First-Principles Study on High Dielectric-Constant and Breakdown Mechanism of PVDF and Its Copolymer

Dielectric polymers are crucial for high-power energy storage devices, such as electromagnetic cannons, high-energy pulsed lasers, and automatic external defibrillators, due to their high breakdown strength, fast discharge rate, easily tunable structure, and light weight. However, the low permittivity of polymers results in large-sized energy storage devices, which are difficult to miniaturize. Two approaches are typically employed to enhance the permittivity of polymers. The first one is to synthesize novel polymers of high dielectric constant, while the second one is to add inorganic fillers of high permittivity into the polymers. However, the first approach is faced with a challenge that the microscopic mechanisms of polymer permittivity remain unclear, hindering systematic improvements of permittivity. While the second approach presents a problem that the introduction of inorganic nanofillers into a polymer usually leads to a significant decrease of the breakdown strength, ultimately resulting in a low energy storage density of the composites. The microscopic mechanisms behind the breakdown behavior remain elusive.

To address the two issues, the high-dielectric mechanisms of these polymers are first studied by comparing the computed electronic, ionic, and dipolar permittivity of Polyvinylidene fluoride (PVDF), Polytrifluoroethylene (PTrFE), and their copolymer Poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) by both the density functional perturbation theory and the dipole fluctuation method based on the first-principles molecular dynamics. We find that the permittivity of these polymers at low temperatures are mainly induced by electrons and ions, similar to those of inorganic crystals. Above room temperature, their dielectric constants are mainly contributed by the dipole fluctuation of polar groups in the molecular chains. Moreover, the dielectric property of P(VDF-TrFE) is more sensitive to stress compared to that of PVDF or PTrFE. On the other hand, the microscopic breakdown mechanisms of the BaTiO₃@PVDF nanocomposites are investigated by first-principles thermodynamic and kinetic methods. The results show that the abundant and highly oxidative oxygen vacancies on the surface of BaTiO₃ can react easily with PVDF, consequently damaging the structure of PVDF and reducing the breakdown strength of their composites. Overall, our research reveals three origins of the dielectric constants in polymers and their contributions in different temperature regions, as well as the microscopic breakdown mechanisms induced by oxide additives in polymers. These findings provide a theoretical basis for the design of new polymer dielectric materials and organic-inorganic composite dielectric materials.

Keywords: Dielectric materials for energy storage; breakdown mechanism; first-principles calculations; density functional perturbation theory; dipole fluctuation methodDielectric polymers are crucial for high-power energy storage devices, such as electromagnetic cannons, high-energy pulsed lasers, and automatic external defibrillators, due to their high breakdown strength, fast discharge rate, easily tunable structure, and light weight. However, the low permittivity of polymers results in large-sized energy storage devices, which are difficult to miniaturize. Two approaches are typically employed to enhance the permittivity of polymers. The first one is to synthesize novel polymers of high dielectric constant, while the second one is to add inorganic fillers of high permittivity into the polymers. However, the first approach is faced with a challenge that the microscopic mechanisms of polymer permittivity remain unclear, hindering systematic improvements of permittivity. While the second approach presents a problem that the introduction of inorganic nanofillers into a polymer usually leads to a significant decrease of the breakdown strength, ultimately resulting in a low energy storage density of the composites. The microscopic mechanisms behind the breakdown behavior remain elusive.

To address the two issues, the high-dielectric mechanisms of these polymers are first studied by comparing the computed electronic, ionic, and dipolar permittivity of Polyvinylidene fluoride (PVDF), Polytrifluoroethylene (PTrFE), and their copolymer Poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) by both the density functional perturbation theory and the dipole fluctuation method based on the first-principles molecular dynamics. We find that the permittivity of these polymers at low temperatures are mainly induced by electrons and ions, similar to those of inorganic crystals. Above room temperature, their dielectric constants are mainly contributed by the dipole fluctuation of polar groups in the molecular chains. Moreover, the dielectric property of P(VDF-TrFE) is more sensitive to stress compared to that of PVDF or PTrFE. On the other hand, the microscopic breakdown mechanisms of the BaTiO₃@PVDF nanocomposites are investigated by first-principles thermodynamic and kinetic methods. The results show that the abundant and highly oxidative oxygen vacancies on the surface of BaTiO₃ can react easily with PVDF, consequently damaging the structure of PVDF and reducing the breakdown strength of their composites. Overall, our research reveals three origins of the dielectric constants in polymers and their contributions in different temperature regions, as well as the microscopic breakdown mechanisms induced by oxide additives in polymers. These findings provide a theoretical basis for the design of new polymer dielectric materials and organic-inorganic composite dielectric materials.

[1] ZHANG M H, QI J L, LIU Y Q, et al. High energy storage capability of perovskite relaxor ferroelectrics via hierarchical optimization[J]. Rare Metals, 2022, 41(3): 730-744.
[2] ZHANG B. Mechanisms of dielectric enhancement in innovative polymeric metamaterials[M]. North Carolina State University, 2020.
[3] DONG J F, DENG X L, NIU Y J, et al. Research progress of polymer based dielectrics for high-temperature capacitor energy storage[J]. Acta Physica Sinica, 2020, 69(21): 217701.
[4] JIANG P, HUANG X. Editorial: Dielectric materials for electrical energy storage[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2017, 24(2): 675-675.
[5] XIA W, ZHANG Z. PVDF-based dielectric polymers and their applications in electronic materials[J]. IET Nanodielectrics, 2018, 1(1): 17-31.
[6] RUAN L, YAO X, CHANG Y, et al. Properties and applications of the β phase poly(vinylidene fluoride)[J]. Polymers, 2018, 10(3): 228.
[7] KAWAI H. The piezoelectricity of poly(vinylidene Fluoride)[J]. Japanese Journal of Applied Physics, 1969, 8(7): 975-976.
[8] U.K. Clarivate. Web of Science[DB/OL]. London : U.K. Clarivate, 2020
[2020.12.31]. https://www.webofscience.com/wos/alldb/analyze-results/cf61be13-fa24-4d2d-9c1a-fdb885646195-6935bdca.
[9] BOHLéN M, BOLTON K. Conformational studies of poly(vinylidene fluoride), poly(trifluoroethylene) and poly(vinylidene fluoride-co-trifluoroethylene) using density functional theory[J]. Physical Chemistry Chemical Physics, 2014, 16(25): 12929-12939.
[10] THAKUR V K, LIN M F, TAN E J, et al. Green aqueous modification of fluoropolymers for energy storage applications[J]. Journal of Materials Chemistry, 2012, 22(13): 5951-5959.
[11] THAKUR V K, TAN E J, LIN M F, et al. Poly(vinylidene fluoride)-graft-poly(2-hydroxyethyl methacrylate): A novel material for high energy density capacitors[J]. Journal of Materials Chemistry, 2011, 21(11): 3751-3759.
[12] LIU Y, ZHANG B, XU W, et al. Chirality-induced relaxor properties in ferroelectric polymers[J]. Nature Materials, 2020, 19(11): 1169-1174.
[13] WU C, DESHMUKH A A, LI Z, et al. Flexible temperature-invariant polymer dielectrics with large bandgap[J]. Advanced Materials, 2020, 32(21): 2000499.
[14] WANG Y, YAO M G, MA R, et al. Design strategy of barium titanate/polyvinylidene fluoride-based nanocomposite films for high energy storage[J]. Journal of Materials Chemistry A, 2020, 8(3): 884-917.
[15] FENG Y, WU Q, DENG Q, et al. High dielectric and breakdown properties obtained in a PVDF based nanocomposite with sandwich structure at high temperature via all-2D design[J]. Journal of Materials Chemistry C, 2019, 7(22): 6744-6751.
[16] MAMMERI F. Chapter 3 - Nanostructured flexible PVDF and fluoropolymer-based hybrid films[M]. France: Elsevier, 2019.
[17] LIN B, LI Z T, YANG Y, et al. Enhanced dielectric permittivity in surface-modified graphene/PVDF composites prepared by an electrospinning-hot pressing method[J]. Composites Science and Technology, 2019, 172: 58-65.
[18] PIPERTZIS A, ASADI K, FLOUDAS G. P(VDF-TrFE) copolymer dynamics as a function of temperature and pressure in the vicinity of the curie transition[J]. Macromolecules, 2022, 55(7): 2746-2757.
[19] MAO P, WANG J, ZHANG L, et al. Tunable dielectric polarization and breakdown behavior for high energy storage capability in P(VDF–TrFE–CFE)/PVDF polymer blended composite films[J]. Physical Chemistry Chemical Physics, 2020, 22(23): 13143-13153.
[20] GUO R, LUO H, ZHOU X, et al. Ultrahigh energy density of poly(vinylidene fluoride) from synergistically improved dielectric constant and withstand voltage by tuning the crystallization behavior[J]. Journal of Materials Chemistry A, 2021, 9(48): 27660-27671.
[21] YAGI T, TATEMOTO M, SAKO J. Transition behavior and dielectric properties in trifluoroethylene and vinylidene fluoride copolymers[J]. Polymer Journal, 1980, 12(4): 209-223.
[22] LIU S, XUE S, ZHANG W, et al. Significantly enhanced dielectric property in PVDF nanocomposites flexible films through a small loading of surface-hydroxylated Ba0.6Sr0.4TiO3 nanotubes[J]. Journal of Materials Chemistry A, 2014, 2(42): 18040-18046.
[23] BO R, LIU J, WANG C, et al. Molecular dynamics simulation on structure and dielectric permittivity of BaTiO3/PVDF composites[J]. Advances in Polymer Technology, 2021, 2021: 9019580.
[24] LIU Y, AZIGULI H, ZHANG B, et al. Ferroelectric polymers exhibiting behaviour reminiscent of a morphotropic phase boundary[J]. Nature, 2018, 562(7725): 96-100.
[25] ZHOU X, CHU B, NEESE B, et al. Electrical energy density and discharge characteristics of a poly(vinylidene fluoride-chlorotrifluoroethylene) copolymer[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2007, 14(5): 1133-1138.
[26] LI J, SUN Z, YAN F. Solution processable low-voltage organic thin film transistors with high-k relaxor ferroelectric polymer as gate insulator[J]. Advanced Materials, 2012, 24(1): 88-93.
[27] TAN D Q. The search for enhanced dielectric strength of polymer-based dielectrics: A focused review on polymer nanocomposites[J]. Journal of Applied Polymer Science, 2020, 137(33): 32.
[28] PRATEEK, THAKUR V K, GUPTA R K. Recent progress on ferroelectric polymer-based nanocomposites for high energy density capacitors: synthesis, dielectric properties, and future aspects[J]. Chemical Reviews, 2016, 116(7): 4260-4317.
[29] HAO Y, WANG X, BI K, et al. Significantly enhanced energy storage performance promoted by ultimate sized ferroelectric BaTiO3 fillers in nanocomposite films[J]. Nano Energy, 2017, 31: 49-56.
[30] WANG Y U, TAN D Q, KRAHN J. Computational study of dielectric composites with core-shell filler particles[J]. Journal of Applied Physics, 2011, 110(4): 044103.
[31] ANAND A, BHATNAGAR M C. Role of vertically aligned and randomly placed zinc oxide (ZnO) nanorods in PVDF matrix: Used for energy harvesting[J]. Materials Today Energy, 2019, 13: 293-301.
[32] ZHANG X, SHEN Y, ZHANG Q, et al. Ultrahigh energy density of polymer nanocomposites containing BaTiO3@TiO2 nanofibers by atomic-scale interface engineering[J]. Advanced Materials, 2015, 27(5): 819-824.
[33] SUN Q, MAO P, ZHANG L, et al. Significantly enhanced dielectric and energy storage performance of AlN/KNbO3/PVDF sandwich-structured composites via introducing the AlN/PVDF insulating layers[J]. Ceramics International, 2020, 46(8): 9990-9996.
[34] SHEHZAD K, ULHAQ A, AHMAD S, et al. All-organic PANI–DBSA/PVDF dielectric composites with unique electrical properties[J]. Journal of Materials Science, 2013, 48(10): 3737-3744.
[35] RAHAMAN M H, YAQOOB U, KIM H C. The effects of conductive nano fillers alignment on the dielectric properties of copolymer matrix[J]. Advanced Manufacturing: Polymer & Composites Science, 2019, 5(1): 29-36.
[36] WANG Y, CUI J, YUAN Q, et al. Significantly enhanced breakdown strength and energy density in sandwich-structured barium titanate/poly(vinylidene fluoride) nanocomposites[J]. Advanced Materials, 2015, 27(42): 6658-6663.
[37] CUI Y, WANG X, CHI Q, et al. Sandwich structured BT-Fe3O4/PVDF composites with excellent dielectric properties and energy density[J]. Journal of Materials Science: Materials in Electronics, 2017, 28(16): 11900-11906.
[38] KARASAWA N, GODDARD W A. Dielectric properties of poly(vinylidene fluoride) from molecular dynamics simulations[J]. Macromolecules, 1995, 28(20): 6765-6772.
[39] CHENG H P, CHEN G H, QIN R, et al. Electronic structures and optical properties of poly(vinylidene fluoride) crystals[J]. Acta Physico-Chimica Sinica, 2014, 30(2): 281-288.
[40] BARGAIN F, PANINE P, DOMINGUES DOS SANTOS F, et al. From solvent-cast to annealed and poled poly(VDF-co-TrFE) films: New insights on the defective ferroelectric phase[J]. Polymer, 2016, 105: 144-156.
[41] TOMAR R, PANDEY R, SINGH N B, et al. Electrical properties of barium titanate in presence of Sn2+ dopant[J]. SN Applied Sciences, 2020, 2(2): 226.
[42] DWIJ V, DE B K, SHARMA G, et al. Revisiting 70 years of lattice dynamics of BaTiO3: Combined first principle and experimental investigation[J]. arXiv, 2020, 2012: 12669.
[43] BOKOV A A, YE Z G. Recent progress in relaxor ferroelectrics with perovskite structure[J]. Journal of Materials Science, 2006, 41(1): 31-52.
[44] GRIFFITHS D J, SCHROETER D F. Introduction to quantum mechanics[M]. Cambridge: Cambridge University Press, 2018.
[45] CEPERLEY D, ALDER B. Quantum Monte Carlo[J]. Science, 1986, 231(4738): 555-560.
[46] BARTLETT R J, MUSIAŁ M. Coupled-cluster theory in quantum chemistry[J]. Reviews of Modern Physics, 2007, 79(1): 291-352.
[47] SCHLEGEL H B. Moeller-Plesset perturbation theory with spin projection[J]. The Journal of Physical Chemistry, 1988, 92(11): 3075-3078.
[48] TEWARY V K. Green-function method for lattice statics[J]. Advances in Physics, 1973, 22(6): 757-810.
[49] ORIO M, PANTAZIS D A, NEESE F. Density functional theory[J]. Photosynthesis Research, 2009, 102(2): 443-453.
[50] MAZUREK A H, SZELESZCZUK Ł, PISKLAK D M. Periodic DFT calculations: Review of applications in the pharmaceutical sciences[J/OL]. Pharmaceutics, 2020, 12(5):415
[2020-12-23]. https://arxiv.org/abs/2012.12669. DOI:10.3390/pharmaceutics12050415.
[51] COMBES J M, DUCLOS P, SEILER R. The Born-Oppenheimer approximation[M]. Boston, MA: Springer US, 1981.
[52] EISBERG R, RESNICK R. Quantum physics of atoms, molecules, solids, nuclei, and particles, 2nd Edition[M]. Ann Arbor, Michigan: Wiley, 1985.
[53] HOHENBERG P, KOHN W. Inhomogeneous electron gas[J]. Physical Review, 1964, 136(3B): B864-B871.
[54] KOHN W, SHAM L J. Self-consistent equations including exchange and correlation effects[J]. Physical Review, 1965, 140(4A): A1133-A1138.
[55] MARTIN R M. Determination of electronic structure: The three basic methods[M]. Cambridge: Cambridge University Press, 2004.
[56] PERDEW J P, BURKE K, ERNZERHOF M. Generalized gradient approximation made simple[J]. Physical Review Letters, 1996, 77(18): 3865-3868.
[57] CONSTANTIN L A, FABIANO E, DELLA SALA F. Meta-GGA exchange-correlation functional with a balanced treatment of nonlocality[J]. Journal of Chemical Theory and Computation, 2013, 9(5): 2256-2263.
[58] CORDERO E, TRAPASSO S I. Linear perturbations of the Wigner distribution and the Cohen class[J]. Analysis and Applications, 2019, 18(03): 385-422.
[59] PERDEW J P, ZUNGER A. Self-interaction correction to density-functional approximations for many-electron systems[J]. Physical Review B, 1981, 23(10): 5048-5079.
[60] COLE L A, PERDEW J P. Calculated electron affinities of the elements[J]. Physical Review A, 1982, 25(3): 1265-1271.
[61] VOSKO S H, WILK L, NUSAIR M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis[J]. Canadian Journal of Physics, 1980, 58(8): 1200-1211.
[62] HEYD J, SCUSERIA G E, ERNZERHOF M. Hybrid functionals based on a screened Coulomb potential[J]. The Journal of Chemical Physics, 2003, 118(18): 8207-8215.
[63] PERDEW J P, BURKE K, ERNZERHOF M. Perdew, Burke, and Ernzerhof reply[J]. Physical Review Letters, 1998, 80(4): 891-891.
[64] BURKE K, PERDEW J P, WANG Y. Derivation of a generalized gradient approximation: The PW91 density functional[M]. New Orleans, LA: Springer, 1998.
[65] ZHANG T, YANG X, GE Q. Surface chemistry and reactivity of α-MoO3 toward methane: A SCAN-functional based DFT study[J]. The Journal of Chemical Physics, 2019, 151(4): 044708.
[66] ADAMO C, BARONE V. Toward reliable density functional methods without adjustable parameters: The PBE0 model[J]. The Journal of Chemical Physics, 1999, 110(13): 6158-6170.
[67] HEYD J, SCUSERIA G E. Efficient hybrid density functional calculations in solids: Assessment of the Heyd–Scuseria–Ernzerhof screened Coulomb hybrid functional[J]. The Journal of Chemical Physics, 2004, 121(3): 1187-1192.
[68] MARSMAN M, PAIER J, STROPPA A, et al. Hybrid functionals applied to extended systems[J]. Journal of Physics: Condensed Matter, 2008, 20(6): 064201.
[69] HANSSON T, OOSTENBRINK C, VAN GUNSTEREN W. Molecular dynamics simulations[J]. Current Opinion in Structural Biology, 2002, 12(2): 190-196.
[70] PECHUKAS P. Transition state theory[J]. Annual Review of Physical Chemistry, 1981, 32(1): 159-177.
[71] HOSPITAL A, GOñI J R, OROZCO M, et al. Molecular dynamics simulations: advances and applications[J]. Advances and Applications in Bioinformatics and Chemistry, 2015, 8: 37-47.
[72] ALBINA J M, KUBO A, SHIIHARA Y, et al. Coarse-grained molecular dynamics simulations of boundary lubrication on nanostructured metal surfaces[J]. Tribology Letters, 2020, 68(1): 49.
[73] CHAMOLLY A, LAUGA E. Stochastic dynamics of dissolving active particles[J]. The European Physical Journal E, 2019, 42(7): 88.
[74] MARK E T. Ab initio molecular dynamics: Basic concepts, current trends and novel applications[J]. Journal of Physics: Condensed Matter, 2002, 14(50): R1297.
[75] JINNOUCHI R, LAHNSTEINER J, KARSAI F, et al. Phase transitions of hybrid perovskites simulated by machine-learning force fields trained on the fly with bayesian inference[J]. Physical Review Letters, 2019, 122(22): 225701.
[76] FRIEDERICH P, HäSE F, PROPPE J, et al. Machine-learned potentials for next-generation matter simulations[J]. Nature Materials, 2021, 20(6): 750-761.
[77] FEYNMAN R P. Forces in molecules[J]. Physical Review, 1939, 56(4): 340-343.
[78] KRESSE G, HAFNER J. Ab initio molecular dynamics for liquid metals[J]. Physical Review B, 1993, 47(1): 558-561.
[79] GIANNOZZI P, BARONI S, BONINI N, et al. QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials[J]. Journal of Physics: Condensed Matter, 2009, 21(39): 395502.
[80] GONZE X, AMADON B, ANGLADE P M, et al. ABINIT: First-principles approach to material and nanosystem properties[J]. Computer Physics Communications, 2009, 180(12): 2582-2615.
[81] BROOKS C L, CASE D A, PLIMPTON S, et al. Classical molecular dynamics[J]. The Journal of Chemical Physics, 2021, 154(10): 100401.
[82] THOMPSON A P, AKTULGA H M, BERGER R, et al. LAMMPS: A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales[J]. Computer Physics Communications, 2022, 271: 108171.
[83] SMITH W, YONG C W, RODGER P M. DL_POLY: Application to molecular simulation[J]. Molecular Simulation, 2002, 28(5): 385-471.
[84] WANG H, ZHANG L, HAN J, et al. DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics[J]. Computer Physics Communications, 2018, 228: 178-184.
[85] GRIFFITHS R B. Microcanonical ensemble in quantum statistical mechanics[J]. Journal of Mathematical Physics, 1965, 6(10): 1447-1461.
[86] BRYAN G H. Elementary principles in statistical mechanics[J]. Nature, 1902, 66(1708): 291-292.
[87] DILL K, BROMBERG S. Molecular driving forces: Statistical thermodynamics in biology, chemistry, physics, and nanoscience[M]. New York, NY: Garland Science, 2010.
[88] ANDERSEN H C. Molecular dynamics simulations at constant pressure and/or temperature[J]. The Journal of Chemical Physics, 1980, 72(4): 2384-2393.
[89] HOOVER W G, LADD A J C, MORAN B. High-strain-rate plastic flow studied via nonequilibrium molecular dynamics[J]. Physical Review Letters, 1982, 48(26): 1818-1820.
[90] NOSé S. A unified formulation of the constant temperature molecular dynamics methods[J]. The Journal of Chemical Physics, 1984, 81(1): 511-519.
[91] MOU S, WU T, XIE J, et al. Boron phosphide nanoparticles: A nonmetal catalyst for high-selectivity electrochemical reduction of CO2 to CH3OH[J]. Advanced Materials, 2019, 31(36): 1903499.
[92] RAO D, ZHANG L, MENG Z, et al. Ultrahigh energy storage and ultrafast ion diffusion in borophene-based anodes for rechargeable metal ion batteries[J]. Journal of Materials Chemistry A, 2017, 5(5): 2328-2338.
[93] AIERKEN Y, SEVIK C, GüLSEREN O, et al. MXenes/graphene heterostructures for Li battery applications: A first principles study[J]. Journal of Materials Chemistry A, 2018, 6(5): 2337-2345.
[94] SHEPPARD D, TERRELL R, HENKELMAN G. Optimization methods for finding minimum energy paths[J]. The Journal of Chemical Physics, 2008, 128(13): 134106.
[95] HENKELMAN G, UBERUAGA B P, JóNSSON H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths[J]. The Journal of Chemical Physics, 2000, 113(22): 9901-9904.
[96] LAIDLER K J, KING M C. Development of transition-state theory[J]. The Journal of Physical Chemistry, 1983, 87(15): 2657-2664.
[97] ZHU L, WANG Q. Novel ferroelectric polymers for high energy density and low loss dielectrics[J]. Macromolecules, 2012, 45(7): 2937-2954.
[98] GONZE X, LEE C. Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory[J]. Physical Review B, 1997, 55(16): 10355-10368.
[99] ZUAZUA E. Propagation, observation, and control of waves approximated by finite difference methods[J]. SIAM Review, 2005, 47(2): 197-243.
[100] YU P Y, CARDONA M. Electronic band structures[M]. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996.
[101] SHARMA V, WANG C, LORENZINI R G, et al. Rational design of all organic polymer dielectrics[J]. Nature Communications, 2014, 5(1): 4845.
[102] PETOUSIS I, CHEN W, HAUTIER G, et al. Benchmarking density functional perturbation theory to enable high-throughput screening of materials for dielectric constant and refractive index[J]. Physical Review B, 2016, 93(11): 115151.
[103] RUUSKA H, AROLA E, KORTELAINEN T, et al. A density functional study on dielectric properties of acrylic acid grafted polypropylene[J]. The Journal of Chemical Physics, 2011, 134(13): 134904.
[104] CHOUDHARY K, GARRITY K F, SHARMA V, et al. High-throughput density functional perturbation theory and machine learning predictions of infrared, piezoelectric, and dielectric responses[J]. npj Computational Materials, 2020, 6(1): 64.
[105] KIM C, CHANDRASEKARAN A, HUAN T D, et al. Polymer genome: A data-powered polymer informatics platform for property predictions[J]. The Journal of Physical Chemistry C, 2018, 122(31): 17575-17585.
[106] KRISHNAMOORTHY A, NOMURA K I, BARADWAJ N, et al. Dielectric constant of liquid water determined with neural network quantum molecular dynamics[J]. Physical Review Letters, 2021, 126(21): 216403.
[107] WANG Y, ZHANG Z, ZHENG R, et al. Calculation method for the dielectric constant of thioglycolic acid grafted modified SBS dielectric elastomer[J]. Arabian Journal of Chemistry, 2021, 14(10): 103361.
[108] HOU W, YANG L, MO Y, et al. Static dielectric constant and dielectric loss of cellulose insulation: Molecular dynamics simulations[J]. High Voltage, 2021, 6(6): 1051-1060.
[109] MARZARI N, VANDERBILT D. Maximally localized generalized Wannier functions for composite energy bands[J]. Physical Review B, 1997, 56(20): 12847-12865.
[110] WANG V, XU N, LIU J C, et al. VASPKIT: A user-friendly interface facilitating high-throughput computing and analysis using VASP code[J]. Computer Physics Communications, 2021, 267: 108033.
[111] TOGO A, TANAKA I. First principles phonon calculations in materials science[J]. Scripta Materialia, 2015, 108: 1-5.
[112] SANVILLE E, KENNY S D, SMITH R, et al. Improved grid-based algorithm for Bader charge allocation[J]. Journal of Computational Chemistry, 2007, 28(5): 899-908.
[113] STUKOWSKI A. Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool[J]. Modelling and Simulation in Materials Science and Engineering, 2010, 18(1): 015012.
[114] MOMMA K, IZUMI F. VESTA: A three-dimensional visualization system for electronic and structural analysis[J]. Journal of Applied Crystallography, 2008, 41(3): 653-658.
[115] MEUNIER M, ROBERTSON S. Materials Studio 20th anniversary[J]. Molecular Simulation, 2021, 47(7): 537-539.
[116] SHEPPARD D, XIAO P, CHEMELEWSKI W, et al. A generalized solid-state nudged elastic band method[J]. The Journal of Chemical Physics, 2012, 136(7): 074103.
[117] JAMES F. Monte Carlo theory and practice[J]. Reports on Progress in Physics, 1980, 43(9): 1145.
[118] LOWNDES R P, MARTIN D H, BATES L F. Dielectric constants of ionic crystals and their variations with temperature and pressure[J]. Proceedings of the Royal Society of London A Mathematical and Physical Sciences, 1970, 316(1526): 351-375.
[119] LIU J, SU J, ZHAO L, et al. Influence of dielectric constant on dielectric strength by defect discharge and molecular polarization in solid insulation materials[J]. Journal of Applied Physics, 2019, 125(11): 115103.
[120] ZANG G, ZHANG J, ZHENG P, et al. Grain boundary effect on the dielectric properties of CaCu3Ti4O12 ceramics[J]. Journal of Physics D: Applied Physics, 2005, 38(11): 1824.
[121] GRIMME S, ANTONY J, EHRLICH S, et al. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu[J]. The Journal of Chemical Physics, 2010, 132(15): 154104.
[122] KRISHNAMOORTHY A, NOMURA K, BARADWAJ N, et al. Dielectric constant of liquid water determined with neural network quantum molecular dynamics[J]. Physical Review Letters, 2021, 126(21): 216403.
[123] SPALDIN N A. A beginner's guide to the modern theory of polarization[J]. Journal of Solid State Chemistry, 2012, 195: 2-10.
[124] CAVENDISH H. Experiments on rathbone-place water: By the Hon. Henry Cavendish, F. R. S[J]. Philosophical Transactions, 1767, 57: 92-108.
[125] LOVINGER A J. Ferroelectric polymers[J]. Science, 1983, 220(4602): 1115-1121.
[126] ACOSTA M, NOVAK N, ROJAS V, et al. BaTiO3-based piezoelectrics: Fundamentals, current status, and perspectives[J]. Applied Physics Reviews, 2017, 4(4): 041305.
[127] KITTEL C, MCEUEN P. Introduction to solid state physics[M]. John Wiley & Sons, 2018.
[128] COCHRAN W, COWLEY R A. Dielectric constants and lattice vibrations[J]. Journal of Physics and Chemistry of Solids, 1962, 23(5): 447-450.
[129] YANG Z, WANG J, HU Y, et al. Simultaneously improved dielectric constant and breakdown strength of PVDF/Nd-BaTiO3 fiber composite films via the surface modification and subtle filler content modulation[J]. Composites Part A: Applied Science and Manufacturing, 2020, 128: 105675.
[130] KIM P, DOSS N M, TILLOTSON J P, et al. High energy density nanocomposites based on Surface-Modified BaTiO3 and a Ferroelectric Polymer[J]. ACS Nano, 2009, 3(9): 2581-2592.
[131] LUO H, ZHOU X, ELLINGFORD C, et al. Interface design for high energy density polymer nanocomposites[J]. Chemical Society Reviews, 2019, 48(16): 4424-4465.
[132] WANG Z, KEITH NELSON J, HILLBORG H, et al. Dielectric constant and breakdown strength of polymer composites with high aspect ratio fillers studied by finite element models[J]. Composites Science and Technology, 2013, 76: 29-36.
[133] HUSSAIN S, YANGPING L. Review of solid oxide fuel cell materials: Cathode, anode, and electrolyte[J]. Energy Transitions, 2020, 4(2): 113-126.
[134] JIANG M, FU C, YANG J, et al. Defect-engineered MnO2 enhancing oxygen reduction reaction for high performance Al-air batteries[J]. Energy Storage Materials, 2019, 18: 34-42.
[135] CHEN J Y, HSIN C L, HUANG C W, et al. Dynamic evolution of conducting nanofilament in resistive switching memories[J]. Nano Letters, 2013, 13(8): 3671-3677.
[136] DISSADO L A, FOTHERGILL J C. Electrical degradation and breakdown in polymers[M]. leicester,Leics: IET, 1992.
[137] LAGHARI J R, SARJEANT W J. Energy-storage pulsed-power capacitor technology[J]. IEEE Transactions on Power Electronics, 1992, 7(1): 251-257.
[138] CHIU F C. A review on conduction mechanisms in dielectric films[J]. Advances in Materials Science and Engineering, 2014, 2014: 578168.
[139] SIMMONS J G. Poole-Frenkel effect and Schottky effect in metal-insulator-metal systems[J]. Physical Review, 1967, 155(3): 657.
[140] ARYA B, SAMANTRAY N, CHOUDHARY R. Sr(Sn, Se)O3 modified Bi0.5K0.5TiO3 ferroelectric ceramics: Structural, electrical and leakage current characteristics[J]. Applied Physics A, 2023, 129(1): 55.
[141] ZHOU X, ZHAO X, SUO Z, et al. Electrical breakdown and ultrahigh electrical energy density in poly(vinylidene fluoride-hexafluoropropylene) copolymer[J]. Applied Physics Letters, 2009, 94(16): 162901.
[142] SHEN Z H, WANG J J, JIANG J Y, et al. Phase-field modeling and machine learning of electric-thermal-mechanical breakdown of polymer-based dielectrics[J]. Nature Communications, 2019, 10(1): 1843.