材料的介電性質一直是科學上的重要研究課題，廣泛應用於學術、工業和食品等領域。透過精密的寬頻介電量測，我們可以更微觀地了解材料中的分子特性和相互作用，從而提升對材料的理解和應用。

本研究的成果已發表在 Journal of Molecular Liquids 的期刊中，探討了碳酸丙烯酯（PC）及其與甲醇和乙醇的二元混合物的介電性能和弛豫行為。我們利用同軸-圓波導管從 0.1 GHz 至 18 GHz 範圍內獲取了寬頻介電譜，並利用兩組 Debye 模型擷取了弛豫參數。透過這些分析，我們能夠觀察到不同混合濃度下的變化趨勢，並進一步呈現出超額熱力學性質參數、Kirkwood 取向相關因子和 Bruggeman 因子等。這些研究基於熱力學，使我們能夠更深入地分析分子內部的微觀過程，包括醇的氫鍵網絡的連續解離、PC 和醇之間的氫鍵網絡形成以及異質偶極子的平行排列。

為了更直觀地研究分子間的行為，我們進一步基於 TraPPE-UA 的力場，使用了分子動力學（MD）的理論計算。根據從 MD 模擬中提取的徑向分布函數和氫鍵生命期，我們觀察到，隨著 PC 濃度的增加，其混合物中會逐漸形成 PC 的籠狀和醇類的簇狀微結構。

綜合以上，我們認為本研究的數據量測以及所提出的物理概念具有重要的參考價值，特別是在高能量電池和製藥行業方面，具有潛在的應用價值。

The dielectric properties of materials have long been a significant research topic in science, with broad applications across academic, industrial, and food-related fields. Through precise broadband dielectric measurements, we can gain deeper insights into the molecular characteristics and interactions within materials, thus enhancing our understanding and applications of them.

This study investigates the dielectric performance and relaxation behavior of propylene carbonate (PC) and its binary mixtures with methanol and ethanol. The result of the work was also published in the Journal of Molecular Liquids. Using a coaxial-circular waveguide, we obtained broadband dielectric spectra ranging from 0.1 GHz to 18 GHz and extracted relaxation parameters using two sets of Debye models. Through these analyses, we observed trends in different mixing concentrations and presented excess thermodynamic parameters, Kirkwood correlation factors, and Bruggeman factors. These investigations, grounded in thermodynamics, allow for a more in-depth analysis of molecular processes, including the continuous dissociation of alcohol hydrogen-bond networks, the formation of new PC-alcohol hydrogen-bond networks, and the parallel alignment of heterogeneous dipoles.

To further understand molecular behavior, we employed molecular dynamics (MD) simulations based on the TraPPE-UA force field. We observed the gradual formation of PC cage-like structures and alcohol-cluster microstructures in PC-rich mixtures based on radial distribution functions, radial dipole-dipole spatial correlation, and hydrogen-bond lifetime extracted from MD simulations.

In summary, the data measurement and physical insights provided by this study are expected to be valuable references, particularly in high-energy battery applications and the pharmaceutical industry.

Abstract (Chinese) I
Acknowledgements (Chinese) II
Abstract III
Contents IV
List of Figures VII
List of Tables IX
List of Algorithms 1
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Permittivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Permittivity Characterization . . . . . . . . . . . . . . . . . . . . . 4
1.4 Molecular Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Experimental Setup 7
2.1 Experimental Setup for Broadband Dielectric Characterization . . 7
2.2 Callibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Standard OSL Calibration . . . . . . . . . . . . . . . . . . . 9
2.2.2 Three Sample Calibrations . . . . . . . . . . . . . . . . . . . 9
2.3 Optical Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Measurement Samples and Environment . . . . . . . . . . . . . . . 11
2.5 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Dielectric Properties of Liquids 12
3.1 Static Dielectric Properties . . . . . . . . . . . . . . . . . . . . . . . 12
3.1.1 Pure substance . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1.2 Binary Mixture . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 Relaxation Processes . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Experimental Results of Pure Substances . . . . . . . . . . . . . . . 19
3.4 Experimental Results of Binary Mixtures . . . . . . . . . . . . . . . 21
3.4.1 Relaxation Behavior . . . . . . . . . . . . . . . . . . . . . . 21
3.4.2 Static Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 26
4 Concept of Molecular Dynamics 29
4.1 Force Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1.1 Bonded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.1.2 Non-bonded . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.1.3 Types of force fields . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 Integration Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2.1 Leapfrog algorithm . . . . . . . . . . . . . . . . . . . . . . . 35
4.2.2 Velocity Verlet algorithm . . . . . . . . . . . . . . . . . . . . 36
4.3 Some Assumptioms . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3.1 Long-range cutoff . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3.2 Particle Mesh Ewald (PME) . . . . . . . . . . . . . . . . . . 37
4.3.3 Periodic boundary condition (PBC) . . . . . . . . . . . . . . 39
4.4 Ensembles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5 Computational Results 42
5.1 Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.2 Density and Static Permittivity . . . . . . . . . . . . . . . . . . . . 43
5.3 Computed Time Autocorrelation Function . . . . . . . . . . . . . . 44
5.4 Radial Distribution Function (RDF) . . . . . . . . . . . . . . . . . 46
5.4.1 Introduction to radial distribution functions . . . . . . . . . 46
5.4.2 RDF results . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.5 Radial Dipole-dipole Spatial Correlation . . . . . . . . . . . . . . . 50
5.6 H-bond lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.7 Cluster Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6 Conclusion 56
Bibliography 61

[1] S.-D. Tsai, H.-Y. Yao, and T.-H. Chang, “Exploring relaxation behaviors in
hydrogen-bond networks within binary mixtures of propylene carbonate and
primary alcohols through broadband dielectric spectroscopy and molecular
dynamic simulation,” J. Mol. Liq., p. 125043, 2024.
[2] Y.-C. Wang, “Investigation of relaxation processes and intermolecular inter-
actions of polar liquids through broadband permittivity characterization,”
Master’s thesis, National Tsing Hua University, Hsinchu City, 2022.
[3] W. Humphrey, A. Dalke, and K. Schulten, “Vmd: visual molecular dynam-
ics,” J. Mol. Graph., vol. 14, no. 1, pp. 33–38, 1996.
[4] J. Barthel, R. Buchner, C. G. H ̈olzl, and M. M ̈unsterer, “Dynamics of benzoni-
trile, propylene carbonate and butylene carbonate: The influence of molecular
shape and flexibility on the dielectric relaxation behaviour of dipolar aprotic
liquids,” 2000.
[5] J. Barthel, K. Bachhuber, R. Buchner, and H. Hetzenauer, “Dielectric spectra
of some common solvents in the microwave region. water and lower alcohols,”
Chem. Phys. Lett., vol. 165, no. 4, pp. 369–373, 1990.
[6] W. M. Haynes, ed., CRC handbook of chemistry and physics. London, Eng-
land: CRC Press, 97 ed., July 2016.
[7] “Propylene carbonate as an ecofriendly solvent: Stability studies of ripretinib
in rphplc and sustainable evaluation using advanced tools,” Sustain. Chem.
Pharm., vol. 37, p. 101355, 2024.
[8] S. K¨onig, P. Kreis, L. Reinders, R. Beyer, A.Wego, C. Herbert, M. Steinmann,
E. Frank, and M. R. Buchmeiser, “Melt spinning of propylene carbonateplasticized
poly (acrylonitrile)-co-poly (methyl acrylate),” Polym Adv Technol.,
vol. 31, no. 8, pp. 1827–1835, 2020.
[9] M. Sathish, A. Gopinath, B. Madhan, V. Subramanian, and J. R. Rao, “Cyclic
carbonate: A green multifunctional agent for sustainable leather manufacture,”
J. Clean. Prod., vol. 356, p. 131818, 2022.
[10] Y. Kondo, K. Yuki, T. Yoshida, and N. Tokura, “Nucleophilic substitution
in binary mixed solvents. kinetics and transfer enthalpies of anions in the
mixed solvents methanol+ propylene carbonate and methanol+ n-methyl-2-
pyrrolidone,” J. Chem. Soc., Faraday Trans., vol. 76, pp. 812–824, 1980.
[11] P. K. Muhuri and D. K. Hazra, “Effect of solvent composition on ionic mobilities
of some tetraalkylammonium and common ions in propylene carbonate+
methanol media at 25 c,” ZPC, vol. 190, no. 1, pp. 111–122, 1995.
[12] A. Piekarska, “Ion solvation in methanol—organic cosolvent mixtures part 5.
enthalpies of transfer of inorganic ions in mixtures of methanol and propylene
carbonate at 298.15 k,” Thermochim. Acta, vol. 244, pp. 61–67, 1994.
[13] T. N. Borhani and M. Wang, “Role of solvents in co2 capture processes: The
review of selection and design methods,” Renew. Sust. Energ. Rev., vol. 114,
p. 109299, 2019.
[14] W. Deng, L. Shi, J. Yao, and Z. Zhang, “A review on transesterification of
propylene carbonate and methanol for dimethyl carbonate synthesis,” CRC,
vol. 2, no. 3, pp. 198–212, 2019.
[15] F. Tache, S. Udrescu, F. Albu, F. Mic˘ale, and A. Medvedovici, “Greening
pharmaceutical applications of liquid chromatography through using propylene
carbonate–ethanol mixtures instead of acetonitrile as organic modifier in
the mobile phases,” J. Pharm. Biomed. Anal., vol. 75, pp. 230–238, 2013.
[16] P. K. Muhuri, B. Das, and D. K. Hazra, “Viscosities and excess molar volumes
of binary mixtures of propylene carbonate with tetrahydrofuran and methanol
at different temperatures,” J. Chem. Eng. Data, vol. 41, no. 6, pp. 1473–1476,
1996.
[17] D. Wankhede, N. Wankhede, M. Lande, and B. Arbad, “Molecular interactions
in propylene carbonate+ n-alkanols at 25 c,” J. Solut. Chem., vol. 34,
pp. 233–243, 2005.
[18] R. Francesconi and F. Comelli, “Excess enthalpies and excess volumes of the
liquid binary mixtures of propylene carbonate+ six alkanols at 298.15 k,” J.
Chem. Eng. Data, vol. 41, no. 6, pp. 1397–1400, 1996.
[19] P. K. Muhuri and D. K. Hazra, “Density and viscosity of propylene carbonate+
2-methoxyethanol at 298.15, 308.15, and 318.15 k,” J. Chem. Eng.
Data., vol. 40, no. 3, pp. 582–585, 1995.
[20] H.-Y. Yao, Y.-C. Wang, and T.-H. Chang, “Investigation of dielectric spectrums,
relaxation processes, and intermolecular interactions of primary alcohols,
carboxylic acids, and their binary mixtures,” J. Mol. Liq., vol. 353,
p. 118755, 2022.
[21] N. Nahman, “Dielectric constant measurements on n-heptane and 2-
heptanone,” tech. rep., Los Alamos National Lab.(LANL), Los Alamos, NM
(United States); Nahman (NS), 1994.
[22] U. Kaatze, “Reference liquids for the calibration of dielectric sensors and
measurement instruments,” Meas. Sci. Technol., vol. 18, no. 4, p. 967, 2007.
[23] H. Frohlich, Theory of dielectrics. Monographs on the Physics & Chemistry
of Materials, London, England: Oxford University Press, 2 ed., Dec. 1958.
[24] R. Clausius, Die Mechanische Behandlung der Electricit¨at. Wiesbaden, Germany:
Vieweg & Teubner, 2 ed., Jan. 1879.
[25] L. Onsager, “Electric moments of molecules in liquids,” J. Am. Chem. Soc.,
vol. 58, no. 8, pp. 1486–1493, 1936.
[26] J. G. Kirkwood, “The dielectric polarization of polar liquids,” J. Chem. Phys.,
vol. 7, no. 10, pp. 911–919, 1939.
[27] H. Chaube, V. Rana, P. Hudge, and A. Kumbharkhane, “Dielectric relaxation
studies of binary mixture of ethylene glycol mono phenyl ether and methanol
by time domain reflectometry,” J. Mol. Liq., vol. 193, pp. 29–36, 2014.
[28] S. Pradhan and S. Mishra, “An eye on molecular interaction studies of nonaqueous
binary liquid mixtures with reference to dielectric, refractive properties
and spectral characteristics,” J. Mol. Liq, vol. 279, pp. 317–326, 2019.
[29] S. M. Puranik, A. C. Kumbharkhane, and S. C. Mehrotra, “The static permittivity
of binary mixtures using an improved bruggeman model,” J. Mol.
Liq., vol. 59, no. 2-3, pp. 173–177, 1994.
[30] P. Debye, “Polar molecules, the chemical catalog company,” Inc., New York,
vol. 89, 1929.
[31] S. Havriliak and S. Negami, “A complex plane analysis of α-dispersions in
some polymer systems,” in J. Polym. Sci., Part C: Polym. Symp., vol. 14,
pp. 99–117, Wiley Online Library, 1966.
[32] S. Havriliak and S. Negami, “A complex plane representation of dielectric and
mechanical relaxation processes in some polymers,” Polymer, vol. 8, pp. 161–
210, 1967.
[33] J. Winkelmann, “Zur dielektrischen theorie polarer stoffe und ihrer bin¨aren
gemische,” Zeitschrift f¨ur Phys. Chemie, vol. 255, no. 1, pp. 1109–1124, 1974.
[34] J. L. MacCallum and D. P. Tieleman, “Structures of neat and hydrated 1-
octanol from computer simulations,” J. Am. Chem. Soc., vol. 124, no. 50,
pp. 15085–15093, 2002.
[35] J. Cardona, M. B. Sweatman, and L. Lue, “Molecular dynamics investigation
of the influence of the hydrogen bond networks in ethanol/water mixtures on
dielectric spectra,” J. Phys. Chem. B, vol. 122, no. 4, pp. 1505–1515, 2018.
[36] P. Petong, R. Pottel, and U. Kaatze, “Dielectric relaxation of h-bonded liquids.
mixtures of ethanol and n-hexanol at different compositions and temperatures,”
J. Phys. Chem. A, vol. 103, no. 31, pp. 6114–6121, 1999.
[37] S. Glasstone and etc., Theory of rate processes. New York, NY: McGraw-Hill,
Dec. 1941.
[38] R. S. Mulliken, “Electronic population analysis on lcao–mo molecular wave
functions. i,” J. Chem. Phys., vol. 23, no. 10, pp. 1833–1840, 1955.
[39] W. L. Jorgensen, D. S. Maxwell, and J. Tirado-Rives, “Development and testing
of the opls all-atom force field on conformational energetics and properties of organic liquids,” J. Am. Chem. Soc., vol. 118, no. 45, pp. 11225–11236,
1996.
[40] W. L. Jorgensen and J. Tirado-Rives, “The opls [optimized potentials for
liquid simulations] potential functions for proteins, energy minimizations for
crystals of cyclic peptides and crambin,” J. Am. Chem. Soc., vol. 110, no. 6,
pp. 1657–1666, 1988.
[41] J. Wang, R. M. Wolf, J. W. Caldwell, P. A. Kollman, and D. A. Case, “Development
and testing of a general amber force field,” J. Comput. Chem.,
vol. 25, no. 9, pp. 1157–1174, 2004.
[42] B. R. Brooks, C. L. Brooks III, A. D. Mackerell Jr, L. Nilsson, R. J. Petrella,
B. Roux, Y. Won, G. Archontis, C. Bartels, S. Boresch, et al., “Charmm: the
biomolecular simulation program,” J. Comp. Chem., vol. 30, no. 10, pp. 1545–
1614, 2009.
[43] J. M. Stubbs, J. J. Potoff, and J. I. Siepmann, “Transferable potentials for
phase equilibria. 6. united-atom description for ethers, glycols, ketones, and
aldehydes,” J. Phys. Chem. B, vol. 108, no. 45, pp. 17596–17605, 2004.
[44] A. C. Van Duin, S. Dasgupta, F. Lorant, and W. A. Goddard, “Reaxff: a
reactive force field for hydrocarbons,” J. Phys. Chem. A, vol. 105, no. 41,
pp. 9396–9409, 2001.
[45] K. Chenoweth, A. C. Van Duin, and W. A. Goddard, “Reaxff reactive force
field for molecular dynamics simulations of hydrocarbon oxidation,” J. Phys.
Chem. A, vol. 112, no. 5, pp. 1040–1053, 2008.
[46] T. Darden, D. York, and L. Pedersen, “Particle mesh ewald: An n log (n)
method for ewald sums in large systems,” J. Chem. Phys., vol. 98, no. 12,
pp. 10089–10092, 1993.
[47] H. J. Berendsen, J. v. Postma, W. F. Van Gunsteren, A. DiNola, and J. R.
Haak, “Molecular dynamics with coupling to an external bath,” J. Chem.
Phys., vol. 81, no. 8, pp. 3684–3690, 1984.
[48] G. J. Martyna, M. L. Klein, and M. Tuckerman, “Nos´e–hoover chains: The
canonical ensemble via continuous dynamics,” J. Chem. Phys., vol. 97, no. 4,
pp. 2635–2643, 1992.
[49] G. Bussi, D. Donadio, and M. Parrinello, “Canonical sampling through velocity
rescaling,” J. Chem. Phys., vol. 126, no. 1, 2007.
[50] M. Parrinello and A. Rahman, “Polymorphic transitions in single crystals: A
new molecular dynamics method,” J. Appl. Phys., vol. 52, no. 12, pp. 7182–
7190, 1981.
[51] Z. Luo, S. A. Burrows, S. K. Smoukov, X. Fan, and E. S. Boek, “Extension
of the trappe force field for battery electrolyte solvents,” J. Phys. Chem. B,
vol. 127, no. 10, pp. 2224–2236, 2023.
[52] B. Chen, J. J. Potoff, and J. I. Siepmann, “Monte carlo calculations for alcohols
and their mixtures with alkanes. transferable potentials for phase equilibria.
5. united-atom description of primary, secondary, and tertiary alcohols,”
J. Phys. Chem. B, vol. 105, no. 15, pp. 3093–3104, 2001.
[53] B. L. Eggimann, Y. Sun, R. F. DeJaco, R. Singh, M. Ahsan, T. R. Josephson,
and J. I. Siepmann, “Assessing the quality of molecular simulations for vapor–
liquid equilibria: An analysis of the trappe database,” J. Chem. Eng. Data,
vol. 65, no. 3, pp. 1330–1344, 2019.
[54] B. Hess, H. Bekker, H. J. Berendsen, and J. G. Fraaije, “Lincs: A linear constraint
solver for molecular simulations,” J. Comput. Chem., vol. 18, no. 12,
pp. 1463–1472, 1997.
[55] M. J. Abraham, T. Murtola, R. Schulz, S. P´all, J. C. Smith, B. Hess, and
E. Lindahl, “Gromacs: High performance molecular simulations through
multi-level parallelism from laptops to supercomputers,” SoftwareX, vol. 1,
pp. 19–25, 2015.
[56] N. Michaud-Agrawal, E. J. Denning, T. B. Woolf, and O. Beckstein, “Mdanalysis:
a toolkit for the analysis of molecular dynamics simulations,” J.
Comput. Chem., vol. 32, no. 10, pp. 2319–2327, 2011.
[57] R. J. Gowers, M. Linke, J. Barnoud, T. J. E. Reddy, M. N. Melo, S. L. Seyler,
J. Domanski, D. L. Dotson, S. Buchoux, I. M. Kenney, et al., “Mdanalysis:
a python package for the rapid analysis of molecular dynamics simulations,”
tech. rep., Los Alamos National lab.(LANL), Los Alamos, NM (United
States), 2019.
[58] P. Smith, R. M. Ziolek, E. Gazzarrini, D. M. Owen, and C. D. Lorenz, “On
the interaction of hyaluronic acid with synovial fluid lipid membranes,” Phys.
Chem. Chem. Phys., vol. 21, no. 19, pp. 9845–9857, 2019.
[59] A. Hagberg, P. J. Swart, and D. A. Schult, “Exploring network structure,
dynamics, and function using networkx,” tech. rep., Los Alamos National
Laboratory (LANL), Los Alamos, NM (United States), 2008.
[60] J.-P. Hansen and I. R. McDonald, Theory of simple liquids: with applications
to soft matter. Academic press, 2013.
[61] K. A. Maerzke, N. E. Schultz, R. B. Ross, and J. I. Siepmann, “Trappe-ua
force field for acrylates and monte carlo simulations for their mixtures with
alkanes and alcohols,” J. Phys. Chem. B, vol. 113, no. 18, pp. 6415–6425,
2009.
[62] M. D. Hanwell, D. E. Curtis, D. C. Lonie, T. Vandermeersch, E. Zurek, and
G. R. Hutchison, “Avogadro: an advanced semantic chemical editor, visualization,
and analysis platform,” J. Cheminformatics, vol. 4, pp. 1–17, 2012.
[63] C. Zhang and G. Galli, “Dipolar correlations in liquid water,” J. Chem. Phys.,
vol. 141, no. 8, 2014.