Polyimide-Based Dielectric Materials for High-Temperature Capacitive Energy Storage

Abstract

Polyimide (PI) has received great attention for high-temperature capacitive energy storage materials due to its remarkable thermal stability, relatively high breakdown strength, strong mechanical properties, and ease of synthesis and modification. In this review, several key parameters for evaluating capacitive energy storage performance are introduced. Subsequently, the properties of the commercially available PIs are presented. Then, the recent development of designing and tailoring all-organic PI-based polymers is discussed in detail, focusing on molecular composition and spatial configuration to enhance dielectric constant, breakdown strength, discharged energy density, and charge-discharge efficiency. Finally, we outline the current challenges and future development directions of PI-based high-temperature energy storage dielectric materials.

1. Introduction

Dielectric capacitors are one type of electrostatic components which are applied for storing and releasing energy with extremely fast charge-discharge rate [1,2,3,4,5]. For capacitors requiring high capacitance, polymers are generally favored over inorganic materials as the dielectric materials. This is due to the fact that large-area, high-quality polymer films could be produced by low-cost, high-throughput manufacturing techniques. Additionally, polymers exhibit a unique self-clearing behavior that ensures a localized dielectric breakdown in large-area capacitor films and results in an open circuit rather than a short circuit, thus preventing catastrophic system failure. In recent decades, there has been an explosive growth in the demand for dielectric capacitors with the high-speed development of hybrid electric vehicles, aerospace, oil and gas exploration, and wind power generation [6,7,8,9,10,11,12]. These fields usually require dielectric capacitors to operate with high performance and long lifetime under harsh conditions such as high temperatures. For example, operation temperature in the inverter of hybrid electric vehicles can exceed 140 °C [13,14,15,16]. Biaxially oriented polypropylene (BOPP) film capacitors are commonly commercially available. However, its operation temperature below 105 °C makes BOPP less desirable in the field of high-temperature dielectric capacitors [15,17]. Currently, numerous attentions are given on design of high-temperature tolerant polymer dielectrics with high breakdown strength and charge-discharge efficiency ($\eta$) [18,19]. Considering that many polymers lose their dielectric stability at their glass transition temperature ($T_g$) and melting temperature ($T_m$), people tend to prioritize polymer materials with naturally high $T_g$ or $T_m$ for dielectric film capacitors, such as fluorene polyester (FPE) ($T_g$ ~ 330 °C) [20,21], poly(arylene ether urea) (PEEU) ($T_g$ ~ 250 °C) [22,23], polyetherimide (PEI) ($T_g$ ~ 217 °C) [24,25], and polyimide (PI) ($T_g$ ~ 360 °C) [1,26,27]. Among them, much effort has been put into engineering PI-involved dielectrics.

PIs refer to a class of thermoset polymers containing imide groups. They usually can be synthesized by a two-step method in which the soluble precursor poly(acrylic acid) (PAA) is firstly obtained by polycondensation of dianhydride and diamine monomers, then further imide ring is formed by thermal or chemical imidization process. Another method is a one-step polycondensation method in which the intermediate PAA is cyclized spontaneously at high temperatures (Scheme 1) [28,29,30]. PIs exhibit exceptional thermal stability, chemical resistance, and great mechanical strength owing to the structural characteristic of the imide ring in conjunction with the aromatic backbone [13]. Besides, by simply employing different chemical compositions of commercial or laboratory-designed dianhydride and diamine monomers, PI-derived polymers with various molecular compositions and structures can be obtained, which is beneficial for systematically investigating energy storage properties and large-scale industrial production [17]. The highly conjugated structure of PIs also brings several disadvantages, which restricts their development in the field of high-temperature dielectric capacitors. For example, due to their infusibility and insolubility, PIs are difficult to handle in industry. Manufacturing thin films with a thickness below 10 μm is also one of the processing challenges [1]. More importantly, high-$T_g$ PIs possess relatively high breakdown strength and relatively low dissipation factor at up to 200 °C, but dramatically increased conduction loss occurs under a high electric field which results in a significant drop in discharged energy density and charge-discharge efficiency [1,26,31]. Besides, limited self-clearing ability during film breakdown is also an issue [32,33].

In this review, we first introduce fundamental parameters for capacitive energy storage in Section 2. Section 3 highlights recent research on the design and modification of all-organic PI-derived polymers, focusing on their molecular composition and structure. We present strategies aimed at enhancing capacitive energy storage performance at high temperatures by increasing the dielectric constant, improving breakdown strength, and decreasing energy loss, thereby advancing their applications in high-temperature dielectric capacitors. In the final section, we summarize the current achievements, future developments, and challenges of PI-based high-temperature dielectric materials.

2. Basic Parameters for Capacitive Performance at High Temperatures

The most basic and important parameters to evaluate polymer capacitive energy storage performance are dielectric constant, dissipation factor, breakdown strength, discharged energy density, and charge-discharge efficiency. In addition, considering their applications under high-temperature conditions, other key aspects such as thermal stability and self-clearing ability will also be demonstrated in this section.

2.1. Capacitance, Dielectric Constant, and Dissipation Factor

The dielectric constant (${\epsilon }_r$), known as permittivity as well, determines the capacitance ($C$) of dielectric material. Both ${\epsilon }_r$ and $C$ describe the charge-storage ability of dielectric materials. $C$ is also related to geometry, which can be defined by:

$$C={\epsilon }_r{\epsilon }_0{\displaystyle \frac{A}{d}}$$

(1)

In Equation (1), ${\epsilon }_0$, a constant value of ~8.85 × 10⁻¹² F/m represents vacuum permittivity; $A$ and $d$ mean the area of the electrode and the distance between two electrodes, respectively. In most cases, the latter is the thickness of dielectric material.

Dissipation factor, also referred to as the dielectric loss tangent (tan $\delta$), quantifies the rate at which energy is lost during the polarization and depolarization processes in dielectric materials [13]. It denotes dielectric loss at low electric fields, which causes dissipation of energy in dielectrics. Both ${\epsilon }_r$ and tan $\delta$ are temperature and electric field frequency-dependent, therefore, an ideal energy storage material should have a high ${\epsilon }_r$, low tan $\delta$, and be insensitive to temperature and electric field frequency.

2.2. Discharged Energy Density and Charge-Discharge Efficiency

The working process of a capacitor involves cycles of charging and discharging. Figure 1 describes a typical charge-discharge cycle, where another significant performance parameter-discharged energy density ($U_d$) is clearly displayed (blue area), which is calculated by:

$$U_d={\int }_{D_{max}}^{0}EdD$$

(2)

where $E$ represents the applied electric field and $D$ means dielectric displacement. $D$ is related to the polarization of material $P$ by $D=P+{\epsilon }_{0}E$. For linear dielectric materials in which the dielectric constant is independent of the applied electric field, $U_d$ can be approximately expressed as:

$$U_d={\displaystyle \frac{1}{2}}{\epsilon }_r{\epsilon }_0{E}^2$$

(3)

From the above formula, discharged energy density is proportional to the dielectric constant and the square of the applied electric field.

During the process of charge-discharge, energy loss ($U_l$) resulting from e.g., conduction loss inevitably occurs, especially under high temperature/electric field conditions. In this situation, leakage current density ($J$) cannot be ignored as it exponentially increases, which results in large energy loss. The stored energy cannot be 100% released, and the charge-discharge efficiency ($\eta$) of dielectric is a key parameter to evaluate the extent of energy loss which is given by:

$$\eta ={\displaystyle \frac{U_d}{U_d+U_l}}$$

(4)

Energy loss causes reduced $U_d$, low $\eta$, and waste heat, thus deteriorating energy storage characteristics, eventually causing permanent damage to the capacitor.

2.3. Breakdown Strength

Breakdown strength ($E_b$) is the maximum electric field that the material can withstand without losing its functionality. From Equation (3), it clearly shows that $E_b$ is one of the governing factors in determining the maximum $U_d$, i.e., improving $E_b$ levels up charge/discharge energy density at a square rate. $E_b$ value can be affected by applied voltage type and frequency, electrode area, film conditions such as composition, thickness, defects, and environmental conditions such as temperatures and humidity [33,34]. The main breakdown mechanisms of polymers at high temperatures include free volume breakdown, thermal breakdown, and electromechanical breakdown [1,12,35]. Particularly, free volume increases with temperatures approaching to $T_g$, inducing free volume breakdown which is the most common breakdown process [12,36]. Therefore, it is feasible to increase $E_b$ by employing crosslinking with the purpose of reducing free volume.

2.4. Thermal Stability and Thermal Conductivity

A prerequisite for dielectric polymer materials to be applied under high-temperature environments is their high thermal stability which is intuitively reflected in the value of $T_g$ for amorphous polymers and $T_m$ for crystalline polymers. In order to improve $T_g$ of polymers, one approach is to increase rigid units in molecular chains and chemical cross-links between molecular chains. Thanks to the rigidity of the aromatic backbone of PIs, they present extraordinarily high $T_g$, making them a good candidate in high-temperature dielectric capacitor material. Another critical thermal property is thermal conductivity, which gradually plays a decisive role in many electronic devices because electronic components are highly integrated in the pursuit of being lightweight and minimizing size in recent years [37]. It is noted that PIs have low thermal conductivity (0.1–0.4 W/m·K) [38,39,40]. The introduction of inorganic materials with high thermal conductivity such as Al₂O₃, SiC, and BN is a simple and effective way to improve their thermal conductivity [37,41,42]. However, this sacrifices the flexibility and mechanical properties of PIs. Currently, it is a promising yet challenging issue to boost their thermal conductivity and facilitate their application in high-temperature dielectric capacitors by modifying all-organic PIs.

2.5. Self-Clearing Ability

Compared with inorganic capacitors, another significant advantage of polymer film capacitors with thin-layer metal electrodes is their self-clearing capability (i.e., the ability to clear the breakdown site and function its capacitance properly). This ability only sacrifices a small amount of discharged energy density and charge-discharge efficiency but prolongs the reliability of the material, which is of great significance in practical industry. As shown in Figure 2, when the polymer film is partially broken down, the metal thin layer can be evaporated due to intensive Joule heat generated in the breakdown site [43]. If the freshly exposed upper and lower film is large enough to prevent from building of conductive paths between metal electrodes and carbonized perforations, self-clearing is successful [1]. Besides appropriate metallization resistivity, extensive research also indicates successful self-clearing depends on the chemical composition of the polymer. It seems plausible that a polymer with a high ratio of (carbon + nitrogen + sulfur) to (hydrogen + oxygen) correlates with poor self-clearing ability [44,45,46]. High-temperature dielectric polymers such as PI, PEI, and FPE have limited self-clearing ability, matching their high ratio of (carbon + nitrogen + sulfur) to (hydrogen + oxygen) (1.4~1.6) [1].

3. Dielectric Polyimide Films

In this section, several commercial PI films and new laboratory research in high-temperature PI dielectrics based on differences in chemical composition and structure in the last 5 years are highlighted.

3.1. Commercially Available PI Films

Kapton^® PI films (Table 1) produced by Dupont were first commercially available in the 1960s. The largest advantage of Kapton is great thermal stability with high $T_g$ value more than 360 °C. Besides, they offer excellent electrical, mechanical, and chemical properties and are widely applied for aircraft as high-temperature wire and cable insulation materials over a wide range of temperatures (−269–400 °C) [47]. For instance, Kapton-CRC films are mainly designed for withstanding the damaging effects of corona discharge under high voltage environments and are widely used in industrial motor and generator applications as coating of magnet wire. Kapton is prepared by a condensation reaction of pyromellitic dianhydride (PMDA) and oxydianiline (ODA) in dimethylacetamide (DMAc) [48]. Typically, Kapton films with a thickness of 25 μm present a dielectric breakdown strength of around 300 MV/m, a dielectric constant of 3.4, and a dissipation factor of 0.002 at 1 kHz and room temperature [12]. Their discharged energy density is below 1.5 J/cm³ at 30 °C [49]. However, at 150 °C, their $U_d$ reduces to ~0.5 J/cm³ and $\eta$ is less than 20% [26], resulting from catastrophic conduction loss [49]. This severely restricts the capacitive energy storage applications of Kapton at high temperatures.

UPILEX^® PI films (Table 1) synthesized by UBE Corporation are derived from polycondensation reaction between 3,3′,4,4′-biphenyltetracarboxylic dianhydride (BPDA) monomers and a diamine such as p-phenylene diamine (PDA). They present also ultrahigh thermal stability with $T_g$ value around 355 °C. UBE has developed several types of UPILEX films including UPILEX-S, UPILEX-RN, UPILEX-VT, and UPILEX-SGA. They currently play their thermomechanical properties in base films, cover films, circuit boards, and insulating members. UPILEX-S shows almost no deterioration in its electrical properties over a temperature range of 25–200 °C. The dielectric constant is around 3.5 and the dissipation factor is ~0.0013 with a film thickness of 25 μm at 1 kHz and room temperature. The $E_b$ is 272 MV/m, both at 25 and 200 °C. $U_d$ and $\eta$ of UPILEX-S is 2.5 J/cm³ and ~55% at 150 °C, respectively [16].

One of the drawbacks of Kapton and UPILEXPI films is difficult processibility due to high aromatic molecular composition. In order to increase the flexibility of the PI chain, one feasible approach is to add flexible alkyl groups and/or ether linkages. Perfluoro PI (PFPI) produced from diamine of 2,2-bis(4,4-aminophenoxy)-phenyl-hexafluoropropane (4-BDAF) and PMDA by TRW Inc. (Cleveland, OH, USA), and SIXEF-44 produced from polymerization of 2,2-bis(3,4-dicarboxybenzene) hexafluoro propane dianhydride (6FDA) and 2,2-bis(4-aminobenzene) hexafluoro propane diamine(4,4′-6F diamine) by Hoechst Celanese are two series of commercial fluorinated polyimides (Table 1) [50]. Incorporation of bulky trifluoromethyl (CF₃) groups can destroy the stacking of molecular chains and increase the free volume of the chain segments, as a result, the solubility and processability of PFPI and SIXEF-44 is increased. Moreover, due to the presence of a strong chemical bond of C-F, their thermal stability and mechanical properties are not severely compromised. The $T_g$ value of PFPI is over 300 °C and SIXEF-44 is 323 °C [51]. However, the introduction of high electronegativity and low electric polarity of fluorine atoms alter the electrical properties of PI films, especially in decreasing dielectric constant as low as 1.8–2.9 [52]. The dielectric constant of PFPI is 3.1 at 25 °C while that is 2.9 at 300 °C, and SIXEF-44 is 2.8 with negligible change in temperature. Their dielectric loss (tan $\delta$ ~0.001) at high temperatures is significantly better than Kapton PI films. Reduced dielectric constant makes them become more promising electrical insulating materials in mobile communication and microelectronics industry than the dielectric capacitor field [53,54,55].

As a PI-modified version, poly(ether imide) (PEI) called Ultem (Table 1) is a thermoplastic material produced from the disodium salt of bisphenol A and 1,3-bis(4-nitrophthalimido) benzene by SABIC. It gives good processability to PEI by employing flexible ether linkage in the backbone of the chain. Although this causes a relatively low $T_g$ value of 217 °C, PEI is still an excellent material working under high temperatures (160~180 °C). At 150 °C, the $U_d$ is 1.0 J/cm³ and $\eta$ is up to 90% [33,50,56].

Table 1. Comparison of dielectric properties of commercially available PI films.

Name	Structure	${\mathit{T}}_{\mathit{g}}$ (°C)	${\mathit{\epsilon }}_{\mathit{r}}$	$\mathbf{tan}\mathit{\delta }$%	${\mathit{E}}_{\mathit{b}}$ (MV/m)	${\mathit{U}}_{\mathit{d}}$ (J/cm3)	$\mathit{\eta }$%	Ref.
Kapton-HN		360	3.4@25 °C 2.5@300 °C	0.2	~300	0.5	20	[12,26]
UPILEX-S		355	3.5@25–200 °C	0.13	272	2.5	55	[16]
PFPI		>300	3.1@25 °C 2.9@300 °C	0.1	-	-	-	[51]
SIXEF-44		323	2.8@−55–300 °C	0.1	-	-	-	[50,51]
Ultem		217	3.1@25–200 °C	0.2	439	1.0	90	[50,56]

Note: all of ${\epsilon }_r$ are measured at 1 kHz; $E_b$ of Kapton-HN and UPILEX-S are measured at 25 °C, $U_d$ and $\eta$ of Kapton-HN and UPILEX-S are measured at 150 °C. Ultem is measured at 150 °C.

Table 1. Comparison of dielectric properties of commercially available PI films.

Name	Structure	${\mathit{T}}_{\mathit{g}}$ (°C)	${\mathit{\epsilon }}_{\mathit{r}}$	$\mathbf{tan}\mathit{\delta }$%	${\mathit{E}}_{\mathit{b}}$ (MV/m)	${\mathit{U}}_{\mathit{d}}$ (J/cm3)	$\mathit{\eta }$%	Ref.
Kapton-HN		360	3.4@25 °C 2.5@300 °C	0.2	~300	0.5	20	[12,26]
UPILEX-S		355	3.5@25–200 °C	0.13	272	2.5	55	[16]
PFPI		>300	3.1@25 °C 2.9@300 °C	0.1	-	-	-	[51]
SIXEF-44		323	2.8@−55–300 °C	0.1	-	-	-	[50,51]
Ultem		217	3.1@25–200 °C	0.2	439	1.0	90	[50,56]

Note: all of ${\epsilon }_r$ are measured at 1 kHz; $E_b$ of Kapton-HN and UPILEX-S are measured at 25 °C, $U_d$ and $\eta$ of Kapton-HN and UPILEX-S are measured at 150 °C. Ultem is measured at 150 °C.

3.2. PIs Based on Molecular Chain Modification

So far, many works have been done to improve the energy storage properties of dielectric materials under high temperatures based on PI-based dielectrics. For instance, PI nanocomposite dielectric PI-SiO₂ [57], PEI/Al₂O₃@ZrO₂ [58], PI/AgNWs (silver nanowires) [40,59], PEI/BNNS (boron nitride nanosheets) [26,60], polymer/molecular semiconductor all-organic composites PEI/PCBM([6,6]-Phenyl C61 butyric acid methyl ester) [56], PI blending with PEEU (poly(arylene ether urea)) [23], PNFA([1,4-poly(ether fluoromethyl naphthalene amide))/PEI polymer blends [61], PEI with 50%mol SPDD(3,3,3′,3′-tetramethyl-1,1′-spirobisindane-5,5′diamino-6,6′-diol) copolymers [25], PI filling with PSF (polysulfone) [62], and PI physically crosslinked by negative aromatic molecules with negatively-charged phenyl groups [4]. These composite and blend works reported significant improvements in dielectric constant, discharged energy density, charge-discharge efficiency, and breakdown strength, which will not be elaborated in detail in this review. Instead, recent progress in tailoring molecular composition and structure of neat high-temperature PI dielectrics is presented (as shown in Table 2).

It was reported that introducing a high polar group-nitride group (–CN) into the PI backbone could increase dielectric constant and thus electrical energy storage 10 years ago [63,64]. Incorporation of rigid bipyrimidine units also highly improved the dielectric constant of PI up to 7.1(@100 Hz, RT) and kept thermal stability ($T_g$ 291 °C) [65]. Tong et al. prepared aromatic carbonyl-containing PI films by employing carbonyl dianhydride reacting with diamines with different molecular structures such as –O–, –CH₂–, –SO₂–, and different length of repeating unit and linked positions as shown in Figure 3a [66,67]. The correlation between molecular composition and dielectric properties is revealed. CPI-1-CPI-5 show outstanding $T_g$ values range from 241 to 352 °C. Take CPI-1, CPI-2, and CPI-3 as examples, it again illustrates that the rigidity of the backbone chain affects $T_g$ values, and CPI-2 with longer ether linkage than CPI-1 ($T_g$ 300 °C) owe lower $T_g$ value (267 °C). Additionally, CPI-2 which has a more symmetrical structure than CPI-3 ($T_g$ 241 °C) display higher $T_g$ value. Regarding their dielectric properties, all five CPIs show relatively high dielectric constant from 3.99 to 5.23 (@1 kHz, RT) and a low dissipation factor of 0.00307–0.00395 (Figure 3b). Their $E_b$ range from 425–552 MV/m at room temperature (Figure 3c). It is confirmed that the introduction of polar groups/structures with large dipole movement and shorter repeating units increases ${\epsilon }_r$. CPI-5 which has an extra highly polar sulfonyl group in the diamine possesses a very stable dielectric constant and dissipation factor at temperatures ranging from −50 to 200 °C. The $U_e$ and η of CPI-5 is 6.34 J/cm³ and 92.3% at 500 MV/m, room temperature, and 10 Hz. The considerable design strategy of PI with high capacitive energy storage performance in harsh environments could be summarized as follows: (i) incorporating high polar groups such as sulfonyl group to increase dipole movement; (ii) introducing flexible linkages such as ether bond to facilitate dipole reorientation; and (iii) preserving the rigid aromatic backbone to maintain high $T_g$ value. These structure units could help to fulfill high dielectric constant, low dissipation factor, and high thermal stability simultaneously.

Wang et al. established a library of PI-derived polymers with diverse combination structural blocks by applying a machine learning approach and experimentally tested the dielectric capacitive performance of 12 representative predicated structures (Figure 4a) [17]. The structure units have direct contributions to $T_g$ value and energy bandgap ($E_g$) which is usually considered to have a positive correlation to the insulating properties of polymers [68,69,70] (Figure 4b). To be specific, the following applies: (i) the $T_g$ values of polymers with m-benzene structural unit are smaller than those with p-benzene structural unit; (ii) isopropyl structural unit gives a higher $T_g$ and $E_g$ than ether unit in diamine monomer while the incorporation of ether structural unit in dianhydride monomer leads to significant changes in $T_g$ (decline) and $E_g$ (rise); (iii) pendant group connected to the benzene ring is beneficial to increase $T_g$ and $E_g$ simultaneously; and (iv) replacement of benzene ring with cyclohexane structure offers dramatically increased $E_g$ but decreased $T_g$. Figure 4c shows the changes of $T_g$ and $E_g$ values of modified PIs when the above structural units are added or replaced. However, it turns out $E_g$ is not a decisive structural factor in obtaining high-electric field insulating and capacitive performance under high-temperature conditions. Due to the dominant conduction mechanism changing from Poole-Frenkel emission to hopping conduction over a critical point (~3.3 eV of PI-derived polymers), the spatial structure of the polymers represented by dihedral angle (θ) between the adjacent plane of conjunction becomes the decisive factor. As evidence, PI-oxo-iso which has the largest θ (81.3) but moderate $E_g$ (3.5 eV), presents the highest $U_e$(6.4 J/cm³) and extraordinary $\eta$ among all the polymers including PI-cyc-iso which has the largest $E_g$ (4.15 eV) (Figure 4d). Therefore, when designing PI-derived polymers for pursuing high energy storage capability, in addition to making $E_g$ greater, it should be considered to enlarge the dihedral angle between adjacent conjugated rings when $E_g$ is over the critical value of 3.3 eV.

As we know that the rigid conjugated aromatic structure of PIs renders better thermal stability but inevitably compromises the flexibility and high electric field capacitive performance, Song et al. introduced two alicyclic polyimides, i.e., CBDA/DCHM and CBDA/TFMB (Figure 5a) [71]. Owing to saturated non-coplanar alicyclic structure, carrier migration is suppressed, hence their leakage currents are 1–2 orders of magnitude lower than conventional aromatic PIs under high electric field and high-temperature conditions. It greatly improves their breakdown strength, discharged energy density, and charge-discharge efficiency. At 200 °C, $E_b$ values of CBDA/DCHM is 605 MV/m (Figure 5b) which is more than two times of aromatic PMDA/ODA (270 MV/m), and its maximum $U_e$ reaches 5.01 J/cm³ at 600 MV/m which is superior to most dielectric polymers and polymer composites (Figure 5c,d) [26,70,72,73]. It still maintains 2.55 J/cm³ at $\eta$ = 90%. Besides, saturated alicyclic PIs possess a lower ratio (carbon + nitrogen + sulfur) to (hydrogen + oxygen) (0.76) endowing good self-clearing ability to fulfill long-term practical applications.

In addition, several modifications on the side chain of PIs are also proposed. Zou et al. designed and synthesized PI-derived materials containing a cross-linkable olefin group and a long alkyl chain with biphenyl, which have good thermal stability, pinhole-free dense film morphologies, and small dielectric loss [74]. Tang et al. optimized molecular structure and orientational polarization of polyimides by introducing high dipolar sulfonyl, urea, carbamate, and also methyl pendant groups associating a rigid biphenyl backbone to improve capacitive energy storage performance of materials, respectively [75,76]. Zheng et al. discussed the effects of side chain flexibility on dielectric constant by using different alkyl chain lengths of PIs [77].

It is challenging to obtain high-performance dielectric materials by merely engineering homopolymers, because the pursuit of high ${\epsilon }_r$ by introducing polar groups in the main or side chain usually increases tan $\delta$, reduces $\eta$ and $U_d$, while the pursuit of high $E_b$ and high $U_d$ by increasing segment flexibility loses part of thermal stability. Engineering copolymers are expected to break the paradoxical relation between ${\epsilon }_r$, $E_b$, $U_d,$ and $T_g$. PI copolymers that combine polar sulfonyl group, ether linkage, and alicyclic group into the backbone of PIs are synthesized by Dong et al. (Figure 6a–c) [27]. Sulfonyl-containing PI homopolymers (SO-PI) possess ${\epsilon }_r$ as high as 4.25 at 200 °C (Figure 6e) and high $T_g$ of 311.2 °C. By introducing the alicyclic segment structure in the main chain, intramolecular and intermolecular charge transfer interaction is suppressed, so the conduction loss is reduced (Figure 6d). The semi-alicyclic sulfonyl-containing PI copolymers achieve high $U_d$ of 4.3 J/cm³ at a relatively low electric field of 485 MV/m with $\eta$ > 90% at 200 °C (Figure 6f).

3.3. PIs Based on Spatial Structure Modification

In Section 3.2, we elucidated the impact of modification of primary structure (i.e., chemical composition) on capacitive energy storage performance, barely involving advanced spatial structure. Recently, a type of double-stranded ladderphane structured copolymers with decent discharged energy density and high efficiency at up to 200 °C was proposed, providing new insights towards structural tailoring for developing dielectric capacitive performance [78]. Inspired by unique double-helix strand structure of DNA, two spiral-structured dielectric PI-derived polymers by utilizing a nonplanar precursor 4,4′-oxydiphthalic anhydride (ODPA) reacting with two spiral-structured diamine, i.e., 9,9′spirobi[9H-fluorene]−2,2′-diamine and (R)−2,2′,3,3′-tetrahydro1,1′-spirobi[1H-indene]−7,7′-diamine were synthesized, respectively [14]. On the one hand, the huge rigid diamine unit breaks up the stacking interaction between molecular chains and expands free volume, on the other hand, the energy-favored non-planar geometric structure possessing corresponding dihedral angles of 87.3° and 65.4° gives a large rotation energy barrier, thus restrains the formation of planar conjunction and $\pi$-$\pi$ stacking interaction, further weakening electrostatic potential interaction (Figure 7a,b). As a result, two spiral-structured PIs endow very low conduction loss and high Weibull characteristic breakdown strength. For example, the dissipation factor of PI-spiro-2–5 (5% PI-sprio-2 blended compositions) is only 55.9% of regular PI at 200 °C and 100 Hz, and its $E_b$ is 667.5 MV/m (Figure 7c). The maximum discharged energy density of PI-spiro-2–5 is 6.13 J/cm³ at 200 °C with η above 90% (Figure 7d).

4. Conclusions and Outlook

Polyimide (as matrix) is becoming a promising high-temperature dielectric capacitor film candidate due to its solid fundamental properties such as excellent thermal stability, flexibility of synthesis, and great mechanical strength. This review compiles a broad portfolio of methods to improve the high-temperature capacitive energy storage performance of PI-based dielectrics by altering the molecular composition and spatial structure of polymers. These studies are primarily conducted from two perspectives: (i) Increasing ${\epsilon }_r$ which can be achieved by the introduction of high polar function groups such as nitride, carbonyl, and sulfonyl groups; and (ii) Enhancing $E_b$ and decreasing conduction loss by enlarging bandgap and reducing conjugation interaction of polymers, which is able to be fulfilled by (partial) alicyclic substitution of aromatic backbone or the introduction of unique spatial structure instead of original conjugated, planar structure. The most advanced all-organic neat PI-modified dielectric films in these studies possess a discharged energy density of more than 6 J/cm³ at 200 °C with charge-discharge efficiency above 90% in the laboratory (Table 2) [14]. In order to further optimize the capacitive energy storage performance of PI-derived polymers and fulfill both theoretical and large-scale practical applications, the following challenges still need to be addressed:

Table 2. Summary of all-organic PI-derived materials.

Polymer	Dielectric Constant (ɛr) at 1 kHz RT	Dissipation Factor (tanδ) at 1 kHz and 25 °C	$\mathbf{Breakdown} \mathbf{Strength}$(Eb) (MV/m)	Leakage Current Density (A/cm2)	Max Discharged Energy Density (Ud) (J/cm3)	Efficiency at Max Ud (%)	Max Ud with 90% Efficiency (J/cm3)	Glass Transition Temperature (°C)	Ratio of (C + N + S) to (H + O)	Ref.
SO-PI	4.25	0.002	439@200 °C	1.25 × 10−7@200 °C, 200 MV/m	3.2@200 °C, 450 MV/m	70	1.6@200 °C, 300 MV/m	312	1.48	[27]
Semi-alicyclic SO-PI	4.08	0.002	545@200 °C 610@150 °C	2.81 × 10−8@200 °C, 200 MV/m	4.7@200 °C, 500 MV/m	86.5	4.3@200 °C, 485 MV/m	284	-	[27]
PEI with 50 mol% SPDD	4.7	0.0017	386@150 °C	1.17 × 10−7@150 °C, 150 MV/m	4.6@200 °C, 500 MV/m and 1 kHz	81	2.2 @200 °C, 350 MV/m and 1 kHz	302	-	[25]
PI-spiro-1–5	3.07 (200 °C)	0.0037 (200 °C)	644@200 °C	~10−12@200 °C, 200 MV/m	5.8@200 °C, 700 MV/m	64	4.2@200 °C, 550 MV/m	258	1.51	[14]
PI-spiro-2–5	3.15 (200 °C)	0.0035 (200 °C)	667@200 °C	~10−12@200 °C, 200 MV/m	6.45@200 °C, 700 MV/m	72	6.13@200 °C, 650 MV/m	256	1.5	[14]
PI-oxo-iso	3.08 (150 °C)	0.00136 (150 °C)	606@200 °C	5.5 × 10−9@200 °C, 200 MV/m	6.4@200 °C, 700 MV/m and 100 Hz	70.5	5.32@200 °C, 600 MV/m and 100 Hz	258	1.2	[17]
PI-CF3-iso	-	-	-	-	3.7@200 °C, 550 MV/m and 100 Hz	67.2	2.8@200 °C, 450 MV/m and 100 Hz	276	1.36	[17]
CPI-5	5.23	0.00324	-	-	6.34@25 °C, 500 MV/m and 10 Hz	92.3	6.34@25 °C, 500 MV/m and 10 Hz	277	1.6	[66]
SPI-1	5.98	0.00373	468@150 °C	-	7.04@25 °C, 500 MV/m and 10 Hz	91.3	7.04@25 °C, 500 MV/m and 10 Hz	290	1.48	[67]
CBDA/DCHM	2.6	<0.001	605@200 °C	5.3 × 10−8@150 °C, 300 MV/m	5.01@200 °C, 600 MV/m	78	2.55@200 °C, 400 MV/m	>275	0.76	[71]
CBDA/TFMB	2.7	<0.001	497@200 °C	3.99 × 10−7@150 °C 300 MV/m	3.86@200 °C, 500 MV/m	72	2.05@200 °C, 350 MV/m	>275	1.71	[71]
PI-DPEM	3.5@100 Hz	<0.02	-	1.68 × 10−7@25 °C, 100 MV/m	-	-	-	163	1.32	[74]
PI-BDPD	3.8@100 Hz	<0.02	-	1 × 10−7@25 °C, 100 MV/m	-	-	-	148	1.02	[74]
DSDA-BSBPA	6.95	0.012	270@150 °C	-	1.82 @150 °C, 250 MV/m and 100 Hz	93	1.82@150 °C, 250 MV/m and 100 Hz	358	1.25	[75]
BU-PI	6.14	0.0097	402@150 °C	3.8 × 10−8@25 °C, 200 MV/m	4.27@150 °C, 400 MV/m and 10 Hz	83	2.36@150 °C, 300 MV/m and 10 Hz	238	1.27	[76]
BC-PI	4.33	0.0078	407@150 °C	1.8 × 10−8@25 °C, 200 MV/m	3.1@150 °C, 400 MV/m and 10 Hz	85	2.03@150 °C 325 MV/m and 10 Hz	216	1.53	[76]
DM-PI	3.28	0.0043	416@150 °C	8.8 × 10−9@25 °C, 200 MV/m	2.4@150 °C, 400 MV/m and 10 Hz	87	1.97@150 °C, 360 MV/m and 10 Hz	334	1.39	[76]
C0-SPI	5.5	0.0078	-	-	3.04@200 °C, 300 MV/m and 100 Hz	80	3.4@25 °C, 300 MV/m and 100 Hz	-	2	[77]
C1-SPI	5.9	0.01	-	-	3.68@200 °C, 300 MV/m and 100 Hz	84	5.4@25 °C, 400 MV/m and 100 Hz	-	1.85	[77]
C2-SPI	6.4	0.01	-	-	2.59@200 °C, 300 MV/m and 100 Hz	71	5.4@25 °C, 380 MV/m and 100 Hz	-	1.73	[77]

Note: SO-PI: sulfonated polyimide PDS/ODPA (4,4′-diaminodiphenyl sulfonyl-4,4′-oxydiphthalic anhydride); Semi-alicyclic SO-PI: semi-alicyclic sulfonyl-containing PI copolymer; PEI with 50 mol% SPDD: a PEI with hydroxy groups and a twisted spirane structure; SPDD(3,3,3′,3′-tetramethyl-1,1′-spirobisindane-5,5′diamino-6,6′-diol); PI-spiro-1–5: PI-B with 5 mol% spiral structured PI-1 composite films; PI-spiro-2–5: PI-B with 5 mol% spiral structured PI-2 composite films; CPI-5: BTDA-mDS (benzophenone 3,30,4,40 tetracarboxylic dianhydride/3,30-diaminodiphenyl sulfone); SPI-1: ODPA-pDS (4,4′-oxydiphthalic anhydride-4,4′-diaminodiphenyl sulfonyl); CBDA/DCHM: (all-alicyclic) cyclobutane-1,2,3,4-tetracarboxylic dianhydride/4,4′-diaminodicyclohexyl methane; CBDA/TFMB: (semi-alicyclic) cyclobutane-1,2,3,4-tetracarboxylic dianhydride/2,2′-bis(trifluoromethyl)benzidine; PI-DPEM: DPEM–6FDA (2-(2,4-diaminophenoxy)ethyl methacrylate-4,4′-(hexafluoroisopropylidene)diphthalic anhydride); PI-BDPD: BDPD–6FDA (1-([1,1′-biphenyl]-4-ylmethyl)12-(2-(2,4-diaminophenoxy)ethyl)dodecanedioate-4,4′-(Hexafluoroisopropylidene)diphthalic anhydride); DSDA-BSBPA: 3,3′,4,4′-diphenylsulfonetetracarboxylic dianhydride-2,2′-bis((methylsulfonyl)methyl)-[1,1′-biphenyl]-4,4′-diamine; BU-PI: PI with urea pendant group; BC-PI: PI with carbamate pendant group; BS-PI: PI with sulfonyl pendant group; DM-PI: PI with methyl pendant group; C0-SPI: PI with methyl sulfone group; C1-SPI: one methylene group in C1-SPI (with sulfone groups); C2-SPI: two methylene groups in C2-SPI (with sulfone groups).

Table 2. Summary of all-organic PI-derived materials.

Polymer	Dielectric Constant (ɛr) at 1 kHz RT	Dissipation Factor (tanδ) at 1 kHz and 25 °C	$\mathbf{Breakdown} \mathbf{Strength}$(Eb) (MV/m)	Leakage Current Density (A/cm2)	Max Discharged Energy Density (Ud) (J/cm3)	Efficiency at Max Ud (%)	Max Ud with 90% Efficiency (J/cm3)	Glass Transition Temperature (°C)	Ratio of (C + N + S) to (H + O)	Ref.
SO-PI	4.25	0.002	439@200 °C	1.25 × 10−7@200 °C, 200 MV/m	3.2@200 °C, 450 MV/m	70	1.6@200 °C, 300 MV/m	312	1.48	[27]
Semi-alicyclic SO-PI	4.08	0.002	545@200 °C 610@150 °C	2.81 × 10−8@200 °C, 200 MV/m	4.7@200 °C, 500 MV/m	86.5	4.3@200 °C, 485 MV/m	284	-	[27]
PEI with 50 mol% SPDD	4.7	0.0017	386@150 °C	1.17 × 10−7@150 °C, 150 MV/m	4.6@200 °C, 500 MV/m and 1 kHz	81	2.2 @200 °C, 350 MV/m and 1 kHz	302	-	[25]
PI-spiro-1–5	3.07 (200 °C)	0.0037 (200 °C)	644@200 °C	~10−12@200 °C, 200 MV/m	5.8@200 °C, 700 MV/m	64	4.2@200 °C, 550 MV/m	258	1.51	[14]
PI-spiro-2–5	3.15 (200 °C)	0.0035 (200 °C)	667@200 °C	~10−12@200 °C, 200 MV/m	6.45@200 °C, 700 MV/m	72	6.13@200 °C, 650 MV/m	256	1.5	[14]
PI-oxo-iso	3.08 (150 °C)	0.00136 (150 °C)	606@200 °C	5.5 × 10−9@200 °C, 200 MV/m	6.4@200 °C, 700 MV/m and 100 Hz	70.5	5.32@200 °C, 600 MV/m and 100 Hz	258	1.2	[17]
PI-CF3-iso	-	-	-	-	3.7@200 °C, 550 MV/m and 100 Hz	67.2	2.8@200 °C, 450 MV/m and 100 Hz	276	1.36	[17]
CPI-5	5.23	0.00324	-	-	6.34@25 °C, 500 MV/m and 10 Hz	92.3	6.34@25 °C, 500 MV/m and 10 Hz	277	1.6	[66]
SPI-1	5.98	0.00373	468@150 °C	-	7.04@25 °C, 500 MV/m and 10 Hz	91.3	7.04@25 °C, 500 MV/m and 10 Hz	290	1.48	[67]
CBDA/DCHM	2.6	<0.001	605@200 °C	5.3 × 10−8@150 °C, 300 MV/m	5.01@200 °C, 600 MV/m	78	2.55@200 °C, 400 MV/m	>275	0.76	[71]
CBDA/TFMB	2.7	<0.001	497@200 °C	3.99 × 10−7@150 °C 300 MV/m	3.86@200 °C, 500 MV/m	72	2.05@200 °C, 350 MV/m	>275	1.71	[71]
PI-DPEM	3.5@100 Hz	<0.02	-	1.68 × 10−7@25 °C, 100 MV/m	-	-	-	163	1.32	[74]
PI-BDPD	3.8@100 Hz	<0.02	-	1 × 10−7@25 °C, 100 MV/m	-	-	-	148	1.02	[74]
DSDA-BSBPA	6.95	0.012	270@150 °C	-	1.82 @150 °C, 250 MV/m and 100 Hz	93	1.82@150 °C, 250 MV/m and 100 Hz	358	1.25	[75]
BU-PI	6.14	0.0097	402@150 °C	3.8 × 10−8@25 °C, 200 MV/m	4.27@150 °C, 400 MV/m and 10 Hz	83	2.36@150 °C, 300 MV/m and 10 Hz	238	1.27	[76]
BC-PI	4.33	0.0078	407@150 °C	1.8 × 10−8@25 °C, 200 MV/m	3.1@150 °C, 400 MV/m and 10 Hz	85	2.03@150 °C 325 MV/m and 10 Hz	216	1.53	[76]
DM-PI	3.28	0.0043	416@150 °C	8.8 × 10−9@25 °C, 200 MV/m	2.4@150 °C, 400 MV/m and 10 Hz	87	1.97@150 °C, 360 MV/m and 10 Hz	334	1.39	[76]
C0-SPI	5.5	0.0078	-	-	3.04@200 °C, 300 MV/m and 100 Hz	80	3.4@25 °C, 300 MV/m and 100 Hz	-	2	[77]
C1-SPI	5.9	0.01	-	-	3.68@200 °C, 300 MV/m and 100 Hz	84	5.4@25 °C, 400 MV/m and 100 Hz	-	1.85	[77]
C2-SPI	6.4	0.01	-	-	2.59@200 °C, 300 MV/m and 100 Hz	71	5.4@25 °C, 380 MV/m and 100 Hz	-	1.73	[77]

Note: SO-PI: sulfonated polyimide PDS/ODPA (4,4′-diaminodiphenyl sulfonyl-4,4′-oxydiphthalic anhydride); Semi-alicyclic SO-PI: semi-alicyclic sulfonyl-containing PI copolymer; PEI with 50 mol% SPDD: a PEI with hydroxy groups and a twisted spirane structure; SPDD(3,3,3′,3′-tetramethyl-1,1′-spirobisindane-5,5′diamino-6,6′-diol); PI-spiro-1–5: PI-B with 5 mol% spiral structured PI-1 composite films; PI-spiro-2–5: PI-B with 5 mol% spiral structured PI-2 composite films; CPI-5: BTDA-mDS (benzophenone 3,30,4,40 tetracarboxylic dianhydride/3,30-diaminodiphenyl sulfone); SPI-1: ODPA-pDS (4,4′-oxydiphthalic anhydride-4,4′-diaminodiphenyl sulfonyl); CBDA/DCHM: (all-alicyclic) cyclobutane-1,2,3,4-tetracarboxylic dianhydride/4,4′-diaminodicyclohexyl methane; CBDA/TFMB: (semi-alicyclic) cyclobutane-1,2,3,4-tetracarboxylic dianhydride/2,2′-bis(trifluoromethyl)benzidine; PI-DPEM: DPEM–6FDA (2-(2,4-diaminophenoxy)ethyl methacrylate-4,4′-(hexafluoroisopropylidene)diphthalic anhydride); PI-BDPD: BDPD–6FDA (1-([1,1′-biphenyl]-4-ylmethyl)12-(2-(2,4-diaminophenoxy)ethyl)dodecanedioate-4,4′-(Hexafluoroisopropylidene)diphthalic anhydride); DSDA-BSBPA: 3,3′,4,4′-diphenylsulfonetetracarboxylic dianhydride-2,2′-bis((methylsulfonyl)methyl)-[1,1′-biphenyl]-4,4′-diamine; BU-PI: PI with urea pendant group; BC-PI: PI with carbamate pendant group; BS-PI: PI with sulfonyl pendant group; DM-PI: PI with methyl pendant group; C0-SPI: PI with methyl sulfone group; C1-SPI: one methylene group in C1-SPI (with sulfone groups); C2-SPI: two methylene groups in C2-SPI (with sulfone groups).

For a long time, the bandgap has been a key factor in evaluating and explaining capacitive energy storage performance. However, recent studies have shown that the bandgap alone cannot serve as a reliable criterion for comparing the capacitive energy storage performance of two dielectrics. A large bandgap is a necessary but not sufficient condition for superior energy storage capabilities. The introduction of a critical point of bandgap seems to complicate the theoretical framework, as it requires a comprehensive consideration of the bandgap value, individual spatial structure, and different conduction mechanisms. This necessitates more details and clarification to enrich the theory. Beyond the bandgap, further exploration of additional theoretical foundations is needed to guide the rational design of various molecular compositions and structures in polymers.

By utilizing molecular engineering and established polymer chemistry, multiple functional structure blocks are integrated to obtain high-temperature polymers for capacitive energy storage. However, this process is usually time-consuming, labor-intensive, and low-sustainable. Very recently, artificial intelligence (AI)-assisted prediction, discovery, and screening of promising dielectric polymers lights the shed of efficient and universal design of high-temperature capacitive energy storage materials [79]. The development of more efficient artificial intelligence algorithms can assist in the exploration of novel polymer dielectrics, enabling us to develop high-performance materials in a more cost-effective and environmentally friendly way.

Currently, many works focus on the impacts of the primary structure of PI polymers on capacitive energy storage properties. Several pioneer works have investigated the relationship between advanced spatial structure and energy storage performance, which mainly concentrate on weakening conjugation interaction of the aromatic backbone of PIs [14,27,71]. Analogous to complicated but well-designed protein structures, there are many other interactions such as ionic interaction, dipole-dipole interaction, hydrophobic interaction, hydrogen bonds, and disulfide bonds playing significant roles in forming local secondary structure (such as $\alpha$-helices and $\beta$-sheets), and integrated tertiary or even quaternary structure. Not limited to PIs, polymers with novel structures based on various interactions should be designed and studied to further summarize connections between the structure and function of polymers. Additionally, optimizing the synthetic process of polymers and preparing more uniform and ordered polymer chains is also helpful for studying the impact of polymer structure on capacitive energy storage properties.

Thermal conductivity is another issue to be addressed. Conventional polymers are naturally poor conductors of heat. Particularly under high temperatures and high electric fields, large Joule heat which conduction loss generates, and low heat dissipation ability make the temperature of the capacitor increase gradually, eventually leading to thermal breakdown and permanent damage to the device. Besides, the shrinking of electronic devices increasingly requires a larger heat dissipation ability of polymers. The introduction of thermally conductive fillers into the polymer matrix, improving the order of polymer chains, moderate cross-linking between chains, and some other modifications targeting increasing intramolecular and intermolecular interaction of chains are efficient to enhance heat dissipation.

The relatively weak self-clearing ability of PIs is also a factor that restricts their future development in the field of high-temperature dielectrics. Designing a new chemical composition with a low ratio of (carbon + nitrogen + sulfur) to (hydrogen + oxygen) could be an effective way to boost self-clearing ability.

It is challenging to acquire desired dielectric PIs with high thermal stability, high discharged energy density, high charge-discharge efficiency, and excellent self-clearing ability simultaneously by simply modifying the molecular composition and structure of homopolymers. Compared with PI nanocomposites, PI copolymers which are able to integrate both their individual monomer advantages and possess easy processability, large-scale production, low cost, etc., is another direction of future development of PI dielectrics.