**4. Recently developed polyimides**

Over the past 10 years, research efforts have continued to develop new polyimides for capacitor dielectrics. The thermal stability of these new polymers is primarily derived from a high degree of aromaticity and fused-ring heterocyclic rigid structures. As energy density of a capacitor scales with the dielectric constant, some researchers have specifically focused on designing new aromatic polyimides

(PIs) that have a higher dielectric constant than the typical value of 3 while preserving the essential thermal/mechanical properties.

One common approach to increasing the dielectric constant is by incorporating polar moieties into the backbone of a polymer chain to enhance the dipole moment. The nitrile group (▬CN) is one of the polar moieties that was explored by Wang et al. [75, 76] and Treufeld et al. [77], in which the number of ▬CN dipoles on the diamine was varied between 0, 1, and 3. The nitrile-containing diamines synthesized in the study were aminophenoxy-benzonitrile (APBN)-based with the two amino groups varying between three isomeric positions (m,m, m,p, and p,p) (**Figure 15**) to explore the effect of isomeric position on the 6FDA-based PIs. A nitrile-free analog, LaRC-CP2™ [78, 79], was used as a control.

Among the 6FDA-based PIs, the addition of one nitrile group in the diamine increased the room temperature dielectric constant from 2.9 (independent of frequency between 0.1 Hz and 1 MHz for the nitrile-free PI) to between 3.1 and 3.5 depending on the frequency and isomeric positions of the diamine linkage. In general, the m,m- and m,p-positions exhibited higher values (3.25–3.5) as compared to the p,p-position (**Figure 16**). Further increasing the nitrile content to three nitrile groups per diamine monomer resulted in an additional increase of the room temperature dielectric constant to between 3.5 and 3.7 (frequency dependent) for the 6FDA-based PIs with p,p-linkage. Interestingly, substitution of the other two isomeric positions had no significant effect (**Figure 17**). The investigators explained that the greater flexibility of the three ▬CN dipoles in the p,p-linkage as compared to the m,m- or m,p-linkage in the diamine resulted in greater dipolar polarization. An increase in dielectric constant was also observed in the OPDA-based PIs with m,m diamine linkage with increasing content of ▬CN dipoles.

### **Figure 15.**

*Reaction schemes of various polyimides: (a) LaRC-CP2 from 2,2-bis(phthalic anhydride)-1,1,1,3,3,3 hexafluoroisopropane (6FDA) and the 1,3-bis(3-aminophenoxy) benzene (APB) diamine, (b) with one benzonitrile (BN) group, (c) with three benzonitrile groups. Reaction schemes adapted from [75, 76].*

### **Figure 16.**

*Dielectric constant and dielectric loss as a function of frequency at ambient conditions for 6FDA-APB nitrile free PI and the three analogs containing one* ▬*CN dipole per diamine at different isomeric positions. Data adapted from [75].*

The key drawback of the addition of nitrile groups was the increase in temperature dependence in both the dielectric constant and dissipation factor, as illustrated in **Figure 17**. For example, the dielectric constant of the nitrile-free 6FDA-based PI at 10 kHz increased by only 1.4% over a temperature range of −150 to 190°C, whereas that of the three nitrile-containing analogs with the m,m-, p,p-, and m,plinkages rose 6.3, 8.3, and 15%, respectively. With respect to the dissipation factor, the nitrile-free PI remained below 0.5% over the tested temperature/frequency

### **Figure 17.**

*Dielectric constant and dissipation factor as a function of temperature at various frequencies for the 6FDA-based PIs containing three nitrile groups in different isomeric positions (a–c) and the nitrile-free analog, LaRC-CP2 (d). Data taken from [77].*

range, while the same nitrile-containing PIs increased from below 0.1% at −150°C to above 1% at 190°C between 10 Hz and 100 kHz. The temperature scan was limited to 190°C to avoid deforming the sample significantly. The investigators attributed the increase in dielectric constant with temperature at high frequencies to increased short-range segmental motion as the Tg was approached, which resulted in stronger dipolar polarization. However, since the ▬CN dipoles were attached to the polymer backbone in a 90° configuration, the segmental motion was hindered, causing friction with the neighboring chains and leading to high dissipation factor at high temperatures and frequencies. At low frequencies (<10 Hz), the increase in dielectric constant and dissipation factor with temperature was attributed to ions present from residual solvent and unreacted poly(amic acid) precursors in the 35–50 μm thick samples.

The investigators also compared the structural effect of four dianhydrides on the dielectric properties of PIs with three ▬CN dipoles in the diamine unit. The four dianhydride monomers under study were 2,2-bis(phthalic anhydride)-1,1,1,3,3,3 hexafluoroisopropane (6FDA), 4,4′-oxydiphthalic dianhydride (OPDA), 4,4′-benzophenonetetracarboxylic dianhydride (BTDA), and pyromellitic dianhydride (PMDA). The chemical structures of these dianhydrides are shown in **Figure 15**. A comparison of the increase in dielectric constant (Δε) from −150 to +190°C shows that for the p,p-linkage, PMDA exhibited the largest increase (e.g. ~25% at 10 kHz from ~3.4 at −150°C), followed by OPDA (23% from ~3.3), 6FDA (16% from ~3.4), and finally BTDA with the lowest increase (10% from ~3.6 at 10 kHz at −150°C) (**Figure 18a, c,** and **e**). The values of Δε decreased with increasing frequency for all four PIs and followed a decreasing order PMDA > OPDA > 6FDA > BTDA, which agreed with the trends observed in the polarization from dipole orientation determined experimentally and predicted based on a freely rotating single-dipole model. This model assumes an anti-parallel configuration for the dianhydride and diamine dipoles, such that the net dipole moment of a repeat unit is the difference between the dianhydride and diamine dipole moments without an external electric field. PMDA, being a symmetrical dianhydride, has no net dipole moment, whereas BTDA has the largest dipole moment (2.96 Debye) as a result of the benzophenone functional group. The 1.14 D dipole moment of OPDA results from the diphenyl ether, and the 2.0 D dipole moment of 6FDA from the 1,1,1,3,3,3-hexafluoropropane. The diamine portion has a dipole moment of 17.1 D which is the sum of three benzonitrile groups (4.18 D) and four diphenyl ethers (1.14 D). The largest Δε value for PMDA-based PI was accompanied by the highest dissipation factor relative to the other three PIs, but all four PIs had dissipation factor in the range of 3–8% at 190°C between 1 and 100 kHz (**Figure 18b, d,** and **f**). The results suggest that the PMDA-based PI with p,p diamine linkage had greater chain flexibility, which led to larger dipole motion at 190°C. In comparison to the p,p-linkage, the m,m-linkage resulted in a smaller increase in dielectric constant and slightly lower dissipation factor at 190°C, although the trends with respect to the dianhydrides and frequency dependence were similar. In addition, the 6FDA-based PI with m,m-linkage shows a dielectric constant of 3.1, which is noticeably lower than the p,p-linkage (ε = 3.4) and other PIs (ε ~ 3.3 to 3.6) at −150°C.

In terms of discharge energy density and efficiency, as characterized by measuring electric displacement as a function of electric field, the nitrilecontaining PIs delivered 25–40% greater discharge energy density than the nitrilefree analog at an applied electric field of 100 MV/m at 190°C and frequencies of 10 Hz and 1 kHz (**Figure 19a**). For comparison, the investigators also evaluated Kapton® PI and Ultem® PEI, both of which gave similar discharge energy density to the nitrile-free PI. While the nitrile-containing PIs delivered more energy than the nitrile-free counterparts, their discharge efficiency was generally lower, as

*Polyimides as High Temperature Capacitor Dielectrics DOI: http://dx.doi.org/10.5772/intechopen.92643*

### **Figure 18.**

*(a, c, and e) increase in dielectric constant (Δε) from −150 to +190°C and (b, d, and f) dissipation factor at 190°C at various frequencies for PIs containing three nitrile groups per diamine with various dianhydride (labeled as 3–6) and different isomeric diamine linkage (denoted as a: p,p; b: m,m; c: m,p). 3–6 represent PMDA-based, OPDA-based, 6FDA-based, and BTDA-based, respectively. Data adapted from [77].*

### **Figure 19.**

*(a) Discharge energy density and (b) percent energy loss of various polyimides (PIs) at 100 MV/m at various temperatures and frequencies. PI-1 is nitrile-free 6FDA/m,m-APB (LaRC-CP2). Group 2 represents one nitrile group with OPDA. Groups 3–6 contain three nitrile groups with various dianhydrides labeled 3 as PMDA, 4 OPDA, 5 6FDA, and 6 BTDA. Labels a–c denote p,p-, m,p-, and m,m diamine linkage, respectively, while K and U represent Kapton® PI and Ultem® PEI, respectively. Electrode area: 0.05 cm<sup>2</sup> . Data adapted from [77].*

shown in **Figure 19b**. The discharge energy losses for the nitrile-containing PIs were 15–40% compared to ~5% for the nitrile-free counterpart at 190°C at 10 Hz. Kapton® PI and Ultem® PEI exhibited 15–20% loss at that temperature and frequency.

With respect to the thermal properties, based on the limited glass transition temperature (Tg) data provided by the investigators, the addition of nitrile groups in the polymer backbone appears to increase Tg, but the enhancement decreased with increasing nitrile content, as indicated by the comparison of Tg for the seven 6FDA-based PIs (**Figure 20**). The structure of the dianhydride also affects the Tg. The four PMDA-based nitrile-containing PIs appear to have the highest Tg values (300–350°C with high crystallinity), whereas the other three dianhydride families of 6FDA, BTDA, and OPDA were mostly amorphous with Tg values ranging from 220 to 300°C. By comparison, these values were at least 20°C above that of the nitrile-free LaRC-CP2 (Tg = 200°C). Additionally, the PIs with m,m diamine linkage appeared to have lower Tg than those with a p,p linkage. This effect was attributed to the greater free volume created between polymer chains by the two bent amino groups in the m,m-linkage.

An ether (▬O▬) linkage is another polar moiety explored for the potential enhancement in dielectric constant of PIs [80, 81]. Jeffamines® EDR-104, D230 and HK511 (**Figure 21**), which are commercial polyether aliphatic diamines, were used to introduce ether linkages into PIs. The rationale behind the use of linear alkyl diamines was to impart close-packing for reducing the overall free volume while maintaining a high density of the imide functional groups in the polymer backbone. For comparison, 1,3-diaminopropane (1,3-DAP) and 1,6-diaminohexane (1,6-DAH), were synthesized as ether-free PIs with commercial linear alkyl diamines. The dianhydrides used in the study were PDMA, BTDA, OPDA, and 6FDA. Depending on the dianhydride, the PIs with diamine D230 exhibited dielectric constants of 2.5 for 6FDA and ~4.5 for the other three dianhyrides at room temperature and 1 kHz, while those containing diamine HK511, because of the greater ether content, produced higher dielectric constants (~5.3 for PMDA and 6FDA, 6.2 for OPDA, and 7.8 for BTDA) (**Figure 22a**). Hence, the general trend for dielectric constant of the ether-containing PIs with respect to the dianhydrides followed the order BTDA ≥ OPDA > PMDA > 6FDA. The lowest dielectric constant of 2.5 observed in the PI with 6FDA/D230, was attributed to the weak electronic interaction between chains caused by the bulky CF3 groups, which disrupted close

### **Figure 20.**

*Glass transition temperatures of PIs prepared from various dianhydrides: PMDA, 6FDA, BTDA, OPDA, and APB diamine isomers containing 0, 1 or 3 benzonitrile (BN) groups. Data adapted from [75–77].*

*Polyimides as High Temperature Capacitor Dielectrics DOI: http://dx.doi.org/10.5772/intechopen.92643*

**Figure 21.**

*Chemical structures of polyether aliphatic diamines: Jeffamines EDR-104, D230, and HK511, and linear alkyl diamines of 1,3-DAP and 1,6-DAH.*

### **Figure 22.**

*(a) Dielectric constant and (b) dissipation factor at room temperature as a function of frequency for various ether-containing PIs with A–D represent PMDA, BTDA, OPDA, and 6FDA, respectively, while 3 denotes D230 polyether diamine and 4 is HK511. Figure reproduced from Figure 2 of [80] with permission from American Chemical Society.*

packing. In comparison, the ether-free PIs, namely PMDA/1,3-DAP, BTDA/1,3- DAP, and BTDA/1,6-DAH exhibited dielectric constants of 5.6, 4, and 3.6, respectively. While the dielectric constants at room temperature were frequency independent in the range from 0.1 Hz to 10 kHz; the dissipation factor of the ethercontaining PIs showed a strong frequency dependence with dielectric relaxation peaks of 1–2% occurring at 1 kHz and above, except for BTDA/D230 and OPDA/ D230, which remained below 1% at 10 kHz (**Figure 22b**). In terms of temperature dependence, the ether-containing PIs showed almost an order of magnitude increase in dissipation factor up to 1% at frequencies of 1 kHz and 10 kHz as the temperature approached their corresponding Tg (50–100°C) (**Figure 23**). The low Tg was attributed to free volume created by the methyl side groups in the two diamines, D230 and HK511. In comparison, the two ether-free PIs, BTDA/1,3-DAP and BTDA/1,6-DAH, which were prepared from linear alkyl diamines, showed Tg of 175°C and 150°C, with crystal melting temperature of 271 and 234°C, respectively.

Another group of researchers utilized bipyridines and bipyrimidines, which are electron-rich diamines, to enhance the dielectric constant of PIs [82, 83]. The compounds of interest included 5,5′-bis(4-aminophenoxy)-2,2′-bipyridine (BPBPA) and 5,5′-bis(4-aminophenoxy)-2,2′-bipyrimidine (BAPBP) (**Figure 24**). The dianhydrides used in the study were BTDA, OPDA, PMDA, and BPDA

**Figure 23.**

*Dissipation factor at (a) 1 kHz and (b) 10 kHz as a function of temperature for various ether-containing PIs (solid symbols) and an ether-free analog (inverted green triangle). Data adapted from [80, 81].*

### **Figure 24.**

*Chemical structures of (a) 5,5*′*-bis(4-aminophenoxy)-2,2*′*-bipyridine (BPBPA) and (b) 5,5*′*-bis (4-aminophenoxy)-2,2*′*-bipyrimidine (BAPBP), and (c) various dianhydrides.*

(3,3′,4,4′-biphenyltetracarboxylic dianhydride). The resulting PIs with BPBPA diamine possessed relatively high Tg, which differed depending on the dianhydride unit, giving a decreasing order PMDA (320°C) > BTDA (296°C) > BPDA (285°C) > OPDA (275°C). Analogously, the PI containing BAPBP diamine and BPDA dianhydride showed a Tg of 291°C. The dielectric constants for the BPBPA-based PIs ranged from ~5.5 for the PMDA-based PI to ~6.9 for the BTDA-based at room temperature and frequencies from 1 to 100 kHz, following a decreasing order of BTDA > BPDA > OPDA > PMDA (**Figure 25**). At 220°C, the dielectric constants decreased about 4% with the same decreasing trend with respect to the dianhydrides over the same frequency range. The dissipation factor for all the BPBPA-based PIs was below 4% at both room temperature and 220°C from 100 Hz to 100 kHz. For the BAPBP/BPDA PI, the dielectric response at room temperature was similar to that of the BPBPA analog.

The demand for even higher operating temperatures (~350°C) for avionics prompted researchers to develop new polymers with increased degrees of aromaticity and heterocyclic rings in the polymer backbone. In the work by Venkat et al. [84], one of the polymers synthesized was a fluorinated polyimide based on 6FDA and a diamine of 2,2-bis(4-aminophenyl) hexafluoropropane grafted with adamantane (ADE) ester pendant groups (**Figure 26**). The Tg of the PI-ADE is 305°C with a dielectric constant of 2.85–2.91 for the temperature range of 25–250°C at 10 kHz while the dissipation factor increased from 0.6% at 25°C to 0.8% at 250°C (**Figure 27**).

*Polyimides as High Temperature Capacitor Dielectrics DOI: http://dx.doi.org/10.5772/intechopen.92643*

**Figure 25.**

*Dielectric constant and dissipation factor as a function of frequency for the BPBPA-based PIs with various dianhydrides at (a) room temperature and (b) 220°C. data adapted from [82] and supporting information.*

### **Figure 26.** *Chemical structure of PI-ADE. Structures adapted from [84].*

**Figure 27.**

*Capacitance (a) and dissipation factor (b) of PI-ADE as a function of temperature at 10 kHz. Data adapted from [84].*
