The dielectric constants (Dk) and dissipation factors (Df) of 11 types of polyimides (PIs) were systematically measured between 25 and 330 GHz using Fabry–Pérot resonators. Herein, the relationships between their frequency dependence and chemical structure are discussed. As the frequency increased, all the PIs exhibited a continuous decrease in Dk and a consistent increase in Df. Notably, no distinct peaks were observed over the entire frequency range. The decrease in Dk with frequency gradually approached the square of the refractive index (n2) in the near-infrared region. Additionally, based on the correlation between the dielectric dispersion and dielectric polarization (Pt), Dk showed a stronger correlation with the electronic polarization (Pe) at higher frequencies than with the dipolar orientational polarization (Pd). Moreover, in fluorine-containing PIs, Dk declined faster with increasing frequency as the fluorine content (F%) increased. Meanwhile, the increase in Df showed a negative correlation with the weight fraction of polar groups (polar%), and the PIs containing –CF3 groups in the diamine moieties exhibited a similar rapid increase in Df with frequency, suggesting characteristic absorptions in the terahertz (THz) domain. These data will be beneficial for developing high-performance polymer-based insulating materials for 5th/6th generation wireless communication technologies.
REFERENCES
1.
T. S.
Rappaport
,
Y.
Xing
,
O.
Kanhere
,
S.
Ju
,
A.
Madanayake
,
S.
Mandal
,
A.
Alkhateeb
, and
G. C.
Trichopoulos
, “
Wireless communications and applications above 100 GHz: Opportunities and challenges for 6G and beyond
,” IEEE Access
7
, 78729
–78757
(2019
).2.
S.
Dang
,
O.
Amin
,
B.
Shihada
, and
M.-S.
Alouini
, “
What should 6G be?
,” Nat. Electron.
3
(1
), 20
–29
(2020
).3.
N. D.
Orloff
,
R.
Ubic
, and
M.
Lanagan
, “
Special topic on materials and devices for 5G electronics
,” Appl. Phys. Lett.
120
(6
), 060402
(2022
).4.
A. J.
Bur
, “
Dielectric properties of polymers at microwave frequencies: A review
,” Polymer.
26
(7
), 963
–977
(1985
).5.
G.
Maier
, “
Low dielectric constant polymers for microelectronics
,” Prog. Polym. Sci.
26
(1
), 3
–65
(2001
).6.
Y.
Qiao
,
X.
Yin
,
T.
Zhu
,
H.
Li
, and
C.
Tang
, “
Dielectric polymers with novel chemistry, compositions and architectures
,” Prog. Polym. Sci.
80
, 153
–162
(2018
).7.
Y.
Liu
,
C.
Qian
,
L.
Qu
,
Y.
Wu
,
Y.
Zhang
,
X.
Wu
,
B.
Zou
,
W.
Chen
,
Z.
Chen
,
Z.
Chi
,
S.
Liu
,
X.
Chen
, and
J.
Xu
, “
A bulk dielectric polymer film with intrinsic ultralow dielectric constant and outstanding comprehensive properties
,” Chem. Mater.
27
(19
), 6543
–6549
(2015
).8.
C.
Qian
,
R.
Bei
,
T.
Zhu
,
W.
Zheng
,
S.
Liu
,
Z.
Chi
,
M. P.
Aldred
,
X.
Chen
,
Y.
Zhang
, and
J.
Xu
, “
Facile strategy for intrinsic low-k dielectric polymers: Molecular design based on secondary relaxation behavior
,” Macromolecules
52
(12
), 4601
–4609
(2019
).9.
P. D.
Cunningham
,
N. N.
Valdes
,
F. A.
Vallejo
,
L. M.
Hayden
,
B.
Polishak
,
X. H.
Zhou
,
J.
Luo
,
A. K. Y.
Jen
,
J. C.
Williams
, and
R. J.
Twieg
, “
Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials
,” J. Appl. Phys.
109
(4
), 043505
(2011
).10.
S.
Sahin
,
N. K.
Nahar
, and
K.
Sertel
, “
Dielectric properties of low-loss polymers for mmW and THz applications
,” J. Infrared Millim. Terahertz Waves
40
(5
), 557
–573
(2019
).11.
R.
Sawada
and
S.
Ando
, “
Polarization analysis and humidity dependence of dielectric properties of aromatic and semialicyclic polyimides measured at 10 GHz
,” J. Phys. Chem. C
128
(16
), 6979
–6990
(2024
).12.
C.-C.
Kuo
,
Y.-C.
Lin
,
Y.-C.
Chen
,
P.-H.
Wu
,
S.
Ando
,
M.
Ueda
, and
W.-C.
Chen
, “
Correlating the molecular structure of polyimides with the dielectric constant and dissipation factor at a high frequency of 10 GHz
,” ACS Appl. Polym. Mater.
3
(1
), 362
–371
(2021
).13.
Q.
Yin
,
Y.
Qin
,
J.
Lv
,
X.
Wang
,
L.
Luo
, and
X.
Liu
, “
Reducing intermolecular friction work: Preparation of polyimide films with ultralow dielectric loss from MHz to THz frequency
,” Ind. Eng. Chem. Res.
61
(49
), 17894
–17903
(2022
).14.
Y. C.
Cheng
,
Y. C.
Chen
,
Y. C.
Lin
,
C. C.
Kuo
, and
W. C.
Chen
, “
Exploring the cross-linking effect on decreasing the dielectric constant and dissipation factor of poly(ester imide)s at a high frequency of 10-40 GHz
,” ACS Appl. Polym. Mater.
5
(10
), 7907
–7917
(2023
).15.
T.
Matsuura
,
Y.
Hasuda
,
S.
Nishi
, and
N.
Yamada
, “
Polyimide derived from 2,2′-bis(trifluoromethyl)-4,4′-diaminobiphenyl. 1. Synthesis and characterization of polyimides prepared with 2,2-bis(3,4-dicarboxyphenyl)hexafluoropropane dianhydride or pyromellitic dianhydride
,” Macromolecules
24
(18
), 5001
–5005
(1991
).16.
S.
Ando
,
T.
Matsuura
, and
S.
Sasaki
, “
Perfluorinated polyimide synthesis
,” Macromolecules
25
(21
), 5858
–5860
(1992
).17.
R.
Sawada
and
S.
Ando
, “
Colorless, low dielectric, and optically active semialicyclic polyimides incorporating a biobased isosorbide moiety in the main chain
,” Macromolecules
55
(15
), 6787
–6800
(2022
).18.
M. D.
Janezic
and
J.
Baker-Jarvis
, “
Full-wave analysis of a split-cylinder resonator for nondestructive permittivity measurements
,” IEEE Trans. Microwave Theory Tech.
47
(10
), 2014
–2020
(1999
).19.
K.
Hirayama
,
Y.
Yanagimoto
,
J. I.
Sugisaka
, and
T.
Yasui
, “
Permittivity measurement method for thin sheets using split-cylinder resonator with protrusions
,” IEEE Trans. Instrum. Meas.
71
, 1
–9
(2022
).20.
A. M.
Nicolson
and
G. F.
Ross
, “
Measurement of the intrinsic properties of materials by time-domain techniques
,” IEEE Trans. Instrum. Meas.
19
(4
), 377
–382
(1970
).21.
J.
Baker-Jarvis
,
E. J.
Vanzura
, and
W. A.
Kissick
, “
Improved technique for determining complex permittivity with the transmission/reflection method
,” IEEE Trans. Microwave Theory Tech.
38
(8
), 1096
–1103
(1990
).22.
A. L.
Cullen
and
P. K.
Yu
, “
The accurate measurement of permittivity by means of an open resonator
,” Proc. R. Soc. London. A.: Math. Phys. Sci.
325
, 493
–509
(1971
).23.
S.
Ando
,
T.
Matsuura
, and
S.
Sasaki
, “
Synthesis of perfluorinated polyimides for optical applications
,” ACS Symp. Ser.
537
, 304
–322
(1993
).24.
R.
Ishige
,
T.
Masuda
,
Y.
Kozaki
,
E.
Fujiwara
,
T.
Okada
, and
S.
Ando
, “
Precise analysis of thermal volume expansion of crystal lattice for fully aromatic crystalline polyimides by x-ray diffraction method: Relationship between molecular structure and linear/volumetric thermal expansion
,” Macromolecules
50
(5
), 2112
–2123
(2017
).25.
K.
Goto
,
T.
Akiike
,
Y.
Inoue
, and
M.
Matsubara
, “
Polymer design for thermally stable polyimides with low dielectric constant
,” Macromol. Symp.
199
(1
), 321
–332
(2003
).26.
K. C.
Kao
, Dielectric Phenomena in Solids with Emphasis on Physical Concepts of Electronic Processes
(
Academic Press
,
Amsterdam, Boston
, 2004
).27.
D.
Klempner
and
F. E.
Karasz
, Electrical Properties of Polymers
, 2nd ed. (
Cambridge University Press
,
Cambridge, New York
, 1972
).28.
T. J.
Lin
, “
The influence of large pendent groups on chain anisotropy and electrical energy loss of polyimides at high frequency through all-atomic molecular simulation
,” ChemPhysChem
24
(24
), e202300479
(2023
).29.
L.
Zhu
, “
Exploring strategies for high dielectric constant and low loss polymer dielectrics
,” J. Phys. Chem. Lett.
5
(21
), 3677
–3687
(2014
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
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