps and simulation times should be considered to study different phenomena.

6.1 Magnetics Interactions

As mentioned earlier, we first focus on magnetics interactions among particles by considering both

simple dipolar and mutual dipolar models. In such cases, it is known that in low magnetization

regimes, particles would not see a noticeable magnetic moment enhancement while interacting

with each other in a chain. As a result, utilizing the simple dipolar model would be a good

approximation for modeling magnetic interactions. To further verify this claim, Figure 1a depicts

the average moment enhancement for different chain lengths and magnetizations where in the case

of χ=0.1 the curve saturates at a nominal 2% enhancement. On the contrary, in most experimental

cases, we deal with particles that have much higher magnetizations where the moment

enhancement can be as high as 1.5 times (χ=1.7) the value reported by the dipolar model. Notice

60

Figure 6.1) a) magnetic moment saturation shown for different susceptibilities by increasing the

number of particles. b) Polynomial trend observed for different chain sizes by increasing the

magnetization of particles. c) Ratio of increase in magnetic moment in a Brownian case over a

zero temperature case defined as 1 / 1 . d) Ratio of magnetostatic

energy over thermal energy for cases presented in c. d) Effects of Brownian motion presented by

reducing the size of particles for a chain of N=10 where the field is held constant at 10 Gauss. d)

Snapshots of N=10 chain for different sizes at χ=2.1 and H=10 Gauss.

61

in simple cases where hydrodynamics interactions are not considered, there is a direct correlation

between moment enhancement and chain velocity. This means that final chain velocity for

different chain lengths would show the exact trend and enhancement that is presented in figure 1a

for magnetic moments. Moreover, it can be seen in figure 1a that moment enhancements will

eventually saturate as the number of particles in the chain is increased. In this case, the saturated

moment enhancement value is extracted and plotted for different magnetizations where a fitting

curve that relates the average moment enhancement value to susceptibility is suggested (Figure

1b). Such simplifications can be used to roughly approximate the final chain velocity without using

the exact mutual dipolar model. Finally, in this section, we present numerical simulations with

Brownian motion for a chain of N=10, where field strength, size, and susceptibility of the particles

are changed. In this case, we first present results for a chain of 1 µm particles and compare the

increase in moment in presence of Brownian motion with the expected increase in moment at zero

temperature (Figure 6.1c). Also, for further clarification, the ratio of magnetostatic energy over

thermal energy ( / ) is presented in figure 6.1d. As it can be seen, at low values of / ,

increase in moment can be as low as half of the expected value. Although, by further increasing

both susceptibility and field strength, it is seen that surprisingly at 18 the average moment

enhancement can reach (less than 10% discrepancy) the expected non Brownian value. This means

that fields as low as 2 mT can be applied to get adequate magnetic response among commercial 1

µm particles. Moreover, we show moment enhancement for a chain of 10 particles, where both

susceptibility and size of the particles are changed while the field is kept constant at 1 mT. In this

case, it is seen that microparticles with a size of 2.8 µm are not affected by Brownian motion and

values obtained for moment enhancement match the suggested non-Brownian curve. As the size

of the particles is decreased, the structural integrity of the chain is lost. This can be seen for both

62

1µm particles at low susceptibilities and in all magnetization cases for 500 nm particles (Figure

6.1e, f). In these cases, Brownian motion dominates the system and leads to breakage of chains

where no reformation of the chain can be observed. On the other hand, it should be noted that

although 1µm particles respond weakly to magnetic fields at low magnetizations, their response is

improved in the high magnetization limits and reaches the presented non Brownian case.

6.2 Hydrodynamics Interactions

To further characterize the mobility of chained magnetic particles, effects of hydrodynamics

interactions were studied. In this section, we present results for mobility of chains with different

lengths based on FF interactions, FF+NF interactions, and slender body theory. Notice that

calculation of friction coefficients based on FF and FF+NF interactions has been discussed in great

detail in the theory section and here we only present friction coefficient (ξ) calculations based on

slender body theory for motion parallel to the main axis of the chain87

ξ||

.

. (6.1)

Where 2

Our results show that inclusion of hydrodynamics interactions can depict much higher impacts on

chain mobility where by increasing the number of particles, we can observe an improved chain

velocity due to hydrodynamics shielding among particles (Figure 6.2a, b, c). It should be noticed

that all aforementioned models depict the qualitative exponential behavior for improvement in

velocities vs. the length of the chain but the question is rather which model is more accurate. In

this case, we present experiments done, in high magnetic field strengths and gradients (630 Gauss,

300 Gauss/cm) and also in proximity of a hard wall, on 2.8 µm magnetic particles with χ=0.512 in

63

order to see which model can also depict quantitative agreements. As it can be noticed from figure

6.2a, the comparison among different models with experiments shows that slender body theory

has the lowest accuracy for chains with low anisotropy. Furthermore, although the FF model is

somewhat an accurate model but it neglects the shearing and squeezing motions among particles

at contact hence leading to overestimation of the chain velocity. As a result, the best quantitative

agreement can be seen with the more sophisticated FF+NF model (Figure 6.2a). Finally, although

the FF+NF model is predicting the chain velocities close to experimental measurements, it is

noticed that there is a discrepancy between numerical simulations and experimental data. This is

due to the fact that experimental measurements were done in proximity of a wall where friction

coefficients among particles can be changed significantly based on the distance they have from the

surface. In order to account for that, we use a correction coefficient, based on movement of a single

Figure 6.2) a) Mobility of chains presented for three different models and experiments. Brownian

dynamics simulations presented where b) is depicting initial position of chains at t=0 s and c)

shows the distance (δ) traveled by chains after 5 seconds.

64

sphere in proximity of a hard wall, to match the velocities acquired in simulations with

experiments. Still, since this approximation is not considering the interaction of particles with each

other in proximity of a hard wall, the discrepancy between simulation and experiment increases as

the number of particles is increased. In order to resolve this issue, more complicated models can

be used that account for particle interactions near a no slip boundary88. Notice that this model is

not considered in this work and it is unknown to what degree it can resolve the discrepancy

between simulations and experiments.

In conclusion, in this section, we discussed the mobility of chained magnetic particles from both

magnetics and hydrodynamics point of view. Furthermore, effects of thermal fluctuations on chain

stability were discussed. In general, results presented here suggest that aggregates of magnetic

particles can achieve a better transport velocity in comparison with individual particles. This

finding can be used in magnetic targeting systems to guide magnetic particles in a more controlled

way in order to achieve higher drug delivery efficiencies.

65

7. Improving in-vitro Magnetic Targeting with Advanced Magnetic Field

Functions

In this section, we investigate applying dynamic fields to the topic of magnetic targeting. This

application creates a novel additional step (i.e. penetration) to the typical four step process

conventionally envisioned for magnetic targeting applications as shown in fig. 7.1. The penetration

step relies upon the application of dynamic fields to disaggregate MNPs. Again, these dynamic

magnetic fields are characterized by time-dependent changes in the applied magnetic field

magnitude, the magnetic field direction, or the magnetic gradient.

Figure 7.1) Generic schematic of the proposed five step process for magnetic drug targeting.

The envisioned five step magnetic targeting process starts with the assembly of the magnetic

carriers, where in this case particles that are passive against proteins are required. By obtaining the

functionalized particles, an aggregated transport phase is developed to achieve better transport

velocities where detailed discussions on this section were presented in chapter 6. Once these

aggregations reach the fibrotic tissue, time dependent magnetic fields are used to dynamically tune

the direction (but not magnitude) of the field. As discussed earlier, this can lead to better diffusion

of nanoparticles through the porous tissue as compared to constant magnetic fields39. Finally, by

passing through the extra cellular matrix (ECM) and reaching the cancer cells, the delivery mode

66

is triggered where the coated nanoparticles get endocytosed by the cells and then small interfering

RNA acts to knockdown cancerous cell genes.

In this chapter, the assembly of functionalized particles, the penetration, the endocytosis, and the

delivery of MNPs are discussed. Results presented here are based on three cases of no magnetic

field, constant magnetic field, and dynamic magnetic field. Notice that the transport mode has been

discussed in the previous chapter and will not be presented here in great detail (Figure 7.2).

Figure 7.2) Detailed description of the proposed five step process where coated MNPs are guided

by utilizing high field gradients. By reaching the tumor site, transport mode is triggered where

dynamic magnetic fields are used for disaggregation and then endocytosis of particles is observed

where eventually the designed complex degrades and siRNA acts to silent the cancerous genes.

67

7.1 Identification of Potential Applications for Advanced Magnetic Targeting

As previously discussed, it is known that in some cases current drug delivery techniques are not

efficient because of not being able to target specific areas in the body with enough drug

concentration. In these cases, magnetic targeting becomes a compelling method for guiding and

concentrating drug at desired areas. For example, in patients dealing with hearing loss, the drug

needs to be delivered throughout the cochlea with high concentrations but the current existing

method is based on painful injections with low efficiencies (Figure 7.3, left panel). In this case,

clinical studies done with magnetic drug targeting have shown a much better efficiency in guiding

and concentrating the drug at cochlea89. Moreover, it has been shown that magnetic targeting can

also be used for transsclera drug delivery where by applying magnetic fields the dosage of the drug

would stay the same and drug is not going to be flushed in fluid exchange90 (Figure 7.3, mid panel).

In this work, we develop the five step process to target pancreatic cancer cells. Patients diagnosed

with pancreatic ductal adenocarcinoma (PDAC) have a five year survival rate of less than 5% and

a median survival rate of only six months91 (Figure 7.3, right panel). In this case, in collaboration

with Gino Karlo Delos Reyes and Hicham Fenniri, in-vitro magnetic targeting studies on

pancreatic cancer cells have been done based on delivering genes to silence the mutated KRAS

gene that is implicated in 95% of PDAC patients92.

This choice is justified by the fact that in this case since pancreas is vascularized, it is relatively

easy to get drugs near the cancer cells. Furthermore, it should be noted that the fibrotic tissue

around the cancer cells is hypoxic, but porous. As a result, the penetration mode needs to be

triggered to enable better diffusion of drugs for reaching the tumors.

68

Figure 7.3) Proposed clinical studies for magnetic targeting techniques by other groups and this

work. Main challenges with conventional methods used are listed in the figure89,90.

7.2 Assembly of Magnetic Carriers for Magnetic Targeting

In order to target pancreatic cancer cells effectively, we can use biocompatible Rosette Nanotubes

(RNTs) as a tunable carrier to carry a therapeutic RNA payload to silence the gene93. The building

blocks of the RNTs are fused guanine-cytosine bases, hereby referred to as GC bases, entropically

form a six membered hexameric rosette through Watson-Crick hydrogen bonding. These rosettes

then stack upon one another through π-π interactions, forming nanotubes of tunable length. The

major advantage to the RNT motif is that the GC building blocks can be functionalized with a

variety of functional groups such as aptamers, proteins, or polypeptides. These functional groups

are then decorated on the surface of the RNT, allowing for the attachment of different

functionalities such as cellular targeting, drug loading, and immune evasion. In this case, we use

69

Figure 7.4) a) Schematic of the layer by layer assembly where both b) hydrodynamic diameter and

c) Zeta potential measurements have been done to verify the LbL assembly. TEM images of

nanoparticles d) before and e) after RNT coating can be seen.

small interfering RNA (siRNA) where this synthetic RNA is engineered to match the native RNA

and it is designed to disrupt the translation of messenger RNA to prteins and genes. Inspired by

the layer-by-layer (LbL) assembly technique developed in Paula Hammond’s Group at the

Massachussetts Insitute of Technology, we constructed multifunctional magnetic nanoparticles

70

that are layered with RNTs and siRNA (Figure 7.4a). To achieve this LbL assembly, we use

carboxylic acid (-COOH) functionalized iron oxide nanoparticles (130 nm average diamater). The

–COOH functinoalization imparts on the nanoparticles a net negative charge on the surface of the

nanoparticles in aquous conditions. Because of this net negative charge, we can thus take

advantage of the facile LbL assembly schema94. By introducing the SPIONs into a solution

containing 1 µM of positively charged RNTs (in this case, we are using lysine functionalized

RNTs), we can efficiently and effectively coat the surface of the SPIONs. This process of assembly

can then be extended by “dipping” these functianolzied SPIONs into a 1 µM bath of siRNA. The

negatively charged phosphodiester backbone of the siRNA electrostatically interacts with the

positively charged RNT coating, creating a multifunctional nanoparticle. We further assessed the

efficiency of our nanoparticle coating using Dynamic Light Scattering (DLS), by measuring the

effective hydrodynamic diameter (Figure 7.4b) and also zeta potential (Figure 7.4c) to confirm

that subsequent layers of interchanging charges are coating the nanoparticle. As it can be observed

in Figure 7.4b, as more layers are added using the LbL approach, the effective diamater of the

particles increases in a predictable manner. By analzing the zeta potential of each layer, we notice

this saw tooth pattern emerge, characteristic of the interchanging surface charges of each layer.

Furthermore, Figure 7.4d and e show the TEM image of a RNT-coated and uncoated Iron oxide

nanoparticle. Finally, using the Ribogreen assay, which chelates and subsequently fluorescences

when bound to intact, free siRNA, it was determined that 16.65% of the siRNA solution gets

adsorbed to the RNT-coated Iron oxide nanoparticles. This corresponds to 886 molecules of

siRNA per nanoparticle and agrees with previously published data on layer by layer

nanoparticles94.

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7.3 Magnetic Transport of Magnetic Carriers

As it was previously discussed in chapter 6, by aggregating magnetic carriers, better transport

velocities under high field gradients can be achieved. To be able to guide magnetic suspensions

within the body, using an endoscopic probe that is equipped with a high field gradient magnet is

suggested. In this case, particles can easily be attracted to the probe without losing much of the

drug concentration, since there is relatively a short distance between the probe and the point of

injection.

7.4 Penetration of Magnetic Carriers through Porous Tissue

Though disaggregation in magnetic targeting systems is aided by Brownian motion, nanoparticles

of sufficient size and magnetic susceptibility still form linear chains in experiments under modest

applied fields (100 Oe). Experiments were completed with synthesized 150 nm magnetic particles

exhibiting magnetic susceptibility of 4.36. In these nanoparticle suspensions, linear

aggregation of 150 nm magnetic nanoparticles occurs very quickly in 100 Oe magnetic fields

(Figure 7.5c). Under rotating fields of low frequencies, 150 nm magnetic particles will still form

chains despite the influence of Brownian motion (Figure 7.5a). These chains can easily reach

lengths of 3 μm within short times which is, for example, above the characteristic porosity of tumor

tissue. This observation establishes the significance of running these field setups at higher

frequencies to allow for the proper disaggregation of the magnetic particles. At higher frequencies

of 2.5 Hz, the magnetic nanoparticles were found to disaggregate below the visible length-scale of

the dark field microscope setup (Figure 7.5b). This frequency is still well below the critical

frequency (for these strongly magnetic particles at 4.36). Therefore it is believed that though

complete disaggregation down to individual nanoparticles is not occurring, the longer particle

72

chains are indeed being broken apart. For most delivery applications, maintaining aggregate sizes

below 500 nm is sufficient to penetrate porous tissues.

Figure 7.5) Experimental dark-field micrographs of 150 nm magnetic particles under rotating

fields of a) 0.1 Hz frequency and b) 2.5 Hz frequency. c) significant aggregation in 150 nm

magnetic nanoparticles under static fields after 2 minutes. The magnetic field gradient was 60

Oe/cm and the applied magnetic field was 165 Oe. d) Dynamic fields studied here immediately

de-aggregate nanoparticles while maintaining 165 Oe and 60 Oe/cm.

73

Figure 7.6) a, d) Schematics depicting how gradient and dipolar forces can affect the sytem under

constant and rotating magneti fields where by applying constant magnetic fields, particles

aggregate at the edges (b, c) and by initiating the dynamic magnetic field, disaggregation is

triggered and nanoparticles diffuse through the membrane (d, e). Relative concentartion

measurements for these field condition is presented in section g.

74

A rotating field was then combined with a magnetic field gradient by using the motorized

permanent magnet setup. In this system, the permanent magnet attracted the 150 nm particles to a

target area (Figure 7.5c,d). Clear linear aggregation of the magnetic particles occurred during this

step. Then, the magnetic field was rotated with a known frequency and the chains quickly

disaggregated within seconds. The field rotation was then interrupted and the nanoparticles again

quickly reformed linear aggregates near the target area.

To further characterize the system, we perform diffusion studies by using Matrigel transwell

membrane inserts with 3 µm pore sizes where the inserts act as a barrier to replicate the extra

cellular matrix (ECM). These experiments are done at three different field conditions with both

constant and rotating magnetic fields and to further characterize these different field conditions

with respect to Brownian motion, we use the equation below

9 7.1

Where represents the magnetostatic energy, is the susceptibility, is the strength of the field,

is the radius of the particle, is the field gradient, is vacuum permability, is Boltzmann’s

constant, and is the temperature.

In these experiments, it is seen that by applying constant magnetic fields and gradients,

nanoparticles aggregate at the edges of the membrane inserts. This can be explained by the fact

that the gradient of the magnet is much stronger at the edges close to the poles (Figures 7.6a, b, c).

By enabling the dynamic magnetic field setup which in this case is a rotating magnetic field,

disaggregation of magnetic nanoparticles is seen (Figures 7.6d, e, f). Qualitatively comparing the

concentration of MNPs at the end vs. the beginning of the experiment depicts a vast color

difference suggesting that most of the MNPs have penetrated (Figure 7.6c, f). Finally, quantitative

75

measurements for penetration of magnetic nanoparticles under constant and rotating magnetic

fields was done by Ultraviolet visible spectroscopy where these results are depicted in Figure 7.6g.

It is seen that in both experimental conditions, dynamic magnetic fields outperform constant fields.

In this case, 3 and 10 fold increase in penetration of magnetic nanoparticles is achieved by using

the dynamic field setup for each experimental condition.

7.5 Endocytosis of Magnetic Carriers

It is known that large charged molecules do not have the ability to diffuse through the cell

membrane in a passive format. In such cases, an active transport form known as endocytosis occurs

where cells transport molecules by engulfing them. In order to characterize the uptake mechanism

in our work, we used Fluorescent microscopy to determine and visualize the transfection efficiency

of the SPION-RNT nanoparticles. As illustrated in Figure 7.7, Panc-1 pancreatic cancer cells were

transfected with Alexa 555 labeled, non-targeting siRNA molecules (si555) both without (Figure

7.7b) and with (Figure 7.7c) delivery using the SPION-RNT nanoparticles for 4 hours. Untreated

Panc-1 cells were also used as a negative control (Figure 7.7a). These images demonstrated that

the cells transfected using the SPION-RNT nanoparticles exhibited higher signal in the Alexa 555

channel than the cells that were treated with si555 alone. In comparison, little to no fluorescent

signal is observed in the cells treated with si555 alone. This can be explained by the fact that

siRNA molecule is a large negatively charged molecule, which makes it difficult to cross the

cellular membrane as previously discussed. The SPION-RNT delivery vehicles, on the other hand,

are uptaken by the cells in an active manner through interactions with various surface receptors. It

is also worth noting the strong, diffuse signal within the cytoplasm of the cells transfected with the

SPION-RNTs, suggesting that the siRNA has escaped the endosome into the cytoplasm where it

can exert its therapeutic effect. We theorize that the RNTs have the ability to encourage endosomal

76

escape through its ability to buffer the pH of the late endosome, which can lead to swelling and,

thus, a leakier endosomal membrane. These results indicated that the nanoparticles can effectively

protect the siRNA and deliver it within the cytoplasm, exhibiting a higher delivery efficiency than

cells treated without a delivery vehicle.

Figure 7.7) a) Untreated Panc-1 pancreatic cancer cells. b) Treated cancer cells with siRNA only.

c) Treated cancer cells with MNP+RNT+siRNA. Note that blue areas are the nucleus and the

orange areas are the siRNA.

7.6 Delivery of Cargo from Magnetic Carriers

Finally, viability of cancer cells was studied under different conditions (Figure 7.8). In this case,

cells were transfected for 4 days and then Cell Titer Glo Luminescent Assay was used to evaluate

the viability of cells. It is seen that MNP+RNT+siRNA under rotating magnetic field can match

the viability results obtained by RNT+siRNA only where in both cases 50% of the cancer cells

were found dead. On the other hand, it can be seen that both no magnet and stationary magnet

cases were not effective in reducing the viability of cancer cells which implies that concentration

of the siRNA is below the efficacy threshold. Also, our results confirm that indeed attachment of

RNTs to MNPs does not reduce the efficacy.

77

Figure 7.8) Viability of cells evaluated under different conditions.

78

8. Conclusions and Future Work

The goal of this work is to investigate less explored concepts in magnetic manipulation with a

specific focus on magnetic targeting techniques for localized drug delivery and also smart

assembly of particles for possible applications in tunable optical systems and magnetorheology. In

this work, we first investigated the non-linear response of dilute particle suspensions. More

specifically chains of two and four particles were studied in great detail and phase transitions were

reported based on the driving frequency of the rotating magnetic field. There are still open

questions concerning this section of the dissertation where the existence of molecules presented

by numerical simulations is yet to be reported in experiments. In order to take a step toward

answering this question, particles with great uniformity in size and susceptibility should be

achieved. In this case, synthesizing stable ferrofluid emulsions can be considered as a path to be

taken for answering this question. Furthermore, more detailed studies on effects of Mason number

and Brownian motion should be done to be able to effectively target formation of such structures

experimentally. Finally, it should be noted that the effects of such time dependent magnetic fields

on rheological properties of particle suspensions is a less explored concept and more detailed

studies need to be done. Moving beyond 2D magnetic fields, I presented a unique 3D magnetic

field that is capable of both smart assembly and disassembly of magnetic particles. In this section

we reported on formation of stable monomers, dimers, and quadramers both numerically and

experimentally by looking at 8 particle-chains. Uniform distribution of coherent assemblies

demonstrated in this work opens up new possibilities for building unique and reconfigurable

colloidal devices for optical95-97 or microfluidic applications98. The design space for incoherent

fields is immense and assuredly offers many more undiscovered and exciting islands of stability.

Notice that in this chapter, in order to match experimental data with numerical simulations,

79

modifications in applied magnetic fields were suggested. This discrepancy between numerical

simulations and experiments can be explained by the non-uniform size and susceptibility of the

particles. Furthermore, it is unknown to what extent hydrodynamics interactions are affecting the

system. More detailed studies both in numerical and experimental sections should be considered

to be able to resolve this discrepancy.

Finally, in the last two chapters of this thesis, we discussed a novel five step method for assembly,

transport, penetration, endocytosis, and delivery of drugs for treating pancreatic cancer cells. More

specifically, initially it was shown how RNTs can be used as a drug carrier in tandem with MNPs.

Moreover, it was discussed how aggregations of magnetic particles can gain a better transport

velocity vs. individual particles. We discussed this from both magnetics and hydrodynamics point

of view. In this case, applying a constant magnetic field with high gradient is suggested as the

transport mode to concentrate the MNPs at tumor site. Upon reaching the tumor site, we suggested

the use of dynamic magnetic fields to trigger the penetration mode and disaggregate magnetic

nanoparticles. By exploiting dynamic fields, a dynamic energy landscape is generated that can

catch particles in repulsive configurations, causing them to break apart. This disassembly process

allows the magnetic nanoparticles to travel into the smallest capillaries such as the extracellular

channels between tumor cells. Furthermore, both in-situ and in-vitro experiments have shown that

dynamic magnetic fields enhance the diffusion of magnetic nanoparticles. In this case, we also

demonstrated that using this method can lead to bringing down the viability of Panc-1 pancreatic

cancer cells by 50%. Future work in this section includes repeating experiments with a 3D cell

culture where this is a more representative model of the actual tumor that would be targeted in in-

vivo studies. Upon completion of these complicated in-vitro models, we can think about using

animal models to test our system.

80

A major concept that was not discussed in this work, is improving tunable optical materials with

advanced field functions. As it was mentioned earlier by using directed assembly techniques,

reconfigurable optical fluids can be achieved that can bend, adsorb, or accentuate light. In order to

achieve this, magnetic fields can be used since they allow for the remote control of particle

assembly in a massively parallel format in bulk fluid. In this case, either magnetic field setup

suggested in chapter 5 or magnetic templates can be used to reversibly assemble optical particles

(Figure 8.1). Development of such optical systems can lead to a new generation of optical devices

that can be used for many different applications.

Figure 8.1) a) Schematics of how these formed structures can change either transmission or

absorption peaks of infrared light going through the suspension. b) Schematics of suggested

approaches for assembling these structures.

81

References

1 Erb, R. M., Martin, J. J., Soheilian, R., Pan, C. & Barber, J. R. Actuating Soft Matter with Magnetic Torque. Advanced Functional Materials, n/a-n/a, doi:10.1002/adfm.201504699 (2016).

2 Domínguez-García, P., Melle, S., Pastor, J. M. & Rubio, M. A. Scaling in the aggregation dynamics of a magnetorheological fluid. Physical Review E 76, 051403 (2007).

3 Erb, R. M. et al. Beyond diffusion-limited aggregation kinetics in microparticle suspensions. Physical Review E 80, 051402 (2009).

4 Promislow, J. H. E., Gast, A. P. & Fermigier, M. Aggregation kinetics of paramagnetic colloidal particles. The Journal of Chemical Physics 102, 5492-5498, doi:doi:http://dx.doi.org/10.1063/1.469278 (1995).

5 Climent, E., Maxey, M. R. & Karniadakis, G. E. Dynamics of Self-Assembled Chaining in Magnetorheological Fluids. Langmuir 20, 507-513, doi:10.1021/la035540z (2004).

6 Hynninen, A.-P. & Dijkstra, M. Phase Diagram of Dipolar Hard and Soft Spheres: Manipulation of Colloidal Crystal Structures by an External Field. Physical Review Letters 94, 138303 (2005).

7 David, A. E., Cole, A. J., Chertok, B., Park, Y. S. & Yang, V. C. A combined theoretical and in vitro modeling approach for predicting the magnetic capture and retention of magnetic nanoparticles in vivo. Journal of Controlled Release 152, 67-75, doi:http://dx.doi.org/10.1016/j.jconrel.2011.01.033 (2011).

8 Zhou, J., Zhang, J., David, A. E. & Yang, V. C. Magnetic tumor targeting of β-glucosidase immobilized iron oxide nanoparticles. Nanotechnology 24, 375102 (2013).

9 Biswal, S. L. & Gast, A. P. Mechanics of semiflexible chains formed by poly(ethylene glycol)-linked paramagnetic particles. Physical Review E 68, 021402 (2003).

10 Biswal, S. L. & Gast, A. P. Rotational dynamics of semiflexible paramagnetic particle chains. Physical Review E 69, 041406 (2004).

11 Biswal, S. L. & Gast, A. P. Micromixing with Linked Chains of Paramagnetic Particles. Analytical Chemistry 76, 6448-6455, doi:10.1021/ac0494580 (2004).

12 Vuppu, A. K., Garcia, A. A. & Hayes, M. A. Video Microscopy of Dynamically Aggregated Paramagnetic Particle Chains in an Applied Rotating Magnetic Field. Langmuir 19, 8646-8653, doi:10.1021/la034195a (2003).

13 Gao, Y., Hulsen, M. A., Kang, T. G. & den Toonder, J. M. J. Numerical and experimental study of a rotating magnetic particle chain in a viscous fluid. Physical Review E 86, 041503 (2012).

14 Kang, T. G., Hulsen, M. A., Anderson, P. D., den Toonder, J. M. J. & Meijer, H. E. H. Chaotic mixing induced by a magnetic chain in a rotating magnetic field. Physical Review E 76, 066303 (2007).

15 Melle, S., Calderón, O. G., Rubio, M. A. & Fuller, G. G. Microstructure evolution in magnetorheological suspensions governed by Mason number. Physical Review E 68, 041503 (2003).

16 Melle, S., Fuller, G. G. & Rubio, M. A. Structure and dynamics of magnetorheological fluids in rotating magnetic fields. Physical Review E 61, 4111-4117 (2000).

82

17 Casic, N., Schreiber, S., Tierno, P., Zimmermann, W. & Fischer, T. M. Friction-controlled bending solitons as folding pathway toward colloidal clusters. EPL (Europhysics Letters) 90, 58001 (2010).

18 Yan, J., Bae, S. C. & Granick, S. Rotating crystals of magnetic Janus colloids. Soft Matter 11, 147-153 (2015).

19 Weddemann, A., Wittbracht, F., Eickenberg, B. & Hütten, A. Magnetic Field Induced Assembly of Highly Ordered Two-Dimensional Particle Arrays. Langmuir 26, 19225-19229, doi:10.1021/la102813w (2010).

20 Müller, K. et al. Pattern Formation and Coarse-Graining in Two-Dimensional Colloids Driven by Multiaxial Magnetic Fields. Langmuir 30, 5088-5096, doi:10.1021/la500896e (2014).

21 Ray, A. & Fischer, T. M. Magnetic Field Controlled Composite Paramagnetic–Diamagnetic Colloidal Phases. The Journal of Physical Chemistry B 116, 8233-8240, doi:10.1021/jp212222z (2012).

22 Martin, J. E., Anderson, R. A. & Williamson, R. L. Generating strange magnetic and dielectric interactions: Classical molecules and particle foams. The Journal of chemical physics 118, 1557-1570 (2003).

23 Martin, J. E. & Solis, K. J. Fully alternating, triaxial electric or magnetic fields offer new routes to fluid vorticity. Soft Matter 11, 241-254 (2015).

24 Sing, C. E., Schmid, L., Schneider, M. F., Franke, T. & Alexander-Katz, A. Controlled surface-induced flows from the motion of self-assembled colloidal walkers. Proceedings of the National Academy of Sciences 107, 535-540, doi:10.1073/pnas.0906489107 (2010).

25 Lamar, O. M. et al. Highly controllable near-surface swimming of magnetic Janus nanorods: application to payload capture and manipulation. Journal of Physics D: Applied Physics 44, 125001 (2011).

26 Goldman, A. J., Cox, R. G. & Brenner, H. Slow viscous motion of a sphere parallel to a plane wall—II Couette flow. Chemical Engineering Science 22, 653-660, doi:http://dx.doi.org/10.1016/0009-2509(67)80048-4 (1967).

27 Franceschini, A., Filippidi, E., Guazzelli, E. & Pine, D. J. Dynamics of non-Brownian fiber suspensions under periodic shear. Soft Matter 10, 6722-6731, doi:10.1039/C4SM00555D (2014).

28 Franceschini, A., Filippidi, E., Guazzelli, E. & Pine, D. J. Transverse Alignment of Fibers in a Periodically Sheared Suspension: An Absorbing Phase Transition with a Slowly Varying Control Parameter. Physical Review Letters 107, 250603 (2011).

29 Moses, K. B., Advani, S. G. & Reinhardt, A. Investigation of fiber motion near solid boundaries in simple shear flow. Rheol Acta 40, 296-306, doi:10.1007/s003970000135 (2001).

30 Jenness, N. J., Erb, R. M., Yellen, B. B. & Clark, R. L. 776227-776227-776213. 31 Petousis, I., Homburg, E., Derks, R. & Dietzel, A. Transient behaviour of magnetic micro-

bead chains rotating in a fluid by external fields. Lab on a Chip 7, 1746-1751, doi:10.1039/B713735B (2007).

32 Martinez-Pedrero, F. & Tierno, P. Magnetic Propulsion of Self-Assembled Colloidal Carpets: Efficient Cargo Transport via a Conveyor-Belt Effect. Physical Review Applied 3, 051003 (2015).

33 Jemal, A., Siegel, R., Xu, J. & Ward, E. Cancer Statistics, 2010. CA: A Cancer Journal for Clinicians 60, 277-300, doi:10.3322/caac.20073 (2010).

83

34 Rooseboom M., C. J. N., Yermeulen N.P. Enzyme-catalyzed activation of anticancer prodrugs. pharmacol. rev. 56 (2004).

35 Elias, A., Crayton, S. H., Warden-Rothman, R. & Tsourkas, A. Quantitative Comparison of Tumor Delivery for Multiple Targeted Nanoparticles Simultaneously by Multiplex ICP-MS. Sci. Rep. 4, doi:10.1038/srep05840 (2014).

36 Kirpotin, D. B. D., D.C.; Shao, Y.; Shalaby, M.R.; Hong, K.; Nielsen, U.B.; et al. . Antibody targeting of long-circulating lipidic nanoparticles does not increase tumor localization but does increase internalization in animal models. The Journal of Cancer Research 66, 6732-6740 (2006).

37 Fan Yuan, M. D., Dai Fukumura, Michael Leunig, David A. Berk, Vladimir P. Torchilin, and Rakesh K. Jain. Vascular Permeability in a Human Tumor Xenograft: Molecular Size Dependence and Cutoff Size. . Cancer Res. 55, 3752-3756 (1995).

38 Wang, J., Lu, Z., Gao, Y., Wientjes, M. G. & Au, J. L. S. Improving delivery and efficacy of nanomedicines in solid tumors: role of tumor priming. Nanomedicine 6, 1605-1620, doi:10.2217/nnm.11.141 (2011).

39 Soheilian, R. et al. Toward Accumulation of Magnetic Nanoparticles into Tissues of Small Porosity. Langmuir 31, 8267-8274, doi:10.1021/acs.langmuir.5b01458 (2015).

40 Anselmo, A. C. & Mitragotri, S. Nanoparticles in the clinic. Bioengineering & Translational Medicine 1, 10-29 (2016).

41 Jolly, M. R., Bender, J. W. & Carlson, J. D. 262-275. 42 Phenomenological Model for Magnetorheological Dampers. Journal of Engineering

Mechanics 123, 230-238, doi:doi:10.1061/(ASCE)0733-9399(1997)123:3(230) (1997). 43 Ukai, T., Morimoto, H. & Maekawa, T. Cluster-cluster aggregations of superparamagnetic

particles in a rotational magnetic field. Physical Review E 83, 061406 (2011). 44 Lin, H.-C., Li, Y.-H. & Chen, C.-Y. Structural instability of an oscillating

superparamagnetic micro-bead chain. Microfluidics and Nanofluidics 17, 73-84, doi:10.1007/s10404-013-1286-6 (2014).

45 Li, Y.-H., Chen, C.-Y., Sheu, S.-T. & Pai, J.-M. Dynamics of a microchain of superparamagnetic beads in an oscillating field. Microfluidics and Nanofluidics 13, 579-588, doi:10.1007/s10404-012-0974-y (2012).

46 Erb, R. M., Son, H. S., Samanta, B., Rotello, V. M. & Yellen, B. B. Magnetic assembly of colloidal superstructures with multipole symmetry. Nature 457, 999-1002, doi:http://www.nature.com/nature/journal/v457/n7232/suppinfo/nature07766_S1.html (2009).

47 Yang, Y., Gao, L., Lopez, G. P. & Yellen, B. B. Tunable Assembly of Colloidal Crystal Alloys Using Magnetic Nanoparticle Fluids. ACS Nano 7, 2705-2716, doi:10.1021/nn400118e (2013).

48 Yang, Y. et al. Assembly of Colloidal Molecules, Polymers, and Crystals in Acoustic and Magnetic Fields. Advanced Materials 27, 4725-4731, doi:10.1002/adma.201500462 (2015).

49 Xia, Y., Gates, B. & Li, Z. Y. Self-Assembly Approaches to Three-Dimensional Photonic Crystals. Advanced Materials 13, 409-413, doi:10.1002/1521-4095(200103)13:6<409::AID-ADMA409>3.0.CO;2-C (2001).

50 Alert, R., Casademunt, J. & Tierno, P. Landscape-Inversion Phase Transition in Dipolar Colloids: Tuning the Structure and Dynamics of 2D Crystals. Physical Review Letters 113, 198301 (2014).

84

51 Tierno, P. Magnetic Assembly and Annealing of Colloidal Lattices and Superlattices. Langmuir 30, 7670-7675, doi:10.1021/la501273b (2014).

52 Yellen, B. B., Erb, R. M., Halverson, D. S., Hovorka, O. & Friedman, G. Arraying Nonmagnetic Colloids by Magnetic Nanoparticle Assemblers. Magnetics, IEEE Transactions on 42, 3548-3553, doi:10.1109/TMAG.2006.879623 (2006).

53 Yellen, B. B., Hovorka, O. & Friedman, G. Arranging matter by magnetic nanoparticle assemblers. Proceedings of the National Academy of Sciences of the United States of America 102, 8860-8864, doi:10.1073/pnas.0500409102 (2005).

54 Demirörs, A. F. et al. Long-Ranged Oppositely Charged Interactions for Designing New Types of Colloidal Clusters. Physical Review X 5, 021012 (2015).

55 Leunissen, M. E. et al. Ionic colloidal crystals of oppositely charged particles. Nature 437, 235-240, doi:http://www.nature.com/nature/journal/v437/n7056/suppinfo/nature03946_S1.html (2005).

56 Cullity B. D., G. C. D. Introduction to magnetic materials. John Wiley & Sons (2011). 57 C., O. h. R. Modern magnetic materials: principles and applications. Wiley New York

830622677 (2000). 58 Erb, R. M. Magnetic Manipulation and Assembly of Mulit-component Particle

Suspensions. Thesis, Duke University (2009). 59 van Oene, M. M. et al. Biological Magnetometry: Torque on Superparamagnetic Beads in

Magnetic Fields. Physical Review Letters 114, 218301 (2015). 60 Fonnum, G., Johansson, C., Molteberg, A., Mørup, S. & Aksnes, E. Characterisation of

Dynabeads® by magnetization measurements and Mössbauer spectroscopy. Journal of Magnetism and Magnetic Materials 293, 41-47, doi:http://dx.doi.org/10.1016/j.jmmm.2005.01.041 (2005).

61 Furst, E. M. & Gast, A. P. Dynamics and lateral interactions of dipolar chains. Physical Review E 62, 6916-6925 (2000).

62 Zhang, H. & Widom, M. Field-induced forces in colloidal particle chains. Physical Review E 51, 2099-2103 (1995).

63 Du, D. & Biswal, S. L. Micro-mutual-dipolar model for rapid calculation of forces between paramagnetic colloids. Physical Review E 90, 033310 (2014).

64 Keaveny, E. E. & Maxey, M. R. Modeling the magnetic interactions between paramagnetic beads in magnetorheological fluids. Journal of Computational Physics 227, 9554-9571, doi:http://dx.doi.org/10.1016/j.jcp.2008.07.008 (2008).

65 Kang, T. G., Gao, Y., Hulsen, M. A., den Toonder, J. M. J. & Anderson, P. D. Direct simulation of the dynamics of two spherical particles actuated magnetically in a viscous fluid. Computers & Fluids 86, 569-581, doi:http://dx.doi.org/10.1016/j.compfluid.2013.08.003 (2013).

66 Durlofsky, L., Brady, J. F. & Bossis, G. Dynamic simulation of hydrodynamically interacting particles. Journal of Fluid Mechanics 180, 21-49, doi:doi:10.1017/S002211208700171X (1987).

67 Jeffrey, D. J. & Onishi, Y. Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow. Journal of Fluid Mechanics 139, 261-290, doi:doi:10.1017/S0022112084000355 (1984).

68 SIEROU, A. & BRADY, J. F. Accelerated Stokesian Dynamics simulations. Journal of Fluid Mechanics 448, 115-146, doi:doi:10.1017/S0022112001005912 (2001).

85

69 Phung, T. N., Brady, J. F. & Bossis, G. Stokesian dynamics simulation of Brownian suspensions. Journal of Fluid Mechanics 313, 181-207 (1996).

70 Kumar, A. Microscale Dynamics in Suspensions of Non-spherical Particles. Thesis, University of Illinois Urbana-Champaign (2010).

71 Jager, S. Nonequilibrium dynamics and self-organization in field-driven dipolar colloidal particles. Thesis, Technical University of Berlin (2013).

72 Krishnamurthy, S. et al. Dynamics of rotating paramagnetic particle chains simulated by particle dynamics, Stokesian dynamics and lattice Boltzmann methods. Microfluid Nanofluid 5, 33-41, doi:10.1007/s10404-007-0214-z (2007).

73 Dickinson, E., Allison, S. A. & McCammon, J. A. Brownian dynamics with rotation-translation coupling. Journal of the Chemical Society, Faraday Transactions 2: Molecular and Chemical Physics 81, 591-601, doi:10.1039/F29858100591 (1985).

74 Ermak, D. L. & McCammon, J. A. Brownian dynamics with hydrodynamic interactions. The Journal of Chemical Physics 69, 1352-1360, doi:doi:http://dx.doi.org/10.1063/1.436761 (1978).

75 Mériguet, G., Jardat, M. & Turq, P. Brownian dynamics investigation of magnetization and birefringence relaxations in ferrofluids. The Journal of Chemical Physics 123, 144915, doi:doi:http://dx.doi.org/10.1063/1.2056551 (2005).

76 Sebastian, J., Holger, S. & Sabine, H. L. K. Dynamics of cluster formation in driven magnetic colloids dispersed on a monolayer. Journal of Physics: Condensed Matter 25, 195104 (2013).

77 Banchio, A. J. & Brady, J. F. Accelerated stokesian dynamics: Brownian motion. The Journal of chemical physics 118, 10323-10332 (2003).

78 Fixman, M. Simulation of polymer dynamics. I. General theory. The Journal of Chemical Physics 69, 1527-1537 (1978).

79 Cole, A. J. D., A.E.; Wang, J.; Galbán, C.J.; Hill, H.L.; Yang, V.C. . Polyethylene glycol modified, cross-linked starch-coated iron oxide nanoparticles for enhanced magnetic tumor targeting. . Biomaterials 32, 2183-2193 (2011).

80 Promislow, J. H., Gast, A. P. & Fermigier, M. Aggregation kinetics of paramagnetic colloidal particles. The Journal of chemical physics 102, 5492-5498 (1995).

81 Weddemann, A., Wittbracht, F., Eickenberg, B. & Hütten, A. Magnetic field induced assembly of highly ordered two-dimensional particle arrays. Langmuir 26, 19225-19229 (2010).

82 Martin, J. E. & Solis, K. J. Symmetry-breaking magnetic fields create a vortex fluid that exhibits a negative viscosity, active wetting, and strong mixing. Soft Matter 10, 3993-4002 (2014).

83 van Reenen, A., de Jong, A. & Prins, M. Transportation, dispersion and ordering of dense colloidal assemblies by magnetic interfacial rotaphoresis. Lab on a Chip 15, 2864-2871 (2015).

84 Lumsdon, S. O., Kaler, E. W. & Velev, O. D. Two-dimensional crystallization of microspheres by a coplanar AC electric field. Langmuir 20, 2108-2116 (2004).

85 Brenner, H. Effect of finite boundaries on the Stokes resistance of an arbitrary particle. Journal of Fluid Mechanics 12, 35-48 (1962).

86 Batchelor, G. Slender-body theory for particles of arbitrary cross-section in Stokes flow. Journal of Fluid Mechanics 44, 419-440 (1970).

86

87 Meunier, A. Friction coefficient of rod-like chains of spheres at very low Reynolds numbers. II. Numerical simulations. Journal de Physique II 4, 561-566 (1994).

88 Swan, J. W. & Brady, J. F. Simulation of hydrodynamically interacting particles near a no-slip boundary. Physics of Fluids 19, 113306 (2007).

89 Depireux, D. A. et al. Magnetic Delivery of Therapy to the Cochlea. The Hearing Journal 70, 14-16 (2017).

90 Mousavikhamene, Z., Abdekhodaie, M. J. & Ahmadieh, H. Facilitation of transscleral drug delivery by drug loaded magnetic polymeric particles. Materials Science and Engineering: C 79, 812-820 (2017).

91 Michl, P. & Gress, T. M. Current concepts and novel targets in advanced pancreatic cancer. Gut 62, 317-326, doi:10.1136/gutjnl-2012-303588 (2013).

92 Pecot, C. V. et al. Therapeutic Silencing of KRAS Using Systemically Delivered siRNAs. Molecular Cancer Therapeutics 13, 2876-2885, doi:10.1158/1535-7163.mct-14-0074 (2014).

93 Fenniri, H. et al. Helical Rosette Nanotubes:  Design, Self-Assembly, and Characterization. Journal of the American Chemical Society 123, 3854-3855, doi:10.1021/ja005886l (2001).

94 Deng, Z. J. et al. Layer-by-Layer Nanoparticles for Systemic Codelivery of an Anticancer Drug and siRNA for Potential Triple-Negative Breast Cancer Treatment. ACS Nano 7, 9571-9584, doi:10.1021/nn4047925 (2013).

95 Fenollosa, R., Meseguer, F. & Tymczenko, M. Silicon colloids: from microcavities to photonic sponges. Advanced Materials 20, 95-98 (2008).

96 Shi, L., Tuzer, T. U., Fenollosa, R. & Meseguer, F. A New Dielectric Metamaterial Building Block with a Strong Magnetic Response in the Sub‐1.5‐Micrometer Region: Silicon Colloid Nanocavities. Advanced materials 24, 5934-5938 (2012).

97 Pazos‐Perez, N. et al. Organized plasmonic clusters with high coordination number and extraordinary enhancement in surface‐enhanced raman scattering (sers). Angewandte Chemie International Edition 51, 12688-12693 (2012).

98 Sawetzki, T., Rahmouni, S., Bechinger, C. & Marr, D. W. In situ assembly of linked geometrically coupled microdevices. Proceedings of the National Academy of Sciences 105, 20141-20145 (2008).