Recent Progress on Ferroelectric Polymer-Based Nanocomposites

Ali Shayesteh Zeraati , Mohammad Arjmand , and Uttandaraman Sundararaj ..... Yuri A. Barnakov , Omari Paul , Akinwunmi Joaquim , April Falconer , Rich...
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Recent Progress on Ferroelectric Polymer-Based Nanocomposites for High Energy Density Capacitors: Synthesis, Dielectric Properties, and Future Aspects Prateek,† Vijay Kumar Thakur,‡ and Raju Kumar Gupta*,†,§ †

Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India School of Mechanical and Materials Engineering, Washington State University, Pullman, Washington 99164, United States § DST Thematic Unit of Excellence on Soft Nanofabrication and Center for Environmental Science and Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India Chem. Rev. 2016.116:4260-4317. Downloaded from pubs.acs.org by UNIV OF READING on 08/12/18. For personal use only.

‡

ABSTRACT: Dielectric polymer nanocomposites are rapidly emerging as novel materials for a number of advanced engineering applications. In this Review, we present a comprehensive review of the use of ferroelectric polymers, especially PVDF and PVDF-based copolymers/blends as potential components in dielectric nanocomposite materials for high energy density capacitor applications. Various parameters like dielectric constant, dielectric loss, breakdown strength, energy density, and flexibility of the polymer nanocomposites have been thoroughly investigated. Fillers with different shapes have been found to cause significant variation in the physical and electrical properties. Generally, one-dimensional and two-dimensional nanofillers with large aspect ratios provide enhanced flexibility versus zero-dimensional fillers. Surface modification of nanomaterials as well as polymers adds flavor to the dielectric properties of the resulting nanocomposites. Nowadays, three-phase nanocomposites with either combination of fillers or polymer matrix help in further improving the dielectric properties as compared to two-phase nanocomposites. Recent research has been focused on altering the dielectric properties of different materials while also maintaining their superior flexibility. Flexible polymer nanocomposites are the best candidates for application in various fields. However, certain challenges still present, which can be solved only by extensive research in this field.

CONTENTS 1. Introduction 2. Applications 3. Polymer Nanocomposites: Theory 3.1. Polarization Mechanisms and Various Types of Losses: Searching for Ways To Get Optimum Dielectric Properties 3.2. Effect of Interfaces in the Polymer Nanocomposites 3.2.1. Lewis’s Model 3.2.2. Tanaka’s Model 3.3. Theoretical Models for Predicting Effective Permittivity of Polymer Nanocomposites 3.3.1. Lichtenker’s Formula 3.3.2. Maxwell−Garnett Equation 3.3.3. Bruggeman Self-Consistent Effective Medium Approximation 3.3.4. Percolation Theory 3.4. Different Types of Dielectrics: Relation with Energy Density 4. Fluoropolymers as Novel Dielectric Materials: Structure and Chemistry 4.1. PVDF (Homopolymer) 4.1.1. Ferroelectricity in PVDF 4.2. Binary Copolymers © 2016 American Chemical Society

4.2.1. P(VDF−TrFE) 4.2.2. P(VDF−HFP) 4.2.3. P(VDF−CTFE) 4.3. Relaxor and Ternary Copolymers 4.3.1. Irradiated P(VDF−TrFE) 4.3.2. P(VDF−TrFE)-Based Ternary Copolymers 5. PVDF-Based Nanocomposites 5.1. Nonconducting Fillers-Based Polymer Nanocomposites 5.1.1. Two-Phase Composites Based on Spherical Fillers 5.1.2. Two-Phase Composites Based on OneDimensional Fillers 5.1.3. Three-Phase Composites 5.2. Conducting Fillers-Based Polymer Nanocomposites 5.2.1. Two-Phase Composites Based on Spherical Fillers 5.2.2. Two-Phase Composites Based on OneDimensional Fillers 5.2.3. Two-Phase Composites Based on Different Shapes of Fillers

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Received: September 22, 2015 Published: April 4, 2016 4260

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Chemical Reviews 5.2.4. Three-Phase Composites 6. Challenges and Summary Author Information Corresponding Author Notes Biographies Acknowledgments References

Review

the polymers depends on the presence of polar groups as well as chain geometry. The polarity arises due to the electronegativity difference between the elements of a bond. The more electronegative elements withdraw the electron cloud toward its side, giving rise to partial negative charge at the cost of the other element, which acquires a partial positive charge. For example, among various forms of poly(vinylidene fluoride) (PVDF), in all-trans β-PVDF, dipoles are in one direction, giving rise to polar behavior (see section 4.1). In general, PVDF has a dielectric constant of ∼10 with higher breakdown strengths. At 2 400 kV/cm, it has a discharged energy density of 2.8 J/cm3 (Table 1). Thus, it has better energy density as compared to other polymers like polyimides, poly(arylene ether nitrile), etc. due to comparatively higher dielectric constant and breakdown strength. Apart from polymers, proper selection of fillers of different types and shapes also helps in improving the electrical properties of the polymer nanocomposites. Generally two different types of fillers (i.e., nonconducting and conducting fillers) have been employed to synthesize different polymer-based nanocomposites. Nonconducting fillers include ceramics like barium titanate (BaTiO3),67−69 strontium titanate (SrTiO3),70 Bi2O3−ZnO− Nb2O5,71 calcium titanate (CaTiO3),72 etc. These ceramics behave as insulators as they have high band gap so that accumulation of charges takes place only on the application of an electric field.7,73 On the other hand, conducting fillers like graphene,74,75 carbon black (CB),76,77 carbon nanotubes (CNTs),78−80 etc. are also widely used. By the use of conducting fillers, comparatively higher values of dielectric constant can be easily achieved at low concentrations in comparison to nonconducting fillers, but the properties change abruptly near the percolation threshold, i.e., the critical concentration above which continuous channels begin to form over the whole system, thereby limiting further addition of fillers.81 Fillers shapes and sizes are also important factors that can further improve the dielectric properties of the polymer nanocomposites.82,83 Fillers of different shapes, like zero-, one-, two-dimensional, etc., and sizes lead to different percolation limits, which in turn is related with loading as well as flexibility of the polymer nanocomposites. The percolation limits of higher-dimensional fillers can be easily achieved as compared to lower-dimensional fillers for the same loading. The dielectric constant and breakdown strengths are two important parameters in deciding the energy density of the polymer nanocomposites. The energy density of linear dielectrics is related to breakdown strength as follows (eq 1),84,85

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1. INTRODUCTION Dielectric nanocomposites have drawn the attention of researchers worldwide due to their applications in various fields such as optoelectronics,1−7 pulsed power systems,8−10 temperature and vapor/liquid sensing,11−17 energy harvesting,18−22 transistors, and inverters.16,23−26 Dielectric nanocomposites are usually composed of dielectric polymers as matrix materials and inorganic/organic fillers as the reinforcement, utilizing the properties of both. Polymers have been found to exhibit high breakdown strength along with high energy density, while the fillers, especially ceramics, have high dielectric constant.27 The combination of both provides enhanced dielectric properties depending on the type and nature of polymer matrices as well as fillers.28 A large number of polymers have been used based on their different properties, including epoxy,29−36 polyimides,37−41 poly(methyl methacrylate) (PMMA),42−45 polydimethylsiloxane (PDMS),46 etc., to prepare polymer nanocomposites. For example, epoxy resins have been found to exhibit high reactivity, easier processing, lightweight, and low cost.47 These polymers are considered as insulating polymers. For this reason, these are widely used in electrical insulation, printed circuit boards, electronic packaging, excellent chemical resistance, and very large scale integrated microelectronics technology.48 However, epoxy polymers are not able to meet the heat-dissipating requirements because of their low thermal conductivity (0.17−0.21 W/m/K).49 In addition, these polymers are also brittle in nature, thereby restricting their applications to be used in high-performance applications.50 Polyimides are among one of the thermosetting polymers with good thermal stability, low moisture absorption, chemically inert in nature, optically transparent, ease of film preparation, and good mechanical properties.51−56 PMMA is also a widely used polymer to prepare nanocomposites. It is an amorphous polymer with high strength, is resistant to many inorganic and organic reagents, and exhibits good optical properties and good wearing properties.49,57−59 PDMS, a silicon based elastomer, is a well-known flexible polymer, which is transparent and biocompatible in nature.60,61 The glass transition temperature of PDMS is quite low, i.e., −113.15 °C, which is responsible for its rubbery behavior.62,63 Different polymers exhibit different properties; thereby, selection of suitable polymers plays a pivotal role in deciding the final properties of the resulting polymer nanocomposites. Polymers can be classified into polar and nonpolar polymers based on their mean dipole moments.64−66 In a nonpolar polymer, the individual dipole moments cancel out each other due to symmetry and are hence responsible for lower dielectric constant. Examples of some nonpolar polymers are polytetrafluoroethylene (PTFE), low-density polyethylene (LDPE), polyolefins, etc. However, in polar polymers, the dipoles usually do not cancel out each other giving rise to reinforcement of individual dipole moments and exhibit comparatively higher dielectric constant than nonpolar polymers. The polar nature of

energy density =

1 εoεrE b 2 2

(1)

where εr and εo are the dielectric permittivity of the material and vacuum (8.85 × 10−12 F/m), respectively, Eb is the breakdown strength of the medium, which is the maximum electric field that can be applied to a dielectric material without making it conducting. As energy density has a square relationship with the breakdown strength, higher breakdown strength is required to achieve higher energy density. Fillers with good dielectric constant are necessary to get improved energy density, but at the same time, its loading cannot be increased beyond a limit that leads to agglomeration and hence lowering of breakdown strength. Moreover, a large contrast in dielectric constants of fillers and matrix results in inhomogeneity in the electric fields of polymers as well as fillers and should be avoided to enhance the breakdown strength and hence energy density.86 Another 4261

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vehicles; medical devices such as defibrillators, surgical lasers, and X-ray equipment; power-conditioning equipment; high-frequency filtering; solid-state switch snubbers; pulsed-plasma thrusters; high-power microwave; weapon systems including electric guns (electromagnetic railguns and coil guns, electrothermal guns, and electrothermal−chemical guns); ballistic missile applications; electric ships; etc.8,84,89,90,92−98 Whittingham compared the energy/power densities of fuel cells, batteries, pseudocapacitors, double-layer capacitors, electrostatic capacitors, and internal combustion engines and depicted that electrostatic capacitors exhibit the best power densities (∼104 to ∼107 W/kg) but poor energy densities (0.001−0.1 Wh/kg).99 Thus, lots of research is going on to improve the energy density of the polymer nanocomposites. Automotive inverters are used in electric as well as hybrid electric vehicles to convert the battery’s dc power to ac current at the desired frequency needed for maintaining motor speed, drive torque, and power. The basic requirements for the electric drive systems of vehicles are small size to ensure installations, high output, high efficiency, and ability to sustain a harsh environment inside the vehicle. dc-link capacitors play an important role in electric vehicles’ inverter systems.93 These help in attenuating ripple current, reducing the electromagnetic interference, suppressing voltage spikes associated with leakage inductance, and switching operations as well as providing reactive power.100 To fulfill the need for short period peak power, the capacitors store energy by increasing the capacitor voltage to a higher voltage in a low-power mode, while delivering much higher power than the continuous power in high power mode.101 Film capacitors are found to improve the dc capacitor reliability used in the inverter system.93 Wen et al. analyzed the viability of two 220-μF film capacitors (AVX FFVE6K0227K) based on 80-kW permanent-magnet motor drive system.100 Film capacitors give promising results in terms of low power loss (20.6 W) as well as improved power density (13.3 W/cm3). Capacitors are also used in electrotherapy. One of the most successful and widely recognized applications of electrotherapy is in defibrillators. Defibrillators are the devices that are planted in the chest and measure the heart’s electrical signals. It should be simple in design and provide a safe shock. Implantable cardioverter defibrillators can deliver one or more electric shocks that range from a few microjoules to very powerful shocks of 25−40 J in ∼5−10 s.102 The modern defibrillator capacitors can have an energy density greater than 5 J/cm3.103 High power density of capacitors also has applications in defense; the most integral part is in electromagnetic propulsion. There is a need for compact high-energy systems (up to 250 MJ). Depending on system requirements, the required energy density ranges from 1.0 to 1.5 J/cm3 with operating voltages in the range of 15−25 kV, although there is a demand for an increase in capacitive energy density as well as operating ranges to make it enabled for various applications.104,105 For example, General Atomics (GA) developed one-quarter-megajoule millisecond discharge capacitor (GA model 38964) having energy density and shot life of 2.68 J/ cm3 and 1 000, respectively, while that of GA model 32944 are 2.4 J/cm3 and 10 000, respectively. Later, they modified the existing abilities of the capacitor with 13 kJ microsecond discharge capacitors (GA model 32944) with energy density of 1.3 J/cm3 and dc life of >2 000 h.92 Also, there is a need for high power density in electromagnetic railguns that require >100 MJ of energy into the railgun breech per shot with a pulse length of a few milliseconds needed to transit through the barrel.106 Another important necessary consideration for the guns is that the average

important parameter is dielectric loss, which arises due to the rate of energy transfer associated with molecular collisions on the application of an electric field. The dielectric loss, in turn, is related with the average dissipated power density in a dielectric medium, i.e., the amount of energy absorbed by the dielectric per unit volume per unit time is given by eq 2,87,88 dissipated power density =

1 ωεoε″Eo 2 2

(2)

where ε″ is the imaginary permittivity of the system, ω is the frequency, and Eo is the electric field applied across the film. Thus, the higher the ε″ for the same ω and Eo, the higher will be the power dissipation in a dielectric material. In real applications, capacitors are also required to work at high-temperature conditions. A material with high thermal conductivity can give fruitful results. For example, biaxially oriented polypropylene (BOPP) can work at temperatures up to 100 °C. Certain polymers like polyethylene naphthalate (PEN) (up to 150 °C) and polyphenylene sulfide (PPS) (up to 175 °C) can withstand comparatively higher temperatures than BOPP, but at higher cost. So, there is a need to develop polymer nanocomposites that can work at higher temperatures without degrading their performance.89 Thus, apart from selected electrical properties required for a polymer film, it should withstand all kinds of thermal stresses during operation, being impervious to chemicals, mechanically flexible, easy to handle, and of lower cost.90 To meet the need of industry and obtain high energy density nanocomposites, relaxor ferroelectrics as well as materials with antiferroelectric behaviors having high dipole reversibility exhibit a very high potential.91 Polar polymers such as PVDF and PVDFbased copolymers serve as the best selected polymers for high energy density applications. To address the various issues confronted in the use of fluoropolymers as dielectric materials, in the present Review we summarize the current research efforts devoted to the use of these polymers and their respective nanocomposite materials for energy-storage applications. The Review has been primarily divided into six major sections. The second section covers applications of dielectric capacitors. The third section covers the detailed study of various types of polarization mechanisms along with different types of dielectrics and their relation with energy density. The fourth section gives an overview of chemistry and electrical properties of PVDFbased binary copolymers as well as relaxor and ternary copolymers. The fifth section is devoted to the study of dielectric properties of polymer nanocomposites synthesized from PVDF and PVDF-based copolymers/blends, respectively. This section will give a comprehensive review of the effect of shapes of nonconducting and conducting fillers on the dielectric properties. The sixth section gives an idea regarding challenges for further modification of the electrical properties followed by summary and perspective.

2. APPLICATIONS Dielectric capacitors find a wide range of applications. They are used in audio and video equipment, industrial electronics and telecommunications equipment, and automotive electronics, as well as in various other pulsed-power applications. Dielectric capacitors utilize inherent high power density, i.e., fast energy uptake and delivery, thus making them suitable to use in highperformance power electronics. The stored energy should be delivered within 10−6 to 10−3 s for pulse-discharge applications.92 These are used in inverters of electric as well as hybrid electric 4262

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Table 1. Dielectric Properties of Various Polymers and Fillers fillers

dielectric constant (1 kHz)

LDPE

2.3

high-density polyethylene (HDPE) PTFE

2.3 2

BOPP

loss tangent (1 kHz)

dielectric strength (kV/cm)

discharged energy density (J/cm3)

nonpolar polymers 0.003 308.9

thermal conductivity (W/m/K) 0.33

2.2

0.0002−0.0007 0.0001 polar polymers 0.0002

7500

3 (at 5000 kV/cm)

2.1−2.35

polystyrene

2.4−2.7

0.008

2000

0.55 (at 2000 kV/cm)

0.04−0.16

poly(ethylene terephthalate) (PET) PMMA

3.6 4.5

0.01 0.05

2750−3000 2500

polyvinyl chloride (PVC) polyetheretherketone (PEEK) poly(phthalazinone ether ketone) polycarbonate (PC)

3.4 4 3.5 3.0

400

epoxy

4.5

0.018 0.009 (100 kHz) 0.0063 0.0015 (at 1000 kV/cm) 0.015

PVDF

10

0.04

1500−5000

2.8 (at 2400 kV/cm)

0.24

PDMS polyimide

2.6 3.5

0.01 0.04

660 2380

1.4

0.17−0.26 6.58−11.7

polyurethane polyvinyl alcohol poly(arylene ether nitrile) aromatic polyurea (poly(diaminodiphenylmethane diphenylmethane diisocyanate) [P(MDA/MDI)]

4.6 12 4 4.2

0.02 0.3 0.025 0.005

200 1000 2314 8000

0.965 12

boron nitride

4.2 (at 1 MHz) 1235 10.1 (at 1 MHz) 3.8 (at 1 MHz) ∼5000

BaTiO3 alumina (Al2O3) quartz Ba0.7Sr0.3TiO3

fillers 0.00034 (at 1 MHz) 0.012 0.0002 (at 1 MHz)

222.9 880−1760

4700 2520

0.45−0.52 0.25

1.5 (at ∼3300 kV/cm)

0.29 0.15−0.25 0.12−0.17 0.25

3.9 (at 4500 kV/cm) 0.19

250−450

0.17−0.21

references 49, 112, 113, 114 49, 112, 114 49, 114 113, 115−117 8, 113, 114, 118 49, 114, 119 42, 44, 45, 49 113, 114 49, 120, 121 122 8, 113, 114 8, 29, 31, 49, 113, 114 31, 114, 123, 124 46, 49 113, 125−127 114, 128 129, 130 131, 132 133

380

29−300

49, 114

150 135

6.2 38−42

49, 134, 135 32, 49, 114

0.0038 (at 1 MHz)

114

0.03

136

power should match the firing rate of the gun. For example, in the beginning, there may be a faster rate of firing followed by a slower rate. For a typical tank gun with a firing rate of 4 rounds/min, the average power needed for electrothermal−chemical guns, electromagnetic railguns, and electrothermal guns are 250, 2 000, and 4 500 kW, respectively, with a capacitive energy density of 7 J/cm3.98 Also, the discharge currents vary from several 100 kA (electrothermal guns) to several MA (rail guns).107 Recently, a pulsed power system of 16 MJ for electromagnetic railgun is established that uses the capacitor having energy density of 1.5 J/cm3 and life of ∼3 000 shot times.108 There are various manufacturers of film capacitors, like G.E. (U.S.A.), Nissei/Arcotronics (Japan), Matsushita (Japan), ABB (Europe), Aerovox (U.S.A.), Cooper Industry (U.S.A.), Vishay (Europe), Rubycon Corporation (Japan), KEMET Corporation (U.S.), etc. Apart from energy applications, there is a wide range of applications that utilizes polymer nanocomposites that are flexible in nature. Flexible nanocomposites’ synthesis has opened a new era in the field of high energy density applications. In recent years, lots of work has been going on to obtain new materials with good flexibility. Flexible nanocomposites find

enormous use in synthesis of wearable devices. The wearable devices, which are used in the industries, should be of small size, lightweight, low power consumption, and portable.109 With integration of sensors, it can apply to biomedical application as well.110,111

3. POLYMER NANOCOMPOSITES: THEORY This section gives an overview of the basic concepts that determine the optimum dielectric properties as well as high energy density of the polymer nanocomposites. It includes polarization as well as breakdown mechanisms, nanofillers interaction, and various types of dielectric materials. 3.1. Polarization Mechanisms and Various Types of Losses: Searching for Ways To Get Optimum Dielectric Properties

Polarization is defined as total dipole moments in a dielectric per unit volume. It is related to dielectric constant under the homogeneous applied field as in eq 3,137 P = (εr − 1)εoE 4263

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electronic polarization.116 In a recent study, much higher dielectric constant of 47 was obtained for −CH2(SnF2)3−, which included both electronic and ionic polarization. Replacing carbon with group 14 elements for a new polymeric material having a structure of −XY2− will be a better way to utilize the electronic and ionic polarizabilities, although chemical stability is an issue. Here, X and Y refer to Si, Ge, Sn and H, F, Cl, respectively.145 Thus, the dielectric properties of the polymers are significantly affected by their polarity. As depicted earlier, the electronic and atomic polarizations respond at higher frequencies and are instantaneous. It gives an indication that, whether the polymer is polar or nonpolar, the dielectric constant in this region is usually small. So, the orientational polarization plays a pivotal role in determining effective permittivity of the polymeric system. Orientation or dipolar polarization exists in polar materials carrying permanent dipoles such as H2O, HCl, etc. As the molecules need energy to overcome the resistance offered by the surrounding molecules, this phenomenon is temperaturedependent. However, when the field is removed, the molecules take time to relax back to equilibrium. So, this type of polarization falls in the relaxation regime and usually relaxes in radio frequencies as shown in Figure 1.87,137 In real capacitors, nonhomogeneity, presence of impurities, and incomplete contact of the film with the electrode lead to regions of accumulated trap charges in dielectric medium, which is known as Maxwell−Wagner−Sillars interfacial polarization.146,147 It usually takes hours to years to discharge.88 Interfacial polarization usually exists in almost all polymer nanocomposites, but its effect can be nullified by making good electrical contact between electrode and film148 as well as multilayer films, which effectively traps the charges ejected from the electrode and restricts their movement in the device. 149,150 Complex permittivity, ε*, can be correlated with dielectric permittivity and loss as in eq 6,

where P is the polarization developed and E is the applied electric field. The degree of polarization under the influence of applied field is measured by a term called susceptibility, χ (eq 4):138 χ = (εr − 1) =

P εoE

(4)

The Clausius−Mossotti equation relates dielectric permittivity with the polarizability for the isotropic, nonpolar material (eq 5),139 εr − 1 Nα = εr + 2 3εo

(5)

where N is the number of atoms or molecules per unit volume and α is the polarizability of the material. There are four main types of polarizations that exist in a dielectric material, viz. electronic, ionic, dipolar, and interfacial polarizations, as shown in Figure 1. These polarizations can be subdivided into two regimes, i.e., resonance and relaxation regimes.88,91,140−143

ε* = ε′ − jε″

(6)

where ε′ is the real permittivity of the system. Moreover, these two dielectric parameters can be further combined for a certain frequency and temperature by the term called loss tangent, tan δ (eq 7): tan δ =

ε″ ε′

(7)

For an ideal capacitor, ε″ is zero or there are no losses. However, for a real capacitor, two types of losses are present. First, one is frequency-independent ohmic conduction losses that are due to long-range movement of charges, whereas the second is frequency-dependent dielectric losses associated with absorption of energy to move the charges with the field.138 In a polymeric material, usually two types of dipolar relaxations exist: dipolar segmental relaxation, i.e., associated with microBrownian motion of the whole chain, known as α relaxation, and dipolar group relaxation, i.e., associated with localized motion of the molecules as well as small chain units, known as β and γ relaxation (Figure 2).139,151,152 The β relaxation is associated with relaxation of side groups such as −CH2Cl and −COOC2H5 about the C−C chain, conformational shift of cyclic unit that leads to changes in the orientation of polar groups, or local motion of the dipolar group across the main chain, whereas γ relaxation occurs at much lower temperature and is associated with movement of small units of the main chain or side chain. Figure 2 suggests that the activation energy required for the α

Figure 1. Different types of polarizations and their frequency dependences. Here, Pe, Pi, Pd, and Pint refer to electronic, ionic, dipolar, and interfacial polarizations. Dielectric constant and corresponding losses depicted with blue and red lines, respectively.

Electronic or optical polarization is associated with displacement of electron cloud with respect to nucleus under the influence of applied electric field. Ionic polarization is present in ionic materials and responds in the infrared (IR) frequency. Both electronic and ionic polarization show resonance at frequencies in the optical and IR range, respectively, so these are classified in the resonance regime.144 Moreover, they are temperatureindependent, as the phenomenon is intramolecular in nature.139 To improve electronic and ionic polarizations, delocalization of electrons and addition of foreign elements in ionic materials can give fruitful results. However, delocalization of electrons sets an upper limit for enhancement in dielectric properties for polymeric materials because it results in a reduction in band gap, and usually ionic polarization is only 10−50% of the 4264

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computations were performed for one-dimensional structure determination and density functional perturbation theory (DFPT) and effective medium theory (EMT) were used to estimate dielectric constant due to electronic and ionic contributions. It is found that the most promising polymers that satisfy the initial screening step and are suitable for the application of high energy density capacitors consist of at least one of the polar units, −NH−, −CO−, and −O−, and at least one of the aromatic rings, −C6H4− and −C6H2S−. The breakdown strength plays an important role in order to get optimized dielectric properties. Now, section 3.2 will discuss the nature of interfaces, when fillers are added in the polymer matrix. 3.2. Effect of Interfaces in the Polymer Nanocomposites

The incorporation of different kinds of nanomaterials ranging from nonconducting to conducting nanomaterials significantly affects the overall properties of the resulting dielectric nanocomposites. A number of parameters like polymer chain mobility, chain confirmation, crystallinity, Coulombic potential, etc. have been reported to control the interaction of the nanomaterials with the polymer matrices.28,151,161−164 To understand the effect of interface in the polymer nanocomposites, two important models are hypothesized, namely, Lewis’s model and Tanaka’s model, which are discussed in the following subsections.160,165−167 3.2.1. Lewis’s Model. The addition of nanofillers in polymer matrix results in the creation of numerous interfaces in nanometric dimensions. The nanofillers surface or at least part of it eventually gets charged due to the difference in Fermi levels or chemical potential of the nanoparticles and polymer matrix.168 The matrix, in turn, responds by developing counter charges near the nanofillers surface.141,169 Consider a positively charged particle is present inside the polymer matrix as shown in Figure 3a. Here, the nanoparticle surface is shown to be planar for

Figure 2. Schematic of different types of relaxations at different temperatures.

relaxation is more than that of β and γ relaxation, which is due to a narrower relaxation peak.153−155 Another important factor, which is crucial in determining the dielectric properties of the polymer nanocomposites, is breakdown strength. Breakdown is not desired for high energy density applications as it severely affects the performance of the capacitor and leads to early failure of the device. Various mechanisms that lead to breakdown in solids are electronic breakdown, thermal breakdown, electromechanical breakdown, internal discharges, insulation aging, and external discharges, which are discussed elsewhere.88,155−160 The breakdown strength is also dependent on the dielectric constants of individual fillers and polymer matrix. There should not be much contrast in the conductivity as well as dielectric constant of the nanofillers and polymer matrix. This often results in inhomogeneity of the field across the film. From the expression of the electric field in the filler and polymer matrices (eqs 8 and 9),86 it can be inferred that, when the dielectric constant of the filler is comparatively larger than that of the polymer matrix, the electric field in the polymer increased to a much greater extent, leading to lowering of the breakdown strength. ⎤−1 ⎡ ⎛ε ⎞ f ⎢ Ef = Eo φm⎜ − 1⎟ + 1⎥ ⎥⎦ ⎢⎣ ⎝ εm ⎠

(8)

−1 ⎡ ⎛ εm ⎞ εm ⎤ ⎥ Em = Eo⎢φm⎜1 − ⎟+ ⎢⎣ ⎝ εf ⎠ εf ⎥⎦

(9)

where Ef and Em are the electric field in the filler and polymer matrix, respectively. When metals are used as fillers, the chances of early breakdown are more prominent because Ef will be nearly zero and Em will be sufficiently high to cause breakdown.91 Breakdown strength can also be increased by homogeneous dispersion of fillers. It is not an issue for low nanofiller loading, however; as the loading is increased, the interconnection of nanofillers leads to conducting channel along with the presence of voids. So, surface modification is necessary to extend the limit of loading for a nanofiller. Also, the choice of polymer should be such that the breakdown strength of the polymer nanocomposites should be increased. Sharma et al.116 have proposed a strategy of hierarchical modeling to screen 267 polymers with four-block repeat units based on their properties, which satisfied a total dielectric constant and band gap greater than 4 and 3 eV, respectively. On the basis of various monomers as well as their connectivity sequence, density functional theory (DFT)

Figure 3. (a) Diffuse electrical double layer produced by a positively charged particle in a polymer matrix containing mobile ions, along with the resulting electrical potential distribution ψ(r). (b) Conduction via diffuse double layers in a composite system.

simplicity. The charged nanoparticle causes redistribution of charges in the matrix due to Coulomb attraction, which results in formation of an electrical double layer consisting of a Stern layer and a Gouy−Chapman diffused layer.165 The Stern layer or Helmholtz double layer is formed on the nanoparticle surface due to the adsorption of counterions. The diffused layer is formed around the Stern layer by the distribution of negative and positive ions. This layer determines the dielectric properties of the polymer nanocomposites and become more predominant near percolation threshold of the fillers (Figure 3b; also see section 3.3.4). Figure 3a shows the electrical potential 4265

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distribution, ψ(r), with distance from the nanoparticle surface.170−172 This behavior has been found to satisfy the solutions of Poisson and Boltzmann equations.173 The combined Poisson−Boltzmann equation can be represented as eq 10, ∇2 Ψ(r ) = −eε−1 ∑ zini(∞) e−zieΨ(r)/ kT i

third or loose layer is loosely coupled to the bound layer with thickness ranging from several tens of nm. In this region, the polymer matrix has different chain conformation, mobility, free volume, and crystallinity than those of the bulk polymer matrix.82,151,173−175 Tanaka’s model looks into the various possibilities in tailoring the dielectric properties of the polymer nanocomposites. The dipole orientation of the polar radicals is adversely affected in the bound layer. On the other hand, the loose layer reduces the free volume. Both effects lead to reduction in the dielectric constant. Therefore, the selection of an appropriate coupling agent is an important factor to obtain high energy density.

(10)

where ψ(r) is the potential distribution function that varies with distance, r, from the surface of the nanoparticle, ε is the dielectric constant of the medium, k is the Boltzmann constant, and zi and ni(∞) are the valency and concentration of ion species i in the bulk matrix, respectively. For the small potential, known as Debye−Hückel approximation, the equation is given below:

3.3. Theoretical Models for Predicting Effective Permittivity of Polymer Nanocomposites

zie Ψ(r ) φc

(19)

σc ∝ σm(φc − φp)−q for φp < φc

(20)

σc ∝ σpuσm1 − u for |φp − φc| → 0

(21)

references

(22)

where l is the distance between the centers of particles of radius b and d is the typical tunnelling range. When the interparticle distance l decreases, i.e., near the percolation threshold, σt begins to rise exponentially. The percolation threshold depends on the shape, size, and orientation of the fillers.191 For a homogeneous polymer nanocomposite with uniformly sized spherical fillers, the percolation threshold is ∼0.16 (also called Sher−Zallen invariant), although in practical situations, it varies from 0.013 to 0.17.82,83 However, when the size of the fillers are changed to ellipsoid, percolation can be achieved at much lower concentration due to the fact that fillers will be more easily connected to form a continuum. Thus, for large aspect ratio fillers, percolation threshold varies inversely with the aspect ratio of the fillers.143 Table 2 summarizes the relation of percolation threshold with fillers of different aspect ratios. From Table 2, it can be seen that the percolation threshold depends on the shapes of the fillers. For BaTiO3 nanoparticles, the one with the larger diameter (i.e., 700 nm)193 has a lower percolation threshold than the one with the smaller diameter of 100 nm.192,193 As the shape changes from nanoparticles to onedimensional, the percolation thresholds reduce to comparatively lower values. For graphenes, due to large dimensions as compared to other fillers, the percolation threshold is further reduced to 0.31 vol %.197 In another study, Tong et al. synthesized reduced graphene oxide (RGO)-based poly(vinylidene fluoride-co-hexafluoropropene) (P(VDF−HFP)) polymer nanocomposites.198 They found that percolation thresholds could be altered by varying the synthesis procedure. For example, the polymer nanocomposites synthesized from spin-coating resulted in more percolation thresholds of 0.8 vol %, due to successful synthesis of well aligned fillers, while that synthesized from a traditional drop-casting approach exhibited a comparatively lower percolation threshold of Pin and hence Epol > Edepol. During reverse poling, although Epol and Edepol decreases with time, there may be two possibilities, i.e., Pin > Q + Pcomp or Pin < Q + Pcomp. For Pin > Q + Pcomp or Edepol > Epol, some of the mobile dipoles move in opposite direction and often lead to minimum or even net zero remnant polarization. The behavior is termed as antiferroelectriclike behavior. However, for Pin< Q + Pcomp, Edepol is always lower than Epol, which is referred as normal ferroelectric behavior. Thus, DHL is developed based on the difference in the magnitudes of Epol and Edepol. A detailed discussion of these behaviors is mentioned in section 4, which will describe the electrical properties of different PVDF-based polymers.

4. FLUOROPOLYMERS AS NOVEL DIELECTRIC MATERIALS: STRUCTURE AND CHEMISTRY PVDF-based polymers are one of the most frequently used dielectric materials for high-energy capacitors.223 These are among the highest dielectric constant materials in the category of polymers and exhibit high breakdown strength.229 Certain PVDF-based copolymers have been frequently used to modify the electrical properties of the nanocomposites, namely, P(VDF−TrFE), P(VDF−HFP), poly(vinylidene fluoride-cochloride trifluoride ethylene) (P(VDF−CTFE)), and poly(vinylidene fluoride−trifluoroethylene−chlorofluoroethylene) (P(VDF−TrFE−CFE)), etc.230 Martins et al. discussed thoroughly different phases of PVDF and PVDF-based copolymers and their properties, especially electroactive properties, along with their preparation methods.231 In the following section, we will be discussing the structure, chemistry, and dielectric properties of PVDF-based materials. 4269

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4.1. PVDF (Homopolymer)

orientation of the dipoles would have been restricted, resulting in relatively lower dielectric constant. The dielectric loss of PVDF is relatively high (0.02 at 1 kHz) in comparison to BOPP (0.0002 at 1 kHz).236 In addition, PVDF polymers also possess high DC breakdown strength, having value of 7000 kV/cm (for 10-μm capacitor grade films), but relatively lower discharged energy density of 2−3 J/cm3 at 2000 kV/cm.123,236,237 Relatively lower discharged energy density is due to the achievement of saturation polarization at a much lower electric field. Out of various types of PVDF mentioned above, only β-phase is ferroelectric in nature with thermodynamically stable spontaneous polarization (see section 4.1.1). It is synthesized from various methods like stretching of α-phase,238,239 which induces alignment of polymer chains to all−trans confirmation, melt under high pressure240 or melt crystallization under high cooling rates,241 electrospinning,242 heat−controlled spin−coating,243 addition of nucleating agents244−246 and crystallization of PVDF from various solvents like dimethylformamide (DMF) or dimethylacetamide (DMAC).247,248 The α-phase is synthesized from the melt by cooling at normal rate, whereas δ-phase is obtained from α-phase by poling at room temperature under high electric field of 1000− 2000 kV/cm. The γ-phase is either obtained at low temperature by solution-casting (SC) from polar solvents or at high temperature by annealing/crystallization.231 PVDF-based polymers have also been modified to obtain the new polymer system with tailored dielectric properties. Hence, modifications of PVDF, by either ordinary chemical means or exposing it to irradiating beams, become necessary that can alter the polymer configuration and thus help in attaining higher dielectric properties. Because of the inert nature of PVDF, surface modification by using irradiating beam is much more easier than that of chemical means.237 For example, Thakur et al. conducted a series of work in modifying the PVDF properties by using irradiated beam of electrons.237,249,250 The detailed mechanism of grafting of (2-hydroxyethyl methacrylate) (HEMA) onto PVDF polymer is shown in Figure 8.249 The irradiating electron beam caused scission of C−C, C−H, and C− F bonds in the PVDF molecule. Considering the initiation site as −CF2−C*H−CF2−, addition and propagation of HEMA resulted in the formation of polymer chains followed by termination reaction. The grafted PVDF polymer exhibited enhanced dielectric constant (45 at 1 kHz) and reduced loss tangent (∼0.0011 at 1 kHz). In continuation of work, the same group has grafted PS.250 The dielectric constant and dielectric loss were ∼90 and 0.005, respectively, at 1 kHz, which showed that grafting of PVDF with PS provided better dielectric properties as compared to HEMA. Moreover, dopamine (PDOPA), a bioinspired protein, was also used as grafting agent to modify PVDF polymer.237 The preparation involved activation of PVDF by bombardment with electron beams followed by incorporation of peroxides and hydroperoxides groups onto the PVDF surface by exposing it to the atmosphere, thus providing a means for functionalizing with PDOPA (Figure 9).The dielectric constant of the PDOPA−modified PVDF nanocomposites was 32 (1 kHz), while the loss tangent was ∼0.001 (1 kHz). Energy density was found to be 2.7 J/cm3 at 1400 kV/cm. Therefore, the dielectric properties of pristine PVDF polymer can be further enhanced by use of proper grafting agent. In another work, Li et al. blended PVDF polymer with aromatic polythiourea resulted in improved dielectric constant and dielectric loss of 9.2 and 0.02 at 1 kHz along with energy density of 10.8 J/cm3.251 So, surface modification or blending of PVDF polymer with an organic compound has enormous

PVDF is the polymer of vinylidene fluoride (VDF) containing 59.4 wt % fluorine and 3 wt % hydrogen atoms with 50−70% crystallinity, having glass and melting temperatures in the range of −40 to −30 °C and 155−192 °C for amorphous and crystalline phases, respectively.232 The Curie temperature of PVDF is in between 195−197 °C.233 PVDF polymer exists in five different phases, namely, α-, β-, γ-, δ-, and ε-phases, based on different chain confirmations.231 Figure 6 shows the majorly used polymers with confirmations of TGTG′ for α and δ, TTT for β, and T3GT3G′ for γ phases.

Figure 6. Schematic representation of the chain conformation for the α/ δ, β, and γ phases of PVDF. Reprinted with permission from ref 231. Copyright 2014 Elsevier Ltd.

In terms of polarization, β-phase of the PVDF has highest dipole moment of 2.10 D in perpendicular to chain length, while α-, γ-, and δ-phases having dipole moments of 1.20 and 1.02 D in perpendicular and parallel to the direction of chain length, respectively (Figure 7a−d).223

Figure 7. Unit cells of (a) α, (b) δ, (c) γ, and (d) β forms of PVDF crystals viewed along the c-axes. Red, cyan, and blue spheres represent fluorine, carbon, and hydrogen atoms, respectively. The projections of dipole directions are indicated by green arrows. Reprinted and modified with permission from ref 223. Copyright 2012 American Chemical Society.

Among different types of PVDF, α-phase is nonpolar as the dipole moments cancel out each other, while δ-, γ-, and β-phases exhibit high polarizability due to the presence of net dipole moments and hence have high dielectric constants as compared to α-phase.234 The dielectric constant of PVDF lies in the range of 6−12.235 Moreover, direction of c-axes of PVDF molecule with respect to the applied electric field also results in contributing to high dielectric properties. Relatively higher dielectric constant can be obtained for the dipoles (CH2CF2) that are arranged in parallel direction to the field, as the orientation of the dipoles will be easier in the presence of applied electric field. In contrast, if the dipoles are present in perpendicular direction to the field, 4270

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Figure 9. Surface modification of PVDF polymer powder. Reprinted and modified with permission from ref 237. Copyright 2012 The Royal Society of Chemistry.

potential to enhance the dielectric properties. The next section insights a brief discussion on the ferroelectric behavior of PVDF polymer. 4.1.1. Ferroelectricity in PVDF. PVDF was first polymerized in 1940s and its ferroelectric nature was discovered in the 1970s. Naegele and Yoon observed the orientation of molecular dipoles as well as ferroelectric behavior using IR spectroscopy.252 Two IR absorptions at 512 and 446 cm−1 were associated with transition moments along and perpendicular to the CF2 dipole. Kepler and Anderson found that the axes of crystalline regions of PVDF oriented themselves on the application of electric field, based on the X-ray diffraction (XRD) of the sample before and after poling. They concluded that the molecular orientation occurred in 60° increment.253 Although, the results were contradicting with those of Aslaksen,254 as they found that there was 180° increment in molecular reorientations in the presence of applied field. Later, Dvey-Aharon et al.255 compared the results of Kepler and Anderson253 as well as Aslaksen.254 They concluded that 60° increment was more energetically favorable as compared to 180° increments in addition to small distortion of lattice. Furthermore, for the 60° model, they found the minimum in the interchain potential at 30° for the chain labeled 1 (Figure 10a,b). The minimum in potential was related with the ease of reorientation of the chain. It was deduced that very few chains in a crystallite can participate during poling process. These chains were either present at the boundary surface of differently polarized sections of crystallite or at the boundary of twinned regions as well as along the directed line of polarizations in that surface. Thus, the minima in potential energy at 30° allowed the kink formation in the middle of the chain (labeled as 1 in Figure 10a) and propagated along the chain to produce 60° chain rotation. Assuming the number of monomer units to be three or four units long, the total twist energy was predicted to be ∼13 kcal/mol. Clark and Taylor experimentally calculated the value of 18 kcal/ mol, which supported the prediction of Dvey-Aharon et al.255,256

Figure 8. Mechanism for graft copolymerization of HEMA onto PVDF polymer. (a−c2) depicts chain initiation, (d,e) depicts chain propagation, and (f,g) depicts chain termination. Reprinted with permission from ref 249. Copyright 2011 The Royal Society of Chemistry. 4271

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1300 kV/cm) that may even reduce to zero, when electric field becomes zero.218,230,263 The dielectric constant of P(VDF− TrFE) has higher value of ∼18 than that of PVDF (6−12) with loss tangent of