High-density electrostatic energy storage in a multi-layer P(VDF-TrFE-CFE)/2D mica nanocomposite heterostructure capacitor

Abstract

The growing need for renewable energy has drawn significant attention to the development of energy storage systems with ultra-high capacity and efficiency. Polymer-based dielectric capacitors are important in modern electronics and energy storage systems because of their inherent flexibility, fast charge–discharge capabilities, low dielectric loss, and high power density. However, the conflicting relationship between dielectric polarization and electric breakdown behavior frequently hinders further advancements in energy storage performance. In this study, we incorporated mechanically exfoliated 2D mica as nanofillers into a poly (vinylidene fluoride-trifluoroethylene-chlorofluoroethylene) (P(VDF-TrFE-CFE)) or PTC polymer to fabricate multilayered heterostructure capacitors and arranged them in a PTC/mica/PTC (PMP) and PTC/mica/PTC/mica/PTC (PMPMP) configuration. PMP and PMPMP nanocomposite films exhibit maximum discharged energy densities of 50 J cm⁻³ (E = 750 MV m⁻¹) and 45 J cm⁻³ (E = 625 MV m⁻¹), respectively, compared to the typical PTC capacitor with a maximum discharged energy density of 15 J cm⁻³ (E = 500 MV m⁻¹). The PMPMP capacitors demonstrate a discharge time of 6.64 μs with high cyclic stability (98%) after thousands of cycles at an applied voltage of 400 V. This study provides a comprehensive understanding of the development of polymer- and 2D nanofiller-based capacitors for industrial applications.

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1. Introduction

In recent years, the development of energy storage systems with ultra-high capacity and efficiency has received considerable attention due to the increasing demand for renewable energy. With the rising need for energy storage systems, many studies have focused on various solutions, such as chemical storage systems (lithium and sodium-ion batteries), electrochemical capacitors, solid-state fuel cells (SOFCs), superconducting magnetic energy storage (SMES) systems and dielectric capacitors.^1–9 Li-ion batteries possess high energy density and durability, but the devices are very slow to deliver the energy needed for many microelectronics and fast operation electronic devices. Due to chemical reactions, Li-ion batteries can degrade quickly and have a low life span. On the other hand, supercapacitors could sustain longer charge–discharge cycles with higher power density than Li-ion batteries, but their self-discharge rate and high cost prevent these capacitors from reaching a wide range of applications. Despite the challenges, Li-ion batteries and supercapacitors have potential applications in many devices where high-density energy is required, such as EVs, hybrid vehicles and electronic devices requiring longer power times. Among the current energy storage systems, dielectric capacitors, which are electrostatic energy storage devices, offer significant advantages over other systems because of their small volume and fast discharge rate (requiring microseconds) compared to Li-ion batteries (requiring several seconds), longer lifespan, and improved efficiency.^1,2,10,11 These capacitors have a wide range of applications where a fast discharge energy is required, such as advanced portable electronic devices; pulsed power systems in laser, radar and defense technology as well as biomedical fields. As a result, there has been considerable interest in research focused on electrostatic energy storage. Dielectric materials with high energy and high power density are essential in energy storage application, particularly for power electronics, including hybrid electric vehicles, electromechanical weapon systems, and medical devices, as well as modern electronics in miniaturized form. These lightweight devices have promising applications for unmanned spacecraft and satellites; capacitors with high capacitance, low equivalent series resistance (ESR) and compact size are critical components due to their ability to reduce space and weight. Recently, polymer dielectrics have shown promising potential in many electrical and electronic systems due to their relatively high electric breakdown strength, low dielectric loss, low cost, light weight, superior flexibility, thermal stability and ease of processing.^12,13 However, the limited energy storage density of dielectric capacitors significantly restricts their practical applications to a wider range, particularly in miniaturized and integrated energy storage systems that require higher capacitances and reduced packing dimensions.^14,15 Therefore, developing polymer dielectrics with high discharge energy density is crucial for energy storage capacitors.

Discharged energy density (U_d), efficiency (η), and breakdown strength (E_BD) are three critical parameters that determine the figure of merit of a capacitor device. The discharged energy density of a dielectric material can be obtained using the area under the electric polarization vs. electric field loop (P–E loop) during discharging. For a linear dielectric material, the maximum discharged energy density of a capacitor , where ε_r is the dielectric constant of the material or polymer composites and E_BD is the maximum electric field that the capacitor can sustain before the leakage current increases. Thus, ε_r and E_BD are the two essential parameters in the optimization of U_d. However, simultaneously enhancing both U_d and E_BD is still a challenging task, as E_BD degrades with the increasing ε_r.

At present, many high-performance linear polymers, such as polyimide (PI),¹⁶ polyetherimide¹⁶ (PEI), polyester,¹⁷ polycarbonate (PC),¹⁷ polymethyl methacrylate (PMMA),¹⁸ polyether ketone,¹⁹ polystyrene,²⁰ polypropylene (BOPP),¹⁹ aromatic polyurea,¹⁷ aromatic polythiourea (ArPTU),²¹ and poly(tetrafluoroethylene-hexafluoropropylene) (PVDF-H),¹⁹ are currently widely used as possible materials for high-temperature dielectric capacitors. Among them, poly (vinylidene fluoride-trifluoroethylene-chlorofluoroethylene) (P(VDF-TrFE-CFE)) or (PTC) is an advanced relaxor terpolymer that has received much attention for energy storage applications due to its unique combination of high dielectric permittivity, strong flexibility, and high breakdown strength.^22,23 It is a member of the polyvinylidene fluoride (PVDF) family and derived from the copolymer PVDF-TrFE by adding a third monomer unit, chlorofluoroethylene (CFE). This structural alteration modifies the long-range ferroelectric ordering, changing the polymer from a standard ferroelectric to a relaxor ferroelectric. Thus, PVDF-TrFE-CFE has a broad and dispersed phase transition, high dielectric permittivity, and thin polarization–electric field (P–E) loops, making it perfect for electrostatic capacitors and energy storage applications.²⁴

In recent years, researchers have shown that polymer-based nanocomposite materials exhibit improved dielectric constant, breakdown strength, and storage energy density.^25–28 These improvements are achieved by incorporating nanomaterials as fillers within the polymer matrix to improve the desired properties. Among the various systems of polymer nanofiller composites, the incorporation of two-dimensional (2D) nanomaterials is pioneering compared to other nanofillers because of their larger surface area-to-volume ratio, which allows for greater accumulation and trapping of charge at the polymer-2D interface, leading to increased polarization.^29–32 Among the wide range of two-dimensional (2D) materials used as nanofillers, mica has emerged as an economical, easily exfoliable, thermally stable material with a high dielectric constant, making it a particularly attractive candidate for integration into polymer matrices to develop advanced, energy-efficient dielectric capacitors.²⁹ Recent studies have shown that multilayer films of 2D-polymer nanocomposites exhibit superior dielectric properties and energy storage performance compared to pure polymer films.^33–35 These nanocomposites are typically prepared by directly mixing 2D materials with polymers, resulting in randomly distributed fillers throughout the polymer matrix.

Despite these encouraging features, the specific behavior and effectiveness of 2D mica as a nanofiller in P(VDF-TrFE-CFE) polymer composites are not fully understood. Nevertheless, some studies on P(VDF-TrFE-CFE) polymer nanocomposites have already been conducted. For example, Li et al.³⁶ reported that the energy density of a 15 mm thick P(VDF-TrFE-CFE)/h-BN nanocomposite enhanced by barium titanate (BaTiO₃) nanoparticles increased from 7 J cm⁻³ at an electric field of 35 MV m⁻¹ to 16 J cm⁻³ at 550 MV m⁻¹. Mao et al.²² showed that the blended polymer composite film containing 20 wt% P(VDF-TrFE-CFE) terpolymer in PVDF achieved a remarkable discharge energy density of 13.63 J cm⁻³ along with an enhanced breakdown strength of 480 MV m⁻¹. Tu et al.³⁷ observed that the dielectric constant of the P(VDF-TrFE-CFE)-Ti₃C₂T_x nanocomposite increased from 50 to 10⁵ with 15 wt% MXene loading, although the energy density value was not reported in their study. In all the blended polymer nanocomposite systems, the dielectric constant and energy density increased as a function of nanofiller contents to a certain vol% of the filler, after which the percolation effect plays a crucial role in reducing the energy density and breakdown strength due to the increase in leakage and dielectric loss. This provides the opportunity to develop a method of incorporating nanofillers within the polymer host in such a way as to minimize the leakage and dielectric loss and increase the breakdown strength as well as energy density. In our previous research, we successfully combined 2D mica with the PVDF polymer using a mechanical exfoliation method where the 2D mica fillers were placed in a stratified geometry within the PVDF matrix without dispersing them inside the PVDF matrix. This geometry provides a smaller quantity of 2D mica nanofillers to fill the surface area of the capacitor to enhance the dielectric constant, breakdown strength, and energy density. The resulting PVDF/mica/PVDF thin heterostructure capacitors of < micron thickness exhibited a critical energy density of 75 J cm⁻³ and a high breakdown field of 1270 V m⁻¹, achieved with only 1 vol% exfoliated mica as fillers.²⁹ In another study, we integrated 2D mica nanosheets directly into a homopolymer PVDF matrix to form a thicker capacitor of PVDF/mica/PVDF (PMP) and two layers of mica to form PVDF/mica/PVDF/mica/PVDF (PMPMP) heterostructure capacitors. The maximum discharge energy of PMP and PMPMP nanocomposite films reached 27.5 J cm⁻³ (E = 670 MV m⁻¹) and 44 J cm⁻³ (E = 570 MV m⁻¹), while the pristine PVDF capacitor achieved only 11.2 J cm⁻³ (E = 396 MV m⁻¹).³⁸ However, the effect of stratified 2D nanofillers in a multi-polymer matrix requires additional elucidation to determine the effects of various interfaces from the polymer and the nanofiller matrix.

In this study, we incorporated 2D mica into a PTC polymer matrix and fabricated mica-PTC multilayer nanocomposite devices layer by layer. This method enabled the alignment of 2D fillers in stratified geometry within a thin film of polymer layers. The multilayer stack of the polymer and 2D filler device demonstrated a considerable increase in energy density (U_d) of about 50 J cm⁻³ at an electric field of 750 MV m⁻¹, as well as a high efficiency (η) of around 80%. We believe that this study advances our understanding of the impact of 2D nanofiller stratification in polymer nanocomposites and will aid in the future development of high-energy density polymeric nanocomposite capacitors.

2. Experimental procedure

2.1 Materials and methods

(P(VDF-TrFE-CFE)) or (PTC) was purchased from polyK, PA, USA. 2D bulk mica disks were purchased from Ted Pella Inc., USA. Indium tin oxide (ITO) substrates, with a sheet resistance of 3–5 Ω per sq, were purchased from MSE supplies, USA. Acetone, isopropyl alcohol and methyl ethyl ketone were purchased from Sigma Aldrich. All the chemicals were used as received.

2.2 Measurement procedures

The distribution of 2D mica flakes was examined using an optical microscope equipped with 20× objectives, in conjunction with a Signatone probe station, both before and after transfer from the Si/SiO₂ substrates. The transfer of the exfoliated mica flakes from the SiO₂ substrate onto the PTC-coated ITO substrates was confirmed. The thickness of the polymer layers was characterized using a Veeco Dimension 3100 atomic force microscope (AFM) operated in the tapping mode. Polarization and breakdown strength measurements were conducted using a radiant ferroelectric precision instrument, utilizing a high-voltage power amplifier (TREK, 10 kV). The cyclic stability was performed using poly K, 10 kV.

3. Results and discussion

A 5% (w/w) solution of PTC was prepared by dissolving PTC powder in 10 ml of a ketone-based solvent under continuous magnetic stirring for 13 hours at ambient temperature. Subsequently, an ITO substrate was cleaned by sequential immersion in acetone, isopropyl alcohol (IPA), and deionized (DI) water using an ultrasonic cleaning bath. Following the cleaning, a base layer of PTC polymer was deposited onto the ITO substrate via spin-coating. The coated substrate was then annealed on a hot plate at 100 °C for 5 minutes, after which it was stored in a desiccator. At the same time, we mechanically exfoliated 2D mica onto clean Si/SiO₂ substrates using the blue scotch tape method. Fig. 1(a–c) shows the optical images of exfoliated (2D) mica flakes on Si/SiO₂ substrates, exhibiting various thicknesses, sizes, and orientations and regions within the 2D plane of the substrate, a typical pattern often seen with mechanically exfoliated methods. Afterward, a thin PTC layer was spin-coated onto the mica-exfoliated Si/SiO₂ substrate, followed by a post-annealing process at 100 °C for 5 minutes. Fig. 1(d–f) displays the optical images of mica flakes coated with a PTC layer on the Si/SiO₂ substrate, revealing that the 2D flakes maintain their integrity following the spin-coating process on the substrate, which is crucial for future applications.

Fig. 1 (a–c) Various regions and orientations of exfoliated 2D mica flakes on SiO₂ substrates. The exfoliated mica flakes exhibit high uniformity and high density across the substrate. (d–f) Various regions and orientation of (P(VDF-TrFE-CFE)) or PTC-coated 2D mica flakes on the SiO₂ substrates.

Subsequently, the 2D mica flakes and PTC polymer were removed from the Si/SiO₂ substrate by dipping it in a 30 wt% KOH aqueous solution, where SiO₂ was etched. The resulting film (mica/PTC film) was then transferred to deionized (DI) water to remove residual KOH and later coated onto the PTC-coated ITO substrate. This process yielded a 2D-polymer nanocomposite film, specifically a PTC-Mica-PTC monolayer heterostructure (PMP), which was fabricated by placing a PTC-coated mica film on top of a PTC-coated ITO substrate, as shown in Fig. 2(a). To construct a PTC-Mica-PTC-Mica-PTC bilayer heterostructure (PMPMP), an additional mica-PTC layer was deposited on the PMP architecture, as shown in Fig. 2(b). After sequentially transferring the polymer and 2D material layers onto the PTC-coated ITO substrate, the final devices were subjected to vacuum conditions for several hours or overnight to remove entrapped water and moisture and minimize the interfacial gaps, leading to the formation of a smooth, well-integrated sandwich-like layered structure.

Fig. 2 Schematics of the geometrical stacking of a 2D mica-based polymer heterostructure where 2D mica acts as a nanofiller. (a) Schematic representation of a PTC/2D mica/PTC (PMP) heterostructure capacitor. (b) Schematic representation of a PTC/2D mica/PTC/2D mica/PTC (PMPMP) heterostructure capacitor. (c and d) AFM images and the thickness profile of a single layer of PTC on the SiO₂ substrate, indicating a thickness of 305 nm.

To determine the thickness of only the PTC layer on SiO₂ substrates, we have utilized AFM in a tapping mode, capturing the cross-section of the polymer after scratching the film, as illustrated in Fig. 2(c). Fig. 2(d) shows the height profile of a single-layer PTC film thickness measured across the scratch, indicating an average thickness of 300 nm. In terms of device specifications, we believe the PMP device has an overall thickness of 600 nm. Conversely, devices referred to as PMPMP, which include additional layers or modifications, demonstrate a greater total thickness of 900 nm. The thickness of 2D mica flakes varies from a single layer to a few layers, exhibiting an average thickness of 20 nm as shown in Fig. S1.

To determine the surface absorbed functional groups, we have performed the Fourier-transform infrared spectroscopy (FTIR) of PTC, mica and PMPMP heterostructure, as shown in Fig. S2. The characteristic crystalline band located around 890 cm⁻¹ confirms the C–C stretching of the P(VDF-TrFE-CFE) terpolymer, which is consistent with previous literature reports.^39,40 The FTIR spectrum of mica shows the presence of metal–O–H bending modes in the 600–950 cm⁻¹ region, whereas the 400–600 cm⁻¹ spectral region is predominantly attributed to Si–O and Al–O bending modes. The distinct modifications in the vibration spectra of PMPMP indicate significant interfacial interaction between P(VDF-TrFE-CFE) and mica sheets. The increased intensity ratios of peaks at a low-frequency region, such as 435 and 510 cm⁻¹, confirm that the Al–OH and K–O groups from mica form a strong hydrogen bonding interaction with the fluorine atoms of the polymer.⁴¹ Also, the reduced intensity of C–C skeletal vibrations at 890 cm⁻¹ in PMPMP indicates an alteration in crystallinity due to the incorporation of mica, as shown in Fig. S2(a). A distinct peak at 2916 cm⁻¹ is observed in mica, which corresponds to the C–H vibration mode. Interestingly, we noted that in the PTC samples, the intensity of the C–H peak is low. However, after incorporating mica into the polymer matrix, the peak intensity is significantly enhanced, as shown in Fig. S2(b). These results indicate both physical and weak chemical interactions between the polymer and mica.

Energy density is an important physical parameter for evaluating energy storage devices.^29,42 To characterize the energy storage capabilities of capacitors, polarization was measured as a function of the applied electric field. Fig. 3(a) illustrates the representation of a polarization–electric field (P–E) loop for ferroelectric capacitor materials, highlighting hysteresis loss in blue, along with the charge and discharge energy densities. Generally, non-ferroelectric polymers exhibit lower hysteresis loss compared to their ferroelectric counterparts. The electric polarization of polymer nanocomposite films was evaluated at room temperature. Fig. 3(b–d) illustrates polarization as a function of the applied electric field for various configured capacitor films from PTC, PMP, and PMPMP films, labeled as C₁ to C₉. Several capacitors were measured in each of these configurations to determine the statistical range of polarization and behavior as a function of the applied electric field. In each case, the electric field gradually increased to form complete P–E loops without dielectric breakdown. The maximum polarization of pristine PTC is ∼12.8 μC cm⁻² at an electric field of 523.3 MV m⁻¹ for C₂ capacitors, as shown in Fig. 3(b). All the capacitors show hysteresis loss, indicating the ferroelectric nature of the PTC polymer. The variation in polarization could depend upon several factors, such as interface charge due to contact with silver electrodes, polymer structure such as the amorphous or crystalline region, defects and non-homogeneous grain boundaries, which can create non-uniform localized charge accumulation that can influence the polarization to vary within the same batch of capacitors, potentially leading to variation in measurements. The P–E loop of the PMP capacitor achieves a higher polarization of about 22.0 μC cm⁻² at 727.7 MV m⁻¹ for the C₅ capacitor, as shown in Fig. 3(c). The PMPMP capacitor reaches a maximum value of 24.05 μC cm⁻² at 625 MV m⁻¹ for the C₃ capacitor, as shown in Fig. 3(d). This steady increase in polarization in PMPMP capacitors is mainly due to the enhanced interfacial interactions between the polymer and mica in the multilayer geometry, where the density of the 2D nanofiller is higher than in the PMP capacitor. This makes the PMPMP capacitor reach the higher polarization at a lower applied field strength; however, the maximum operation voltage of PMPMP is lower than that of the PMP capacitor. The higher charge accumulation in PMPMP capacitors may cause a lower breakdown strength, where charges can percolate through the PTC polymer quickly from the interface of mica/PTC by applying an increasing electric field. Adding a mica layer between the PTC films creates various interfaces or boundaries, which are important for enhancing interfacial polarization. When an electric field is applied, these surfaces accumulate charges and increase the interfacial polarization effect. Furthermore, recent studies^43–46 suggest that adding 2D layers to a multilayer dielectric leads to increased interfacial polarization, as evidenced in our results.

Fig. 3 (a) Schematics of charging–discharging cycles from the polarization–electric field (P–E) loop, highlighting remnant polarization (P_r), maximum polarization (P_max) and discharged energy density (U_d). (b) P–E loop measurements of various PTC capacitors ranging from C₁ to C₆. (c) P–E loop measurements of various PMP heterostructure-based capacitors ranging from C₁ to C₇. (d) P–E loop measurements of various PMPMP heterostructure-based capacitors ranging from C₁ to C₉.

Energy storage performance in capacitors is quantified by charged energy density (U_e) and discharged energy density (U_d), corresponding to the areas under the charging and discharging curves of the P–E loop, as shown in Fig. 3(a). The discharged energy density can be calculated as , and the area of the P–E loop refers to the hysteresis loss (U_I). The charged energy density can be calculated as U_e = U_d + U_l. The ratio of energy densities at a particular electric field is referred to as efficiency, To optimize the P–E loop for ultra-high voltage (U_d) and efficiency (η), it is necessary to increase the maximum electrical polarization (P_max) and reduce the remanent electrical polarization (P_r), while ensuring strong stability of the electric field.

We fabricated several capacitors on three different material geometries, PTC, PMP, and PMPMP, and measured their energy densities by applying an electric field near the breakdown strength, as shown in Fig. 4(a–c). The large variation in discharge energy densities of PMP and PMPMP capacitors is due to the non-uniform distribution of the 2D mica nanofillers. The low discharge energy originates from the region where the mica filler density is poor, and it exhibits a very similar energy density compared to PTC capacitors. Comparing the energy density of the PTC capacitor at the highest applied voltage of E = 500 MV m⁻¹ is U_d ∼ 15 J cm⁻², the average energy density measured in PMP capacitors is higher, U_d ∼ 25 J cm⁻², which suggests the incorporation of the mica filler provides the additional interfacial charge accumulation leading to higher energy density. The PMP capacitor also sustains a higher electric field (up to 900 MV m⁻¹) compared to the PTC capacitors (up to 600 MV m⁻¹). The slope of the U_d also provides information on the incorporation of mica, which enhances polarization and energy density. The maximum discharge energy density (U_d) of the PTC capacitor is shown in Fig. 4(d), which indicates a moderate U_d of 15 J cm⁻³ with an efficiency (η) of 60% at an electric field strength of 500 MV m⁻¹. Therefore, to obtain a higher U_d, it is important to improve the polarization of the polymer by incorporating suitable nanofillers. Our capacitor exhibits enhanced polarization by incorporating 2D mica nanofillers between the polymer films. The maximum discharge energy density of the PMP capacitor is shown in Fig. 4(e). These capacitors exhibit an energy density as high as U_d ∼ 50 J cm⁻³ at an applied field of E = 750 MV m⁻¹, a 230% enhancement over that of the PTC polymer. The variation in energy density enhancement is also observed due to the non-uniform 2D fillers, which exhibit lower energy densities, but the average energy density is always higher in the PMP capacitor than in the PTC. The efficiency is one of the striking differences between the PMP and PTC capacitors. We observed an 85% efficiency at E = 500 MV m⁻¹, compared to the PTC film, which shows 60%. The efficiency of the PMP capacitor even reaches 80% at the highest field strength (E = 750 MV m⁻¹) applied. In contrast, PMPMP capacitors exhibit a U_d of 45 J cm⁻³ at 625 MV m⁻¹. The efficiency of this capacitor shows 80% at 500 MV m⁻¹ and is reduced to 70% at 625 MV m⁻¹. The increase in energy density in the multilayer polymer nanocomposites can be attributed to a higher dielectric constant. The maximum stored energy density (U_d) in a capacitor is proportional to the dielectric constant (ε) of the material. We have extracted the dielectric constant values of PTC, PMP and PMPMP capacitors through U_d by fitting the U_dvs. E curves with U_d = (1/2) ε₀ε E², which are 31.5, 42.3 and 45.7, respectively, as shown in Fig. S3. The incorporation of two-dimensional (2D) nanofillers into the polymer matrix can significantly enhance the overall dielectric constant of the composite compared to bare PTC. Previous density functional theory simulations revealed that dielectric enhancements were caused by interface polarization between mica and the polymer layer.²⁹

Fig. 4 (a–c) Variation in discharged energy densities (U_d) of PTC, PMP and PMPMP capacitors as a function of applied electric field. (d–f) Maximum variation in discharged energy densities (U_d) and efficiency (η) of PTC, PMP and PMPMP capacitors with an applied electric field.

In high-voltage applications, polymer-based dielectrics are commonly used as insulating materials because of their intrinsic high breakdown strength. In addition, when combined with suitable nanofillers, it can possess high charge accumulation while maintaining high resistance to charge leakage by providing organized traps and scattering centers and increasing the tortuosity of the path for the propagation of carrier charges. This may not be true with increasing nanofiller concentration above a percolation limit, where the accumulated charge percolation may provide higher leakage current. But incorporating suitable nanofillers in an appropriate method may reduce this charge percolation effect and increase the breakdown strength. Our method of incorporation of 2D mica in the PTC polymer in a stratified geometry not only enhances the interface charges but also can prevent charge percolation. Based on the geometry of incorporation of mica layers in our capacitor, the 2D surface of mica is oriented perpendicular to the applied electric field. This shows a large area coverage of mica, which can prevent charge percolation through the materials due to the high dielectric constant of mica. The pristine mica has a dielectric constant that varies in the range 2–6 from monolayer to several layers, suggesting that in our exfoliated mica, which contains many multilayer flakes, the high dielectric constant can prevent charge percolation from passing through. This provides the breakdown strength to increase. We have calculated the breakdown field (E_b) of these polymer films, which was calculated using the Weibull probability distribution , where P represents the probability of failure, E is the electric field at dielectric failure, E_BD is the dielectric breakdown strength (the dielectric strength at a 63.2% probability of failure), and β is a shape parameter that defines the uniformity of the sample. Fig. 5a–c shows the obtained breakdown fields of PTC, PMP, and PMPMP capacitors, which are 530, 835, and 665 MV m⁻¹, respectively. The β value in a Weibull fit represents the variation of data points within the distribution. The higher value of β suggests the compact distribution and higher reliability of the breakdown strength of the capacitor. The shape parameter β for pristine PTC, PMP and PMPMP capacitors is 11.5, 5, and 8.6, respectively. Generally, multilayered polymer films demonstrate higher electrical breakdown strength compared to a single-layer film.^47,48 During the process of electrical treeing in a multilayer dielectric nanocomposite exposed to high electric fields, the propagation of electrical trees diverges at multiple interfaces through the PTC film along the direction of the applied electric field,^46,49 as shown in Fig. 5(d and e). The stratified geometry of the 2D mica fillers enhanced the breakdown strength, but the density of the accumulated charge carriers might also play a crucial role in breakdown. For the PMP capacitor, the accumulated charge carrier density is lower than that of the PMPMP capacitor, which shows higher breakdown strength, while the PMPMP capacitor shows lower breakdown strength due to charge percolation occurring quicker than in the PMP capacitor. Baer et al.⁴⁸ have reported that the interfacial polarizations within a multilayer nanocomposite film increase and propagation also increases along the thickness of the film, resulting in a reduction of dielectric breakdown strength, which closely aligns with our findings for PMPMP capacitors. Using a phase field model theoretical study, Shen et al.⁵⁰ demonstrated that integrating the 2D nanofillers in the polymer matrix in a stratified geometry, where the 2D surface of the fillers faces the direction of the electric field called as parallel orientation of the filler, enhances the breakdown field strength significantly compared to the randomly dispersed or fillers oriented along the direction of the applied electric field. The phase field simulation also predicted that the breakdown strength of the composite using a stratified 2D filler yields the highest among all the nanofiller-based polymer composites.

Fig. 5 Weibull fits and probability of failure distribution of (a) PTC, (b) PMP, and (c) PMPMP capacitors at room temperature. The β values and breakdown strength (E_bd) were obtained from the fitting for each capacitor. (d and e) Schematic of electrical treeing propagation in PTC and PTC/2D mica heterostructures, suggesting enhanced resistance after the incorporation of the 2D nano filler in polymeric heterostructures.

Cycling reliability and the lifetime of the dielectric capacitor are critical parameters for practical applications. During the measurement of the P–E loop, the stored energy is discharged in a controlled way. In a typical discharging curve, the voltage drop exhibits an exponential dependence on discharge time, which is evaluated by equation V(t) = V₀ e ^(−t/RC), where V(t) is the voltage at time t, V₀ is the applied voltage across the capacitor, t is the discharge time and RC is the time constant (τ) of the circuit, representing R as the resistance and C is the capacitance. We measured the discharge time of our multilayer capacitors using a charge–discharge setup where an initial voltage is applied to the capacitor and allowed to discharge as a function of time through a resistor coupled with a capacitor in an RC circuit. Fig. 6(a) shows the self-discharge time of the PMPMP capacitor, which is 6.68 μs, when a constant voltage of 300 V is applied, indicating fast discharge capability suitable for high pulse power applications. We have also extracted the discharge time of the PMPMP capacitor at different applied voltages of 200 V and 400 V, which are 6.47 μs and 6.64 μs, respectively, as shown in Fig. S4, suggesting uniform discharge behavior. However, the discharging times of the PTC capacitor are 5.97 and 5.94 μs with applied voltages of 150 and 200 V, respectively, indicating faster discharging than that of the PMPMP capacitor, as shown in Fig. S5. The presence of mica in the polymer matrix causes interfacial polarization, which causes trapping charges at the interface, resulting in a slightly longer discharge time for the PMPMP capacitors compared to pure PTC capacitors. This discharging time is typically similar to that of other polymer-based composites. Fig. 6(b) shows the stability or charge–discharge cycling test of the PMPMP capacitor, exhibiting nearly constant energy density over a thousand cycles at room temperature, measured using different batches of the samples. The discharge energy density increases with increasing electric field and shows the same trend as the P–E loop. We obtained energy densities of approximately 34 J cm⁻³ and 50 J cm⁻³ at applied voltages of 300 V and 400 V. After 1000 cycles, the PMPMP capacitor shows high stability, maintaining 97.1% and 98% at 300 V and 400 V, respectively, indicating good physical and chemical reliability of the polymer nanocomposite film.

Fig. 6 (a) Discharge time behavior of the PMPMP capacitor, and (b) discharged energy density as a function of cycles at applied voltages of 300 and 400 V, indicating high cyclic stability performance.

4. Conclusion

In the present study, we mechanically exfoliated 2D mica flakes and integrated them with the (P(VDF-TrFE-CFE)) polymer to form stratified nanocomposite films with a single exfoliated 2D mica integrated layer of PTC-Mica-PTC (PMP) and two mica integrated layers interfaced (bilayer) PTC-2D mica-PTC-2D mica-PTC (PMPMP). Interestingly, we have observed that, as the number of mica layers or mica–polymer interfaces increases from PMP to PMPMP capacitors, the dielectric polarization of the films also increases. The electric breakdown field strength in mica-incorporated capacitors is higher than that of pristine PTC films because the mica–PTC interfacial interaction hinders charge migration and prevents the formation of electrical trees in the direction of the applied electric field. The fabricated PMPMP capacitor shows high cyclic stability of 97.1% and 98% with applied voltages of 300 and 400 V, respectively. Our method of integrating a 2D nanofiller with a polymer matrix and fabricating a nanocomposite multilayer film with stratified geometry can be applied to other 2D material–polymer combinations to create high-density-film-based energy storage capacitors for various applications.

Conflicts of interest

The authors declare that there are no competing financial interests.

Data availability

The data in this article will be available from the authors upon reasonable request.

Supplementary information is available. See DOI: https://doi.org/10.1039/d5ta06081h.

Acknowledgements

This work was supported by the Airforce Research Laboratory, award # FA8650-20-2-5853 and Princeton Alliance for Collaborative Research and Innovation (PACRI) grant# PACRI-JSU-02. N. R. P. and R. R. S. acknowledge the funding support from NASA SMD division, grant number 80NSSC24K1072, the authors acknowledge that the use of the Center for Nanoscale Materials, a Department of Energy Office of Science User Facility, was supported by the U.S. DOE, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. N. R. P. and R. P. acknowledge the funding provided by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences program under award number DE-SC0024072 which support the 2D and 3D heterostructure materials. The optical properties were studied using the transfer station microscope supported by Department of Energy.

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