Facile Strategy for Intrinsic Low-k Dielectric Polymers - ACS Publications

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Article Cite This: Macromolecules 2019, 52, 4601−4609

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Facile Strategy for Intrinsic Low‑k Dielectric Polymers: Molecular Design Based on Secondary Relaxation Behavior Chao Qian, Runxin Bei, Tianwen Zhu, Weiwen Zheng, Siwei Liu, Zhenguo Chi, Matthew. P. Aldred, Xudong Chen, Yi Zhang,* and Jiarui Xu

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PCFM Lab, GD HPPC Lab, Guangdong Engineering Technology Research Centre for High-performance Organic and Polymer Photoelectric Functional Films, State Key Laboratory of Optoelectronic Materials and Technologies, School of Chemistry, Sun Yat-sen University, Guangzhou 510275, China S Supporting Information *

ABSTRACT: An original design strategy for the preparation of polymers with a low dielectric constant is presented. The key to this design strategy is taking the most advantage of the secondary relaxation behavior of the polymer chains to obtain more free volume in the bulk, which can effectively reduce the dielectric constant of the polymer. By using this design strategy, we have successfully synthesized a novel polyimide TmBPHF with a pendant group that consists of a biphenyl unit attached to the meta-position of a phenyl ring that is part of a triaryl unit. The intrinsic k and dielectric loss values of the TmBPHF are 2.09 and 0.0012 at 10 kHz, respectively. More importantly, such outstanding low-k performance remains stable up to 300 °C. The excellent low-k performance of TmBPHF is mainly due to the secondary relaxation, especially the β relaxation, which occurs from the rotation of the pendant group. The TmBPHF film shows an ultralow moisture rate (∼0.17%), which is able to maintain the low-k property stability in different humid environments. Meanwhile, the TmBPHF film also shows excellent thermal stability and excellent mechanical properties, with a glass transition temperature (Tg) of 302 °C, 5 wt % decomposition temperature (Td5%) of 549 °C, and residual of 70% at 800 °C under N2. The tensile strength and tensile modulus of the polyimide film are equal to 85.8 MPa and 2.02 GPa, respectively. In addition, the TmBPHF film is soluble in common solvents, which allows simple solution processing and efficient, low-cost, and continuous roll-to-roll processes. The design strategy is beneficial for lowering the k value and simultaneously maintaining the overall properties of polyimides, which possibly could also be extended to other novel high-performance polymer systems.

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INTRODUCTION Nowadays, the development of microelectronics and communication technology has revolutionized the way we live. With the development of the wireless communication industry, the high-speed and high-frequency transmission, especially the upcoming fifth generation mobile communication technology (5G technology), has been a hot research subject.1,2 The signal transmission speed (V) and signal propagation loss rate (α) are two key indexes in the high-speed and high-frequency transmission technology. The V and α values are both closely related to the dielectric constant (k) of the substrate materials, as shown in the deformation Maxwell’s equation3,4 C k

(1)

α ∝ f tan δ k

(2)

V∝

proportional to the k value and dielectric loss of the substrate materials. Hence, an urgent demand for low-k and low loss dielectric materials has arisen in the wireless communication industry. Low-k materials have once attracted industrial-wide research interest for their potential applications in the field of integrated circuits (ICs) because of the continued scaling of the ICs. Great efforts have been made in both academic and industrial research spaces in the 1990s.5−9 The reported low-k dielectric materials are mainly inorganic, organic/inorganic hybrids, and organic materials.10−12 Compared with the inorganic dielectric materials, organic polymer dielectric materials show obvious advantages, such as low-cost solution processability, possible flexible device fabrication, and a wide range of possible chemical structure modifications to alter material properties. Previously, several polymeric materials, such as polybenzobisoxazole,13,14 polysilsesquioxane,15 SILK (k = 2.65, Dow Chemical), and polyimide (PI),16−22 have been developed as low-k dielectric materials. To further reduce the k value, nanosized air voids (with a k value of approximately 1.0) have

Here, V is the signal transmission speed, C is the speed of light in vacuum, and k is the dielectric constant of the substrate materials. α is the signal propagation loss rate, f is the frequency of the signal transmission, and tan δ is the dielectric loss. The V value of the high-frequency circuit board is inversely proportional to the k value of the substrate materials, and the α value of the high-frequency circuit board is © 2019 American Chemical Society

Received: January 23, 2019 Revised: May 27, 2019 Published: June 10, 2019 4601

DOI: 10.1021/acs.macromol.9b00136 Macromolecules 2019, 52, 4601−4609

Article

Macromolecules been introduced into the low-k polymer materials.23,24 The k value of such porous polymer materials can be less than 1.5.25−31 However, the process of introducing nanosized air voids is complicated, difficult to control, and costly. Moreover, the structure, size, and distribution of the nanopores would greatly affect the homogeneity and stability of low-k polymer materials. Too many nanosized pores in the bulk will also damage the mechanical properties of the polymer and enhance the moisture absorption, resulting in deterioration of the low dielectric properties during further processing and application. Therefore, the development of flexible high-performance intrinsic low-k or ultralow-k polymer materials remains a great challenge in the microelectronics industry. For the intrinsic low-k polymer systems, numerous studies have indicated that increasing the intrinsic free volume might be the most effective way to reduce to the k value. This is because of the additional free volume in the polymer molecular chains that will introduce more ultralow-k air component to dilute the polar molecular concentration and weaken the interaction between the polymer chains.32−37 Most of the prior-art has focused on introducing bulky side groups or incorporating fluorine atoms to the polymeric structure to enlarge the free volume of the polymer chains. To some extent, these molecular design strategies can increase the free volume and reduce the k value, but the complicated molecular structure and high manufacturing cost make them difficult to realize commercial production and industrial application. Therefore, a facile and effective molecular design strategy to extend the free volume of polymers is the vital approach to obtain intrinsic low-k polymers. Different from the reported molecular design methods,26−31 here, we propose a brand new molecular design strategy to obtain a high-performance intrinsic low-k PI by fully considering the secondary relaxation of the polymer chains, especially the β relaxation. For the movement behaviors of thermoplastic-based polymer chains, there are a number of motion types, such as α relaxation (represents the segment relaxation), β relaxation (represents the torsion of groups in the polymer backbone or the rotation of the pendant group), γ relaxation (represents the crank motion of the chain link), and δ relaxation (represents the motion of end-groups in the pendant group) according to the reduction of the activation temperature. Among them, β relaxation, γ relaxation, and δ relaxation are collectively known as secondary relaxation.38−42 When the temperature is below the Tg, the chemical structures that are smaller than a chain segment, such as phenyl units in the pendant group, still exhibit rotational motions, whilst the segmental motion is frozen within the polymer system. The rotation of aromatic homocyclic rings in the pendant group might offer a new strategy for decreasing the intrinsic k value by enhancing the free volume in polymers if the aromatic homocyclic unit has been specially designed. In view of this, herein we report the synthesis and characterization of PIs incorporating homocyclic aromatic rings in the pendant group and examine the changes in the dielectric constant and investigate the free volume by wide angle X-ray diffraction (WAXD) and positron annihilation lifetime spectroscopy (PALS). In this work, we selected PIs because of their excellent thermal, mechanical, and dielectric properties.43−45 A novel diamine monomer (A-TmBP) was designed and successfully introduced into the polymer backbone to form a novel PI (TmBPHF) (Figure 1). The solution-cast TmBPHF film

Figure 1. Chemical structures of A-TmBP and TmBPHF.

shows an intrinsic k value of 2.09 with a dielectric loss on the order of 10−3 at 10 kHz. More importantly, the dielectric properties remain stable up to 300 °C. The excellent low-k properties are mainly due to the molecular design and exploitation of the secondary relaxation of the polymer, which leads to the formation of uniformly distributed freevolume holes with sizes at Ångström scale (i.e., a hole radius of approximately 3.05 Å). Additionally, the PI shows excellent thermostability with Tg of 302 °C, Td5% of 549 °C, and a residual of 70% at 800 °C under N2, which means that it meets the requirement of Cu damascene metallization in microelectronics fabrication. The PI is soluble in common solvents, which enables spin-on or roll-to-roll device fabrication processes. The PI also shows an ultralow moisture rate (∼0.17%), which could maintain the low-k property stability in different humid environments. Our strategy provides a new design solution for obtaining intrinsic low-k polymers and successfully delivers a flexible high-performance intrinsic low-k polymer film by solution processing that could lead to important advances in the development of microelectronics.

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EXPERIMENTAL SECTION

Materials. 3-Bromoaniline, 4-bromoaniline, 1-fluoro-4-nitrobenzene, 4-biphenylboronic acid, aniline, hydrazine monohydrate (NH2NH2·H2O), and cesium fluoride were purchased from Aladdin Industrial Corporation and used as received. Aliquat 336 (tricaprylylmethylammonium chloride), palladium 10% on carbon (10% Pd/C), and tetrakis(triphenylphosphine) palladium (Pd(PPh3)4) were purchased from J&K company and used as received. 4,4′-(Hexafluoro-isopropylidene)-diphthalic anhydride (6FDA) was purchased from Alfa Aesar and was heated at 150 °C under vacuum for 12 h prior to use. Chromatographically pure dimethylacetamide (DMAc) was purified by distillation under an inert nitrogen atmosphere. All other solvents and reagents as analytical grade were purchased from Guangzhou Dongzheng Company and used without further purification. Instrumentation. All NMR spectra were recorded on a Bruker Model AVANCE III 400 spectrometer. The samples (10−30 mg of each compound) were dissolved in 0.5 mL of deuterated dimethyl sulfoxide (DMSO-d6) or deuterated chloroform (CDCl3) using tetramethylsilane as the internal reference. The elemental analysis was performed on a CHNS elemental analyzer. Mass spectra were measured using a Thermo EI mass spectrometer (DSQ II). Fouriertransform infrared (FT-IR) spectra were recorded on a Bruker Tensor 27 spectrometer. WAXD patterns were obtained by a SmartLab X-ray diffractometer (Rigaku Company, Japan). The range of the scan angle was 5°−70°, and the scan speed was 10°/min. A thermogravimetric analysis (TGA) was performed with a TA thermal analyzer (Q50) under N2 with a heating rate of 20 °C/min from 50 to 900 °C, and the samples were heated under flowing nitrogen (40 mL/min). The Tg was obtained by a DMA Q800 analyzer (TA Company, USA) with a heating rate of 10 °C/min from 50 to 400 °C. A thermal mechanical analysis (TMA Q400 analyzer, TA Company, USA) was used to study the coefficient of thermal expansion (CTE) of the polymer film with a 4602

DOI: 10.1021/acs.macromol.9b00136 Macromolecules 2019, 52, 4601−4609

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Macromolecules Scheme 1. Synthesis Route of the PIs

(400 MHz, DMSO, δ): 8.21 (d, J = 9.2 Hz, 4H), 7.56 (d, J = 7.3 Hz, 1H), 7.50 (t, J = 1.9 Hz, 1H), 7.46 (t, J = 8.0 Hz, 1H), 7.30 (d, J = 7.3 Hz, 1H), 7.24 (d, J = 9.2 Hz, 4H). 13C NMR (100 MHz, CDCl3, δ): 151.17, 145.99, 142.33, 132.24, 129.65, 126.25, 125.54, 122.81. HRMS (ESI) m/z: 413 [M + H]+ calcd for C18H12BrN3O4, 413.0011. Anal. Calcd for C18H12BrN3O4: C, 52.19; H, 2.92,;N, 10.14. Found: C, 52.07; H, 2.87; N, 9.87. Synthesis of N-TmBP. The N-TmBr (4.142 g, 10 mmol) and 4biphenylboronic acid (2.178 g, 11 mmol) were added into a 500 mL three-neck round-bottom flask and then moderate Aliquat 336 was added. Next, tetrakis(triphenylphosphine)palladium (Pd(PPh3)4) (0.207 g, 0.18 mmol), aqueous K2CO3 solution (2 N) (35 mL), and tetrahydrofuran (THF) (200 mL) were also charged, followed by refluxing under nitrogen for 24 h. After removing the aqueous layer, the yellow precipitates were collected by rotary evaporation and purified by chromatography on silica gel with dichloromethane/ hexane as an eluent. The purified product was light yellow needle-type crystals with a yield of 91%. 1H NMR (400 MHz, DMSO, δ): 8.22 (d, J = 9.2 Hz, 4H), 7.75 (d, J = 7.5 Hz, 5H), 7.70 (d, J = 7.4 Hz, 2H), 7.64 (d, J = 1.5 Hz, 1H), 7.62 (t, J = 7.8 Hz, 1H), 7.49 (t, J = 7.6 Hz, 2H), 7.39 (t, J = 7.3 Hz, 1H), 7.29 (d, J = 9.2 Hz, 5H). 13C NMR (100 MHz, CDCl3, δ): 151.81, 145.45, 143.42, 142.88, 141.02, 140.32, 138.42, 130.95, 128.89, 127.62, 127.03, 125.86, 125.61, 122.78, 122.47. HRMS (ESI) m/z: 487 [M + H]+ calcd for C30H21N3O4, 487.1532. Anal. Calcd for C30H21N3O4: C, 73.91; H, 4.34; N, 8.62. Found: C, 73.56; H, 4.21; N, 8.33. Synthesis of A-TmBP. The N-TmBP (4.875 g, 10 mmol), one spoonful of 10% Pd/C catalyst (∼0.05 g), and ethanol (100 mL) were charged into a 500 mL three-neck round-bottom flask, and then, hydrazine hydrate (3 mL) was added dropwise. The reaction was followed by refluxing under nitrogen for 24 h. After removing the ethanol by rotary evaporation, the gray precipitates were collected and then purified by chromatography on silica gel with dichloromethane/ hexane as an eluent. The purified product was gray crystals with a yield of 72%. 1H NMR (400 MHz, DMSO, δ): 7.69 (t, J = 7.9 Hz, 4H), 7.55−7.42 (m, 4H), 7.36 (t, J = 7.3 Hz, 1H), 7.17 (t, J = 7.9 Hz, 1H), 6.96 (d, J = 7.7 Hz, 1H), 6.89 (d, J = 8.5 Hz, 5H), 6.58 (t, J = 11.8 Hz, 5H), 5.03 (s, 4H). 13C NMR (100 MHz, CDCl3, δ): 146.20, 140.62, 140.29, 140.10, 139.44, 136.20, 129.77, 129.41, 128.01, 127.61, 127.43, 127.00, 116.50, 116.05, 115.33, 114.83. HRMS (ESI) m/z: 427 [M + H]+ calcd for C30H25N3, 427.2048. Anal. Calcd for

heating rate of 10 °C/min from 50 to 400 °C, and the CTE of the polymer film was calculated at the temperature range from 50 to 250 °C. A tensile test was performed on samples cut from a 50 μm thick sheet, and the test was performed using a SANS CTN6103 instrument according to GB/T16421-1996. The specimen size was 10 mm × 100 mm. The morphology of the surface of the polymer film was studied using a Bruker Multimode 8 microscope atomic force microscope with the contact mode. The moisture rate was measured using high precision electronic balance. The sample film was dried in oven at 110 °C for 24 h and measured its weight (m1). Then, the sample film was soaked into water at 30 °C for 3 days, and its weight (m2) was measured. The moisture rate was calculated by the equation: (m2 − m1)/m1. The film density was measured by a density balance (Mirage SD-200 L, Japan) with an accuracy of 0.1 mg. The dielectric constant was measured at frequencies between 102 and 106 Hz at 25 °C and 60% relative humidity using a Solartron SI 1260 impedance/gain phase analyzer in conjunction with two copper electrodes (10 mm × 10 mm). The samples were thin films with a size of 12 mm × 12 mm. Silver paste was coated onto both surfaces of the polymer film to ensure excellent contact between the electrodes and polymer film (Figure S3 in the Supporting Information). The refractive index (n) was measured on UVISEL 2 automatic spectral type ellipsometer (Horiba, Japan). The measuring parameter was setting as follows: the angle of incidence was 70°, scanning range was 1−6.5 eV, scan interval was 0.02 eV, and acquisition time of each step is 500 ms. The sample was the spin-coated PI film with the thickness less than 500 nm. The fitting model is a three-layer structure model, which is contains monocrystalline silicon (substrate layer), silicon dioxide (oxide layer), and PI (polymer layer). The fitting variance (X2) is less than 100. Positron lifetime was measured using positron annihilation life spectroscopy (PALS) which was specifically introduced in our previous work.18 Synthesis of N-TmBr. 3-Bromoaniline (5.160 g, 30 mmol), CsF (9.120 g, 60 mmol), 1-fluoro-4-nitrobenzene (10.582 g, 75 mmol), and DMSO (150 mL) were added into a 500 mL three-neck roundbottom flask and reacted for 24 h at 150 °C under nitrogen. After pouring into 500 mL of cold saturated salt water, yellow precipitates were collected and purified by chromatography on silica gel with dichloromethane (DCM)/hexane as an eluent. The purified product was light yellow needle-type crystals with a yield of 65%. 1H NMR 4603

DOI: 10.1021/acs.macromol.9b00136 Macromolecules 2019, 52, 4601−4609

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Macromolecules

Figure 2. (a) Photograph of a rolled up TmBPHF film. (b) AFM 3D image of the TmBPHF film surface. C30H25N3: C, 84.28; H, 5.89; N, 9.83. Found: C, 83.87; H, 5.81; N, 9.56. Synthesis and Preparation of PI Film (TmBPHF). The ATmBP (0.428 g, 1 mmol), 6FDA (0.444 g, 1 mmol), and purified dimethyl-formamide (DMF) (5.8 mL) were added in a 50 mL flask, achieving a solid content of approximately 15 wt %. The mixture was stirred at room temperature under argon for about 4 h to form a viscous poly(amic acid) (PAA) solution. The PAA solution was subsequently coated uniformly on a clean and dry glass plate with a controlled film thickness and then thermally imidized in a vacuum oven with the temperature program of 100 °C(1 h)/200 °C (1 h)/ 350 °C (1 h) to produce the TmBPHF film. The TmBPHF film was removed from the glass substrate after the oven cooled to room temperature. IR (KBr, ν, cm−1): 1780 and 1728 (CO stretching), 1500 (CC stretching), 1087−725 (Ar−H stretching), 1371 (C−N stretching). The intrinsic viscosity ([η]) of TmBPHF (0.5 g/L in DMF) is 0.52 dL/g.

structures are likely to expand the distance between the neighboring polymer chains, thus impeding their interactions. This excellent solubility makes the PI a potential candidate in microelectronics, enabling simple spin-on or continuous rollto-roll processes to be used during device manufacturing. As shown in Figure 2a, the TmBPHF film produced by a solution casting process exhibits good flexibility. The atomic force microscopy (AFM) image (Figure 2b) shows that there are no apparent pores on the film surface. The surface roughness (Rq) is 0.493 nm, which indicates that the PI film contains no nanoporous structures after solution casting and subsequent solvent evaporation. The PI shows ultralow moisture rate (∼0.17%), in which the low-k property is maintained in different humid environments. The thermal properties of the PI were investigated by dynamic mechanical analysis (DMA), thermomechanical analysis (TMA), and TGA (Table S2 in the Supporting Information). The DMA measurements reveal that the PI exhibits high maximum service temperature in air and its Tg is equal to 302 °C. In addition, TmBPHF exhibits good dimensional stability and its CTE is about 38 ppm/K in the range of 50−250 °C. The results obtained from TGA show that the PI exhibits excellent thermal stability, with a Td5% of 549 °C in N2, and the amount of carbonized residue (char yield) in N2 is 70% at 800 °C. The PI also shows excellent mechanical properties (Table S3 in the Supporting Information), with tensile strength and tensile modulus of the as-casting PI film equal to 85.8 MPa and 2.02 GPa, respectively. The high Tg, excellent thermal stability, and excellent mechanical properties of the PI film are expected to meet the requirements of heat resistance and high processing and application temperatures required for the microelectronics industry. Dielectric Properties of TmBPHF Film. The dielectric properties of the PI film were measured at the frequencies between 100 Hz and 1 MHz at 25 °C and 60% relative humidity using a Solartron SI 1260 impedance/gain phase analyzer. The measurements were carried out as follows. First, a capacitance measurement was carried out, and then, the dielectric constant was calculated using eq 3

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RESULTS AND DISCUSSION Synthesis and Characterization of TmBPHF Film. As shown in Scheme 1, the TmBPHF PI was prepared by a conventional two-step method. The diamine A-TmBP was reacted with commercially available 4,4′(hexafluoroisopropylidene)diphthalic anhydride (6FDA) in DMF to prepare the precursor poly(amic acid). The viscous PAA solution with a solid content of approximately 15 wt % was coated uniformly on a clean and dry glass plate with a controlled film thickness and then thermally imidized in a vacuum oven with a temperature program of 100 °C(1 h)/200 °C (1 h)/350 °C (1 h) to produce the TmBPHF film. The chemical structure and degree of imidization of the TmBPHF solid film were confirmed by FT-IR spectra (Figure S1 in the Supporting Information). Compared with the spectrum of ATmBP, the characteristic absorption at 3350 and 1621 cm−1 (N−H stretching) disappears in the FT-IR spectrum of TmBPHF. Meanwhile, the characteristic absorption peaks of the imide group at 1780 cm−1 (asymmetrical stretching of carbonyl), 1728 cm−1 (symmetrical stretching of carbonyl), and 1371 cm−1 (C−N stretching) are clearly shown in the FTIR spectra of TmBPHF, which means that the imidization reaction of TmBPHF was complete. The intrinsic viscosity ([η]) of TmBPHF in DMF (0.5 g/L) is 0.52 dL/g, which was measured using an Ubbelohde viscometer at 30 °C. The density of the TmBPHF film is about 1.21 g/cm3 which is exactly about 85% times of ordinary commercial PI (Kapton, dKapton = 1.42 g/cm3). The qualitative solubility behaviors of TmBPHF are summarized in Table S1 in the Supporting Information, which reveals that the PI has excellent solubility in many common organic solvents such as N-methylpyrrolidone, DMAc, dimethyl sulfoxide (DMSO), DMF, THF, DCM, and m-cresol. The impressive solubility can be attributed to the propeller-like structure of the triarylamine unit and rotating terphenyl unit in the pendant group. Such

k=

C ji l zy jj zz k0 k A {

(3)

Here, k is the dielectric constant of the material between the plates, C is the capacitance of the material (in Farads), k0 is the vacuum dielectric constant (∼8.854 × 10−12 F/m), l is the thickness of the film (in meters), and A is the area of overlap of the two plates (in square meters). The results are shown in Figure 3. TmBPHF exhibits good electrical properties, with a dielectric constant of 2.09 and dissipation factor of 0.0012 at 10 kHz, which is much lower compared with the commercial Kapton film (dielectric constant of 3.40) and most of the 4604

DOI: 10.1021/acs.macromol.9b00136 Macromolecules 2019, 52, 4601−4609

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Macromolecules

The reason for that may be due to the existence of six F atoms in the dianhydride part of TmBPHF. The F atom has the strongest electronegativity and can effectively reduce the k value. Therefore, it may be inappropriate to compare the TmBPHF with polystyrene. As we know, there are many polymers which have the larger d value and smaller n value compared with polystyrene (dPS = 1.07 g/cm3, nPS = 1.59), just like polyvinyl chloride (dPVC = 1.40 g/cm3, nPVC = 1.54), polymethyl methacrylate (dPMMA = 1.18 g/cm3, nPMMA = 1.49), polyvinyl alcohol (dPVA = 1.29 g/cm3, nPVA = 1.50), Teflon (dTeflon = 2.15 g/cm3, nTeflon = 1.35), polyvinylidene fluoride (dPVDF = 1.78 g/cm3, nPVDF = 1.42), and so on. In our opinion, the n value of the polymer not only just depends on the d value but also depends on the average polarizability (α) of molecular units. Therefore, the fact that the nTmBPHF value of the TmBPHF film became smaller than the nPS value is entirely possible. Free Volume and Secondary Relaxation Behavior of the TmBPHF Film. Free volume is a kind of sub-nanoscale interspace that intrinsically exists in the amorphous region of polymeric materials. More free volume can dilute polaritybased interactions within the polymer backbone per unit volume, which can greatly reduce the dielectric constant of the polymer. We believe that the key to obtain an intrinsic low-k polymer is to effectively introduce more free volume. The structural units that are smaller than the actual polymer segments such as a pendant group, end group, or phenyl are still movable when the temperature is below the Tg. This kind of movement is generally named the secondary relaxation behavior (including β relaxation, γ relaxation, and δ relaxation). The rotational internal motion of the terphenyl unit that is the pendant group is a typical β relaxation. When the temperature is below than the Tg, all the segments are frozen; however, the terphenyl units can still rotate. Based on this kind of β relaxation, we designed the PI TmBPHF that contains a 1,3-disubstituted phenylene unit in the pendant group with a substituted biphenyl unit (Scheme 1) to obtain more free volume. To verify that this design strategy is effective or not, one should answer two very important questions. The first one is whether the β relaxation behavior occurs below the Tg. The second one is whether the β relaxation behavior can introduce more free volume in the PI.

Figure 3. Dielectric constant (k) and dielectric loss of the TmBPHF film as a function of frequency at room temperatures, inset shows the dielectric constant and the dielectric loss of the TmBPHF film at different temperatures at 10 kHz.

intrinsic low-k polymer films (with k values greater than 2.20) reported to date. Moreover, these outstanding dielectric properties remain stable up to 300 °C (inset in Figure 3), which is near the Tg of TmBPHF. The optical dielectric constant (kn) can be calculated by the deformation Maxwell’s equation (eq 4)

kn = n2

(4)

Here, kn is the optical dielectric constant, and n is the refractive index, which can be measured by the ellipsometer. The n of TmBPHF is 1.46 and the kn is 2.13, which is close to the dielectric constant (2.09) calculated by the capacitance. The k and kn of TmBPHF both indicate that it has excellent low dielectric property. The synthesized TmBPHF film has a mass density (d) of 1.21 g/cm3 and a refractive index (n) of 1.46. According to the Lorentz−Lorenz (LL) equation (eq 5) with N and α being the number density and average polarizability of molecular units in the material, one may notice that compared with the known polymer, such as polystyrene (PS) with a d value of 1.07 g/cm3 and a n value of 1.59, the refractive index expected from the LL equation is larger for TmBPHF than for PS (because dTmBPHF > dPS), but the reported nTmBPHF value is actually smaller than the nPS value. n2 − 1 4π = Na 3 n2 + 2

(5)

Figure 4. Activation energy of the terphenyl unit in the pendant group (the chemical structure is shown on the right hand side) as a function of dihedral angle. The illustrations below are the molecular conformations at different dihedral angles when the backbone is fixed: (a) −170°. (b) −130°. (c) −50°. (d) −30°. (e) 10°. (f) 90°. (g) 130°. 4605

DOI: 10.1021/acs.macromol.9b00136 Macromolecules 2019, 52, 4601−4609

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Macromolecules To answer the first question, the rotational barrier of the 1,3disubstituted phenylene unit in the pendant group that is attached to the nitrogen atom was calculated using the Gaussian computation (Figure 4). The rotational barrier of the pendant group of TmBPHF is about 23.33 KJ/mol. In real polymer chains, the state of the aromatic unit is very complicated, so DMA was used to study the β relaxation behavior of TmBPHF (Figure 5). The β relaxation peak (Tβ)

Figure 6. (a) WAXD pattern of the TPAHF film, TpBPHF film, TmBPHF film, and DuPont Kapton PI film. (b) Imaginary spatial configuration of TmBPHF.

TmBPHF film (d = 5.93 Å) has a larger interlayer distance than the TPAHF film (d = 5.61 Å), TpBPHF film (d = 5.67 Å), and Kapton film (d = 4.74 Å) (Table S4 in the Supporting Information). These results indicate that only the metasubstitution in the pendant group can greatly increase the free volume when the backbone structure is kept the same. PALS is a useful method for probing atomic- and subnanometer-sized holes in the materials,46−48 and is often used to characterize the free volume of polymeric materials. It was used to further study the PI films. If a fraction of the positrons from a radioactive source form positronium injected into liquids or porous solids, the positrons will annihilate from the para state (p-Ps, singlet spin state) or the ortho state (o-Ps, triplet spin state). p-Ps decays mainly via self-annihilation by emitting two γ-rays with a lifetime of 125 ps. The selfannihilation lifetime of o-Ps, which emits three γ-rays, is as long as 142 ns. Because of collisions of Ps with molecules, the lifetime of o-Ps confined in local free volumes will be reduced to a typical value of 1−5 ns. The o-Ps will pick off one electron from the surrounding molecules and annihilate it by emitting two γ-rays, which are called “pick-off” annihilation. The “pickoff” annihilation lifetime of o-Ps is highly sensitive to the size of the free volume. The PALS measured for the TPAHF, TpBPHF, TmBPHF, and Kapton films are shown in Figure 7. From a detailed

Figure 5. DMA curve of the TmBPHF film as a function of temperature. The inset below is the enlarged curve of the tan δ at a temperature range between 75 and 225 °C, and the inset above is the schematic diagram of the β relaxation behavior in the pendant group of TmBPHF.

can be observed at about 154 °C, which is far below the temperature of α relaxation peak (Tg). This means that the 1, 3-disubstituted phenylene unit in the pendant group still can rotate when the temperature is within the range of 154−302 °C while the main chain segments are frozen. To answer the second question, we synthesized two other PIs (TPAHF and TpBPHF, Schemes S1 and S2 in the Supporting Information) and purchased the commercially available product DuPont Kapton PI film as a reference. As shown in Scheme 1, the TPAHF has the same polymer backbone structure as TmBPHF but only contains a phenyl ring attached to the nitrogen atom as the pendant group, that is, with no biphenyl unit attached to the meta-position of the phenyl ring. The TpBPHF also has the same backbone structure as TmBPHF; however, in this case the phenyl ring is substituted with a biphenyl unit at the para-substitution. The β relaxation behavior occurs in all three PIs (TTPAHF : 135 °C, β TTpBPHF : 142 °C, TTmBPHF : 154 °C, shown in Figure S2 in the β β Supporting Information), but only the TmBPHF with metasubstitution shows more free volume by the rotation of its terphenyl unit in the pendant group. To verify this, the distance between the polymer chains and free volume were measured by WAXD and PALS. WAXD is a useful test instrument for studying the distance between the polymer chains using the Bragg equation (eq 6) 2d sin θ = nλ

(6) Figure 7. Positron lifetime spectra measured for the TPAHF film, TpBPHF film, TmBPHF film, and DuPont Kapton PI film.

Here, d is the interlayer distance of the polymer, θ is the included angle between the incidence X-ray and interlayer of the polymer, λ is the wavelength of the X-ray, and n is the diffraction series. As shown in Figure 6a, the WAXD peak is broad in all the PI films because of the amorphous structure. As compared to the TPAHF, TpBPHF, and Kapton films, the TmBPHF film has the smallest 2θ (14.92°). The WAXD peak at 2θ may be assigned to the interlayer distance of the polymer. The interlayer distance calculated from 2θ data indicates that the

analysis of the lifetime spectra using the PATFIT routine (Table 1),46 we have found two exponential decay components (τ1 and τ2) for the Kapton film and three exponential decay components (τ1, τ2, and τ3) for the other PI films. The shortest lifetime τ1 is due to the p-Ps lifetime and free annihilation lifetime of the positrons. The second lifetime component τ2 is attributed to positron annihilation in the amorphous region. 4606

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Table 1. Analyzed Data for the Positron Lifetime in the TPAHF Film, TpBPHF Film, TmBPHF Film, and DuPont Kapton PI Film sample

τ1 (ns)

τ2 (ns)

τ3 (ns)

I1 (%)

I2 (%)

I3 (%)

rPLASa (Å)

VPLASb (Å3)

f vc (%)

Kapton TPAHF TpBPHF TmBPHF

0.29 0.17 0.19 0.18

0.41 0.38 0.39 0.40

1.71 1.76 2.22

34.4 27.9 16.7 35.6

65.6 69.9 80.5 57.1

2.2 2.8 7.3

2.57 2.63 3.05

71.07 76.16 118.79

0.28 0.38 1.56

a

Calculated by eq 7. bCalculated by the formulas for the volume of the sphere: VPLAS = 1.33πrPLAS3. cCalculated by the formulas: f v = CVPLASI3, C = 0.0018.50

Figure 8. (a) Dielectric constant k of the Kapton, TPAHF, TpBPHF, and TmBPHF films as a function of frequency at room temperature. (b) Dielectric loss of the Kapton, TPAHF, TpBPHF, and TmBPHF films as a function of frequency at room temperature.

Figure 9. Schematic diagram showing the kinetic state of the backbone and the pendant group of TmBPHF during cooling and heating thermal processes. (a) T ≥ Tg. (b) Tβ ≤ T ≤ Tg. (c) T ≤ Tβ.

The long-lifetime component τ3 is attributed to “pick-off” annihilation of o-Ps at holes in the amorphous phase and can be used to estimate the size of the free volumes in the amorphous phases by eq 7.48 ÄÅ É r 1 ij 2πr yzÑÑÑÑ ÅÅÅ zzÑ + sinjj τo ‐ Ps = 0.5ÅÅ1 − ÅÅÇ r + Δr 2π k r + Δr {ÑÑÑÖ (7)

(60°) with the rotation axis, the rotation of the 1,3disubstituted phenylene unit connected to the nitrogen atom will create additional free volume like a cone. The additional free volume will not be influenced by the segment packing below or above the Tg (Figure 9). When the temperature is higher than the Tg, both the backbone and pendant groups are movable, and the rotation of the meta-substituted biphenyl unit will create additional conical holes (Figure 9a). In the cooling process, when the temperature is below Tg but higher than Tβ, the motions of the chain segments will be frozen. However, the rotational motions of the pendant groups are still active and the conical holes created by the rotation of the pendant groups can be well preserved (Figure 9b). When the temperature further drops below the Tβ, these conical holes will be frozen and maintain in the polymer (Figure 9c) due to the fact that the frozen segments cannot move to occupy these conical holes. Similarly, in the heating process, the rotational motions of the pendant groups occur at lower temperature than the motions of the chain segments. Therefore even at the temperature above the Tg, the motion of the chain segments will still not destroy the conical holes that are protected by the rotational rod-like pendant groups. Compared with physical pore-forming strategy,25−31 this molecular design strategy can offer homogeneous, controllable, and thermostable incremental free volume. Using this design strategy, the synthesized PI has a simple chemical structure and exhibits excellent comprehensive performance (such as good solubility, low

Here, a value of Δr = 0.166 nm is obtained by fitting eq 7 to the observed porous materials and was determined by Eldrup.49 As shown in Table 1, the mean radius (rPLAS) of free volume in the TmBPHF film is 3.05 Å, and the mean volume (VPLAS) of the free-volume size is about 118.79 Å3. The relative fee-volume fraction (f v) of the TmBPHF film is about 1.56% which is much larger than that of the TPAHF film (0.28%), TpBPHF film (0.38%), and reference Kapton film. The tendency of free volume in these PIs is also reflected in the dielectric constant (Figure 8). The dielectric constant of the TmBPHF film (2.09) is significantly less than those of the TPAHF film (2.66), TpBPHF film (2.51), and Kapton film (3.40). It is thus believed that the more free volume will depress the close packing of the polymer chains and introduce more voids or/and air (k = 1) into the PI bulk, in which both would lead to reduce the dielectric constant. For the TmBPHF film, the incremental free volume is attributed to the rotation of the pendant meta-terphenyl unit attached to the nitrogen atom. Because the biphenyl group keeps a constant included angle 4607

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Fundamental Research Funds of Sun Yat-sen University are gratefully acknowledged.

moisture absorption, thermostability, and good mechanical properties).

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CONCLUSION In summary, we have presented a completely original design strategy to effectively reduce the dielectric constant of PI film. The principal of this design strategy is using the secondary relaxation behavior of the pendant group, especially the rotation of the meta-terphenyl unit in the pendant group to obtain more free volume in the bulk. Using this strategy, we have successfully obtained a novel PI (TmBPHF), which exhibits an excellent low dielectric property. The k and dielectric loss of the TmBPHF film are as low as 2.09 and 0.0012 at 10 kHz, respectively. More importantly, this design strategy efficiently retains the excellent thermal and mechanical properties of the PI. The TmBPHF film is able to maintain its low dielectric property up to 300 °C (near its Tg). The good solubility gives the TmBPHF excellent solution processability. The excellent thermal properties and efficient mechanical properties, as well as good solubility, makes TmBPHF a promising candidate for the needs of semiconductor and communication industries. This design strategy is beneficial for lowering the k value and simultaneously maintaining the overall advantageous properties of PIs, and it is also our belief that this strategy can be extended to other novel highperformance polymer systems.

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(1) Hecht, J. The Bandwidth Bottleneck That is Throttling the Internet. Nature 2016, 536, 139−142. (2) Andrews, J. G.; Buzzi, S.; Choi, W.; Hanly, S. V.; Lozano, A.; Soong, A. C. K.; Zhang, J. C. What Will 5G Be? IEEE J. Sel. Area. Commun. 2014, 32, 1065−1082. (3) Egorov, V. N.; Masalov, V. L.; Nefyodov, Y. A.; Shevchun, A. F.; Trunin, M. R.; Zhitomirsky, V. E.; McLean, M. Dielectric Constant, Loss Tangent, and Surface Resistance of PCB Materials at K-band Frequencies. IEEE Trans. Microw. Theory Tech. 2005, 53, 627−635. (4) Mori, N.; Sugimoto, Y.; Harada, J.; Higuchi, Y. Dielectric Properties of New Glass-ceramics for LTCC Applied to Microwave or Millimeter-wave Frequencies. J. Eur. Ceram. Soc. 2006, 26, 1925− 1928. (5) Volksen, W.; Miller, R. D.; Dubois, G. Low Dielectric Constant Materials. Chem. Rev. 2010, 110, 56−110. (6) Miller, R. D. In Search of Low-k Dielectrics. Science 1999, 286, 421−423. (7) Maier, G. Low Dielectric Constant Polymers for Microeletronics. Prog. Polym. Sci. 2001, 26, 3−65. (8) Hatton, B. D.; Landskron, K.; Hunks, W. J.; Bennett, M. R.; Shukaris, D.; Perovic, D. D.; Ozin, G. A. Materials Chemistry for Lowk Materials. Mater. Today 2006, 9, 22−31. (9) Long, T. M.; Swager, T. M. Molecular Design of Free Volume as a Route to Low-k Dielectric Materials. J. Am. Chem. Soc. 2003, 125, 14113−14119. (10) Shamiryan, D.; Abell, T.; Iacopi, F.; Maex, K. Low-k Dielectric Materials. Mater. Today 2004, 7, 34−39. (11) Morgen, M.; Ryan, E. T.; Zhao, J.-H.; Hu, C.; Cho, T.; Ho, P. S. Low Dielectric Constant Materials for ULSI Interconnects. Annu. Rev. Mater. Sci. 2000, 30, 645−680. (12) Kohl, P. A. Low-Dielectric Constant Insulators for Future Integrated Circuits and Packages. Annu. Rev. Chem. Biomol. Eng. 2011, 2, 379−401. (13) Ishida, H.; Low, H. Y. A Study on the Volumetric Expansion of Benzoxazine-Based Phenolic Resin. Macromolecules 1997, 30, 1099− 1106. (14) Tao, L.; Yang, H.; Liu, J.; Fan, L.; Yang, S. Synthesis of Fluorinated Polybenzoxazoles with Low Dielectric Constants. J. Polym. Sci., Part A: Polym. Chem. 2010, 48, 4668−4680. (15) Kessler, D.; Roth, P. J.; Theato, P. Reactive Surface Coatings Based on Polysilsesquioxanes: Controlled Functionalization for Specific Protein Immobilization. Langmuir 2009, 25, 10068−10076. (16) Liaw, D.-J.; Wang, K.-L.; Huang, Y.-C.; Lee, K.-R.; Lai, J.-Y.; Ha, C.-S. Advanced Polyimide Materials: Syntheses, Physical Properties and Applications. Prog. Polym. Sci. 2012, 37, 907−974. (17) Liu, Y.; Zhang, Y.; Lan, Q.; Liu, S.; Qin, Z.; Chen, L.; Zhao, C.; Chi, Z.; Xu, J.; Economy, J. High-Performance Functional Polyimides Containing Rigid Nonplanar Conjugated Triphenylethylene Moieties. Chem. Mater. 2012, 24, 1212−1222. (18) Liu, Y.; Qian, C.; Qu, L.; Wu, Y.; Zhang, Y.; Wu, X.; Zou, B.; Chen, W.; Chen, Z.; Chi, Z.; Liu, S.; Chen, X.; Xu, J. A Bulk Dielectric Polymer Film with Intrinsic Ultralow Dielectric Constant and Outstanding Comprehensive Properties. Chem. Mater. 2015, 27, 6543−6549. (19) Hougham, G.; Tesoro, G.; Shaw, J. Synthesis and Properties of Highly Fluorinated Polyimides. Macromolecules 1994, 27, 3642−3649. (20) Lee, Y. K.; Murarka, S. P.; Jeng, S.-P.; Auman, B. Investigations of The Low Dielectric Constant Fluorinated Polyimide for Use as The Interlayer Dielectric in ULSI. MRS Proc. 1995, 381, 31−43. (21) Sydlik, S. A.; Chen, Z.; Swager, T. M. Triptycene Polyimides: Soluble Polymers with High Thermal Stability and Low Refractive Indices. Macromolecules 2011, 44, 976−980. (22) Pellerin, J.; Fox, R.; Ho, H. M. Low Dielectric Constant Fluorinated Polyimides for Interlayer Dielectric Applications. MRS Proc. 1997, 476, 113−119.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.9b00136. Synthesis and characterization of intermediates and PIs (TPAHF and TpBPHF); solubility, thermal, and mechanical properties of the TmBPHF film; FT-IR spectra of diamines and PIs; WXRD date of the PIs; and experimental setup of the dielectric constant measurement (PDF) Supplementary dynamic images, showing the rotation of the pendant group of TmBPHF (AVI)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Siwei Liu: 0000-0001-9537-941X Zhenguo Chi: 0000-0001-9772-5363 Xudong Chen: 0000-0001-9499-5421 Yi Zhang: 0000-0003-0309-8675 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial supports by the National Natural Science Foundation of China (nos. 51373204 and 51873239), the National 973 Program of China (no. 2014CB643605), the Science and Technology Project of Guangdong Province (nos. 2015B090915003 and 2015B090913003), the Leading Scientific, Technical and Innovation Talents of Guangdong Special Support Program (no. 2016TX03C295), the China Postdoctoral Science Foundation (no. 2017M612801), and the 4608

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Article

Macromolecules (23) Meador, M. A. B.; Wright, S.; Sandberg, A.; Nguyen, B. N.; Van Keuls, F. W.; Mueller, C. H.; Rodríguez-Solís, R.; Miranda, F. A. Low Dielectric Polyimide Aerogels as Substrates for Lightweight Patch Antennas. ACS Appl. Mater. Interfaces 2012, 4, 6346−6353. (24) Grosso, D.; Boissière, C.; Sanchez, C. Ultralow-DielectricConstant Optical Thin Films Built from Magnesium Oxyfluoride Vesicle-like Hollow Nanoparticles. Nat. Mater. 2007, 6, 572−575. (25) Lee, B.; Park, Y.-H.; Hwang, Y.-T.; Oh, W.; Yoon, J.; Ree, M. Ultralow-k Nanoporous Organosilicate Dielectric Films Imprinted with Dendritic Spheres. Nat. Mater. 2005, 4, 147−150. (26) Meador, M. A. B.; Malow, E. J.; Silva, R.; Wright, S.; Quade, D.; Vivod, S. L.; Guo, H.; Guo, J.; Cakmak, M. Mechanically Strong, Flexible Polyimide Aerogels Cross-Linked with Aromatic Triamine. ACS Appl. Mater. Interfaces 2012, 4, 536−544. (27) Eslava, S.; Urrutia, J.; Busawon, A. N.; Baklanov, M. R.; Iacopi, F.; Aldea, S.; Maex, K.; Martens, J. A.; Kirschhock, C. E. A. ZeoliteInspired Low-k Dielectrics Overcoming Limitations of Zeolite Films. J. Am. Chem. Soc. 2008, 130, 17528−17536. (28) Wang, W.-C.; Vora, R. H.; Kang, E.-T.; Neoh, K.-G.; Ong, C.K.; Chen, L.-F. Nanoporous Ultra-Low-k Films Prepared from Fluorinated Polyimide with Grafted Poly(acrylic acid) Side Chains. Adv. Mater. 2004, 16, 54−57. (29) Zhao, G.; Ishizaka, T.; Kasai, H.; Hasegawa, M.; Furukawa, T.; Nakanishi, H.; Oikawa, H. Ultralow-Dielectric-Constant Films Prepared from Hollow Polyimide Nanoparticles Possessing Controllable Core Sizes. Chem. Mater. 2009, 21, 419−424. (30) Krause, B.; Koops, G.-H.; van der Vegt, N. F. A.; Wessling, M.; Wübbenhorst, M.; van Turnhout, J. Ultralow-k Dielectrics Made by Supercritical Foaming of Thin Polymer Films. Adv. Mater. 2002, 14, 1041−1046. (31) Wang, W.; Grozea, D.; Kim, A.; Perovic, D. D.; Ozin, G. A. Vacuum-Assisted Aerosol Deposition of a Low-Dielectric-Constant Periodic Mesoporous Organosilica Film. Adv. Mater. 2010, 22, 99− 102. (32) Lew, C. M.; Li, Z.; Shuang, L.; Hwang, S.-J.; Liu, Y.; Medina, D. I.; Sun, M.; Wang, J.; Davis, M. E.; Yan, Y. S. Pure-Silica-Zeolite MFI and MEL Low-Dielectric-Constant Films with Fluoro-Organic Functionalization. Adv. Funct. Mater. 2008, 18, 3454−3460. (33) Yuan, C.; Jin, K.; Li, K.; Diao, S.; Tong, J.; Fang, Q. NonPorous Low-k Dielectric Films Based on a New Structural Amorphous Fluoropolymer. Adv. Mater. 2013, 25, 4875−4878. (34) Wang, J.; Zhou, J.; Jin, K.; Wang, L.; Sun, J.; Fang, Q. A New Fluorinated Polysiloxane with Good Optical Properties and Low Dielectric Constant at High Frequency Based on Easily Available Tetraethoxysilane (TEOS). Macromolecules 2017, 50, 9394−9402. (35) Zhang, K.; Han, L.; Froimowicz, P.; Ishida, H. A Smart Latent Catalyst Containing o-Trifluoroacetamide Functional Benzoxazine: Precursor for Low Temperature Formation of Very High Performance Polybenzoxazole with Low Dielectric Constant and High Thermal Stability. Macromolecules 2017, 50, 6552−6560. (36) Chern, Y.-T.; Shiue, H.-C. Low Dielectric Constants of Soluble Polyimides Based on Adamantane. Macromolecules 1997, 30, 4646− 4651. (37) Chern, Y.-T.; Shiue, H.-C. High Subglass Transition Temperatures and Low Dielectric Constants of Polyimides Derived from 4, 9Bis(4-aminophenyl) diamantine. Chem. Mater. 1998, 10, 210−216. (38) Johari, G. P.; Goldstein, M. Viscous Liquids and the Glass Transition. II. Secondary Relaxations in Glasses of Rigid Molecules. J. Chem. Phys. 1970, 53, 2372−2388. (39) Jho, J. Y.; Yee, A. F. Secondary Relaxation Motion in Bisphenol A Polycarbonate. Macromolecules 1991, 24, 1905−1913. (40) Wimberger-Friedl, R.; Schoo, H. F. M. On the Secondary Relaxation of Substituted Bis-A Polycarbonates. Macromolecules 1996, 29, 8871−8874. (41) Ngai, K. L.; Beiner, M. Secondary Relaxation of the Johari− Goldstein Kind in Alkyl Nanodomains. Macromolecules 2004, 37, 8123−8127.

(42) Coburn, J. C.; Soper, P. D.; Auman, B. C. Relaxation Behavior of Polyimides Based on 2, 2′-Disubstituted Benzidines. Macromolecules 1995, 28, 3253−3260. (43) Wilson, D.; Stenzenberger, H. D.; Hergenrother, P. M. Polyimides; Chapman & Hall: London, 1990. (44) Ge, J. J.; Li, C. Y.; Xue, G.; Mann, I. K.; Zhang, D.; Wang, S.-Y.; Harris, F. W.; Cheng, S. Z. D.; Hong, S.-C.; Zhuang, X.; Shen, Y. R. Rubbing-Induced Molecular Reorientation on an Alignment Surface of an Aromatic Polyimide Containing Cyanobiphenyl Side Chains. J. Am. Chem. Soc. 2001, 123, 5768−5776. (45) Lim, H.; Cho, W.-J.; Ha, C.-S.; Ando, S.; Kim, Y.-K.; Park, C.H.; Lee, K. Flexible Organic Electroluminescent Devices Based on Fluorine-Containing Colorless Polyimide Substrates. Adv. Mater. 2002, 14, 1275−1279. (46) Dlubek, G.; Saarinen, K.; Fretwell, H. M. The Temperature Dependence of the Local Free Volume in Polyethylene and Polytetrafluoroethylene: A Positron Lifetime Study. J. Polym. Sci., Part B: Polym. Phys. 1998, 36, 1513−1528. (47) Kirkegaard, P.; Pederson, N. J.; Eldrup, M. M. PATFIT-88. Riso National Laboratory Report No. PM-2724; Risø National Laboratory: Roskilde, Denmark, 1989. (48) Tao, S. J. Positronium Annihilation in Molecular Substances. J. Chem. Phys. 1972, 56, 5499−5510. (49) Eldrup, M.; Lightbody, D.; Sherwood, J. N. The Temperature Dependence of Positron Lifetimes in Solid Pivalic Acid. Chem. Phys. 1981, 63, 51−58. (50) Hougham, G. G.; Jean, Y. C. Relative Contributions of Polarizability and Free Volume in Reduction of Refractive Index and Dielectric Constant with Fluorine Substitution in Polyimides by Positron Annihilation Spectroscopy. Macromol. Chem. Phys. 2014, 215, 103−110.

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