ABSTRACT MUKAI, YUSUKE. Dielectric

ABSTRACT

MUKAI, YUSUKE. Dielectric Properties of Cotton Fabrics and Their Applications. (Under the direction of Drs. Minyoung Suh and Stephen Michielsen).

Uncovering relationships between the structural parameters and the dielectric properties of cotton fabrics brings two consequential benefits: development of a structural analysis method for cotton fabrics and establishment of a reference point to engineer the dielectric properties of cotton fabrics for development of high-performance textile-based electronics. In this context, the goal of this research was to explore the structure-dielectric property relationships in cotton fabrics in a wide range of frequencies and their applications in developing a wearable medical apparatus on a cotton fabric platform.

In order to achieve this goal, three experiments were designed and conducted. In the first experiment (Experiment I), the dielectric properties of cotton fabrics were investigated in relation to the fabric construction (either plain-woven or plain-knit), thread count (picks per inch (PPI), ends per inch (EPI), courses per inch (CPI) and wales per inch (WPI)) and solid volume fraction

(SVF) in a low-frequency domain (20 Hz – 1 MHz). By manipulating the relative humidity (RH), three major dielectric relaxations were identified in cotton fabrics and those were of electrode polarization, interfacial polarization, and dipolar polarization of bound water. Also, at an elevated

RH, both electrode and interfacial polarizations were enhanced due to an increased ionic conductivity in absorbed free water.

At 1 MHz, the real part of the relative permittivity of both woven and knitted cotton fabrics reasonably increased with thread count, and this was primarily elucidated with associated increase in the SVF as substantiated by the dielectric mixture theory. On the other hand, the imaginary part of the relative permittivity and loss tangent did not show clear monotonic trends to the thread count or SVF at higher RH levels, and this was interpreted that additional mixing factors such as the structure-dependent interfacial polarization and/or electrode polarization could also be influencing

the dielectric properties of highly moist cotton fabrics.

The effect of the fabric construction was investigated through the comparisons of the

dielectric properties of woven and knitted fabrics of the same SVFs. It was revealed at 1 MHz that

the fabric construction plays an important role in the dielectric properties – for all the comparisons

of the same SVF, the knitted fabrics showed higher values of the complex relative permittivity and loss tangent than the woven fabrics. This observation was interpreted that although the current mainstream in the low-frequency dielectric investigations on textile fabrics deals primarily with the SVF and RH in literature, the fabric construction also needs to be treated as a key influencer.

The second experiment (Experiment II) examined the effect of the fabric construction, thread count and SVF on the microwave dielectric properties of cotton fabrics. In this experiment,

the cotton fabrics were adopted from Experiment I and the complex relative permittivity and loss tangent were characterized based on the microstrip line method in the frequency range of 100 MHz to 6 GHz under five different RH conditions. For a further analysis, the patch antenna method, which measures only the real part of the relative permittivity and only at a single frequency (~2.45

GHz) but in a greater resolution, was also incorporated.

Both microstrip line and patch antenna measurements reasonably agreed that the real part of the relative permittivity tend to increase with RH at near 2.45 GHz. The imaginary part and loss tangent also exhibited tendencies to increase with RH from the microstrip line measurements at

2.45 GHz. These increases in the complex permittivity and loss tangent were most likely due to an increased free water content at a higher RH.

The thread count was also found to increase the real part of the relative permittivity of both woven and knitted fabrics from both microstrip line and patch antenna measurements at near 2.45 GHz, and this was primarily due to an associated increase in the SVF as corroborated by the

dielectric mixture theory. However, the imaginary part of the relative permittivity and loss tangent of woven and some knitted fabrics predominantly exhibited weak or no correlations to the thread count or SVFs, and this was most probably due to limited loss resolution of the microstrip line method.

Under the controlled SVF and at near 2.45 GHz, the woven and knitted cotton fabrics did not exhibit a significant difference (probability (p)-value ≥ 0.19) in their complex permittivities and loss tangents from the microstrip line method due to limited resolution. However, the patch antenna method disclosed that the woven fabrics exhibit higher dielectric constants than the knitted fabrics (p-value, p < 0.01) under the controlled SVF, and it was interpreted that the patch antenna method provided a better resolution in spotting the differences in the dielectric properties of woven and knitted fabrics. By considering the yarn orientation within the fabrics, the dielectric mixture theory, and the anisotropic nature of cotton fibers, these dielectric constant differences between the woven and knitted constructions were successfully elucidated by the evidence that the woven samples had more fibers in the normal direction than the knitted samples of the same SVF.

The third and last experiment (Experiment III) presents a cotton fabric antenna developed for wearable breast thermotherapy. A cotton fabric with the optimal dielectric properties was chosen based on the results from Experiment II and was incorporated as the substrate and padding layers of the antenna, and the electromagnetic (EM) and heating performance of the developed antenna were both theoretically and experimentally examined with a tissue-equivalent phantom in relation to the dielectric properties of the cotton fabric under three RH conditions.

From EM simulations and measurements, the dielectric constant variation with RH had only a minor impact on the antenna impedance matching since the cotton fabric antenna had a wide impedance bandwidth. Thanks to this, the antenna sample demonstrated temperature rises of over

4.7 °C and 2.3 °C at the tissue depths of 5 mm and 15 mm after 900 seconds of heating, respectively. Also, a slightly better heating performance was obtained at a lower RH due to a lower dielectric loss in the cotton substrate and padding layers. These results provide an evidence that a satisfactory heating for a hyperthermia treatment is possible with the proposed textile antenna applicator.

by Yusuke Mukai

A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Fiber and Polymer Science

Raleigh, North Carolina 2019

APPROVED BY:

______Dr. Jacob J. Adams Dr. Elizabeth C. Dickey

______Dr. Stephen Michielsen Dr. Minyoung Suh Co-Chair of Advisory Committee Co-Chair of Advisory Committee

DEDICATION

To Neta for her support

BIOGRAPHY

Yusuke Mukai was born in Osaka, Japan in February 1992. He received the Bachelor of

Engineering degree in Chemistry from Shinshu University (Nagano, Japan) in March 2014, and the Master of Science degree in Textiles from North Carolina State University in May 2016. His recent academic awards include the Second-Place Award in the Graduate Student Paper

Competition from the Fiber Society (2019) and the Provost’s Doctoral Fellowship Award from

North Carolina State University (2016–2017).

iii

ACKNOWLEDGMENTS

First and foremost, I would like to express my sincere appreciation to my advisers, Drs.

Minyoung Suh and Stephen Michielsen, whose expertise, understanding, generous guidance and

support made it possible to work on a topic of great interest to me. I would also like to extend my

sincere appreciation to the members of advisory committee, Drs. Jacob J. Adams and Elizabeth C.

Dickey, for their valuable advice and guidance to complete this work.

My thankfulness also goes to Dr. Jon P. Rust and Mr. William M. Barefoot for funding me

through teaching assistantship in the Springs Weaving Laboratory and the Textile Fundamentals

eLearning project. I am also grateful to Drs. Jacob L. Jones and Ching-Chang Chung for giving us

access to the LCR meter and micro-computed tomography (micro-CT). I am also thankful to Dr.

Harvey A. West II for conditioning the samples in the environmental chamber. I would also like to thank Ms. Janie F. Woodbridge, Mr. Tri D. Vu, Mr. James B. Davis and Ms. Teresa J. White for their guidance during yarn preparation, fabric manufacturing and physical testing. My sincere appreciation also goes to Mr. Vivek T. Bharambe, Mr. Junyu Shen and Mr. Bill Zhou for their support during the microwave simulations and measurements. I am also grateful to all my friends who have supported and encouraged me to complete this work. Last but not least, I would like to offer special thanks to my family.

TABLE OF CONTENTS

LIST OF TABLES ...... viii LIST OF FIGURES ...... x LIST OF ABBREVIATIONS ...... xiv CHAPTER 1. INTRODUCTION ...... 1 CHAPTER 2. LITERATURE REVIEW ...... 6 2.1. Cotton Fabric Formation, Structures and Properties ...... 6 2.1.1. Cotton chemistry and morphology...... 6 2.1.2. Spinning ...... 7 2.1.3. Weaving ...... 10 2.1.4. Knitting ...... 13 2.2. Electronic Textiles ...... 18 2.2.1. Concepts ...... 18 2.2.2. Cutting-edge applications ...... 19 2.3. General Theory of Dielectrics ...... 22 2.3.1. Dielectrics ...... 22 2.3.2. Dipole moment, electric polarization vector and permittivity ...... 24 2.3.3. Losses in dielectrics ...... 27 2.3.4. Dispersion ...... 31 2.3.5. Non-linearity, inhomogeneity and anisotropy in dielectrics ...... 35 2.3.6. Dielectric mixture theory ...... 39 2.3.7. Theory in dielectric measurements ...... 45 2.4. Dielectric Properties of Textiles ...... 51 2.4.1. Dielectric properties of fibers and fabrics – an overview ...... 51 2.4.2. Motions in polymers ...... 54 2.4.3. Dielectric properties of cotton fibers ...... 56 2.4.4. Dielectric properties of cotton fabrics ...... 59 CHAPTER 3. EXPERIMENT I ...... 62 3.1. Introduction ...... 62 3.2. Research Questions ...... 64 3.3. Methods ...... 66 3.3.1. Yarn preparation ...... 66 3.3.2. Fabric design and manufacturing ...... 67 3.3.3. Laundering and Conditioning ...... 70 3.3.4. Structural properties ...... 70 3.3.5. Hygroscopic properties ...... 75 3.3.6. Parallel-plate measurements ...... 76

3.4. Results and Discussion ...... 77 3.4.1. Dielectric spectroscopy ...... 77 3.4.2 Effect of thread count, construction and SVF ...... 82 3.5. Chapter Conclusions ...... 89 CHAPTER 4. EXPERIMENT II ...... 91 4.1. Introduction ...... 91 4.2. Research Questions ...... 94 4.3. Methods ...... 96 4.3.1. Materials ...... 97 4.3.2. Microstrip line measurements ...... 98 4.3.3. Patch antenna measurements ...... 109 4.4. Results and Discussion ...... 114 4.4.1. Microstrip line measurement results ...... 114 4.4.2. Patch antenna measurement results ...... 126 4.5. Chapter Conclusions ...... 132 CHAPTER 5. EXPERIMENT III ...... 135 5.1. Introduction ...... 135 5.2. Research Questions ...... 138 5.3. Methods ...... 139 5.3.1. Breast model ...... 140 5.3.2. Antenna design...... 141 5.3.3. Theoretical evaluation ...... 143 5.3.4. Preparation of breast phantom ...... 144 5.3.5. Antenna fabrication ...... 145 5.3.6. Experimental evaluation ...... 146 5.4. Results and Discussion ...... 147 5.4.1. Reflection coefficient ...... 147 5.4.2. SAR distribution ...... 149 5.4.3. Temperature rise distribution ...... 152 5.5. Chapter Conclusions ...... 156 CHAPTER 6. CONCLUSIONS ...... 159 CHAPTER 7. RECOMMENDATIONS ...... 163 REFERENCES ...... 165 APPENDICES ...... 182 Appendix A. Effect of the Ground Plane Size and the Use of the PLA Template ...... 183 Appendix B. Characterization Frequencies and Extracted Dielectric Constants...... 185 Appendix C. Calculation of Yarn Orientation ...... 186 Appendix D. Measurement of Yarn Orientation ...... 191

D-1. Sample Preparation ...... 191 D-2. Micro-CT scan and data visualization ...... 191 D-3. Determination of average yarn orientation ...... 191

vii

LIST OF TABLES

Table 2-1. Dielectric and electrical properties of polymers at 1 MHz...... 30 Table 2-2. Dielectric strength of polymers [92]...... 36 Table 3-1. Designed woven and knitted fabric parameters...... 68 Table 3-2. Thread counts in woven fabric samples before and after laundering...... 73 Table 3-3. Thread counts in knitted fabric samples before and after laundering...... 73 Table 3-4. Fabric thickness, grammage and SVF of the washed woven fabric samples (65% RH at 21 °C)...... 74 Table 3-5. Fabric thickness, grammage, and SVF of the washed knitted fabric samples (65% RH at 21 °C)...... 74 Table 3-6. Relaxation frequencies of the cotton fabric samples...... 82 Table 3-7. Qualitative description of the effects of the fiber orientation on the complex relative permittivity in cotton fabrics at low frequencies...... 87 Table 4-1. Structural parameters of the woven cotton fabric samples (data adopted from Table 3-2 and Table 3-4)...... 97 Table 4-2. Structural properties of the knitted cotton fabric samples (data adopted from Table 3-3 and Table 3-5)...... 98 Table 4-3. Assumed dielectric constants and optimal antenna dimensions (in millimeters) at 2.45 GHz...... 111 Table 4-4. Correlations between the RH and the dielectric properties of the cotton fabric samples...... 120 Table 4-5. Correlations between the thread counts and the dielectric properties of the cotton fabric samples...... 121 Table 4-6. Correlations between the SVFs and the dielectric properties of the cotton fabric samples...... 122 Table 4-7. Results of the paired t-test...... 125 Table 4-8. Correlations between the RH and the dielectric constants of the cotton fabric samples...... 127 Table 4-9. Correlations between the thread counts and the dielectric constants of the cotton fabric samples...... 128 Table 4-10. Correlations between the SVFs and the dielectric constants of the cotton fabric samples...... 128 Table 4-11. Qualitative description of the effects of the fiber orientation on the dielectric constant of cotton fabrics at microwave (~2.45 GHz) frequencies...... 130 Table 5-1. Materials properties of the breast phantom...... 141 Table 5-2. Dielectric properties of the cotton fabric sample (W3)...... 141 Table 5-3. Average dielectric constants of the cotton fabric samples over the RH range of 20% to 80% (calculated from the data obtained by the patch antenna method in Chapter 4)...... 142

viii

Table 5-4. RH dependences of the dielectric constant of the cotton fabric samples (calculated from the data obtained by the patch antenna method in Chapter 4)...... 142 Table 5-5. Materials properties used in the thermal simulation...... 144 Table 5-6. Operating frequencies of the simulated and measured and antennna applicator...... 148 Table 5-7. Simulated and measured reflection coeffieients and FBWs at 2.45 GHz...... 149 Table 5-8. Calculated rates of energy deposition and heating efficiencies with an input power of 1 W...... 151 Table 5-9. Simulated and measured temperature rises at the tissue depths of 5 mm and 15 mm after 900 seconds of continuous heating...... 155

LIST OF FIGURES

Figure 2-1. Chemical structure of cellulose...... 6 Figure 2-2. Structure of a mature cotton fiber (adopted from [49])...... 7 Figure 2-3. Spinning preparatory and spinning processes (redrawn from [9,p.6])...... 8 Figure 2-4. (a) Schematic of the interlaced structure of weft (white) and warp (black) yarns of the plain weave and (b) its representation on design paper (redrawn from [60,p.130])...... 11 Figure 2-5. (a) 2/2 warp rib, (b) 2/2 weft rib and (c) 2/2 basket weaves (redrawn from [61,p.49, 51, 52])...... 11 Figure 2-6. (a) 1/3 twill and (b) 2/2 twill weaves (redrawn from [63,p.4])...... 12 Figure 2-7. (a) 1/4 sateen and (b) 4/1 satin weaves (redrawn from [61,p.69])...... 13 Figure 2-8. (a) Technical face and (a) technical back of the interlooped structure in plain weft-knit and their representations on point and graph papers (adopted from [64,p.61–62])...... 15 Figure 2-9. Basic tricot structure (adopted from [64,p.316])...... 17 Figure 2-10. (a) Plain-woven fabric capacitive sensor and (b) double-layer fabric capacitive sensor (adopted from [30,p.1490])...... 20 Figure 2-11. Schematic of capacitive pressure sensor (adopted from [30,p.1491])...... 20 Figure 2-12. Fabric antenna fabricated by 3D weaving (adopted from [19,p.148])...... 21 Figure 2-13. (a) Model and (b) sample of a stitched textile coaxial cable (transmission line) (adopted from [78,p.1048,1049])...... 22 Figure 2-14. Schematic of a) electronic, b) ionic and c) dipolar polarizations (adopted from [82])...... 23 Figure 2-15. Dielectric sphere in an uniform electric field, showing (a) the polarization and (b) the polarization charge with its associated, opposing electric field ( ) (modified from [88,p.151])...... 25 Figure 2-16. Internal and external (applied) electric fields relation...... 26 𝐸𝐸𝐸𝐸 Figure 2-17. Frequency dependence of the complex relative permittivity of an ideal dielectric material, where interfacial and dipolar polarizations exhibit relaxation processes, and ionic and electronic polarizations show resonant processes (adopted from [83,p.608])...... 32 Figure 2-18. Examples of randomly positioned inclusions of various shapes in the environment (εe): (a) isotropic spheres, (b) aligned isotropic ellipsoids, (c) randomly oriented isotropic ellipsoids, (d) aligned anisotropic spheres, (e) aligned anisotropic ellipsoids and (f) randomly oriented anisotropic ellipsoids...... 40 Figure 2-19. Parallel-plate capacitor...... 47 Figure 2-20. General measurement setups for the (a) coaxial probe, (b) transmission line and (c) free space techniques (adopted from [115,p.31,34,36])...... 50

Figure 2-21. Porosity (R) and real part of the relative permittivity of cellulosic fabrics (adopted from [38,p.6])...... 59 Figure 2-22. Grammage and real part of the relative permittivity of a variety of cellulosic fabrics (flax, jute, cotton, etc) at 35% RH (adopted from [39,p.7])...... 60 Figure 3-1. Flowchart for Experiment (I)...... 66 Figure 3-2. Yarn plying process...... 67 Figure 3-3. Hand weaving process: (a) warping on a warper, (b) warp beam, (c) side-on and (d) top-view of a loom after drawing-in, (e) ends being rolled onto the take-up roll, and (f) newly made fabric (cloth fell)...... 69 Figure 3-4. Fully automated knitting process...... 70 Figure 3-5. Fabric samples under zoom microscope (Bausch & Lamp Monozoom-7) (65% RH at 21 °C)...... 72 Figure 3-6. Moisture content vs RH plot...... 75 Figure 3-7. Parallel-plate test fixture connected to an LCR meter for dielectric measurement...... 76 Figure 3-8. Real part of the relative permittivity of the fabric samples at the different RH levels...... 77 Figure 3-9. Imaginary part of the relative permittivity of the fabric samples at the different RH levels...... 78 Figure 3-10. Loss tangent of the fabric samples at different RH levels showing three major relaxations (labeled as 1, 2, and 3)...... 78 Figure 3-11. Dielectric relaxations in mortar at 67% RH, where relaxation process 3 is masked by relaxation process 2 (adopted from [94])...... 81 Figure 3-12. RH dependences of the dielectric properties of the fabric samples at 1 MHz, where the error bars indicate the 95% confidence intervals determined from 5 specimens for each fabric sample...... 83 Figure 3-13. Dielectric properties of the woven fabric samples...... 83 Figure 3-14. Dielectric properties and the SVF at 1 MHz, where the error bars indicate the 95% confidence intervals determined from 5 specimens for each fabric sample...... 84 Figure 3-15. Dielectric properties of the knitted fabric samples...... 85 Figure 3-16. Comparisons of the woven and knitted fabric samples of the same SVF (W4 and K2), excerpted from Figure 3-12...... 86 Figure 3-17. Comparisons of the woven and knitted fabric samples of the same SVF (W5 and K3), excerpted from Figure 3-12...... 86 Figure 4-1. Flowchart for Experiment (II)...... 96 Figure 4-2. Designed microstrip line in the (a) perspective and (b) side views (not to scale)...... 99 Figure 4-3. Designed microstrip line with the template (not to scale)...... 100

Figure 4-4. Microstrip line sample...... 101 Figure 4-5. (a) CAD model of the template for 3D printing and (b) 3D-printed template with the bolts and nuts...... 102 Figure 4-6. Polyester microstrip line sample placed on the 3D-printed template...... 102 Figure 4-7. Concepts of (a) the embedded transmission line structure with two fixtures on each end and (b) the thru structure having only the fixtures (adopted from [186,p.1])...... 103 Figure 4-8. Schematic side views of (a) the micropstrip line with two SMA connectors on each end and (b) the thru calibration standard (not to scale)...... 104 Figure 4-9. Thru standard for de-embedding...... 105 Figure 4-10. Models of (a) an adhesive-mounted fabric, (b) capacitors in series and (c) an equivalent capacitor...... 109 Figure 4-11. Designed rectangular patch antenna geometry...... 110 Figure 4-12. Patch antenna sample...... 112 Figure 4-13. Raw and fitted dielectric property data of the fabric samples from the microstrip line measurements in the RH range of 20% to 80%...... 115 Figure 4-14. Real components of the relative permittivity of the cotton fabrics having different SVF and RH levels...... 117 Figure 4-15. Imaginary components of the relative permittivity of the cotton fabrics having different SVF and RH levels...... 118 Figure 4-16. Loss tangent of the cotton fabrics having different SVF and RH levels...... 119 Figure 4-17. Dielectric properties of the cotton fabric samples as a function of the RH at 2.45 GHz...... 120 Figure 4-18. Dielectric properties of the woven fabric samples, plotted as a function of the thread count...... 121 Figure 4-19. Dielectric properties and the SVF at 2.45 GHz...... 122 Figure 4-20. Dielectric properties of the knitted fabric samples...... 124 Figure 4-21. Comparisons of the dielectric properties of the woven and knitted fabric samples of the same SVF (W4 and K2), excerpted from Figure 4-17...... 125 Figure 4-22. Comparisons of the dielectric properties of the woven and knitted fabric samples of the same SVF (W5 and K3), excerpted from Figure 4-17...... 125 Figure 4-23. Dielectric constants plotted as a function of the RH, determined by the patch antenna method in the vicinity of 2.45 GHz...... 127 Figure 4-24. Dielectric constants of the (a) woven and (b) knitted fabric samples as a function of the thread count...... 128 Figure 4-25. Dielectric constants as a function of the SVF...... 129 Figure 4-26. Comparisons of the woven and knitted fabric samples of the same SVF ((a) W4 and K2; (b) W5 and K3), excerpted from Figure 4-23...... 130 Figure 4-27. Plotted average yarn angles of the cotton fabric samples of the same SVFs: (a) W4 and K2; (b) W5 and K3...... 132

xii

Figure 5-1. Flowchart for Experiment (III)...... 140 Figure 5-2. Sketch of the designed patch antenna conforming the hemispheric breast phantom in the (a) YZ-plane and (b) ZX-plane (not to scale)...... 143 Figure 5-3. One-way EM-thermal link in the Ansys Workbench software...... 144 Figure 5-4. (a) Breast phantom, (b) antenna sample (ground plane side), (c) antenna sample (antenna element side) placed in an antenna folder, (c) padding layer placed on the patch, (e) temperature probes, and (f) antenna sample placed in the holder for measurements...... 145 Figure 5-5. (a) Flat patterns of the antenna components and (b) cut fabric pieces...... 146 Figure 5-6. Antenna powering setup for temperature measurement...... 147 Figure 5-7. (a) Simulated and (b) measured reflection coefficients of the antennna applicator...... 148 Figure 5-8. (a) YZ and (b) ZX cuts of the simulated SAR distribution in the standard condition (65%RH)...... 149 Figure 5-9. Simulated SARs as a function of the tissue depth...... 150 Figure 5-10. (a) YZ and (b) ZX cuts of the simulated SAR distribution at 80% RH...... 151 Figure 5-11. (a) YZ and (b) ZX cuts of the simulated SAR distribution at 20% RH...... 151 Figure 5-12. Simulated temperature increment distributions at 65% RH (t = 0–900 s)...... 152 Figure 5-13. Simulated temperature increment distributions at 80% RH (t = 0–900 s)...... 153 Figure 5-14. Simulated temperature increment distributions at 20% RH (t = 0–900 s)...... 154 Figure 5-15. (a) Simulated and (b) measured temperature increments at the 5 mm and 15 mm locations in the breast phantom...... 155

xiii

LIST OF ABBREVIATIONS

3D Three-dimensional CAD Computer-aided design CPI Courses per inch DUT Device under test EM Electromagnetic EPI Ends per inch E-textiles Electronic textiles FBW Fractional bandwidth ISM Industrial, scientific and medical Micro-CT Micro-computed tomography MUT Material under test NMR Nuclear magnetic resonance PE Poly(ethylene) PET Poly(ethylene terephthalate) PLA Poly(lactic acid) PPI Picks per inch p-value Probability-value RF Radiofrequency RH Relative humidity RIS Rotational isomeric state RQ Research question SAR Specific absorption rate SMA SubMiniature version A S-parameter Scattering parameter SVF Solid volume fraction T-parameter Transfer parameter TPM Twists per meter VNA Vector network analyzer WBAN Wireless body area network WPI Wales per inch Z-parameter Impedance parameter

xiv

CHAPTER 1. INTRODUCTION

The dielectric properties of textile materials have been the subject of study for decades in the textile industry. The dielectric properties, which quantify internal responses of dielectric materials under an alternating electric field, offer a wide-range of knowledge from the atomic and molecular-level information such as chemical composition, bonding strength, polymer backbone chain flexibility, mobility of side chains and impurities, to the structural information such as size, arrangement and orientation of various internal components in both microscopic and macroscopic scales [1,2]. Thus, investigations on the dielectric properties of a variety of fibers and yarns have been carried out for processing and quality control in the field of textile product development and manufacturing [1,3–

5].

Particularly, the dielectric properties [1,4,6,7] of cotton materials have been of great interest for textile mills, because cotton has been the most produced natural polymers worldwide

[8] and finds a wide range of applications from daily wears and homewares to military and firefighter uniforms [9–13]. Having cellulose molecules as its main composition, cotton fibers have great moisture absorbing properties – up to 20% moisture content could be achieved at 96 °F

(35.6 °C) [14]. This hygroscopic property as well as excellent tensile and tear strength [15], abrasion resistance [16] and dyability [17] of cotton are ideal for many apparel products.

With the recent booming of wearable electronics and smart textiles, the dielectric properties of cotton fabrics have been spotted for development of textile-based electronic devices [18].

Microwave interfaces such as transmission lines and antennas have been inherently integrated into fabrics by weaving [19–21], knitting [22,23], embroidering [24–26] and laminating [27,28] techniques with electrically conductive yarns and fabrics. These seamless additions of electronic

functionalities to the conventional fabrics not only enable constructions of conformable and

lightweight devices in a highly wearable form but could also enable better electronic performance.

For instance, certain textile fabrics including cotton were reported to have dielectric properties

desirable for fabrication of microwave devices [29]. The highly porous nature of the fabric structures results in a permittivity close to that of air which enables construction of low-loss microwave systems [29]. Therefore, investigations on the dielectric properties of fabrics are of great interest in the field of smart clothing.

The dielectric properties of cotton fabrics have also gained attention for wearable sensing applications at low-frequencies. For example, Zhang et al. [30] and Hasegawa et al. [31] reported

that pressures applied to cotton fabrics could be determined through measurements of the

capacitance. Also, the possibility of relative humidity (RH) sensing through capacitance

measurements of cotton fabrics was suggested by Feddes et al. [32] and Zhangmin [33]. Currently, the utilization of dielectric properties of cotton fabrics in sensors is regarded as another emerging topic in the smart clothing field.

Additionally, the dielectric investigations could be useful in fabric structural analysis for quality and performance assessment. It is well known that the structural properties of fabrics critically influence the aesthetic, physical and mechanical properties of fabrics [34,35], and thus

the characterization of the fabric structure is vital. Since the dielectric properties contain structural

information in both microscopic and macroscopic scales, investigations on the relationships between the fabric structural parameters and dielectric properties of cotton fabrics could also be beneficial in this context.

Although the dielectric properties of cotton fabrics could lead to various novel applications

from both smart textiles and fabric structural analysis points of view, there are several challenges

with dielectric characterization of cotton in fabric form at both low and microwave frequencies.

Firstly, cotton fabrics are three-dimensional assemblies of moist fibers, and hence, the behavior of cotton fabrics as dielectrics depend not only on the dielectric properties of cotton fibers but also on the shapes, positions, orientations and amount of the moisture and fiber in air [1,2]. Secondly,

there is no standardized dielectric characterization method specifically developed for fabrics at

low and microwave frequencies [1]. For these reasons, the dielectric analysis of textile materials

in fabric form is generally more challenging than that of the quasi-linear forms such as fibers and

yarns [36].

The dielectric properties of cotton fabrics have been recently studied by the parallel-plate

method [37–39] at low frequencies and by the microwave resonator method [40] and patch antenna

method [41–43] at microwave frequencies. However, few papers report the roles of structural

parameters such as the fabric construction, thread count and solid (fiber) volume fraction (SVF)

altogether on the dielectric properties of cotton fabrics. Building a scientific link between the

dielectric properties and fabric structural parameters is a new topic of research that could be

beneficial not only for development of a novel structural analysis method but also to establish a

reference point to engineer a cotton fabric for best-performing wearable systems.

This dissertation, therefore, aims to investigate the dielectric properties of cotton fabrics in relation to the fabric structural parameters in both low and high frequency regimes. In addition,

based on investigated dielectric properties cotton fabrics, an optimal antenna is developed for

wearable medical treatment on a cotton fabric platform, and the electromagnetic (EM) and heating

performances of the developed antenna are examined in relation to the humidity-dependent dielectric properties of cotton fabrics.

The second chapter of this dissertation is dedicated for literature review. Techniques in textile processing, recent applications of textile dielectrics in smart textiles, and dielectric

properties of cotton and other cellulose materials are reviewed from literature.

The third chapter (Experiment I) examines the effect of the fabric construction, thread

count, and SVF on the dielectric properties of cotton fabrics in the frequency range of 20 Hz to 1

MHz. Because cotton fibers themselves were reported to exhibit different dielectric properties

primary due to different moisture absorbability [44], plain-woven and plain-knitted (single jersey)

cotton fabrics were prepared from the same cotton yarn. Conditioning was carried out at five RH

levels, and the complex relative permittivity and loss tangent of the fabric samples were

characterized by the parallel-plate method.

The fourth chapter (Experiment II) investigates the relationships between the microwave

dielectric properties and the fabric construction, thread count, and SVF under various RH

conditions. In order to achieve this goal, two research phases were designed. In the first phase, the

dielectric properties of cotton fabrics adopted from Experiment I were measured by using the

microstrip line method. Although this method provides information on the electric permittivity in

the complex form at broadband frequencies, its measurement resolution is often limited by various

factors [45–48]. Thus, for a further analysis, the patch antenna method, which measures only the

real part of the relative permittivity and only at a single frequency (~2.45 GHz) but in a greater

resolution, was also incorporated.

The fifth chapter (Experiment III) presents a development of a textile antenna for

wearable medical treatment. A cotton fabric with the optimal dielectric properties was chosen

based on the results from Experiment II and was incorporated as the substrate and padding layers of the antenna, and the EM and heating performances of the developed antenna were examined in relation to the dielectric properties of the cotton fabric under various RH conditions.

CHAPTER 2. LITERATURE REVIEW

2.1. Cotton Fabric Formation, Structures and Properties

2.1.1. Cotton chemistry and morphology

Cotton is a natural fiber made of 90% to 99% of cellulose (Figure 2-1) [49,50] and is the most produced natural polymer worldwide [8]. In general, a cotton fiber can be broken down into six parts: cuticle, primary wall, winding layer, secondary wall, lumen wall and lumen, and different layers possess different chemical compositions and microstructures [49]. The cuticle is a smooth, waxy layer of pectin to protect the fiber; the primary wall is the original thin cell made of networking fine fibrils; the winding layer is made of fibrils aligned at 40- to 70-degree angles to the fiber axis in an open netting type of pattern; the secondary layer consists of concentric layers of cellulose fibrils oriented at 70- to 80-degree angles to the fiber axis, which constitute the main portion of the cotton fiber; the lumen layer is the inner wall that protect the secondary wall with wax and pectic materials [49,51].

Figure 2-1. Chemical structure of cellulose.

Figure 2-2. Structure of a mature cotton fiber (adopted from [49]).

2.1.2. Spinning

Raw cotton collected from cotton plants is turned into a yarn by spinning preparatory and spinning processes. In the spinning preparation, fibers are manipulated in various ways to convert their massive bulk into a linear fiber strand that is ready to spun into a yarn [9]. A typical preparation consists of pre-opening (bale opening), progressive opening, cleaning, blending, carding, drawing, combing and roving [9] as shown in Figure 2-3.

Figure 2-3. Spinning preparatory and spinning processes (redrawn from [9,p.6]).

Pre-opening is a process to mix cottons from different lots (called bales) to attain required

quality parameters for enabling later spinning while ensuring the lowest possible cost and

acceptable consistency in the yarn quality for a long run [52]. The mixed fiber mass is then opened

gradually by dividing and re-dividing the fiber clumps to form a mix of smaller fiber tufts [9].

Foreign particles (such as seeds, coats, leaves, sand and dust) intermingled with the fibers are

removed by a series of mechanical cleaning operations, which usually utilize the gravitational

force, centrifugal force and/or air flow [53]. In the carding process, fine opening and cleaning are

further applied until the fiber mass is reduced to single fibers laid in a thin web, followed by a

condensation to form a soft, weak, rope-like fiber strand called a “carded sliver” [9]. The fibers in the carded sliver are further aligned using several drafting rollers in the drawing step [53]. Coming process is an optional process in which the carded sliver is further cleaned and then fine combed to remove short and entangled fibers and foreign materials that have not been removed during the early stages of processing [54]. Primarily for ring spinning, drawn sliver is further attenuated in a roving machine to produce a much thinner, yarn-like fiber strand called a “roving” [9]. 8

Prepared fiber strand (sliver or roving) is converted into a spun yarn by a spinning process,

and any spinning process involves three mechanisms: drafting, consolidation and winding [9].

Drafting is to reduce the size (thickness) of fiber strand down to the desired yarn size by

mechanical (drafting rolls or opening rolls) and/or aerodynamic means, and consolidation is to

provide the necessary integrity to the yarn using twisting or wrapping techniques [9]. Winding

wraps the yarn on a package (bobbin or cone) that is suitable for shipping to other sectors of the

industry [9].

There are several spinning methods available for cotton fibers, and those include ring,

open-end (rotor) and air-jet spinning. Ring spinning is the oldest method of cotton spinning and

uses a bobbin that rotates constantly for insertion of twist [9]. Although this method provides a

relatively strong yarn and thus is still widely employed in the industry, the production rate is often limited by the longer and stronger fiber requirements to maintain acceptable spinning stability [9].

The open-end spinning was developed primarily to improve the spinning speed [55]. In this method, the sliver is completely separated into individual fibers in an opening roll and contaminates are first removed [9]. The separated fibers are then transported with an air stream to a rotor, where consolidation is achieved by inserting twists by a high-speed rotation of the rotor

[9]. Since the spool does not rotate to insert twists, much larger spools can be wound at a higher speed [55]. Open-end spinning thus offers a cost-effective yarn production, but the resulting yarns are usually weaker in strength than those spun by a ring spinning machine [55].

Air-jet spinning uses the principle of false twist to produce a yarn of uniquely different structure from that of ring or open-end spun yarn [9]. While ring spinning is characterized by the

continuity in the fiber flow and rotator spinning is characterized by the complete separation of

fibers prior to spinning, this pneumatic method creates an intermediate feature in which the

majority of fibers flow continuously and a small portion of the fibers is separated to create a wrapping effect [9]. The consolidation mechanism is air vortex generated from compressed air, and fibers attain more twists at the surface than in the core, leading to a relatively low pilling propensity of the air-jet spun yarns [56,57].

2.1.3. Weaving

Weaving is one of the oldest fabric formation technique and involves interlacing of two orthogonal sets of yarns, warp (end) and weft (pick or filling), in a regular and recurring pattern [58]. The typical weaving process takes place on a weaving loom after weaving preparatory processes, namely winding, warping, sizing, drawing-in and tying-in, where each of these preparatory phases is designed to maximize the efficiency, productivity and quality in the woven fabric production

[59].

Although the initial form of weaving required a large work force of manual operation and hence the production capacity was critically low, the invention of power loom by Edmund

Cartwright in 1785 made it possible for textile manufactures to produce various weave structures in more efficient and productive ways [59]. With further ambition to improve the efficiency and productivity, the modern weaving systems are fully equipped with a number of electronic systems so as to automate the woven fabric production [58].

In forming a fabric sheet, the warp and weft yarns can be interlaced in various ways, and theoretically an endless number of patterns can be formed. The pattern of a woven fabric not only influences the appearance but also affects the fabric performance based on the end use [58].

A weave construction is generally presented on a square design paper having equally

spaced vertical and horizontal lines, and the space between two adjacent vertical lines represents

a warp yarn whereas the space between two adjacent horizontal lines is a weft yarn (Figure 2-4)

[60]. A filled square indicates a warp yarn over a weft yarn and any woven structure can be

expressed in this representation [60].

Figure 2-4. (a) Schematic of the interlaced structure of weft (white) and warp (black) yarns of

the plain weave and (b) its representation on design paper (redrawn from [60,p.130]).

Three basic woven structures are plain weave, twill weave and satin (or sateen) weave, and

all other weaving structures are derivatives of these three fundamental weaves [61]. Plain weave is the simplest and most common woven structure, in which warp and weft yarns interface in an alternate matter (Figure 2-4). Because the maximum number of interlacements is possible by plain-weaving, plain woven fabrics have the best firmness and shear strength [61,62].

Figure 2-5. (a) 2/2 warp rib, (b) 2/2 weft rib and (c) 2/2 basket weaves (redrawn from [61,p.49, 51, 52]).

Warp rib (Figure 2-5(a)), weft rib (Figure 2-5(b)) and basket (matte) (Figure 2-5(c)) weaves are the variations of the plain weave. Due to the interlacement pattern, where two neighboring picks will resist the tearing force together in a pair, warp rib fabrics could demonstrate higher tear strength in the warp direction compared to the plain weave having the same yarns and thread density (number of ends and picks per unit length) [58]. In case of the weft rib structure, warp ends undergo larger number of interlacements than picks, leading to a higher tearing strength

[58]. In the basket weave, more than one ends and picks interlace with each other in groups following the pattern of the pain weave [58]. Because the neighboring yarns resist the tearing together, higher tear strength is possible with basket weaving.

Twill weave is another basic weave, in which weft yarns have floats across the warp yarns in a progression of interlacing to the right or left, forming a distinct diagonal line pattern [58].

Figure 2-6(a) shows 3/1 (three up one down) twill pattern, and 2/2 (two up and two down) twill is given in Figure 2-6(b). With longer floats, twill weaves generally attain smaller slip resistance

(larger slippage), and thus a higher tear resistance is expected as compared to the plain weave construction [61]. Because of less number of interlacements, twill weaves provide smaller tensile strength but better pliability, richer drape and more luster than plain-woven fabrics [61].

Figure 2-6. (a) 1/3 twill and (b) 2/2 twill weaves (redrawn from [63,p.4]).

The last basic weave is the satin and sateen weave, in which only one crossover point in each end and pick within the repeat unit presents [58]. As illustrated in Figure 2-7, satin is warp- faced, which means that all the surface of the fabric shows the warp threads except for one thread interlacement with other series of yarn, whereas sateen is weft-faced, showing the weft threads for the most part [61]. The long-float nature of the satin and sateen weaves enables a significantly higher tearing strength than the twill structures [58]. In addition, because satin and sateen weaves have least interlacement points among the basic weaves, the surface demonstrates excellent luster and smoothness [61]. Also, the satin and sateen weaves allow the highest yarn packing and the maximum achievable cover factor is possible in this weave [61].

Figure 2-7. (a) 1/4 sateen and (b) 4/1 satin weaves (redrawn from [61,p.69]).

2.1.4. Knitting

Another important fabric formation technique is knitting, which constructs a fabric structure by transforming a continuous length of yarn into columns of vertically intermeshed loops [64]. This is achieved by a combination of the intermeshed needle loops and a yarn that passes from one needle loop to one another – a newly-fed yarn is converted into a new loop in each needle hook and this new loop head is drawn through the old loop to build a fabric [64]. Knitted loops are

arranged in rows, roughly equivalent to the weft and warp of woven structures, and these horizontal

and vertical components in knitted fabrics are called courses and wales, respectively [64].

The origin of knitting may date back to the 11th centuries, and the early form of knitting involved manual operation of a pair of needles to produce open loop structures [65]. Although this type of knitting with large manual labor is still popular particularly for traditional handicrafts and hobby, the modern knitting is fully equipped with electronic systems for rapid manufacturing and larger production capacity. Currently, knitting ranks the second largest fabric manufacturing method just after weaving [61,66]. This popularity of knitting is primarily because of lower production cost, higher processability, faster production time, more flexibility of design, and other technical properties [61].

Knitting techniques can be classified into two categories depending on the directions of the yarn feeding and fabric formation: warp and weft knitting. In warp knitting, the direction of yarn feeding and the direction of fabric formation are set perpendicularly to each other, whereas the direction of yarn feeding and the direction of fabric formation are set parallel in weft knitting [61].

In weft knitting, a variety of loop structures can be produced, and this results in different fabric appearance and performance properties. Of such loop structures, the simplest is the plain knit (Figure 2-8). In the plain weft-knit fabric, its technical face is smooth with the side limbs of

the needle loops having the appearance of columns of V’s in the wales [64]. On the other hand, the technical back of the plain knit exhibits heads of the needle loops and the bases of the sinker loops forming columns of interlocking semi-circles [64]. Because of this unbalanced loop structure and the yarn torque inside the fabric that tends to recover the original shape of the yarn, almost all

plain-knitted fabrics tend to curl [67]. Another characteristics of plain knit is its covering power,

Of all the knit structures, the plain knit provides the highest covering power [64], which is

advantageous in applications such as UV protection clothing [68].

(a) (b)

Figure 2-8. (a) Technical face and (a) technical back of the interlooped structure in plain weft- knit and their representations on point and graph papers (adopted from [64,p.61–62]).

Another basic weft-knit construction is rib stiches. In rib knit, a vertical cord appears because of the face loop wales that tend to move over to the front of the reverse loop wales [61].

One of the advantages of the rib weft knit is the balancing of the fabric. For example, 1×1 rib weft knit shown has alternating wales stitched to front and this balanced loop structures solves the curling issue of the plain knit [64]. Another characteristic of the rib weft knit is its extensibility.

Generally, rib fabrics offer better comfort to wear than plain knit because of their superior

stretchability. For example, relaxed 1×1 rib creates theoretically twice the thickness and half the

width of an equivalent plain fabric, but it has twice as much width-wise recoverable stretch [64].

The last basic knit stitch is purl stitches, which are characterized by alternate courses of all

face and all reverse loops, exhibiting the horizontal cord across the fabric [61]. The lateral stretch

of purl weft knit is generally equal to plain weft knit, but its length-wise elasticity is almost double, and this is because when relaxed, the face loop courses cover the reverse loop courses, making it twice as thick as the plain [64].

In contrast to weft knitting, whose yarns are oriented along the course direction (fabric

width direction), warp knitted fabric have yarns that zigzag along the wales (machine direction)

[64]. Accordingly, the possible designs of warp knitted fabrics are totally different from those of

weft knitted fabrics [64]. As do all the other fabric design requirements, design of the warp knitted

fabrics result in different fabric appearance and technical performance in warp-knitted fabrics [64].

In warp knitting, loops are generally called laps, and any warp-knitted structure is made up

of two components: overlap and underlap [69]. The overlap is the warp-knitted stitch itself, which

is formed by wrapping the yarn around a needle and drawing it through the previously knitted loop

[69]. The second component, the underlap, is the linking and is formed by the lateral movement

of yarns across the needles [69]. The size of underlap is basically given by needle spacing, and it

was reported that larger the needle spacing, longer underlap can be produced, which results in a

fabric having higher lateral fabric stability in exchange for the length-wise stability [61]. It was

also reported that the length of the underlap influences the fabric weight and thickness. For

example, warp-knitted fabrics composed of longer underlap tend to be heavier and thicker as a result of more yarn crossing and covering in the wale direction [69]. In warp knitting, the design

process is mainly about the selection of the directions and arrangements as well as the lengths of

the laps [69].

The basic stitch in warp knitting is the plain warp-knit stitch which can be performed using a single guide bar. In plain warp knitted fabrics, stitches are visible only on one side (technical face) and only underlaps are visible on the other side (technical back) [69]. Although the plain warp knitting is the simplest of all warp knitting stitches, fabrics made by the plain warp knitting generally exhibit structural instability due to inclining of loops to left or right as loops are not held

firmly [69]. Therefore, plain warp knitting is usually combined with other stiches for a better

structural stability [61].

In addition to the basic plain warp stitch, there are two commercially important stitches in

warp knitting: Tricot and Raschel. In tricot knitting, overlaps and underlaps are created in an

alternating way by using two needles [69]. Two bar tricot (Figure 2-9) is the simplest two-bar

structure and uses the minimum amount of yarn [64]. The two laps balance each other exactly as

they cross diagonally in-between each wale, producing upright overlaps [64]. Tricot knitting is

especially advantageous for generating fabrics with superior stability, firmness, stretch and

elasticity and hence is most popularly used in the industry [61].

Figure 2-9. Basic tricot structure (adopted from [64,p.316]).

Raschel is another knitting technique that is also common in the commercial knitted fabric production. Having a lacelike open structure with a heavy textured yarn held in place by a much finer yarn, Raschel knits can be made in a variety of types, ranging from fragile to coarse structures.

This leads to a wide range of applications from stretch and non-stretch sportswear, lingerie and tulle to fine and coarse nets [66,70].

2.2. Electronic Textiles

2.2.1. Concepts

Electronic textiles (e-textiles) is an emerging interdisciplinary topic of research that brings together technologies in information, microsystems, materials, and clothing with main focus on developing the enabling technologies and fabrication techniques for the economical production of flexible, conformably, and optionally, large area textile-based information systems that are expected to have unique applications for both civilian and military arenas [71]. e-textiles could be defined as any textile materials in the form of fiber, yarn, and fabrics in which electronic technology is integrated to give a new function as electronics. Although e-textiles are distinct from wearable computing because emphasis is placed on the inherent integration of textiles with electronic elements rather than the portability of the electronic devices [71], the field of e-textiles has its origin in wearable computing [18].

The concept of wearable computing was first introduced in the mid-1990s as ‘data gathering and disseminating devices which enable the user to operate more efficiently’ that are intended to be carried or worn by the user during normal execution of his tasks [71]. A few years later, three requirements were added to this early definition: “First, a wearable computer is worn, not carried, in such a way as it can be regarded as being part of the user; second it is user controllable, not necessarily involving conscious thought or effort and, finally, it operates in real time – it is always active (though it may have a sleep mode) and be able to interact with the user at any time” [71,72].

With the idea of direct integration of these electronic components into clothing by textile processing, the concept of e-textiles was introduced with additional requirements as part of clothing – comfortability and fashionability [18,71,73]. Therefore, e-textiles is one of the advanced

branches of wearable computing, where performance as both electronics and clothing need to be

met without compromise.

E-textiles can be classified into three categories based on the degree of technology integration. The first stage of integration is where clothing is used as “a container for technology”

[18]. In this class of e-textiles, electronic devices such as interfaces, sensors and actuators are

mounted on clothing such as by stitching or bonding. Although there exist electronic components

being part of apparel product design, this type of integration usually impacts the aesthetic

properties and functionalities as clothing [18].

A better integration is the embedding of electronics into clothing or textile substrates [18].

Some examples are touch buttons that are constructed completely in textile forms by using

conductive yarns, and these products reduced impact on the garment appearance and fabric

properties [71]. The most advanced integration is where scientific advances are intrinsically incorporated into fabrics [18]. In this type of integration, fabrics are used as part of electronic components, and the best performance can be achieved with minimum influence on the aesthetics and properties as clothing. For example, the electrical and dielectric properties of conventional fabrics were utilized to build textile antennas which meet both requirements as clothing and electronics [42].

2.2.2. Cutting-edge applications

One of the state-of-the-art applications of e-textiles is the fabric capacitive sensors. A capacitive

sensor is a device that convert physical and chemical stimuli into a variation of an electrical

parameter called capacitance [74]. A capacitive sensor generally has two or more conductors, and

sensing is achieved by electrically responding to a change in the capacitance between the

conductors [75]. Examples of textile capacitive sensors is given in Figure 2-10. In these capacitive

fabric sensors, dielectric-coated metal yarns are used as both warp and weft yarns for measurement

of a lateral force. This device measures the lateral force through monitoring of capacitance [30].

This is possible because yarn deformation (Figure 2-11) was associated with the strength of the

load [30].

Figure 2-10. (a) Plain-woven fabric capacitive sensor and (b) double-layer fabric capacitive sensor (adopted from [30,p.1490]).

Figure 2-11. Schematic of capacitive pressure sensor (adopted from [30,p.1491]).

Another emerging application of e-textiles is the microwave interfaces such as transmission lines and antennas that operate at microwave frequencies. With growing interest in wireless body area network (WBAN) technology for military, aerospace, healthcare, and entertainment applications, textile antennas and transmission lines have gained increasing attention as textile materials provide better conformability, searchability, compressibility and ease of integration into

clothing [28,76,77]. Also, it has been reported that certain textile materials such as cotton,

polyester and glass fibers have dielectric properties desirable for fabrications of antennas and transmission lines [29]. The porous nature of these textile substrates results in a permittivity close to that of air which enables construction of low-loss microwave systems [29].

An example of the electronic interface made of textile materials is given in Figure 2-12.

The illustrated textile patch antenna was built by 3D weaving of E-glass and copper yarns, and its capability for bending was tested based on the measurement of impedance matching and radiation performance [19].

Figure 2-12. Fabric antenna fabricated by 3D weaving (adopted from [19,p.148]).

A variety of transmission lines were also developed on a textile platform. For example,

Figure 2-13 shows a textile-integrated coaxial cable fabricated by stitching a conductive thread on a denim material, and the transmission performance was discussed in relation to the stitch angles.

Figure 2-13. (a) Model and (b) sample of a stitched textile coaxial cable (transmission line) (adopted from [78,p.1048,1049]).

2.3. General Theory of Dielectrics

2.3.1. Dielectrics

A dielectric can be defined as an electrical insulator which is polarizable by an external electric field. Unlike conductors, dielectrics do not support flow of electrons through its body but respond internally to the applied electric field with a phenomenon called dielectric polarization. This internal response leads to the storage and loss of the electrical energy, and dielectrics offer important applications particularly in electronics and atomic and molecular analyses. The study of dielectrics involves physical and analytical models to describe how an electric field interacts with atoms and molecules and behave inside a material [79]. The science of dielectrics is one of the oldest branches of physics and has been pursued for well over a hundred years with close links to chemistry, materials and electrical engineering [79].

Dielectrics can be generally classified into 1) non-polar, 2) polar and 3) dipolar dielectrics based on the applicable polarization mechanisms. Non-polar dielectrics are materials consisting of only atoms and they become polarized in an applied electric field by having relative displacement of electronic charge with respect to the nucleus [80]. This polarization is called electronic (atomic)

polarization, and the associated resonant process generally occurs at optical frequency. Polar

dielectrics are substances made up of molecules which do not possess any permanent dipole

moment but have ionic components [81]. Hence, in addition to the electronic polarization, this type

of dielectrics show ionic polarization, which is induced by modification of relative positions of

ions in the electric field [80]. Dipolar dielectrics, on the other hand, are materials whose molecules

possess a permanent dipole moment [81], and polarization in an electric field is predominantly

caused by the spatial reorientation of permanent dipoles [80]. This type of polarization is called

dipolar or orientation polarization and generally exhibits a relaxation in the radio and microwave

frequency domain.

Figure 2-14. Schematic of a) electronic, b) ionic and c) dipolar polarizations (adopted from [82]).

In addition to the electronic, ionic and dipolar polarizations, there is another class of polarization termed interfacial (or space charge) polarization that could exist in dielectrics having structural interfaces (Bunget & Popescu, 1984). In the interfacial polarization, free charges accumulate at interfaces between two materials or between two regions of different electrical conductivities, and this separation of charges results in local dipole moments [83]. Thus, the

characteristics of the interfacial polarization greatly differ from those of the constituent materials

[84–86]. Although the interfacial polarization could exist in many materials having any kind of

physical interfaces, this type of polarization appears primarily in the lower frequency regime due

to a limited mobility of charges [83,87].

2.3.2. Dipole moment, electric polarization vector and permittivity

When an electric field is applied to a dielectric material, the material responds to the electric field

by polarization. In order to quantify this effect of each dipole under the presence of an electric

field, the concept of local dipole moment ( ; coulomb-meters) can be used. The local dipole

i moment is defined as a function of the electric𝑝𝑝⃗ charge ( q ; coulombs) of each atom or molecule

and the distance ( ; meters) between charges. The expression is given by [45]:

i     𝑑𝑑⃗ d pii qd (2-1)

This procedure, although accurate if performed properly, is very impractical if applied to a

dielectric slab because the spatial position of each atom and molecule in the material must be

known [45]. Instead, in practice, the behavior of these dipole and bound charges is accounted for

in a more qualitative way by introducing the electric polarization vector using a macroscopic model

involving millions of atoms and molecules [45]. In order to find the electric polarization vector ( ; coulombs per square meter), which is the total dipole moment per unit volume (Figure 2-15(a)𝑃𝑃�⃗),

we first obtain the total dipole moment ( ; coulomb-meters) of a material by summing the local

t dipole moments as: 𝑝𝑝⃗

Nve   ppt = ∑ d i (2-2) i=1

where Ne is the number of dipoles per unit volume and v is the volume (cubic meters) of the material [45]. The electric polarization vector can then be ⊿defined as [45]:

11   Nve   Pp limti= lim p (2-3) vv→→00 ∑ vvi=1

Figure 2-15. Dielectric sphere in an uniform electric field, showing (a) the polarization and (b) the polarization charge with its associated, opposing electric field ( ) (modified from [88,p.151]). 𝐸𝐸�⃗𝑝𝑝

The relationship between the electric polarization vector and the electric field inside a

dielectric medium can be obtained by using the constitutive relation. In free space, the electric

field ( ; volts per meter) and the electric flux density ( ; coulombs per square meter) are related

a by [83]𝐸𝐸�⃗: 𝐷𝐷��⃗  

EDa = / ε 0 (2-4)

where is the electric permittivity in free space (8.85× 10−12 F/m ). In a dielectric media, the

0 electric𝜀𝜀 field is to be reduced by the electric field due to the electric polarization ( ) (Figure

𝐸𝐸�⃗p 2-15(b) and Figure 2-16) [88]. Accordingly, the electric filed inside a dielectric ( ) is given by

[45]: 𝐸𝐸�⃗        D P DP− EE=+=−=ap E (2-5) εε00 ε 0

Thus, the larger the electric polarization vector ( ) is, the more reduction of the internal electric

field is due (Figure 2-16). 𝑃𝑃�⃗

Figure 2-16. Internal and external (applied) electric fields relation.

According to the constitutive relation, the electric field in a dielectric can be related to the electric flux density by [45]:   D E = (2-6) ε

where ε is the electric permittivity (farads per meter), which is unique to the polarizability (a

constant that relates the dipole moment with the strength of the electric field [89]) of the dielectric

material. By comparing (2-5) and (2-6), the direct relationship between and is found as [45]:   𝑃𝑃�⃗ 𝐸𝐸�⃗ PE=(εε − 0 ) (2-7)

By defining a dimensionless constant, relative permittivity ( ), by:

𝑟𝑟 ε 𝜀𝜀 ε r  (2-8) ε 0

we can rewrite (2-7) as [45]:  

PE=εε0r( −1) (2-9)

In case of free space, εr is unity and the electric polarization vector becomes zero. For many

dielectrics, εr is larger than unity and thus takes a positive value.

𝑃𝑃�⃗ 26

2.3.3. Losses in dielectrics

For a real dielectric material, there are losses associated with various motions. As such, the electric permittivity of a matter is usually complex (ε*) and is conventionally expressed by [83]:

εε*= ' − j ε '' (2-10)

' '' where εr and εr are the real and imaginary parts of the electric permittivity, respectively.

* Accordingly, the relative permittivity also becomes complex (εr ) as given by [45]:

* ' '' εεrr= − j ε r (2-11)

' '' where εr and εr are the real and imaginary parts of the relative permittivity, respectively, and are defined by [45]:

' ' ε ε r  (2-12) ε 0

' '' ε ε r  (2-13) ε 0

The real part of the relative permittivity is also referred to as the dielectric constant and this quantifies the ability of a material to store the electric energy. The imaginary part of the relative permittivity is also termed loss factor and quantifies the loss in the material associated with the polarization.

In order to analyze the losses in dielectrics, Maxwell equations can be used. Maxwell equations give the relationships between the electric and magnetic field quantities. The complete set of the frequency-domain (time-harmonic) Maxwell equations are given by [45,83,90]:

 *    ∇×H = jωε EJ +ic + J (2-14)     ∇×EjH =− ωµ* (2-15)

  ∇⋅H =0 (2-16)

 ρ ∇⋅E = e (2-17) ε *

where is the magnetic field intensity (amperes per meter); ω is the angular frequency (radians �⃗ per second);𝐻𝐻 is the impressed electric current density (amperes per square meter); is the electric ��⃗ı ��c⃗ conduction current𝐽𝐽 density (amperes per square meter); ρe is the electric charge density𝐽𝐽 (coulombs per cubic meter); and μ* is the complex magnetic permeability (henries per meter). × and · are the curl and divergence operators, respectively. ∇ ∇

The first Maxwell equation (2-14) describes that both time-varying electric field and current densities induce magnetic fields. The second equation (2-15) shows that the existence of a

time-varying magnetic field leads to a generation of an electric field. The third equation (2-16)

shows that there is no magnetic monopole, and the last equation (2-17) indicates that the charge

enclosed divided by the permittivity must equal to the electric flux out of this closed surface. Thus,

with (2-14) to (2-17), Maxwell predicted the transfer of the electric and magnetic energies in the form of EM propagation [91].

For a source-free region ( = 0), substitution of (2-10) into (2-14) gives [45]:

𝐽𝐽��⃗ı      ∇×H = jωε( ' − j ε '') EJ + c (2-18) ' ''   =jωε E ++ ωε EJc

Because the conduction current density could be related to with the static conductivity (σs; siemens) by [45]: 𝐸𝐸�⃗  

JEc = σ s (2-19)

(2-18) can be rewritten as:

    ∇×Hj =ωε' E + ωε'' E + σ E s '   (2-20) =jEωε ++( σas σ ) E

where the alternating frequency conductivity σa is defined as:

'' σa  ωε (2-21)

Therefore, from (2-20), it can be seen that σa and σs are responsible for the loss of energy due to

conduction while ωε' accounts for the storage of energy inside the dielectric media [45].

The tangent of the angle between these loss and storage components is termed electric loss

tangent or dielectric loss (tanδe) and is defined by [45]:

σσ+ tanδ  as (2-22) e ωε '

Generally, a good dielectric shows a small loss compared to its ability for energy storage. Thus,

the requirement for a good dielectric typically satisfies [45]:

σσ+ as1 (2-23) ωε '

On the other hand, a good conductor demonstrates a high conductivity with minimum energy

storing. Thus, a good conductor usually satisfies [45]:

σσ+ as1 (2-24) ωε '

In case of a dielectric medium with a sufficiently low static (DC) conductivity (σa σs),

(2-22) can be reduced to [45]: ≫

σ ωε'' ε '' ε '' δ a = = = r tan e  ' ''' (2-25) ωε ωε ε ε r

Since most of dielectrics do not strongly support a flow of current in DC, (2-25) is the most commonly used form of the loss tangent for dielectric media. The dielectric and electrical

properties of general insulating polymers are given in Table 2-1. Because these polymers have relatively small electrical conductivity values, their loss tangents are given in the form (2-25).

Table 2-1. Dielectric and electrical properties of polymers at 1 MHz.

Dielectric Loss tangent Resistivity (ρ; Polymer type ' Reference constant (εr) (tanδ) Ω·m) Poly(ethylene terephthalate) (PET) 3.2–3.3 0.003 1×1013 [92] Poly(ethylene) (PE) 2.3 – – [92] Polyamide 6,6 3.0–4.3 0.017-0.024 6×109 – 1×103 [92] Cellulose 6.7 0.062 1×1016 [7,92] Cellulose acetate 3.3–7.0 0.15 1×108 – 1×1011 [92]

In order to calculate the power losses in a dielectric material, the Poynting theorem can be used. The Poynting theorem is a statement of power balance that can be derived from Maxwell equations [45]. According to this theorem, the total energy of a system is always conserved. For a source-free region ( = 0), the energy conservation equation is given by [45]:

ı 𝐽𝐽��⃗ PPed++ j20ω ( W m − W e) = (2-26) where

1     Pe = (E× H) ⋅= ds exiting complex power (watts) (2-27) 2 ∫∫ S

1  2 P = (σ ) E⋅= dv dissipated real power ( watts) (2-28) d 2 ∫∫∫V

1   2 W = µ ' H⋅= dv time-averaged stored magnetic energy (joules) (2-29) m ∫∫∫V 4

1  2 W = ε ' E⋅ dv = time-averaged stored electric energy (joules) (2-30) e ∫∫∫V 4

* For a dielectric material with no magnetization (μr = 1), σ = σa + σs. Thus, (2-28) reduces to:

1  2 P = (σσ+⋅) E dv (2-31) d 2 ∫∫∫V a c

As expressed in (2-31), losses in dielectrics can be directly calculated if both materials properties

and electric field intensity are known. Alternatively, because the total energy in the system is

conserved, dielectric losses can also be found by calculating the rest of the power terms in (2-26).

2.3.4. Dispersion

Because the physical mechanisms that are responsible for causing electric polarizations in matter

strongly depend on the time-variation of the excitation, the permittivity is dependent on the

frequency of the field variation [2]. This frequency dependence of the permittivity is called a

dispersion and is given in the functional dependences of the real and imaginary parts of the relative

permittivity [2].

A representative curve displaying various kinds of polarizability mechanisms is shown in

' Figure 2-17 as a function of the frequency. As the dispersion curve of εr shows, the relaxation process of the interfacial polarization is shown in the very low frequency regime. On the other hand, the relaxation process of the dipolar polarization is seen in the radio and microwave frequency regions. The resonant processes of the ionic and electronic polarizations are shown in the infrared and visible-ultraviolet regimes. These relaxation and resonant processes are associated

'' with the corresponding loss (εr ) and loss tangent (tanδe) peaks, which are due to the discrete energy

levels for these motions [83]. Therefore, the dispersions of dielectric materials are generally

analyzed based on all of the real and imaginary parts of the relative permittivity and loss tangent

[83].

Figure 2-17. Frequency dependence of the complex relative permittivity of an ideal dielectric material, where interfacial and dipolar polarizations exhibit relaxation processes, and ionic and electronic polarizations show resonant processes (adopted from [83,p.608]).

Because different polarization mechanisms exhibit distinctive characteristics of the frequency dependence as depicted in Figure 2-17, different physical models have been proposed for the specific polarization category. For electronic polarization, the Lorentz model is one of the most featured models in literature. In this model, an each atom consisting of a positive stationary charge surrounded by a mobile electron cloud is considered to experience damping and tensional forces by a time-harmonic electric field with an analogous to a mechanical spring [45]. The equation of motion for the electronic polarization is thus given by [45]:

dd2ll QE ejtω = m ++ d sl (2-32) 0 ddtt2 where Q is the dipole charge (coulombs); m is the mass (kilograms) of the electron cloud; l is the displaced distance; t is the time (seconds); d is the friction (damping) coefficient; and s is the tension (spring) coefficient.

From this Lorentz model, the real and imaginary parts of the relative permittivity can be derived as a function of the frequency and are given by [45]:

2 NQe 22 (ωω0 − ) ' ε 0m ε r =1 + 2 (2-33) 222 d (ωω0 −+)  ω m

d ω NQ2 ε '' = e m (2-34) r 2 ε 0m 222 d (ωω0 −+)  ω m

where Ne is the number of dipoles per unit volume and ω0 is the resonant (natural) angular frequency (radians per second) of the dielectric material. Thus, the Lorentz model provides a quantitative description of the resonant process of an electronic polarization as expressed in (2-33) and (2-34). For ideal dielectrics (without damping or d/m = 0), (2-33) and (2-34) are reduced to

[45]:

2 NQe ε m (2-35) ε ' = + 0 r 1 22 ωω0 −

'' ε r = 0 (2-36)

and this model can be conveniently used to analyze low-loss dielectrics.

For dipolar dielectrics, both electronic and dipolar polarizations could exist. However, the

electronic polarization can be frequency-independent over the typical frequency range of operation

of a dipolar dielectric, well below optical frequencies [83]. At high frequencies, dipolar

polarization will be too sluggish too respond, and the contribution of the dipolar polarization

becomes negligible [83]. Under this analytical description of the dipolar dielectrics, Debye’s

relaxation model is widely used for the frequency dependences of the real and imaginary parts of

the relative permittivity under the presence of electronic and dipolar polarizations are given by

[93]:

εε''− εε''= + rs r∞ rr∞ 2 (2-37) 1+ (ωτ )

ωτ ε''− ε '' ( rrs ∞ ) ε r = 2 (2-38) 1+ (ωτ )

' ' where εrs and εr∞ are the dielectric constants in static (or the frequency just before the dipolar relaxation occurs) and at a much higher frequency (but not high enough to involve any reduction

' in electronic polarizations) respectively; and τ is the relaxation time (seconds). εr exhibits a peak when ω = 1/τ, and this peak is called the Debye loss peak [83]. Many gases and some liquids with dipolar molecules are reported to follow (2-37) and (2-38) [83].

However, in the case of solids, this peak is typically much broader because the losses cannot be expressed in terms of just a single well-defined relaxation time τ; the relaxation in the solid is usually represented by a distribution of relaxation times [83]. Further, (2-37) and (2-38) assume that the dipoles do not influence each other either through their electric fields or through their interactions with the lattice; however, in solid dielectrics, dipoles can also couple, complicating the relaxation process and limiting the accurate fit of the Debye’s relaxation model

[83].

Although three of the most representative dispersion relationships have been discussed as general analytical tools of dielectric media so far, there are several notations that should be addressed. For example, even in a simple, homogeneous dielectric material, there could be more than just a single type of atoms or molecules. Also, microstructural configurations and arrangements make the atoms and molecules behave differently depending on the position under the electric field. As such, many of polymer dielectrics do not exhibit a simple, well-defined

resonance or a relaxation process. Analyses on dispersion relationships are usually highly complex

due to co-existence of different polarization mechanisms [87,94,95].

2.3.5. Non-linearity, inhomogeneity and anisotropy in dielectrics

Discussions so far were limited to the special situation; the dielectric was considered linear, homogeneous and isotropic. However, in actual dielectrics, these assumptions need to be often relaxed especially for solids. In this section, dielectrics having non-linearity, inhomogeneity and anisotropy are reviewed.

2.3.5.1. Non-linearity

As expressed in (2-10) and (2-11), the permittivity of real media needs to be treated as a complex number because of the presence of losses. In addition to this treatment, there are additional considerations to be made for the permittivity. First such example is the linearity of the permittivity. Dielectrics whose permittivities are linear function of the applied electric field are called linear dielectrics [45]. In this class of dielectrics, the electric polarization has a linear relationship to the applied electric field. Hence, the permittivity is still expressed in the constitutive relation given in (2-6).

Dielectrics whose polarization does not linearly respond to the applied electric field are called non-linear dielectrics [2]. In non-linear dielectrics, permittivity needs to be treated as a non- linear function of the electric field [2]. The non-linearity of dielectrics appears when an applied electric field exceeds the materials’ dielectric strength. Under high voltage conditions, the

dielectric can no longer work as an insulator – a current starts flowing through its body and dielectric breakdown occurs. Under such circumstances, the material exhibits non-linear response to the applied electric field.

In practice, however, many polymers have high breakdown field strength (Emax) in the

order of megavolts per meter as given in Table 2-2. Generally, for an electric field sufficiently below this level, polymers could be conveniently treated as linear dielectrics [45,87].

Table 2-2. Dielectric strength of polymers [92].

Polymer type Breakdown field strength (Emax; MV/m) PET 22–26 PE 39 Polyamide 6,6 30–30.5 Cellulose 30–50 Cellulose acetate 11–19

2.3.5.2. Inhomogeneity and effective medium approximation in dielectrics

Inhomogeneity is another important parameter for the electric permittivity of many dielectrics.

When the permittivity is consistent regardless of the position within a material, the material is

homogeneous. On the other hand, if the permittivity varies as a function of the position, this type

of material is electrically non-homogeneous (heterogeneous) [2]. Often, polymers are non-

homogeneous as they could have semi-crystalline regimes, where amorphous and crystalline

regions could exhibit different electrical polarizability [80].

Mixtures of two or more materials could be also non-homogeneous. For example, the

permittivity in an immiscible polymer blend could depend on the position [96]. Also, materials

such as textile fabrics could be non-homogeneous because they are mixtures of fiber and air (and

in many cases moisture). Materials having defects or impurities may also exhibit non-

homogeneous behaviors. Therefore, in many real dielectrics, some degree of inhomogeneity

potentially exists, and the permittivity needs to be expressed in terms of the positional parameters

(x, y, z for a Cartesian coordinate) to be precise.

� � � Although many materials are microscopically non-homogeneous, they could also be considered homogeneous in a macroscopic point of view [2]. For example, when an observer is close enough to a woven fabric, the individual warp and weft yarns and their interlacing structure can be seen. However, when the fabric is far enough from the observer’s eyes, the detailed structure of the fabric would no longer be seen, and the fabric can be only regarded as an uniform sheet.

The latter case is an example of homogenization [2] of a microscopically non-homogeneous material. Although the distance between the observer and the object was the parameter to describe the homogenization in this example, it is the wavelength (λ; meters) of light that critically distinguishes homogenized and non-homogenized media to be more precise [2]. For example, from practice, structures smaller than the wavelength of visible light (400 to 700 nm) are not separated even with the best optical microscopes, and a wavelength shorter than the inhomogeneity is required to acquire information on such small details [2].

On the other hand, as the wavelength increases, even larger structures can be indistinguishable. In practice, when inhomonegeity is less than ~0.1λ, then the medium could be considered well homogenized, and the positional terms can be dropped [97–99]. This approach of describing microscopically heterogeneous dielectrics with a single, macroscopic permittivity is called the effective medium approximation [100,101] and is the fundamental requirement for the

dielectric mixture theory [102]. For many dielectrics having sub-wavelength heterogeneity, the

permittivity is usually treated as a homogenized number in dielectric analysis. More details of the

effective medium approximation and dielectric mixture theory are discussed in Section 2.3.6.

2.3.5.3. Anisotropy in dielectrics

The simple constitutive relation between the electric field ( ) and the electric flux density ( )

given in (2-6) is only valid when the polarization of a dielectric𝐸𝐸�⃗ medium does not vary depending𝐷𝐷��⃗

on the direction of the applied electric field. However, in many natural and manmade materials,

there exist fibrous or lamellar structures which break the directional symmetry [2]. This type of

material is called an anisotropic medium.

In an anisotropic medium, the applied electric field and the electric flux density could have

different directions, and this makes the constitutive relation be a second-rank tensor division as

given by [2]:   ED= / ε (2-39)

where is a second-rank permittivity tensor. As being a second rank tensor, the permittivity in an

anisotropic𝜀𝜀̿ media needs to be expressed as a nine-entry matrix. In a Cartesian coordinate, the

permittivity tensor is expressed by [45]:

εεε xx xy xz ε = εεε yx yy yz (2-40) εεε zx zy zz

where each entry (εx, εxy, ··· εzz) represents an independent material parameter and may be a

complex number. With (2-40), the constitutive relation (2-39) is then expressed by [45]:

DEεεε x xx xy xz x = εεε DEy yx yy yz y (2-41) εεε DEz zx zy zz z

where Ex, Ey and Ez are x, y and z components of the electric field, respectively; and Dx, Dy and

� � � Dz are x, y and z components of the electric flux density, respectively. Because and are now

tensor multiplication,� � � the directions of these two fields could be different for anisotropic𝐸𝐸�⃗ 𝐷𝐷 ��materials.⃗

In many practical cases of anisotropic media, however, not necessarily each entry is unique.

For example, a rectangular lattice which forms a basic structure in many crystals could be expressed as three principal directions of its material response due to its biaxiality [2]. For uniaxial media, the permittivity component along the axis of crystal is different from the transversal permittivity, and thus it could have only one unique diagonal term in the permittivity matrix [2].

In addition to these symmetrical scenarios, in many physical devices such as planar capacitors, transmission lines and antennas, the electric field is often limited to one principal direction, which is normal to the planar substrate [48,103]. If this is the case, then the permittivity in only one direction needs to be considered.

2.3.6. Dielectric mixture theory

2.3.6.1. Maxwell-Garnett theory and its generalizations

The dielectric mixture theory is a statement of a relationship between the homogenized, macroscopic dielectric properties of a heterogeneous medium and the local dielectric properties of its constituent materials [102]. This relationship is expressed as functions of the volume fractions of the constituents as an averaging factor. Because the geometry plays an important role in the resulting dielectric properties of a heterogeneous medium, each dielectric mixture theory is tailored for a particular geometry [2]. Figure 2-18 shows the representative shapes of inclusions and the analytical formulas for some of these geometries are discussed in this section.

One of the most fundamental mixing theories is the Maxwell-Garnet theory, which discusses the homogenized permittivity (εm) of a heterogeneous system of isotropic, spherical

inclusions of permittivity εi randomly positioned in the environment of permittivity εe (Figure

2-18(a)). According to this theory, the macroscopic permittivity is given by [2]:

εεie− εεme= + 3 f ε e (2-42) εi+−2 ε ef ( εε ie −)

where f is the volume faction of the inclusion phase. Because of its simplicity, (2-42) has been

widely used to analyze various isotropic inclusions of spherical shapes [104].

Figure 2-18. Examples of randomly positioned inclusions of various shapes in the environment (εe): (a) isotropic spheres, (b) aligned isotropic ellipsoids, (c) randomly oriented isotropic ellipsoids, (d) aligned anisotropic spheres, (e) aligned anisotropic ellipsoids and (f) randomly oriented anisotropic ellipsoids.

For many real dielectrics, the spherical requirement for the inclusions needs to be relaxed

– however, numerical effort is required for other shapes, and ellipsoids are the only exceptions for

which the analytical solutions can be found [2]. For locally-isotropic ellipsoids of permittivity εi

randomly positioned in the environment (εe) (Figure 2-18(b)), its homogenized permittivity becomes a tensor (εm) if the ellipsoids are aligned. The x-component (εm,x) of this permittivity

tensor is given by [2]̿ : 40

εεie− εεεm,x= e + f e (2-43) εe+−(1 fN) xi( εε − e)

where f is the volume fraction of the ellipsoidal inclusions; and u is the depolarization factor in the

x-axis direction. Many natural and manmade materials possess this type of anisotropic structure,

where the materials that compose the mixture are isotropic but the geometry of the composition

adds the anisotropic nature in a larger scale [2].

On the other hand, in case of randomly oriented isotropic ellipsoids of a volume fraction

of f (Figure 2-18(c)), the resulting macroscopic permittivity becomes a scalar (εm). The expression

is given by [2]:

f εε− ∑ ie 3 i=x,y,z εe+−N ii( εε e) εm= εε ee + (2-44) f N (εε− ) 1− ∑ ji e 3 i=x,y,z εe+−N ii( εε e) where Nx, Ny and Nz are the depolarization factors in the corresponding axes (Nx + Ny + Nz = 1).

So far, only the locally isotropic inclusions are discussed. However, the inclusions such as

cotton fibers can have anisotropic local permittivity due to the highly oriented polymer chains

[7,105]. If this is the case, then the permittivity of inclusions needs to be treated as a tensor (εi) as discussed in Section 2.3.5.3. For inclusions of randomly positioned anisotropic spheres aligned̿ in

the environment (εe) (Figure 2-18(d)), the macroscopic permittivity tensor (εm) is given by [2]:

̿ εε− I εε= + ie meI (2-45) 32εf ε+−− ε If εε I e i e( ie) where is the unit dyadic. Similarly for inclusions of randomly positioned, aligned anisotropic ̿ ellipsoids𝐼𝐼 (Figure 2-18(e)), the macroscopic permittivity tensor (εm) is given by [2]:

εε− I εε= + ε ie meIf e (2-46) ε+− ⋅ εε − eI(1 fL) ( ie I)

where L is the depolarization dyadic.

�Although the Maxwell-Garnett theory and its extensions have served as the most powerful

analytical tools for dielectric mixtures [106], there are several limitations. For example, in the

Maxwell-Garnett theory the inclusions need to be small so that the interaction between the particles

become negligible [2]. As such, the application of the Maxwell-Garnett theory is limited to dilute

systems [2].

2.3.6.2 Other general mixing theories

The Bruggeman’s theory provides another important mixing rule that is widely used in the EM

literature [2]. In contrast to the Maxwell-Garnett theory, which only applies for inclusions of small

sizes, the Bruggeman mixing formula is symmetric with respect to all medium components and it

can be applied, at least formally, to composites with arbitrary volume fractions without causing

obvious geometrical contradictions [107]. In the Bruggeman’s model for spherical inclusions of

volume fraction f, the homogenized permittivity (εm) is related to its constituent permittivities by

[2]:

εε− εε− (10−ff) em +=im (2-47) εεem++22 εε im where εi and εm are the permittivities of the inclusions and environment, respectively. Similarly for

the ellipsoidal inclusions of random orientation, the homogenized permittivity (εm) is given by [2]:

f ε m εm=+− ε e( εε ie) ∑ (2-48) 3 j= xyz,, εm+−N ji( εε m)

where Nx, Ny and Nz are the depolarization factors in the corresponding axes. As expressed in

(2-47) and (2-48), the Bruggeman formula possesses the mathematical symmetricity (εi → εm, εm

→ εi, f → 1 − f) which overcomes the geometrical contradictions.

The coherent potential formula is another class of mixing rule of great importance. In the

coherent potential theory, the Green’s function enumerates the field of a given polarization density

of the effective medium, leading to the relationship between the macroscopic and constituent

permittivities. For the spherical inclusions of volume fraction f, the coherent potential formula is

given by [2]:

3ε m εm=+− ε ef ( εε ie) (2-49) 31εm+−( f )( εεie −)

For the ellipsoids of volume fraction f, the coherent potential formula is given by [2]:

f (1+−NNj)εε m je εm=+− ε e( εε ie) ∑ (2-50) 3 j=x,y,z εm+−N ji( εε e)

Finally, it should be noted that in case of dilute mixtures (f 1), all of the Maxwell-

Garnett, Bruggeman and coherent potential formulas predict the same results.≪ In the spherical case,

the reduced form is given by [2]:

εεie− εεme + 3 f (2-51) εεie− 2

2.3.6.3 General bounds

General mixing formulas in dielectrics are only given in the special geometries: spherical or

ellipsoidal inclusions. However, many physical composites have different shapes, and these

general mixing rules may not represent all the possible situations appropriately. One of the

analytical approaches to estimate the permittivity of a heterogeneous medium is to use the general

bounds [108]. The general bounds are the descriptions of the upper (εm,max) and lower (εm,min) limits

of the homogenized permittivity that are possible at a given mixing ratio [109]. The absolute

bounds (Wiener bounds) for which any mixture composed of isotropic constituents should follow

are given by [2]:

εεm,max=ff i +−(1 ) εe (2-52)

εεie ε m,min = (2-53) ffεεei+−(1 ) where εi and εe are the permittivities of isotropic constituents of volume fractions of f and 1−f,

respectively. The expressions (2-52) and (2-53) are equivalent in form to those describing capacitors connected in parallel and series, respectively [75,110].

2.3.6.4 Dielectric mixture theory and frequency

One of the largest limitations of the homogenization approach in the dielectric mixture theory is the dynamic nature of the applied electric field. In the dielectric mixture theory, the polarizability and local fields are calculated from the Laplace equation, which does not consider the coupling effect of time-variation of the electric and magnetic fields [2,45]. In other words, the mixing rules were aiming for the static situation.

The approach nonetheless can be valuable for dielectric analysis under time-dependent EM

fields [2]. This could be possible by assuming that the assumptions in the dielectric mixture theory

are static but also quasi-static, and in fact the quasi-static approximations were turned out to be valid for certain range of dynamic fields in many practice [2]. One practical criterion for the satisfactory field dynamics and the size of the inclusion is formulated as [2]:

λ > δ (2-54) 2π

where λ and δ are the wavelength (meters) and the size of the inclusions (meters), respectively.

Because the wavelength cannot be uniquely defined in a mixture [2], (2-54) serves only as an

approximate guideline.

2.3.7. Theory in dielectric measurements

The measurement of dielectric properties has gained increasing importance as the dielectric

properties are found to carry many vital information. For example, atomic and molecular level

information acquired by complex relative permittivity measurements lead to materials’ electrical,

physical and chemical properties. Thus, non-destructive sensing and monitoring of specific

properties of materials could be enabled with the help of dielectric measurements. In this regard,

dielectric measurements are widely conducted as structural and chemical analysis tools in fiber

and polymer science, food and agricultural science, soil science, medical science, and so on.

Uses of dielectric properties are not limited to materials characterization. Dielectric

measurements also help electrical engineers to build high performance RF and microwave circuits.

This is because the dielectric properties, which quantify the materials’ abilities for storing and

dissipating electric field, are essential parameters for design and fabrication of high-performance

radiofrequency (RF) systems such as capacitors, transmission lines and antennas. Therefore, from the applicational points of view in both materials characterization and product development, understanding the applicability and limitations of currently available dielectric measurement

techniques is critical. In this section, some of the most important measurement theories and

techniques are reviewed for dielectric characterization.

2.3.7.1. Low-frequency dielectric characterization

In low frequency measurements typically up to a few megahertz, the most widely used method of characterizing dielectric properties is performed with a capacitor. A capacitor is a device consisting of a pair of conductors that are separated by an insulating material or a material under test (MUT). The simplest geometry for a capacitor is the parallel-plate structure illustrated in

Figure 2-19. In the parallel-plate capacitor, an AC voltage is supplied to the plates to produce an alternating electric field between the plates. One of the fundamental circuit constants, capacitance

(C; farads), which is defined by the amount of charge (Q; coulombs) per unit potential difference

(V; volt), can be directly acquired with the help of an LCR meter [75].

Q C = (2-55) V

Now, we consider a capacitor consisting of two parallel plates of each area A (square

' meters) separated by a thickness d (meters) of a medium of relative permittivity εr (Figure 2-19).

By impressing a charge of +Q to one of the plates, the electric flux density (D; coulombs per square meter) produced between the parallel plates is given by [75]:

Q D = (2-56) A

Because the electric field intensity ( E ; volts per meter) is defined by:

V E  (2-57) d

and the constitutive relation for the electric fields is given by (2-6), the capacitance can be related

to the electric permittivity of MUT as [75]:

Q DAε A C = = = (2-58) V Ed d

Now by substituting (2-8) into (2-58), we get [75]:

ε A εε' A C = = r0 (2-59) dd

Therefore, the parallel-plate method provides a way of determining the real part of the relative permittivity of MUT from a measurement of the capacitance.

Figure 2-19. Parallel-plate capacitor.

Another quantity, dissipation factor (D), can also be acquired from the measurement of a

parallel-plate capacitor with an LCR meter. For a dielectric material whose D.C. conductivity is

infinitesimally small, the dissipation factor is equal to the tangent of the angle (loss tangent)

between the resistance (real part of the impedance R; ohms) and the reactance (imaginary part of

the impedance X; ohms) as given by [75]:

D  tanδ (2-60)

Therefore, the imaginary part of the relative permittivity can be determined by:

'' ' εεrr= ⋅ tan δ (2-61)

Although the lumped circuit technique mentioned so far provides convenient and reliable measurements of various dielectrics, there are several limitations. For instance, it has been reported that charge carriers accumulate at the sample-electrode interface in broadband dielectric spectroscopy, and this generally results in a large electrode polarization that masks the frequency response of the sample [84]. This unwanted parasitic effect is generally pronounced for moderately to highly conductive samples under a low frequency electric field, and can result in extremely high values of real and imaginary parts of the complex dielectric function [87]. There are several models that address this blocking of charges at the electrode-sample interface [87]. However, it is generally challenging to completely compensate the electrode polarization either during measurement or by post processing, and the low frequency dielectric analysis can be often impeded by this polarization

[84,111–113].

2.3.7.2. High-frequency dielectric characterization

Simple wires that perform well at low frequencies behave differently at high frequencies

[114]. This is because at microwave frequencies wavelengths become small compared to the physical dimensions of the measurement devices such that two closely spaced points can have a significant phase difference [114]. Also, there are additional phenomena that strongly occur at high

frequencies including radiation loss, conductor loss, dielectric loss and capacitive coupling, all of

which together make microwave circuits much more complex [114]. The simple low-frequency

lumped-circuit element techniques must be, therefore, replaced by transmission line theory or

antenna theory to analyze the behavior of devices at higher frequencies [114].

Currently available dielectric measurement techniques at microwave frequencies can be

divided into two major categories: resonant methods and non-resonant (reflection/transmission)

methods [46,114]. The common resonant methods are the resonator technique and the resonance

perturbation technique. The resonator technique appreciates the fact that the resonant frequency

and quality factor of a dielectric resonator with given dimensions are determined by its electric

permittivity [43,115]. Common type of a resonator uses a patch antenna or a ring resonator, both

of which could be build using a planar dielectric substrate as an MUT [43,46]. The resonance

perturbation technique, on the other hand, uses the resonance-perturbation theory, where the

alteration of the resonant frequency and quality factor due to the introduction of the dielectric material are effectively related to the complex relative permittivity [28,116].

Although the resonant methods generally have a higher accuracy and a better suitability

for low loss materials than the transmission methods, the resonant methods measure the dielectric

properties only at a single or discrete set of frequencies [115]. Also, in many cases, the

characterizing frequencies are critically affected by the dielectric properties of MUT, and dielectric

properties are often acquired in a frequency that is somewhat different from the target frequency

[43,117].

In the transmission method, the partial or the entire transmission system is filled with MUT,

and the broadband complex relative permittivity can be characterized by measuring the reflected

and transmitted power or scattering (S)-parameters [115]. The common transmission method for

dielectric characterization include the coaxial probe method, waveguide method, microstrip line

method and free space method [48,115,118]. The coaxial cable method uses an open-end coaxial

cable, where MUT is placed at the end of the coaxial probe for a measurement of the reflection

coefficient (Figure 2-20(a)) [119]. In the waveguide technique, an MUT is placed in the

propagating region of the guided wave, and the reflection and transmission with the MUT is

measured (Figure 2-20(b)) [115]. In the microstrip line method, an MUT is used as a substrate of the microstrip line, and the dielectric properties of the substrate are determined by analyzing the reflection and transmission behaviors of the traveling waves along the microstrip line [47,48]

(Figure 2-20(b)). The free space method employs a pair of antennas, where MUT is placed in-

between, and the reflection and transmission coefficients are measured in an anechoic chamber

(Figure 2-20(c)) [120].

Figure 2-20. General measurement setups for the (a) coaxial probe, (b) transmission line and (c) free space techniques (adopted from [115,p.31,34,36]).

2.4. Dielectric Properties of Textiles

2.4.1. Dielectric properties of fibers and fabrics – an overview

The dielectric properties of textile materials have been the subject of study for decades in the textile industry. This is primarily because the electric permittivity of textile materials is an important parameter in process and quality control in textile manufacturing – topics related to impurity and moisture management, yarn evenness, static generation, and so on can often be addressed using the electric permittivity [1,121]. The dielectric properties of textiles could also provide knowledge on the mechanical properties [122,123]. These are all possible because the dielectric properties carry the structural and compositional information from the atomic and molecular level to the macroscopic level [1]. Therefore, one of the most important applications of the dielectric properties of textiles resides in the field of the materials characterization.

In recent years, studies of the electric permittivity of textiles have also been carried out for development of functional systems such as sensors, transmission lines and antennas that are built in or on textile platforms [28,29,118,124,125]. In this type of applications, the dielectric properties have been reported to impact the performance of RF and microwave devices due to the dielectric loss and dielectric loading [29,45]. Therefore, the dielectric properties of textile materials are also vital for engineering highly efficient, top-performing textile electronic devices.

Although the dielectric properties of fiber-forming polymers are governed by their chemical compositions, microstructural differences also affect the dielectric properties of polymers. This is because the great flexibility of fiber-forming polymers in the molecular arrangements, degrees of polymerization, amount of branches and polymer conformations allows various dielectric responses [1]. Additionally, in case of hydrophilic polymers, moisture is another influencer for the dielectric properties [7]. From literature, Bal and Kothari [1] summarized the

factors that influence the dielectric relaxations of polymers as: 1) primary main chain motions, 2)

secondary main chain motions, 3) side chain motions and 4) impurity motions. Because these four motions are also closely related to the polymer crystallinity and chain orientation, chemical composition and dipole moments, interchain and intrachain forces, branches, chain stiffness, etc., microstructural investigations plays an important role in the dielectric analysis of polymers [1].

When fiber-forming polymers form one-dimensional structures such as fibers and yarns,

the dielectric analysis of individual linear structures becomes more challenging than the bulk or

film structures. This is because for both low and some higher (microwave) frequency dielectric

measurements, the required sample size is generally much larger than the size of a single fiber or

yarn for a better measurement sensitivity [114,115]. Therefore, although there are a few exceptions

[36,126], fibers or yarns are generally packed parallel to attain the required sample size [1].

However, because the fiber packing density never reaches to unity, dielectric measurements of

fibers and yarns usually involve air of non-ignorable amount [1,127]. Also, the so-called

macroscopic shape effect [36,105] influences the measurement results for such two-phase systems.

Therefore, although measurements of the dielectric properties of fibers and yarns have been

reported extensively [7], their interpretations involve some uncertainty because of the involvement

of air.

Although the dielectric properties of fiber-forming polymers themselves have been studied

for decades, those of fabrics are relatively of new topic [108]. This is believed to be due to the

difficulty of dielectric analysis of fabrics as fibrous composites [108]. Textile fabrics are 3D

assemblies of fibers of anisotropic microstructures. Hence, the behavior of textile fabrics as

dielectrics depend not only on the dielectric properties of the fiber-forming polymers but also on

the arrangement and orientation of fibers in air [1]. Therefore, the dielectric analysis of fabrics is generally more challenging than that of fibers and yarns.

Two of the most common descriptions of textile fabrics are the two-phase and three-phase systems. In the two-phase systems, fabric constituents are fibers and air, representing the typical hydrophobic fabric system. The three-phase system, on the other hand, considers a composite of fibers, air and moisture, and this is applicable for moisture-absorbing polymers including many natural polymers [7]. Because of the complexity of the various water activities in fabrics, analysis of three-phase fabrics are particularly of great challenge [1].

In dielectric analysis of composites, one of the major approaches is to consider the dielectric mixture theory [2]. For the two-phase system, it was proposed that the dielectric properties of a plain woven fabric can be determined from the dielectric properties of the constituent polymer and the fabric structural parameters [128]. However, this appears to be the only available mixing rule with a theoretical background for fabric structure and is only applicable for plain weaves of monofilament yarns [128]. Thus, geometries such as other woven or any knitted structures may not be analyzed by the mixture theory in literature. It should be also noted that this mixture theory is limited to the moisture-free system [128]. Therefore, except for the very specific case (plain-woven monofilament fabrics in the two-phase system), the analytical prediction of the dielectric properties of fabrics may not be available in literature [1].

Alternative route to the prediction of the dielectric properties of two-phase fabrics is the numerical approach. With a modeled heterogeneous dielectric structure, the electric and magnetic fields can be found by solving Maxwell equations, and by effectively relating the field quantities, the dielectric properties of the mixture can be computed [129]. Although the numerical analysis could generate reasonably accurate prediction of the dielectric properties of composite structures

including fabrics, this approach is usually computationally very expensive [130]. Also, a different

3D model needs to be prepared for a different fabric structure [129].

2.4.2. Motions in polymers

Dielectric relaxation of the backbone (main) chain motion becomes of concern for polymers when at least one type of dipolar group exists in the backbone chain. It has been reported that the mechanical mobility of the backbone chain critically influences the polarizability and relaxation time for amorphous polymers above the glass transition temperature – higher the dipole mobility, the internal friction from the restraints becomes smaller; the polarizability and the relaxation frequency becomes larger and higher, respectively [87]. Therefore, the mechanical mobility of the backbone chain also plays an important role in the dielectric response.

Mechanical mobility of a polymer backbone chain can be analyzed by employing the rotational isomeric state (RIS) model [131]. In the RIS model, conformational availability of a polymer backbone chain is calculated with the statistical weights (Boltzmann factors) of the conformers with the following assumptions [131]:

1) Polymer backbone bonds are confined to any one or small number of discrete rotational

states.

2) Probability of having any rotational state about a given bond depends only on the rotational

state of its nearest neighboring backbone bonds.

With these assumptions, the flexibility of the polymer chain can be addressed by using the conformational partition function (Z) [131]:

n−1 *  Z= J∏ UJi (2-62) i=2 where n is the number of bonds; i is the index of the bond; Ui is the matrix form of statistical weights; and J* and J are the unit row and column vectors. Because Z indices the availability of

conformations, a higher mechanical mobility can be expected with a larger Z [132]. Therefore,

the RIS model serves as an analytical tool of the backbone chain motion.

A variety of measurements of the backbone chain mobility have been carried out to explain

the dipolar relaxations of polymers. For example, the recent advancement with solid-state nuclear

magnetic resonance (NMR) technology has enabled the experimental evaluation of the various

polymer chain motions including the backbone chain motion. The main advantage of NMR is its

capability of scanning molecular mobility in different parts of the polymer chain, and therefore it

enables the identification of the specific molecular motion with the corresponding dielectric

relaxation peak [133–135]. This is especially useful for fibrous polymers, because the actual

mobility of backbone chains highly depends on the local configuration and the available

conformation of polymer chains [136], which are hardly quantified analytically.

Another polymer motion that is related to dielectric relaxation is the mobility of side chain

containing a dipolar group. Just like the backbone chain motions, side chain motions are also

dominated by the local density and microstructure of the polymer sample [135]. As one of the most

powerful characterization techniques of side-chain dynamics, NMR studies have also been carried

out [135].

During fiber formation, residual ions are often trapped inside a polymer, and these impurity

ions are one of the largest attributes for the dielectric relaxation at low frequencies [137]. Another

type of impurity is the moisture that is abundant in non-crystalline regions of hygroscopic

polymers [138]. Because there are distinctive activities of water depending on their

thermodynamic states, usually several different dipolar relaxations are observed at different

frequencies [86]. Also, absorbed water could increase the ionic conduction, and this leads to enhanced electrode and interfacial polarizations at low frequencies [113,139].

2.4.3. Dielectric properties of cotton fibers

As the most produced natural polymer globally [8], the dielectric properties of cotton fibers have been of great concern. Although the cellulose content of a cotton fiber can be as high as 99% after scouring and bleaching, cotton can absorb a large amount of water due to its large surface area. This could allow up to 20% moisture content at 96 °F (35.6 °C) [14], for instance. Thus, the chemical composition of cotton fibers is critically affected by the atmospheric environment.

Generally, absorbed water can be classified into free and bound water [140]. The thermodynamic state of free water is identical to that of water in liquid [141]. On the other hand, bound water is chemically attached to functional groups of polymer chains such as the hydroxyl group of cellulose, and thus the mobility of bound water is impeded by hydrogen bonding in comparison to free water [142]. Thus, free and bound water exhibit different electrical polarizabilities [2].

Also, in terms of the dielectric relaxation, free and bound water behave differently. It has been reported that while free water has a relaxation frequency in the GHz range [143,144], bound water exhibits the relaxation in the MHz range for cellulose due to the limited mobility [86,145].

Free water and bound water are also observed in many other natural fibers such as silk [146] and wool [147,148], where distinct electrical polarizabilities of free and bound are also observable.

Several electric polarizations were reported for moist cellulose at low frequencies near the

room temperature: the electrode polarization of electrical double layers formed at the interface of

the device electrodes and free water on cellulose [85,86,149], interfacial polarization at the

interfaces of free water with cellulose and air [85,86], dipolar polarizations of cellulose molecule

(particularly, hydroxymethyl and hydroxyl groups) [150] and bound [85,86] and free water

[141,151], and electronic polarizations [7]. Among these polarizations, the electrode polarization,

interfacial polarization, and dipolar polarization of bound water were reported to exhibit dielectric

relaxations in the low frequency domain [85,86]. Additionally, a broad, gentle dipolar relaxation

of hydroxymethyl and hydroxyl groups was observed in dried amorphous cellulose [150].

The dielectric anisotropy of cellulose fibers was investigated at various frequencies. It was reported that cellulose fibers show a higher permittivity when placed along the electric field at ~2

MHz and ~27 MHz [1,105,152]. Although there were also the influence of the shape effect [2,7], it was suggested that cotton fibers themselves exhibit a higher local permittivity along the fiber axis. Also, the electronic polarizability was observed to be higher for cotton fibers placed along the electric filed from the optical investigations [7]. Therefore, these investigations showed the locally anisotropic dielectric properties of cellulose fibers.

The effect of solid volume fraction (SVF) on the low-frequency dielectric properties of fiber and yarn bundles was also reported in literature. In 1954, Hearle measured the dielectric properties of cotton yarn wound around cones at various packing densities at frequencies between

50 to 200 kHz [153]. The frequency range of 100 kHz to 10 MHz was also studied [154]. These investigations revealed that the SVF significantly impact the dielectric properties of wound yarns

[153,154].

Another interest in the dielectric properties of cotton fibers is the role of moisture. Hearle

reported that as the moisture content of cotton fibers increase, the dielectric properties increased

significantly in the frequency range of 50 Hz to 300 kHz [153]. Regression fitting of real part of

the relative permittivity as a function of moisture regain was done by Lv et al. [124], and it was

suggested that the relationship was nearly linear in the frequency range of 100 kHz to 5.2 MHz.

Different cotton varieties have also been studied for their dielectric properties at low

frequencies. Kirkwood et al. [155], for example, reported that cotton fibers could exhibit different

dielectric properties depending on the species. This report was followed up by Lyons et al. [44], who revealed that these dielectric differences in different cotton varieties were due to the different moisture contents by providing an evidence that no significant difference was observed between different cotton species of nearly dry samples of the same SVF. Cellulose of different sources were also compared in terms of the dielectric behaviors. It was reported that dielectric spectroscopy of well dried cotton linters, lyocell fibers and highly amorphous bead cellulose showed few signs of differences in local chain dynamics [156]. It was also demonstrated that different cellulose materials showed different dielectric responses primarily because of different microstructures that lead to different moisture contents [156]. From these previous reports, it is seen that the dielectric properties of cellulose could depend primarily on the moisture absorbing properties, which is governed by polymer microstructure and humidity, and the dielectric differences of the cellulose materials could be negligible under dry conditions.

2.4.4. Dielectric properties of cotton fabrics

One of the earliest dielectric investigations on pure cotton fabrics in the low frequency

domain was done by Cerovic [38], who measured the dielectric properties of woven cotton, flax

and hemp fabrics in the frequency range of 80 kHz to 5 MHz [38]. It was reported that a loss peak

was observed around 3 MHz for these fabrics, and this was attributed to a relaxation of some polar

group [38]. The effect of porosity was also discussed based on the measurements of these different

cellulosic fabrics, and it was shown that as the porosity (R) increases, the relative permittivity of

cellulosic fabrics increased (Figure 2-21) [38]. However, because cellulosic fabrics could have

different moisture contents primarily because of different crystallinities as discussed, the different

dielectric properties illustrated in Figure 2-21 would be the combined effects of the porosity and

moisture content [44,156,157].

Figure 2-21. Porosity (R) and real part of the relative permittivity of cellulosic fabrics (adopted from [38,p.6]).

Another low-frequency dielectric investigation of woven cellulosic fabrics was carried out

by Mustata and Mustata [39]. In their report, the fabric grammage (surface mass) was related to the real part of the relative permittivity of cellulosic fabrics as shown in Figure 2-22. Although

the grammage is an important structural parameter for fabrics, the SVF would have been more appropriate since the thickness is also an influencer in dielectric investigations [2,44]. Also, the microstructural differences between the cellulosic fibers, which is known to critically impact the moisture absorption and hence dielectric properties [156], were not considered. Currently, it is challenging to find a report which discusses the pure effect of the SVF on the dielectric properties of cotton fabrics.

Figure 2-22. Grammage and real part of the relative permittivity of a variety of cellulosic fabrics (flax, jute, cotton, etc) at 35% RH (adopted from [39,p.7]).

The high-frequency dielectric properties of cotton fabrics became also available in literature with recent features of wearable electronics. One of the earliest microwave characterization of cotton fabrics was conducted by Ouyang et al. [158], who measured the dielectric properties of a cotton fabric at near 2.6 GHz by using microstrip resonators for applications in textile antennas [158]. In 2010, patch antennas were developed to characterize the

dielectric properties of cotton fabrics at near 2.45 GHz, and it was presented that different cotton fabrics show different microwave dielectric properties [43]. The dielectric properties of cotton/polyester blend were also characterized by adopting the transmission line method [159].

However, these reports did not discuss the effect of the fabric structure or moisture.

CHAPTER 3. EXPERIMENT I Structure-Dielectric Property Relationships in Cotton Fabrics: A Study at Low Frequencies

3.1. Introduction

The low-frequency (below megahertz) dielectric properties of textile materials have been the

subject of study for decades in the textile industry. This is primarily because the electric

permittivity of textile materials contains important information in process and quality control in

textile manufacturing – physical properties of fibers and yarns such as moisture content, evenness, drying, static generation, and so on could be all related to the dielectric properties [1,36,121]. The dielectric properties are also known to provide knowledge on the mechanical properties of textile materials [122,123]. These are all feasible because the dielectric properties carry the structural and compositional information from the atomic and molecular level to the macroscopic level

[1,105,121,124].

In recent years, studies on the electric permittivity of textiles have also been carried out for

development of functional systems such as capacitive sensors built on textile platforms. Among

various conventional textile materials, the dielectric properties of hydrophilic polymers such as

cotton exhibits dependence of dielectric properties on the environment due to moisture sorption.

For example, ambient humidity was found to be characterized from monitoring of the associated

changes in the dielectric properties of cotton fibers [124], leading to potential applications of

hydrophilic textile fibers in moisture sensing devices [125]. Therefore, the dielectric properties of

moisture-absorbing textile materials such as cotton are vital for materials characterization and development of functional textile electronics.

Although the dielectric properties of cotton in fiber and yarn forms have been intensively studied in the low frequency domain [44,105,124,155], cotton in fabric form is relatively new in research and development [38,108]. This is believed to be due to the difficulty of dielectric analysis of fabric structure [108]. Cotton fabrics are 3D assemblies of moist fibers, and hence, the behavior of cotton fabrics as dielectrics depend not only on the dielectric properties of the moist fibers but also on the arrangements and orientations of these components [1,2]. Therefore, the dielectric analysis of cotton fabrics is more challenging than that of quasi-linear structures of fibers and yarns.

One of the earliest investigations on the low-frequency dielectric properties of cotton fabrics was measurements of a woven cotton fabric at various temperatures and RH levels in the range of 80 kHz to 5 MHz. It was reported that there was a peak in the loss tangent around 3 MHz, and this was assumed to represent a relaxation of some polar group [38]. Comparisons of the dielectric behaviors of cotton fabrics with other fabrics were also featured in literature [37–39]. In these reports, the dielectric properties were discussed based on the measurements of a variety of fabrics including cotton, polyester and jute, and widely ranged variations in dielectric properties of these fabrics were reported.

Although the dielectric properties of several woven cotton fabrics were discussed in literature, studies on the roles of the woven fabric structure (such as the picks per inch (PPI), ends per inch (EPI) and SVF) on the low-frequency dielectric properties of cotton fabrics are seldom reported. Also, the dielectric properties of knitted cotton fabrics at low frequencies are rarely examined in literature, and the effect of the knitted fabric structures (such as the courses per inch

(CPI), wales per inch (WPI) and SVF) on the resulting dielectric properties of knitted cotton fabrics

are of current interest. Consequently, another key research topic is the effect of the fabric

construction (whether it is woven or knitted) on the low-frequency dielectric properties of cotton

fabrics. Examinations on these structural and constructional effects on the dielectric properties of

cotton fabrics are particularly important for potential applications in the materials analysis (e.g.,

fabric porosity and moisture content measurements) and development of functional textile systems

that uses RFs.

Therefore, this research explores the effect of the fabric construction, thread count and SVF

on the dielectric properties of woven and knitted cotton fabrics in the frequency range of 20 Hz to

1 MHz. Because cotton fibers themselves were reported to exhibit different dielectric properties

depending on the species primarily due to different moisture absorbability [44,156], exactly the

same cotton yarn was used to produce both woven and knitted fabrics in this work. This is a

particularly rare case both in scientific research and industrial practice, because the yarn

requirements for weaving and knitting are usually different [3,58,59,64,160]. After conditioning

woven and knitted fabric samples at five RH levels, the complex relative permittivity and loss tangent were characterized by operating an LCR meter with a parallel-plate test fixture and the structural impacts on the dielectric properties of cotton fabrics were discussed.

3.2. Research Questions

One of the missing components in the current literature is a comprehensive study on the dielectric

relaxation mechanisms for cotton fabrics. This is critical in understanding the dielectric

polarizations that are governing the resulted dielectric properties of cotton fabrics [87]. In order to expose the underlying dielectric polarizations in cotton fabrics, several RH levels can be incorporated [87]. Hence, the first research (RQ) was set as below.

RQ1: Which dielectric polarizations are significant in moist cotton fabrics in the

low frequency regime?

A study on the relationships between the fabric structure and dielectric properties of cotton fabrics is critical in both materials characterization and development of high-performance RF system points of view. As the structural parameters, both fabric construction and thread count are considered as the independent variables in this work because these are the basic design parameters used by woven and knit fabric manufacturers [61]. Also, because the dielectric properties of a mixture depends on the volume fractions of the constituents and the way of mixing [128], SVF and fabric construction also need to be treated as another critical structural parameters for cotton fabrics. Based on this, the following RQ was synthesized.

RQ2: How do the fabric construction (plain-woven versus plain-knit), thread

count (PPI and CPI) and SVF affect the low-frequency complex relative

permittivity and loss tangent of cotton fabrics at various RH levels?

3.3. Methods

In order to examine the formulated RQs, a flowchart (Figure 3-1) was generated. Firstly, woven

and knitted cotton fabric samples were prepared from a pure cotton yarn. Then, the physical and

hygroscopic properties of these samples were characterized. The dielectric characterization was

performed by using a parallel-plate test fixture, and the dielectric properties were discussed in

relation to the thread count, construction and SVF.

Note: The numbers in parentheses are the relevant section numbers. Figure 3-1. Flowchart for Experiment (I).

3.3.1. Yarn preparation

The first step in the sample preparation was to produce a yarn that is compatible for both weaving

and knitting to eliminate the factors of yarn composition and structure that might influence the

dielectric properties of produced fabrics [156]. Generally, the yarn requirements for knitting and

weaving are quite different – yarns for weaving require a higher breaking strength to withstand a

high tension, while knitting yarns need to be of lower twist for a better mechanical flexibility

[3,58,59,64,160]. In order to meet the requirements for both weaving and knitting, a compatible

yarn was prepared by plying five identical 100% cotton yarns of a liner density of 24.0 Ne (Frontier

Spinning Mills) in 100 Z-twists per meter (TPM) by a twisting device (Agteks DirecTwist 2A)

(Figure 3-2). The linear density of the plied yarn was 4.62 Ne, determined by the ASTM standard

D1907 (Option 4). This plying process was optimized by conducting a series of preliminary testing

using the actual weaving (AVL Studio Dobby Loom) and knitting machines (Shima Seiki Mach 2

XS123).

(a) (b)

5-ply cotton yarns

5 single-ply cotton yarns

Figure 3-2. Yarn plying process.

3.3.2. Fabric design and manufacturing

In order to investigate the pure effect of the fabric construction, both plain-woven and plain-knitted

(single jersey) fabrics were required to have the same SVF. However, because there is no universal

formula that gives an accurate prediction of the resulting SVF from the weaving or knitting parameters (thread counts), fabrics having different thread counts were designed to conjecturally produce woven and knitted fabrics of the same SVF. As the weaving variable, PPI was selected

because it can be easily changed by controlling the beat-up, let-off and take-up motions on the

weaving loom. For knitting, CPI was chosen as a variable because the modern knitting machine has an electronic control system that can automatically change the loop length. On the other hand,

changing EPI requires another warping and drawing-in processes, and changing WPI requires the

rearrangement of the knitting needles, both of which require additional processing time for

implementation. Thus, EPI and WPI were kept constant on the machine settings in this research.

The selected weaving and knitting parameters are given in Table 3-1. The EPI of 20 for weaving and WPI of 8 for knitting were respectively selected based on the linear density of the

cotton yarn. The PPI of 5 to 20 and CPI of 7 to 11 were selected to cover the minimum and

maximum values possible under the given settings so that the similar SVFs of the woven and

knitted constructions can be expected.

Table 3-1. Designed woven and knitted fabric parameters. Plain woven fabrics Plain knitted fabrics Sample # EPI PPI Sample # WPI CPI W1 20 5 K1 8 7 W2 20 8 K2 8 8 W3 20 12 K3 8 9 W4 20 16 K4 8 10 W5 20 20 K5 8 11

The woven fabric production in this work was done in three steps: warping, drawing-in and weaving on a 20-inch-wide computer-assisted dobby loom (AVL Studio Dobby

Loom). As shown in Figure 3-3(a), the cotton yarn was made into 400 ends (to make a 20-inch-

wide fabric of 20 EPI), and these parallel ends were rolled onto the warp beam (Figure 3-3(b)).

The ends were then drawn-in though the heddles attached to the harnesses (Figure 3-3(c,d)).

Although the minimum number of harnesses required to achieve the plain-weave pattern is two,

four harnesses were used to make an enough allowance for a better heddle movement. The ends

were sleyed through the reed (Figure 3-3(c,d)) with even spacing and were rolled onto the take- up beam (Figure 3-3(e)). The weft insertion was performed by manual operation of the shuttle

(Figure 3-3(f)). The shedding pattern was controlled by a built-in electronic dobby system.

Figure 3-3. Hand weaving process: (a) warping on a warper, (b) warp beam, (c) side-on and (d) top-view of a loom after drawing-in, (e) ends being rolled onto the take-up roll, and (f) newly made fabric (cloth fell).

Knit fabric samples were produced by operating a whole-garment weft-knitting machine

(Figure 3-4) (Shima Seiki MACH2X 123) installed with an 8-gauge knitting bed. Since this knitting machine was equipped with a full electronic control system, the number of CPI was changed electronically.

Figure 3-4. Fully automated knitting process.

3.3.3. Laundering and Conditioning

The produced fabric samples were washed by a home laundry machine with cold water for 30

minutes. After drying the samples at room temperature for more than 14 days, these samples were

soaked into 65% RH (21 °C) environment in a conditioned room for over 24 hours. The RH and

temperature were managed to be within ± 5% and ± 2 °C to meet the ASTM standard D1776. The

fabric samples were also conditioned at 80%, 50%, 35%, and 20% RH (21 °C) in a 30-cubic-foot environmental chamber (Parameter Generation & Control, Inc.) for over 24 hours. This chamber was equipped with an external desiccator to achieve the low humidity levels. The environmental fluctuations in this chamber were kept within the ranges of ± 2.5% RH and ± 0.2 °C.

3.3.4. Structural properties

Cotton fabrics of different constructions and structures were successfully produced from the

optimized cotton yarn, and the microscope images of the washed and conditioned fabric samples

are given in Figure 3-5. The number of EPI, PPI, WPI and CPI of the cotton fabric samples were

measured by following the ASTM standard D3775 for the woven fabric samples and the ASTM

standard D8007 for the knitted fabric samples, respectively. 1-inch-long 15 specimens were

measured to obtain the average thread count. The fabric thickness was determined from the sample

size of 10 by following the ASTM standard D1777 (Option 1). The fabric grammage was

determined by following the ASTM standard D3776 (Option C). The area of each fabric sample was 0.0074 m2 for the grammage testing. Finally, from the measured fabric thickness and

grammage, the SVF was calculated by [108]:

G SVF  (3-1) tρ

where G is the fabric grammage (grams per square meter); t is the fabric thickness (meters); and ρ

is the fiber density (grams per cubic meter) and is 1,520,000 g/m3 for cotton fibers at 65% RH [7].

Figure 3-5. Fabric samples under zoom microscope (Bausch & Lamp Monozoom-7) (65% RH at 21 °C).

The measured structural parameters of the woven fabric samples are given in Table 3-2.

Both EPI and PPI of the woven fabric samples (before washing) were slightly higher than the designed values, and this was primarily because the fabric samples experienced a less tension after taking off from the loom. After laundering, further increases in EPI and WPI were observed due to the water sorption of the cotton fibers [7]. Also, from the microscope images, it was observed that the washed W1 and W2 samples had disordered orthogonal structures because of the small

PPI which resulted in the loosely held yarns.

Table 3-2. Thread counts in woven fabric samples before and after laundering. EPI PPI Sample # Before washing After washing Before washing After washing W1 22 (0.46) 24 (2.15) 5 (0.35) 9 (0.56) W2 22 (0.65) 24 (1.19) 9 (0.74) 12 (0.49) W3 22 (0.38) 24 (0.68) 12 (0.59) 15 (0.53) W4 23 (0.26) 24 (0.41) 16 (0.86) 20 (0.74) W5 23 (0.00) 24 (0.35) 20 (0.52) 22 (0.46) Note: The numbers in parentheses are the standard deviations.

The structural parameters of the knitted fabric samples are given in Table 3-3. Both WPI and CPI of the unwashed samples were significantly higher than the designed values due to the release of the tension from the knitting needle bed. After laundering, CPI increased for all the samples whereas WPI increased only for the highest WPI sample (K5). These increases in the CPI and WPI were primarily due to the shrinkage of the cotton yarns. On the other hand, WPI of K1 and K2 were decreased after washing. This type of elongation is generally caused by some tensioning during laundering and drying processes.

Table 3-3. Thread counts in knitted fabric samples before and after laundering. WPI CPI Sample # Before washing After washing Before washing After washing K1 14 (0.46) 11 (0.62) 12 (0.35) 15 (0.46) K2 13 (0.35) 12 (0.46) 13 (0.49) 16 (0.62) K3 13 (0.35) 13 (0.35) 15 (0.26) 17 (0.52) K4 14 (0.35) 14 (0.35) 16 (0.65) 20 (0.41) K5 14 (0.49) 15 (0.00) 23 (0.70) 24 (0.63) Note: The numbers in parentheses are the standard deviations.

The SVF calculated from the measured fabric thickness and grammage are given in Table

3-4. It was observed that as the PPI increased from 9 to 22, the fabric thickness gradually

decreased. The grammage increased from W2 to W5, however, W1 showed an extraordinarily high

value. This was because W1 had a relatively high warp crimp content (56.5%) compared to the

other woven samples (average warp crimp of 29.4%) because PPI was so low that the yarns were

not tightly hold at the intersections of the warp and weft. The resulting SVF showed an increasing

tendency as the filling (pick) density increased.

Table 3-4. Fabric thickness, grammage and SVF of the washed woven fabric samples (65% RH at 21 °C). Sample # Fabric thickness (mm) Grammage (g/m2) SVF W1 1.67 (0.04) 255.9 0.10 W2 1.39 (0.05) 225.7 0.11 W3 1.40 (0.04) 230.9 0.11 W4 1.14 (0.02) 245.7 0.14 W5 1.11 (0.03) 261.4 0.15 Note: The numbers in parentheses are the standard deviations.

The SVF of the knitted fabric samples is given in Table 3-5. The fabric thickness and

grammage showed a decreasing and an increasing tendency as CPI increases from 15 to 24,

respectively. These observations indicate that by increasing CPI, the knit yarn was more compactly packed in the wales, courses, and thickness directions. In fact, the resulting SVF showed an upward trend with the increased CPI. As shown in Table 3-4 and Table 3-5, the same SVF values were successfully obtained for W4 and K2 (0.14), and W5 and K3 (0.15), respectively.

Table 3-5. Fabric thickness, grammage, and SVF of the washed knitted fabric samples (65% RH at 21 °C). Sample # Fabric thickness (mm) Grammage (g/m2) SVF K1 1.73 (0.10) 347.8 0.13 K2 1.64 (0.09) 353.9 0.14 K3 1.61 (0.06) 376.5 0.15 K4 1.42 (0.03) 398.2 0.18 K5 1.44 (0.03) 460.3 0.21 Note: The numbers in parentheses are the standard deviations.

3.3.5. Hygroscopic properties

The moisture contents of the fabric samples conditioned at 80%, 65%, 50%, 35% and 20% RH (21

°C) were characterized with a microwave moisture analyzer (CEM Smart System 5). By following the ASTM standard D629, a 0.5 g sample was taken for the measurement, and its weight before and after drying were measured. The maximum temperature of the samples during microwave heating was set to 105 °C to ensure complete drying without a decomposition of the sample. In order to calculate the moisture content, the following generic formula was used [7]:

WW M (%) =ww ×=×100 100 (3-2) WWdw+ W m

where Ww, Wd and Wm are the weights (grams) of water (moisture), dry fiber and moist fiber,

respectively.

The measured moisture content of the cotton samples is given in Figure 3-6. As the RH

increased from 20% to 80% RH, the moisture content increased from 3.8% to 8.4% due to the

moisture absorption. These moisture content values were within the typical hysteresis range reported in literature [7,161].

Figure 3-6. Moisture content vs RH plot.

3.3.6. Parallel-plate measurements

The complex permittivities and loss tangents of the cotton fabric samples were determined

along the fabric thickness direction based on the parallel-plate method [114] using a parallel-plate

(electrode diameter of 38 mm) test fixture (Keysight 16451B Dielectric Test Fixture) connected to an LCR meter (Keysight E4980A Precision LCR meter) (Figure 3-7). The capacitance and dissipation factor of the conditioned fabric samples (diameter of 38 mm) were monitored in the frequency range of 20 Hz to 1 MHz at 80%, 65%, 50%, 35% and 20% RH (21 °C). Additionally, the capacitance and dissipation factor of 4 more specimens of each fabric samples were measured at 1 MHz. In all the parallel-plate measurements, the voltage of 1.0 V was applied. The complex relative permittivity was then calculated from the measured capacitance and dissipation factor by using the expressions (2-59) and (2-61). This method of dielectric characterization is complied with the ASTM standard D150.

Figure 3-7. Parallel-plate test fixture connected to an LCR meter for dielectric measurement.

3.4. Results and Discussion

3.4.1. Dielectric spectroscopy

The dielectric properties of both woven and knitted cotton fabric samples were successfully measured and are given in Figure 3-8 to Figure 3-10. It was observed for all the fabric samples that as the frequency increased, the real part of the relative permittivity showed decreasing tendencies (Figure 3-8) with the corresponding loss peaks (Figure 3-9 and Figure 3-10). This is the typical low-frequency response of dielectrics; polarizations from various components such as polymer chains, functional groups and impurities start delaying as alternations of the electric field become more frequent, leading to dielectric relaxations [83,87].

Figure 3-8. Real part of the relative permittivity of the fabric samples at the different RH levels.

Figure 3-9. Imaginary part of the relative permittivity of the fabric samples at the different RH levels.

Figure 3-10. Loss tangent of the fabric samples at different RH levels showing three major relaxations (labeled as 1, 2, and 3).

For cellulose materials, it has been reported that the dominant polarizations at the given frequency range are the electrode, interfacial, dipolar and electrode polarizations. The electrode

polarization [85,86,149] is a result of electric double layers that are formed at the interface of the

device electrodes and free water on cellulose, and the interfacial polarization [85,86] is caused by

the ionic conductivity in free water that is significantly higher than cellulose and air. The dipolar

polarizations are the movements of side groups of cellulose chain (hydroxymethyl and hydroxyl

groups) [150]. Bound [85,86] and free [141,151] water are also known to contribute to the dipolar

polarization by their orientational movements. Lastly, the electronic polarizations [7] are also

significant at low frequencies due to the abundant sources of electrons in solid dielectrics including

cotton fibers.

Among these polarizations, the dipolar relaxation of free water and the resonant process of

electronic polarizations are known to occur in the microwave [141,151] and optical [7,83]

frequency domains, respectively, and thus they are not responsible for the relaxations in the

frequency range of interest (20 Hz to 1 MHz). On the other hand, the electrode polarization,

interfacial polarization, and dipolar polarization of bound water were reported to exhibit the three

largest relaxations in highly moist cellulose [85,86]. Although a single, broad dipolar relaxation of the side groups is also known to present from dielectric measurements of dry cellulose, this polarization is generally buried for non-dried samples [150].

From Figure 3-8 to Figure 3-10, it is seen that there are three major relaxations in the cotton fabric samples – the lower frequency range (labeled as 1 in Figure 3-10(a)) (below 100

Hz), the middle frequency range (labeled as 2 in Figure 3-10(a)) (100 Hz to 100 kHz), and the higher frequency range (labeled as 3 in Figure 3-10(e)) (above 100 kHz). As Figure 3-8(a) shows, the relaxation strength in the middle frequency range was the largest and was up to ~40. Also, this middle frequency process was highly affected by the RH level – relaxation strength was merely

~0.5 at 20% RH in the same frequency range (Figure 3-8(e)). This critical RH dependence

indicates that the relaxation was highly susceptible to the water content. Now, since the largest variation of the moisture content of the samples was smaller than 5%, the dipolar relaxation of bound water cannot explain this difference in the real part of the relative permittivity at 80% and

20% RH. Rather, this middle frequency polarization of large magnitude at the high RH levels could be attributed to free water with ionic conduction. It has been reported that the relaxation of the interfacial polarization is known to occur at about 1 to 100 kHz and exhibit a large relaxation strength for cluster of free water on cellulose with a strong correlation to the moisture content at

20 °C [86]. Therefore, the cause for the middle frequency relaxation was ascribed to the interfacial polarization.

As shown in Figure 3-8(a), the lower frequency response also showed a large relaxation strength (~20) at the highest RH level. This relaxation strength also shows a significant RH level dependence – the large relaxation strength of about 20 at 80% RH was reduced to about 0.3 at 20%

RH in the same frequency range (Figure 3-8(e)), suggesting a large contribution of absorbed water.

This could indicate that the increased ion mobility by abundant free water at a higher humidity level enhanced the formation of the electrical double layer at the device electrodes, resulting in the larger electrode polarization [111,112]. In fact, it is widely recognized that the electrode polarization could exist in many water-rich matters including cotton fibers [162,163]. Also, the electrode polarization was reported to show a critical relaxation near 100 Hz for cellulose materials

[86]. Therefore, the relaxation in the lower frequency domain was imputed to the electrode polarization of the electric double layer at the electrode - free water interface.

The last relaxation that starts at about 100 kHz (Figure 3-8(e) and Figure 3-10(e)) was due to the dipolar polarization of bound water. It is reported in literature that the relaxation of bound water on cellulose occurs near 1 MHz [86]. Although the current measurements did not exhibit

clear relaxation of bound water at elevated RH levels, this could be due to the superposition with the interfacial polarization. It is well known that dielectric relaxation curves in small magnitude often suffer from a superposition of neighboring large relaxation curves, impeding the data visibility. An example of this masking effect is shown in Figure 3-11, where Relaxation Process

3 was masked by Relaxation Process 2 as a consequence of the superposition [94]. Therefore, it can be analyzed that whereas the dipolar relaxation of the bound water was buried by the large interfacial polarization at the higher RH levels, as the RH level lowered, the contribution of the bound water became more visible because bound water is the dominant form at a lower RH [164].

Figure 3-11. Dielectric relaxations in mortar at 67% RH, where relaxation process 3 is masked by relaxation process 2 (adopted from [94]).

Based on these analyses of the measured dielectric spectra, the relaxation peaks of each polarization were determined and are given in Table 3-6. The relaxation peaks of the electrode and dipolar polarizations were lower than 20 Hz and higher than 1 MHz, respectively. On the other hand, the relaxation peak of the interfacial polarization was successfully determined from the high

RH measurements, and they were ranging from 112 Hz to 1.04 kHz with the average of 636 Hz.

These variations are considered to be primarily due to the large masking from the electrode

polarization [86,87].

Table 3-6. Relaxation frequencies of the cotton fabric samples. Electrode polarization (Hz) Dipolar polarization (Hz) Interfacial polarization (Hz) Sample# 80%–65% 50%–20% 80% 65% 50%–20% 80%–35% 20% W1 < 20 – 487 – – – > 1,000,000 W2 < 20 – 656 – – – > 1,000,000 W3 < 20 – – – – – > 1,000,000 W4 < 20 – – – – – > 1,000,000 W5 < 20 – – – – – > 1,000,000 K1 < 20 – 931 112 – – > 1,000,000 K2 < 20 – 572 – – – > 1,000,000 K3 < 20 – 1,038 – – – > 1,000,000 K4 < 20 – 656 – – – > 1,000,000 K5 < 20 – – – – – > 1,000,000 Note: Dipolar polarization is of bound water.

3.4.2 Effect of thread count, construction and SVF

The dielectric properties of woven fabric samples at 1 MHz are plotted in Figure 3-12 and Figure

3-13 with error bars that show the 95% confidence intervals. The selection of this frequency was primarily because the electrode polarization would have the least impact at this highest measured frequency.

Figure 3-12. RH dependences of the dielectric properties of the fabric samples at 1 MHz, where the error bars indicate the 95% confidence intervals determined from 5 specimens for each fabric sample.

Figure 3-13. Dielectric properties of the woven fabric samples.

As shown in Figure 3-12(a), with increase in RH, the real part of the permittivity significantly increased for each woven sample (probability (p)-value, p < 0.05). The dielectric loss

(Figure 3-12(b,c)) of these woven samples also increased with RH (p < 0.05). These increases of the dielectric properties were primarily because of the increased moisture content (Figure 3-6) in the fabric samples as discussed in the previous section.

The real part of the relative permittivity showed increasing trends with PPI (Figure

3-13(a)). Now, as given in Table 3-4, increasing PPI lead to a higher SVF. Also, as plotted in

Figure 3-14, the SVF also showed a nearly monotonic tendency to the real part of the relative

permittivity of the woven samples. Therefore, these increases in the real part of the relative

permittivity with thread count were most likely due to the increased SVF as supported by the

dielectric mixture theory [2,128].

Figure 3-14. Dielectric properties and the SVF at 1 MHz, where the error bars indicate the 95% confidence intervals determined from 5 specimens for each fabric sample.

The loss data (Figure 3-13(b)(c)) also showed increasing tendencies with increase in PPI, and this was most likely due to the associated increases in SVF (Figure 3-14). However, these

tendencies were limited in the lower RH (≤ ~35%) regimes. Under the higher RH (≥ ~50%)

conditions, the effect of the PPI on the loss properties did not result in a simple monotonic trend

to the thread count or SVF, indicating that some other structural factor(s) might be influencing in

the highly moist samples.

The dielectric properties of the knitted fabric samples at 1 MHz are given in Figure 3-12

and Figure 3-15 with the 95% confidence interval error bars. Similar to the woven fabric samples, the complex relative permittivity and loss tangent of each knitted sample were increased with RH

(p < 0.05) primarily because of the moisture uptake (Figure 3-12). Also, the real part of the relative permittivity (Figure 3-15(a)) showed moderately increasing tendencies with increase in thread counts (CPI and WPI) (Table 3-3), and this could be elucidated with the associated increase in

SVF (Table 3-5). Also, the loss behaviors (Figure 3-15(b)(c)) of the knitted samples showed an increasing trend at the lower RH (≤ ~35%) environments, while, at elevated RH (≥ ~50%), the loss data did not show a monotonically increasing tendency as also observed in the woven samples.

Figure 3-15. Dielectric properties of the knitted fabric samples.

The dielectric properties plotted as a function of the SVF are shown in Figure 3-14 and comparisons between the woven and knitted fabric samples of the same SVF are given in Figure

3-16 and Figure 3-17. For these comparisons of the same SVF and RH, the knitted fabrics showed statistically higher values (p < 0.05) of complex relative permittivity and loss tangent than the woven fabrics, and this tendency was enhanced at a higher RH. Because the SVF was the same, these permittivity differences between the woven and knitted fabric samples could be the evidence that different mixing rules are taking place [2].

Figure 3-16. Comparisons of the woven and knitted fabric samples of the same SVF (W4 and K2), excerpted from Figure 3-12.

Figure 3-17. Comparisons of the woven and knitted fabric samples of the same SVF (W5 and K3), excerpted from Figure 3-12.

One of the key influencers for the resulting permittivity of the fabric samples would be the orientation of fibers. For example, the dielectric mixture theory (such as the extension of the

Maxwell-Garnet rule) states that the orientation of high aspect ratio materials affects the permittivity of the mixture, and consequently, the permittivity of the fabric in its normal direction could be higher as more fibers and yarns are oriented normal to the fabric plane (Table 3-7)

[2,165,166]. In addition, cotton fibers are well known to exhibit a higher local permittivity along

the fiber axis than the radial direction due to their highly oriented crystal structures [105,167,168],

and this microstructural dielectric anisotropy also contributes to a higher out-of-plane permittivity

when more fibers are oriented in the normal direction (Table 3-7). Another underlying effect is

the direction and shape dependences of the interfacial polarization. Cotton fibers are

microscopically inhomogeneous, and thus the compositional and microstructural parameters

including shape, size, distribution and arrangement of pores, voids, cracks, free water, crystals and

amorphous regions could all influence the strength of the interfacial polarization in a highly

intricate way intertwined with the fiber orientation (Table 3-7) [87,169,170]. Additionally, the electrode polarization could also exhibit fairly intricate response to changes in orientation of moist fibers and yarns [171].

Table 3-7. Qualitative description of the effects of the fiber orientation on the complex relative permittivity in cotton fabrics at low frequencies. Effect on the complex relative permittivity Fiber orientation with Extended Maxwell- Microstructural Interfacial Electrode respect to the fabric plane Garnett rule anisotropy polarization polarization More normal components ↑ ↑ Intricate Intricate More in-plane ∗ ∗ r ↓ r ↓ Intricate Intricate components 𝜀𝜀 𝜀𝜀 ∗ ∗ Note: ↑ indicates an increase and ↓ indicates𝜀𝜀r a decrease. 𝜀𝜀r

Although these four simultaneous effects (Table 3-7) of the fiber orientation could

potentially elucidate the difference in the permittivity of the woven and knit fabric samples of the

same SVFs, this is beyond the scope of the current research due to its complexity of properly

separating such effects in a quantitative way [7,87]. Rather, the more important implication from

the observation is that the dielectric properties of cotton fabrics exhibit strong dependence on the

fabric structure and thus may not be discussed solely with the SVF.

The dielectric measurements below 1 MHz are widely performed for fiber and yarn

structural characterizations in the textile industry [3,172], and they are reported to provide a good

accuracy. This is because the examined fibers are well aligned and perpendicular to the electric

field and the orientational aspect is of lesser concern [36]. Contrastively for fabrics, where fibers

are highly non-linear, orientations need to be treated as a notable influencer to the dielectric

properties. Although this finding suggests that the potential applications such as the absolute

measurements of porosity and moisture content could be more challenging for fabrics than fibers

and yarns, the dielectric sensitivity of fabrics to their structures could lead to a new route to the

structural analysis of cotton fabrics with a further elaboration.

Another important finding is that the low frequency dielectric analysis of cotton fabrics

suffers from the superposition of various polarizations, impeding the establishment of quantitative

structure-property relationships. Particularly, in the presence of electrode and interfacial

polarizations, the structure-dielectric property analysis is of great challenge because of limited

physical models [87]. This, however, implies that with much higher frequencies correlations of

dielectric properties to the fabric structures could be more legitimate because the superposed low

frequency effects (e.g., electrode polarization, interfacial polarization, and dipolar polarizations of

bound water) could be minimal [84,173]. At certain microwave frequencies, for example, the dominant factors affecting the dielectric properties could be limited to the fiber anisotropy (such as the dependence of the electronic polarizability of moist cellulose on the electric field direction

(i.e., birefringence)) and the mixing effect (such as the shapes, orientations and locations of

cellulose and free water in fabric) [2,7,75,83,105,152].

3.5. Chapter Conclusions

A variety of cotton fabric samples were produced, and the dielectric properties were discussed in

relation to the thread count, construction and SVF. From the dielectric measurements at five

different RH levels, three major relaxations were observed, and they were ascribed to the electrode

polarization, interfacial polarization, and dipolar polarization of bound water.

Next, the effect of the thread count and SVF were examined with the dielectric data at 1

MHz. It was found that with increase in thread count (PPI, CPI and WPI), the real part of the

permittivity increased, and this was primarily elucidated with the increase in SVF. On the other

hand, the imaginary part and loss tangent did not show a clear monotonic trend to the thread count

or SVF at the elevated RH levels, and this was interpreted that additional mixing factors such as

the structure-dependent interfacial polarization and/or electrode polarization could also be

influencing the dielectric properties of the highly moist cotton fabrics.

The effect of the fabric construction on the dielectric properties was investigated through

the comparisons of the woven and knitted fabrics of the same SVFs. It was revealed that the fabric

construction played an important role in the resulting dielectric properties – for all the comparisons of the same SVF, the knitted fabrics showed higher values of the complex relative permittivity and loss tangent than the woven fabrics. This observation was interpreted that although the current mainstream in the low-frequency dielectric investigations on textile fabrics deals primarily with the SVF and RH in literature [108,121,128], fabric construction also needs to be treated as a key influencer as supported by the microstructural anisotropic dielectric properties of cellulose fibers

[7,105,152], the dielectric mixture theory (macroscopic shape effect) [2] and the structure- dependent interfacial polarization [87,169,170].

Finally, based on these findings, it was suggested that for potential applications of fabric

dielectric properties such as measurement of the porosity, fiber orientation, and moisture content, a much higher frequency could be more legitimate. This is because superposed low-frequency polarizations cease with increase in frequency, and the structural parameters of cotton fabrics could be more effectively correlated with their resulting dielectric properties. Further discussions on the roles of the fabric construction, thread count, and SVF on the dielectric properties are given in

Chapter 4 at microwave frequencies.

CHAPTER 4. EXPERIMENT II Structure-Dielectric Property Relationships in Cotton Fabrics: A Study at Microwave Frequencies

4.1. Introduction

With the recent booming of wearable electronics and e-textiles, the dielectric properties of textile materials have been featured for development of textile-based microwave interfaces [18,29].

Microwave interfaces such as antennas and transmission lines have been inherently integrated into fabrics by weaving [19–21], knitting [22,23], embroidering [24–26] and laminating

[28,29,41,42,174] with electrically conductive yarns and fabrics. These additions of electronic functionalities to the conventional fabrics not only enable constructions of comfortable and lightweight devices in a highly wearable form with the pre-existing textile manufacturing techniques [18] but could also permits a better electronic performance. For instance, certain textile fabrics including cotton were reported to have dielectric properties desirable for fabrication of microwave devices [29]. The highly porous nature of fabric structure results in a permittivity close to that of air which enables development of a low-loss microwave systems [29].

The microwave dielectric properties of conventional fabrics including cotton, polyester and nylon are reported to be on the lower side, and it typically sits between 1 to 2.1 in the real part of the relative permittivity (dielectric constant) [27,29,42,43]. However, in the context of microwave engineering, even such small variation could be fatal. For instance, the operating frequency of resonant structures including patch antennas exhibits a critical dependence on the dielectric constant of the integrated substrate [103,175], and a fine tuning (impedance matching) must be

performed with the utmost care and attention to the dielectric properties of the antenna substrate

for a successful operation [42,103].

The dielectric constant of the textile substrate not only influences the impedance matching,

but also dominates the device size and performance. For example, while a higher dielectric

constant could reduce the size of patch antennas, a higher gain and a higher bandwidth could be

expected with a substrate of a lower dielectric constant [29,103]. The imaginary part of the relative permittivity and loss tangent also influences the device performance – while a higher imaginary part of the relative permittivity (and hence a higher loss tangent) could help to increase the impedance bandwidth, a higher efficiency and a higher gain could be achieved with a substrate of a lower imaginary part of the relative permittivity (and hence a lower loss tangent) [176].

Therefore, engineering the dielectric properties of textile materials including cotton fabrics is crucial for design and production of optimal textile microwave systems for various wearable applications.

However, microwave investigations on textile fabrics are of great challenge [1]. At microwave frequencies, certain EM phenomena such as the radiation loss, conductor loss, dielectric loss, surface wave loss and capacitive coupling could all be enhanced, and these phenomena make microwave circuits more complex for data collection and analysis compared to the low-frequency dielectric measurements [114]. As such, there is currently no standardized method of microwave dielectric measurements that were specifically developed for textile materials [1].

In previous reports, the microwave dielectric properties of cotton fabrics were determined by the microstrip resonator [40] and the resonant patch antenna [41–43] methods at discrete frequencies. These dielectric characterization techniques were successfully adopted from the

antenna theory [1,45]. The relationship between the RH and the dielectric constant of a cotton fabric was also discussed by the patch antenna method, and a monotonic relationship was reported

[42]. For cotton/polyester blend fabrics, the dielectric measurements were also performed by using the microstrip line method at broadband frequencies [159].

Although reports on the microwave dielectric properties of cotton fabrics are found in literature thanks to the increasing recognition of their potential applications [29,177], fundamental investigation on the effect of the fabric structure such as the construction (e.g., woven and knitted), thread count (PPI, EPI, CPI and WPI) and SVF on the microwave dielectric properties is rarely discussed for cotton fabrics. As detailed in Chapter 3, the dielectric properties of cotton fabrics as air-fiber-moisture mixtures are dependent on the microstructures and moisture content of cotton fibers, in addition to the way of mixing with air, and this also holds at microwave frequencies

[2,87,168]. In order to find a reference point to design a cotton fabric with optimal dielectric properties for development of textile-integrated microwave apparatus, a comprehensive study on relationships between the fabric structural parameters and the microwave dielectric properties of cotton fabrics is necessary.

This paper, therefore, investigates the effect of the fabric construction, thread count and

SVF on the dielectric properties of cotton fabrics in the microwave frequency domain at five RH levels. In the first phase, the properties complex relative permittivity and loss tangent of woven and knitted cotton fabrics were characterized by using the microstrip line method at broadband frequencies (100 MHz–6 GHz), and their correlations to RH, fabric construction, thread count, and

SVF were discussed.

In order to further investigate the real part of the relative permittivity of the cotton fabrics in a greater resolution, the second phase was designed. By using the patch antenna method

[103,178], the real part of the relative permittivity of the cotton fabrics were measured at near 2.45

GHz, and analyses were made between the dielectric constant and the RH, fabric construction,

thread count, and SVF.

4.2. Research Questions

Establishment of relationships between cotton fabric structure and the dielectric properties

is vital for materials characterization and development of high-performance microwave system

points of view. As a dielectric characterization technique in this research, the microstrip line method is considered. The microstrip line method is one of the most commonly employed technique when both real and imaginary parts of the relative permittivity of sheet materials need to be acquired at broadband microwave frequencies. As investigating structural parameters, both

fabric construction and thread count are considered as the independent variables in this work since

these are the fundamental design parameters used by woven and knit fabric manufacturers [61].

Also, because the dielectric mixture theory states that the dielectric properties of a mixture (fabric

as an air-fiber system) could depend on the volume fractions and the way of mixing [2], the SVF and fabric construction are also treated as the additional structural parameters. Based on this, the following research question (RQ) was set in this work.

RQ1: Based on the microstrip line method, how do the fabric construction (plain-

woven versus plain-knit), thread count (PPI and CPI) and SVF affect the complex

relative permittivity and loss tangent of cotton fabrics at various RH levels in the

microwave frequency regime?

The microstrip line method is one of the most convenient method to characterize the complex form of the relative permittivity and have been often successfully employed to characterize various substrates including textile materials in literature [48,118,179]. However, the accuracy of this transmission line technique is usually limited by several factors (e.g., the impedance mismatch, radiation, and loss in conductors) [180,181]. As such, not necessarily all small differences in the dielectric behavior of cotton fabrics in woven and knitted forms may be properly visualized by this technique. Therefore, the patch antenna method [42,43], which generally offers a higher resolution than the microstrip line, was also incorporated in this work.

However, because the patch antenna method measures only the real part of the relative permittivity and only at a single frequency, the structural parameters of cotton fabrics are discussed in relation to the real part of the relative permittivity at a single frequency. Based on this, the following RQ was prepared.

RQ2: Based on the patch antenna method, how do the fabric construction, thread

count and SVF affect the dielectric constant of cotton fabrics at various RH levels

in the microwave frequency regime?

4.3. Methods

Based on the formulated RQs, two research phases were designed, and the flowchart is given in

Figure 4-1. The first phase aims to unveil the effect of the fabric construction, thread count, SVF and RH on the complex relative permittivity and loss tangent of cotton fabrics by the microstrip line method. Then, the second phase further analyzes the relationship between the real part of the relative permittivity and the structural parameters of the cotton fabrics but with a greater characterization accuracy.

Note: The numbers in parentheses are the relevant section numbers. Figure 4-1. Flowchart for Experiment (II).

4.3.1. Materials

A polyacrylic adhesive-backed copper foil with a copper thickness of 0.04 mm and

adhesive thickness of 0.04 mm was selected as a conductor for radiating and ground planes of

microstrip lines and patch antennas. Edge-mount SubMiniature version A (SMA) connectors

(Cinch Connectivity Solutions) were used to feed the transmission line and antenna samples.

In order to investigate the dielectric behaviors of cotton fabrics, five plain-woven and five

plain-knitted cotton samples were adopted from Experiment (I). As described in Chapter 3, all

these fabric samples were prepared from the 5-ply cotton yarn of linear density of 4.62 Ne, and

their structural parameters were characterized based on the ASTM standards.

The structural parameters of the woven fabric samples are summarized in Table 4-1. As shown, the EPI of all the woven samples were 24, but the PPI had five variations (9 to 22) to investigate the effect of the thread count. The knitted samples had five variations in CPI (15 to 24) and another five variations in WPI (11 to 15) as given in Table 4-2. In terms of the SVF, woven samples had four variations (0.10 to 0.15) while the knitted samples had 5 variations (0.13 to 0.21).

Among them, two pairs of woven and knitted fabric samples had the same SVFs – W4 and K2

(0.14), and W5 and K3 (0.15).

Table 4-1. Structural parameters of the woven cotton fabric samples (data adopted from Table 3-2 and Table 3-4). Thread counts Sample # SVF PPI EPI W1 9 24 0.10 W2 12 24 0.11 W3 15 24 0.11 W4 20 24 0.14 W5 22 24 0.15

Table 4-2. Structural properties of the knitted cotton fabric samples (data adopted from Table 3-3 and Table 3-5). Thread counts Sample # SVF CPI WPI K1 15 11 0.13 K2 16 12 0.14 K3 17 13 0.15 K4 20 14 0.18 K5 24 15 0.21

4.3.2. Microstrip line measurements

The microstrip line method is a non-resonant (broadband) technique that measures the complex relative permittivity and loss tangent of a sheet-form substrate embedded in a microstrip line [46]. This method is based on the transmission line theory – a microstrip line, which consists of a conductive trace mounted on a grounded substrate, has reflection and transmission characteristics that are largely dependent on the dielectric properties of the substrate along the substrate thickness direction [45,47,48,182]. Accordingly, by using analytical formulas reported in literature [45,47,48,182], the dielectric properties of the substrate layer along the substrate thickness direction can be calculate from the reflection and transmission measurements.

In this work, the complex permittivities and loss tangents of the cotton fabric samples were characterized along the substrate (cotton fabric) thickness direction by the microstrip line method in the frequency range of 100 MHz to 6 GHz under five different RH levels (80%, 65%, 50%, 35% and 20%). The dielectric properties of the microstrip line substrate were determined fby measuring the reflection and transmission coefficients (S-parameters) of the microstrip line [47,48]. The following subsections give the procedural details of the microstrip line design, fabrication, electrical measurements and dielectric calculations.

4.3.2.1. Microstrip line design

The design of the microstrip line is illustrated in Figure 4-2. The microstrip line consisted

of the copper foils as the conductive trace and the fabric sample as the substrate. In addition to this

configuration, two adhesive layers that were required to mount the copper foils on the fabric layer

were also incorporated as parts of the substrate, but the effect of these adhesive layers on the

dielectric characterization will be eliminated during the calculation of the dielectric properties. The

width and height of the trace and the height of the substrate were chosen for the ease of fabrication,

available sample dimensions, and ease of handing during the transmission and reflection

measurements, because these geometrical factors will also be effectively compensated during the

dielectric calculation [48]. As for the ground plane width, for which the microstrip line method

assumes the infinity [45], 76.2 mm was chosen as the physically realizable and optimal ground

plane width after conducting a preliminary testing using an EM simulation software (Appendix

A).

Figure 4-2. Designed microstrip line in the (a) perspective and (b) side views (not to scale).

Next, because the cotton fabric samples are mechanically flexible and the microstrip line measurements are affected by flexing of substrates [183], a 3D-printed template made of

poly(lactic acid) (PLA) was incorporated to ensure that the fabric samples remain flat during the

measurements. The developed template model consists of a base and a presser, and the fabric

microstrip line was designed to be clamped between the base and presser with stainless bolts and

brass nuts (size of M2 (ISO metric screw thread)) as depicted in Figure 4-3. As a note, the use of

such template could influence the accuracy of the dielectric characterization because the EM

properties of the microstrip lines are sensitive to nearby objects [184], but it was preliminary tested

that placing the designed template has no significant impact on the accuracy of the dielectric

characterization (Appendix A).

Figure 4-3. Designed microstrip line with the template (not to scale).

4.3.2.2. Microstrip line fabrication

Figure 4-4 shows a sample of the microstrip line. The adhesive-backed copper foil and the cotton fabric samples were prepared in the dimensions given in Figure 4-2. In order to cut the copper trace accurately into the 2 mm width, a Cricut Explore AirTM electronic cutting machine

(Provo Craft & Novelty, Inc) was used. Then, the copper tape was mounted on the dielectric

100

substrate to form the designed microstrip line geometry. Two edge-mount SMA connectors were soldered to the edges of the conductive trace and ground plane to allow a power feeding.

Figure 4-4. Microstrip line sample.

The template to hold the fabric substrate during antenna measurement was created by 3D printing (Lulzbot Taz 6, Aleph Objects, Inc.) of PLA. The design file (Figure 4-5(a)) for printing was prepared in a computer-aided-design (CAD) software (Tinkercad, Autodesk, Inc.) in the dimensions given in Figure 4-3. The fabric samples were mounted on this template with the stainless-steel bolts and brass nuts (Figure 4-6) to ensure that fabric sample remains flat during measurements.

101

Figure 4-5. (a) CAD model of the template for 3D printing and (b) 3D-printed template with the bolts and nuts.

Figure 4-6. Polyester microstrip line sample placed on the 3D-printed template.

102

4.3.2.3. Microstrip line measurements

The cotton microstrip lines were conditioned at 80%, 65%, 50%, 35% and 20% RH (21 °C) for over 24 hours in the same manner described in Section 3.3.3. After the sufficient conditioning, the

2-port complex S-parameters of the cotton microstrip lines with were measured by using a vector network analyzer (VNA) (E5071C ENA Series Network Analyzer, Agilent Technologies). Two

50 Ω coaxial cables of the VNA were attached to the SMA connectors of the microstrip line sample, and the complex S-parameters were measured in the frequency range of 100 MHz to 6

GHz.

Next, since the two SMA connectors were embedded as fixtures in the measurements as depicted in Figure 4-7(a), the measured S-parameters included the fixture effects [185–188]. In order to eliminate these parasitic effects of the embedded fixtures from the measured S-parameters and to obtain the pure S-parameters of the device under test (DUT, Figure 4-7(a)), the thru-only de-embedding [185–187] was performed.

Figure 4-7. Concepts of (a) the embedded transmission line structure with two fixtures on each end and (b) the thru structure having only the fixtures (adopted from [186,p.1]).

The thru-only de-embedding [185–187] is a two-step calibration process: (i) complex S- parameter measurements of a thru standard (Figure 4-7(b)) and (ii) mathematical computation.

By following [186], in order to de-embed the two SMA fixtures on each side of the microstrip line

103

and to find the S-parameters of the true-microstrip line component (DUT) (Figure 4-8(a)), the thru standard was designed as depicted in Figure 4-8(b). The designed calibration standard had closely positioned two SMA connectors. Since the measurement length of the microstrip line was 168 mm and the designed calibration standard has a de-embedding length of 28 mm, the DUT length (de- embedded length) (lDUT) was 140 mm.

Figure 4-8. Schematic side views of (a) the micropstrip line with two SMA connectors on each end and (b) the thru calibration standard (not to scale).

The fabricated calibration standard is given in Figure 4-9. Because the performance of the thru standard is governed by the characteristics of the SMA connectors, and the substrate parameters (e.g., geometry and dielectric properties) would affect only in a secondary way, the thru standard could be reasonably made with any cotton fabric sample. In this work, W3 was selected as a representative fabric because it had a thickness of 1.40 mm, which is close to the median thickness of the fabric samples (1.43 mm). Also, unlike the plain-knitted samples, the plain-woven samples including W3 did not exhibit a curling behavior, and thus the woven sample was preferred from handling reasons.

104

Figure 4-9. Thru standard for de-embedding.

The thru standard made of the cotton fabric sample was measured in the same manner as

in the microstrip line measurement – the complex S-parameters were measured in the frequency range of 100 MHz to 6 GHz with the VNA. The calculation process was carried out by considering the cascade (series) configuration of the SMA connectors and the microstrip line (Figure 4-7) by employing the two-port transfer (T)-parameters (T11, T12, T21, T22), which are mathematically related to the S-parameters by [189]:

1 T11 = S21

−S22 T12 = S21 (4-1) S11 T21 = S21

SS12 21− SS 11 22 T22 = S21

With an assumption that SMA connectors are identical on each side, T-parameters can

cascade the two-port network by [185]:

−−11 [TDUT] = [ T SMA] [ TT total][ SMA ] (4-2)

where [TDUT] is the unknown T-parameters of the true microstrip line without the SMA connectors;

[Ttotal] is the measured T-parameters of the two SMA connectors and the microstrip line configured

105

in series; and [TSMA] is the T-parameters of a single SMA connector and can be obtained from the measured T-parameters of the thru standard ([Tthru]) by using the bisection formula:

1/2 [TTSMA] = [ thru ] (4-3)

Finally, the de-embedded S-parameters ([SDUT]) were obtained from [TDUT] by using (4-1).

4.3.2.4. Dielectric calculations

The complex relative permittivity and loss tangent of the cotton fabric samples were determined in 2 steps: (i) calculation of the dielectric properties of the cotton fabric samples with the two adhesive layers from the de-embedded S-parameters and (ii) extraction of the pure dielectric properties of the cotton fabric layer by using the theory of capacitors in series.

In order to find the dielectric properties of the cotton fabric samples with the adhesive layers, the de-embedded S-parameters (S11, S12, S21, S22) [47] were first converted into the impedance (Z)-parameters (Z11, Z12, Z21, Z22) by:

(1+S11 )(1 −+ S 22 ) SS 12 21 ZZ11= 0 (4-4) (1−S11 )(1 −− S 22 ) SS 12 21

2S21 ZZ21= 0 (4-5) (1−S11 )(1 −− S 22 ) SS 12 21

where Z0 is the source impedance (ohms). Then, the propagation constant (γ) was obtained from

the Z-parameters by [47]:

1 −1 Z γα=+=j β cosh 11 (4-6) lZDUT 21

where α is the attenuation constant (nepers per meter); β is the phase constant (radians per meter);

and lDUT is the de-embedded length (meter) of the microstrip line. Based on the microstrip line

106

theory [47,48], the dielectric constant of the cotton fabric substrate with the two adhesive layers

' (εr,t) was obtained by:

' 1 21ε rt, −+ eff 12h 1+ t ' W ε  (4-7) rt, 1 1+ 12h 1+ t W

where W is the trace width (meters); ht is the sum of the thicknesses (meters) of the fabric and

' adhesive layers; and εreff,t is the effective dielectric constant of the cotton fabric layer with the two adhesive layers and is given by [45]:

2 ' cβ ε rt,   (4-8) eff 2π f

The loss tangent of the cotton fabric substrate with the two adhesive layers (tanδt) was calculated

by [47]:

cα tanδ  t ' (4-9) πεf rteff ,

and the imaginary part of the relative permittivity of the cotton fabric substrate with the two

'' adhesive layers (εr,t) was determined by [87]:

'' ' εεrt,,= rt ⋅ tan δ t (4-10)

Next, in the given microstrip line samples, two adhesive layers are incorporated as parts of

the dielectric substrate. In order to eliminate the effect of these adhesive layers and to extract the

* pure dielectric properties of the fabric layer (εr and tanδ), the theory of capacitors in series [75]

was used. For the multilayer geometry of the adhesive-mounted fabric illustrated in Figure 4-10,

* the total complex capacitance (Ct ) is given by [75]:

107

1111 =++ * *** CCCCta a (4-11) 12 = + ** CCa

* * where C is the complex capacitance of the fabric layer and Ca is the complex capacitance of each

* * * adhesive layer. From the definition of the complex capacitance [87,190,191], Ct , C and Ca are respectively given by:

* * εεrt,0A Ct = (4-12) ht

εε* A C* = r 0 (4-13) h

* * εεra,0A Ca = (4-14) ha

Now, the substitution of (4-12), (4-13) and (4-14) into (4-11) gives:

εε**h ε * = ra,, rt r ** (4-15) εεra,,hh t− 2 rt a

* Since a literature value of the complex relative permittivity (εa) of the polyacrylic adhesive is

2.0−0.0002j [46,192], the complex relative permittivity of the pure fabric layer was obtained by

(4-15).

108

Figure 4-10. Models of (a) an adhesive-mounted fabric, (b) capacitors in series and (c) an equivalent capacitor.

4.3.3. Patch antenna measurements

The patch antenna method is a resonant (typically, a single-frequency) technique that determines the real part of the relative permittivity (dielectric constant) of a sheet-form substrate embedded in a patch antenna [46]. This method is based on the antenna theory – a patch antenna, which consists of a conductive patch mounted on a grounded substrate, has a resonant (and hence operating) frequency that is critically dependent on the dielectric constant of the substrate along the substrate thickness direction [103,178]. Accordingly, by using analytical formulas available in literature [103,178], the dielectric constant of the substrate layer along the substrate thickness direction can be calculate from the measurement of the operating frequency.

Based on the patch antenna method, the dielectric constants of the cotton fabric samples were characterized along the substrate (cotton fabric) thickness direction under five different RH levels (80%, 65%, 50%, 35% and 20%). In order to obtain the dielectric constants of the fabric samples using the analytical expressions, the operating frequency of the patch antenna was determined though a measurement of the reflection coefficient in the frequency range of 1 to 6

GHz. The procedural details of the antenna design, fabrication, electrical measurements and dielectric calculations are provided in the following subsections. 109

4.3.3.1. Antenna design

The designed patch antenna (Figure 4-11) consists of a copper foil as a radiating patch and a ground plane and the cotton fabric as a substrate. Additionally, two adhesive layers of polyacrylate to mount the copper foils on the fabric substrate were incorporated as parts of the dielectric substrate, but the effect of these adhesive layers on the dielectric characterization will be compensated during the calculation of the dielectric constant. The antenna was designed to have a microstrip feedline and an SMA connector for powering.

Figure 4-11. Designed rectangular patch antenna geometry.

The resonant (and operating) frequency of a patch antenna critically depends on two factors: (i) the antenna dimension (patch length and width and substrate height) and (ii) the real part of the relative permittivity (dielectric constant) of the substrate. The relationship between the resonant frequency, patch antenna dimension and the dielectric constant of the integrated substrate are known by the patch antenna theory [43,103]. Thus, the dielectric constant of the substrate could be estimated if the antenna dimensions and its resonant frequency are known.

Although the dimensions of the patch antenna (such as the patch length and width, inset length, feedline width and gap) could be almost arbitrary, it is recommended to have the patch length and width that are close to the half-wavelength of the target characterization frequency to

110

ensure that the actual characterization frequency to be near the target frequency (2.45 GHz)

[43,45,103].

As an option to enforce the characterization frequency to be further closer to the target frequency, an EM simulation can be performed with an assumed dielectric constant value to find the optimal antenna dimension [43]. By following [43], the optimal antenna geometries were obtained by running EM simulations using a 3D full-wave EM simulator (Ansys HFSS®) with assumed dielectric constants of the fabric samples. These assumptions of the dielectric constant were based on the previous reports that the typical dielectric constants of cotton fabrics are within the range of 1.3–2.0 at microwave frequencies [42,193]. The assumed dielectric constant values and optimal antenna dimensions for the dielectric characterization at 2.45 GHz are given in Table

4-3.

Table 4-3. Assumed dielectric constants and optimal antenna dimensions (in millimeters) at 2.45 GHz. Assumed Sample Patch Patch Inset Feedline Substrate dielectric Gap (g) # length (Lp) width (Wp) length (Li) width (Wf) height (h) constant W1 1.4 49 58 9 6 2 1.67 W2 1.6 46 52 11 5 2 1.39 W3 1.6 47 53 10 5 2 1.40 W4 1.7 45 53 10 4 2 1.14 W5 1.8 45 52 9 4 2 1.11 K1 1.6 47 54 10 7 2 1.73 K2 1.7 53 46 10 6 2 1.64 K3 1.7 45 52 9 6 2 1.61 K4 1.9 43 51 9 5 2 1.42 K5 2.0 43 51 8 5 2 1.44

111

4.3.3.2. Antenna fabrication

Figure 4-12 shows a sample of the cotton patch antenna. The adhesive-backed copper foil and the cotton fabric substrates were prepared in the dimensions acquired during the antenna simulations (Figure 4-11 and Table 4-3). In order to achieve accurate cuts of the copper foil, the electronic cutting machine was used. The copper foils were then mounted on the cotton fabric substrates, and the edge-mount SMA connectors were attached by soldering.

Figure 4-12. Patch antenna sample.

4.3.3.3. Antenna measurements

The operating frequencies of the cotton antenna samples were characterized through measurements of the one-port S-parameter (reflection coefficient or S11) [43]. The antenna samples were fed with a 50 Ω coaxial cable connected to the VNA, and the reflection coefficient was measured using an electronically calibrated VNA after conditioning at 80%, 65%, 50%, 35% and 20% RH (21 °C) in the environmental chamber for over 24 hours.

112

4.3.3.4. Dielectric calculations

The dielectric constants of the cotton fabric samples were acquired in 2 steps: (i) calculation of the

dielectric constants of the cotton fabric samples with the two adhesive layers from the measured

operating frequencies and (ii) extraction of the pure dielectric constants of the cotton fabric layer

by using the theory of capacitors in series.

First, in order to find the dielectric constant of the cotton fabric sample with the two

' adhesive layers (εr,t) from the measured operating frequencies, the patch antenna theory [103,178]

was used. According to the theory, the effective dielectric constant of the cotton fabric with the

' two adhesive layers (εreff,t ) and the operating (resonant) frequency of the antenna (fr; hertz) are

related by [103]:

 c LLpp −∆2 (4-16) 2 f ε ' r reff ,t where Lp is the patch length (meters); c is the speed of light in free space; and ΔLp is the additional

length of the patch (meters) caused by the fringing fields. Analytically, this electrical extension of

the patch length is given by [103]:

' Wp (ε r ,t ++0.3) 0.264 eff ht ∆Lhpt 0.412 (4-17) ' Wp (ε r ,t −+0.258) 0.8 eff ht

where Wp is the patch width and ht is the substrate height (sum of the heights of the cotton fabric and the two adhesive layers). Since the effective dielectric constant is related to the dielectric

' constant (εr,t) by [103]:

113

1 − εε''+−11  12h 2 ε ' r,t ++r,t 1 t (4-18) reff ,t     22  Wp

the dielectric constant of the fabric layer with the two adhesive layers was determined by (4-18).

Next, in the given patch samples, two adhesive layers were incorporated as parts of the

dielectric substrate. In order to eliminate the effect of these adhesive layers and to extract the pure

' dielectric constant of the fabric layer (εr), the theory of capacitors in series [75] was used. As formulated in Section 4.3.2.4 for the multilayer geometry of the adhesive-mounted fabric, the dielectric constant of the pure fabric layer was extracted by (4-15).

4.4. Results and Discussion

4.4.1. Microstrip line measurement results

The complex permittivities and loss tangents of the cotton fabric samples were determined

by the microstrip line method and are given in Figure 4-13. The measured dielectric data showed

periodic minor peaks in approximately every 1 GHz. These peaks were due to the standing waves,

which were caused by the wave reflection (impedance mismatch) at the source-microstrip line transition [47,180,188]. This ascription was confirmed by the evidence that the half-wavelength

(~150 mm) of the observed peak interval (~1 GHz) nearly equals to the length of the de-embedded transmission line (140 mm) (Figure 4-8(a)).

114

Figure 4-13. Raw and fitted dielectric property data of the fabric samples from the microstrip line measurements in the RH range of 20% to 80%.

115

For any transmission line-based dielectric characterization methods including the microstrip line method, observation of such periodic peaks in dielectric properties are quite commonly reported in literature, but the complete removal of these peaks are hardly achievable by experimental means [47,118,179,180,188]. Although the thru calibration was performed in effort to compensate the effect of the standing waves in this work, the raw data still contained some minor peaks. Since these periodic peaks do not represent the true dielectric properties of the cotton fabric samples, the linear regression with the bi-square weighting function [194] was applied to find baselines for analysis purposes (Figure 4-13).

In order to dissect the effect of the frequency on the dielectric properties of the cotton fabric samples, the real part of the relative permittivity fitted in Figure 4-13 were replotted in Figure

4-14. As shown in Figure 4-14, it was observed that as the frequency increased from 100 MHz to

6 GHz, the real part of the relative permittivity of the cotton fabric samples showed a downward trend at the given RH levels. According to [42,143,144,195], the dielectric constant of free water is known to decrease in this frequency range due to the dipolar relaxation. Therefore, these decreases in the dielectric constants with increase in frequency were ascribed to the dipolar relaxation process of free water in the moist cotton fabric samples (Figure 3-6).

116

Figure 4-14. Real components of the relative permittivity of the cotton fabrics having different SVF and RH levels.

The imaginary part of the relative permittivity and loss tangent of the cotton fabric samples are plotted against the frequency in Figure 4-15 and Figure 4-16, respectively. For both imaginary part of the relative permittivity and loss tangent, an overall decreasing trend was observed with increase in frequency at the given RH levels. However, according to [143,144,195], both imaginary part of the relative permittivity and loss tangent of free water are reported to increase with frequency in this measured range (100 MHz to 6 GHz) by the dipolar relaxation process.

Although a quantitative elucidation is challenging, one possible reason for observing a decreasing tendency instead of an increasing tendency in the acquired loss data would be due to the limited accuracy of the generic equation employed for the dielectric calculation. In particular, the employed formula (4-9) does not fully take account of the frequency-dependent characteristics of the microstrip line such as the frequency-dependent conductor and radiation losses, but such

117

factors are reported to influence the characterization accuracy of the frequency-dependent imaginary part of the relative permittivity and loss tangent in an intricate way [45,181,196].

Figure 4-15. Imaginary components of the relative permittivity of the cotton fabrics having different SVF and RH levels.

118

Figure 4-16. Loss tangent of the cotton fabrics having different SVF and RH levels.

Figure 4-17 shows the measured dielectric properties of the cotton fabric samples plotted as a function of the RH at 2.45 GHz. This frequency was selected because 2.45 GHz is designated as the ISM band and is one of the most commonly used frequencies in commercial microwave devices [42,197]. At this frequency, it was observed that the real part of the relative permittivity showed a mild increasing trend with RH – as given in Table 4-4, the Pearson correlation coefficients [198] support a strong/moderate positive correlation (R ≥ 0.70) between the RH and the dielectric constant for the majority of the samples (7 out of 10 samples). With alteration in RH from 20% to 80%, the calculated average increase was 0.16 in the dielectric constants. The imaginary part of the relative permittivity and loss tangent also increased with RH with a strong/moderate positive correlation (R ≥ 0.70) for the most samples, and the average increases were 0.041 and 0.027 in the imaginary part of the relative permittivity and loss tangent, respectively (Table 4-4). These predominant increases in the complex relative permittivity and

119

loss tangent were most likely due to the increased free water content in the fabric samples at a

higher RH. It is well known that a higher moisture content leads to a higher complex relative

permittivity and a higher loss tangent by the dipolar polarization of free water [7,199].

Figure 4-17. Dielectric properties of the cotton fabric samples as a function of the RH at 2.45 GHz.

Table 4-4. Correlations between the RH and the dielectric properties of the cotton fabric samples. Pearson correlation coefficient Sample # tanδ W1 0.79′ ‡ 0.99′′ † 0.98† r r W2 0.80𝜀𝜀 ‡ 0.78𝜀𝜀 ‡ 0.77‡ W3 0.97† 0.90† 0.88† W4 0.50 0.66 0.67 W5 0.77‡ 0.81‡ 0.81‡ K1 0.84‡ 0.78‡ 0.75‡ K2 0.50 0.63 0.66 K3 0.88† 0.80‡ 0.77‡ K4 0.74‡ 0.79‡ 0.79‡ K5 0.63 0.76‡ 0.78‡ Note: † indicates a strong correlation (|R| ≥ 0.85); ‡ indicates a moderate correlation (0.85 > |R| ≥ 0.70).

Figure 4-18(a) shows the thread count (PPI) plotted against the real part of the relative permittivity of the woven fabric samples (W1–W5). It was observed that as the number of PPI increased from 9 to 22 (Table 3-2), the resulting dielectric constants also increased (by 0.18, on average) with a strong/moderate positive correlation (0.95 ≥ R ≥ 0.82 (Table 4-5)). From the

120

dielectric mixture theory [2,108], it is known that a higher SVF could lead to a higher dielectric

constant. Also, it is seen from Figure 4-19 that the dielectric constant of the woven fabric samples increased with SVF with a strong positive correlation (0.98 ≥ R ≥ 0.85 (Table 4-6)). Therefore, it can be reasonably interpreted that the measured higher dielectric constant in a higher thread count sample was most likely due to the associated increase in the SVF.

Figure 4-18. Dielectric properties of the woven fabric samples, plotted as a function of the thread count.

Table 4-5. Correlations between the thread counts and the dielectric properties of the cotton fabric samples. Pearson correlation coefficient RH PPI (woven samples) CPI (knit samples) WPI (knit samples) (%) tanδ tanδ tanδ 80 0.82′ ‡ 0.60′′ 0.48 0.92′ † 0.87′′ † 0.83‡ 0.92′ † 0.95′′ † 0.93† r r r r r r 65 0.88𝜀𝜀 † 0.10𝜀𝜀 −0.23 0.96𝜀𝜀 † 0.76𝜀𝜀 ‡ 0.55 0.96𝜀𝜀 † 0.79𝜀𝜀 ‡ 0.59 50 0.95† 0.56 0.37 0.96† 0.84‡ 0.76‡ 0.96† 0.92† 0.86† 35 0.86† 0.70‡ 0.64 0.99† 0.92† 0.83‡ 0.99† 0.98† 0.95† 20 0.95† 0.51 0.39 0.95† 0.19 -0.01 0.95† 0.39 0.18 Note: † indicates a strong correlation (|R| ≥ 0.85); ‡ indicates a moderate correlation (0.85 > |R| ≥ 0.70).

121

Figure 4-19. Dielectric properties and the SVF at 2.45 GHz.

Table 4-6. Correlations between the SVFs and the dielectric properties of the cotton fabric samples. Pearson correlation coefficient RH (%) Woven fabrics Knitted fabrics

tanδ tanδ 80 0.86′ † 0.72′′ ‡ 0.62 0.94′ † 0.91′′ † 0.88† r r r r 65 0.85𝜀𝜀 † 0.24𝜀𝜀 −0.08 0.97𝜀𝜀 † 0.76𝜀𝜀 ‡ 0.54 50 0.96† 0.73‡ 0.57 0.98† 0.89† 0.83‡ 35 0.95† 0.76‡ 0.68 0.99† 0.94† 0.87† 20 0.98† 0.68 0.58 0.96† 0.21 0.00 Note: † indicates a strong correlation (|R| ≥ 0.85); ‡ indicates a moderate correlation (0.85 > |R| ≥ 0.70).

Unlike the real part of the relative permittivity, the imaginary part did not show a strong correlation to the PPI as shown in Figure 4-18(c), and the correlation coefficients between the PPI and these loss terms were merely equal or less than the 0.70 threshold (Table 4-5). Also, only the data at 80, 50 and 35% RH showed moderate correlations (R ≥ 0.70) between the SVF and imaginary part of the relative permittivity, and no strong correlation was observed (Table 4-6).

The correlation between the loss tangent and the PPI were also on the lower side (−0.23 ≤ R ≤ 0.64

(Figure 4-18(c) and Table 4-5)), and so was the correlation between the loss tangent and the SVF

(−0.08 ≤ R ≤ 0.68 (Figure 4-19 and Table 4-6)).

Since an increase in the PPI led to a higher SVF and the dielectric mixture theory [2] predicts that a higher SVF leads to a higher imaginary part of the relative permittivity and a higher

122

loss tangent, strong correlations would exist between these loss terms and the SVF and PPI under the controlled RH. One possible interpretation for not observing the expected strong correlation could be the limited loss characterization accuracy of the microstrip line method. As pointed out by [45,46,48,103,182,183], the microstrip line method, like any other microwave dielectric measurement techniques, involves a variety of losses including (but not limited to) the dielectric, radiation and conductor losses, the method makes a number of assumptions to separate and extract the pure dielectric loss term from the other co-existing loss terms. Since the losses in the microstrip line are hardly separable by an experimental mean, these assumptions are of absolute necessity but are known to induce errors in the loss characterization.

The complex relative permittivity and loss tangent of the knitted fabric samples plotted versus the CPI are given in Figure 4-20. It was observed that with increase in CPI from 15 to 24

(and with associated increase in WPI from 11 to 15 (Table 3-3)), the real part of the relative permittivity increased by 0.22 (on average) with a strong positive correlation (0.99 ≥ R ≥ 0.92

(Table 4-5)) at the given RH levels. Also, the imaginary part of the relative permittivity showed a strong/moderate upward trend (0.98 ≥ R ≥ 0.76 (Table 4-5)) with both CPI and WPI (except at

20% RH), and this increase was by 0.026 on average. The loss tangent also has a strong/moderate correlation (0.95 ≥ R ≥ 0.76 (Table 4-5)) to both CPI and WPI (except at 20% and 65% RH), and the average increase was 0.012. As expected from the dielectric mixture theory [2], these rises in the complex relative permittivity and loss tangents were also reasonably associated (R ≥ 0.94 (real part), 0.94 ≥ R ≥ 0.76 except at 20% RH (imaginary part), 0.88 ≥ R ≥ 0.83 except at 20% and 65%

RH (loss tangent) (Table 4-6)) with the SVF.

123

Figure 4-20. Dielectric properties of the knitted fabric samples.

Here, a note should be given that some weak/no correlations were also observed between

the thread count and SVF and loss terms of the knitted samples under the 20% and 65% RH

conditions (Table 4-5 and Table 4-6). As also discussed for the loss properties of the woven

samples, the most probable reason for not observing strong correlations between the SVF and the

loss terms (imaginary part of the relative permittivity and loss tangent) of the knitted samples at

all the RH conditions would be due to the limited reliability of the microstrip line method.

Next, in order to compare the dielectric properties of the cotton fabric samples having the

same SVFs (W4 and K2; W5 and K3), Figure 4-21 and Figure 4-22 are presented. For both sample pairs, no significant difference was observed between the dielectric properties of the woven and knitted samples based on the paired t-test (p-value ≥ 0.19), suggesting that the dielectric properties of cotton fabrics were not vitally affected by the fabric construction.

124

Figure 4-21. Comparisons of the dielectric properties of the woven and knitted fabric samples of the same SVF (W4 and K2), excerpted from Figure 4-17.

Figure 4-22. Comparisons of the dielectric properties of the woven and knitted fabric samples of the same SVF (W5 and K3), excerpted from Figure 4-17.

Table 4-7. Results of the paired t-test. p-value Comparison tanδ W4 vs K2 0.67′ 0.74′′ 0.69 r r W5 vs K3 0.27𝜀𝜀 0.21𝜀𝜀 0.19

Although the fabric construction was not a critical factor for the dielectric properties of

cotton fabrics from the data acquired by the microstrip line method, it could be still possible that the employed method simply did not provide a sufficient resolution for examining the small differences in the fabric permittivities. In order to test this statement, the patch antenna method, which characterizes only the real part of the relative permittivity and only at a single frequency but is known to offer a better accuracy [43,115], was also adopted, and the real part of the relative 125

permittivity of the cotton fabric samples was further analyzed at near 2.45 GHz in relation to the

fabric construction and structure.

4.4.2. Patch antenna measurement results

In order to analyze the effect of the fabric construction, thread count and RH on the dielectric

behavior of the cotton fabric samples in a greater resolution, the dielectric constants were

determined by the patch antenna method. Although the patch antenna method is known to

generally offer a better accuracy than the microstrip line method, this method only characterizes

the real part of the relative permittivity at a discrete frequency. Accordingly, only the real part of

the relative permittivity (at near 2.45 GHz) of the cotton fabric samples are discussed in this

section.

The characterization of the dielectric constants was successfully performed within a small

frequency variation near 2.45 GHz (2.59–2.87 GHz (Appendix B)), and the determined dielectric

constants of the fabric samples are plotted in Figure 4-23 as a function of the RH. It was observed

that the dielectric constant of every fabric sample increased with RH with a strong positive

correlation (1.00 ≥ R ≥ 0.96, except for K2 (R ≥ 0.69) (Table 4-8)), and the average increase was

0.13. As discussed in the previous section, these increases in the dielectric constants of both woven and knitted cotton fabric samples were primarily due to the more abundant free water at a higher

RH [42].

126

Figure 4-23. Dielectric constants plotted as a function of the RH, determined by the patch antenna method in the vicinity of 2.45 GHz.

Table 4-8. Correlations between the RH and the dielectric constants of the cotton fabric samples. Sample # Pearson correlation coefficient W1 0.99† W2 0.99† W3 0.99† W4 0.97† W5 0.99† K1 0.96† K2 0.69 K3 0.98† K4 0.99† K5 1.00† Note: † indicates a strong correlation (|R| ≥ 0.85).

Also, it should be noted that, in comparison to the data acquired by the microstrip line method (Figure 4-17), the patch antenna results (Figure 4-23) showed a more strong correlation to the RH (Table 4-8). Now, because the dielectric constants of a cotton fabric was reported to increase nearly monotonically with RH in literature [42], it could be reasonably said that the patch antenna method was more reliable than the microstrip line method.

Next, it was observed that as the thread count (PPI) of the woven fabric samples increased from 9 to 22 (Figure 2-18), the resulting dielectric constants also increased (by 0. 19, on average) with a strong/moderate positive correlation (0.92 ≥ R ≥ 0.82 (Table 4-9)). As observed in the dielectric constant data acquired by the microstrip line method, these increases in the dielectric

127

constants with thread count were also ascribed (0.98 ≥ R ≥ 0.91 (Table 4-10)) to the increased

SVF (Figure 4-25), supported by the dielectric mixture theory [2].

Figure 4-24. Dielectric constants of the (a) woven and (b) knitted fabric samples as a function of the thread count.

Table 4-9. Correlations between the thread counts and the dielectric constants of the cotton fabric samples. Pearson correlation coeffcient RH (%) PPI CPI WPI 80 0.91† 0.97† 0.93† 65 0.92† 0.98† 0.90† 50 0.89† 0.98† 0.91† 35 0.84‡ 0.97† 0.92† 20 0.82‡ 0.97† 0.91† Note: † indicates a strong correlation (|R| ≥ 0.85); ‡ indicates a moderate correlation (0.85 > |R| ≥ 0.70).

Table 4-10. Correlations between the SVFs and the dielectric constants of the cotton fabric samples. Pearson correlation coeffcient RH(%) Woven fabrics Knitted fabrics 80 0.96† 0.98† 65 0.97† 0.97† 50 0.98† 0.98† 35 0.93† 0.98† 20 0.91† 0.98† Note: † indicates a strong correlation (|R| ≥ 0.85); ‡ indicates a moderate correlation (0.85 > |R| ≥ 0.70).

The knit fabric samples also exhibited a very strong positive correlation (0.93 ≥ R ≥ 0.90

(Table 4-9)) between the thread count and their dielectric properties - with increase in CPI from

128

15 to 24 (and associated increase in WPI from 11 to 15), the dielectric constant increased by 0.12

(on average). Moreover, similar to the woven samples, these increases in the dielectric constants

with thread counts were also due to the associated increase in the SVF (0.98 ≥ R ≥ 0.97 (Table

4-10 and Figure 4-25).

Figure 4-25. Dielectric constants as a function of the SVF.

By comparing the woven and knitted fabrics of the same SVFs, it was found that the woven fabrics showed higher dielectric constants than the knitted samples under the controlled RH

(Figure 4-26). The calculated p-values from the paired t-test for the fabric construction were below

0.01 for both sample pairs. These differences in the dielectric constants of the woven and knitted

cotton fabric samples clearly indicate that although the SVF is primarily responsible for the

resulting dielectric properties of fabrics, additional structural parameter(s) must also be considered

in dielectric analysis.

129

Figure 4-26. Comparisons of the woven and knitted fabric samples of the same SVF ((a) W4 and K2; (b) W5 and K3), excerpted from Figure 4-23.

One of other possible influencers for the different dielectric constants of the woven and knitted cotton fabric samples under the controlled SVF would be the orientation of fibers. As discussed in Chapter 3, the dielectric mixture theory (such as the extension of the Maxwell-Garnet rule) states that the orientation of high aspect ratio materials affects the permittivity of the mixture, and the permittivity of the fabric in its normal (fabric thickness) direction could be higher as more fibers are oriented in the fabric thickness direction (Table 4-11) [2,165,166].

Table 4-11. Qualitative description of the effects of the fiber orientation on the dielectric constant of cotton fabrics at microwave (~2.45 GHz) frequencies. Fiber orientation with respect to Effect on the dielectric constant ( ) the fabric plane Extended Maxwell-Garnett rule Microstructural′ anisotropy 𝐫𝐫 More normal components ↑ 𝜺𝜺 ↑ More in-plane components ′ ↓ ′ ↓ r r Note: ↑ indicates an increase and ↓ indicates a𝜀𝜀 ′decrease. 𝜀𝜀′ 𝜀𝜀r 𝜀𝜀r

In addition, cotton fibers are well known to exhibit a higher local permittivity along the

fiber axis than the radial direction due to their highly oriented crystal structures, and this microstructural dielectric anisotropy would also contribute to a higher out-of-plane permittivity when more fibers are oriented in the fabric thickness direction (Table 4-11) [105,167,168].

130

Due to technical challenges in measuring individual fiber orientations within fabrics, the orientations of yarns were considered in this work. Thus, it was assumed that the average fiber orientation is almost parallel to the yarn orientation in the fabric samples.

The average yarn orientations of the cotton fabric samples (W4, W5, K2 and K3) relative

to the z-axis (fabric thickness direction) were calculated by developing theoretical models and measured in-situ with a micro-computed tomography (micro-CT) (Bruker SkyScan 1174). The procedural details of these theoretical computation and measurements are described in Appendix

C and Appendix D, respectively.

The calculated and measured yarn orientations of the cotton fabric samples of the same

SVFs are given in Figure 4-27. As shown, both calculations and measurements indicate that the

woven fabric samples had more yarns that were oriented in the fabric thickness direction than the

knitted samples of the same SVFs. Now, since a higher fiber orientation along the fabric thickness direction could lead to a higher permittivity [2,105,165–168], the observation that the dielectric

constant of W4 was larger than that of K2 can be explained by the evidence that the cotton fibers

in W4 had a more parallel orientation to the electric field than K2. Similarly, the larger dielectric

constant of W5 than K3 can be explained by the evidence that the fibers in W5 had a more

orientation along the electric field. Therefore, the fiber orientation could effectively elucidate the

different dielectric properties of the woven and knitted cotton fabric samples under the controlled

SVF.

131

Figure 4-27. Plotted average yarn angles of the cotton fabric samples of the same SVFs: (a) W4 and K2; (b) W5 and K3.

4.5. Chapter Conclusions

In the first phase, the complex relative permittivity and loss tangent of the cotton fabric samples were characterized by the microstrip line method in the frequency range of 100 MHz to 6

GHz at five RH levels. There was a general tendency that as the frequency increased from 100

MHz to 6 GHz, the real part of the relative permittivity decreased at the given RH levels, and this was attributed to the dipolar relaxation process of free water [195] that were absorbed by the cotton fibers. Also, decreasing trends with increase in frequency were observed for the imaginary part of the relative permittivity and loss tangent. However, since the dielectric loss due to the dipolar relaxation of free water is known to increase at this frequency range, the observed downward trends in the imaginary part of the relative permittivity and loss tangent were believed to be rather due to the limited loss resolution of the microstrip line method.

Strong/moderate correlations (R ≥ 0.70) were predominantly observed between the RH and both complex relative permittivity and loss tangent, and this was ascribed to the increased free water content at an elevated RH. The real part of the relative permittivity also reasonably increased

132

(R ≥ 0.82) with thread count of both woven and knitted fabric samples, and this was due to the

associated increase in the SVF.

On the other hand, the imaginary part of the relative permittivity and loss tangent of the

woven and some knitted samples exhibit weak/no correlations to the thread count and SVF. Since

an increase in the thread count (PPI, CPI and WPI) led to a higher SVF and the dielectric mixture

theory [2] states that a higher SVF leads to a higher imaginary part of the relative permittivity and

a higher loss tangent, strong correlations would exist between these loss terms and the SVF (and

also the thread count). As a potential interpretation for not observing the expected strong

correlation, the limited loss resolution of the microstrip line method was suggested.

Under the controlled SVF, the woven and knitted cotton fabric samples did not exhibit a

significant difference (p ≥ 0.19) in their complex permittivities and loss tangents. Although this

suggests that the construction is not a critical influencer to the dielectric properties of cotton

fabrics, it was still possible that the microstrip line method simply did not provide a required

resolution to distinguish the small differences in the permittivity. Hence, the further analyses on

the roles of the structural parameters were made based on the dielectric constant data obtained by

the patch antenna method, which is known to offer a better characterization accuracy in general.

Based on the patch antenna measurements, it was shown that with increase in RH, the

dielectric constants of the fabric samples decreased (R ≥ 0.96, except for K2 (R ≥ 0.69)) as also observed by the microstrip line measurements. However, by comparing the dielectric constant data obtained by the patch antenna method and the microstrip line method, a stronger correlation to the

RH was found by the patch antenna method. Since a previous work [42] reports a highly monotonic

RH-dependence of the dielectric constant of a cotton fabric sample, the patch antenna method

133

would offer better characterization accuracy in the real part of the relative permittivity of cotton fabrics.

The relationship between the thread count and the dielectric constants of the woven and knitted fabric samples were also studied by the patch antenna method, and it was found that the dielectric constants showed increasing tendency (R ≥ 0.82) with thread count. As discussed for the data set acquired by the microstrip line method, these increases in the dielectric constants were also reasonably associated with the SVF (R ≥ 0.91).

The effect of the fabric construction was examined by comparing the woven and knitted fabrics of the same SVFs. It was revealed that the woven fabric samples exhibited smaller dielectric constants than the knitted samples of the same SVFs at the same RH levels. Based on the calculations and measurements of the yarn orientation in the fabric samples, these differences between the woven and knitted fabric samples were successfully elucidated by the evidence that the woven samples had more fibers in the normal direction than the knitted samples – according to the mixing theory and the fiber anisotropy, the permittivity of a cotton fabric in its normal direction could be higher as more fibers are oriented in the normal direction [2,105,165–168].

Based on these findings and analyses from the investigations on the dielectric properties in relation to the fabric structural parameters at various RH levels, it was demonstrated that the fabric construction, thread count, SVF, fiber orientation and RH critically impact the resulting dielectric properties of cotton fabrics. Also, since the dielectric properties carry the fabric structural information, the microwave dielectric characterization, if performed accurately, could be a novel structural analysis tool for cotton fabrics. Furthermore, the developed structure-dielectric property relationships could be a reference point to design a fabric for optimal microwave systems on a textile platform.

134

CHAPTER 5. EXPERIMENT III Development of a Conformal Cotton Fabric Antenna for Wearable Thermotherapy

5.1. Introduction

Breast cancer, accounting for 30% of all cancer diagnoses in women, is the most common type of

cancer diagnosed for women in the United States, and the treatment of breast cancer is one of the

most active research areas in the field of health sciences [200,201]. As a supplementary technique

of treating breast cancers, microwave hyperthermia has been featured in clinics. Microwave

hyperthermia is a non-invasive cancer treatment where body temperature is locally/regionally

raised to 39–45 °C by a focused EM radiation to deactivate and damage cancer cells [202]. Because

of limited penetration depth of microwaves, the microwave hyperthermia usually targets tumors

situated on the skin to a depth of ~30 mm [203–205].

Within the given temperature range, it has been proven by both cytological studies

[206,207] and clinical trials [202,208] that malignant (cancerous) tumors substantially shrink while

normal tissues could withstand the heat for an extended period of time owing to their superior

blood flow that allows a rapid thermal dissipation. Heat produced during a breast hyperthermia

treatment can be beneficial, not only to damage malignant tumors, but also to promote the efficacy

of the traditional treatments. A number of clinical trials have shown that better treatment results

were obtained when radiotherapy [209,210] and chemotherapy [211,212] were performed in combination with a hyperthermia therapy.

135

Current microwave hyperthermia is performed in clinics mostly with an aperture antenna

(waveguide) [213]. Aperture antennas are relatively easy to operate, but because they are rigid and

bulky, patient discomfort is an emerging challenge for a continuous treatment [214,215]. Thus, a

development of a more comfortable, personal microwave device is highlof great necessity to

enable a longer treatment duration [214,216].

In order to reduce the antenna size, various compact antenna structures have been proposed and tested in literature. For instance, Montecchia [217], Singh [218] and Singh et al. [219]

examined the performance of the planner antennas built on printed circuit boards (PCBs).

Although these antennas were small and designed specifically for on-body hyperthermia

applications, they did not conform to the body contour because of the high rigidity of the PCBs.

More wearable forms of hyperthermia devices were discussed by Curto et al. [220], Curto

et al. [216] and Curto et al. [214] with patch antennas embedded in water bolus systems. The proposed antennas had water boluses to ease antenna impedance matching, reduce the applicator size and cool both the antenna and the skin surface [216]. It was found that a flared ground plane improved the radiation efficiency and the conformability of the applicator, which led to a satisfactory heating [216].

There are, however, notable drawbacks to include a water bolus [214,216,220] in a wearable system. Firstly, water is a highly lossy dielectric at microwave frequencies [141] and thus bring about low efficiency. Consequently, the input power requirement for the antenna was reported as high as 50 W [214]. Moreover, an additional power is required to circulate water for cooling. Because a power source needs to be physically carried by patients to run the wearable systems, this high-power requirement is a critical disadvantage. Secondly, the hyperthermia

136

applicators become large and heavy with water boluses. Thus, the wearability would deteriorate

for an expected long-time use.

The objective of this research is to present a wearable conformal patch antenna fabricated

with textile materials for a more comfortable breast hyperthermia therapy. The developed textile

antenna follows a female breast contour and consists of a copper-coated woven polyester fabric

for a radiating patch and a ground plane and a cotton fabric for a substrate and a padding. The

textile antenna is lightweight, breathable and flexible and therefore, can be inherently embedded

into clothing such as a brassiere or a slip. Moreover, having a dielectric permittivity close to air

due to the porous nature of textiles, the use of woven polyester accommodates antennas with a

high gain, a high efficiency and a wide bandwidth [28,29,77]. Thanks to this, the power

requirement could stay considerably low.

Although the use of a cotton fabric could be ideal for a comfortable antenna development

primarily because of its superior fabric texture and moisture absorbability than many synthetic

materials such as polyester [7,221], there are also several potential challenges. For example, the

dielectric properties of cotton fabrics are highly susceptible to the environmental factors such as the temperature and RH as discussed in the previous chapters, and thus an antenna made of cotton fabrics may experience a significant detuning during operation. It is well known that the impedance matching and EM performance of a patch antenna is impacted by the dielectric properties of the substrate and padding layers [28,43,77,103].

Therefore, the first RQ set in this work was to investigate how the changes in the RH affect the impedance of the cotton antenna. Then, the second RQ was to test if a sufficient heating could be obtained by a cotton antenna applicator with a low input power (1 W) at various RH levels. In order to answer these RQs, a hemispheric breast phantom was incorporated in this research, and

137

the dimensions of the textile antenna were optimized using a commercially available 3D full-wave

EM simulation software. The reflection coefficient of the antenna and the specific absorption rate

(SAR) distribution in the breast phantom were also calculated by using the EM software for theoretical analysis at various RH conditions. In order to examine the temperature increment distribution under thermal diffusion, a commercially available transient thermal simulator was used. After prototyping the textile antenna, the electrical measurements were performed using a

VNA, and the temperature measurements were conducted using a thermometer for comparisons with the simulated data.

5.2. Research Questions

The operating frequency of a patch antenna is highly influenced by the dielectric constant of the substrate and padding, and hence an antenna made of cotton fabrics may experience a significant detuning during operation under varying RH environment because of the RH dependence of the dielectric properties of cotton fabrics. Thus, in order to develop an effective antenna for microwave hyperthermia, understanding the effect of RH on the impedance matching is critical. As a frequency of study, 2.45 GHz is selected since this is the ISM band and has been widely incorporated in clinical studies [215]. Accordingly, the following RQ was synthesized.

RQ1: Does a cotton fabric antenna operate in the RH range of 20% to 80% with

a good impedance matching (reflection coefficient < −10 dB) at an industrial,

scientific and medical (ISM) band (2.45 GHz)?

138

One of the fundamental requirements for a wearable hyperthermia device is to achieve a sufficient

heating at a low input power under various RH conditions. Based on the typical treatment depth in a superficial breast hyperthermia [203–205], the heating capability needs to be investigated at the tissue depths of 5 mm and 15 mm. Thus, the formulated RQ was as below.

RQ2: Does a cotton antenna offer a sufficient heating in the superficial region (in

the depths of 5 mm and 15 mm) under the RH conditions of 20% to 80% with an

low input power (1 W)?

5.3. Methods

Based on the formulated RQs, two research phases were designed. The first phase examines the

effect of the RH on the antenna impedance matching through EM simulations and measurements

of the reflection coefficient. In the following research phase, temperature rises under microwave

heating are both theoretically and experimentally investigated by incorporating a homogeneous

breast model. Figure 5-1 illustrates the flowchart for these experiments.

139

Note: The numbers in parentheses are the relevant section numbers. Figure 5-1. Flowchart for Experiment (III).

5.3.1. Breast model

In microwave breast hyperthermia, the expected treatment effect varies according to biophysical

(perfusion and dielectric) and dimensional (breast size and composition and tumor location) characteristics of breasts [214]. However, these breast characteristics differ significantly from individual to individual, and therefore, a microwave applicator needs to be customized for each patient in clinics [214,215]. As a model study, a simple homogeneous breast phantom was employed in this work. The breast phantom had a hemispheric shape with a radius of 50 mm and the dielectric properties given in Table 5-1.

140

Table 5-1. Materials properties of the breast phantom. Property Value Reference Specific heat (J·g-1·K-1) 3.63 [222] Thermal conductivity (W·m-1·K-1) 0.55 [222] Density (Kg·m-3) 900 [222] Complex relative permittivity at 2.45 GHz 48.5−23.28j [223]

5.3.2. Antenna design

The proposed patch antenna consisted of a radiating patch, a ground plane, a substrate, a

padding layer, and an SMA connector for powering. A 0.08 mm-thick copper-plated conductive

woven polyester fabric with a fabric weight of 90 g/m2 (LessEMF Inc.) was selected for the patch

and ground plane due to its sufficiently low sheet resistance (0.03 Ω/sq). For the substrate and

padding, the 1.4 mm-thick woven cotton fabric (W3; Table 5-2) was selected.

Table 5-2. Dielectric properties of the cotton fabric sample (W3).

' RH (%) Dielectric constant (εr) Loss tangent (tanδ) 80 1.29 0.037 65 1.29 0.033 20 1.21 0.009 Note: These dielectric constant and loss tangent were respectively determined by the patch antenna method and microstrip line method in Chapter 4.

One of the criteria to select the padding and substrate material was to have a small variation in the dielectric constant (real part of the permittivity) under varying RH levels because a larger variation may lead to a significant antenna detuning (shift in the operating frequency) during operation [103,224]. Another requirement was to have a smaller dielectric constant for a wider bandwidth and a higher gain [28,29,77,224]. Although W2 had a smaller average dielectric constant than W3 (Table 5-3) and both W1 and W2 had smaller dielectric constant variations

141

(Table 5-4) than W3, the yarns in these two samples were too loose to be dimensionally stable for garment applications. Thus, the W3 sample, which had the smallest average dielectric constant and the smallest dielectric constant variation over the 20% to 80% RH range among the structurally stable fabric samples, was chosen for the substrate and padding in this work.

Table 5-3. Average dielectric constants of the cotton fabric samples over the RH range of 20% to 80% (calculated from the data obtained by the patch antenna method in Chapter 4).

Sample# Average dielectric constant (20%–80% RH) W1 1.26 W2 1.23 W3 1.26 W4 1.36 W5 1.39 K1 1.32 K2 1.31 K3 1.34 K4 1.44 K5 1.52

Table 5-4. RH dependences of the dielectric constant of the cotton fabric samples (calculated from the data obtained by the patch antenna method in Chapter 4).

Difference in the dielectric constant (Δε' ) Coefficient of variation (%) in the RH range Sample # r at 80% and 20% RH of 20% to 80% W1 0.051 1.56 W2 0.058 2.67 W3 0.080 2.76 W4 0.127 3.88 W5 0.144 4.19 K1 0.129 3.98 K2 0.135 4.17 K3 0.151 4.44 K4 0.202 5.18 K5 0.218 5.90

For the designed patch antenna geometry, the microwave radiation is achieved by the fringing fields that are generated due to the non-uniform electric field distribution between the patch and the ground plane [45,225]. Because the ground plane serves as a back reflector, the

142

maximum radiation is directed in the normal direction from the patch [175]. This could be ideal

for the hyperthermia application since the focused microwave beam helps to deposit concentrated

thermal energy in the target tumor [216].

The dimensions of the antenna were optimized at 2.45 GHz at 65% RH (21 °C) by using a

3D EM simulator with a finite element solver (Ansys HFSS®). The optimized dimensions in the

cross-sectional cuts are illustrated in Figure 5-2. The optimal width and length of the patch sheet was 16 mm by 44 mm, respectively.

Figure 5-2. Sketch of the designed patch antenna conforming the hemispheric breast phantom in the (a) YZ-plane and (b) ZX-plane (not to scale).

5.3.3. Theoretical evaluation

In order to theoretically evaluate the EM performance of the proposed wearable device, 3D full wave EM simulations were performed by using Ansys HFSS®. The reflection coefficient of

the textile antenna and the SAR distribution in the breast model were computed with an input power of 1 W in the three RH levels: 80%, 65% and 20% RH at 21 °C.

Since the phantom had a high thermal conductivity (0.55 W·m-1·K-1), 3D transient thermal

analysis was also performed by using the Ansys Transient Thermal simulator. By establishing an

EM-thermal link [226,227] in the Ansys Workbench software (Figure 5-3), the SAR distribution 143

obtained in the EM simulation was fed into the thermal analysis as a heat source. The materials properties used in the simulation are given in Table 5-5. All these materials properties were assumed to be independent of the temperature. The temperature increment in the breast tissue were monitored for 900 seconds of continuous microwave irradiation.

Figure 5-3. One-way EM-thermal link in the Ansys Workbench software.

Table 5-5. Materials properties used in the thermal simulation. Isotropic thermal conductivity Materials Density (kg·m-3) Specific heat (J·g-1·K-1) (W·m-1·K-1) Phantom 900 [222] 3.63 [222] 0.55 [222] Cotton fabric (W3) 165 1.5 [228] 0.09 [228] Cu fabric 1000 [229] 0.39 [230] 385 [231] Gold (SMA) 19300 [232] 0.13 [230] 314 [231] Air 1.225 [232] 1.0 [233] 0.024 [231] Note: The density of the cotton fabric (W3) was calculated from the values given in Table 3-4.

5.3.4. Preparation of breast phantom

The breast phantom was prepared as follows [222]. 10.46 g of agar, 3.76 g of sodium chloride,

0.20 g of sodium azide were completely dissolved in 337.50 g of deionized water, followed by

144

heating on a stove. Once the solution reached to the boiling point, the heat was immediately

removed and 8.44 g of TX151 and 33.75 g of Polyethylene powder were sprinkled and mixed

uniformly. The liquid was then poured into a 3D-printed breast mould and then cooled at room

temperature for 24 hours to form the hemispheric shape (Figure 5-4(a)). The phantom was

maintained sealed at room condition for preservation.

Figure 5-4. (a) Breast phantom, (b) antenna sample (ground plane side), (c) antenna sample (antenna element side) placed in an antenna folder, (c) padding layer placed on the patch, (e) temperature probes, and (f) antenna sample placed in the holder for measurements.

5.3.5. Antenna fabrication

In order to fabricate the conformal antenna with the geometry given in Figure 5-2, the flat-pattern

method [234] was used. By following Thyssen [235], the optimized antenna patterns for the patch,

ground plane, substrate and padding layers were created (Figure 5-5(a)). Next, the copper fabric

and cotton fabric (W3) were cut with a Cricut Explore AirTM electronic cutting machine (Provo

Craft & Novelty, Inc) into these dimensions (Figure 5-5(b)). Then, the patch, ground and substrate

145

pieces were respectively jointed together with a cover stitch to construct the hemispheric structure.

The patch and ground plane were mounted on the substrate with a heated polyamide fusible web

(Bostik Inc.). A 50 Ω Panel-mount SMA connector (Amphenol Corp.) was soldered to the patch

and ground plane and then the connection was reinforced with a silver conductive epoxy adhesive

(MG Chemicals Ltd.). Because the conductive fabric had a low melting temperature, this

additional process with the silver epoxy was required to reinforce the resulted cold solder joint.

The completed antenna sample is shown in Figure 5-4(b-d).

Figure 5-5. (a) Flat patterns of the antenna components and (b) cut fabric pieces.

5.3.6. Experimental evaluation

Prior to electrical and thermal measurements, the antenna sample was conditioned at 80%,

65% and 20% RH (21 °C) in the same manner described in Section 3.3.3. Then, the antenna sample

was placed inside the PLA template with the breast phantom (Figure 5-4(c-f)) to ensure that the hemispheric shape of the antenna stayed intact during the measurements (Figure 5-2). Based on

146

the two-port S-parameter network [236], the reflection coefficient (S11) of the antenna sample was measured in the frequency range of 1 to 6 GHz by using a calibrated VNA (Agilent E5071C ENA

Series Network Analyzer) to evaluate the impedance matching.

For thermal measurements, 1-W power was supplied to the antenna as described in Figure

5-6. A 20 dB-gain block (Sireen 2.4GHz 1-W High Gain Amplifier Module) was connected to a computer-controlled 10-dBm-signal generator (Windfreak Technologies SynthNV RF Signal

Generator) to supply the antenna sample with a power of 30 dBm (1 W) at 2.45 GHz. A thermometer (Fluke 52 II Dual Probe Digital Thermometer) with two physical probes monitored the temperature rises in the breast phantom at the two tissue locations in 5 mm and 15 mm depths

(Figure 5-2) for 900 seconds. All thermal measurements were administered inside the plastic template, but this plastic housing was merely for accurate antenna characterization purposes and was not designed as a part of the antenna system.

Figure 5-6. Antenna powering setup for temperature measurement.

5.4. Results and Discussion

5.4.1. Reflection coefficient

Figure 5-7 and Table 5-6 show the simulated and measured reflection coefficients and operating

147

frequencies of the designed antenna in the frequency range of 1 to 4 GHz. Under the standard atmospheric condition (65% RH), the impedance of the fabricated antenna was well matched to the source impedance (50 Ω) at the frequency of 2.45 GHz. The measured reflection coefficient was −30.6 dB, while the simulated value was −25.9 dB (Table 5-7). The effect of the RH on the reflection coefficient was found to be insignificant in the range of 20% to 80% RH. Both simulations and measurements indicated that the reflection coefficients could remain below −10 dB at 2.45 GHz regardless of the RH (Table 5-7). This successful impedance matching confirms that the design of the patch antenna was valid in the wide range of humidity conditions (20%–80%

RH). Having the wide fractional bandwidth (FBW) (Table 5-7), the antenna was proven to be operational in the given RH range.

Figure 5-7. (a) Simulated and (b) measured reflection coefficients of the antennna applicator.

Table 5-6. Operating frequencies of the simulated and measured and antennna applicator. RH (%) Simulated operating frequency (GHz) Measured operating frequency (GHz) 80 2.45 2.46 65 2.45 2.46 20 2.50 2.53 Note: Operating frequency is the frequency at which the reflection coefficient becomes the minimum.

148

Table 5-7. Simulated and measured reflection coeffieients and FBWs at 2.45 GHz. Simulated Measured RH (%) Reflection coefficient (dB) FBW (%) Reflection coefficient (dB) FBW (%) 80 −24.9 20.4 −21.2 33.9 65 −25.9 20.4 −30.6 31.3 20 −20.2 20.4 −21.6 32.0

5.4.2. SAR distribution

The SAR distribution in the breast phantom was successfully calculated in the standard condition

and its YZ and ZX slices are given in Figure 5-8. It was found that the major EM absorption (>

100 W/kg) was observed near the center of the patch. The SAR as a function of the tissue depth

along the normal direction from the tip of the tissue is given in Figure 5-9. This plot illustrates

that there was no significant energy absorbed in the deeper (> ~25 mm) tissue, which indicates

that the proposed system is only applicable to superficial tumors.

Figure 5-8. (a) YZ and (b) ZX cuts of the simulated SAR distribution in the standard condition (65%RH).

149

Figure 5-9. Simulated SARs as a function of the tissue depth.

The SAR distributions at 80% and 20% RH are respectively given in Figure 5-10 and

Figure 5-11. In comparison to the 65% RH case, the heating pattern was not of significant difference. In terms of the heat intensity, however, it was found that heating becomes more effective when the RH was lowered (Figure 5-8 to Figure 5-9). The most probable reasonn for this observation would be the lower dielectric loss of the cotton substrate and padding under the drier condition (Table 5-2). According to the patch antenna theory [45,103], a lower substrate dielectric loss helps patch antennas to have a higher gain and a higher efficiency. Moreover, the

EM dissipation in the padding layer could also be reduced by having a smaller dielectric loss

[45,103], allowing a higher heating efficiency. In fact, by lowering the RH from 80% to 20%, the total power deposited in the cotton fabric was reduced by more than 10% of the input power as given in Table 5-8.

150

Figure 5-10. (a) YZ and (b) ZX cuts of the simulated SAR distribution at 80% RH.

Figure 5-11. (a) YZ and (b) ZX cuts of the simulated SAR distribution at 20% RH.

Table 5-8. Calculated rates of energy deposition and heating efficiencies with an input power of 1 W. Rate of energy deposited (W) in the Rate of energy deposited (W) in Heating efficiency RH (%) breast phantom the cotton fabric (%) 80 0.782 0.152 78.2 65 0.795 0.137 79.5 20 0.854 0.040 85.4 Note: The heating efficiency (%) was calculated by dividing the deposited power in the breast phantom by the input power, and then by multiplying it by 100.

151

5.4.3. Temperature rise distribution

The simulated temperature elevations after continuous heating at 65% RH are given in Figure

5-12. It was observed that there is a significant thermal diffusion in the tissue due to its high thermal conductivity (0.55 W·m-1·K-1). After 900 seconds of heating, the computed temperature rise was over 8.0 °C near the center of the patch under this RH condition. The temperature rises at the 20% and 80% RH levels are shown in Figure 5-13 and Figure 5-14. By comparing these plots of different RH levels, it is seen that the high temperature (> 8.0 °C) region became slightly larger with decrease in RH, and this was due to the higher SAR at a lower RH.

Figure 5-12. Simulated temperature increment distributions at 65% RH (t = 0–900 s).

152

Figure 5-13. Simulated temperature increment distributions at 80% RH (t = 0–900 s).

153

Figure 5-14. Simulated temperature increment distributions at 20% RH (t = 0–900 s).

The temperature rises calculated at the 5 mm- and 15 mm-deep tissue locations are plotted in Figure 5-15(a) as a function of the heating duration. It was found that the lower RH gave slightly higher temperature rises during the course of heating. However, for all the three RH levels, more than 8.0 °C and 3.5 °C of temperature changes were observed at the depths of 5 mm and 15 mm at the end of 900 seconds of heating, respectively (Table 5-9). These high temperature rises suggest that a hyperthermia therapy could be theoretically possible with the proposed antenna applicator in the wide range of RH.

154

Figure 5-15. (a) Simulated and (b) measured temperature increments at the 5 mm and 15 mm locations in the breast phantom.

Table 5-9. Simulated and measured temperature rises at the tissue depths of 5 mm and 15 mm after 900 seconds of continuous heating. Simulated temperature rise (°C) Measured temperature rise (°C) RH (%) 5 mm 15 mm 5 mm 15 mm 80 8.1 3.8 4.7 2.3 65 8.2 3.8 4.8 2.4 20 8.6 4.0 4.9 2.5

The measured temperature rises are given in Figure 5-15(b). After 900 seconds of heating at 65% RH, 4.7 °C and 2.3 °C of temperature rises were observed in the tissue locations of 5 mm and 15 mm depths, respectively (Table 5-9). The temperature measurements at 80% and 20% RH levels showed over 4.7 °C and 2.3 °C of temperature rises at these locations (Table 5-9). In addition, it was found that a slightly more effective heating was obtained at a lower RH, and this tendency was due to a smaller dielectric loss of the cotton fabric in a drier condition as theoretically calculated. These results demonstrate that the temperature rises obtained by the proposed hyperthermia applicator could be satisfactory for the potential hyperthermia applications [215].

Although the heating performance of the proposed antenna applicator was found to meet the temperature requirements [202–205] for the breast hyperthermia application, the measured

155

temperature rises were significnatly less than the calculated results (Figure 5-15(a)). One possible attribute could be the limited fabrication accuracy of the antenna sample. In the simulation model, the antenna was regarded to perfectly conform the hemispheric contour of the breast phantom. In prototyping, however, the textile antenna was constructed from the flat patterns, and thus it did not have the perfect hemispheric surfaces even with the help of the antenna housing. Because it has been reported that the radiation performance of textile antennas is highly sensitive to flexing

[19,21,28], the irregular surfaces of the textile antenna sample could have lowered the radiation efficiency. Additionally, the cold solder joint of the conductive fabric and the SMA connector could have led to an RF power loss at the insertion. Although the silver epoxy adhesive was applied over the solder to help the electrical conduction, the imperfect electrical joint could have led to an unexpected power loss. Another possible reason for observing the smaller temperature rises than the simulations would be the heat leakage into the ambient air from the heated tissue. Because the flow of ambient air which could promote the thermal dissipation was not included in the calculation models, this could be another attribute for the difference.

5.5. Chapter Conclusions

A textile conformal antenna was designed and fabricated with the cotton fabric, and the EM and

heating performance were simulated and measured using a tissue-equivalent phantom. From the

simulations, it was found that the effective heating is limited to a relatively superficial region (<

25 mm) due to the high EM dissipation in the tissue. In addition, the higher dielectric loss of the

substrate at a higher RH was found to critically increase the dielectric loss in the padding and

156

substrate (> 10% of the input power), leading to an inferior heating performance. On the other

hand, both simulations and measurements show that the dielectric constant variation due to the RH

had only a minor impact on the antenna impedance matching since the cotton fabric antenna had

a wide impedance bandwidth.

The temperature measurements with the antenna sample showed that the tissue could be

raised by over 4.7 °C and 2.3 °C at the depths of 5 mm and 15 mm after 900 seconds of heating,

respectively. Also, a better heating performance was obtained at a lower RH due to a lower

dielectric loss of the cotton substrate and padding as simulated. Although the measured

temperature increments were smaller than those of simulated, this reasonable agreement between

the simulations and measurements provides an evidence that a satisfactory heating for a

hyperthermia treatment is possible with the proposed textile antenna applicator in low power (1

W) consumption. Also, since the temperature elevation in the tissue is almost proportional to the

input power, a higher temperature rise could be reasonably achieved by increasing the input power

when a higher temperature is required.

Future work is recommended to improve the fabrication accuracy of the textile antenna.

As suggested in Section 5.4.3, one possible attribute for causing the difference between the simulated and measured temperature rises would be the limited accuracy of the spherical contour of the textile antenna sample. Since the textile antenna components used in this work were all planar, the perfect hemispheric surface could not be obtained by the flat pattern method. In a future work, an investigation of applicability of some advanced fabrications techniques such as 3D knitting is recommended to achieve a better conformability.

Lastly, it should be noted that the results and conclusions obtained in the current research are not intended to (and should not) directly apply to the case of human tissues. The employed

157

breast phantom was homogeneous and does not represent the actual biophysical behaviours of

human body. In the real female breasts, there are various components including but not limited to

skin, fats, benign and malignant tumors and blood vessels of a variety of dielectric, electrical and thermal properties.

158

CHAPTER 6. CONCLUSIONS

This paper presented the structure-dielectric property relationships in cotton fabrics of various

structures in a wide range of frequencies and their applications in developing a wearable medical

device on a cotton fabric platform. In Experiment I, the low-frequency dielectric properties of

woven and knitted cotton fabrics were discussed in relation to the fabric construction, thread count

and SVF. From the dielectric measurements at five different RH levels, three major relaxations,

electrode polarization, interfacial polarization and dipolar polarization of bound water were

observed in the frequency range of 20 Hz to 1 MHz.

The effect of the thread count and SVF were examined with the dielectric data at 1 MHz.

It was found that with increase in thread count (PPI, CPI and WPI), the real part of the permittivity

increased, and this was primarily elucidated with the increase in the SVF. On the other hand, the

imaginary part of the relative permittivity and loss tangent did not show a clear monotonic trend

to the thread count or SVF at the elevated RH levels, and this was interpreted that additional mixing

factors such as the structure-dependent interfacial polarization and/or electrode polarization could also be influencing the dielectric properties of the highly moist cotton fabrics.

The effect of the fabric construction was investigated through the comparisons of the dielectric properties of woven and knitted fabrics of the same SVFs. It was revealed that the fabric construction plays an important role in the resulting dielectric properties – for all the comparisons of the same SVF, the knitted fabrics showed higher values of the complex relative permittivity and loss tangent than the woven fabrics. This observation was interpreted that although the current mainstream in the low-frequency dielectric investigations on textile fabrics deals primarily with the SVF and RH in literature [108,121,128], fabric construction also need to be treated as a key

159

influencer as supported by the microstructural anisotropic dielectric properties of cellulose fibers

[7,105,152], the dielectric mixture theory (macroscopic shape effect) [2] and the orientational structural-dependence of the interfacial polarization [87,169,170].

The first phase of Experiment II studied the role of the fabric construction, thread count,

SVF on the complex relative permittivity and loss tangent of the cotton fabric samples by using the microstrip line method in the frequency range of 100 MHz to 6 GHz at five RH levels. There was a general tendency that as the frequency increases, the real part of the relative permittivity decreased at the given RH levels because of the dipolar relaxation of free water [195] that were absorbed by the cotton fibers. Decreasing trends with increase in frequency were also observed for the imaginary part of the relative permittivity and loss tangent, but since the dielectric loss due to the dipolar relaxation of free water is known to increase at this frequency range, these downward trends in the imaginary part of the relative permittivity and loss tangent were rather attributed to the limited loss resolution of the microstrip line method.

At 2.45 GHz, the complex relative permittivity and loss tangent were found to increase with the RH because of an increased free water content at an elevated RH [141]. The thread count also increased the real part of the relative permittivity of both woven and knitted fabrics, and this was associated with increased SVFs.

However, the imaginary part of the relative permittivity and loss tangent of woven and some knitted fabrics predominantly exhibited weak or no correlations to the thread count or SVFs.

Because an increase in the thread count led to a higher SVF and the dielectric mixture theory [2] states that a higher SVF leads to a higher imaginary part of the relative permittivity and a higher loss tangent, strong correlations would exist between the these loss terms and the SVF (and also

160

the thread count). As a possible interpretation for not observing the expected strong correlation in the woven samples, the limited loss resolution of the microstrip line method was suggested.

Under the controlled SVF, the woven and knitted cotton fabric samples did not exhibit a significant difference (p-value, p ≥ 0.19) in their complex permittivities and loss tangents obtained by the microstrip line method. However, because the microstrip line method has relatively low resolution in dielectric characterization, further analyses on the roles of the structural parameters were made based on the dielectric constant data obtained by the patch antenna method.

From patch antenna measurements in the vicinity of 2.45 GHz, it was demonstrated that with increase in RH, the dielectric constants of the fabric samples decreased as also observed by the microstrip line measurements. The relationship between the thread count and the dielectric constant of the woven and knitted fabrics were also studied by the patch antenna method, and it was found that the dielectric constant could increase with thread count because of an associated increase in the SVF as supported by the dielectric mixture theory [2,108].

The effect of the fabric construction was examined by comparing the woven and knitted fabrics of the same SVFs at near 2.45 GHz. Unlike the microstrip line method, the patch antenna method unveiled that the woven fabrics exhibit smaller dielectric constants than the knitted samples (p < 0.01) under the controlled SVF. Based on the calculations and measurements of the yarn orientation in the fabric samples, these dielectric constant differences between the woven and knitted fabric samples were successfully elucidated by the evidence that the woven samples had more fibers in the normal direction than the knitted samples of the same SVF, as supported by the dielectric mixture theory and the fiber anisotropy [2,105,165–168]. Based on these findings and analyses from the investigations on the microwave dielectric properties in relation to the fabric structural parameters at various RH levels, it was demonstrated that the fabric construction, thread

161

count, SVF, fiber orientation and RH critically impact the resulting dielectric properties of cotton

fabrics.

Experiment III presented a cotton fabric antenna specifically designed for wearable breast thermotherapy. A cotton fabric with the optimal dielectric properties (the W3 sample) was chosen based on the results from Experiment II and was incorporated as the substrate and padding layers

of the antenna, and the EM and heating performance of the developed antenna were both

theoretically and experimentally examined with a tissue-equivalent phantom in relation to the

dielectric properties of the cotton fabric under three RH conditions.

From the simulations, it was found that the effective heating is concentrated in a relatively

superficial region (< 25 mm) due to the high EM dissipation in the tissue. In addition, the higher

dielectric loss of the substrate at a higher RH was found to critically increase the dielectric loss in

the padding and substrate (> 10% of the input power), leading to an inferior heating performance.

On the other hand, both simulations and measurements indicated that the dielectric constant

variation due to the RH led to only a minor impact on the antenna impedance matching since the

cotton fabric antenna had a wide impedance bandwidth.

The temperature measurements with the antenna sample demonstrated that the tissue could

be raised by over 4.7 °C and 2.3 °C at the depths of 5 mm and 15 mm after 900 seconds of heating,

respectively. Also, a better heating performance was obtained at a lower RH due to a lower

dielectric loss in the cotton substrate and padding layers as expected from the simulations.

Although the measured temperature increments were smaller than those of simulated, the

reasonable agreement between the simulations and measurements provides an evidence that a

satisfactory heating for a hyperthermia treatment is possible with the proposed textile antenna

applicator in low power (1 W) consumption.

162

CHAPTER 7. RECOMMENDATIONS

Four recommendations are suggested for future work. Firstly, as explored in Experiment

I and Experiment II, the structural parameters critically impacted the dielectric properties of

cotton fabrics, but only two of the most fundamental fabric constructions, plain weave and plain

knit, were studied in this research. Since knitting and weaving processes offer almost unlimited

number of design options in fabric production, future work is suggested to investigate the dielectric

properties of cotton fabrics in a more variety of constructions.

Another future topic is accurate characterization of the broadband complex permittivity of

cotton fabrics at microwave frequencies. As discussed in Chapter 4, both microstrip line and patch

antenna methods have several drawbacks – microstrip line method offered relatively low

characterization resolution and patch antenna method offered only the real part of the relative

permittivity only at a single frequency. Future work is encouraged to develop a standardized technique that is specifically tailored for textile fabrics and accurately measures the broadband complex permittivity.

With respect to the wearable thermotherapeutic apparatus developed on the cotton fabric platform in Experiment III, future work is recommended to improve the fabrication accuracy and conformability of the textile antenna. As suggested in Section 5.4.3, one possible attribute for causing the difference between the simulated and measured heating performance would be the limited accuracy of the spherical contour of the textile antenna sample. Since the textile antenna components used in this work were all planar fabrics, a smooth hemispheric surface was not be able to obtain. As a potential solution, an investigation on the applicability of some advanced

163

fabrication techniques (e.g., 3D knitting) is recommended to achieve a better fabrication accuracy and conformability.

Lastly, the breast phantom employed in this work was homogeneous and did not fully consider the actual biophysical behaviours of human body. In the real female breasts, there are various components including but not limited to skin, fats, benign and malignant tumors and blood vessels of various dielectric, electrical and thermal properties. Consequently, thermal energy deposition and thermal diffusion are expected to be much more complex. Since temperature management is key in hyperthermia, it is recommended to incorporate a more realistic breast phantom to further examine the heating performance of the developed textile antenna.

164

REFERENCES

[1] Bal K, Kothari VK. Measurement of Dielectric properties of textile materials and their applications. Indian J. Fibre Text. Res. 2009;34:191–199.

[2] Sihvola AH. Electromagnetic mixing formulas and applications. London: Institution of Electrical Engineers; 1999.

[3] Adanur S. Handbook of Weaving. CRC Press; 2000.

[4] Carvalho V, Monteiro JL, Soares FO, et al. Yarn Evenness Parameters Evaluation: A New Approach. Text. Res. J. 2008;78:119–127.

[5] Karthik GT and T. Process control and yarn quality in spinning. Boca Raton, Florida: CRC Press; 2016.

[6] Haleem N, Wang X. Recent research and developments on yarn hairiness. Text. Res. J. Princet. 2015;85:211–224.

[7] Morton WE, Hearle JWS. Physical Properties of Textile Fibres. Woodhead Publishing; 2008.

[8] IHS Markit. Chemical Economics Handbook [Internet]. 2015 [cited 2018 Jun 18]. Available from: https://ihsmarkit.com/products/fibers-chemical-economics- handbook.html.

[9] El-Mogahzy YE-B, Chewning CH, Incorporated C. Cotton fiber to yarn manufacturing technology : optimizing cotton production by utilizing the Engineered Fiber Selection® system. 2nd ed. Cary, NC: Cotton Incorporated; 2002.

[10] Senthilkumar M, Sampath MB, Ramachandran T. Moisture Management in an Active Sportswear: Techniques and Evaluation—A Review Article. J. Inst. Eng. India Ser. E. 2012;93:61–68.

[11] Özdil N, Süpüren G, Özçelik G, et al. A study on the moisture transport properties of the cotton knitted fabrics in single.

[12] Cotton Australia. Uses of Cotton [Internet]. 2018 [cited 2018 Aug 18]. Available from: http://cottonaustralia.com.au/australian-cotton/basics/uses-of-cotton.

[13] Sun G, Yoo HS, Zhang XS, et al. Radiant Protective and Transport Properties of Fabrics Used by Wildland Firefighters. Text. Res. J. 2000;70:567–573.

[14] Wiegerink JG. Moisture relations of textile fibers at elevated temperatures. J. Res. Natl. Bur. Stand. 1940;24:645.

165

[15] Taylor HM. Tensile and Tearing Strength of Cotton Cloths. J. Text. Inst. Trans. 1959;50:T161–T188.

[16] McNally JP, McCord FA. Cotton Quality Study: V: Resistance to Abrasion. Text. Res. J. 1960;30:715–751.

[17] Multimedia produced for CI by M. The science of dyeing & finishing : an interactive guide to the basics of dyeing and finishing. Cotton Inc., Cary, NC; 2007.

[18] Seymour S. Fashionable technology: the intersection of design, fashion, science, and technology [Internet]. Wien: Springer,; 2008. Available from: https://catalog.lib.ncsu.edu/record/NCSU2167654.

[19] Xu F, Zhu H, Ma Y, et al. Electromagnetic performance of a three-dimensional woven fabric antenna conformal with cylindrical surfaces. Text. Res. J. 2017;87:147–154.

[20] Alonso-Gonzalez L, Ver-Hoeye S, Fernandez-Garcıa M, et al. Three-Dimensional Fully Interlaced Woven Microstrip-Fed Substrate Integrated Waveguide. Prog. Electromagn. Res. 2018;163:14.

[21] Yao L, Qiu Y. Design and electromagnetic properties of conformal single-patch microstrip antennas integrated into three-dimensional orthogonal woven fabrics. Text. Res. J. 2015;85:561–567.

[22] Zhang S, Chauraya A, Seager R, et al. Fully fabric knitted antennas for wearable electronics. 2013 USNC-URSI Radio Sci. Meet. Jt. AP- Symp. 2013. p. 215.

[23] Cupal M, Raida Z. Textile Integrated Waveguide Switch. 2018 Int. Conf. Broadband Commun. Gener. Netw. Multimed. Appl. CoBCom. 2018. p. 1–5.

[24] Alharbi S, Chaudhari S, Inshaar A, et al. E-Textile Origami Dipole Antennas With Graded Embroidery for Adaptive RF Performance. IEEE Antennas Wirel. Propag. Lett. 2018;17:2218–2222.

[25] Zhu K, Militello L, Kiourti A. Antenna-Impregnated Fabrics for Recumbent Height Measurement on the Go. IEEE J. Electromagn. RF Microw. Med. Biol. 2018;2:33–39.

[26] Kiourti A. Textile-Based Flexible Electronics for Wearable Applications: from Antennas to Batteries. :4.

[27] Shahariar H, Soewardiman H, Jur JS. Fabrication and packaging of flexible and breathable patch antennas on textiles. SoutheastCon 2017. 2017. p. 1–5.

[28] Mukai Y, Bharambe VT, Adams JJ, et al. Effect of bending and padding on the electromagnetic performance of a laser-cut fabric patch antenna. Text. Res. J. 2018;0040517518801202.

166

[29] Salvado R, Loss C, Gonçalves R, et al. Textile Materials for the Design of Wearable Antennas: A Survey. Sensors. 2012;12:15841–15857.

[30] Zhang RQ, Li JQ, Li DJ, et al. Study of the Structural Design and Capacitance Characteristics of Fabric Sensor [Internet]. Adv. Mater. Res. 2011 [cited 2018 Jun 5]. Available from: http://www.scientific.net/AMR.194-196.1489.

[31] Hasegawa Y, Shikida M, Ogura D, et al. Novel type of fabric tactile sensor made from artificial hollow fiber. 2007 IEEE 20th Int. Conf. Micro Electro Mech. Syst. MEMS. 2007. p. 603–606.

[32] Feddes B, Gourmelon L, Langereis GR. Materials for capacitive sensors [Internet]. 2008 [cited 2018 Aug 19]. Available from: https://patents.google.com/patent/WO2008152588A2/en?q=fabric&q=capacitive+sensor &q=cotton&oq=fabric+capacitive+sensor+cotton.

[33] Zhangmin Y. Sensing system utilizing multifunctional fabric, method, and object [Internet]. 2017 [cited 2018 Aug 19]. Available from: https://patents.google.com/patent/WO2017174031A1/en.

[34] Kawabata S, Niwa M. Fabric Performance in Clothing and Clothing Manufacture. J. Text. Inst. 1989;80:19–50.

[35] Ngan HYT, Pang GKH, Yung NHC. Automated fabric defect detection—A review. Image Vis. Comput. 2011;29:442–458.

[36] ASTM D1425. Standard Test Method for Evenness of Textile Strands Using Capacitance Testing Equipment. 2014.

[37] Cerovic DD, Asanovic KA, Maletic SB, et al. Comparative study of the electrical and structural properties of woven fabrics. Compos. Part B Eng. 2013;49:65–70.

[38] Cerovic DD, Dojcilovic JR, Asanovic KA, et al. Dielectric investigation of some woven fabrics. J. Appl. Phys. 2009;106:084101.

[39] Mustata FSC, Mustata A. Dielectric Behaviour of Some Woven Fabrics on the Basis of Natural Cellulosic Fibers. Adv. Mater. Sci. Eng. [Internet]. 2014 [cited 2018 Jun 5]; Available from: https://www.hindawi.com/journals/amse/2014/216548/.

[40] Ouyang Y, Chappell WJ. High Frequency Properties of Electro-Textiles for Wearable Antenna Applications. IEEE Trans. Antennas Propag. 2008;56:381–389.

[41] Hertleer C, Rogier H, Langenhove LV. The effect of moisture on the performance of textile antennas. 2009 2nd IET Semin. Antennas Propag. Body-Centric Wirel. Commun. 2009. p. 1–1.

[42] Hertleer C, Laere AV, Rogier H, et al. Influence of Relative Humidity on Textile Antenna Performance. Text. Res. J. 2010;80:177–183.

167

[43] Sankaralingam S, Gupta B. Determination of Dielectric Constant of Fabric Materials and Their Use as Substrates for Design and Development of Antennas for Wearable Applications. IEEE Trans. Instrum. Meas. 2010;59:3122–3130.

[44] Lyons DW, Seabolt JA, Graham J. The Dielectric Properties of Various Cotton Varieties. Text. Res. J. 1973;43:110–115.

[45] Balanis CA. Advanced engineering electromagnetics. 2nd ed. Hoboken, N.J.: Wiley; 2012.

[46] Baker-Jarvis J. Dielectric and conductor-loss characterization and measurements on electronic packaging materials. Boulder, CO: U.S. Department of Commerce, National Institute of Standards and Technology; 2001.

[47] Ravelo B, Thakur A, Saini A, et al. Microstrip Dielectric Substrate Material Characterization with Temperature Effect. Appl. Comput. Electromagn. Soc. 2015;30.

[48] Bahl IJ, Trivedi DK. A designer’s guide to microstrip line. Microwaves. 1977;174–182.

[49] Cotton Incorporated. Cotton Fiber Tech Guide - Cotton Morphology and Chemistry [Internet]. Cotton Inc. 2018 [cited 2018 Jun 18]. Available from: https://www.cottoninc.com/quality-products/nonwovens/cotton-fiber-tech-guide/cotton- morphology-and-chemistry/.

[50] Rost TL. Cotton Seed Fibers [Internet]. Cotton Anat. 1998 [cited 2018 Jun 18]. Available from: http://www-plb.ucdavis.edu/labs/rost/cotton/reproduction/frfiber.html.

[51] Hock CW, Ramsay RC, Harris M. Microscopic structure of the cotton fiber. J. Res. Natl. Beaurau Stand. 1940;93–104:21.

[52] Purushothama B. Handbook on Cotton Spinning Industry. WPI Publ. 2015;324.

[53] Toyota Industries Corporation. From Raw Cotton to Cotton Fabrics [Internet]. Raw Cotton Cotton Fabr. 2018 [cited 2018 Jul 2]. Available from: https://www.toyota- industries.com/products/textile/process/.

[54] Cotton Incorporated. The Basics of Yarn Manufacturing: Opening through Carding [Internet]. CottonWorksTM. 2019 [cited 2019 Jan 13]. Available from: https://www.cottonworks.com/topics/sourcing-manufacturing/yarn-manufacturing/the- basics-of-yarn-manufacturing-opening-through-carding.

[55] Ahmed S. Comparative study on ring, rotor and air-jet spun yarn. 2015;15.

[56] Borneman J. Spinning With An Air Jet [Internet]. 2012 [cited 2019 Jan 13]. Available from: https://www.textileworld.com/textile-world/features/2012/03/spinning-with-an-air- jet/.

168

[57] Textile School. Yarn Spinning - Air Jet Spinning [Internet]. Text. Sch. - Enrich Your Text. Knowl. 2010 [cited 2019 Jan 13]. Available from: https://www.textileschool.com/455/air-jet-spinning/.

[58] Majumdar A. Principles of Woven Fabric Manufacturing. Boca Raton, FL: CRC Press; 2016.

[59] Lord PR, Mohamed MH. Weaving: Conversion of Yarn to Fabric. 2nd ed. Great Britain: Merrow Publishing; 1982.

[60] Mathur K, Seyam A-F. Color and Weave Relationship in Woven Fabrics. 2011 [cited 2017 Nov 15]; Available from: http://www.intechopen.com/books/advances-in-modern- woven-fabrics-technology/color-and-weave-relationship-in-woven-fabrics.

[61] Nawab Y, Hamdani STA, Shaker K. Structural textile design: interlacing and interlooping [Internet]. Boca Raton, FL: CRC Press,; 2017. Available from: https://catalog.lib.ncsu.edu/record/NCSU3958338.

[62] Jahan I. Effect of Fabric Structure on the Mechanical Properties of Woven Fabrics. Adv. Res. Text. Eng. 2017;1018.

[63] Nassar K, Abou-Taleb EM. Effect of Selected Fabric Construction Elements on Wicking Rates of PET Fabrics. J. Text. Sci. Eng. [Internet]. 2014 [cited 2018 Mar 11];4. Available from: https://www.omicsonline.org/open-access/effect-of-selected-frabric-construction- elements-on-wicking-rates-of-pet-fabrics-2165-8064.1000158.php?aid=25479.

[64] Spencer DJ. Knitting technology: a comprehensive handbook and practical guide. 3rd ed. Cambridge, England: Woodhead Publishing Limited; 2001.

[65] KasCare. History of knitting, from knotted nets and knitted socks to knitting guilds [Internet]. Knit--Sq. 2009 [cited 2018 Apr 25]. Available from: http://www.knit-a- square.com/history-of-knitting.html.

[66] Ray SC. Fundamentals and advances in knitting technology. New Delhi: Woodhead Publishing India Pvt. Ltd.,; 2012.

[67] Minapoor S, Ajeli S, Hasani H, et al. Investigation into the curling behavior of single jersey weft-knitted fabrics and its prediction using neural network model. J. Text. Inst. 2013;104:550–561.

[68] Wong W-Y, Lam JK-C, Kan C-W, et al. Ultraviolet protection of weft-knitted fabrics. Text. Prog. 2016;48:1–54.

[69] Kothari V. Basic Warp Knit Structure [Internet]. 2009 [cited 2018 Apr 28]. Available from: http://vasantkothari.com/index.php/content/view_presentation/148/21-Basic-Warp- Knit-Structure.

169

[70] Karl Mayer. Raschel machines [Internet]. [cited 2019 Jan 19]. Available from: https://www.karlmayer.com/en/products/warp-knitting-machines/raschel-machines/.

[71] Kumar LA, Vigneswaran C. Electronics in Textiles and Clothing : Design, Products and Applications [Internet]. Boca Raton: CRC Press; 2016 [cited 2018 Apr 30]. Available from: https://proxying.lib.ncsu.edu/index.php?url=http://search.ebscohost.com/login.aspx?direc t=true&db=nlebk&AN=1087813&site=ehost-live.

[72] Mann S. Wearable computing: a first step toward personal imaging. Computer. 1997;30:25–32.

[73] Suh M, Carroll KE, Cassill NL. Critical Review on Smart Clothing Product Development. J. Text. Appar. Technol. Manag. [Internet]. 2010 [cited 2018 May 8];6. Available from: http://ojs.cnr.ncsu.edu/index.php/JTATM/article/view/702.

[74] Nisato G, Lupo D, Ganz S. Organic and Printed Electronics: Fundamentals and Applications. CRC Press; 2016.

[75] Natarajan R. Power system capacitors [Internet]. Boca Raton, FL: CRC Press; 2005. Available from: https://catalog.lib.ncsu.edu/record/NCSU1841878.

[76] Mukai Y. Inkjet-Printed Wearable Antennas for Hyperthermia Treatment. [Internet]. [Raleigh, NC]: North Carolina State University; 2016 [cited 2016 May 15]. Available from: http://www.lib.ncsu.edu/resolver/1840.16/11004.

[77] Mukai Y, Bharambe V, Adams J, et al. Effect of Bending and Padding on the Electromagnetic Performance of a Laser-Cut Woven Fabric Patch Antenna. Raleigh, NC; 2018.

[78] Daniel IH, Flint JA, Seager R. Stitched transmission lines for wearable RF devices. Microw. Opt. Technol. Lett. 2017;59:1048–1052.

[79] Huang A, editor. Recent advances in dielectric materials [Internet]. New York: Nova Science Publishers; 2009. Available from: https://catalog.lib.ncsu.edu/record/NCSU3378016.

[80] Bunget I, Popescu M. Physics of solid dielectrics [Internet]. Amsterdam: Elsevier,; 1984. Available from: https://catalog.lib.ncsu.edu/record/NCSU612501.

[81] Foll H. Electronic Materials [Internet]. [cited 2018 Feb 21]. Available from: http://www.tf.uni-kiel.de/matwis/amat/elmat_en/index.html.

[82] Inoue H. Dielectrics [Japanese] [Internet]. Pers. Noteb. Petit Sci. [cited 2018 Feb 21]. Available from: http://hr-inoue.net/zscience/topics/dielectric1/dielectric1.html.

[83] Kasap SO. Principles of electronic materials and devices. 3rd ed. Boston: McGraw-Hill; 2006.

170

[84] Pizzitutti F, Bruni F. Electrode and interfacial polarization in broadband dielectric spectroscopy measurements. Rev. Sci. Instrum. 2001;72:2502–2504.

[85] Sugimoto H, Miki T, Kanayama K, et al. Dielectric relaxation of water adsorbed on cellulose. J. Non-Cryst. Solids. 2008;354:3220–3224.

[86] Sugimoto H, Takazawa R, Norimoto M. Dielectric relaxation due to heterogeneous structure in moist wood. J. Wood Sci. 2005;51:549–553.

[87] Kremer F, Schönhals A. Broadband dielectric spectroscopy [Internet]. Berlin: Springer; 2003. Available from: https://catalog.lib.ncsu.edu/record/NCSU1604336.

[88] Jackson JD. Classical electrodynamics. New York: Wiley; 1975.

[89] Maroulis G. Atoms, molecules and clusters in electric fields [electronic resource] : theoretical approaches to the calculation of electric polarizability [Internet]. London: Imperial College Press ; distributed by World Scientific Publishing,; 2006. Available from: https://catalog.lib.ncsu.edu/record/NCSU4152193.

[90] Feynman R, Leighton R, Sands M. The Feynman Lectures on Physics [Internet]. Feynmanlectures Phys. 2013 [cited 2018 Mar 1]. Available from: http://www.feynmanlectures.caltech.edu/.

[91] Pelosi G. A Tribute to James Clerk Maxwell on the 150th Anniversary of His Equations. IEEE Antennas Propag. Mag. 2014;56:295–298.

[92] Wypych G. Handbook of polymers [electronic resource] [Internet]. Toronto: ChemTec Publishing,; 2016. Available from: https://catalog.lib.ncsu.edu/record/NCSU3919084.

[93] Onimisi MY, Ikyumbur JT. Comparative Analysis of Dielectric Constant and Loss Factor of Pure Butan-1-ol and Ethanol. Am. J. Condens. Matter Phys. 2015;5:69–75.

[94] Asano M, Miura N, Sudo S, et al. Dielectric Relaxation Spectroscopy to Investigate Structured Water in Mortar. Non-Destr. Test. Civ. Eng. 2003 [Internet]. Berlin; 2003 [cited 2018 Jun 24]. p. 16–19. Available from: https://www.ndt.net/article/ndtce03/papers/v019/v019.htm.

[95] Pelster R. Dielectric relaxation spectroscopy in polymers: broadband ac-spectroscopy and its compatibility with TSDC. 10th Int. Symp. Electrets ISE 10 Proc. Cat No99 CH36256. 1999. p. 437–444.

[96] Orihara H, Sugaya M, Tajiri K, et al. Dielectric Properties of an Immiscible Polymer Blend with Electrorheological Effect. J. Phys. Soc. Jpn. 1998;67:655–657.

[97] Driscoll T, Basov DN, Padilla WJ, et al. Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements. Phys. Rev. B. 2007;75:115114.

171

[98] J.A. Woollam Co., Inc. Basics of Ellipsometry [Internet]. 2009 [cited 2018 Jun 9]. Available from: https://qd-uki.co.uk/admin/images/uploaded_images/%5bbasic- ellipsometry-datasheet%5dBasics%20of%20Ellipsometry.pdf.

[99] Jean-Mistral C, Sylvestre A, Basrour S, et al. Dielectric properties of polyacrylate thick films used in sensors and actuators. Smart Mater. Struct. 2010;19:075019.

[100] Li S, Chen R, Anwar S, et al. Applying effective medium theory in characterizing dielectric constant of solids. 2012 Int. Workshop Metamaterials Meta. 2012. p. 1–3.

[101] Zhuromskyy O. Applicability of Effective Medium Approximations to Modelling of Mesocrystal Optical Properties. Crystals. 2016;7:1.

[102] Tinga WR, Voss W a. G, Blossey DF. Generalized approach to multiphase dielectric mixture theory. J. Appl. Phys. 1973;44:3897–3902.

[103] Balanis CA. Antenna theory: analysis and design. Hoboken, New Jersey: Wiley,; 2016.

[104] Ruppin R. Validity Range of the Maxwell-Garnett Theory. Phys. Status Solidi B. 87:619–624.

[105] Balls WL. Dielectric Properties of Raw Cotton. Nature. 1946;158:9–11.

[106] Levy O, Stroud D. Maxwell Garnett theory for mixtures of anisotropic inclusions: Application to conducting polymers. Phys. Rev. B. 1997;56:8035–8046.

[107] Markel VA. Introduction to the Maxwell Garnett approximation: tutorial. J. Opt. Soc. Am. A. 2016;33:1244.

[108] Bal K, Kothari VK. Permittivity of woven fabrics: A comparison of dielectric formulas for air-fiber mixture. IEEE Trans. Dielectr. Electr. Insul. 2010;17:881–889.

[109] Milton GW. Bounds on the complex dielectric constant of a composite material. Appl. Phys. Lett. 1980;37:300–302.

[110] Aspnes DE. Local‐field effects and effective‐medium theory: A microscopic perspective. Am. J. Phys. 1982;50:704–709.

[111] Chassagne C, Dubois E, Jiménez ML, et al. Compensating for Electrode Polarization in Dielectric Spectroscopy Studies of Colloidal Suspensions: Theoretical Assessment of Existing Methods. Front. Chem. [Internet]. 2016 [cited 2018 Jun 6];4. Available from: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4949231/.

[112] Ishai PB, Talary MS, Caduff A, et al. Electrode polarization in dielectric measurements: a review. Meas. Sci. Technol. 2013;24:102001.

172

[113] Samet M, Levchenko V, Boiteux G, et al. Electrode polarization vs. Maxwell-Wagner- Sillars interfacial polarization in dielectric spectra of materials: Characteristic frequencies and scaling laws. J. Chem. Phys. 2015;142:194703.

[114] Keysight Technologies. Basics of Measuring the Dielectric Properties of Materials [Internet]. 2017 [cited 2018 Mar 10]. Available from: http://literature.cdn.keysight.com/litweb/pdf/5989-2589EN.pdf.

[115] Agilent Technologies. Microwave dielectric spectroscopy workshop [Internet]. Agilent Technologies; 2004 [cited 2017 Feb 17]. Available from: http://academy.cba.mit.edu/classes/input_devices/DS.pdf.

[116] Bharambe VT. Analysis of Liquid Metal Vacuum Filling Approach to Develop 3D Printed Antenna [Internet]. North Carolina State University; 2016 [cited 2019 Jan 8]. Available from: http://www.lib.ncsu.edu/resolver/1840.20/33726.

[117] Chen LF, Ong CK, Neo CP, et al. Microwave electronics : measurement and materials characterization. Chichester: Wiley; 2004.

[118] Declercq F, Rogier H, Hertleer C. Permittivity and Loss Tangent Characterization for Garment Antennas Based on a New Matrix-Pencil Two-Line Method. IEEE Trans. Antennas Propag. 2008;56:2548–2554.

[119] Zajicek R, Oppl L, Vrba J. Broadband Measurement of Complex Permittivity Using Reflection Method and Coaxial Probes. 2008;17:14–19.

[120] Ghodgaonkar DK, Varadan VV, Varadan VK. A free-space method for measurement of dielectric constants and loss tangents at microwave frequencies. IEEE Trans. Instrum. Meas. 1989;38:789–793.

[121] Bal K, Kothari VK. Dielectric behaviour of polyamide monofilament fibers containing moisture as measured in woven form. Fibers Polym. 2014;15:1745–1751.

[122] Kechaou B, Salvia M, Beaugiraud B, et al. Mechanical and dielectric characterization of hemp fibre reinforced polypropylene (HFRPP) by dry impregnation process. Express Polym. Lett. 2010;4:171–182.

[123] Pakula T. Dielectric and Mechanical Spectroscopy — a Comparison. Broadband Dielectr. Spectrosc. Springer, Berlin, Heidelberg; 2003. p. 597–623.

[124] Lv HM, Ma L, Ma CQ, et al. Estimation of the moisture regain of cotton fiber using the dielectric spectrum. Text. Res. J. Princet. 2014;84:2056–2064.

[125] Kawarizadeh B, Kovach A, Ghani RK. Wet garment detector [Internet]. 1999 [cited 2018 Dec 30]. Available from: https://patents.google.com/patent/US5903222/en.

[126] Shaw TM, Windle JJ. Microwave Techniques for the Measurement of the Dielectric Constant of Fibers and Films of High Polymers. J. Appl. Phys. 1950;21:956–961.

173

[127] Balasubramanian N. Yarn diameter Specific volume and Packing density [Internet]. [cited 2018 May 15]. Available from: http://balu1.exactpages.com/yarndiameterspecificvolumepackingdensity.html.

[128] Bal K, Kothari VK. Study of dielectric behaviour of woven fabric based on two phase models. J. Electrost. 2009;67:751–758.

[129] Li Z, Haigh A, Soutis C, et al. Dielectric constant of a three-dimensional woven glass fibre composite: Analysis and measurement. Compos. Struct. 2017;180:853–861.

[130] Sheng XQ, Song W. Essentials of Computational Electromagnetics. Wiley-IEEE Press; 2012.

[131] Tonelli AE, Srinivasarao M. Polymers from the inside out : an introduction to macromolecules. New York: Wiley-Interscience,; 2001.

[132] Flory PJ. Principles of polymer chemistry. Ithaca: Cornell University Press; 1953.

[133] Berjanskii MV, Wishart DS. A Simple Method to Measure Protein Side-Chain Mobility Using NMR Chemical Shifts. J. Am. Chem. Soc. 2013;135:14536–14539.

[134] Botev M, Neffati R, Rault J. Mobility and relaxation of amorphous chains in drawn polypropylene: 2H-NMR study. Polymer. 1999;40:5227–5232.

[135] Clauss J, Schmidt-Rohr K, Adam A, et al. Stiff macromolecules with aliphatic side chains: side-chain mobility, conformation, and organization from 2D solid-state NMR spectroscopy. Macromolecules. 1992;25:5208–5214.

[136] Harris DM, Corbin K, Wang T, et al. Cellulose microfibril crystallinity is reduced by mutating C-terminal transmembrane region residues CESA1A903V and CESA3T942I of cellulose synthase. Proc. Natl. Acad. Sci. 2012;109:4098–4103.

[137] Anada Y. Effect of Motion of Impurity Ions on Electrical Properties of Polymer Materials. Energy Procedia. 2013;34:17–25.

[138] Burkinshaw SM. Physico-chemical aspects of textile coloration [Internet]. Hoboken: John Wiley & Sons Inc. in association with the Society of Dyers and Colorists,; 2016. Available from: https://catalog.lib.ncsu.edu/record/NCSU3545879.

[139] Rogti F, Ferhat M. Maxwell–Wagner polarization and interfacial charge at the multi- layers of thermoplastic polymers. J. Electrost. 2014;72:91–97.

[140] Mashimo S, Kuwabara S, Yagihara S, et al. Dielectric relaxation time and structure of bound water in biological materials. J. Phys. Chem. 1987;91:6337–6338.

[141] Skaar C. Wood-Water Relations [Internet]. Berlin Heidelberg: Springer-Verlag; 1988 [cited 2018 Jun 23]. Available from: //www.springer.com/us/book/9783642736858.

174

[142] Froix MF, Nelson R. The Interaction of Water with Cellulose from Nuclear Magnetic Resonance Relaxation Times. Macromolecules. 1975;8:726–730.

[143] Buchner R, Barthel J, Stauber J. The dielectric relaxation of water between 0°C and 35°C. Chem. Phys. Lett. 1999;306:57–63.

[144] Hippel AR von. The dielectric relaxation spectra of water, ice, and aqueous solutions, and their interpretation. I. Critical survey of the status-quo for water. IEEE Trans. Electr. Insul. 1988;23:801–816.

[145] Kuttich B, Grefe A-K, Kröling H, et al. Molecular mobility in cellulose and paper. RSC Adv. 2016;6:32389–32399.

[146] Yu L, Hu X, Kaplan D, et al. Dielectric relaxation spectroscopy of hydrated and dehydrated silk fibroin cast from aqueous solution. Biomacromolecules. 2010;11:2766– 2775.

[147] Feughelman M. Mechanical Properties and Structure of Alpha-keratin Fibres: Wool, Human Hair and Related Fibres. UNSW Press; 1997.

[148] Windle JJ. Sorption of water by wool. J. Polym. Sci. 21:103–112.

[149] Amor IB, Arous M, Kallel A. Interfacial polarization phenomena in palm tree fiber- reinforced epoxy and polyester composites. J. Compos. Mater. 2014;48:2631–2638.

[150] Montès H, Cavaillé JY. Secondary dielectric relaxations in dried amorphous cellulose and dextran. Polymer. 1999;40:2649–2657.

[151] Christie JH, Sylvander SR, Woodhead IM, et al. The dielectric properties of humid cellulose. J. Non-Cryst. Solids. 2004;341:115–123.

[152] Driscoll JL. The dielectric properties of paper and board and moisture profile correction at radio frequencies. Pap. Technol. Ind. 1976;71–75.

[153] Hearle JWS. Capacity, Dielectric Constant, and Power Factor of Fiber Assemblies. Text. Res. J. 1954;24:307–321.

[154] Hearle JWS. The Dielectric Properties of Fiber Assemblies. Text. Res. J. 1956;26:108– 111.

[155] Kirkwood CE, Kendrick NS, Brown HM. Measurement of Dielectric Constant and Dissipation Factor of Raw Cottons. Text. Res. J. 1954;24:841–847.

[156] Einfeldt J, Kwasniewski A. Characterization of different types of cellulose by dielectric spectroscopy. Cellulose. 2002;9:225–238.

[157] Zeronian SH. Contributions to the Chemistry and Physics of Cotton Fibers. AATCC Rev. 2015;15:6.

175

[158] Ouyang Y, Chappell W. Measurement of electrotextiles for high frequency applications. IEEE MTT- Int. Microw. Symp. Dig. 2005. 2005. p. 4 pp.-.

[159] Scarpello ML, Kazani I, Hertleer C, et al. Stability and Efficiency of Screen-Printed Wearable and Washable Antennas. IEEE Antennas Wirel. Propag. Lett. 2012;11:838– 841.

[160] Banerjee PK. Principles of Fabric Formation. Bosa Roca, United STates: CRC Press; 2014.

[161] Ceylan Ö, Goubet F, Clerck KD. Dynamic moisture sorption behavior of cotton fibers with natural brown pigments. Cellulose. 2014;21:1149–1161.

[162] Triki A, Guicha M, Hassen MB, et al. Studies of dielectric relaxation in natural fibres reinforced unsaturated polyester. J. Mater. Sci. 2011;46:3698–3707.

[163] Wang J, Li X. Fiber Materials AC Impedance Characteristics and Principium Analysis. Phys. Procedia. 2012;25:251–256.

[164] Walsh FL. An Isotopic Study of Fiber-Water Interactions. Ga. Inst. Technol. 2006;172.

[165] Fukushima J, Tsubaki S, Matsuzawa T, et al. Effect of Aspect Ratio on the Permittivity of Graphite Fiber in Microwave Heating. Materials. 2018;11:169.

[166] Salski B. The extension of the Maxwell Garnett mixing rule for dielectric composites with nonuniform orientation of ellipsoidal inclusions. Prog. Electromagn. Res. Lett. 2012;30:173–184.

[167] Hamza AA, Sokkar TZN. Optical Properties of Egyptian Cotton Fibers. Text. Res. J. 1981;51:485–488.

[168] Iyer KRC, Neelakantan P, Radhakrishnan T. Birefringence of native cellulosic fibers. J. Polym. Sci. Part -2 Polym. Phys. 1968;6:1747–1758.

[169] Shen M, Ge S, Cao W. Dielectric enhancement and Maxwell-Wagner effects in polycrystalline ferroelectric multilayered thin films. J. Phys. Appl. Phys. 2001;34:2935– 2938.

[170] Sillars RW. The properties of a dielectric containing semiconducting particles of various shapes. Inst. Electr. Eng. - Proc. Wirel. Sect. Inst. 1937;12:139–155.

[171] Kalvøy H, Johnsen GK, Martinsen ØG, et al. New Method for Separation of Electrode Polarization Impedance from Measured Tissue Impedance. Open Biomed. Eng. J. 2011;5:8–13.

[172] Guangfeng C, Haochun S, Linlin Z, et al. A Capacitance based Circuit Design for Yarn Breaking Detection.

176

[173] Nörtemann K, Hilland J, Kaatze U. Dielectric Properties of Aqueous NaCl Solutions at Microwave Frequencies. J. Phys. Chem. A. 1997;101:6864–6869.

[174] Shahariar H, Soewardiman H, Muchler C, et al. Porous textile antenna designs for improved wearability. Smart Mater. Struct. [Internet]. 2018 [cited 2018 Feb 18]; Available from: http://iopscience.iop.org/10.1088/1361-665X/aaaf91.

[175] Bancroft R. Microstrip and Printed Antenna Design [Internet]. IET Digital Library; 2009 [cited 2018 Nov 10]. Available from: http://digital- library.theiet.org/content/books/ew/sbew048e.

[176] Salman JW, Ameen MM. Effects of the Loss Tangent, Dielectric Substrate Permittivity and Thickness on the Performance. J. Eng. Dev. 2006;10:13.

[177] Loss C, Gonçalves R, Pinho P, et al. Influence of some structural parameters on the dielectric behavior of materials for textile antennas. Text. Res. J. 2018;004051751876400.

[178] Sankaralingam S, Gupta B. Determination of Dielectric Constant of Fabric Materials and Their Use as Substrates for Design and Development of Antennas for Wearable Applications. IEEE Trans. Instrum. Meas. 2010;59:3122–3130.

[179] Narayanan PM. Microstrip Transmission Line Method for Broadband Permittivity Measurement of Dielectric Substrates. IEEE Trans. Microw. Theory Tech. 2014;62:2784–2790.

[180] Yue H, Virga KL, Prince JL. Dielectric constant and loss tangent measurement using a stripline fixture. IEEE Trans. Compon. Packag. Manuf. Technol. Part B. 1998;21:441– 446.

[181] Baker-Jarvis J, Janezic MD, Degroot DC. High-frequency dielectric measurements. IEEE Instrum. Meas. Mag. 2010;13:24–31.

[182] Edwards TC, Steer MB. Foundations for microstrip circuit design. Fourth edition. Chichester, West Sussex, United Kingdom: IEEE Press, Wiley; 2016.

[183] Wadell BC. Transmission line design handbook [Internet]. Boston: Artech House,; 1992. Available from: https://catalog.lib.ncsu.edu/record/NCSU778119.

[184] Barbuto M, Alù A, Bilotti F, et al. Characteristic impedance of a microstrip line with a dielectric overlay. COMPEL - Int. J. Comput. Math. Electr. Electron. Eng. 2013;32:1855–1867.

[185] Keysight Technologies, Inc. De-Embedding and Embedding S-Parameter Networks Using a Vector Network Analyzer [Internet]. Keysight Technologies, Inc; 2017 [cited 2018 Oct 6]. Available from: http://literature.cdn.keysight.com/litweb/pdf/5980- 2784EN.pdf.

177

[186] Chen B, Ye X, Fan J. A novel de-embedding method suitable for transmission-line measurement. 2015 Asia-Pac. Symp. Electromagn. Compat. APEMC. 2015. p. 1–4.

[187] Ito H, Masuy K. A simple through-only de-embedding method for on-wafer S-parameter measurements up to 110 GHz. 2008 IEEE MTT- Int. Microw. Symp. Dig. 2008. p. 383– 386.

[188] Murata Manufacturing Co., Ltd. Factors of making noise problems complex [Internet]. [cited 2018 Jun 4]. Available from: https://www.murata.com/en- us/products/emc/emifil/knowhow/basic/chapter03- p2?intcid5=com_xxx_xxx_cmn_hd_xxx.

[189] Frickey DA. Conversions between S, Z, Y, H, ABCD, and T parameters which are valid for complex source and load impedances. IEEE Trans. Microw. Theory Tech. 1994;42:205–211.

[190] Itagaki M, Suzuki S, Shitanda I, et al. Electrochemical Impedance and Complex Capacitance to Interpret Electrochemical Capacitor. Electrochemistry. 2007;75:649–655.

[191] Takei M. Complex capacitance [Internet]. Available from: http://www.em.eng.chiba- u.jp/~takei/NOTE/nagoya/2.pdf.

[192] SpecialChem. Dielectric Constant: Definition, Units, Formula, Plastic Values &Material List [Internet]. [cited 2019 Feb 24]. Available from: https://omnexus.specialchem.com/polymer-properties/properties/dielectric-constant.

[193] Gil I, Fernandez-Garcia R. Wearable embroidered GPS textile antenna. 2017 Prog. Electromagn. Res. Symp. - Spring PIERS. St Petersburg, Russia: IEEE; 2017. p. 655– 659.

[194] MathWorks, Inc. Robust regression [Internet]. 2019 [cited 2019 Mar 1]. Available from: https://www.mathworks.com/help/stats/robustfit.html.

[195] Artemov VG, Volkov AA. Water and Ice Dielectric Spectra Scaling at 0°C. Ferroelectrics. 2014;466:158–165.

[196] Wu TL. Microwave Filter Design [Internet]. [cited 2019 Feb 23]. Available from: http://ntuemc.tw/upload/file/2011021716275842131.pdf.

[197] AFAR Communications, Inc. FCC Rules for Unlicensed Wireless Equipment operating in the ISM bands [Internet]. [cited 2018 Jun 26]. Available from: http://afar.net/tutorials/fcc-rules/.

[198] Kallner A. Laboratory Statistics : Methods in Chemistry and Health Sciences. Amsterdam, Netherlands: Elsevier; 2018.

178

[199] O’Neill H, Pingali SV, Petridis L, et al. Dynamics of water bound to crystalline cellulose. Sci. Rep. [Internet]. 2017 [cited 2018 Jun 23];7. Available from: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5605533/.

[200] Gradishar W. Optimizing breast cancer management. New York, NY: Springer Berlin Heidelberg; 2017.

[201] Siegel RL, Miller KD, Jemal A. Cancer statistics, 2017. CA. Cancer J. Clin. 2017;67:7– 30.

[202] Peng S, Zeng Q, Yang X, et al. Local Dielectric Property Detection of the Interface between Nanoparticle and Polymer in Nanocomposite Dielectrics. Sci. Rep. 2016;6:38978.

[203] Stauffer PR. Thermal therapy techniques for skin and superficial tissue disease. Bellingham, United States; 2000 [cited 2019 Jan 11]. p. 102970E. Available from: http://proceedings.spiedigitallibrary.org/proceeding.aspx?doi=10.1117/12.375215.

[204] Arce-Salinas C, Garza-Salazar JG de la, Meneses García A. Inflammatory breast cancer. London: Springer,; 2013.

[205] Bellon JR, Wong JS, MacDonald SM, et al. Radiation Therapy Techniques and Treatment Planning for Breast Cancer. Springer; 2016.

[206] Dewey WC, Hopwood LE, Sapareto SA, et al. Cellular Responses to Combinations of Hyperthermia and Radiation. Radiology. 1977;123:463–474.

[207] Song CW, Lokshina A, Rhee JG, et al. Implication of blood flow in hyperthermic treatment of tumors. IEEE Trans. Biomed. Eng. 1984;31:9–16.

[208] Cihoric N, Tsikkinis A, van Rhoon G, et al. Hyperthermia-related clinical trials on cancer treatment within the ClinicalTrials.gov registry. Int. J. Hyperthermia. 2015;31:609–614.

[209] Zagar TM, Oleson JR, VUJASKOVIC Z, et al. Hyperthermia combined with radiation therapy for superficial breast cancer and chest wall recurrence: A review of the randomised data. Int. J. Hyperth. Off. J. Eur. Soc. Hyperthermic Oncol. North Am. Hyperth. Group. 2010;26:612–617.

[210] Linthorst M, Baaijens M, Wiggenraad R, et al. Local control rate after the combination of re-irradiation and hyperthermia for irresectable recurrent breast cancer: Results in 248 patients. Radiother. Oncol. 2015;117:217–222.

[211] Dunne M, Dou YN, Drake DM, et al. Hyperthermia-mediated drug delivery induces biological effects at the tumor and molecular levels that improve cisplatin efficacy in triple negative breast cancer. J. Controlled Release. 2018;282:35–45.

179

[212] Klimanov MY, Syvak LA, Orel VE, et al. Efficacy of Combined Regional Inductive Moderate Hyperthermia and Chemotherapy in Patients With Multiple Liver Metastases From Breast Cancer. Technol. Cancer Res. Treat. 2018;17:1533033818806003.

[213] Van Der Zee J, De Bruijne M, Mens JWM, et al. Reirradiation combined with hyperthermia in breast cancer recurrences: Overview of experience in Erasmus MC. Int. J. Hyperthermia. 2010;26:638–648.

[214] Curto S, Garcia-Miquel A, Suh M, et al. Design and characterisation of a phased antenna array for intact breast hyperthermia. Int. J. Hyperthermia. 2018;34:250–260.

[215] Pang L, Lee K. Hyperthermia in oncology. Boca Raton, FL: CRC Press; 2016.

[216] Curto S, Prakash P. Design of a compact antenna with flared groundplane for a wearable breast hyperthermia system. Int. J. Hyperthermia. 2015;31:726–736.

[217] Montecchia F. Microstrip-antenna design for hyperthermia treatment of superficial tumors. IEEE Trans. Biomed. Eng. 1992;39:580–588.

[218] Singh V. Design and Simulation of Hyperthermia Antenna. 2015;6:3.

[219] Singh S, Singh S. Microstrip slot antenna for hyperthermia applications. 2015 IEEE Appl. Electromagn. Conf. AEMC. 2015. p. 1–2.

[220] Curto S, Ramasamy M, Suh M, et al. Design and analysis of a conformal patch antenna for a wearable breast hyperthermia treatment system. In: Ryan TP, editor. 2015 [cited 2018 Jun 21]. p. 93260I. Available from: http://proceedings.spiedigitallibrary.org/proceeding.aspx?doi=10.1117/12.2079718.

[221] Mukai Y, Suh M. Development of a Conformal Textile Antenna for Thermotherapy [Internet]. Davis, CA; 2018 [cited 2019 Jan 7]. Available from: https://www.thefibersociety.org/Portals/0/Past%20Conferences/2018_Fall_Abstracts.pdf ?ver=2019-01-22-095426-997.

[222] Ito K, Furuya K, Okano Y, et al. Development and characteristics of a biological tissue- equivalent phantom for microwaves. Electron. Commun. Jpn. Part Commun. 2001;84:67–77.

[223] Zajicek R, Vrba J. Broadband Complex Permittivity Determination for Biomedical Applications. Adv. Microw. Circuits Syst. 2010;24.

[224] Guha D, Siddiqui JY. Resonant frequency of circular microstrip antenna covered with dielectric superstrate. IEEE Trans. Antennas Propag. 2003;51:1649–1652.

[225] Balanis CA. Antenna Theory: Analysis and Design. 4th edition. Wiley; 2016.

[226] Ansys Inc. HFSS Two-Way Mechanical Coupling for Full-Wave Electromagntics to Thermal Stress Simulation [Internet]. Ansys Inc.; 2012 [cited 2018 Dec 26]. Available

180

from: https://www.ansys.com/-/media/ansys/corporate/resourcelibrary/presentation/hfss- 2way-thermal-dimensions.pdf.

[227] Sabbagh ME. Electromagnetic-Thermal Analysis Study Based on HFSS-ANSYS Link. Syracuse Univ. 2011;10.

[228] Udayraj, Talukdar P, Das A, et al. Simultaneous estimation of thermal conductivity and specific heat of thermal protective fabrics using experimental data of high heat flux exposure. Appl. Therm. Eng. 2016;107:785–796.

[229] LessEMF, Inc. Electromagnetic Field Shielding Fabrics with a Natural Look and Feel [Internet]. [cited 2018 May 20]. Available from: http://www.lessemf.com/fabric4.html#1212.

[230] Serway RA, Jewett JW, Peroomian V. Physics for scientists and engineers. Australia: Cengage; 2019.

[231] Young HD, Sears FW. University physics. Reading, Mass.: Addison-Wesley Pub. Co.; 1992.

[232] Ansys Inc. Ansys Workbench. 2017.

[233] Hilsenrath J, Klein M. Tables of thermodynamic properties of air in chemical equilibrium including second virial corrections from 1500k to 15,000k [Internet]. Fort Belvoir, VA: Defense Technical Information Center; 1965 [cited 2018 Dec 24]. Available from: http://www.dtic.mil/docs/citations/AD0612301.

[234] Hollen NR, Kundel CJ. Pattern making by the flat-pattern method. 7th ed. New York: Maxwell Macmillan Canada; 1993.

[235] Thyssen A. Hemisphere Parachute Design [Internet]. 1997 [cited 2018 Nov 13]. Available from: https://www.kiteplans.org/planos/hemisphere/hemisphere.html.

[236] Huang Y, Boyle K. Antennas: from theory to practice. Chichester, UK: John Wiley & Sons Ltd.; 2008.

[237] Ansoft Corporation. Ansys High Frequency Structure Simulator.

[238] Dichtl C, Sippel P, Krohns S. Dielectric Properties of 3D Printed Polylactic Acid [Internet]. Adv. Mater. Sci. Eng. 2017 [cited 2018 Mar 13]. Available from: https://www.hindawi.com/journals/amse/2017/6913835/.

[239] Mogahzy YE. Understanding fibre-to-yarn system:Yarn Characteristics. 1993.

[240] Körner TW. Vectors, pure and applied: a general introduction to linear algebra. Cambridge, UK: Cambridge University Press; 2013.

181

APPENDICES

182

Appendix A. Effect of the Ground Plane Size and the Use of the PLA Template

In order to numerically investigate the effect of the ground plane size on the dielectric characterization, four different sizes (1,500, 152.4, 76.2 and 38.1 mm) were simulated using a 3D full-wave EM simulator (HFSS, ANSYS Inc.) for the frequency range of 100 MHz to 6 GHz.

Although 1,500 mm is not a practical size for fabrication, this was included in simulation to cover the half wavelength of the lowest frequency (100 MHz) as a reference.

The developed simulation model had the same geometry as the one illustrated in Figure

4-2 but the cotton fabric substrate was replaced with a polyester layer for a model study. Based on the materials parameters given in Table A-1, the reflection and transmission coefficients (2-port complex S-parameters) were computed with four different widths (38, 76, 152 and 1,500 mm) of

* ' '' the ground plane. Then, by using (4-4) to (4-15), the complex relative permittivity (εr = εr jεr ) and loss tangent (tanδ) of the polyester layer were calculated from the simulated S-parameters.−

Table A-1. Materials parameters used in the simulation. Materials properties Thickness Materials Conductivity Dielectric Loss tangent References (mm) ' (σ; S/m) constant (εr) (tanδ) Copper sheet 0.04 5.8×107 – – [237] Woven polyester 0.32 – 1.55 0.009 [28,77] Acrylic adhesive 0.04 – 2.00 0.0001 [46,192] PLA template – – 2.75 0.005 [238] Stainless bolts – 1.1×106 – – [237] Brass nuts – 1.5×107 – – [237]

' The real part of the relative permittivity (dielectric constant (εr)) and loss tangent values computed with the three ground plane widths (38, 76 and 152 mm) were compared with those calculated with the 1,500 mm-wide ground plane in terms of the impact on the percent change in

' ' the dielectric constant (Δεr/εr) and the loss tangent (Δtanδ), respectively. As given in Table A-2,

183

the impact of reducing the ground plane width from 1,500 mm to either 38, 76 or 152 mm was small – the percent change in the dielectric constant was less than 0.5% and the change in the loss tangent was less than 0.0004. Therefore, the effect of the ground plane size on the dielectric characterization was regarded infinitesimal.

Table A-2. Computed impact of the ground plane width on the dielectric characterization. ' ' Width (mm) Δεr/εr (%) Δtanδ 38 −0.5 0.0004 76 −0.5 0.0002 152 −0.4 0.0001

The effect of the 3D template on the dielectric characterization was also computed by running a simulation using the EM solver. The produced simulation model had the same geometry as the one illustrated in Figure 4-3 but the cotton fabric substrate was again replaced with the polyester layer for a model study. The computed S-parameters were then converted into the complex relative permittivity and loss tangent by using (4-4) to (4-15).

The dielectric properties with and without the 3D template compared in terms of the impact

' ' on the dielectric constant (Δεr/εr) and the loss tangent (Δtanδ) were less than 0.05% and less than

0.0003, respectively. Therefore, the use of the 3D template was regarded to have no significant impact on the dielectric characterization based on these theoretical computation results.

184

Appendix B. Characterization Frequencies and Extracted Dielectric Constants

Table B-1. Characterization frequencies and extracted dielectric constants from the patch antenna measurements in the RH range of 20% to 80%. ' Characterization frequency (fr; GHz) Dielectric constant (ε ) Sample # r 80% 65% 50% 35% 20% 80% 65% 50% 35% 20% W1 2.59 2.60 2.60 2.61 2.63 1.28 1.27 1.27 1.26 1.23 W2 2.79 2.79 2.77 2.82 2.85 1.24 1.24 1.27 1.21 1.18 W3 2.73 2.73 2.76 2.78 2.80 1.29 1.29 1.26 1.24 1.21 W4 2.70 2.71 2.75 2.78 2.81 1.42 1.40 1.36 1.32 1.29 W5 2.69 2.72 2.76 2.78 2.82 1.46 1.43 1.38 1.35 1.31 K1 2.63 2.64 2.69 2.71 2.75 1.38 1.37 1.32 1.30 1.25 K2 2.68 2.69 2.74 2.76 2.80 1.37 1.35 1.30 1.28 1.23 K3 2.71 2.73 2.78 2.80 2.84 1.42 1.39 1.34 1.32 1.27 K4 2.69 2.76 2.80 2.81 2.87 1.55 1.47 1.43 1.41 1.35 K5 2.69 2.71 2.78 2.81 2.87 1.62 1.59 1.50 1.47 1.40

185

Appendix C. Calculation of Yarn Orientation

In order to find the yarn orientation in a plain-woven fabric, a simplified model is

considered, where the directions of the orthogonal weft and warp yarns are along x-axis and y-

axis, respectively (Figure C-1). For this model, the average angle ( θwoven ; degrees) between the z-axis (fabric thickness direction) and the woven yarns can be given by:

 θwoven =90 − arctan ( Swoven ) (C-1)

where

Tz,woven Swoven = Txy,woven

Txy,woven = Yarn travel distance (meters) in the xy-plane in a 1,000 mm by 1,000 mm fabric

Tz,woven = Yarn travel distance (meters) in zˆ in a 1,000 mm by 1,000 mm fabric

Thus, this problem is to find the traveling distances of the yarns with respect to the coordinate

axes.

186

Figure C-1. (a) zx and (b) zy cuts of a plain-woven fabric with the repeat units of weft and warp yarns (shaded).

For a fabric of 1,000 mm by 1,000 mm, the number of weft yarns is given by:

1,000 N= PPI (C-2) P 25.4

and the number of warp yarns is given by:

1,000 N= EPI (C-3) E 25.4

Therefore, the total traveling distance in the xy plane is given as:

1,000 T=⋅11 N +⋅ N =( PPI + EPI ) (C-4) xy,woven P E 25.4

Next, Tz,woven of the weft yarn is the multiplication of the z-component averaged over the

repeat unit of the weft yarn, the number of repeat units in a single weft yarn of 1,000 mm long, and the number of weft yarns in 1,000 mm by 1,000 mm fabric. Similarly, for warp yarns, Tz,woven

of the warp yarn is the multiplication of the z-component averaged over the repeat unit of the warp

187

yarn, the number of repeat units in a single warp yarn of 1,000 mm long, and the number of warp yarns in 1,000 mm by 1,000 mm fabric. Hence, Tz,woven is given by:

(rr++) (rr) T= PE ⋅+ NNPE ⋅ z,woven 25.4 P 25.4 E  2EPI ⋅⋅ 1,000 2PPI 1,000 (C-5) 4,000,000 =()r +⋅ r PPI ⋅ EPI 25.42 PE

Therefore, the yarn orientation (degrees) in woven fabric with respect to the z-axis is given by:

 θwoven =90 − arctan ( Swoven ) T = − z,woven 90 arctan  Txy,woven 4,000,000 +⋅ ⋅ 2 ()rPE r PPI EPI (C-6)  25.4 =90 − arctan  1,000 (PPI+ EPI ) 25.4 4,000(r+⋅ r ) PPI ⋅ EPI =90 − arctan PE 25.4(PPI+ EPI )

For a knit fabric (Figure C-2), in which the primary traveling direction of the yarns are

along the x-axis and the z-axis is placed in the fabric thickness direction, the average angle between

the z-axis (fabric thickness direction) and the knit yarn ( θknit ; degrees) can be obtained from:

 θknit  90− arctan ( Sknit ) (C-7)

where

Tz,knit Sknit  Txy,knit

Txy,knit = Average taveling distance in the xy-plane in millimeters for a repeat unit

Tz,knit = Average traveling distance in zˆ in millimeters for a repeat unit

188

In order to use this equation, traveling distances of the knit yarns need to be formulated in the

Cartesian coordinate. By projecting the knit yarn onto the xy-plane, Path A can be obtained as shown in Figure C-2 (a). Then, by drawing a straight line from the start point to the end point of

Path A, Path B is defined (Figure C-2 (a)). Although the Path A is longer than path B in physical knit fabrics, an assumption is made that the xy-plane components of Paths A and B are approximately equal in order to ease the calculation of the traveling distance in the xy-plane. Based on this assumption, the yarn structure in Figure C-2 (a) can be transformed into Figure C-2 (b)

where the yarn projected onto the xy-plane is now linear. Accordingly, Txy,knit is given by:

22 25.4  25.4  Txy,knit =  +  (C-8) 2,000WPI  1,000 CPI 

The yarn traveling along the z-axis is drawn in Figure C-2 (c). Because Tz,knit is the z-

component averaged over the repeat unit, Tz,knit is given by:

Trz,knit = 4 F (C-9)

Therefore, the average yarn orientation ( θknit ) in a plain-knit fabric with respect to the z-axis can be calculated as:

 θknit =−90 arctan Sknit  Tz,knit =90 − arctan  Txy,knit (C-10)  4r =90 − arctan F 22 25.4  25.4   +  2,000WPI  1,000 CPI 

189

Figure C-2. (a) Top view of a knit yarn and (b) yz-cut of a yarn crossed with two neighboring yarns, in a plain-knit fabric.

Based on the two developed yarn models, the average yarn orientations in both woven and knitted fabric samples can be calculated. The radius (r; millimeters) of the 5-ply cotton yarn sample was empirically obtained for this computation by [127,239]:

0.0009755 r =−+=0.00008775 0.18 mm (C-11) N where N is the cotton count (4.62).

190

Appendix D. Measurement of Yarn Orientation

D-1. Sample Preparation

In order to increase the micro-CT sensitivity, the cotton fabric samples (W4, W5, K2 and K3) were immersed in a Lugol’s solution (4 wt% potassium iodide and 2 wt% iodine dissolved in 94 wt% distilled water supplied from J.Crow Company). After 24 hours, the samples were taken out from the staining bath and were dried in a fume hood at room temperature for 24 hours.

D-2. Micro-CT scan and data visualization

A micro-CT system (Bruker SkyScan 1174), which provides the spatial (theoretical) resolution of

6.41 μm, was operated at 40 kV and 0.67 mA to capture cone-beam x-ray projections of the stained cotton fabric samples. The acquired projection images were then reconstructed into cross-sectional images by using a reconstruction software (Bruker NRecon).

D-3. Determination of average yarn orientation

The angle (θ0; degrees) between two arbitrary vectors, a = (a1,a2, a3) and b = (b1,b2, b3), are given

in the definition of their inner product [240]: �⃗ �⃗   ab⋅⋅ a bcosθ0 (D-1)

  or ab⋅ ab++ ab ab θ = = 11 2 2 33 cos 0  (D-2)  ⋅ 2 2 2 222 ab aa1++⋅ 2 a 3 bbb 123 ++

or  ab11++ ab 2 2 ab 33 θ0 = arccos (D-3) 2 2 22 2 2 aa++ abbb ++ ( 1 2 3123)( )

191

in the Cartesian coordinate system. Accordingly, the angle between the axis normal to the fabric

plane (i.e., z = (0, 0, 1)) and the discretized orientation vector of the yarn (l = (e1 s1, e2 s2, ⃗ e3 s3)) (Figure� D-1) is given by: − −

−  es− θ = arccos33 (D-4) −222 +− +− (es11) ( es 2 2) ( es 33)

The average yarn orientation ( θ ) can therefore be obtained by taking an average of angles (θi)

over the discretized yarn length (li) as:

n ∑θiil θθ11ll+ 2 2 +⋅⋅⋅+ θnn l i=1 θ = = n (D-5) ll12+ +⋅⋅⋅+ ln ∑li i=1 where i and n are the discretization index and total number of discretization, respectively. Now, for the woven fabric, the average yarn orientation was respectively calculated for the weft and warp yarns using (B-5), and then the total average was obtained by using the formula:

θθ⋅+PPI ⋅ EPI θ = weft warp (D-6) woven PPI+ EPI

Figure D-1. Yarn discretization and constituent orientation vector (Δ ).

𝑙𝑙⃗

192

In order to find the discretized vectors in the fabric samples, a 3D visualization software

(Bruker DataViewer) was operated, and the plied yarns were extracted as shown in Figure D-2.

The examined lengths of the yarns for each fabric samples are given in Table D-1 along with the average discretized length. These measurements included at least 4 repeat units in both woven and knitted samples to ensure that the population is properly represented.

Figure D-2. Examples of (a) cross-sectional visualization of a fabric sample in the DataViewer software and (b) extracted 5-ply warp yarn for calculation of the yarn orientation.

Table D-1. Yarn discretization profile. Sample # Examined yarn length (mm) Average discretized yarn length (mm) W4 45.0 0.140 (0.036) W5 64.0 0.149 (0.043) K2 40.3 0.127 (0.037) K3 47.1 0.140 (0.047) Note: The numbers in parentheses are the standard deviations.

193