Perspective pubs.acs.org/Macromolecules
Novel Ferroelectric Polymers for High Energy Density and Low Loss Dielectrics Lei Zhu*,† and Qing Wang*,‡ †
Department of Macromolecular Science and Engineering, Case Western Reserve University, Cleveland, Ohio 44106-7202, United States ‡ Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, United States ABSTRACT: The state-of-the-art polymer dielectrics have been limited to nonpolar polymers with relatively low energy density but ultralow dielectric losses for the past decades. With the fast development of power electronics in pulsed power and power conditioning applications, there is a need for next-generation dielectric capacitors in areas of high energy density/low loss and/or high temperature/low loss polymer dielectrics. Given limitations in further enhancing atomic and electronic polarizations for polymers, this Perspective focuses on a fundamental question: Can orientational polarization in polar polymers be utilized for high energy density and low loss dielectrics? Existing experimental and theoretical results have suggested the following perspectives. For amorphous polar polymers, high energy density and low loss can be achieved below their glass transition temperatures. For liquid crystalline side-chain polymers, dipole mobility is so high that they saturate at relatively low electric fields, and only limited electrical energy can be further stored after dipole saturation. Crystalline polar polymers are promising and can be divided into three categories: normal ferroelectric, paraelectric, and novel ferroelectric. For normal ferroelectric crystalline polymers, switching of a high spontaneous polarization results in a large hysteresis. To reduce the hysteresis, ultrafine crystallites or ferroelectric domains are desired to reduce the spontaneous polarization. For paraelectric crystalline polymers, dipoles have the potential to align in an external electric field. However, a high degree of dipole reversibility is required for the high energy density and low loss application. Novel ferroelectric behaviors include relaxor ferroelectric and antiferroelectric-like behaviors are highly desired because of their high degree of dipole reversibility. To achieve the relaxor ferroelectric behavior, structural defects such as bulky comonomers need to be introduced into the crystalline lattice to expand the lateral unit cell dimensions and speed up the mobility and reversibility of crystalline dipoles. So far, true antiferroelectric crystalline polymers have not yet been discovered. Nevertheless, the antiferroelectric-like behavior has been realized by reducing the compensation polarization via nanoconfinement. In the future, more research is needed to develop new paraelectric and novel ferroelectric polymers for high energy density and low loss dielectrics. reduced breakdown strength and cycle life above 85 °C.8 With the fast growth of microelectronics and power electronics worldwide, polymer film capacitors await breakthrough for high energy density while maintaining a low loss in order to meet the stringent requirements for next generation electronics, e.g., dc link capacitors in hybrid electric vehicles,9 inverters for grid-connected photovoltaics and wind power,10 and pulsed power systems.11 Before proposing any detailed strategies for high energy density and low loss dielectrics, it is necessary for us to understand the fundamentals of dielectric polarization in polymers. As shown in Figure 1, in total five types of polarization can exist in polymers, namely, electronic, atomic, orientational, ionic, and interfacial polarization.1,12,13 Each type of polarization has its own characteristics. Electronic and atomic polarizations originate from electron cloud and skeletal atom movements deviated away from the equilibrium position as induced by an external field, and thus they occur at very high
1. ELECTRIC CHARGE STORAGE IN DIELECTRIC POLYMERS Different from a conductor or a semiconductor, a dielectric is an electric insulator, whose band gap is so large that no electric charges can freely flow through the material. Instead, dielectric polarization is induced by the applied electric field, resulting in accumulations of positive charges on one side of the dielectric toward the field and negative charges on the opposite side.1 These charge accumulations enabled a direct application, namely, electric charge storage in capacitors. After the success of uniform and large scale metallization of polymers,2 polymer film capacitors have nearly replaced paper foil and metalized paper capacitors for most applications.3−5 Among all kinds of polymer films, biaxially oriented polypropylene (BOPP) has remained as the state-of-the-art capacitor film and dominated the market for the past decades because of its high electric breakdown strength (730 MV/m at 63.2% Weibull failure probability and ∼600 MV/m at 1% Weibull failure probability for a test area of 2.0 cm2),6 low dielectric loss (tan δ ∼ 0.0002 at 1 kHz),7 excellent self-clearing,3,4 and low cost. Nevertheless, disadvantages for BOPP films include low energy density and © 2012 American Chemical Society
Received: October 30, 2011 Revised: January 19, 2012 Published: February 10, 2012 2937
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polymers (see Figure 1). Finally, the question remains as: can orientational polarization in polymers be utilized for high energy density (or high K) and low loss dielectric applications?
2. UTILIZING ORIENTATIONAL POLARIZATION FOR HIGH ENERGY DENSITY AND LOW LOSS DIELECTRICS Whether orientational polarization in polymers can be used for high energy density and low loss dielectrics depends on the frequency where dipole relaxation occurs in addition to the applied electric field. If the dipole relaxation occurs in the frequency range (i.e., 1 kHz to several hundred kHz) and the electric field (e.g., a few tens to several hundreds of MV/m) of power electronics, orientational polarization may not be suitable for high energy density dielectrics because high losses will result in significant dielectric heating due to dipole switching. If the dipole relaxation occurs at high frequencies, i.e., above tens of MHz, orientational polarization shall be suitable for high energy density and low loss dielectrics. Generally speaking, dipole relaxation in polymers depends on temperature and electric field. At low temperatures, dipole motion can be frozen and the corresponding relaxation will be low. At high temperatures, the relaxation frequency of permanent dipoles often increases with increasing the temperature. The temperature effect has been well-studied for polymers in the literature.17 On the other hand, the external electric field can also significantly affect the dipole relaxation frequency. However, this effect has not been well-investigated for polymers. Under a low electric field (e.g., 30 MV/m), nearly all types of crystalline dipoles in polymers can respond to the external field. With increasing the electric field, the dipole relaxation rate will increase and more crystalline dipoles can be polarized. Nonetheless, high-field dielectric spectroscopy has not been widely used to characterize dielectric properties of polymers because high-frequency switching under high fields is difficult to achieve instrumentally. Instead, high-field electric displacement−electric field (D−E) hysteresis loops are commonly used to characterize the dielectric behavior of polymers.18 Figure 2 shows the unipolar
Figure 1. Different types of polarization as a function of frequency in polymers. Pe: electronic polarization; Pat: atomic polarization; Pdip: (dipolar) orientational polarization; Pion: ionic polarization; Pint: interfacial polarization. The top panel shows the molar polarization (or the real part of permittivity), and the bottom panel shows the dissipation factor (the imaginary part of permittivity).
frequencies, i.e., in the infrared and optical range. These two types of polarization exist in all polymers, no matter if they are polar or nonpolar, amorphous or crystalline. If a polymer is polar and contains permanent dipoles, these permanent dipoles may respond to the external field by rotation, resulting in orientational polarization in the polymer. Depending on the nature of these dipoles, amorphous or crystalline, and temperature, they relax between 10 Hz and a few GHz, covering the power and radio frequency ranges. If a polymer contains ionic species, either impurity ions or ions in polymer electrolytes and polyelectrolytes, ionic polarization occurs below a few hundred Hz. Finally, for a multicomponent polymer system, interfaces exist and interfacial polarization takes place due to the Maxwell− Wagner effect.1,12 The relaxation of these interfacial charges may take from seconds to hours or even years (e.g., charges trapped in polymer electrets).14 For electric charge storage purpose, the higher the molar polarization, the more the charge storage; however, there will be a greater tendency that the stored charged cannot be quickly released. Obviously, for high voltage power and radio frequency applications, ionic and interfacial polarizations are not suitable due to their high losses. The remaining types of polarization that can be utilized for high energy density and low loss dielectrics are electronic, atomic, and orientational. It is known that electronic polarization is high for semiconducting conjugated polymers. Although their electronic conductivity is fairly low at low fields, semiconducting polymers are not suitable for high-field applications because the electronic conductivity can dramatically increase under high electric fields.15 Therefore, there is a trade-off between electron polarization (or electron delocalization) by lowering the band gap and electron conductivity under high electric fields. Unlike ceramic materials,16 it is difficult to further enhance atomic polarization in polymers because atoms are linked together via covalent bonds with well-defined bond lengths and bond angles, rather than ionic interactions. Therefore, atomic polarization usually contributes less to electric charge storage than other types of polarization for
Figure 2. Schematic representation of unipolar electric displacement− electric field (D−E) hysteresis loops for both linear and nonlinear dielectric polymers under high-field switching.
D−E loop for both linear and nonlinear dielectric materials. For linear dielectric materials, the relative dielectric constant is independent of electric field and is defined as εr = D/ε0E, where ε0 is the vacuum permittivity. Typical examples are nonpolar 2938
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Figure 3. Bipolar D−E hysteresis loops (10 Hz) for P(VDC-co-AN) at (A) 25 °C and (B) 50 °C, respectively. For each poling field, the second loop is shown and the field increment is 25 MV/m. D−E loops for a capacitor-grade BOPP film is shown in (A) for comparison.
polar polymers as a function of frequency, temperature, and electric field. Polar polymers can exist in the form of amorphous, liquid crystalline, and crystalline polymers. Examples of polar amorphous polymers include vinylidene cyanide (VDCN) and vinylidene chloride (VDC) containing polymers. Figure 3 shows the D−E hysteresis loops for a poly(vinylidene chlorideco-acrylonitrile) [P(VDC-co-AN)] random copolymer (SigmaAldrich) at different temperatures. The number-average molecular weight (Mn) is 80 000 g/mol, and the polydispersity index is 1.88. This random copolymer has a glass transition temperature (Tg) of 50 °C. When polarized below the Tg (25 °C), nearly linear D−E loops are observed for the poling field below 200 MV/m because permanent dipoles are frozen. Above 300 MV/m, hysteresis loops somewhat open up, possibly due to a small amount of ionic polarization of impurity ions in the polar polymer. It is known that ions can transport in glassy polymers via the free volume.25−30 It is reasonable that a certain amount of ionic polarization can take place even below the Tg as long as the ions are small enough. From the slopes for the linear loops below 100 MV/m, the relative permittivity for P(VDC-co-AN) is calculated to be 4.77, which is higher than that (2.25) for BOPP. However, when the temperature increases to near the Tg (50 °C), significant dipole switching and/or ionic polarization appear above 100 MV/m due to the sluggish motion of molecular dipoles. Above the Tg, the sample breakdown strength dramatically decreases. Therefore, only at temperatures far below the Tg, polar amorphous polymers may be able to store higher energy than nonpolar polymers because of a higher permittivity. We speculate that the hysteresis loss can be low only when impurity ions are absent in the polar polymer. However, complete removal of impurity ions (and moistures) from polar polymers has always been a challenge for industrial practices. Liquid crystalline polymers often contain polar groups such as cyanobiphenyls or aromatic esters and amides. Because of the liquid crystalline nature, dipole mobility is so high that dipoles are susceptible even to a relatively low electric field. Liquid crystalline dipole switching involves either out-of-plane (for twist nematics) or in-plane (for ferroelectric chiral smectics) large-scale molecular motions, which usually results in a large hysteresis behavior in both electrical and optical properties.18,31−39 In an electro-optical switching study of a side-chain chiral smectic C (SC*) liquid crystalline polymer at 115 °C, different switching behaviors are observed.18 At a low field (7.3 MV/m), the electro-optic response behaves like a
polymers such as BOPP, polyethylene (PE), polystyrene (PS), etc. The stored energy density is thus Ue,stored = ∫ E dD = 0.5εrε0E2, which is represented by the total (shaded) triangular area in Figure 2. Upon discharge for linear materials, the discharge curve nearly follows the charge curve and there is negligible hysteresis loss. For nonlinear dielectrics, the discharge curve does not follow the charge curve and part of the stored energy is unrecovered, as shown in Figure 2. Typical examples include polar polymers, polymers with impurity ions, and immiscible polymer blends with poor interfaces. The linear part of the dielectric constant, εr(E), becomes electric field dependent and the discharged energy density Ue,released = ∫ E dD ≠ 0.5εr(E)ε0E2. Both dissipation factor (tan δ) from dielectric spectroscopy and hysteresis from D−E hysteresis loop tests are needed for the evaluation of low- and high-field dielectric properties of polymers. Generally speaking, all relaxation modes observed in the low-field dielectric spectroscopy should also contribute to the hysteresis loss at high fields but at higher frequencies. On the basis of the above discussion, an ideal high energy density and low loss dielectric requires the following characteristics: (1) high permittivity (or high K), (2) high electric breakdown strength (or field), (3) low dissipation factor at low fields, and (4) low hysteresis at high fields in a frequency range between 10 Hz and a few hundred kHz. The high breakdown field appears more important than high dielectric constant because the stored energy density is a linear function of dielectric constant but square of electric field. Impurity-free polar solvents seem to be good candidates to meet these requirements because they have high dielectric constants and low dielectric loss between 10 Hz and a few hundred kHz.19−21 However, electrochemical redox reactions often occur for polar solvents on electrodes under high enough electric fields22,23 and result in low breakdown strength and significant polarization hysteresis (due to the socalled electrode polarization). Therefore, polar liquids are not suitable for high energy density and low loss dielectrics. On the contrary, polar polymers are much more stable than polar liquids electrochemically. It is known that polar polymers, like nonpolar polymers, can also exhibit high breakdown strengths if the ionic impurity level is very low.24 Therefore, polar polymers may be good candidates for high energy density and low loss dielectrics. The fundamental question then is: can dipole relaxation in polar polymers take place above tens of MHz in order to minimize the dielectric loss between 10 Hz and a few hundred kHz? Bearing this question in mind, it is necessary to study the dielectric relaxation of different 2939
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Figure 4. Unit cells of (A) α, (B) δ, (C) γ, and (D) β forms of PVDF crystals viewed along the c-axes and schematic chain conformations for (E) TGTG′ (α/δ), (F) TTTGTTTG′ (γ), and (G) all-trans (β) rotational sequences. Red, cyan, and blue spheres represent F, C, and H atoms. The projections of dipole directions are indicated by green arrows.
nonpolar-to-ferroelectric transition is not 100% reversible because the free energies of both forms are fairly similar. As a result, the sample will be trapped in the δ form even after the applied field is removed. Because of the inclination of C−F dipoles at an angle to the molecular axis (Figure 4E), the components of the dipole moment perpendicular and parallel to the chain axis are 1.20 and 1.02 D (D), respectively.42 The γ form has a TTTGTTTG′ chain conformation and is often obtained by solution-casting from polar solvents at temperatures below 100 °C18,42,43 or annealing/crystallization at high temperatures.18,44 Again, since C−F dipoles are inclined (Figure 4F), the components of the dipole moment are perpendicular and parallel to the chain axis, and their values are similar to those for the α/δ phases.42 The β form is often obtained by mechanical stretching or high field poling (400− 500 MV/m) of α or γ form samples and has an all-trans conformation.18,42 The dipoles are perpendicular to the chain axis (Figure 4G) and have the highest dipole moment per chain per repeat unit, i.e., 2.10 D. Because of the large dipole moment, the β form has the highest spontaneous polarization. Semicrystalline ferroelectric polymers are different from ferroelectric ceramics (usually 100% crystalline) due to their semicrystalline nature. Let us consider a simple serial capacitor model, as shown in Figure 5A, where a ferroelectric PVDF lamella (in β, γ, or δ forms) is sandwiched between two amorphous PVDF layers. Electrodes are in direct contact with the amorphous layers. The chain direction is perpendicular to the external field (i.e., in the horizontal direction). Upon application of an external electric field (E0) at room temperature, the amorphous dipoles will be polarized first. However, because of a large thermal fluctuation above the Tg of PVDF (−35 to −40 °C18), this polarization is usually small. As the external field increases above the coercive field (Ec), dipoles in the ferroelectric PVDF crystal will align along the field direction, thus creating a local depolarization field (Edepol) as shown in Figure 5A:12,45
typical electroclinic effect. At an intermediate electric field (17.7 MV/m), the electro-optic response starts to deviate from the electroclinic effect. Finally, at 24.8 MV/m, a ferroelectric hysteresis switching behavior is observed. From this result, we can see that all the dipoles in ferroelectric liquid crystalline polymers saturate (i.e., aligned along the electric field) at relatively low dielectric fields (i.e., 24.8 MV/m). As we know, early saturation of dipoles at low electric fields will result in low electric energy storage. Therefore, polar liquid crystalline polymers are not suitable for high energy density and low loss dielectrics.
3. NORMAL FERROELECTRIC CRYSTALLINE POLYMERS Polar crystalline polymers can be divided into three categories: normal ferroelectric, paraelectric, and novel ferroelectric. For ferroelectric crystalline polymers, famous examples include poly(vinylidene fluoride) (PVDF) and its copolymers, oddnumbered nylons, cyanopolymers, polyurea/polythiourea, and biopolymers (e.g., keratin and silk fibroin).18 Nonetheless, large hysteresis loops are commonly observed for normal ferroelectric crystalline polymers because of the switching of a high spontaneous polarization, and their normal ferroelectricity is intimately dependent upon the crystalline structure and morphology. Before we embark on ferroelectric crystalline polymers for high energy density and low loss dielectrics, it is important for us to understand the nature of normal ferroelectricity and its suitable applications. Since PVDF and its copolymers have been intensively studied in the past, we will focus on these polymers for the discussion. 3.1. Polarization Mechanism in Ferroelectric PVDF. PVDF is a radically polymerized flexible polymer typically with 3−6 mol % head-to-head/tail-to-tail (HHTT) linkages. Because of these structural defects, its crystallinity is often limited to 50−60 wt %. In general, four major crystalline modifications are observed, i.e., α, δ, γ, and β forms, as shown in Figure 4A−D. Among them, the α form is nonpolar and δ, γ, and β forms are ferroelectric. Both α and δ forms have exactly the same unit cell dimensions and the same TGTG′ rational sequence; however, the dipole moments cancel out in the α form, and they point to the same direction in the δ form. The α form can be obtained by cooling from the melt at a normal rate and the δ form is obtained by poling the α form sample under an electric field of 100−200 MV/m at room temperature.40−42 However, this
Edepol =
Pin ε0
(1)
where Pin is the polarization inside the PVDF crystal induced by aligned dipoles. Because Edepol is a local electric field, the relative permittivity of the crystal should not appear in the denominator. In turn, the large Pin in the PVDF crystal will induce more polarization of the amorphous PVDF at the 2940
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Figure 5. Schematic illustrations of (A) an electrically polarized ferroelectric PVDF crystal sandwiched between two amorphous layers and (B) many electrically polarized ferroelectric PVDF crystals in an amorphous matrix, showing different coupling interactions among ferroelectric domains. The chain direction in the lamellar crystals is perpendicular to the dipole moment or the external electric field E0.
Therefore, the antiferroelectric-like behavior will not be observed, resulting in normal ferroelectric behavior (see Figure 11A). For ferroelectric polymers, the second scenario is commonly observed and has found numerous practical applications.18 When many ferroelectric crystals are polarized by an external electric field, ferroelectric domain coupling46−48 is realized via induced polarizations (i.e., Pcomp) from the media (either amorphous or crystalline PVDF) among the domains. Different situations are shown in Figure 5B. First, there are three types of coupling interactions: I (within the ferroelectric crystal), II (between ferroelectric crystals but along the external field direction), and III (between ferroelectric crystals but perpendicular to the external field direction). Note that for the coupling interaction type I the Pcomp is induced by neighbor domains inside the crystal (i.e., the ferroelectric domain is much smaller than the PVDF crystal; see the top left and top middle panels in Figure 5B), and it may be defined as12
amorphous−crystalline interface, resulting in an enhanced compensation polarization (Pcomp) outside the ferroelectric PVDF domain. The Pcomp in amorphous PVDF is determined by the dipole density in the amorphous phase (N0,am), the polarizability for amorphous PVDF (αam), and the local electric field in the amorphous phase (EL,am):12
Pcomp = N0,am αamEL,am
(2)
Note that the Pin may not equal the Pcomp, especially during a dynamic poling process. Based on the serial capacitor model in Figure 5A, the local polarization field for the PVDF crystal is imposed from the charges on the electrodes and can be defined as12,45
Q + Pcomp D = ε0 ε0 (3) where Q is the charge density induced in the vacuum, i.e., Q = ε0E0. Again, Epol is a local electric field, and the relative permittivity should not appear in the denominator. Dipole switching depends on the local electric field in the crystal (EL,cryst), which has at least three sources: (i) Epol (positive), (ii) Edepol (negative), and (iii) other contributions from dipoles nearby.12,13 If we consider that contribution from nearby dipoles can cancel out due to a random orientation, the contribution (iii) may be neglected.12,13 Then, the local electric field largely depends on the competition between Epol and Edepol, which is determined by the relationship between Pin and Q + Pcomp. Upon a forward poling, Q + Pcomp > Pin and thus Epol > Edepol. Crystalline dipoles will be polarized along the external electric field. During a reverse poling process, two scenarios can take place. First, as both Edepol and Epol decrease with decreasing the external electric field, at a certain point Pin > Q + Pcomp and then Edepol > Epol. Fully aligned dipoles will become less stable than they are in a situation where some mobile (or reversible) dipoles revert to the opposite direction, resulting in a minimum (or even net zero) remanent polarization. This behavior is the so-called antiferroelectric-like behavior reported in the literature and will be discussed in detail below (see Figure 11C). Second, when Pin < Q + Pcomp as Edepol and Epol decrease with the external field, the Edepol turns out to be always lower than the Epol. E pol =
Pcomp = N0,cryst αcrystEL,cryst
(4)
where N0,cryst is the dipole density in the crystalline phase, αcryst the polarizability for crystalline PVDF, and EL,cryst the local electric field in the crystal. Because the coupling interactions are anisotropic,49 coupling type III is much weaker than coupling types I and II. For ferroelectric polymers, the αcryst is generally higher than the αam, and thus coupling type I is stronger than coupling type II (see the left panel in Figure 5B). Second, dipole moments in β-PVDF crystals are larger than those in δ-PVDF crystals, and thus the local electric field is higher near β domains compared to δ domains. As a result, the Pcomp induced by β domains is higher than that by δ domains. Therefore, the coupling interactions (types I + II) among β domains are stronger than those among δ domains (see left and middle panels of Figure 5B). Third, when the crystallite size is very small and contains one single ferroelectric domain (right panel of Figure 5B), coupling type I interaction disappears, and thus the overall coupling interaction becomes weaker than the situation where a crystallite contains multiple domains at the same electric field. From the above discussion, we understand that normal ferroelectricity in ferroelectric polymers originates from high spontaneous polarization (inside the ferroelectric domain) and 2941
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Figure 6. (A) 2D XRD patterns for solution-cast (SC) and hot-pressed/stretched (HP&Str) P(VDF-HFP) 96/4 films along the z and x directions, respectively. Crystal orientations in the SC and HP&Str films are shown in the schematics on the right. (B) Dielectric spectroscopy results: the real part (εr′) and imaginary part (εr″) of relative permittivity as a function of frequency for SC and HP&Str films at room temperature. (C) and (D) show D−E hysteresis loops (10 Hz) at room temperature with a field increment of 50 MV/m. (E) Stored and released energy densities (Ue) and unreleased% (inset) as a function of electric field for SC and HP&Str films. (Reproduced and adapted with permission from ref 65.)
to the film normal direction are obtained by solution-casting (SC) and hot-pressing and stretching (HP&Str), respectively. Two-dimensional (2D) X-ray diffraction (XRD) patterns in Figure 6A prove these different crystal orientations (see the schematics on the right). From analyses of these XRD patterns, the SC film contains 40.8% pure α-form, and the HP&Str film contains 32.9% α-form and 7.3% β-form because of mechanical stretching at 110 °C. Frequency-dependent lowfield dielectric spectroscopy results at room temperature are shown in Figure 6B. The HP&Str film exhibits a higher (nearly twice) εr′ than the SC film because the component dipole moment perpendicular to the chain axis (1.20 D) is higher than that parallel to the chain (1.02 D) for α-form PVDF and a small amount (7.3%) of β-form exists in the HP&Str film. From the εr″, two (half) relaxation peaks are observed at both low and high frequencies, respectively. The relaxation peak centered around 10 Hz (the αc relaxation) is attributed to the dipole relaxation along the chain axes of the α-form,25,62,66 and the relaxation peak around 1 MHz (the αa relaxation) is attributed to both amorphous dipoles66−68 and dipoles at the crystal/ amorphous interfaces.69 Note that the interface between crystalline and amorphous phases for α-form PVDF is not sharp because the TG conformation can exist in both amorphous and crystalline phases. From the loss dielectric constant results in Figure 6B, it is obvious that the SC film with a perpendicular crystal orientation is undesired for high energy density and low loss dielectrics because the αc relaxation at 10 Hz is within the power frequency range. Instead, the HP&Str film with a parallel crystal orientation may be a better candidate because the αa relaxation peak is around 1 MHz and can be shifted to higher frequencies with increasing the temperature.62,67,68 We therefore
high compensation polarization or interdomain coupling (outside the ferroelectric domain). This high Pcomp in normal ferroelectric polymers has enabled a number of applications. First, the rectangular-shaped D−E loop (see Figure 11A) enables applications such as nonvolatile capacitor- and transistor-type ferroelectric memories (FeRAMs).50−54 The advantages of these nonvolatile FeRAMs include fast read/write speed, minimum energy consumption, and long cycle life. P(VDF-co-trifluoroethylene) [P(VDF−TrFE)] with a VDF content of 70−75 mol % is usually chosen for polymer FeRAMs because of its large polarization (∼0.1 C/m2), excellent polarization stability, fast switching time (e.g., 20 ns at 840 MV/m for 20 nm thin film55), and easy processing.50,54 In addition, all ferroelectric polymers also possess piezoelectric properties, which have been used for transducers,18,56 piezoactuators,18,57,58 and mechanical energy harvesting devices.59−61 For these applications, high piezoelectric responses benefit from the large dipolar polarization. 3.2. Crystal Orientation Effect. For high energy density and low loss dielectrics, it is now necessary to understand whether or not normal ferroelectric crystalline polymers are suitable for this application. This is examined by studying effects of crystal orientation, polymorphism, crystallite size (or domain size), and crystallinity for PVDF and its random copolymers. It is known that the dielectric properties of PVDF are anisotropic; namely, the dielectric constants perpendicular and parallel to the chain axes are different.62−64 In a recent study, this crystal orientation effect is revisited with an emphasis on the charge and discharge behaviors for electric energy storage.65 Corresponding results are shown in Figure 6. In this study, P(VDF-co-hexafluoropropylene) [P(VDF−HFP) 96/4 (mol/mol)] films with chain axes parallel and perpendicular 2942
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Figure 7. (top) Schematic illustration of PVDF and P(VDF−HFP) films A−D with different β and α contents obtained by different processing conditions. SC&Str and HP&Str stand for “solution-cast and stretched” and “hot-pressed and stretched”, respectively. The crystallite size along the [110] direction, the D110 for both α and β phases, are estimated by the Scherrer equation. The symbols “||” and “⊥” stand for the chain axes parallel and perpendicular to the film, respectively. (bottom) (A−D) Bipolar D−E hysteresis loops at 10 Hz for films A−D, respectively. (E) Stored and released energy densities and (F) unreleased% as a function of electric field for films A−D, respectively. [Reproduced with permission from refs 70 and 71 (Copyright 2011 IEEE).]
loss, the irreversible α → δ → β phase transformations upon repeated poling at high enough fields prevent it from being suitable for high energy density and low loss dielectrics. 3.3. Polymorphism and Crystallite Size Effects. Effects of polymorphism and crystallite size are studied via a series of PVDF and P(VDF−HFP) films obtained by different processing conditions, as shown in the top panel of Figure 7.70,71 From film C to films B and A, the β content gradually increases from 2.7% to 38.2%. The crystallite sizes in films A−C are relatively small, ranging from 10 to 15 nm for parallel β crystals. Instead, the biaxially oriented PVDF has an intermediate β content of 19.6% and a large crystallite size of 25 nm for parallel β crystals. Bipolar D−E hysteresis loops for films A−D are shown in Figures 7A−D, respectively. It is obvious that a high β content (film A) and a large crystallite size (film D) favor normal ferroelectric (or rectangular-shaped) loops because of high coupling interactions (or Pcomp) among large β domains (see discussion for Figure 5B). Although both films A and D exhibit the highest charged energy densities, they have low released energy densities (Figure 7E) and high hysteresis losses (Figure 7F). Different from films A and D, film C with the lowest β content and small parallel crystallite sizes shows a much lower stored energy density but a similar released energy density (Figure 7E). As a result, the unreleased% for film C is much lower than those for films A and D (Figure 7F). This result is consistent with recent reports that parallel α-crystals are favorable for high energy density dielectrics.72−75 Intriguingly,
consider that the parallel PVDF crystal orientation may work better at elevated temperatures for the low loss purpose. The high-field performance is studied by unipolar hysteresis loops shown in Figures 6C and 6D for the SC and HP&Str films, respectively. Corresponding stored and released energy densities are calculated from these polarization loops (see Figure 6E). The unreleased%, defined as 100(1 − Ue,released/ Ue,stored), is shown as the inset in Figure 6E. In spite of high energy storage (i.e., up to 20 J/cm3 at 500−550 MV/m), the discharged energy densities are only ∼11 J/cm3 for samples with different crystal orientations. In other words, high values of unreleased% are obtained at high fields. In accordance with the low-field dielectric spectroscopy study, the SC film with a perpendicular crystal orientation shows high unreleased% values from 50 to 600 MV/m; therefore, perpendicular crystal orientation in α-form PVDF indeed is undesired for high energy density and low loss dielectrics. On the other hand, the HP&Str film shows a higher Ue,released but a lower unreleased% than the SC film at low fields (105 Hz)139,140 because the paraelectric-to-ferroelectric transition is much broader and the observed εr′ is significantly lower during cooling than during heating. We speculate that structural defects such as the disordered trans−gauche conformation in the cooled ferroelectric phase may be responsible for the observed relaxor-like behavior during cooling under high frequencies. In spite of numerous reports on the relaxor ferroelectric behavior since its discovery in P(VDF−TrFE)-based ferroelectric polymers,88,89 the underlying physics is yet to be well-understood. We speculate that the origin for the relaxor ferroelectric behavior in polymers is similar to that for relaxor ferroelectric ceramics,46,85 i.e., ferroelectric nanodomains dispersed in a compositionally disordered paraelectric matrix. The only difference between ferroelectric polymers and ceramics is that the polarization mechanism is orientational for polymers and atomic for ceramics. The concept of ferroelectric nanodomains and reversible nonpolar−ferroelectric (α−β) phase transitions are used to explain the high energy storage in PVDF copolymers in a recent computer simulation using the density function theory.141 Currently, there are no effective experimental methods to directly visualize and determine the size of ferroelectric nanodomains in polymers. Our hypothesis will need to wait for experimental and/
or theoretical proof in the future. Only after we fully understand the underlying physics of the relaxor ferroelectric behavior can we design new ferroelectric polymers for high energy density and low loss dielectrics. 5.2. Nanoconfined Ferroelectric Behavior in Polymers. Although the relaxor ferroelectric behavior is a good candidate, the antiferroelectric behavior with minimum hysteresis in the antiferroelectric ↔ ferroelectric transitions and a zero Drem appears to be a better choice for high energy density and low loss dielectrics (see Figure 11C). So far, no genuine antiferroelectric crystalline phase has been identified for polymers. In the future, research is needed to discover crystalline polymers with true antiferroelectric phases and study whether or not the antiferroelectric ↔ ferroelectric phase transition is reversible with minimum hysteresis. However, an antiferroelectric-like behavior with a reduced or minimum remanent polarization (Pr) in the P−E hysteresis loop study has been experimentally observed. Strictly speaking, because of the nonzero Pr, this behavior is more appropriate to be termed as ferrielectric, similar to that for liquid crystals,142,143 rather than antiferroelectric. However, to be consistent with the literature, we still use the antiferroelectriclike terminology here. The antiferroelectric-like behavior with double hysteresis loops is first reported for β-PVDF at temperatures below −60 °C144 and P(VDF−TrFE) with the VDF content less than 50 mol %.145−147 The double hysteresis loop consists of a dipole depolarization step at low fields and a polarization reversal step at high fields, and it only appears in the first a few cycles and eventually transforms into a single 2948
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example, double hysteresis are easily observed in P(VDF− TrFE) copolymers with >50 mol % TrFE, rather than in β-PVDF, because the dipole moments per repeat unit in a chain for TrFE and β-PVDF are 1.05 and 2.1 D, respectively. Double hysteresis loops are also observed in α/δ-PVDF since the component dipole moment perpendicular to the chain axis per chain per repeat unit is only 1.20 D. To test the above hypothesis that the antiferroelectric-like behavior is a result of a lower Q + Pcomp (or Epol) than Pin (or Edepol) during reverse poling, we confined ferroelectric PVDF crystals with a low polarizability polymer such as PS to purposely reduce Q + Pcomp (see Figure 14F). To achieve this, PS side chains are grafted from a P(VDF−TrFE−CTFE) 88.2/ 7.7/3.5 terpolymer using atom transfer radical polymerization (ATRP),150 following an established method in the literature.151 Dechlorination by n-Bu3SnH is conducted to avoid cross-linking of the graft copolymer under further thermal treatments. Proton (1H) NMR result shows that the PS content is 14 wt %, corresponding to 3.2 styrene repeating units per PS side chain. A P(VDF−TrFE) 93/7 (mol/mol) copolymer is used as a control to compare with the graft copolymer. P(VDF−TrFE) 93/7 and P(VDF−TrFE−CTFE)-g-PS(14%) films are obtained by hot-pressing at 240 °C followed by uniaxial stretching at 110 °C. The 2D XRD patterns in the insets of Figure 14A,B indicate that the chains in the P(VDF−TrFE) crystals are parallel to the stretching direction. Bipolar D−E hysteresis loops for P(VDF−TrFE) 93/7 and
hysteresis loop upon repeated cycling. Therefore, this behavior is attributed to imperfect P(VDF−TrFE) crystals cooled from the melt with the coexistence of ferroelectric and paraelectric phases.147 Later, it is attributed to the nonpolar “antiferroelectric-like phase” in P(VDF−TrFE).54,80,148,149 Recently, we explain the antiferroelectric-like behavior as a rather universal phenomenon for semicrystalline ferroelectric polymers, using the model shown in Figure 5A.70,150 According to this explanation, double hysteresis loops will take place as long as Q + Pcomp < Pin. In other words, when the local Edepol becomes higher than the local Epol during discharging, part of aligned dipoles or domains in the poled ferroelectric crystal will depolarize and revert back to their original direction, resulting in a minimum Pr at zero electric field. There are several methods to achieve the antiferroelectriclike behavior in ferroelectric polymers.70,150 First, decreasing the polarizability of the amorphous phase at the amorphous/ crystal interface can directly result in a lower Q + Pcomp (or Epol) than Pin (or Edepol). For example, decreasing the temperature to below the Tg can effectively reduce the polarizability of the amorphous phase due to frozen dipoles. As a result, double hysteresis loops are observed for β-PVDF at temperatures below −60 °C.144 Second, Pcomp will be low when the poling field and temperature are relatively low. This is exactly observed for PVDF and P(VDF−HFP) in Figures 6−8. Third, Pcomp will be low when the dipole moment per repeat unit in a chain is decreased. Several cases could fit into this category. For
Figure 14. (top) Synthesis of P(VDF−TrFE−CTFE)-g-PS graft copolymer from the P(VDF−TrFE−CTFE) terpolymers using atom transfer radical polymerization followed by dechlorination. (A, B) Bipolar D−E hysteresis loops for uniaxially stretched P(VDF−TrFE) 93/7 and P(VDF−TrFE− CTFE)-g-PS(14%) films. Corresponding 2D XRD patterns are shown as insets. A D−E loop for the graft copolymer at a poling field of 150 MV/m is shown as inset in (B). (C, D) Stored and released energy densities and (E) unreleased% as a function of electric field for P(VDF−TrFE) 93/7 and P(VDF−TrFE−CTFE)-g-PS(14%). (F) Schematic model of a PS-confined ferroelectric P(VDF−TrFE) crystal under a poling electric field. The chain folding direction is perpendicular to the applied electric field. (Reprinted with permission from ref 150.) 2949
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in P(VDF−CTFE)-g-PS graft copolymers with the PS content above 30 wt % is still not clear. We consider that after PVDF crystallization PS grafts are rejected out of the PVDF crystal, forming a PS-rich confining layer surrounding the PVDF crystal (similar to the model in Figure 14F but with a much thicker PS-rich layer due to a higher PS content). Because of a large difference in the dielectric constants for the PVDF crystal and the amorphous PS/PVDF phase, electric field distribution must be nonuniform in the crystalline PVDF and amorphous PS/PVDF phases. For example, assuming that the dielectric constant of the PVDF crystal is 12 and that for the amorphous PS/ PVDF phase is around 4, the nominal electric field in the PVDF crystal will be 1/3 of that in the amorphous phase. Under such a low nominal electric field in PVDF crystals, no dipole switching is possible and linear hysteresis loops are observed. This will need further investigations to prove our hypothesis.
P(VDF−TrFE−CTFE)-g-PS(14%) are shown in Figures 14A and 14B, respectively, and a clear difference is seen.150 For P(VDF−TrFE) 93/7, double hysteresis loops are seen at the poling field below 200 MV/m, above which only normal ferroelectric loops are seen. For P(VDF−TrFE−CTFE)-gPS(14%), double hysteresis loops are seen at the poling field up to 400 MV/m. Especially, a typical antiferroelectric-like behavior with a clear double hysteresis loop (Drem ∼ 0) at the poling field of 150 MV/m is shown in the inset of Figure 14B. Also, different from the double hysteresis loops in P(VDF−TrFE) with more than 50 mol % TrFE, these double hysteresis loops for P(VDF−TrFE−CTFE)-g-PS(14%) do not disappear even after repeated poling processes, indicating that the observed antiferroelectric-like behavior is fairly stable. Comparisons of stored and released energy densities and unreleased% between P(VDF−TrFE) 93/7 and P(VDF− TrFE−CTFE)-g-PS(14%) are shown in Figures 14C−E, respectively. Obviously, although P(VDF−TrFE−CTFE)-gPS(14%) stores much less energy than P(VDF−TrFE) 93/7, it discharges a similar energy density as that of P(VDF−TrFE) 93/7. This results in a significant reduction in the unreleased% for P(VDF−TrFE−CTFE)-g-PS(14%). The observed antiferroelectric-like behavior in P(VDF− TrFE−CTFE)-g-PS(14%) can be explained using the model in Figure 14F. After the crystallization-induced microphase separation, a low polarizability PS-rich interfacial layer confines (or insulates) the P(VDF−TrFE) crystal. As a result, the Pcomp in P(VDF−TrFE−CTFE)-g-PS(14%) greatly decreases, as compared with that in P(VDF−TrFE). During reverse poling (or discharge), the Epol will be lower than the Edepol, and finally the crystalline dipoles aligned at a high electric field will easily revert to the opposite direction, resulting in an antiferroelectric-like behavior at high poling fields with a low Drem and a reduced hysteresis loss. However, as we can see from Figures 14B,E, the dipole switching hysteresis is still significant enough to result in a nearly 40% loss above 200 MV/m. In the future, more research is needed to further reduce the hysteresis for the P(VDF−TrFE−CTFE)-g-PS graft copolymers. A natural extension of the above work is to further increase the PS content in the PVDF copolymer. In a recent study, we grafted different length PS side chains (1.9−7.6 repeat units in each side chain) from P(VDF−CTFE) 93/7 using ATRP followed by dechlorination.152,153 When the PS graft content is 17 wt %, a similar antiferroelectric-like behavior as that for the P(VDF−TrFE−CTFE)-g-PS(14%) in Figure 14B is seen. When the PS graft content is above 30 wt %, linear hysteresis loops are observed for the P(VDF−CTFE)-g-PS graft copolymers. It is because of these linear hysteresis loops that P(VDF−CTFE)-g-PS graft copolymers exhibit significantly reduced unreleased% at a relatively high PS content. For example, the best performance in terms of high energy density and low loss is observed in P(VDF−CTFE)-g-PS(34%): a relatively high released energy density of ∼10 J cm−3 at 600 MV m−1, a fairly low dielectric loss (tan δ = 0.006 at 1 kHz), and a low ferroelectric/conduction loss (unreleased% = 17.6% at 550 MV m−1). The energy density for P(VDF− CTFE)-g-PS(34%) at 600 MV/m is about 2.8 times that of BOPP. Meanwhile, the P(VDF−CTFE)-g-PS graft copolymers exhibit a fast discharge speed down to 8 μs.152 The higher unreleased% for P(VDF−CTFE)-g-PS(34%) may be resulted from the residue metal catalyst during ATRP and subsequent dechlorination. Currently, the reason for the linear hysteresis loops
6. CONCLUDING REMARKS AND OUTLOOK As we have discussed, there is clearly a need in the pulsed power and power conditioning industry that next generation dielectric capacitors be developed in areas of high energy density/low loss and/or high temperature/low loss dielectrics. In this Perspective, we do not tackle this challenge from the viewpoints of high dielectric constant and high breakdown strength because dielectric constant of a material is a macroscopic quantity and thus does not have a physical meaning at the molecular level, and electric breakdown strength is rather an extrinsic physical property of dielectric materials. Instead, we focus on the concept of polarization because of its clear physical meaning at the molecular level. Meanwhile, the intent of this Perspective is to understand the fundamental physics of orientational polarization in polar polymers and to propose general guidance for molecular/structural design of high energy density and low loss dielectrics, rather than to propose any detailed functional groups or chemical structures of polymers. For insulating dielectric polymers, opportunity is limited for further increasing the atomic polarization because bond lengths and bond angles are well-defined for covalently linked bonds. There should be some room for enhancing the electronic polarization in dielectric polymers. Because electronic polarization is in the resonance regime (see Figure 1), enhancing electronic polarization seems to be the first choice for high energy density and low loss dielectrics. However, the trade-off between electron delocalization by lowering the band gap and electron conductivity (especially at high electric fields) dictates how much enhancement one can achieve for the electronic polarization. Generally speaking, the band gap should at least be greater than 2 eV in order to be considered as insulating (at least at low fields). In a recent first-principles calculation,154 the polarizability per unit mass for a −Si(CN)2− homopolymer is nearly twice that of PE or PP, suggesting that −Si(CN)2− may store twice the electric energy that of PE or PP while maintaining a low loss. However, the band gap decreases from ca. 9 eV for PE or PP to slightly below 3 eV for −Si(CN)2−. Therefore, we consider that high (electronic) polarizability and relatively low band gap polymers are only suitable for low-field (e.g.,
