ABSTRACT 
 
 
 

 
Title of Dissertation: MAGNETIC NANOPARTICLE INKS FOR 

SYRINGE PRINTABLE INDUCTORS 
  
 Rebecca Fedderwitz, Doctor of Philosophy, 2023 
  
Dissertation directed by: Professor & Chair, Peter Kofinas, Chemical and 

Biomolecular Engineering  

 
 
Direct Ink Writing (DIW) additive manufacturing (AM) has the transformative potential to 

construct complex shapes and devices with a single apparatus by exchanging the printable material 

at the print head. Iron cobalt (FeCo), permalloy (Ni80Fe20), and iron (II, III) oxide (Fe2O3·FeO) 

nanoparticles with varying magnetic properties were incorporated in resins to explore the influence 

of particle loading on printability and inductor device performance. It was generally found that 

increasing particle loading increased ink viscosity, with a loading maximum approaching 29 – 42 

vol% depending on the particle type and resin mixtures due to differences in particle shape and 

size and resin viscosity. With more magnetic content, composites had higher magnetic 

permeability and inductance. Syringe printable, colloidal, aqueous magnetic inks were made using 

both stabilized iron oxide and MnZn doped ferrite nanoparticles with added free polymers. MnZn-

doped ferrite inks are printed into toroids, sintered to improve magnetic permeability and 

mechanical robustness, and constructed into an inductor device. Inductors with high magnetic 

permalloy nanoparticle content were also syringe printed into toroids and hand-wound to 

demonstrate their viability in fabricating three-dimensional inductors. The effect of particle size 



  

on stability and printability was observed. The research presented in this thesis investigates various 

methods for formulating magnetic nanoparticle inks and evaluates the contributions of particle 

stabilization, free polymer content, solvent composition, and particle loading on the rheological 

behavior required for syringe printing. Material properties and device performances were 

characterized using methods such as zeta potential and settling studies to observe particle 

functionalization and stability, rheology to study viscoelastic flow behavior, and vector network 

analysis to measure inductance and device efficiency to showcase the viability of this technique to 

manufacture passive electronic devices.  

 

  



  

 
 

 
 
 
 
 
 
 
 
 

MAGNETIC NANOPARTICLE INKS FOR SYRINGE PRINTABLE INDUCTORS 
 
 
 

by 
 
 

Rebecca Fedderwitz 
 
 
 
 
 

Dissertation submitted to the Faculty of the Graduate School of the  
University of Maryland, College Park, in partial fulfillment 

of the requirements for the degree of 
Doctor of Philosophy 

2023 
 
 
 
 
 
 
 
 
 
 
Advisory Committee: 
Professor Peter Kofinas, Chair 
Associate Professor Siddhartha Das 
Professor Srinivasa Raghavan 
Professor Robert Briber 
Associate Professor Isabel Lloyd 
Associate Professor Luz Martinez-Miranda 



  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

© Copyright by 
Rebecca Fedderwitz 

2023 
 
 
 
 
 
 
 
 
 
 
 
 
 



 

 

ii 
 

Acknowledgments 

I would like to thank my advisor Dr. Peter Kofinas for seeing something in me at the 

beginning of my graduate research journey and then for his patience, guidance, and 

dedication to my success throughout.  

I would like to thank my committee and the weekly group meeting for their listening 

ears and advice, scientific or otherwise. Thank you to my lab mates for their 

companionship in the lab and to the undergraduate students who worked on my project 

with me for letting me practice mentorship.  

I would also like to thank the Printed Hybrid Electronics group at the Laboratory of 

Physical Sciences for providing me with my research scope and trusting me with their 

expensive equipment, especially Jason and Donghun who never seemed to be bothered 

by my countless questions.  

Thank you to my classmates who supported me through difficult classwork, research 

strife, and all the other aspects of life. Thank you to my friends and family who 

encouraged me even if they didn’t know what I was talking about. Thank you to all my 

therapists who provided me with the tools to cope when the experiments didn’t go as 

planned.  

Thank you to my parents, who taught me to try hard but were always there for me even 

if it didn’t work out. And thanks to Abi, who has been right by my side through 

everything.  



 

 

iii 
 

Table of Contents 
 
 
Acknowledgments......................................................................................................... ii 
Table of Contents ......................................................................................................... iii 
List of Tables ................................................................................................................ v 
List of Figures .............................................................................................................. vi 
 
Chapter 1: Introduction ................................................................................................. 1 

1.1 Broader Impacts .................................................................................................. 1 
1.2 Intellectual Merit ................................................................................................. 3 
1.3 Significance......................................................................................................... 5 
1.4 Project Description.............................................................................................. 6 

1.5 Ph.D. Thesis Organization and Research Contributions ................................. 7 
1.5.1 Chapter 3: Inductors fabrication from mixed magnetic particles in curable 
resin ....................................................................................................................... 7 
1.5.2 Chapter 4: Magnetic ferrite nanoparticle inks for syringe printable 
inductors ................................................................................................................ 8 
1.5.3 Chapter 5: Stabilization of permalloy nanoparticles for syringe printable 
inductors ................................................................................................................ 9 

 
Chapter 2: Background Information ........................................................................... 10 

2.1 Additive Manufacturing with a Focus on Direct Ink Writing (DIW) ........... 10 
2.2 Rheological Requirements for DIW ............................................................. 12 
2.3 Inductors ....................................................................................................... 17 
2.4 Magnets ......................................................................................................... 19 
2.5 Magnets in inductors ..................................................................................... 19 
2.6 High-frequency device operation .................................................................. 21 
2.7 Review of printed electronics ....................................................................... 23 
2.8 Printing inductors .......................................................................................... 23 
2.9 Printing magnetic inductors .......................................................................... 25 

 
Chapter 3: Inductors Fabricated from Magnetic Nanoparticles Mixed in Curable 
Resin ........................................................................................................................... 28 

3.1 Introduction ....................................................................................................... 28 
3.2 Results & Discussion ........................................................................................ 29 

3.2.1 Printability as a function of particle loading .............................................. 29 
3.2.2 Printability and rheological study with solvents added to NEA121 ink 
mixtures............................................................................................................... 31 
3.2.3 Magnetic characterization using vibrating sample magnetometry (VSM) 33 
3.2.4 Construction into an inductor mounted to a transmission line .................. 36 
3.2.5 Inductance characterization using a vector network analyzer (VNA) ....... 38 
3.2.6 FEM modeling of a composite inductor .................................................... 43 

3.3 Conclusion ........................................................................................................ 49 
3.3 Experimental Methods ...................................................................................... 50 

3.3.1 Materials .................................................................................................... 50 



 

 

iv 
 

3.3.2 Methods...................................................................................................... 51 
3.3.3 Characterization ......................................................................................... 54 

 
Chapter 4: Magnetic Ferrite Inks for Syringe Printable Inductors ............................. 57 

4.1 Introduction ....................................................................................................... 57 
4.2 Results & Discussion ........................................................................................ 61 

4.2.1 Fabrication of syringe-printed magnetic inks ............................................ 61 
4.2.2 Ink formulation and preparation ................................................................ 61 
4.2.3 Ink flow properties ..................................................................................... 65 
4.2.4 Crystal structure and magnetism changes with sintering ........................... 70 
4.2.5 Inductor Characterization ........................................................................... 75 

4.3 Conclusion ........................................................................................................ 77 
4.4 Experimental Methods ...................................................................................... 79 

4.4.1 Sample preparation .................................................................................... 79 
4.4.2 Material Characterization ........................................................................... 80 

 
Chapter 5:  Stabilization of Permalloy Nanoparticles for Syringe Printable Inductors
..................................................................................................................................... 86 

5.1 Introduction ....................................................................................................... 86 
5.2 Results and Discussion ..................................................................................... 88 

5.2.1 Permalloy particle stability ........................................................................ 88 
5.2.2 Behavior of permalloy inks ........................................................................ 89 
5.2.3 Printed inductor .......................................................................................... 91 
5.2.4 Small and large diameter permalloy .......................................................... 92 
5.2.6 Coating with poly(acrylic acid) (PAA) ...................................................... 94 
5.2.7 Coating with silica ..................................................................................... 95 

5.3 Conclusion ...................................................................................................... 101 
5.4 Experimental Procedures ................................................................................ 102 

5.4.1 Materials .................................................................................................. 102 
5.4.2 Methods.................................................................................................... 102 
5.4.3 Characterization ....................................................................................... 107 

 
Chapter 6:  Perspectives and Future Work ............................................................... 110 
Appendix ................................................................................................................... 115 
Bibliography ............................................................................................................. 117 
 
 
 
 
 
 
 
 
 
 



 

 

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List of Tables 
 
 
Table 3.1. Comparison of permeability calculated from EMT with experimental results. 

The max permeabilities used in the calculations are from experimental VSM data of 

pure powder. The permeability of the polymer matrix is assumed to be 1. The samples 

tested in this chart are of the highest possible syringe printable particle loading in 

NEA121 ink……………………………………………………………………….…45 

Table 4.1: Magnetic properties of MnZn doped ferrite as a function of sintering 

temperature and oven time…………………………………………………………...72 

Table 4.2: Atomic positions from Rietveld analysis of sintered MnZn doped 

ferrite…………………………………………………………………………………75 

Table 4.3: Atomic positions from Rietveld analysis of unsintered MnZn doped 

ferrite…………………………………………………………………………………75 

Table 4.4: Inductance properties of toroids with polymer and sintered MnZn ferrite 

cores with 12 windings. L, AL, L vol-1, Q, and μr values reported at 7 MHz………77 

Table 5.1: DLS particle size and description of the morphology of silica-coated 250 nm 

diameter permalloy…………………………………………………………………..98 

Table 5.2: DLS measured size and zeta potential between pH 6.5-7.5 of large diameter 

permalloy with each successive coating. …………………………………………...100 

 



 

 

vi 
 

List of Figures 

 
Figure 2.1: Typical B-H curve for magnetic material………………………………..19 

Figure 3.1: (a) 50 wt% and (b) 75 wt% particle loading of iron oxide in polyimide…30 

Figure 3.2: 80 wt% FeCo in NEA121 (a) molded into a toroid (b) TEM cross-sectional 

image displaying particles dispersed in cured resin…………………………………..30 

Figure 3.3: Rheology of (a) 75wt% FeCo in NEA121 without solvent (b) 80wt% FeCo 

in NEA121 with methylene chloride as a solvent. …………………………………..32 

Figure 3.4: Interpretation of magnetic hysteresis acquired with VSM to calculate 

magnetic saturation, relative permeability, coercivity, and hysteresis loss of 80 wt% 

FeCo in NEA121. ……………………………………………………………………35 

Figure 3.5: VSM of FeCo bare powder showing its magnetic response. The graph to 

the right is zoomed in to make the coercivity clearer…………………………………35 

Figure 3.6: VSM of 75 wt% FeCo in NEA121 showing its magnetic response. The 

graph to the right is zoomed in to make the coercivity clearer………………………36 

Figure 3.7: Printed and molded 75 wt% FeCo in NEA121 inductors hand wound and 

soldered to an SMA for connection to a VNA for inductance measurements……….37 

Figure 3.8: The plan for printing windings around the magnetic cone core………….38 

Figure 3.9: Syringe printed 75wt% FeCo in NEA121 magnetic core mounted to a 

transmission line with AJ printed silver NP conductive windings and interconnects…38 

Figure 3.10: Inductance as a function of frequency for 50wt% (blue) and 75wt% 

(orange) FeCo in NEA121 toroids. …………………………………………………..40 



 

 

vii 
 

Figure 3.11: Inductance as a function of frequency for iron oxide (orange) and FeCo 

(blue) at the same particle loading of 75 wt%.……………………………………….42 

Figure 3.12: Nominal inductance, resonant frequency, resistance, and quality factor of 

iron oxide in PDMS at various particle loadings as calculated from reflectance 

data…………………………………………………………………………………...43 

Figure 3.13: Geometries drawn in COMSOL of (a) random placement of spherical 

particles at 75 wt% and (b) their magnetic response in the presence of an electric field, 

and (c) random placement of 50 wt% cubic particles, and (d) their magnetic flux density 

distribution [T] in the presence of an electric field…….…………………………….46 

Figure 3.14: Relative permeability of FeCo in NEA121 at 75 wt% (blue) and 50 wt% 

(orange) calculated using COMSOL, EMT, and experimental methods…………….49 

Figure 3.15: TEM images of (a) synthesized cubic FeCo, (b) synthesized spherical 

permalloy, (c) as purchased iron oxide, and (d) magnetic hysteresis of magnetic 

materials used in this study acquired with VSM…………………………………….53 

Figure 4.1: (a) Schematic of coating iron oxide with polyacrylic acid (Darvan), and (b) 

solution of uncoated iron oxide is inhomogeneous, but after sufficiently coating is 

stable in solution. …………………………………………………………………….62 

Figure 4.2: TEM image of (a) uncoated and (b) PAA-coated iron oxide and (c) its zeta 

potential without (blue) and with (orange) its PAA coating. TEM image of (d) uncoated 

and (e) PAA coated MnZn doped ferrite and (f) its surface zeta potential without (blue) 

and with (orange) its PAA coating…………………………………………………..63 

Figure 4.3: (a) Schematic of iron oxide ink-making process.  (b) iron oxide weakly 

flocculating with the addition of the PEO free polymer. ……………………………..64 



 

 

viii 
 

Figure 4.4: Five layers of iron oxide inks printed into a cylindrical shape with (a) 10% 

(b) 30% and (c) 50% aqueous glycerol solution as the ink solvent……………………65 

Figure 4.5: Rheological performance of (a) 41vol% iron oxide ink with no glycerol and 

(b) 45vol% iron oxide ink with 10% aqueous glycerol solvent under increasing shear 

stress………………………………………………………………………………….66 

Figure 4.6: (a) Side view and (b) top view of printed iron oxide toroid, (c) strain sweep, 

and (d) creep test of 41 vol% solids loading ink. (e) Side and (f) top view, (g) strain 

sweep, and (h) creep test of 37.5 vol% solids loading ink. ………………………….68 

Figure 4.7: Figure 4.7: (a, c, e) top view of printed iron oxide toroid and (b, d, f) 

oscillatory stress sweep of iron oxide ink with (a, b) 3k, (c, d) 30k, and (e, f) 600k MW 

PEO…………………………………………………………………………………..70 

Figure 4.8: VSM of MnZn doped ferrite before and after sintering at 1050°C for two 

hours and 1400°C for two and four hours…………………………………………….72 

Figure 4.9 SEM of (a) unsintered and (b) sintered printed MnZn ferrite toroids. (c) 

Rietveld refined XRD patterns of sintered and unsintered MnZn ferrite…………….74 

Figure 4.10: (a) Hand-wound and soldered polymer and MnZn ferrite toroids and their 

(b) inductance as a function of frequency. ……………………………………………77 

Figure 5.1: (a) settling behavior of 20 nm diameter permalloy uncoated, coated with 

PEO, and glycerol after sitting overnight, and (b) comparison of zeta potential of 

permalloy coated with glycerol and PEO. ……………………………………………89 

Figure 5.2: (a) top view (b) 45° (c) side views of printed permalloy toroids after drying. 

The toroid shape is regular, and the layers are distinct………………………………90 



 

 

ix 
 

Figure 5.3: (a) The AJ printer tool path for making silver conductive windings and 

circuit traces, (b) printed inductor with permalloy ink as the magnetic core, and (c) 

inductance of syringe printed inductors with a polymer core and the permalloy ink 

core……………………………...……………………………………………………92 

Figure 5.4: TEM of (a) 30 nm and (b) 250 nm diameter permalloy and (c) magnetic 

hysteresis of the two permalloy particle sizes………………………………………...93 

Figure 5.5: Settling behavior of permalloy of two different sizes with various coatings 

listed in order from right to left after 20 minutes and after 24 hours: small PAA, large 

PAA, small histidine, large histidine, large silica, small silica, small PSS, large PSS, 

large uncoated, small uncoated. ……………………………………………………..94 

Figure 5.6: TEM images of (a) 250 nm diameter (b) silica particles, and (c) 250 nm 

diameter permalloy particles coated with citrate and then silica. (d) Comparison of zeta 

potential of the three particles. ………………………………………………………96 

Figure 5.7: TEM images of permalloy with various methods of coating with silica (a) 

base layer citrate, (b) base layer propylene glycol, (c) dilute silica coating with 

intermediate citrate layer……………………………………………………………..97 

Figure 5.8: Zeta potential of 250 nm diameter permalloy uncoated, with citrate, then 

silica, then PAH, then PSS. ………………………………………………………….99 

Figure A1: TEM images of FeCo cubic nanoparticles with a silica shell made with (a) 

0.5 wt% TEOS (10 nm silica shell) (b) 1wt% TEOS (20 nm silica shell) (c) 5 wt% 

TEOS (35 nm silica shell) and (d) 10 wt% TEOS (60 nm silica shell thickness). (e) 

VSM of FeCo with varying silica shell thicknesses shows a slight decrease in magnetic 

saturation but no effect on coercivity……………………………………………….115 



 

 

x 
 

Figure A2: Iron oxide in water with (a) 0.4 wt% poly(acrylic acid):iron oxide, (b) 0.2 

wt%, and (c) 0.1 wt%. Decreasing the amount of stabilizing polymer increases the 

homogeneity of particles in solution indicating an optimal concentration required for 

particle stability in water. Adding polymer beyond that concentration causes particles 

to settle……………………………………………………………………………..116 

 
 
 



 

 

1 
 

Chapter 1: Introduction 

 

1.1 Broader Impacts 

To maximize the storage capabilities of an inductor, a magnetic core is included within 

the coils. The motivation for this research is to utilize additive manufacturing to create 

a magnetic core in an appropriate geometry at small scales (within a few mm). Printing 

magnetic inks has been a challenge, especially when it comes to the percentage of 

magnetic material within the final printed product. Mixing magnetic particles within a 

thermoplastic filament requires a large percentage of polymer to retain desirable flow 

properties for printing. Adding magnetic particles in a curable resin increases the 

viscosity of the ink and limits the particle loading. Creating a high-density magnetic 

nanoparticle ink for an additive manufacturing system, especially for the application of 

high-frequency inductors, has not yet been extensively explored. Easily printed, shape-

retentive AM of highly concentrated ceramic nanoparticle solutions has been 

demonstrated for syringe systems. The transference of ceramic material to another type 

of material, namely metallic and magnetic nanoparticles, will allow the fabrication of 

complex shaped and nonconformal prints that can be applied to electronic devices. 

 

The intricate and complex shapes possible through additive manufacturing (AM) 

facilitate the tailoring of parts to the desired application. The ability to do shape 

iterations leads to the rapid development and optimization of a prototype. This 

simplified fabrication process, especially for direct ink writing (DIW) was the 



 

 

2 
 

capability of allowing the exchange of materials at the print head, giving the potential 

to enable the creation of parts on demand, even in remote, supply-limited locations. 

Simplifying additive manufacturing technology will increase accessibility and 

opportunity for creative problem-solving from end users of different backgrounds and 

perspectives. The ability to expand this technique to magnetic materials will accelerate 

material discovery and advancement to produce passive electronics, increasing the 

speed of communication in electronics to keep up with the current integrated circuit 

advancements.  

 

The rapid material development of integrated circuit technologies to nanometer 

dimensions has allowed operating frequencies to approach THz, as the operating 

frequency is inversely proportional to device size. Such high-frequency circuits allow 

for improved optical fiber communications in television broadcasting, automotive radar 

and sensor communications, personal radio services such as Wi-Fi and Bluetooth, 

satellite communication such as GPS, military targeting and tracking, and inter-space 

satellite communications. As operating frequencies increase, circuit topology requires 

a design change, affecting the technology generation, type, size, and bias current of all 

the passive components. Magnetic devices such as inductors, transformers, and 

transistors have operating frequencies inversely proportional to their size. As the 

demand for higher operating frequencies increases, so does the demand for smaller 

components.  

 



 

 

3 
 

An important consideration of device fabrication is to maximize operating bandwidth 

and efficiency while minimizing power consumption and component size and cost, 

which means choosing circuit components with low loss at targeted frequencies. A 

common additively manufactured inductor geometry is the planar spiral due to its easy 

two-dimensional fabrication. The operating frequency (𝑓𝑓𝑅𝑅) of an inductor is inversely 

proportional to the product of its inductance (L) and capacitance (C) (𝑓𝑓𝑅𝑅 =  1
√𝐿𝐿𝐿𝐿

). While 

a high value of inductance is necessary for increased energy storage, the capacitance 

must be minimized to maintain low loss. The insulating substrate is largely responsible 

for capacitive behavior; hence a planar geometry increases the capacitive losses and 

ultimately decreases operating frequency. A more suitable geometry is one that is 

oriented away from the substrate instead of directly in contact with it, which can be 

easily fabricated using three-dimensional AM technologies.  

 

1.2 Intellectual Merit 

AM has the potential to construct complex shapes using a single apparatus by 

exchanging the printable material at the print head, simplifying the fabrication process 

and making this technology accessible to the end user at any physical location. 

Formulating printable magnetic inks has been a challenge, especially when trying to 

make a final product with high particle content. Previous efforts to additively 

manufacture electronic devices containing magnetic composite materials have required 

a large weight fraction of polymeric material to provide mechanical integrity at the cost 

of a reduced volume fraction of magnetic material and inferior device performance. 

Colloidal stabilization of the magnetic nanoparticles using particle coatings enables the 



 

 

4 
 

fabrication of an ink with tunable rheological behavior that allows the printed part to 

retain its shape after extrusion with minimal organic additives, maximizing its magnetic 

content. This technique has been successful for dense ceramic and silver suspensions. 

This research aims to enable its transition to the fabrication of AM electronic devices 

with magnetic components.  

 

Though research on colloidal printing of ceramic nanoparticle inks is robust, the 

colloidal printing of metal nanoparticles – specifically magnetic nanoparticle inks – is 

nascent to the field. Further insight into the extent of particle stability and degree of 

flocculation or agglomeration within a magnetic nanoparticle ink allows deliberate 

rheology control to enable printing easily extrudable through a fine-tipped nozzle, 

retaining its shape after deposition and solvent evaporation. Dynamic light scattering 

and sediment measurements will be used to quantify order within the ink.  

 

Demonstrating printable inks of varying particle types, sizes, stabilization methods, and 

ink components will illustrate the interrelationship between the degree of flocculation 

and optimal print while understanding the influence of ink composition on magnetic 

properties and device performance.  Understanding the fundamental mechanism of 

what constitutes a successful, syringe-printable magnetic ink will allow this technique 

to span across several classes of electronic devices. 

 



 

 

5 
 

1.3 Significance 

Additive manufacturing (AM) is the creation of 3-dimensional material layer-by-layer 

based on a digital model. This research aims to better understand how magnetic, 

mechanical, and rheological properties in AM influence printed electronic device 

performance. This research investigates the AM of passive electronic devices with a 

direct write syringe printing method that takes advantage of the shear-thinning 

properties of a stabilized nanoparticle ink. This method is used to print magnetic 

elements, such as inductor cores, into customizable shapes with minimal organic 

additives. Magnetic nanoparticles (iron cobalt (FeCo), iron (II, III) oxide (Fe2O3·FeO), 

MnZn doped ferrite, and permalloy (Ni80Fe20)) with low hysteresis loss and high 

permeability of varying sizes (between 20-250 nm) are either synthesized or purchased 

commercially and coated with various polymers to stabilize in solution. Differing 

particle surface properties influence magnetic behavior, printability, and packing 

printable ink formation for high weight fraction nanoparticle inks. Higher magnetic 

material content in the composite results in a larger magnetic response and high 

inductance and energy storage capability. This is accomplished through a 

characterization of the nanoparticles’ surface properties, which influence their 

stabilization within the ink. High particle loading affects the print properties and drying 

of the ink. Additionally, magnetic, mechanical, and rheological properties determine 

the printability of the overall device and the final inductor performance. 

 

Magnetic nanoparticles with a rapid magnetic response and low loss are used and 

stabilized in water with various polymers, depending on the type of particle used. A 



 

 

6 
 

balance of repulsive and attractive forces produced shear-thinning fluids, allowing flow 

through the nozzle without clogging it, and then ceasing to flow after it is deposited on 

the substrate. A stability map is created to determine the optimal concentration and 

coating behavior of the polymer on the particle surface and observe how this 

concentration changes with the size and metallic composition of the magnetic 

nanoparticle. 

 

1.4 Project Description 

AM has the transformative potential to construct complex shapes with one machine by 

exchanging the printable material at the print head, simplifying the fabrication process, 

and making this technology accessible to the consumer population in any physical 

location. Printing magnetic inks has been a challenge, especially when it comes to the 

high-volume fraction of magnetic material within the final product. More magnetic 

material in the composite results in a larger magnetic response and high inductance and 

energy storage capability of magnetic inductor cores. Previous efforts to additively 

manufacture magnetic composite materials have required a large weight fraction of 

organic material to provide mechanical integrity at the cost of a reduced volume 

fraction of magnetic material. Colloidal stabilization of the magnetic nanoparticles 

using particle coatings enables the fabrication of an ink with tunable rheological 

behavior that allows the printed part to retain its shape after extrusion with minimal 

organic additives, maximizing its magnetic content. This technique has proved 

successful when fabricating dense ceramic and silver suspensions, and this research 

aims to understand how this technique can be transferred across material classes.  



 

 

7 
 

 

Below is a summary of the direct research contributions covered in this thesis: 

1. Determined the relationship between solvent pH, polymer coating, and particle surface 

charge on the degree of stabilization, exhibited by settling behavior and zeta potential 

for iron (II, III) oxide, MnZn doped ferrite, and permalloy ink systems.  

2. Deciphered the role of excess polymer as a rheology modifier on ink printability and 

shape retention after deposition. Particle stability and ink yield stress directly affected 

rheology and cracking behavior, with an optimal ink composition displaying a yield 

stress high enough to support its weight after deposition and exhibiting minimal 

cracking after solvent evaporation. 

3. Evaluated how the printed device composition affects the efficiency of a printed 

inductor. in full configuration. The magnetic cores were connected to a transmission 

line with printed conductive windings and characterized by a vector network analyzer 

to record inductance and operating frequency.  

 

1.5 Ph.D. Thesis Organization and Research Contributions 

1.5.1 Chapter 3: Inductors fabrication from mixed magnetic particles in 

curable resin 

Iron cobalt (FeCo), permalloy (Ni80Fe20), and iron (II, III) oxide (Fe2O3·FeO) magnetic 

particles with varying magnetic properties were incorporated in different resins to 

explore the influence of particle loading on printability and inductor device 

performance. It was generally found that increasing particle loading increased ink 

viscosity, with a loading maximum approaching 29 – 42 vol% depending on the particle 



 

 

8 
 

type and resin mixtures due to differences in particle shape and size and resin viscosity. 

With more magnetic particles, composites had higher magnetic saturation and 

permeability. Coercivity was not affected by particle loading because there was no 

change in crystal structure with increased particle loading. Increased particle loadings 

of up to 80 wt% were attainable by mixing volatile solvent into the particle-resin 

formulas to decrease the viscosity of the ink. Various compositions of toroids were 

both molded and printed and then hand-wound to investigate the influence of particle 

loading on inductor device performance. Generally, increasing particle loading 

increased inductance due to the increase in magnetic saturation and permeability. The 

operating frequency does decrease with particle loading due to compounding magnetic 

hysteresis loss. Inductors were constructed into both a toroid and a cone using 75 wt% 

FeCo in NEA121 to showcase the difference in behavior with core shape, showing a 

higher operating frequency with a conical structure due to its orientation away from the 

substrate minimizing stray capacitance. From these initial studies, it was of interest to 

explore magnetic inks with higher particle loadings to increase inductance.  

 

 

1.5.2 Chapter 4: Magnetic ferrite nanoparticle inks for syringe printable 

inductors 

In this chapter, syringe printable, colloidal magnetic inks are made using both iron 

oxide and MnZn doped ferrite nanoparticles by stabilizing them with poly(acrylic acid) 

(PAA) and adding a free polymer polyethylene oxide (PEO) of various molecular 

weights and glycerol to control ink viscosity and evaporation rates. Printability is 



 

 

9 
 

further explained using complex rheology. MnZn-doped ferrite inks are printed into 

toroids and sintered at 1400°C to increase magnetic permeability. A sintered toroid is 

constructed into an inductor device and characterized using a Vector Network Analyzer 

(VNA), which exhibits an inductance of 4.26 μH at 8.5 MHz. This study lays out a 

template for ferrite inks with the potential to be fabricated into useful passive electronic 

devices.   

 

1.5.3 Chapter 5: Stabilization of permalloy nanoparticles for syringe printable 

inductors 

This chapter investigates syringe printing parts with high magnetic permalloy 

(Ni80Fe20) nanoparticle content (> 35 vol%). Two different metal alloy particle sizes of 

250 nm and 30 nm were synthesized to observe the effect of particle size on stability. 

Zeta potential was measured to discern a change in surface charge after coating 

procedures. Settling behavior was documented to perceive the success of coating 

procedures on particle stability in water. Permalloy nanoparticle inks were 

concentrated with polyethylene oxide (PEO) to increase viscosity and glycerol to 

decrease evaporation rates while printing. It was found that PEO and glycerol stabilize 

30 nm permalloy in addition to increasing ink viscosity. Permalloy inks were printed 

into toroid shapes to demonstrate their viability in fabricating three-dimensional 

magnetic structures and were processed into inductors that exhibited an inductance of 

180 nH and 30 MHz.   



 

 

10 
 

Chapter 2: Background Information 
 
 

2.1 Additive Manufacturing with a Focus on Direct Ink Writing (DIW) 

Additive manufacturing has fewer size and shape limitations in comparison to 

subtractive manufacturing methods. Subtractive manufacturing involves specialized 

machinery that cuts away from a solid block of material, creating more waste and 

limiting the special resolution of fabricated parts [1]. Additive manufacturing has 

advantages over traditional manufacturing in rapid prototyping, complicated design, 

and material sustainability [1], [2]. Comparing different printing techniques that can 

print particles in 3-dimensional structures, stereolithography (SLA) has a high 

resolution and material utilization rate, but the process is complicated and takes a long 

time. Stereolithography techniques require vats of photopolymer resins in which 

particles can scatter the light required for polymerization. Filament printing uses 

thermoplastic filaments that can only incorporate so many particles until the integrity 

of the filament is compromised. Electrohydrodynamic printing (EHD) has high 

resolution and can print many types of materials, but the process is complex and 

inefficient. Powder bed fusion (PBF) has high resolution, but also is complex to prepare 

and is not very efficient [3]. Powder bed diffusion can print typically metal or ceramic 

particles; however, the bed of powder is susceptible to aging and especially when 

working with precious metals, can become costly. Direct ink writing (DIW) allows 

printing inks with various compositions and a range of ink viscosities, but its resolution 

is typically lower. Direct ink writing, including syringe printing, is much more versatile 

and introduces the possibility of multi-material extrusion on a single tool [4]. Among 



 

 

11 
 

recently developed AM techniques, extrusion-based ones such as DIW are the most 

versatile due to simple printing mechanisms and low-cost fabrication processes. DIW 

also allows broad material selection including ceramics, metal alloys, polymers, and 

even edible materials [4]. Other AM technologies outside of DIW are limited in the 

type and particle loading of materials that can be printed. 

 

The successes in nanomaterial development increase the possible materials used with 

AM, making this fabrication technique available to create a vast array of functional 

materials, including electronics. Particle/polymer composites enhance material 

properties, however, the large influence of particle loading, microstructure, and 

orientation means there are endless avenues of study [5]. Understanding the interaction 

of the nanoparticles with each other, the solvent, and the additives in the ink is pertinent 

because there is great potential in the tunability of parts by altering particles and their 

interactions. DIW filaments need to flow under shear stress and behave as a liquid 

during extrusion. For fabricating metal or ceramic parts at low processing temperatures, 

this means mixing metal or ceramic particles into a liquid solution. An inherent 

requirement for DIW filaments is a liquid-like flow under shear stresses present during 

extrusion. For low-temperature DIW fabrication of metals or ceramic parts requires a 

solution of these components in particle form. Methods of stabilizing particles in 

solutions have been in practice for hundreds of years, for example with clay and 

pottery. However, the desire for a shape-retentive part with shear-thinning behavior to 

enable 3-dimensional material fabrication from a filament extruded through a fine-tip 

nozzle requires very careful rheological control. The challenge then is to create a 



 

 

12 
 

filament with high enough particle loading to develop desirable functional properties, 

uniformity in print, and sufficient structural strength while preventing agglomeration 

and clogging[6].  

 

In the case of magnetic material, the more concentrated the inorganic material in the 

ink, the better the performance properties. Defined in 1998 by Sandia National Labs 

based on a ceramic ink system, Robocasting (another name for DIW) is a method of 

additively fabricating 3D structures by extruding high-density colloidal solutions 

consisting of typically more than 50 vol % nanoparticle content, < 1 vol % particle 

coatings or binder, and the remaining amount is a volatile solvent that will be removed 

from the final product [7]. The rheology of the colloid must lend itself to its ease of 

extrusion, requiring it to exhibit shear-thinning behavior, while still maintaining 

mechanical integrity after deposition of several layers. Robocasting allows intricate 

patterns to be fabricated with an automated computer-aided design (CAD) program. 

Alternatively, traditional printing methods such as screen-printing and inkjet printing 

produce features that rely on a supportive substrate [8]. However, there are hurdles to 

using ceramic three-dimensional (3D) printing for printing metals due to poor 

resolution, low printing accuracy, pore formation during burnout binders, and complex 

postprocessing [9].  

 

2.2 Rheological Requirements for DIW  

This specific rheological behavior is influenced by the interaction between the 

dominant particle forces. The particle structure’s assembly is a result of hydrophobic 



 

 

13 
 

interactions, hydrogen bonding, and electrostatic attraction, which competes with 

electrostatic repulsion and solvation [10]. Inks that have decreasing viscosity with 

increasing shear stress are shear-thinning fluids, easily flowing through a syringe 

nozzle under pressure but resisting flow under low shear stresses, therefore, retaining 

their shape after deposition. Shear-thinning occurs because these forces are weak 

against applied shear stresses [11]. Particle and solvent interactions are controlled by 

tuning particle size and distribution and the method of stabilization by modifying the 

particle surface chemistry and its interactions with one another.  

 

Interparticle forces influence suspension behavior. The degree of stabilization of 

solutions alters the printability of the ink and the final shape of the product after the 

solvent is evaporated. Important parameters of a syringe printable ink include viscosity 

(at shear rates experienced during printing), yield stress, and the complex shear moduli. 

Most inks solidify by liquid evaporation, which requires control of the liquid-to-solid 

rheological transition to match that of deposition. This is done by tuning the balance 

between repulsive, stabilizing forces and attractive networking forces within the ink 

solution, as well as choosing an appropriate solvent that evaporates within a reasonable 

time frame. Repulsive forces prevent clogging at the nozzle while attractive forces 

produce a yield stress allowing shape retention and the possibility of spanning elements 

[12]. Yield stress is defined as the stress at which the ink begins to flow. Viscosities 

around 104 Pa ∙ s at low shear stresses have been reported as a viscosity high enough 

to maintain shape after deposition [13]. At shear stresses experienced in the nozzle 

during extrusion, the paste must behave as a liquid, or have a loss modulus larger than 



 

 

14 
 

the storage modulus at frequencies representing rest, around 1 Hz. In this way, the 

liquid is extrudable through a fine-tipped nozzle [14].  

 

Suspensions typically used to explore robocasting ink development consist of a 

nanoparticle powder, a polyelectrolyte dispersant, and a rheology modifier. Control of 

ink viscosity becomes more dependent on coating efficiency as the solid loading 

fraction increases. A stability map can be created to visualize how polyelectrolyte 

coating and solution pH changes the stabilization of the colloidal solution [15]. An 

optimal degree of flocculation (particle aggregation) is required for the ink to exhibit 

its yield stress. A completely stabilized solution with no yield stress will not retain its 

shape after deposition and is not desirable for printing [16], [17]. Free-polymers, which 

are not physically or chemically adsorbed to any particle, either promote flocculation 

or stabilization (dispersion) depending on the initial conditions of particle stability and 

operate similarly to solvation at length scales of several nanometers [18]. For printable 

inks, it is intended to use free-polymers to induce slight flocculation as a result of an 

osmotic pressure difference attributed to its absence between particles [19].  

 

Printed inks with uncoated, unstable particles require higher pressures for extrusion 

and clog at the nozzle more easily than inks with coated, stabilized particles. The 

resulting data of this study will provide design parameters for producing concentrated 

(> 30vol%) magnetic inks that effectively separate the stability effect of polymer 

adsorbed to the surface and the flocculation caused by the excess polymer in solution. 

Polyelectrolytes are common stabilizing agents that have successfully coated and 



 

 

15 
 

dispersed ceramic particles in aqueous systems, specifically for high-density (> 30 

vol%) continuous syringe printing due to their charge providing an electrostatic 

repulsion effect [15]. Neutral polymers can alternatively provide a steric stabilization 

effect. For either, an optimum concentration is required, where excess polymer in the 

solution can induce flocculation [16]. Below the saturation limit, the repulsion between 

particles may not be enough to prevent flocculation. Polymer coatings combine both 

repulsive and attractive forces to form a suspension, are easily controlled, and can be 

applied to particles of many types of materials [20]. The surface energy of the 

nanoparticles determines which polymer is appropriate to use as a coating, and the 

adsorption efficiency is influenced by concentration, solution pH, and salt 

concentration. When using polyelectrolytes, the nanoparticles must have enough 

adsorbed dissociated or charged polyelectrolytes to enhance the electrostatic effects 

and enable stability. The design route of using stabilized particles in solution with 

minimal organic additives is an attempt to create a final shape with the highest possible 

solids loading.  

 

The additional polymer will not adsorb to the surface of a nanoparticle if its 

concentration exceeds a level of saturation.  The polymer chains will instead exist 

freely in the solution. Flocculation is induced by the free polymer possibly due to a 

bridging effect, where polymer chains adsorb to multiple particles. For the application 

of printing, slight flocculation is desired [21]. This interaction is more suitable for 

printing than a simply unstable particle solution because it induces enough of a yield 

stress without completely aggregating the particles in the solution, making it suitable 



 

 

16 
 

to print while minimizing the amount of polymer required to experience shape retention 

[22], [23]. Alternatively, if particles are not adequately coated with polyelectrolyte, the 

excess polymer can induce a less reversible bridging flocculation by attaching to 

multiple particles. As an example, polyvinylpyrrolidone (PVP) is a commonly used 

rheology modifier for dense ceramic aqueous suspensions and has been shown to 

improve flow properties during deposition whose yield point can be controlled by 

varying its content and molecular weight [12], [22], [24], [25]. 

 

Flocculation due to a free-polymer induces a high yield stress without significantly 

altering the viscosity. An insufficiently coated particle comparatively induces 

irreversible flocculation that results in a much higher viscosity but insufficient yield 

stress [22]. The rheological behavior desired for printing is that of a shear-thinning 

fluid with a yield stress, a result of the slight flocculation of the particles. Rheology 

studies are used to quantify the optimal shear rate and yield stresses that result in 

minimized slumping behavior of the printed part, measured as the percent change in 

ideal shape [24]. With a sufficient attractive potential between particles, printed parts 

have displayed a mechanical integrity that withstands machining [26]. It is expected 

that the yield stress of the ink and the mechanical strength of the green printed part will 

increase for inks with increasing concentrations of added free polymer. The challenge 

arises in understanding repulsive and attractive potential effects in concentrated 

solutions and drying stresses, as well as ink flow in reduced nozzle diameters.  

 



 

 

17 
 

2.3 Inductors 

An inductor is used to store energy within an induced magnetic field. Changes in 

current flow induce a perpendicular magnetic field according to Maxwell’s equations, 

which in a coiled wire, concentrates the field within the windings. Inductors are 

essential circuit components used to store and release energy as current fluctuates. 

Including a magnetic material within the looped wire generates significantly higher 

magnetic field densities. There are many types of inductors, made into varying shapes, 

using a wide range of magnetic materials, and oriented in numerous constructions 

depending on the application. The unit for inductance is the Henry [H], which equals 

an induced voltage of 1 V when the current is varying at a rate of 1 A·s-1 [27].  

𝐻𝐻 = 𝑉𝑉
𝐴𝐴∙𝑠𝑠−1

    (1) 

Inductor operation is described by the relationship between Ampere’s and Faraday’s 

laws [28]. These Maxwell equations couple the magnetic and electrical phenomenon 

that makes energy storage possible in this system. Ampere’s Law relates a magnetic 

field around a closed loop to the electric current passing through. Total magnetic force 

is proportional to the applied field along the length of a wire.  

𝐹𝐹 =  ∮𝐻𝐻𝐻𝐻𝐻𝐻 = 𝑁𝑁𝑁𝑁 ≈ 𝐻𝐻𝐻𝐻        (2) 

Faraday’s law of induction states that any change in the magnetic environment induces 

a voltage, and vice versa. Flux changes with time.  

𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑

=  − 𝐸𝐸
𝑁𝑁

;   ∆𝜙𝜙 =  𝑁𝑁∫𝐸𝐸𝐻𝐻𝐸𝐸        (3) 

Energy storage and removal can be understood by integrating the applied field in terms 

of the time-dependent magnetic response. This area describes the total energy, while 



 

 

18 
 

the area before the hysteresis describes energy stored and the area within the hysteresis 

curve describes energy lost with each direction change of current.  

𝑊𝑊
𝑚𝑚3 =  ∫𝐻𝐻𝐻𝐻𝐻𝐻          (4) 

Magnetic permeability, a material characteristic, is defined as the amount of flux a field 

can push through a unit volume of material. Permeance applies the material 

characteristic to a defined area and length. Finally, inductance is the permeance coupled 

among all the conductive windings.  

𝜇𝜇 =  𝜇𝜇0𝜇𝜇𝑟𝑟 = 𝐻𝐻/𝐻𝐻         (5) 

𝑃𝑃 = 𝑑𝑑
𝐹𝐹

= 𝐵𝐵𝐴𝐴
𝐻𝐻𝐻𝐻

          (6) 

𝐿𝐿 = 𝑁𝑁2𝑃𝑃 = 𝜇𝜇𝑁𝑁2𝐴𝐴
𝐻𝐻

         (7) 

The performance of an inductor is measured by its inductance, L. Its energy efficiency 

is defined by the quality factor, or Q-factor, the ratio of the energy stored to the energy 

dissipated in the inductor, or more specifically a ratio of the component’s inductance 

to its equivalent resistance. The range of frequencies in which it may effectively 

operate, defined as its bandwidth, is a function of the circuit’s resonant frequency and 

quality factor, with the resonating frequency being dependent on the inductance and 

capacitance experienced in the circuit.  

𝑓𝑓𝑟𝑟 = 1
2𝜋𝜋√𝐿𝐿𝐿𝐿

          (8) 

 



 

 

19 
 

2.4 Magnets 

A magnet is defined by its saturation (Bsat), 

permeability (μ), resistivity (ρ), remanence (Br), and 

coercivity (Hc), all of which are notated in Figure 

2.1. A hysteresis loop (or B-H curve) can be 

recorded using a Vibrating Sample Magnetometry 

device (VSM). The material is exposed to a sweep 

of applied magnetic field, and the strength of the 

magnetic response is measured. Saturation is defined 

as the state in which all the magnetic domains within the material are aligned, which 

occurs after enough of a magnetic field is applied to encourage alignment. Permeability 

is the ability of the magnetic field to be supported throughout the material and is 

illustrated as the slope of the hysteresis curve. Domain alignment is not a linear 

response; therefore permeability varies with the applied magnetic field.  Resistivity is 

a measure of the energy barrier necessary to overcome to align the magnetic domains. 

Magnetic remanence is the magnetic strength of the domains aligned after the applied 

field has been removed. Coercivity is the magnitude of the opposing applied field 

required to cause a net magnetic moment of zero [29].  

 

2.5 Magnets in inductors 

Including a magnet within the core of the turns of an inductor increases its inductance 

by providing an easy path for magnetic flux, the quantity of which is defined by the 

magnet’s permeability. The core is magnetized by the current passed through the 

Figure 2.1: Typical B-H curve for 
magnetic material 



 

 

20 
 

windings. The time dependence of the flux change is a function of the voltage applied. 

These three items sum up the energy acting within the core. Inductance must remain 

constant throughout a range of applied currents. This requires the magnetic 

permeability to remain constant over a range of magnetizing forces and the effective 

resistance of the coil and the core losses to be minimized [1]. Recoverable energy is 

stored in non-magnetic inclusions of the core, such as the polymer binder holding 

magnetic particles together. Too much of the polymer, however, can reduce the 

beneficial magnetic properties by preventing magnetic flux coupling between particles 

[30]. 

 

Losses are a result of eddy current production and magnetic hysteresis, both of which 

are influenced by frequency. Eddy currents are produced as a result of the finite 

resistivity of the magnetic material and are compounded to the low-frequency 

hysteresis loss. Ferrite materials are highly resistive and are therefore often the material 

of choice for high frequency because eddy currents cannot conduct throughout the 

material. Alloyed ferrous magnets are engineered to have permeabilities magnitudes 

larger than ceramic iron oxide, maximizing at 100,000 for bulk nickel-iron alloys, but 

their resistivity is significantly lower and conducive to eddy current production, and 

they are therefore not suitable for high-frequency use without further modification. 

Typically, this involves laminating layers of magnetic material, or more recently, 

coating particles with an insulating shell [7].  Losses of the inductor can be modeled in 

an equivalent circuit with a resistor in parallel, which encompasses winding losses, core 

eddy current losses, and magnetic hysteresis losses [10].  



 

 

21 
 

 

The inclusion of magnetic materials in structures enhances some properties just as it 

has for planar inductors. A 3D-printed solenoid by the means of filling in microfluidic 

channels with conductive liquid metal paste has been characterized with a varying 

number of turns with and without the inclusion of a magnetic bar. The results are a 300-

600% inductance enhancement (corresponding to 2-6 turns) after including the magnet 

in the same geometry [31]. The core material used is a commercially produced NiZn 

soft ferrite magnet, typically used for frequency ranges above 200 MHz. This 

comparison has been made again using microchannels filled with two different kinds 

of ferrofluids as the magnetic core within the inductor windings. The inductance is 

enhanced 1.3 - 2.6 times with the ferrofluids. The quality factor remains the same for 

low frequencies while becoming more lossy at higher frequencies. Their operating 

limit, however, remains relatively unchanged. The ferrofluids used in this study have 

the composition of magnetite suspended in hydrocarbon with permeabilities ranging 

from 3.6-19.6. The higher permeability material shows the highest increase in 

inductance [32].  

 

2.6 High-frequency device operation 

Higher frequency waves provide information faster; however, the signal attenuates 

faster and must be modulated to transport over long distances. A bias-tee is a circuit 

topology that couples a high-frequency signal containing information with a lower-

frequency power wave, with a parallel inductor passing the lower-frequencies. The role 



 

 

22 
 

of an inductor, when connected to a capacitor, is to act as a filter to decouple modulated 

signals and generate sinusoidal signals.  

 

As semiconductor devices become more efficient, passive components such as 

inductors and capacitors and their topologies become the limiting factors in frequency 

performance with losses exacerbated at faster time domains. Passive electronics exhibit 

losses when operating at high frequencies and irretractable energy dissipates through 

the material as heat. Losses are a result of eddy current production and magnetic 

hysteresis, both of which are accumulated with increasing frequency. Minimizing these 

losses will increase the frequency range in which the device can be used efficiently. 

Eddy currents are produced because of the finite resistivity of the magnetic material 

and are compounded by the low-frequency hysteresis loss.  

 

Ferrite materials are highly resistive and are therefore often the material of choice for 

high-frequency. Alloyed ferrous magnets are engineered to have relative permeabilities 

magnitudes larger than ceramic iron oxide, maximizing at 100,000 for bulk nickel-iron 

alloys, but their resistivity is significantly lower and conducive to eddy current 

production, making them unsuitable for high-frequency use without further 

modification. Typically, this involves laminating layers of magnetic material, or more 

recently, coating particles with an insulating shell [29].  Losses of the inductor can be 

modeled in an equivalent circuit with a resistor in parallel, which encompasses winding 

losses, core eddy current losses, and magnetic hysteresis losses [33]. 



 

 

23 
 

2.7 Review of printed electronics 

Printed electronics, including passive components such as the inductor (without a 

magnetic core), have been produced since the 1950s when conductive inks were 

discovered and first utilized [34]. Since then, significant research efforts have been 

made in the additive manufacturing of electronic components, with a focus on 

conductive traces [35], [36]. 3D printing can create stretchable and flexible electronics, 

considering the same fundamental principles of allowing the extrudability of particles 

in polymer solution can be used to pattern the filament into deformable geometries 

[37].  Electronic devices [38] that have been printed using DIW include electrodes [39], 

conductive wiring for electric circuitry [40], [41], and other functional components 

such as sensors [42] and quantum dynamic light emitting diodes (QDLEDs) [43]. The 

underlying principles of controlling printability are the same but are accomplished with 

specific types of particles focusing on efficient current flow. A major hurdle in the 

fabrication process of conductive inks is converting the ink from a non-conductive state 

to an optimized, efficient conductive state. Often, heat is used to remove organic 

surfactants and densify parts.  

 

2.8 Printing inductors 

The employment of additive manufacturing techniques to fabricate magnetic 

composites, specifically inductors, is a relatively recent research interest. Inductors are 

the major size-limiting component in power converters. Decreasing size increases the 

frequency range of the device. However, with increasing frequency, there are more 

compounding losses. Inductors are typically the largest components of a circuit board 



 

 

24 
 

[44]. Typical, non-additive methods of fabricating a magnetic core for inductors 

involve using high-pressure powder-compaction, followed by sintering, and then hand 

winding [45]. There is a need to develop fabrication technology to reduce the size of 

inductor parts. The traditionally printed inductor is in the form of a planar spiral, printed 

directly on the circuit board substrate with the same conductive ink used for 

interconnects. An inductor’s performance is hindered by its geometry and size-

dependent parasitic capacitances [46]. Parasitic capacitances are a result of capacitive 

behaviors in neighboring materials that cause the operating component to veer from 

ideal performance. These parasitic capacitances become increasingly more important 

at higher frequencies [47]. To optimize the self-resonant frequency (SRF), parasitic 

capacitances must be minimized or eliminated. Typically, printed planar inductors have 

a large substrate contact area and are plagued by substrate capacitances and leading to 

the exploration of different 3D geometries [48], [49]. Solenoid inductors achieve a 

higher inductance density with reduced substrate parasitic losses compared to planar 

inductors due to confined parallel magnetic field lines to the substrate [50]. External 

magnetic fields from inductors can cause electromagnetic interference issues. Toroids 

have a weaker external magnetic field compared to solenoids and planar structures [51]. 

Solenoid inductors have a higher efficiency and inductance density compared to planar 

inductance by better confining the magnetic field lines. Many magnetic core solenoid 

inductors have been fabricated in many ways (electroplating, manual filling, spin 

spraying, enclosing in polymer, or hand winding a commercial part), but not by 3D 

printing [52]. All of these processes have disadvantages, but the greatest disadvantage 

is the increased time and cost of processing. Ahn et al. claim using fabricating an 



 

 

25 
 

inductor on a planar substrate is “an extremely difficult task”, and requires “quasi-

three-dimensional micromachining techniques [53].” Most of the efforts in 3D printing 

an inductor have been focused on the quality of 3D printed conductive traces, and in 

that realm, there have been significant achievements. The inclusion of the magnetic 

core is far less studied. The challenge arises in fabricating a core with optimized 

permeability. Efforts to print a core often include inserting a traditionally manufactured 

core into printed windings [54] or printing the core separately and then hand-winding 

it to form the final inductor device [55].  

 

2.9 Printing magnetic inductors 

The 3D fabrication of the magnetic core itself has yet to be extensively studied. Some 

examples of ferrite–thermoplastic composites have been demonstrated to print using 

the traditional fused deposition modeling (FSDM) printing process. A study of NiZn 

ferrite in ABS demonstrates printed products with low volume fraction (< 25 vol%) 

and therefore low relative permeability (< 3) [56]. A commercially available metal 

powder – PLA composite provided by the company Proto-pasta displays similar results 

[57].  

 

Another effort to incorporate magnets into an inductor device is to coat a thin layer of 

magnetic ink onto a planar spiral. A reported printed planar inductor with 1.5-3.5 turns 

and a 42 mm2 footprint has a maximum inductance of 75 nH, Q of 3.3. A 10 nH inductor 

has a resonant frequency slightly below 1 GHz. No magnetic material is involved  [45]. 

Another planar printed inductor has an added layer of NiZn doped ferrite ink to improve 



 

 

26 
 

inductance and operates to 1MHz with an inductance near 200 nH [58]. In another 

study, printed micro inductors were fabricated on top of a flexible polyimide substrate. 

The magnetic core was screen printed using an MnZn-doped ferrite magnetic ceramic 

mixed in a thermoplastic resin with solvent. Conductive copper windings are planar, 

with the screen printed magnetic film on the front and back to shield [59]. In another 

study, iron oxide nanoparticles were synthesized and functionalized with oleic acid and 

mixed into a commercially available, proprietary UV-curable polymeric resin (SU-8) 

at a particle loading of 50 wt% to screen print a “free-standing” magnetic substrate. 

Functionalized particles were suspended in water to inkjet print a thin film in which a 

silver ink planar inductor was printed on top [60]. In another study, NiZn ferrite inks 

were coated with a dispersant (proprietary) and mixed in dimethylformamide (DMF) 

at 30 wt% to inkjet print a thin film [61].  

 

Only a few studies report printing three-dimensional inductor cores or printing non-

planar inductors with included magnets. This study by Bellaredj et al. reports 

fabricating an entirely 3D-printed inductor, including the core, insulating materials, and 

windings. The core is made of a NiZn ferrite epoxy composite made in-house by mixing 

functionalized magnetic particles in a formulated curable epoxy binder at an 85 wt% 

particle loading [62]. The curing occurs at 180°C. The final part has a volume of 

approximately 6.5 mm3 and reports an inductance of 30 nH and a Q-factor of 6.4 at 100 

MHz [52]. Yan et al. [55] have published about additive manufacturing of soft 

magnetics, using a 3D printer to extrude optimized magnetic pastes. A multi-extruder 

printer co-extruded a poly-mag (polymer magnetic composite) paste consisting of 



 

 

27 
 

permalloy (NiFe) powder and benzocyclobutene for the core and a nanosilver paste for 

the windings. A stable permeability of 10 is reported up to 30 MHz with no discussion 

of inductance [63]. The same group then reports working with a NiCuZn ferrite-coated 

planar inductor that after sintering has a permeability near 100 up to 10 MHz [64]. 

Hodaei et al. report on ink made of iron oxide functionalized with a single block 

copolymer to attain an 81 wt% in water that is printed into a 3D toroidal structure for 

inductance characterization. These structures were robust and hand-wound without any 

additional heat treatment steps. A 1206 mm3 volume toroid with 60 turns had an 

inductance of 20 μH up to 1 MHz [65].  

 

The additive manufacturing of conductive traces for circuitry is an established practice 

used in modern-day electronics. For inductors, the most studied devices fabricated 

using AM technologies are planar spiral structures, but the 3D printing of magnetic 

cores for inductors has much room for investigation, especially for the application of 

high-frequency electronics. 

 



 

 

28 
 

Chapter 3: Inductors Fabricated from Magnetic Nanoparticles 
Mixed in Curable Resin 

 

3.1 Introduction 

The rapid material development of integrated circuit technologies to nanometer 

dimensions has allowed operating frequencies to approach THz, as the operating 

frequency is inversely proportional to device size. Such high-frequency (HF) circuits 

allow for improved optical fiber communications in television broadcasting, 

automotive radar and sensor communications, personal radio services such as Wi-Fi 

and Bluetooth, satellite communication such as GPS, military targeting, and tracking, 

and inter-space satellite communications. As operating frequencies increase, circuit 

topology requires a design change, affecting the technology generation, type, size, and 

bias current of all the passive components, including magnetic devices such as 

inductors, transformers, and transistors.  

 

To maximize the storage capabilities of an inductor, a magnetic core is included 

within the coils. The motivation for this research is to utilize additive manufacturing 

to create a functional inductor magnetic core in an appropriate geometry. Printing 

magnetic inks has been a challenge, especially when it comes to the percentage of 

magnetic material within the final printed product, which directly affects its 

performance. Mixing magnetic particles within a thermoplastic filament requires a 

large percentage of polymer to retain desirable flow properties for printing. The 

ability to extend this technique to magnetic materials will accelerate material 



 

 

29 
 

discovery and advancement to produce passive electronics with greater efficiency, 

increasing the speed of communication in electronics to keep up with current 

integrated circuit advancements.  

 

There have been many efforts to manufacture magnetic polymer composites with the 

simplest and most common method being mixing just two ingredients – magnetic 

particles and a polymer matrix that gets crosslinked through thermal or UV 

curing[66]–[68]. This technique was explored initially here to understand the 

limitations of using this method and the balance between inductance and resonant 

frequency as a function of particle loading. The magnetic particles tested were 

spherical, 50-100 nm diameter iron oxide (Fe2O3·FeO, Sigma), and both cubic, 300 

nm face length FeCo (1:1) and 250 nm permalloy (Ni80Fe20) synthesized in-house. 

The polymers used as the matrices in these studies were UV and thermally curable 

NEA121 (Nordland Adhesives), thermally curable polyimide, and the epoxy resin 

polydimethylsiloxane (PDMS, Gelest).  

 

3.2 Results & Discussion 

3.2.1 Printability as a function of particle loading 

Particle loading drastically influences ink viscosity (Figure 3.1). Particle mixtures were 

tested at various weight fractions to determine the maximum particle loading that can 

still be extruded through an 18 G nozzle. At the maximum particle loadings, printed 

parts had enough strength to retain their shape after deposition and before curing. 



 

 

30 
 

Toroids of iron oxide in NEA121 were printed at 50, 60, 70, and 80 wt%. The 50 wt% 

compositions flowed too easily, and a shape was retained by using UV to cure the skin 

and maintain shape between layers. 60 wt% composition printed part looks identical to 

the toroid shape that had been molded. Beyond 70 wt% composition requires a solvent 

(methylene chloride) to reduce viscosity enough for extrusion. Particles appear to be 

distributed evenly throughout the cured resin (Figure 3.2). 

 

Figure 3.1: (a) 50 wt% and (b) 75 wt% particle loading of iron oxide in polyimide 

 

Figure 3.2: 80 wt% FeCo in NEA121 (a) molded into a toroid and its (b) cross-
sectional TEM image displaying the particles dispersed in the cured resin 



 

 

31 
 

3.2.2 Printability and rheological study with solvents added to NEA121 ink 

mixtures 

Uncured NEA121 was first evaluated for solubility in high-volatility solvents. It was 

found that NEA121 is soluble in tetrahydrofuran (THF), methylene chloride, methanol, 

and ether. Then it was determined whether the crosslinking process was affected by the 

addition of these solvents. THF and methylene chloride were the only solvents that did 

not inhibit the curing behavior or final morphology of the cured part when using both 

oven heating or UV light to cross-link. FeCo in NEA121 is printable below 80 wt% but 

requires 30 wt% of solvent (solvent: resin) to extrude at 80 wt% particles in resin. The 

resulting shape is self-supporting, and the resulting material is completely oven curable 

with no observable bubbling or discoloration. For iron oxide mixed in NEA121, the ink 

mixture becomes difficult to extrude at 70 wt% but is printable at 80 wt% (33 vol%) 

with the addition of methylene chloride as a solvent. Attempts to print at 50 vol% were 

made by increasing the addition of solvent to allow extrusion, but extreme volume 

change was experienced during the oven cure due to the large volume of solvent that 

evaporates during the oven curing process. Moreover, the particles were not stable in 

the solvent and the mixture was not truly homogeneous. These results led us to 

investigate alternative ink formulation methods to achieve higher particle loadings.  

 

The rheology of inks with FeCo in NEA121 was evaluated with and without methylene 

chloride as a solvent. The 75 wt% ink with no added solvent (Figure 3.3 (a)) has a zero-

shear rate viscosity of 750 Pa·s, while the sample with added solvent (Figure 3.3 (b)) 



 

 

32 
 

has a zero-shear rate viscosity of 230 Pa·s. Both still exhibit shear thinning behavior as 

evidenced by the decreasing viscosity with increasing shear rate.  

 

 

Figure 3.3: Rheology of (a) 75wt% FeCo in NEA121 without solvent (b) 80wt% FeCo 
in NEA121 with methylene chloride as a solvent.  
 

The addition of low-viscosity solvent improves printability as long as it does not 

influence the curing behavior or morphology of the resin. Too much solvent causes a 

large volume change as the solvent evaporates. 80 wt% FeCo with the addition of 

30wt% methylene chloride (solvent:resin) allowed a flow rate of 0.45 𝑚𝑚𝑚𝑚3𝑠𝑠−1 at 80 



 

 

33 
 

psi. The curing of the composite is not hindered, and the solvent evaporates with no 

volume change. 

 

3.2.3 Magnetic characterization using vibrating sample magnetometry (VSM) 

Molded or printed samples with various particle loadings are mounted to a VSM for 

magnetic characterization. The hysteresis curve recorded with this device provides 

insight into the behavior of an inductor constructed with the magnetic composite 

material as the core. From the hysteresis curve, the maximum magnetic saturation, 

relative permeability, coercivity, and hysteresis loss can be interpreted. All of these 

values hold some significance to the performance ability of the final constructed device. 

Magnetic saturation is the point at which all of the magnetic domains within the 

material are aligned, and this determines the limit of current or voltage that can be 

stored within the inductor. If exposed to current beyond the saturation limit, the 

inductor is less efficient and behaves more like a resistor than an inductor. The relative 

permeability is the ratio of magnetism to the applied magnetic field. The higher the 

value, the more responsive the material is. For an inductor, this value should be 

maximized, as it is directly related to the inductance. Coercivity is the magnetic field 

strength required for the magnetic domains to switch to the opposite direction. Ideally 

for an inductor, this value is nearly zero. The magnetic field is what is being stored 

within the material, and if it is spent switching domain direction then it is lost in 

operation. The hysteresis loss is the energy that is wasted in the form of heat when the 

magnetic direction is switched. This is calculated as the area within the forward and 



 

 

34 
 

backward curves. An ideal inductor would have no hysteresis loss. Figure 3.4 

exemplifies how to interpret these values from the VSM curve for 80wt% FeCo in 

NEA121.  

 

From the hysteresis curve recorded by VSM, we can compare the bare FeCo powder 

(Figure 3.5) to FeCo particles mixed in resin (Figure 3.6). For the bare powder, the 

magnetic saturation approaches 200 emu/g, which is consistent with the literature 

values. The coercivity is approximately 210 Oe. The maximum relative permeability 

calculated from the slope of the curve is 8.96 (a relative, unitless value). After mixing 

in resin at an 80wt% particle loading, the magnetic saturation of the composite 

approaches 180 emu/g, a decrease from the bulk value due to isolation between 

particles in the polymer resin. The coercivity is similar to bulk values indicating that 

the resin does not alter the magnetic field strength required to switch directions of the 

magnetic domains within the material. The maximum relative permeability calculated 

from the slope of VSM is μr = 3.93, which is less than the pure powder due to the 

inclusion of the polymeric material. Since permeability is directly related to inductance, 

we can predict that the more magnetic material included in the composite, the higher 

the permeability and therefore inductance. 

 

 



 

 

35 
 

 

Figure 3.4: Interpretation of magnetic hysteresis acquired with VSM to calculate 
magnetic saturation, relative permeability, coercivity, and hysteresis loss of 80 wt% 
FeCo in NEA121. 
 

 

Figure 3.5: VSM of FeCo bare powder showing its magnetic response. The graph to 
the right is zoomed in to make the coercivity clearer.  
 
 
 



 

 

36 
 

 

Figure 3.6: VSM of 75 wt% FeCo in NEA121 showing its magnetic response. The graph 
to the right is zoomed in to make the coercivity clearer. 
 

3.2.4 Construction into an inductor mounted to a transmission line 

Toroids were printed or molded into a target dimension of 12 mm outer diameter, 6 

mm inner diameter, and 5 mm height. A thin copper was carefully hand-wound around 

the toroids at least 15 times, making sure they were tight around the composite material. 

The wire was then soldered to an SMA (“sub-miniature version A” coaxial cable 

connection) connection part for attaching to the VNA for measurement (Figure 3.7). 

When comparing directly, the same number of windings were used between samples. 

At a high enough particle loading, the uncured ink was sufficiently viscous and shape-

retentive to resemble the desired toroid dimensions. Only a few ink compositions per 

system fit these criteria because if the ink viscosity was too low the printed shape had 

no semblance to a toroid and was unusable.  



 

 

37 
 

 

Figure 3.7: Printed and molded 75 wt% FeCo in NEA121 inductors hand wound and 
soldered to an SMA for connection to a VNA for inductance measurements. 
 
 
One composite ink formulation was successfully printed into a cone instead of a toroid 

to reduce stray capacitances and achieve higher bandwidths. The results of this study 

have been published [69]. FeCo was mixed into NEA121 at 75wt% and printed through 

an 18 G nozzle with the syringe printer without a tool path but by manually lifting the 

nozzle in the z-direction at increasing speed while maintaining a constant extrusion 

pressure. The printed cone was then thermally cured, removed from its substrate, and 

mounted onto an AJ printer. The conductive windings were AJ printed using a silver 

nanoparticle (NP) ink using the tool path as shown in Figure 3.9 and mounted onto a 

transmission line at a fixed angle by resting onto a dielectric mount. Interconnects were 

AJ printed using the same silver NP ink to complete the circuit and reflectance 

parameters were measured using the VNA (Figure 3.8, 3.9).  



 

 

38 
 

 

Figure 3.8: The plan for printing windings around the magnetic cone core.  

 

Figure 3.9: Syringe printed 75wt% FeCo in NEA121 magnetic core mounted to a 
transmission line with AJ printed silver NP conductive windings and interconnects. 
 

3.2.5 Inductance characterization using a vector network analyzer (VNA) 

A Vector Network Analyzer (VNA) from Agilent Technologies that sweeps between 1 

kHz to 1.5 GHz using an SMA connection is used to measure reflectance at high 

frequencies, in which complex impedance and therefore total resistance and inductance 

can be calculated. Hand wound toroids of various compositions either syringe printed 

or molded were soldered to an SMA connection so that reflectance parameters can be 

measured and compared as a function of particle loading and magnetic composition.  

 

From reflectance data, we can observe the resonant frequency and calculate the value 



 

 

39 
 

of inductance at frequencies below resonance. Below the resonance frequency, we can 

assume predominant inductive behavior and negligible capacitive behavior. We can 

also calculate the Q factor, which is the ratio of stored to dissipated energy, or the ratio 

of imaginary to real impedance.  

𝑍𝑍𝐿𝐿 = 𝑅𝑅 + 𝑗𝑗𝑋𝑋𝐿𝐿 ,𝑤𝑤ℎ𝑒𝑒𝑒𝑒𝑒𝑒 𝑋𝑋𝐿𝐿 =  𝜔𝜔𝐿𝐿,𝑎𝑎𝑎𝑎𝐻𝐻 𝑄𝑄 =  𝑋𝑋𝐿𝐿
𝑅𝑅

     (1) 

𝑅𝑅 is the resistance, 𝜔𝜔 is the angular frequency, 𝑋𝑋𝐿𝐿 is the inductive reactance, 𝐿𝐿 is the 

inductance, and 𝑄𝑄 is the quality factor. The resistance measured using this method 

includes the resistance of the entire circuit system and should not be attributed entirely 

to the magnetic core material.  

 

Effective permeability can be calculated as a function of frequency from inductance 

data, as well. The following equation is used specifically for a cylindrical structure: 

𝜇𝜇𝑒𝑒𝑒𝑒𝑒𝑒 = 𝐿𝐿 𝐻𝐻
𝜇𝜇0 𝑁𝑁2𝐴𝐴

          (2) 

Where 𝐿𝐿 = inductance, 𝐻𝐻 = length of flux path, 𝜇𝜇0 = permeability constant, 𝑁𝑁 = number 

of turns, 𝐴𝐴 = cross-sectional area of flux.  

 

The inductance is measured as a function of frequency for hand-wound toroidal 

inductors with two different particles loading of FeCo in NEA121. The higher particle-

loaded sample (75wt%) has a higher inductance of 960 nH at a frequency of 20 MHz 

compared to the 50wt% which has an inductance of 620 nH at the same frequency 

(Figure 3.10). The decrease in inductance is due to the lower concentration of magnetic 

material which reduces the magnetic coupling, minimizing the inductance. The 

resonant frequency, however, increases with decreased particle loading, with the 



 

 

40 
 

75wt% sample experiencing resonance at 83 MHz while the 50 wt% experiences it at 

160 MHz. This is due to the less magnetic loss with the reduced magnetic particle 

loading. These measured device performances are supported by the magnetic behavior 

observed with VSM. Increasing the polymer content reduces the magnetic response or 

permeability of the composite material, which reduces the inductance.  

 

The resonant frequency observed for the toroids made with added solvent was higher 

than the ones made without added solvent. A possible explanation can be that bubbles 

formed while the solvent evaporated, and the resin cured. The particle concentration is 

nearly the same, but there is isolation provided from the void space that inhibits eddy 

current losses. 

 

 

 

Figure 3.10: Inductance as a function of frequency for 50wt% (blue) and 75wt% 
(orange) FeCo in NEA121 toroids.  
 

 



 

 

41 
 

The conical inductor of 77.5 wt% (30 vol%) FeCo in NEA121 had a resonant frequency 

of 20 GHz due to its size, geometry, and orientation. The inductance of the conical 

inductor was 100 nH at 20 MHz, which normalized to volume comes to 50 nH mm-3. 

The toroid comparatively has a normalized inductance to volume of 2 nH mm-3. This 

speaks to the better efficiency of the conical inductor which can more effectively 

produce inductance than the toroid due to its shape.  

 

The type of particle (FeCo or iron oxide) also impacts the performance of the 

constructed inductor device due to their different magnetic properties. Two samples 

with the same particle loading of 75wt% in NEA121 but different magnetic materials 

were created, hand-wound, and analyzed as an inductor using VNA (Figure 3.11). The 

iron oxide composite core inductor had a lower inductance of 820 nH (measured at 20 

MHz) compared to 960 nH of the inductor with the FeCo composite core. The 

permeability measured from the magnetic hysteresis of iron oxide is μr = 6.5 which is 

lower than that of FeCo which is measured to be μr = 9. Due to the lower permeability 

of iron oxide, the inductance of the composite is lower than that of the FeCo composite 

core at the same particle loading. The resonant frequency, however, is higher for the 

iron oxide composite measured at 135 MHz compared to the FeCo composite. The self-

resonance of the circuit is inversely proportional to the inductance, and therefore with 

a lower inductance, the circuit experiences a higher resonant frequency. This allows 

the iron oxide composite core inductor to behave efficiently at a broader range of 

frequencies compared to the FeCo composite core inductor which has a higher 

permeability and inductance and lower resonance.  



 

 

42 
 

 

Figure 3.11: Inductance as a function of frequency for iron oxide (orange) and FeCo 
(blue) at the same particle loading of 75 wt%.  
 

Only a couple of compositions were able to be tested with the FeCo material because 

it was made in-house and had a low yield per synthesis. To better understand the impact 

of particle loading on device performance, a study was conducted with a larger particle 

concentration range of iron oxide in PDMS molded toroids (Figure 3.12). The general 

trend of nominal inductance (inductance normalized to the number of windings 

squared) is that it increases with increasing magnetic particle concentration. This is due 

to the increasing magnetic response with increased magnetic material. The resonant 

frequency has a decreasing trend with increasing particle loading. The resistance 

measured does not appear to have a trend but is relatively unchanging with particle 

loading. The quality factor does increase due to the increase in inductance and 

consistent resistance with increasing particle loading. From this information, we can 

conclude that increased magnetic material increases inductance and efficiency but 

limits the frequency range of operation of the constructed magnetic inductor device.  

 

 



 

 

43 
 

  

 

Figure 3.12: Nominal inductance, resonant frequency, resistance, and quality factor of 
iron oxide in PDMS at various particle loadings as calculated from reflectance data. 
 
 

3.2.6 FEM modeling of a composite inductor 

Effective medium theory (EMT) describes the macroscopic properties of composite 

materials by averaging the properties of their constituents. EMT can be used to predict 

permeability- and permittivity-dependent behaviors of a composite device, such as 

inductance (L) and self-resonant frequency (SRF). There are a few widely known 

models used for EMT calculations, the Maxwell-Garnett model and the Bruggeman 

model[28]. The Maxwell-Garnett model is only good for homogeneous medium, which 

assumes particles are anisotropic and uniformly dispersed in a matrix and ignores 

interactions between inclusions. It is therefore most accurate for extremely dilute 

composites. The equation used for this model is as follows: 



 

 

44 
 

𝜀𝜀𝑒𝑒𝑒𝑒𝑒𝑒 = 𝜀𝜀𝑑𝑑 �1 + 3𝑐𝑐𝑚𝑚
𝜀𝜀𝑚𝑚−𝜀𝜀𝑑𝑑

𝜀𝜀𝑚𝑚+2𝜀𝜀𝑑𝑑−𝑐𝑐𝑚𝑚(𝜀𝜀𝑚𝑚−𝜀𝜀𝑑𝑑)�      (3) 

where 𝜀𝜀𝑑𝑑 is the permittivity of background medium, in this case, the polymer matrix, 

𝜀𝜀𝑚𝑚 is the permittivity of individual inclusions, in this case, the magnetic nanoparticles, 

and 𝑐𝑐𝑚𝑚 is the vol% of inclusions (particles). This calculation applies to both permittivity 

and permeability. To calculate permeability, all cases of permittivity are replaced by 

permeability.  

 

The Bruggeman model is claimed to be more accurate than the Maxwell-Garnett model 

by accounting for interparticle interactions. The model has many modifiers to consider 

isotropic, high aspect ratio particles, although that is not necessary in the case of this 

study. The model was developed to model metallic particles <10nm in diameter. The 

equations used for this model are as follows: 

𝜀𝜀𝑒𝑒𝑒𝑒𝑒𝑒 =
𝐻𝐻𝑏𝑏+�𝐻𝐻𝑏𝑏

2+8𝜀𝜀𝑚𝑚𝜀𝜀𝑑𝑑

4
         (4) 

𝐻𝐻𝑏𝑏 = (2 − 3𝑐𝑐𝑚𝑚)𝜀𝜀𝑑𝑑 − (1 − 3𝑐𝑐𝑚𝑚)𝜀𝜀𝑚𝑚       (5) 

Where 𝜀𝜀𝑑𝑑 is the permittivity of the background medium (polymer), 𝜀𝜀𝑚𝑚 is the 

permittivity of individual inclusions (particles), and 𝑐𝑐𝑚𝑚 is the vol% of inclusions 

(particles). This calculation also applies to both permittivity and permeability. To 

calculate permeability, all cases of permittivity are again replaced by permeability [70]. 

 

Using bulk electromagnetic properties of the magnetic material the nanoparticles are 

made of predictions of the permeability of the composite can be calculated using these 

EMT models and compared to experimental values.  



 

 

45 
 

 

Table 3.1. Comparison of permeability calculated from EMT with experimental results. 
The max permeability used in the calculations are from experimental VSM data of pure 
powder. The permeability of the polymer matrix is assumed to be 1. The samples tested 
in this chart are of the highest possible syringe printable particle loading in NEA121 
ink.  
 

 

Permeability calculated from VNA which measures across a range of frequencies does 

not match values calculated from either the EMT model or from VSM data. The EMT 

models do not account for frequency and the VSM measures at very low frequencies, 

between 50-100 Hz. Typically, the permeability should decrease with increasing 

frequency. The permeability calculations from VNA data could be inflated because of 

inaccurate modeling of the equivalent circuit or incorrect assumptions made that there 

is no capacitive behavior below the resonance observed within the tested frequency 

range.  

 

Finite element method (FEM) based simulation in COMSOL Multiphysics software is 

used to predict intrinsic material properties of magnetic-polymer composites of varying 

Material 
Particle size 
Max permeability 
wt% 
vol% particle loading 

Permalloy  
250 nm 
μ = 10 
85 wt% 
42 vol% 

FeCo  
250 nm  
μ = 9 
75 wt% 
29.4 vol% 

Iron Oxide (II, III) 
130 nm 
μ = 6 
70 wt% 
34.1 vol% 

Maxwell-Garnett 2.38 1.82 1.81 

Bruggeman 3.22 2.14 2.03 

Experimental VNA 12.94 4.49 5.37 

Experimental VSM N/A 3.93 N/A 



 

 

46 
 

compositions. Composite geometries are drawn as spherical or cubic magnetic particles 

within a polymer block (Figure 3.13).  

 

Figure 3.13: Geometries drawn in COMSOL of (a) random placement of spherical 
particles at 75 wt% and (b) their magnetic response in the presence of an electric field, 
and (c) random placement of 50 wt% cubic particles, and (d) their magnetic flux density 
distribution [T] in the presence of an electric field. 
 

To calculate permeability and permittivity, COMSOL Multiphysics calculates an 

average volumetric response to an applied magnetic or electric field, respectively. One 

of the faces of the box is set as an input of the applied field, while its opposite boundary 



 

 

47 
 

is set as an opposing field to create a potential difference. All other boundaries are made 

to be periodically continuous.  

 

Polarization 𝑃𝑃� is proportional to the total macroscopic field 𝐸𝐸�, 

𝑃𝑃� =  𝜀𝜀0𝜒𝜒𝑒𝑒𝐸𝐸�          (6) 

where 𝜀𝜀0 is the dielectric permittivity of free space and 𝜒𝜒𝑒𝑒 is the electric susceptibility. 

Dividing 𝐸𝐸� form 𝑃𝑃� provides the relative permittivity 𝜀𝜀𝑟𝑟, where 

𝜀𝜀𝑟𝑟 = (1 +  𝜒𝜒𝑒𝑒)          (7) 

Similarly, magnetic flux density 𝐻𝐻�  is proportional to the magnetic field 𝐻𝐻�, 

𝐻𝐻� =  𝜇𝜇0𝜇𝜇𝑟𝑟𝐻𝐻�          (8) 

where 𝜇𝜇0 is the magnetic permeability of free space and 𝜇𝜇𝑟𝑟 is the relative permeability 

of interest. 

 

To simulate, the electrical conductivity, permeability, and permittivity of the 

constituent materials are defined. Electrical conductivity and permittivity values are 

input as reported in the literature. The permeability of magnetic material is input from 

in-lab VSM measurements of dry powder samples.  

 

Simulated results are compared to experimental data acquired from VNA and VSM 

measurements to confirm accuracy (Figure 3.14). Modifications to the simulation can 

be made to improve data fitting, as necessary. It could then be justified to use these 

simulations to predict the behavior of materials prior to fabrication, creating a more 

targeted and efficient approach to developing device structures.   



 

 

48 
 

 

COMSOL experiments of modeled composites with spherical particles with the 

magnetic properties of FeCo show no difference in whether particles are ordered within 

the matrix or randomly placed (Figure 3.13). The simulation does show an increase in 

permeability when the particles are modeled as cubes instead of spheres, which for the 

75 wt% composite shows a closer semblance to the experimental VSM calculated 

permeability than the spherical particles. The FeCo particles measured with VSM are 

indeed cubic in shape and the model is truer to reality. The EMT Maxwell-Garnett 

(MG) and Bruggeman (Brugg) equations were developed to model spherical particles, 

and so they match the spherical particle COMSOL model values for permeability more 

than the cubic model. Only the random placement of cubic particles at 50 wt% was 

modeled in COMSOL because the MatLab code was unable to produce a random order 

of cubic particles that fit within the confined space. These modeling attempts can be 

improved with a more realistic design of the composite material. There is a limited 

picture drawn from the COMSOL simulation only at direct current or with no frequency 

dependence. The behavior of an inductor is complex and dependent on frequency. A 

model done with no frequency dependence can allow only a limited prediction of 

behavior at higher frequencies. 



 

 

49 
 

 

Figure 3.14: Relative permeability of FeCo in NEA121 at 75 wt% (blue) and 50 wt% 
(orange) calculated using COMSOL, EMT, and experimental methods.  
 

3.3 Conclusion 

FeCo, NiFe (permalloy), and iron (II, III) oxide magnetic particles with varying 

magnetic properties were incorporated in different resins to explore the influence of 

particle loading on printability and inductor device performance. It was generally found 

that increasing particle loading increased ink viscosity, with a loading maximum 

approaching 29 – 42 vol% depending on the particle type and resin mixtures due to 

differences in particle shape and size and resin viscosity. With more magnetic particles, 

composites had higher magnetic saturation and permeability. Coercivity was not 

0
0.5

1
1.5

2
2.5

3
3.5

4
4.5

5
R

el
at

iv
e 

Pe
rm

ea
bi

lit
y

Relative Permeability of FeCo Composites

75wt% 50wt%



 

 

50 
 

affected by particle loading because there was no change in crystal structure with 

increased particle loading. Increased particle loadings of up to 80 wt% were attainable 

by mixing volatile solvent into the particle-resin formulas to decrease the viscosity of 

the ink. Various compositions of toroids were both molded and printed and then hand-

wound to investigate the influence of particle loading on inductor device performance. 

Generally, increasing particle loading increased inductance due to the increase in 

magnetic saturation and permeability. The operating frequency does decrease with 

particle loading due to compounding magnetic hysteresis loss. Inductors were 

constructed into both a toroid and a cone using 75 wt% FeCo in NEA121 to showcase 

the difference in behavior with core shape, showing a higher operating frequency with 

a conical structure due to its orientation away from the substrate minimizing stray 

capacitance. From these initial studies, it was of interest to explore magnetic inks with 

higher particle loadings to increase inductance.  

 

3.3 Experimental Methods 

3.3.1 Materials 

Polyethylene oxide (PEO, MW = 30k g/mol), FeSO4, CoCl2, sodium hydroxide, 

cyclohexane, hydrazine, argon, DI water, ethanol, acetone, iron (II, III) oxide, hydrous 

nickel chloride, hydrous ferrous chloride, sodium hydroxide, propylene glycol, 

NEA121, polyimide, polydimethylsiloxane, tetrahydrofuran (THF), methylene 

chloride, methanol, and ether. 

 



 

 

51 
 

3.3.2 Methods 

FeCo was made in-house following a published protocol [71]. Namely, 8.256 g of 

polyethylene glycol (PEG-400), 1.251 g of FeSO4·7H2O, 0.357 g of CoCl2·6H2O, 

2.964 g of sodium hydroxide, and 0.96 mL of cyclohexane were dissolved in 53.688 

mL of DI water and stirred with a magnetic stir rod for 30 minutes at 80°C, capped and 

under argon. Then, 31.567 mL of 80 wt% hydrazine was quickly injected into the 

solution, turning the solution from a pink color to a brown, blue, then finally black 

color. The solution is then transferred to a Teflon-lined stainless-steel autoclave. The 

autoclave was heated at 120°C for three hours and air-cooled to room temperature. The 

result is a black magnetic sediment in a clear solution, which was separated using a 

strong permanent magnet and washed with DI water five times and ethanol five times, 

and placed in a desiccator to dry. The final product was about 2 g of single phase, cubic 

FeCo (3:1) with a face length of 150 nm (Figure 1 (a)). These particles were selected 

for use because of their high saturation magnetization, high permeability, and low 

coercivity.  

 

Permalloy nanoparticles were synthesized using a procedure from Qin et al [72]. The 

procedure was quadrupled to produce a higher yield at a time, from approximately 0.5 

g per synthesis to about 2 g. Hydrous nickel chloride and hydrous ferrous chloride were 

mixed at a 1:1 molar ratio with 32 g sodium hydroxide in 400 mL of polypropylene 

glycol. The kinetics of the reduction reaction was just so the final molar ratio of the 

crystallites is 4:1 nickel to iron (Ni80Fe20). The solution was mixed using a mechanical 

mixing arm at 1300 rpm. The synthesis solution is heated in an oil bath at 80°C for 2 



 

 

52 
 

hours to dissolve all the salts and then raised to 180°C for 2 hours for the particles to 

grow. After allowing it to cool overnight, a cleaning solution of 1:1:1 acetone, ethanol, 

and DI water was added to the flask and placed in a sonicating bath to dilute and 

decrease the viscosity of the synthesis solution. A magnet was used to collect the 

particles and the supernatant was discarded. The cleaning solution was added, and the 

solution was sonicated, using the magnet to collect the particles and discard the 

supernatant at least five times. Ethanol was then used an additional five times to wash 

the particles with the same sonicating and magnet collecting steps and dried in a 

desiccator overnight. The result was a spherical particle consisting of crystallites with 

a 250 nm diameter (Figure 3.1 (b)).  

 

Ferrites such as iron (II, III) oxide (Sigma, SEM 50-100 nm) (Figure 3.1 (c)) were used 

for inductor applications due to their high resistivity, especially at increased 

frequencies. Purchased from a manufacturer, it was able to be used extensively in 

prototyping procedures that were then applied to other types of magnetic particles.  

 



 

 

53 
 

 

Figure 3.15: TEM images of (a) synthesized cubic FeCo, (b) synthesized spherical 
permalloy, (c) as purchased iron oxide, and (d) magnetic hysteresis of magnetic 
materials used in this study acquired with VSM.   
 
 
NEA121 (Nordland Products, NJ, USA) is a UV and thermally curable electronics 

adhesive. It is used as an insulation material due to its high dielectric constant (ε = 4.04, 

tanδ = 0.045 at 1MHz) [73]. It cures by exposing it to UV light or oven curing at 125°C 

for 16 hours. 

 

Photo-definable polyimide coating (HD Microsystems HD4100) is a photosensitive 

polyimide resin used in printed packaging applications (ε = 3.0 – 4.0, tanδ = 0.02)[74]. 

It cures with UV exposure or oven curing at 200°C for 8 hours. 

 



 

 

54 
 

Polydimethylsiloxane (PDMS), (Gelest) is an epoxy resin that cures with added 

activator at a 10:1 ratio. The reaction takes 24 hours in air to complete (ε