材料的電磁特性量測技術已經研究了數十年，並廣泛應用於各種實際領域，如熱療法和食品品質控制。在科學方面，這些技術還促進了對分子動力學的研究，如弛豫時間和分子網絡結構。
在本研究中，我們提出了一個易於組裝的同軸波導系統，能夠提供材料在100 MHz到約17 GHz範圍內的寬頻介電係數和介磁係數曲線資訊。通過加入常見樣品，如空氣、庚烷和水，我們能夠利用Nicolson-Ross-Weir法校準系統並獲得頻率響應曲線。本方法可同時量測液體多個特性參數且非破壞性量測，我們在研究中呈現了甲醇、乙醇和兩種商業用磁流體的測量數據。
我們對甲醇和乙醇的介電常數結果與文獻研究結果高度一致。然而，在磁流體研究中，一些模型產生了不良的擬合結果。通過比較模型之間的差異我們得出結論，奈爾弛豫的磁導率貢獻應該被視為一個獨立的Debye型群，這意味著簡化的有效介質理論在多弛豫機制作用的情況下不適用。此外，鐵磁共振頻率的準確性顯著依賴於異向能和熱能的比值。這項工作提供的擬合參數不僅為闡述液體弛豫過程提供更明確的資訊，也在生物技術中具有應用價值，例如在熱療法中用於計算特定吸收速率，或在核磁共振成像中用作對磁流體對比劑的品質控制。

In this work, we propose an easy-to-assemble coaxial system, which is able to provide broadband permittivity and permeability information of material from 100 MHz to around 17 GHz. By inserting standard sample such as air, heptane, water, we are able to calibrate the system and get frequency response curve by the help of Nicolson-Ross-Weir method. The measurement offers as a non-destructive method to measure multiple interested parameters at a same time.
Our permittivity results of methanol and ethanol show good agreement with previous research from Barthel, J., et al. In ferrofluid research, however, some models make poor fitting results. By comparing the difference between models, we conclude the permeability contribution of Neel relaxation should be consider as a Debye-type group independently, which means simplified effective medium theory is not suitable in our case. Furthermore, the accuracy of ferromagnetic resonance frequency is significantly relied on the ratio of anisotropy energy and thermal energy. This work not only provide insight for liquid relaxation processes, also have application value in bio technology, such as decide the specific absorption rate in hyperthermia therapy, or as a quality control for ferrofluid using in magnetic resonance imaging as contrast agent.

[1] M. Kouzai, A. Nishikata, K. Fukunaga, and S. Miyaoka, “Complex permittivity measurement at millimetre-wave frequencies during the fermentation process of Japanese sake,” Journal of Physics D: Applied Physics, vol. 40, no. 1, pp. 54, 2006.
[2] A. Prociak, L. Szczepkowski, J. Ryszkowska, M. Kurańska, M. Auguścik, E. Malewska, M. Gloc, and S. Michałowski, “Influence of chemical structure of petrochemical polyol on properties of bio-polyurethane foams,” Journal of Polymers and the Environment, vol. 27, pp. 2360-2368, 2019.
[3] S. D. Romano, and P. A. Sorichetti, Dielectric spectroscopy in biodiesel production and characterization: Springer Science & Business Media, 2010.
[4] N. D. Thorat, S. A. Tofail, B. von Rechenberg, H. Townley, G. Brennan, C. Silien, H. M. Yadav, T. Steffen, and J. Bauer, “Physically stimulated nanotheranostics for next generation cancer therapy: Focus on magnetic and light stimulations,” Applied Physics Reviews, vol. 6, no. 4, 2019.
[5] S. Laurent, S. Dutz, U. O. Häfeli, and M. Mahmoudi, “Magnetic fluid hyperthermia: focus on superparamagnetic iron oxide nanoparticles,” Advances in colloid and interface science, vol. 166, no. 1-2, pp. 8-23, 2011.
[6] P.-E. Le Renard, F. Buchegger, A. Petri-Fink, H. Hofmann, E. Doelker, and O. Jordan, “FORMULATIONS FOR LOCAL, MAGNETICALLY MEDIATED HYPERTHERMIA TREATMENT OF SOLID TUMORS,” Nanotechnology Research Journal, vol. 7, no. 1, pp. 1, 2014.
[7] Y.-T. Chen, A. G. Kolhatkar, O. Zenasni, S. Xu, and T. R. Lee, “Biosensing using magnetic particle detection techniques,” Sensors, vol. 17, no. 10, pp. 2300, 2017.
[8] "Agilent Basics of Measuring the Dielectric Properties of Materials," http://cp.literature.agilent.com/litweb/pdf/5989-2589EN.pdf.
[9] V. Mandrić Radivojević, S. Rupčić, M. Srnović, and G. Benšić, “Measuring the dielectric constant of paper using a parallel plate capacitor,” International journal of electrical and computer engineering systems, vol. 9, no. 1, pp. 1-10, 2018.
[10] T. Van Hoi, and B. G. Duong, "Designing Wideband Microstrip Bandpass Filter for Satellite Receiver Systems." pp. 140-143.
[11] D. M. Pozar, Microwave engineering: John wiley & sons, 2011.
[12] N. Nahman, Dielectric constant measurements on n-heptane and 2-heptanone, Los Alamos National Lab.(LANL), Los Alamos, NM (United States); Nahman (NS …, 1994.
[13] U. Kaatze, “Reference liquids for the calibration of dielectric sensors and measurement instruments,” Measurement Science and Technology, vol. 18, no. 4, pp. 967, 2007.
[14] J. Barthel, K. Bachhuber, R. Buchner, and H. Hetzenauer, “Dielectric spectra of some common solvents in the microwave region. Water and lower alcohols,” Chemical physics letters, vol. 165, no. 4, pp. 369-373, 1990.
[15] P. Debye, “Polar molecules, the chemical catalog company,” Inc., New York, vol. 89, 1929.
[16] S. Havriliak, and S. Negami, "A complex plane analysis of α‐dispersions in some polymer systems." pp. 99-117.
[17] O. Oehlsen, S. I. Cervantes-Ramírez, P. Cervantes-Avilés, and I. A. Medina-Velo, “Approaches on ferrofluid synthesis and applications: current status and future perspectives,” ACS omega, vol. 7, no. 4, pp. 3134-3150, 2022.
[18] L. Landau, and E. Lifshitz, "On the theory of the dispersion of magnetic permeability in ferromagnetic bodies," Perspectives in Theoretical Physics, pp. 51-65: Elsevier, 1992.
[19] E. C. Stoner, and E. Wohlfarth, “A mechanism of magnetic hysteresis in heterogeneous alloys,” Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 240, no. 826, pp. 599-642, 1948.
[20] Y. L. Raikher, and M. Shliomis, “Theory of dispersion of the magnetic susceptibility of fine ferromagnetic particles,” Soviet Physics-JETP, vol. 40, no. 3, pp. 526-532, 1975.
[21] Y. L. Raĭkher, and M. I. Shliomis, “The effective field method in the orientational kinetics of magnetic fluids and liquid crystals,” Advances in chemical physics: relaxation phenomena in condensed matter, vol. 87, pp. 595-751, 1994.
[22] C. Kittel, Elementary statistical physics: Courier Corporation, 2004.
[23] K. J. Laidler, “The development of the Arrhenius equation,” Journal of chemical Education, vol. 61, no. 6, pp. 494, 1984.
[24] J. Dormann, and D. Fiorani, Magnetic properties of fine particles: Elsevier, 2012.
[25] L. Bessais, L. B. Jaffel, and J. Dormann, “Relaxation time of fine magnetic particles in uniaxial symmetry,” Physical Review B, vol. 45, no. 14, pp. 7805, 1992.
[26] M. Shliomis, and Y. Raikher, “Experimental investigations of magnetic fluids,” IEEE Transactions on magnetics, vol. 16, no. 2, pp. 237-250, 1980.
[27] W. F. Brown Jr, “Thermal fluctuations of a single-domain particle,” Physical review, vol. 130, no. 5, pp. 1677, 1963.
[28] W. Coffey, P. Cregg, D. Crothers, J. Waldron, and A. Wickstead, “Simple approximate formulae for the magnetic relaxation time of single domain ferromagnetic particles with uniaxial anisotropy,” Journal of magnetism and magnetic materials, vol. 131, no. 3, pp. L301-L303, 1994.
[29] W. T. Coffey, D. Crothers, Y. P. Kalmykov, E. S. Massawe, and J. Waldron, “Exact analytic formula for the correlation time of a single-domain ferromagnetic particle,” Physical Review E, vol. 49, no. 3, pp. 1869, 1994.
[30] G. Kenrick, “XIX. The analysis of irregular motions with applications to the energy-frequency spectrum of static and of telegraph signals,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol. 7, no. 41, pp. 176-196, 1929.
[31] I. Torres-Díaz, and C. Rinaldi, “Recent progress in ferrofluids research: novel applications of magnetically controllable and tunable fluids,” Soft matter, vol. 10, no. 43, pp. 8584-8602, 2014.
[32] P. Fannin, “Wideband measurement and analysis techniques for the determination of the frequency-dependent, complex susceptibility of magnetic fluids,” Advances in chemical physics, pp. 181-292, 2007.