Exploring Strategies for High Dielectric Constant and Low Loss

PE polymers refer to a class of polar materials whose dipoles can quickly respond to ... Repeat unit isomorphism refers to a mixed crystal structure f...
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Perspective pubs.acs.org/JPCL

Exploring Strategies for High Dielectric Constant and Low Loss Polymer Dielectrics Lei Zhu* Department of Macromolecular Science and Engineering, Case Western Reserve University, Cleveland, Ohio 44106-7202, United States ABSTRACT: Polymer dielectrics having high dielectric constant, high temperature capability, and low loss are attractive for a broad range of applications such as film capacitors, gate dielectrics, artificial muscles, and electrocaloric cooling. Unfortunately, it is generally observed that higher polarization or dielectric constant tends to cause significantly enhanced dielectric loss. It is therefore highly desired that the fundamental physics of all types of polarization and loss mechanisms be thoroughly understood for dielectric polymers. In this Perspective, we intend to explore advantages and disadvantages for different types of polarization. Among a number of approaches, dipolar polarization is promising for high dielectric constant and low loss polymer dielectrics, if the dipolar relaxation peak can be pushed to above the gigahertz range. In particular, dipolar glass, paraelectric, and relaxor ferroelectric polymers are discussed for the dipolar polarization approach.

igh dielectric constant (or relative permittivity, εr) and low loss dielectric polymers are highly desired for advanced electrical applications, such as film capacitors,1−4 artificial muscles,5−8 and electrocaloric cooling.9,10 This is primarily owing to their advantages over inorganic ceramic materials, that is, easy melt or solution processing, high voltage rating, and self-clearing capability.1,2 For decades, the state-ofthe-art polymer dielectric has been biaxially oriented polypropylene (BOPP) because it has an ultralow loss (dissipation factor tan δ of ∼0.0002) at temperatures up to 85 °C.11 Above 85 °C, significant dielectric loss from electronic conduction is observed for BOPP.12 In addition, BOPP has a low dielectric constant of 2.25, resulting in a lower energy density and a higher cost than those of ceramic and metal oxide dielectrics. With the recent development of power electronics, however, it has become apparent that next-generation polymer dielectrics with high energy density, high temperature capability, and low loss are urgently needed. For example, wide band gap semiconductor (SiC and GaN)-based power electronics for electric and hybrid electric vehicles usually operate above 150 °C.13 This requires that polymer film capacitors operate at an ambient temperature of 140 °C or above.1,3 In addition, to keep the cost similar or even lower than that of BOPP, high energy density (or high dielectric constant) is required for new polymer dielectrics because miniaturization is the only way to save material and capacitor packaging costs. In this Perspective, we will review and discuss several current approaches and suggest a potentially viable method of utilizing orientational polarization to afford polymer dielectrics with high dielectric constant and low loss. Understanding Various Types of Polarization and Loss Mechanisms in Polymers. As we know, there are five types of polarization (P) for dielectric materials.4,14,15 They are

H

© XXXX American Chemical Society

How do we achieve polymer dielectrics with high dielectric constant and low loss? This turns out to be a nontrivial question and is somewhat difficult to answer. electronic, vibrational (or atomic), orientational (or dipolar), ionic [i.e., migration of ions over a large distance (>10 nm); note that this is different from slight shifts ( EP, resulting in electron tunneling or conduction. For example, it is reported that the Coulomb blockade effect disappears for metallic nanoparticles larger than 2 nm at room temperature.39−41 Consequently, the breakdown strength of the overall nanodielectric will further decrease. Given these considerations, high dielectric constant contrast between nanoparticles and the polymer matrix should be avoided, and highly resistive, nonspherical-shaped ceramic nanoparticles should be considered for polymer nanodielectrics for high-field electrical applications. In a recent work, hexagonal boron nitride nanoplatelets with a dielectric constant of 3−4 and a bulk resistivity of 1013 Ω·m were incorporated into a FE poly(VDFco-chlorotrifluoroethylene) [P(VDF-CTFE)] copolymer, together with 100 nm BaTiO3 nanoparticles.42 At a composition of 12 wt % boron nitride, 15 wt % BaTiO3, and 73 wt % P(VDF-CTFE), an apparent dielectric constant of 12 and a discharge energy density of 21.2 J/cm3 at 550 MV/m were achieved at room temperature. Although interfacial polarization has been difficult to manage for random-phase polymer nanocomposites, it can become beneficial for a unique type of polymer composites, that is, multilayer films (see Figure 3A), as long as the distance between opposite interfacial charges is large enough (e.g., >100−200 nm). Using multilayer coextrusion technology,43 alternating layers of a high breakdown dielectric polymer [e.g., polycarbonate (PC) or polysulfone] and a high energy density FE polymer (e.g., PVDF or its random copolymers) have been fabricated. This technology is flexible in varying the composition, layer thicknesses, and even different polymer pairs. Because all interfaces are perpendicular to the electric field direction, space charges (i.e., electrons and/or holes), as well as impurity ions, can be accumulated at the multilayer interfaces upon electric poling, again owing to contrasts in both dielectric constant (εr,PVDF = 10−12 and εr,PC = 2.8) and bulk conductivity (σPVDF = 10−13 S/m and σPC = 10−16 S/m). These interfacial charges form effective traps for injected electrons from the metal electrode.44 Intriguingly, instead of a decrease, an enhanced electric breakdown strength is observed for multilayer films as compared to the linear average of PC and PVDF controls.45−47 In the future, it is necessary to prove and quantify these interfacial charges and their relationship with enhanced electrical insulation properties. Ionic Polarization in Polymer Dielectrics. Polymer electrolytes have been used to enhance the capacitance of gate dielectrics for organic field effect transistors.48 The fundamental principle is to utilize the EDL at the interface between the polymer electrolyte and the electrode to store electric energy.17,48 According to the Helmholtz equation, C ≈ kε0/λ,48 where k is the effective dielectric constant of the EDL, ε0 is the vacuum permittivity, and λ is the Debye screening length or the thickness of the double layer, the capacitance of the EDL can be

three-phase polymer nanodielectrics that exhibit a reasonably high dielectric constant at a volume fraction of only ∼5−10 vol %. Even though the above technological challenges can be adequately addressed, there are still scientific obstacles for polymer nanodielectrics. First, high dielectric constant contrast between inorganic nanoparticles and the polymer matrix will result in nonuniform electric field distribution in polymer nanodielectrics34,35 −1 ⎡ ⎛ εr,P ⎞ εr,P ⎤ ⎢ ⎥ ⎜ ⎟ E P = E0 fP ⎜1 − ⎟+ ⎢⎣ ⎝ εr,F ⎠ εr,F ⎥⎦

(1)

⎡ ⎛ε ⎤−1 ⎞ r,F − 1⎟⎟ + 1⎥ E F = E0⎢fP ⎜⎜ ⎢⎣ ⎝ εr,P ⎥⎦ ⎠

(2)

where EP and EF are nominal electric fields in the polymer matrix and fillers, f P is the volume fraction of the polymer matrix, and εr,P and εr,F are the dielectric constants for the polymer matrix and fillers, respectively. From these equations, the nominal field in the fillers is lower and the nominal field in the polymer matrix is higher than the applied external electric field, that is, EP > E0 > EF.29,34 For metallic nanoparticles (Figure 2A), conduction electrons will be so much polarized

Figure 2. Schematics of interfacial polarization in (A) metallic and (B) ceramic (e.g., BaTiO3) nanoparticles in a dielectric polymer matrix due to large contrasts in dielectric constants (εr,F ≫ εr,P) and bulk conductivity (σF ≫ σP). εr,F and εr,P are dielectric constants, and σF and σP are bulk conductivities of particular fillers and the polymer matrix, respectively. EP,L is the local field between adjacent particles aligned in the external field (E0) direction. EF and EP are the nominal fields in fillers and the polymer matrix, respectively.

that the EF literally will be zero (EF = 0). In other words, the dielectric constant of metallic nanoparticles can be considered as nearly infinity. For high dielectric constant ceramic nanoparticles, the EF is greater than zero (EF > 0; see Figure 2B). Depending on the volume fraction of the nanofillers and the dielectric constant contrast (εr,F/εr,P) (see eq 1), the nominal field in the polymer matrix can be several times higher than the applied electric field E0. As a result, the apparent electric breakdown strength will appear lower. In addition, there can be a large contrast in bulk electronic conductivity between inorganic fillers and the polymer matrix. For example, the bulk conductivity of a typical high-permittivity material such as BaTiO3 is ∼10−11 S/m,36 and the bulk 3679

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Figure 3. (A) AFM phase images of the cross sections of PC/PVDF 50/50 (vol/vol) multilayer films: (a) 2, (b) 8, (c) 32, and (d) 256 layers. (B) Dissipation factor, tan δ, as a function of frequency for PVDF and PC controls and PC/PVDF 50/50 multilayer films with 2, 8, 32, and 256 layers at 75 °C. All films are 12 μm in total thickness. (C) Schematic of confined impurity ion transport in PC/PVDF multilayer films with thick versus thin PVDF layers. Due to the fact that cations are usually smaller than anions and can diffuse faster, we assume that only cations migrate in the PVDF layers. Reproduced with permission from ref 51. Copyright 2012 American Chemical Society.

estimated. For example, a C value of 4.4−8.8 μF/cm2 is obtained for λ ≈ 1−2 nm and k ≈ 10, and it is orders of magnitude higher than that of a typical linear dielectric polymer (e.g., BOPP at 3 μm thick has a capacitance of only 6.64 nF/ cm2). Ideally, only the EDL is needed for the energy storage. Because any transport of ion species over a long distance will incur a high dielectric loss, there should not be transport of ions in the middle layer of the polymer electrolyte. The time of ionic polarization in EDL depends on the ionic conductivity of the polymer electrolyte, which is on the order of 10−3 ≈ 1 S/m (for ionic liquids and gels).48 Although theoretical estimation predicts that the polarization time can be as short as 0.1 μs, it is actually limited to 0.1−1 ms (or 103−104 Hz).48 The dissipation factor, tan δ, is usually around 0.10−0.15 below 103 Hz and is not very dependent on frequency.48 In addition, DC leakage current is much higher than linear dielectric polymers, which is probably due to the presence of impurities in real samples. Finally, electrochemically stable ions need to be used in polymer electrolytes for gate dielectrics, and the maximum gate voltage (typically 3−5 V) is limited by the electrolytic stability of the ions or the polymer electrolyte. Therefore, although polymer electrolytes are promising for electrolytegated transistors,48 they are not suitable for high dielectric constant, low loss, and fast discharge film capacitors. As we mentioned above, transport of ions will result in high dielectric loss. This is often observed for impurity ioncontaining polar dielectric polymers such as PVDF and nylons, even though the impurity ion concentration is only at or below the ppm level.49,50 An effective way to mitigate high dielectric loss from impurity ion migration in polar polymers is multilayer films. As shown in Figure 3A, PC/PVDF 50/50 (vol/vol) multilayer films are successfully fabricated using the multilayer coextrusion technology.51 The dielectric spectra of loss tan δ for PC and PVDF controls and various multilayer films at 75 °C are shown in Figure 3B. Note that both the control and multilayer films have the same total thickness of 12 μm. Between 10 and 105 Hz, the αc relaxation peaks from the αphase PVDF crystals are observed.52,53 In addition to this αc peak, there is another low-frequency peak for PVDF below 1 Hz (note that the intensity is too high to show the entire peak), and it is assigned to the migration of impurity ions.51 Although the concentration of these impurity ions is estimated to be just

below the ppm level,49 a significant loss is observed for polar PVDF. Note that the impurity ions in PVDF are inherited from the suspension polymerization used in industry.54 Intriguingly, with increasing the number of layers or decreasing the PVDF layer thickness, this low-frequency peak gradually decreases its intensity. Finally, the low-frequency peak for impurity ion migration nearly disappears for the 256-layer film. This is explained by confined ion transport in nanolayers, as shown in Figure 3C, because thin PVDF layers (∼50 nm) can effectively stop the long-range transport of impurity ions. Therefore, multilayer films are a viable approach to decrease impurity ion migrational loss for polar dielectric polymers, whose glass transition is below room temperature. Can Electronic and Vibrational Polarizations be Further Enhanced for Polymers? As we mentioned above, interfacial and ionic polarizations cannot be directly utilized to achieve high dielectric constant and low loss polymer dielectrics for fast discharge (i.e., μs to ms) and high field applications, although they may be helpful in unique multilayer films. One can naturally ask a question, can electronic and vibrational polarizations be further enhanced for polymer dielectrics? Because both polarizations have no dielectric losses in the power and radio frequency ranges, they are the most desirable. On the basis of polarization mechanisms for organic polymers, electrons need to be further delocalized in order to increase electronic polarization, and atoms need to change from carbon (C) to other elements such as Si in order to enhance vibrational polarization. However, delocalization of electrons (e.g., in conjugated polymers) will generally decrease the band gap of polymers, as is evidenced in a computational study that used density functional theory for 267 polymer systems.55 Because vibrational polarization is usually smaller than electronic polarization (i.e., 10−50% of electronic polarization55), the overall dielectric constant from both electronic and vibrational polarizations exhibits an inverse relationship with an upper limit boundary as a function of the band gap. If we take the high band gap of 8.8 eV for polyethylene as the gold standard,56 polymers with a band gap lower than 3−5 eV are not suitable for high-field applications. On the basis of the upper-limiting boundary, the total dielectric constants are limited to approximately 7 and 4 for band gaps of 3 and 5 eV, respectively. To enhance the dielectric constant from electronic 3680

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used for high-voltage dielectrics. Similarly, other polar solvents, such as N-methylformamide, also have a low electrolysis voltage,61 although their dielectric constant can be fairly high (e.g., the dielectric constant of N-methylformamide is 18462). However, the dielectric constant of polymers is relatively low, and dipole relaxation happens between 0.1 and 107 Hz, depending on the nature of the dipoles (amorphous versus crystalline), temperature, and frequency (see Figure 4). In order to achieve high dielectric constant and low loss, the dipole relaxation peak of polar polymers needs to be shifted to above 108 Hz while maintaining a similar dipole moment density and dipole mobility as water (Figure 4). In the following, we will discuss how to tailor orientational polarization for high dielectric constant and low loss polymer dielectrics. For polar polymers containing permanent dipoles, two extremes are well-known (see Figure 5). One extreme is linear dielectric polymers, which exhibit a linear electric displacement−electric field (D−E) behavior, D = εrε0E0 = ε0E0 + P.14,15 Typical examples are poly(ethylene terephthalate) (PET) and even-numbered nylons such as nylon-6. Because of the lack of any FE domain structures (a FE domain contains spontaneously aligned dipoles), a linear D−E loop with a relatively low dielectric constant is obtained, for example, 3.4 for PET and 3.2 for nylon-6 below their glass transition temperatures (Tg’s, 70 °C for PET and 50 °C for nylon-6). The other extreme is FE polymers, which exhibit a broad rectangularshaped hysteresis loop. Typical examples include PVDF and its copolymers and odd-numbered nylons.63 FE polymers show significant hysteresis loss, although their dielectric constant could appear relatively high (e.g., 10−12 for PVDF above its Tg at ∼−40 °C).63 This rectangular-shaped hysteresis loop behavior can be ascribed to the switching of large FE domains, which contain a large number of spontaneously aligned dipoles, in crystalline FE polymers.64 In between these two extremes, there are intermediate domain structures with progressively developed D−E hysteresis loops (Figure 5). First, isolated dipoles can be added into a linear dielectric polymer. The interactions among these dipoles and between the dipoles and the matrix are weak, and no domain structure is formed. This is termed as a dipolar glass, and it has been mostly reported for ceramic materials65 but rarely for polymers. Under an external field, dipole rotations are more or less independent, resulting in a slim D−E loop without any hysteresis. Upon adding more dipoles into the dielectric polymer, a PE structure is obtained with enhanced dipole− dipole and dipole−matrix interactions, but still no FE domain can form. Upon electric poling, a similar slim D−E loop is obtained. For both dipolar glass and PE polymers, a higher dielectric constant can be obtained in the linear region before dipole saturation. Second, nanosized FE domains (or nanodomains) comprised of a limited number of aligned dipoles can form due to the formation of symmetry-breaking crystals or liquid crystals in polymers. From a recent report, we understand that these nanodomains are the origin for the socalled relaxor ferroelectric (RFE) behavior in electron beam (ebeam)-irradiated P(VDF-co-trifluoroethylene) [P(VDFTrFE)] 66,67 and P(VDF-TrFE)-based random terpolymers.68−70 Depending on whether there is an electric fieldinduced RFE-to-FE conformation transition, narrow double hysteresis loop (DHL) and single hysteresis loop (SHL) behaviors can be obtained.64,71 Due to enhanced domain− domain interactions,64,72 further enhancement in dielectric

and vibrational polarization, group 14 elements (i.e., Si, Ge, and Sn) are proposed to replace C for new dielectric polymers with a structure of −XY2−, where X = Si, Ge, Sn and Y = H, F, Cl.55 For example, a −CH2−(SnF2)3− polymer can exhibit a total dielectric constant of 47 from electronic and vibrational polarizations with a band gap slightly higher than 3 eV. Nonetheless, the chemical stability of backbone −SiY2−, −GeY2−, and −SnY2− bonds (Y = F and Cl) needs careful examination [e.g., the −(CH2SiF2)n− polymer is susceptible to moisture57]. In addition, the challenge of synthesizing such inorganic polymers, however, is admittedly great.

Now only dipolar polarization is left for enhancing dielectric constants of polymer dielectrics. What are advantages and disadvantages for dipolar polarization in polymers? Can Orientational Polarization Be Used for High Dielectric Constant and Low Loss Polymer Dielectrics? Given the difficulty of further enhancing electronic and vibrational dielectric constants without lowering the band gap (or increasing the electronic conductivity), the last strategy is to utilize orientational polarization in polymers. At room temperature, pure water has a dielectric constant of ∼80 due to orientational polarization, and the dipolar relaxation peak is around 20 GHz (Figure 4).58 At 108 Hz, the dielectric loss, tan δ, is as low as

Figure 4. Schematic of the frequency dependence of real (εr′) and imaginary (εr″) permittivity for pure water at room temperature and a polar polymer. The results for water at room temperature are reproduced with permission from ref 58. Copyright 2005 American Physical Society.

0.005. This is attributed to free rotations of dipolar H2O molecules and hydrogen bonds under an alternating electric field. Intriguingly, H2O dipoles and hydrogen bonds can still respond to the external field in the solid state because ice shows a dielectric constant of ∼90−120 at low frequencies, and the dipole relaxation peak decreases to 103−104 Hz.59,60 Therefore, pure water seems to be a good polar liquid dielectric. However, electrolysis of water above 1.23 V makes it impossible to be 3681

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Figure 5. Different dipole and FE domain structures with increasing dipole−dipole or domain−domain interactions from left to right (the top panel) and corresponding electroactive responses in D−E loops (the bottom panel).

constant is observed for RFE polymers. In the following, we will discuss how to implement various domain structures in polymers and use their novel FE behaviors for high dielectric constant and low loss dielectrics. Polymer dipolar glasses can be considered as a class of amorphous polar polymers with high Tg’s. Polar groups with a large dipole moment, such as −CN [∼4.0 D], −NO2 (∼3.6 D), and −SO2− (∼4.3 D), can be attached to either the main chain or the side chains. Sub-Tg transitions, such as β and γ transitions, allow the rotation of these polar groups in the free volume of a glassy polymer.73 A good example is poly(methyl methacrylate), where the β transition involves the rotation of methyl ester side groups.74 In general, the side-chain polar groups are more desired than the main-chain polar groups because polymer main chains are more sterically hindered than the side chains. This is evidenced in recent reports for polar group-modified PC. When two fluorines are attached onto the aromatic main chain of a tetraaryl bisphenol A PC, the dielectric constant of the glassy polymer only increased about 10% to 3.3 as compared to the PC without the two aromatic fluorines.75 A further increase in dielectric constant is seen for a side-chain-modified, nitrile-containing PC (CN-PC), as shown in Figure 6.76 At around 125 °C, a dielectric constant of as high as 4.0 is observed, and the dielectric loss is reasonably low (tan δ ≈ 0.005). Compared to the Onsager theoretically predicted permittivity value (εr = 17), only 10% of the CN dipoles are able to rotate in the glassy state. In other words, rotation of −CH2CN dipoles are largely hindered by neighboring chains. A similar phenomenon is also observed for the rotation of methyl ester groups in poly(methyl methacrylate), where the main chain has to slightly adjust its position in order to accommodate the full rotation of the side chain.77 Therefore, a potential dielectric loss can originate from intermolecular friction when side chain dipoles flip in the power and radio frequencies. Future research is needed to further enhance dipole rotation and push the dipole relaxation toward GHz in order to decrease dielectric loss. PE polymers refer to a class of polar materials whose dipoles can quickly respond to the applied electric field. As soon as the

Figure 6. Real (εr′) and imaginary (εr″) parts of the relative permittivity at 103 Hz as a function of temperature for PC and CN-PC (chemical structures are shown on the top). Reproduced with permission from ref 76. Copyright 2013 American Chemical Society.

applied field is removed, all dipoles can completely return to the original random state.64 According to this definition, PE polymers can be either a liquid, such as amorphous or molten PET, PVDF, or nylons, or a solid, such as P(VDF-TrFE) or poly(VDF-co-tetrafluoroethylene) [P(VDF-TFE)] above the Curie temperature. From the low loss point of view, molten polymers are not good candidates due to significantly enhanced electronic conduction in the molten state. Solid PE polymers should supposedly be better than molten polymers. However, relatively high electronic conduction loss is still observed for PE P(VDF-TrFE) and P(VDF-TFE) samples above the Curie temperature.64 This is possibly due to the molten amorphous 3682

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Figure 7. (A) Real (εr′) and (B) imaginary (εr″) parts of the relative permittivity as a function of temperature for bisphenol A PC/PVDF 50/50 (vol/vol) 32-layer films at different frequencies.

Figure 8. Schematics of nanodomain formation in P(VDF-TrFE)-based terpolymers and e-beam-irradiated P(VDF-TrFE). Room-temperature bipolar D−E loops at 10 Hz (triangular wave function) are shown for (a) P(VDF-TrFE-CFE) 59.2/33.6/7.2, (b) P(VDF-TrFE-CTFE) 62.2/30.2/ 7.6, and (c) e-beamed P(VDF-TrFE) 50/50 (60 Mrad at 70 °C). D−E loops for P(VDF-TrFE-CFE) and e-beamed P(VDF-TrFE) are adapted with permission from ref 64. Copyright 2013 Elsevier.

(1.5 × 10−13 S/m) of polysulfone but much lower than that (10−11 S/m) of PVDF.44 Via multilayering two polymers having different dielectric constants, the overall permittivity obeys a serial capacitor model.78 Figure 7 shows the real and imaginary parts of the relative permittivity as a function of temperature for a bisphenol A PC/PVDF 50/50 (vol/vol) 32-layer film. At 1 Hz, the εr′ increases from 2.85 at −150 °C to 5.06 at 25 °C, and this is primarily attributed to the devitrification of amorphous PVDF at ∼−43 °C. It is reported that the dipole

phase and/or high mobility of the PE crystalline phase in both samples. In order to utilize PE polymers for high dielectric constant and low loss dielectrics, their electronic conduction needs to be significantly reduced. This has been achieved by multilayering them with a highly insulating linear dielectric polymer such as PC,45−47,49,51,78,79 polysulfone,44 and PET.80 For example, the electric conductivity of a polysulfone/PVDF 30/70 (vol/vol) 32-layer film at 100 MV/m is ∼6 × 10−13 S/m, similar to that 3683

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(see Figure 8. Note that it is idealized to show the pinning by aligning a few larger third comonomer units together. In reality, they may not align together; however, the pinning effect shall still exist). Although the nanodomains are difficult to visualize experimentally, a fully atomic molecular dynamics simulation suggests that their lateral dimensions may be 5−8 ab unit cells.64 It is these pinned FE nanodomains in the isomorphic crystal that result in the RFE structure. Namely, narrow D−E hysteresis loops are observed, and the RFE-to-PE conformation transition becomes broader or relaxor-like in broad-band dielectric spectroscopy.66,67 However, CFE is different from CTFE in both size and dipole moment. Due to the smaller size and larger dipole moment (∼1.8 D) of CFE, the physical pinning is weak, and P(VDF-TrFE-CFE) exhibits DHLs as a result of a reversible, electric field-induced RFE ↔ FE conformation transition (Figure 8a).64 Here, the RFE structure for P(VDF-TrFE-CFE) contains more or less random TmG (m ≤ 4) sequences, and the FE structure contains relatively long Tn (n > 4) sequences (note that T and G represent the trans and gauche conformations, respectively).71 On the contrary, CTFE is larger and has a low dipole moment (∼0.64 D). Therefore, the physical pinning is strong, and P(VDF-TrFECTFE) exhibits relatively narrow SHLs (Figure 8b).71 Here, the RFE structure for P(VDF-TrFE-CTFE) contains a mixture of long Tn (n > 4) and random TmG or TmS (m ≤ 4) conformations (S is the skew linkage83). In the second method, an e-beam or γ-rays are used to crosslink and chemically modify P(VDF-TrFE) crystals in situ. Interestingly, only P(VDF-TrFE), not PVDF nor its other copolymers, is sensitive to e-beam or γ-ray radiation. As a result of this radiation, the interchain distance, d110/200, of P(VDFTrFE) increases to 0.480 nm after a sufficient dose of radiation. This interchain distance is similar to that of P(VDF-TrFECFE). On the basis of solid-state 19F nuclear magnetic resonance spectroscopy studies,84,85 a small amount of −CF3 is formed after e-beam irradiation. We speculate that some −CF3 groups in the cross-linked crystal expand the interchain distance. Meanwhile, these cross-links permanently (or chemically) pin the VDF/TrFE units in between, forming nanodomains. The RFE structure again contains more or less random TmG (m ≤ 4) conformations, similar to the ones in P(VDF-TrFE-CFE). The corresponding RFE behavior is shown in Figure 8c, where narrow SHLs are exclusively observed. Obviously, this is because of the strong pinning effects from chemical cross-links in the crystals. If we look at the linear or low-field regions of the above three samples, the apparent dielectric constants are 55 for P(VDF-TrFE-CFE), 70 for P(VDF-TrFE-CTFE), and 30 for e-beam-irradiated (60 Mrad at 70 °C) P(VDF-TrFE). Indeed, high dielectric constants are achieved for the above RFE P(VDF-TrFE)based copolymers at a cost of a slight broadening of the D−E loops. In the future, crystal pinning and nanodomain concepts for the RFE behavior shall also be applied for other FE polymers such as odd-numbered nylons. In summary, we have discussed what types of polarization could be used as a strategy to achieve polymer dielectrics with high dielectric constant and low loss. Interfacial and ionic polarizations cannot be directly used to enhance dielectric constants because they inherently have slow discharge processes. On the basis of a recent computer simulation, further enhancing electronic and vibrational polarizations without decreasing the band gap to below 3−5 eV is also challenging. This leaves only orientational polarization for

relaxation of amorphous PVDF occurs at around 10 MHz at room temperature and gradually shifts to higher frequencies with increasing temperature.53 Therefore, utilizing multiplayer films comprised of PE polymers is a promising approach to achieve high dielectric constant and low loss dielectric, especially for high-temperature applications. From Figure 7B, in addition to the αa (i.e., glass transition) loss, the αc relaxation (a typical relaxation process for the α-phase PVDF crystals52,53) and ionic migration losses are also observed at 5 and 95 °C (1 Hz), respectively. Meanwhile, the γ transition and the onset of the glass transition for the PC layers are observed at −101 and 140 °C, respectively.73,76 Given all of these losses, the dissipation factor, tan δ, is reasonably low, about 0.005 at room temperature. At high temperatures, electronic conduction becomes significant for multilayer films. In order to be able to replace BOPP for film capacitors, further reduction of the dissipation factor, especially at elevated temperatures, is needed for future research on multilayer films. RFE behavior was first discovered in e-beam-irradiated P(VDF-TrFE)66,67 and later in P(VDF-TrFE)-based random terpolymers.68,69 The difference of RFE polymers from dipolar glass and PE polymers lies in the fact that RFE polymers still contain nanosized FE domains (nanodomains) whereas dipolar glass and PE polymers do not. Consequently, RFE polymers are expected to exhibit higher permittivity than dipolar glass and PE polymers. The disadvantage is that RFE polymers show some FE hysteresis in the D−E loops, while dipolar glass and PE polymers do not.64 If the requirement for dielectric loss is not that high, RFE polymers are promising for certain highvoltage applications such as pulsed power or defibrillator capacitors.4 On the basis of our recent report,64 the fundamental mechanism for the RFE behavior is the formation of nanodomains via repeat unit crystal isomorphism (i.e., a defect-modified crystal structure) and pinning of mobile dipoles in the P(VDF-TrFE) crystal (see Figure 8). Repeat unit isomorphism refers to a mixed crystal structure for a random copolymer consisting of similar comonomers in terms of size and property. By copolymerizing VDF with TrFE, the interchain distance in the FE crystal increases from d110/200 = 0.426 nm for the β-phase PVDF to d110/200 = 0.442 nm for the low-temperature FE phase of P(VDF-TrFE). However, this increase cannot warrant the formation of nanodomains because TrFE is not large enough and its dipole moment (∼1.4 D81) is not small enough to pin the chains in the crystal. A further increase of interchain distance is needed and has been realized in two ways, terpolymerization68,69 and e-beam irradiation.66,67 For terpolymerization, 1,1-chlorofluoroethylene (CFE) and chlorotrifluoroethylene (CTFE) are chosen as the third comonomer. Here, TrFE is critical to pre-expand the interchain distance and to allow the larger third comonomer to be included in the isomorphic or defect-modified crystal. For example, without TrFE, CTFE will be largely excluded from the PVDF crystal.64 However, the third comonomer cannot be too large. For example, the hexafluoropropylene unit cannot be included in the isomorphic crystal even in the presence of TrFE in PVDF.82 After incorporation of either CFE or CTFE in the P(VDF-TrFE) crystal, the interchain distance, d110/200, increases to 0.484 nm for the P(VDF-TrFE-CFE) 59.2/33.6/7.264 and 0.490 nm for the P(VDF-TrFE-CTFE) 62.2/30.2/7.6,71 respectively, providing extra room for the friction-free rotation of P(VDF-TrFE) dipoles. Ideally, these large comonomers physically pin ∼10−14 VDF/TrFE units, forming nanodomains 3684

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organic polymers. Stimulated by the dielectric property of pure water, we propose that high dielectric constant and low loss dielectrics are possible if we can substantially enhance dipole mobility and shift its relaxation peak into the GHz range for polar polymers. The first strategy is dipolar glass polymers, where side-chain dipoles are more desirable than the mainchain dipoles because of decreased steric hindrance for sidechain rotation. The second strategy is PE polymers. Due to the high electronic conduction loss in PE polymers (both liquid and solid), multilayering a PE polymer with a highly insulating polymer is a viable way to achieve high dielectric constant and low loss polymers. The third strategy is RFE polymers, which exhibit a higher dielectric constant than dipolar glass and PE polymers. Crystal isomorphism is utilized to achieve nanodomains with enlarged interchain distance and pinning of crystalline dipoles. Both P(VDF-TrFE)-based terpolymers and e-beam radiation can achieve the RFE structure. However, either DHL or SHL behavior can be obtained depending on the pinning force. Namely, a weak pinning force favors the DHL behavior, whereas a strong pinning force favors the SHL behavior. Depending on different requirements, different strategies can be used for various applications. For example, if dielectric loss needs to be extremely low, such as in DC-link capacitors for electric vehicles,86 dipolar glass and PE polymers are more advantageous. If dielectric loss does not need to be extremely low, such as in defibrillators and pulsed power,4 RFE polymers appear more appealing. In the future, more research is needed to develop dipolar glasses and multilayer films. Meanwhile, RFE polymers need to extend their high temperature capability to go beyond 150 °C.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work on novel ferroelectric polymers is supported by National Science Foundation (NSF) Grants DMR-0907580 and DMR-1402733. The work on fundamental polarization mechanisms in multilayer films is supported by NSF through the Science and Technology Center for Layered Polymeric System (CLiPS) under Grant DMR-0423914. The work on multilayer film capacitors for pulsed power applications is supported by the Office of Naval Research (N00014-11-10251).

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P(VDF-TFE) Poly(vinylidene fluoride-co-tetrafluoroethylene) P(VDF-TrFE) Poly(vinylidene fluoride-co-trifluoroethylene) P(VDF-TrFE-CFE) Poly(vinylidene fluoride-co-trifluoroethylene-co-1,1-chlorofluoroethylene) P(VDF-TrFE-CTFE) Poly(vinylidene fluoride-co-trifluoroethylene-co-chlorotrifluoroethylene) RFE Relaxor ferroelectric SHL Single hysteresis loop

GLOSSARY

BOPP Biaxially oriented polypropylene DHL Double hysteresis loop D−E loop Electric displacement−electric field loop EDL Electric double layer FE Ferroelectric Tg Glass transition temperature PE Paraelectric PC Polycarbonate PET Poly(ethylene terephthalate) PVDF Poly(vinylidene fluoride) P(VDF-CTFE) Poly(vinylidene fluoride-co-chlorotrifluoroethylene) 3685

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