Characterization of Electronic Transitions in Polyimide Films Based on

J. Phys. Chem. B 2009, 113, 8835–8846

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Characterization of Electronic Transitions in Polyimide Films Based on Spectral Variations Induced by Hydrostatic Pressures up to 400 MPa Junji Wakita and Shinji Ando* Department of Chemistry and Materials Science, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8552, Japan ReceiVed: March 24, 2009; ReVised Manuscript ReceiVed: May 13, 2009

To clarify the nature of optical absorptions in polyimides (PIs), the ultraviolet-visible optical absorption spectra of PI thin films were observed at high pressures up to 400 MPa using a custom-built hydrostatic pressure optical cell. A pressure-induced bathochromic shift with increasing bandwidth was observed in the locally excited (LE) absorption band for s-BPDA/DCHM PI (poly(4,4′-dicyclohexylmethylene biphenyltetracarboximide), which is related to increases in van der Waals interactions due to decreased intermolecular distances. A pressure-induced increase in absorbance was observed for the charge transfer (CT) absorption band of PMDA/ODA PI (poly(4,4′-oxidiphenylene pyromellitimide) and PMDA/TFDB PI (poly(2,2′bis(trifluoromethyl)-4,4′-biphenylene pyromellitimide), which indicates that the bands are assignable to intermolecular CT transitions. On the other hand, a pressure-induced bathochromic shift without an increase in absorbance was observed for the CT band of s-BPDA/PDA PI (poly(p-phenylene biphenyltetracarboximide), which indicates that the band is assignable to intramolecular CT transitions. These characteristic changes observed in pressure-induced variations can be used to characterize absorption bands at longer wavelengths in PIs. 1. Introduction The fully aromatic polyimide (PI) derived from pyromellitic dianhydride and bis(4-aminophenyl)ether (PMDA/ODA) and that from 3,3′,4,4′-biphenyltetracarboxylic dianhydride and p-phenylene diamine (s-BPDA/PDA) are known as high performance engineering plastics exhibiting high thermal and chemical stability, flame resistance, radiation resistance, mechanical strength, and good flexibility.1 They have been widely used in the aerospace, electric, and electronic industries. Recently, fluorinated PIs and semiaromatic PIs have been attracting much attention as new classes of electronic and optical material due to their colorlessness, high transparency, and low refractive indices.2-4 For example, they have been applied to electronic insulators with low dielectric constants5 and optical waveguides with low optical losses in the visible and near-IR regions.6 For further developing novel engineering plastics, it is mandatory to understand the nature of optical absorptions and the refractive index dispersion of PIs at the molecular level. It has been shown that two kinds of one-electron transitions occur in aromatic and semiaromatic PIs.7-13 The first one is the locally excited (LE) transition occurring between the occupied and unoccupied molecular orbitals (MOs) which are located around the dianhydride moiety, including the imide ring structure.12 Hasegawa and co-workers12 measured the absorption spectra of various model compounds of PIs in the solution state, and reported that the LE transition can be assigned to the π f π* transition occurring in the imide ring. This type of transition is widely observed in both fully aromatic and semiaromatic PIs. The second one is the charge transfer (CT) transition excited from MOs located around the diamine moiety to those around the dianhydride moiety. It is known that the CT transition is significantly influenced by the electron-donating property of * To whom correspondence should be addressed. E-mail: sando@ polymer.titech.ac.jp.

diamine and the electron-accepting property of dianhydride.13 CT transitions accompanied by electron transfer are commonly observed in fully aromatic PIs.7-12 It was found that intra- and intermolecular CT transitions can occur in PI films.8-11 Previously, Ishida and co-workers8 reported that an intramolecular CT absorption band was observed near the absorption edge at around 400 nm in a thin film of PMDA/ ODA PI, and the band could be assigned using the absorption spectrum of a corresponding model compound: N,N′-bis(phenoxyphenyl) pyromellitic imide. In particular, they concluded that the observed CT absorption band was attributable to an intramolecular CT transition due to the fact that the absorbance of the shoulder peak at 371 nm was linearly correlated with the concentration. In contrast, Erskine and co-workers9 measured pressure-induced variations in the optical transmission spectra of PMDA/ODA. A diamond anvil cell was utilized in their experiments, in which the pressure was raised up to 12 GPa. They concluded that intermolecular CT transitions exist in the PI because a significant bathochromic shift of the absorption edges was caused by pressurization. They tentatively ascribed the bathochromic shift to the enhancement of the CT interactions because the decrease in the intermolecular distances at elevated pressures should intensify the intermolecular CT interactions. Moreover, Hasegawa and co-workers10,11 reported that the intensity of CT fluorescence was enhanced by high temperature annealing of a thin film of s-BPDA/PDA PI, which is due to the enhancement of the intermolecular CT interactions by changes in the molecular aggregation states. The above results clearly indicate that not only the chemical structure but also the variations in the intermolecular interactions caused by pressurization or annealing significantly affect the optical properties of PI thin films. The interatomic and/or intermolecular distances in chemical substances affect intermolecular interactions such as electrostatic, dipolar-dipolar, hydrogen-bonding, van der Waals, and

10.1021/jp902679g CCC: $40.75  2009 American Chemical Society Published on Web 06/08/2009

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CT interactions. Pressure is a versatile parameter to perturb such intermolecular interactions, in particular for small molecules and polymers in the solid state. To investigate the influence of intermolecular interactions on molecular structures and physical properties in the solid state, a large number of optical measurements have been made under high pressure for molecular crystals and polymers. For instance, ultraviolet-visible (UV/ vis) absorption and fluorescence spectra,14-22 IR and Raman spectra,23-28 X-ray diffraction,29,30 and refractive index measurements31,32 have been carried out. It was found by Nicol14 that bathochromic shifts of the absorption and fluorescence spectra of anthracene dispersed in poly(methylmethacrylate) (PMMA) were induced by hydrostatic compression. It was shown by Gupta and co-workers19 that nonhydrostatic compression induced an excimer emission at around 550 nm in anthracene crystal, which is related to an increase in the crystal defects. Drickamer and co-workers16,20-22 reported the pressure-induced variations in the UV/vis absorption and fluorescence spectra of small molecules where either twisted intramolecular CT (TICT) or excited-state intramolecular proton transfer (ESIPT) was observed. The decreases in the TICT or ESIPT fluorescence intensities were attributed to the prohibition of TICT and ESIPT at elevated pressures. Webster and Batchelder17 measured pressure-induced variations in the UV/vis absorption and fluorescence spectra for poly(p-phenylene vinylene). The bathochromic shift and decrease in fluorescence intensities with increasing pressures were ascribed to the formation of excimer sites at elevated pressures. These results demonstrate that intermolecular interactions are significantly changed by elevating pressures, resulting in variations in optical absorption and fluorescence spectra. To the best of our knowledge, however, the pressure dependence of LE and CT transitions in PIs, and the effects of intermolecular interactions on the optical absorptions of PI thin films, have not been examined in detail so far. In this study, we report on pressure-induced variations in the absorption spectra of PI thin films, in particular the pressure dependence of LE and CT transitions, in order to clarify the nature of optical absorptions in PI thin films at the molecular level. 2. Experimental Section Materials. Pyromellitic dianhydride (PMDA) purchased from Kanto Chemical Co., Inc., was dried and purified by sublimation under reduced pressure. 3,4,3′,4′-Biphenyltetracarboxylic dianhydride (s-BPDA) from Wako Pure Chemical Industries, Ltd., was dried at 170 °C for 12 h under reduced pressure. pPhenylenediamine (PDA) and 4,4-diaminodiphenyl ether (ODA) from Wako Pure Chemical Industries, Ltd., were recyrstallized from tetrahydrofuran followed by sublimation under reduced pressure. 2,2′-Bis(trifluoromethyl)-4,4′-diaminobiphenyldiamine (TFDB) supplied by Central Glass Co., Ltd. was used as received. 4,4′-Diaminocyclohexylmethane (DCHM) purchased from Tokyo Kasei Kogyo Co., Ltd., was recystallized from n-hexane and sublimed under reduced pressure. N,O-Bis(trimethylsilyl)trifluoroacetamide (99+%, BSTFA) and N,N-dimethylacetamide (anhydrous, DMAc) purchased from Aldrich were used without further purification. Preparation of Polyimide Films. The molecular structures of PIs used in this study are shown in Chart 1. The precursors of aromatic PIs, poly(amic acid)s (PAAs), were prepared by mixing equimolar amounts of dianhydride and diamine in a DMAc solution under dry nitrogen. The PAA solutions were stirred at room temperature for 48 h. The precursors of semiaromatic PIs, poly(amic acid) silyleter (PASE), were

Wakita and Ando CHART 1: Structures of the Polyimides (PIs) and the Corresponding Model Compounds Used for DFT Calculations

prepared by the in situ silyation method reported by Matsumoto33 and Oishi.34,35 For instance, DCHM was dissolved in DMAc and stirred for a few minutes, and then, a 1.05 molar amount of BSTFA was slowly added. An equimolar amount of dianhydride was then added and stirred at room temperature for 48 h to give a PASE solution. Trimethylsilyated amino groups of diamines can avoid salt formation between unreacted amino groups and the carboxyl groups of dianhydride moieties. In general, PAA and PASE solutions become viscous after stirring for several hours, depending on the degree of polymerization and the rigidity of the molecular structures. PI films were prepared by thermal imidization of the corresponding PAA or PASE precursors. The solutions were spin-coated onto fused silica substrates (12 mm × 12 mm, 1 mm thick), followed by soft-baking at 70 °C for 1 h and subsequent thermal imidization by a one-step imidization protocol: the final curing conditions were 350 °C/1.5 h and 300 °C/1.5 h for aromatic and semiaromatic PIs, respectively. The heating rate was 4.6 °C/ min from 70 °C to the final curing temperatures, and all curing procedures were conducted under dry nitrogen flow. Measurements. The UV/vis absorption spectra of PI films formed on silica substrates were measured by a Hitachi U-3500 spectrophotometer. A silica substrate without PI film was used as a reference. The measurements of the UV/vis spectra were carried out under various high pressures using a custom-built hydrostatic pressure optical cell designed and manufactured by TERAMECS Co., Ltd. The schematic cross section and the top view of the high pressure optical cell are shown in Figure 1a and b, respectively. The cell body, having three optical windows, plumbing pipes, and connecters, is made of stainless steel (SUS630H1025). The pressure-proof windows are made of 9.0 mmφ and 7 mm thick sapphire disks. The temperature inside the cell was set at 21-22 °C by circulating water at controlled temperatures. The inside pressure up to 400 MPa was generated by a hand-pump using distilled water as a pressure medium. A strain-gage-type pressure transducer (Minebea, STD-500MP) with a digital indicator (Minebea, CSD-701B-74) was used to monitor the pressure inside. Before the measurements of UV/ vis spectra, a pressure up to 20 MPa was applied and gradually released to remove air bubbles attached to the sapphire windows because small bubbles may dislocate the baseline under high pressure. The UV/vis spectra were measured at each pressure after 5 min intervals, followed by changing the pressure. To reduce the shock of pressure and hysteresis effects, all measurements were conducted in the process of releasing pressure. To remove the influence of the spectral changes in the silica

Characterization of Electronic Transitions in PI Films

J. Phys. Chem. B, Vol. 113, No. 26, 2009 8837

Figure 2. Optical absorption spectra of PI thin films at atmospheric pressure.

Figure 1. (a) Schematic cross section of a high pressure cell under pressures up to 400 MPa. (b) Top view of the high pressure cell.

substrate, the absorption spectra of a substrate measured at each pressure were subtracted from the observed spectra of the PIs. The film thicknesses of the PIs were measured with a sensingpin-type surface profilometer (DEKTAK-III). Quantum Chemical Calculation. The density functional theory (DFT) with the three-parameter Becke-style hybrid functional (B3LYP)36-38 was adopted for the calculations of the electronic structures and spectroscopic properties of the PIs and their source materials. The 6-311G(d) basis set was utilized for the geometry optimizations, while the 6-311++G(d,p) basis set was used for the calculation of the oscillator strengths and ionization potential of the diamines. All calculations were performed with the Gaussian 0339 program package. For reproducing the shapes of the experimental absorption spectra, each calculated transition was replaced by a Gaussian broadening function with a full width at half-maximum (fwhm) of 0.3 eV. The calculated absorbance was represented by an oscillator strength divided by a van der Waals volume (nm3) of molecules.40-42 The van der Waals volumes were calculated on the basis of Slonimski’s method43 using the optimized geometries, in which van der Waals radii of atoms reported by Bondi44 were used. The molecular structures of the model compounds devoted to the DFT calculation are depicted in Chart 1. 3. Results and Discussion 3.1. Absorptions at Atmospheric Pressure. Figure 2 shows the absorption spectra of thin films of s-BPDA/DCHM (4.1 µm thick), PMDA/ODA (0.8 µm), PMDA/TFDB (0.8 µm), and s-BPDA/PDA (0.7 µm) PIs measured at atmospheric pressure. Figure 3 exhibits the calculated absorption spectra of the model compounds corresponding to the PIs. The magnified spectra around the wavelength (λ) at 450 nm are shown in the inset. The details of the one-electron transitions from the ground state (S0) to excited states around the absorption edge, such as vertical excitation wavelengths, oscillator strengths, and related molec-

Figure 3. Calculated optical absorption spectra of model compounds. The inset shows a magnified representation at around 450 nm.

ular orbitals of the four model compounds, are listed in Tables 1-4. In addition, the spatial distributions of the second highest and highest occupied molecular orbitals (HOMO-1 and HOMO) and the lowest and second lowest unoccupied molecular orbitals (LUMO and LUMO+1) of the model compounds are depicted in Figure 4. The semiaromatic s-BPDA/DCHM exhibits optical absorption at wavelengths shorter than 400 nm without tailing to longer wavelengths, and the calculated transitions of the corresponding model compound, m(BP/DC), are located at wavelengths shorter than 335 nm. From Table 1 and Figure 4, all MOs involved in the transitions (S0 f Si) are localized around the dianhydride moiety consisting of central aromatic rings and imide rings. This indicates that these transitions are readily assigned to LE transitions. Since the large majority of the calculated transitions below 300 nm are also assigned to LE transitions (see Table S1 in the Supporting Information), the major contribution of the observed absorption in the UV region of s-BPDA/DCHM originates from the LE transitions occurring within the dianhydride moiety. This agrees with the previous results of PI model compounds.12 In contrast, the UV/vis spectrum of PMDA/ODA shows strong absorption at wavelengths shorter than 360 nm, with extensive tailing from 360 to 520 nm. The calculated spectral shape of m(PM/OD) agrees well with the observed UV/vis spectrum: it shows strong absorption at wavelengths shorter than 400 nm with extensive tailing from 500 to 700 nm. As depicted in Figure 4, the HOMO is localized around the diamine moiety, including the imide nitrogen, but the LUMO is localized around the dianhydride moiety. Thereby, the HOMO f LUMO transitions at 520 nm can be interpreted as a direct CT excitation, which can be characterized by an electron transfer from the electron-donating diamine moiety to the electron-accepting dianhydride moiety. Considering the one-electron transitions calculated for m(PM/OD) (see Table 2), the other transitions

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TABLE 1: Transition Energies, Oscillator Strengths, and Character of S0 f Si Transitions in m(BP/DC)a,b state

transition wavelength (nm)

oscillator strength

orbitals

character of transition

contributionc

1

336.6

0.2263

2

330.1

0.0017

3

329.6

0.0039

4

313.6

0.0008

5

299.0

0.0009

HOMO f LUMO HOMO-1 f LUMO+1 HOMO-3 f LUMO HOMO-2 f LUMO HOMO-3 f LUMO+1 HOMO-2 f LUMO+1 HOMO-2 f LUMO HOMO-3 f LUMO HOMO-2 f LUMO+1 HOMO-3 f LUMO+1 HOMO f LUMO+1 HOMO-1 f LUMO HOMO-1 f LUMO HOMO f LUMO+1 HOMO-11 f LUMO HOMO-12 f LUMO+1 HOMO-7 f LUMO HOMO-5 f LUMO HOMO f LUMO+3 HOMO-8 f LUMO

LE LE LE LE LE LE LE LE LE LE LE LE LE LE CT LE LE CT LE LE

0.96 0.04 0.54 0.18 0.17 0.11 0.52 0.19 0.18 0.11 0.68 0.32 0.49 0.25 0.08 0.04 0.04 0.04 0.03 0.03

a TD-DFT calculations at the [B3LYP/6-311G++(d,p)] level. b Prohibited transitions are not listed. c According to the time-dependent perturbation theory, the wave function of the system Ψ is expressed as Ψ ) ∑k ck exp(-iEkt/p)Φk, where ck denotes the expansion coefficient and Φk is the eigenfunction of the time-independent Schro¨dinger equation having eigenvalues Ek. Values of ck larger than 0.1 were obtained by the TD-DFT calculations, and the contribution of each Φk value to the electronic transition can be approximated by the normalized expansion coefficient, which is defined as ci2/∑i ck2.

Figure 4. HOMO-1, HOMO, LUMO, and LUMO+1 orbitals of model compounds (TD-DFT method at the B3LYP/6-311++G(d,p) level). HOMO-1 is the second highest occupied orbital, HOMO the highest occupied orbital, LUMO the lowest occupied orbital, and LUMO+1 the second lowest occupied orbital.

TABLE 2: Transition Energies, Oscillator Strengths, and Character of S0 f Si Transitions in m(PM/OD)a,b state


oscillator strength

orbitals


contributionc

1 3

524.4 382.3

0.0016 0.0008

5

362.6

0.0011

7 8

358.6 355.3

0.4253 0.0002

HOMO f LUMO HOMO-2 f LUMO HOMO f LUMO HOMO-4 f LUMO HOMO-6 f LUMO HOMO-5 f LUMO HOMO f LUMO+1 HOMO-8 f LUMO HOMO-9 f LUMO+2

CT CT CT CT CT CT CT LE LE

1.00 0.98 0.02 0.50 0.44 0.06 1.00 0.96 0.04

a TD-DFT calculations at the [B3LYP/6-311G++(d,p)] level. b Prohibited transitions are not listed. c Normalized expansion coefficient (see footnote of Table 1).

appearing from 350 to 380 nm are also attributable to CT transitions. Since the wavelength range of the observed absorption tailing agrees with that of the calculated CT excitations, the tailing is readily assigned to a CT absorption. This agrees with the previous results of PI model compounds.8 On the other hand, the electronic transitions involved in the absorption band

at the corresponding wavelengths for PMDA/ODA are principally a mixture of LE and CT transitions because the calculated transitions appearing at wavelengths shorter than 350 nm for m(PM/OD) are assignable to both LE and CT transitions (see Table S2 in the Supporting Information). This is typical for the strong absorptions appearing in the UV region of PIs.



TABLE 3: Transition Energies, Oscillator Strengths, and Character of S0 f Si Transitions in m(PM/TF)a,b state


oscillator strength

orbitals


contributionc

1

425.3

0.0023

2

396.5

0.0001

3

355.8

0.0003

4

348.9

0.0001

7

338.8

0.0001

HOMO f LUMO HOMO-2 f LUMO HOMO-1 f LUMO HOMO-3 f LUMO HOMO-8 f LUMO HOMO-2 f LUMO HOMO-9 f LUMO+2 HOMO-2 f LUMO HOMO-6 f LUMO HOMO-8 f LUMO HOMO-4 f LUMO HOMO-6 f LUMO HOMO-4 f LUMO HOMO-2 f LUMO HOMO-8 f LUMO+2

CT CT CT CT LE CT LE CT CT LE CT CT CT CT LE

0.97 0.03 0.96 0.04 0.83 0.13 0.04 0.61 0.25 0.10 0.04 0.42 0.31 0.24 0.03


TABLE 4: Transition Energies, Oscillator Strengths, and Character of S0 f Si Transitions in m(BP/PD)a,b state


oscillator strength

orbitals


contributionc

1

387.0

0.0465

2

378.4

0.005

4

336.3

0.0006

5

334.3

0.0025

6

330.3

0.0257

HOMO f LUMO HOMO-1 f LUMO+1 HOMO-1 f LUMO HOMO f LUMO+1 HOMO-3 f LUMO HOMO-2 f LUMO HOMO-2 f LUMO+1 HOMO-3 f LUMO+1 HOMO f LUMO+1 HOMO-1 f LUMO HOMO-2 f LUMO HOMO-4 f LUMO+1 HOMO-6 f LUMO HOMO-5 f LUMO+1 HOMO-4 f LUMO HOMO-1 f LUMO+1

CT CT CT CT CT CT CT CT CT CT CT LE LE LE LE CT

0.90 0.10 0.83 0.17 0.74 0.13 0.09 0.03 0.77 0.17 0.03 0.03 0.59 0.28 0.10 0.03


PMDA/TFDB shows strong absorption at wavelengths shorter than 350 nm with extensive tailing from 350 to 420 nm. Considering the one-electron transitions calculated for m(PM/ TF) and the spatial distribution of the related MOs (see Table 3 and Figure 4, as well as Table S3 in the Supporting Information), the transitions below 350 nm are a mixture of LE and CT transitions, and those involved in the absorption tailing of PMDA/TFDB are identified as CT transitions, similar to the case of PMDA/ODA. However, the CT transition wavelength of PMDA/TFDB (380 nm) is shorter than that of PMDA/ODA (440 nm). The calculated absorption spectrum of m(PM/TF) shows tailing around 450 nm, which is also shorter than that of m(PM/OD) (550 nm). Mulliken’s CT complex theory45 can explain the higher CT transition energy of PMDA/ TFDB than that of PMDA/ODA. According to the theory, the transition energy (∆E) is written as

∆E ∝ Ip(D) - Ea(A)

(1)

where Ip(D) and Ea(A) are the ionization potential of the donor molecule and the electron affinity of the acceptor molecule, respectively. Equation 1 indicates that the CT transition energy can be determined by the Ip(D) of diamine, and a larger Ip(D) results in a higher transition energy (i.e., hypochromic shift) if the Ea(A) is constant. The electron-donating moiety of PIs is

the diamine moiety, as mentioned already, and the Ip(D) of TFDB (7.55 eV) is higher than that of ODA (6.80 eV). Thus, PMDA/TFDB exhibited absorption tailing at a shorter wavelength than PMDA/ODA. The higher Ip(D) of TFDB originates from the lowered HOMO due to the electron-withdrawing -CF3 groups which are directly attached to the skeletal biphenyl structure. In contrast to the cases of PMDA/ODA and PMDA/TFDB, no apparent tailing is observed near the absorption edge of s-BPDA/PDA, and strong absorption at wavelengths shorter than 400 nm is observed. The calculated absorption spectrum of m(BP/PD), however, shows tailing at around 400 nm. Considering the one-electron transitions calculated for m(BP/PD) and the spatial distribution of the related MOs (see Table 4 and Figure 4), the HOMO and HOMO-1 are mainly localized around the diamine moiety, whereas the LUMO and LUMO+1 are localized around the dianhydride moiety. Thus, the transitions at 387 and 378 nm (S0 f S1 and S0 f S2 transitions) can be identified as direct CT excitations. This suggests that the CT transition band in s-BPDA/PDA should exist at around 400 nm, which agrees well with the previous results.10 In contrast, the electronic transitions involved in the absorption band at the corresponding wavelengths for s-BPDA/PDA are principally a mixture of LE and CT transitions because the calculated transitions appearing at wavelengths shorter than 340 nm for

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Figure 5. Calculated Gaussian function, difference from standard, and first derivative: (a) increase in absorbance; (b) bathochromic shifts; (c) increase in absorbance with a bathochromic shift; (d) bathochromic shift with an increase in fwhm.

m(BP/PD) are assignable to both LE and CT transitions (see Table S4 in the Supporting Information). Hence, the absence of tailing, which is assignable to CT transitions, could be explained by the overlap of the CT band with the strong absorptions of the mixture band of LE and CT transitions in the UV region.

3.2. Simulated Variations in the Differential and First Derivative of Gaussian Function. Several reports have demonstrated that optical properties, such as absorbance (absorption intensity), spectral bandwidth represented by a full width at halfmaximum (fwhm), and peak positions of absorption spectra, are significantly influenced by hydrostatic pressure.14-22,46



TABLE 5: Variations in Differential (∆) and First Derivative (D) of Gaussian Function in Cases A-D (See Text)a ∆

∂

case

location

intensity

location

intensity

A B C D E

( f f f f

v v v v v

( f f f f

v ( V v V

(, unchanged; v, increase; V, decrease; f, shift to longer wavelengths. a

Possible variations for an optical absorption band originating from one-electron transitions are classified by the following four cases: (Case A) An increase in absorbance (Case B) A bathochromic shift (Case C) An increase in absorbance with a bathochromic shift (Case D) A bathochromic shift with an increase in fwhm Unfortunately, all PI films investigated in the present study exhibit no distinctive absorption peaks due to the saturated absorbance in the UV region (see Figure 2), suggesting serious problems in characterizing variations in the absorption spectra under high pressure. Previously, Yoshizawa et al.47 analyzed changes in absorption spectra due to external filed effects using differential and first derivative spectra, which are sensitive to changes in the original spectrum and exhibit more apparent changes. In addition, it was shown48 that an absorption band was expressed by the Gaussian function. These analytical methods were applied to the present study of hydrostatic pressure. In order to elucidate the correlation between the variations in the absorption spectrum and those in the differential and first derivative spectra, a Gaussian broadening function was simulated in cases A-D. Equation 2 shows the general formulas of the Gaussian function:

[ ( Bx - C) ]

y ) A exp -

2

(2)

where A is the peak height (intensity), B the bandwidth (fwhm), and C the peak position. Here, the standard Gaussian function is defined with a parameter set of (A, B, C) ) (1.0, 4.0, 0.0), and the corresponding coefficients are varied as follows: A ) 1.0, 1.1, 1.2, 1.3, 1.4 B ) 4.0, 4.5, 5.0, 5.5, 6.0 C ) 0.0, 0.2, 0.4, 0.6, 0.8 The standard Gaussian function, the difference from the standard, i.e., (A-B-C)-(1.0, 4.0, 0.0), and the first derivative spectra, i.e., ∂(A-B-C)/∂x, were calculated with the above coefficients, and were conveniently abbreviated as (A-B-C), ∆(A-B-C), and ∂(A-B-C), respectively. All calculated results are shown in Figure 5, and the characteristic changes of the line shapes are summarized in Table 5. At first glance, the variations in the peak intensities and locations of ∆(A-B-C) and ∂(A-B-C) are different in each case. (Case A) Increase in absorbance (see Figure 5a): All peaks for ∆(A-B-C) stay at the same peak positions as (A-B-C). A positive and a negative peak in ∂(A-B-C) appear in the leftand right-hand sides of the peak position of (A-B-C). With

increasing absorbance, the peak intensities are enhanced in the cases of both ∆(A-B-C) and ∂(A-B-C) without peak shifts. (Case B) Bathochromic shifts (see Figure 5b): A positive and a negative peak for ∆(A-B-C) and ∂(A-B-C) appear on both sides of the peak position of (A-B-C). With an increase in the bathochromic shifts in (A-B-C), bathochromic shifts with enhanced peak intensities are observed for ∆(A-B-C), whereas only bathochromic shifts are observed for ∂(A-B-C). (Case C) Increase in absorbance with bathochromic shifts (see Figure 5c): A positive and a negative peak for ∆(A-B-C) and ∂(A-B-C) appear on both the sides of the peak position of (A-B-C). With an increase in the absorbance and bathochromic shift in (A-B-C), bathochromic shifts with enhanced peak intensities are observed for ∆(A-B-C), and the magnitude of the increase in intensity for the right-hand peak is much larger than that of the left-hand peak in ∆(A-B-C). Bathochromic shifts with enhanced peak intensities are also observed for ∂(A-B-C). (Case D) Bathochromic shifts with increases in fwhm (see Figure 5d): A positive and a negative peak for ∆(A-B-C) and ∂(A-B-C) appear on both the sides of the peak position of (A-B-C). With increasing absorbance and fwhm, bathochromic shifts with enhanced peak intensities are observed for ∆(A-B-C), and the magnitude of the increase in intensity for the right-hand peak is larger than that of the left-hand peak in ∆(A-B-C). On the other hand, bathochromic shifts with reduced peak intensities are observed for ∂(A-B-C). The above simulations fully clarify that the spectral variations in peak intensities and displacements for ∆(A-B-C) and ∂(A-B-C) are highly sensitive to those in the original spectrum (A-B-C). Accordingly, it is possible to characterize the variations in absorption spectra under high pressure by examining the differential and the first derivative spectra. 3.3. Variations in LE Absorption at High Pressure. Figure 6 illustrates the experimental pressure-induced changes in the absorption (a), the differential (b), and the first derivative (c) spectra of a semiaromatic s-BPDA/DCHM film. Only the longer wavelength regions (outskirts) of the absorption spectra of PIs were observed due to the very strong π f π* LE absorptions appearing in the UV region. Hence, as explained in the previous section, in order to clarify the changes in the absorption spectra, the experimental variations in the differential and the first derivative spectra are compared with those simulated in the range of x > 0. Since the absorption band observed for s-BPDA/ DCHM was assigned to the LE transition (see section 3.1), the spectral changes shown in Figure 6 exhibit pressure-induced changes in the LE band. With increasing pressure, the positive peak at around 365 nm in the differential spectra (see Figure 6b) was shifted to longer wavelengths with increasing intensity. This bathochromic shift can also be verified by the displacement of the normalized differential spectra (see Figure S1 in the Supporting Information). In the first derivative spectra (see Figure 6c), the negative peak at around 365 nm was shifted to longer wavelengths with decreasing intensity. Since these spectral variations agree well with those in case D (see Figure 5d), it is expected that bathochromic shifts and an increase in bandwidth (fwhm) simultaneously occurred for s-BPDA/DCHM with increasing pressure. The pressure-induced bathochromic shift is attributable to an enhancement of the van der Waals interactions, as represented by the dispersion force,19,46 in a similar case where the transition energy of the isolated molecules in a vacuum is higher than that in a solution (solvent effect). The solvent effect is generally caused by an enhancement of van der Waals interactions, which is due to increases in the dielectric constant and the polarizability

8842


Wakita and Ando

∆Ehigh ) εex,high - εgr,high

′ ′ ) ∆Eatm - (Wex,high - Wgr,high ) ′ ′ ) + (∆Wex - ∆Wgr)] ) ∆Eatm - [(Wex,atm - Wgr,atm (4) where

′ εex,high ) εgr,atm - Wex,high ′ εgr,high ) εgr,atm - Wgr,high ∆Eatm ) εex,atm - εgr,atm

′ ) Watm ′ + ∆W Whigh W′ex ∝ Cex/rn > 0,

(

∆W ∝ C

Figure 6. Pressure dependence of (a) optical absorption spectra, (b) absorption differential spectra, and (c) first derivative spectra for s-BPDA/DCHM thin film.

of solute and solvent molecules.49 The transition energy in solution (∆Esol) is written as

∆Esol ) εex,sol - εgr,sol where

(3)

) ∆Evac - (Wex - Wgr) εex,sol ) εex,vac - Wex εgr,sol ) εgr,vac - Wgr ∆Evac ) εex,vac - εgr,vac Wex ∝ Cex/rn > 0,

Wgr ∝ Cgr/rn > 0

in which the subscripts “ex” and “gr” indicate the “excited” and “ground” states, respectively, ∆Evac the transition energy in vacuum, εsol the potential energy in solution, εvac the potential energy in vacuum, W the stabilized energy in solution derived from the van der Waals interactions, C the coefficient which is related to the dipole moment and polarizability of the solute and solvent molecules, and r the intermolecular distance. Note that Cex is larger than Cgr because the dipole moment and polarizability are significantly enhanced in the excited state; for example, the value of the polarizability of benzene was reported to increase by 25-30% in the excited state.50 This means that the value of Wex is larger than that of Wgr, i.e., (Wex - Wgr) > 0. Hence, the transition energy in solution (∆Esol) is lower than that in vacuum (∆Evac). On analogy with eq 3, the transition energy under high pressure (∆Ehigh) is written as

′ ∝ Cgr/rn > 0 Wgr 1 n rhigh

-

1 n ratm

)

in which the subscripts “high” and “atm” refer to “high” and “atmospheric” pressure, respectively, r the intermolecular distance, ∆E the transition energy, ε the potential energy, W′ the stabilized energy in the solid state caused by the van der Waals interactions, C the coefficient which is related to the dipole moment and polarizability of PIs, and ∆W the changes in W′ under high pressure. ′ - Wgr,atm ′ ) in eq 4 is On analogy with eq 3, the value of (Wex,atm positive. Note that the pressure-induced decreases in r should enhance W′ex and W′gr, i.e., ∆Wex, ∆Wgr > 0, because W′ is inversely proportional to the nth power of r. Since Cex is expected to be larger than Cgr, as explained above, ∆Wex is larger than ∆Wgr, i.e., ′ - Wgr,high ′ ) in eq (∆Wex - ∆Wgr) > 0. Hence, the value of (Wex,high 4 should be positive, resulting in a decrease in the transition energy (bathochromic shift) under high pressure. In addition, the increase in the bandwidth (fwhm) observed for s-BPDA/DCHM can be explained by the broadening of the distribution in the intermolecular interactions caused by the increase in the local inhomogeneity in the intermolecular aggregation states under high pressure.19 The enhancement of the inhomogeneity may be due to the bulky and bent structure of s-BPDA/DCHM (see Figure S2 in the Supporting Information), which is unfavorable for making ordered structures. 3.4. Variations in CT Transition Bands under High Pressure. The pressure-induced changes in the absorption, differential, and first derivative spectra are shown in Figures 7-9 for PMDA/ODA, PMDA/TFDB, and s-BPDA/PDA films, respectively. The absorption band of PMDA/ODA (see Figure 7a) is gradually shifted to longer wavelengths with increasing pressure. The displacement of the absorption edge (absorbance ) 0.05) is ca. 15 nm from 0.1 to 409 MPa, which corresponds to a reduction in the band gap of 0.0769 eV. However, it is difficult to ascertain whether the variations in the spectral changes were caused by an absorption enhancement (along the vertical axis) or a bathochromic shift of the absorption band (along the horizontal axis). Hence, similar to the cases of s-BPDA/DCHM, the variations in the differential and first derivative spectra were examined to clarify the variations in the absorption spectra. In the differential spectra (see Figure 7b), a significant enhancement of the peak intensities without peak shifts is observed at 410 nm. The absence of peak shifts can be verified by their normalized differential spectra (see Figure S3 in the Supporting Information). In the first derivative spectra (see Figure 7c), no distinct peaks are observed, but some



Figure 7. Pressure dependence of (a) optical absorption spectra, (b) absorption differential spectra, and (c) first derivative spectra for PMDA/ ODA thin film.

Figure 8. Pressure dependence of (a) optical absorption spectra, (b) absorption differential spectra, and (c) first derivative spectra for PMDA/ TFDB thin film.

folding points are observed in the range from 400 to 500 nm. The folding points are stable and their peak positions are independent of pressure, whereas their intensities in the range from 420 to 500 nm are enhanced with increasing pressure. Since the changes in the differential and first derivative spectra at around 400 nm (where the CT absorption band exists)8,9 agree well with those in case A (with an increase in absorbance), as shown in Figure 5a, the pressure-induced spectral changes are caused by the enhancement of the absorbance in the CT band. From Figure 8, the differential spectra of PMDA/TFDB show significant enhancement of the peak intensities at 370 nm without peak shifts, and the first derivative spectra exhibit folding points in the range from 370 to 420 nm. The positions of the folding points in the first derivative spectra are independent of pressure and their intensities at wavelengths from 370 to 420 nm are enhanced with increasing pressure. Since the changes in the differential and first derivative spectra at around 370 nm where the CT absorption band exists (see Figure 2) agree well with case A, as shown in Figure 5a, the pressureinduced spectral changes observed in PMDA/TFDB are also caused by the enhancement of the absorbance in the CT band. As mentioned before, it was reported that the increase in the bandwidth (fwhm) occurs under high pressure,14-22,46 and the first derivative spectra is sensitive to the changes in fwhm (see section 3.2). However, it is difficult to clarify whether the increase in fwhm occurs or not in PMDA/ODA and PMDA/ TFDB (PMDA-PIs). This is because the variations in the first derivative spectra induced by the increase in absorbance are clearly different from those induced by the increase in fwhm (see Figure 5a and Figure S4 in the Supporting Information). The former causes the enhancement of the peak intensities, but

the latter causes the reduction in the peak intensity. Therefore, if these two changes coincide and the changes of fwhm are small, the spectral changes caused by the variations in fwhm could be offset. Hence, even if the intensities of the first derivative spectra increase, it is nearly impossible to verify that there are no changes in fwhm. From Figure 9, it can be seen that the absorption spectra of s-BPDA/PDA exhibit pressure-induced changes similar to those of PMDA/ODA and PMDA/TFDB. However, it is also difficult to ascertain whether the variations in the spectral changes were caused by an absorption enhancement or a bathochromic shift of the absorption band. The positive peaks at around 370 nm in the differential spectra of s-BPDA/PDA (see Figure 9b) were shifted to longer wavelengths with increasing intensity. In the first derivative spectra (see Figure 9c), the negative peaks at around 370 nm were shifted to longer wavelengths without changes in their intensity. Since the major contribution of the absorption in the UV region for s-BPDA/PDA originates from the LE and CT transitions (see section 3.1), the spectral changes observed in Figure 9b and c indicate pressure-induced changes in the mixture band of the LE and CT transitions. These spectral variations observed in Figure 9 agree well with those in case B (see Figure 5b); hence, bathochromic shifts simultaneously occurred for s-BPDA/PDA with increasing pressure. Unlike s-BPDA/DCHM, no increase in fwhm was observed. This is because the rigid and planar structure of s-BPDA/PDA (see Figure S1 in the Supporting Information) should suppress the broadening of the distribution in intermolecular interactions. Note that, despite the fact that the CT band of s-BPDA/PDA exists at around 400 nm,10,11 no significant enhancement of absorbance was observed and only the bathochromic shift was observed in the CT band at around 400 nm for s-BPDA/PDA.

8844


Wakita and Ando of the dative bond wave function Ψ1(D+-A-) to the no-bond wave function Ψ0(D,A) in the ground state wave function ΨN

ψN ) aψ0(D, A) + bψ1(D+ - A-)

Figure 9. Pressure dependence of (a) optical absorption spectra, (b) absorption differential spectra, and (c) first derivative spectra for s-BPDA/PDA thin film.

These results demonstrate that there are two types of CT transitions in PIs; the first one exhibits pressure-induced enhancement of CT absorption (along the vertical axis), and the second one exhibits pressure-induced bathochromic shifts (along the horizontal axis). The current explanation is that the former variation indicates that the intermolecular CT interaction is enhanced by the pressurization. In contrast, the latter variation shows that enhancement of intramolecular CT interactions does not significantly occur, and the spectral change mainly originates from enhancement of the van der Waals interaction, similar to the LE band, as already discussed in section 3.3. Therefore, it is expected that the intermolecular CT band can be distinguished from the intramolecular CT band with analysis of pressureinduced variations in the CT band. In the following paragraphs, the CT complex theory by Mulliken45,46 is explained to show the origin of the pressure-induced enhancement of the intraand intermolecular CT interactions. Then, the variations in the CT absorption band of s-BPDA/PDA and PMDA-PIs are separately discussed to achieve the above understanding. According to Mulliken’s theory,45,46 the oscillator strength f of the CT transition depends on the overlap Sda- between the appropriate orbital of the donor and acceptor:

√f ≈ eR(b + Sda- / √2)

(5)

f ∝ ∫ ε dν

(6)

where R is the distance between the donor (D) and acceptor (A) moieties, ε and ν are, respectively, the molar absorption coefficient and wavenumber, and b measures the contribution

(7)

The intensification of the CT absorption (ε) is easily visualized as a consequence of the increase in Sda-, i.e., enhancement of the CT interactions. The structural changes that increase the intra- and intermolecular CT absorption are as follows. Intramolecular CT transition: The increase in Sda- due to the decrease in the bond length and the increase in the coplanarity between the dianhydride (electron acceptor) and diamine (electron donor) moieties. Intermolecular CT transition: The increase in Sda- due to the decrease in the intermolecular distance. In the case of s-BPDA/PDA, it was found that it exhibits high molecular orientation parallel to the surface,51 and X-ray diffraction patterns show clear peaks originating from ordered structures parallel and perpendicular to the surface.52,53 In ordered structures, the dianhydride and diamine moieties stack individually and cannot form the intermolecular CT complexes.54 Hence, few intermolecular CT complexes form in s-BPDA/PDA, and the dominant CT interaction in s-BPDA/PDA is the intramolecular CT interaction. However, it is expected that enhancement of Sda- in the intramolecular CT transition does not occur because enhancement of the CT absorption was not observed in s-BPDA/PDA. This indicates that enhancement of the intra- and intermolecular CT interactions contributed less to the spectral change, and the observed bathochromic shift is due to enhancement of the van der Waals interaction. This suggests that a bathochromic shift of the CT band should be observed for PIs in which the intramolecular CT interaction is dominant. In contrast, PMDA-PIs do not exhibit high molecular orientation parallel to the surface,51 and their X-ray diffraction patterns show broad amorphous peaks.55-59 In the amorphous region, the dianhydride and diamine moieties can stack on each other and form intermolecular CT complexes.54 Hence, the intermolecular CT complexes form in PMDA-PIs, and then, both intraand intermolecular CT transitions contribute to their CT absorption bands. It was found by Dlubek and co-workers60 that the free volume in fluoroelastomers can be compressed under high pressure up to 200 MPa. This indicates that the intermolecular distance will be reduced under high pressure; hence, the intermolecular CT interaction is enhanced. In contrast, it is expected that the intramolecular CT absorption would not increase similarly to s-BPDA/PDA. Since PMDA-PIs are composed of the same chemical bonds (CdC, CsN, etc.) as s-BPDA/PDA, the magnitude of the decrease in bond length under high pressure is similar to that of s-BPDA/PDA. In addition, the dihedral angles around the CsN bond of the optimized structures obtained by DFT calculation are close to each othersPMDA/ODA (44.2°), PMDA/TFDB (41.3°), BPDA/ PDA (42.7°)swhich shows that there is no large difference in the steric hindrance around the CsN bond. Thus, assuming that the pressure-induced change in the coplanarity between dianhydride and diamine moieties is determined by the steric hindrance around the CsN bond, the change in the coplanarity of PMDA-PIs is also similar to that of s-BPDA/PDA. Therefore, the variations in Sda- of the intramolecular CT interaction for PMDA-PIs, which is influenced by the bond length and coplanarity described before, are close to those of s-BPDA/ PDA in which the intramolecular CT absorbance does not


Figure 10. Pressure dependence of the peak intensity of differential spectra for PMDA/ODA and PMDA/TFDB thin films.

increase. It is clear from these results that the pressure-induced intensification of the CT absorption in PMDA-PIs is attributed to the enhancement of the intermolecular CT interactions. Actually, the enhancement of the van der Waals interaction should cause a bathochromic shift, but the spectra changes caused by the bathochromic shift should be obscured by the large spectral change due to the increase in absorption. As a result, the pressure-induced enhancement of CT absorption will be mainly observed for PIs in which the intermolecular CT complex exists. The decrease in the intermolecular distance in PMDA-PIs caused by pressurization can be inferred from the increase in the intermolecular CT absorption. As shown in Figure 10, the increase in peak intensities in the differential spectra of PMDA/ ODA is larger than that of PMDA/TFDB. As described above, the intermolecular CT absorption in PIs is enhanced by the increase of Sda- in the intermolecular CT complex, which is caused by the decrease in intermolecular distance. Hence, the larger increase in the CT absorption of PMDA/ODA under high pressure than that of PMDA/TFDB indicates that the pressureinduced reduction in the intermolecular distance of the former is larger than that of the latter. This is because the bulky and less-polarizable trifluoromethyl (-CF3) substitutes in PMDA/ TFDB do not enhance the intermolecular attractive interactions and prevent dense chain packing under high pressure (see Figure S1 in the Supporting Information). 4. Conclusions The pressure-induced variations in the absorption spectra of aromatic and semiaromatic PIs have been measured at atmospheric pressure up to 400 MPa. A semiaromatic s-BPDA/ DCHM exhibited a strong absorption in the UV region without tailing to longer wavelengths. This absorption was assigned to LE transitions based on TD-DFT calculations. On the other hand, PMDA/ODA and PMDA/TFDB showed strong absorptions in the UV region with tailings extending to the visible region at around 400 and 370 nm, respectively. These tailings were assigned to the CT transitions. Although apparent tailing was not observed in s-BPDA/PDA, the TD-DFT indicated that a CT absorption existed at around 400 nm. To examine the characteristic behavior of the pressureinduced variations in the absorption spectra of PIs, the differential ∆(A-B-C) and first derivative ∂(A-B-C) spectra of a Gaussian broadening function (A-B-C) were simulated. The results clarified that the spectral variations in the peak intensities and the displacements in ∆(A-B-C) and ∂(A-B-C) were useful to characterize the variations in the original broadening function.

J. Phys. Chem. B, Vol. 113, No. 26, 2009 8845 As the pressure increases, the long wavelength region of the absorption of s-BPDA/DCHM was gradually shifted to longer wavelengths with increasing bandwidths. The observed bathochromic shift was caused by enhanced intermolecular interactions, such as van der Waals interactions, due to the decrease in intermolecular distances. In addition, the broadening of the absorption band was caused by a broadened distribution of van der Waals interactions under high pressure, which may be due to an increase in the local inhomogeneity in the aggregation states. On the other hand, the CT absorptions of PMDA/ODA and PMDA/TFDB were significantly enhanced with increasing pressure, which was caused by enhancement of the intermolecular CT interactions. In addition, the increase in the CT absorption of PMDA/ODA which is larger than that of PMDA/ TFDB indicates that the magnitude of the pressure-induced decrease in the intermolecular distance of the former is larger than that of the latter. In contrast, a bathochromic shift was observed in s-BPDA/PDA under high pressure, which was due to enhancement of the van der Waals interaction. This suggests that the major part of the CT absorption in s-BPDA/PDA should originate from intramolecular CT transitions. Finally, the assignment of the electronic transitions of PI films can be obtained as follows: (1) LE and CT absorption band: From the difference in the band position and absorbance, a distinction between the LE and CT absorption band was possible. The LE band was observed at a wavelength shorter than 400 nm, and its absorption was strong. In contrast, the CT band was observed at the absorption edge at around 400 nm and its absorption was weak. This assignment is mainly based on the TD-DFT calculation. (2) Intra- and intermolecular CT absorption band: From the difference in the variations in absorption spectra under high pressure, a distinction between the intra- and intermolecular CT absorption band is possible. The intramolecular CT band exhibited a bathochromic shift under high pressure. In contrast, the intermolecular CT band exhibited enhancement of the absorption under high pressure. The variations in the UV-vis spectra under high pressure can be clarified by analyses of the differential and first derivative spectra. Supporting Information Available: Normalized absorption differential spectra for s-BPDA/DCHM and PMDA/ODA thin films, optimized structures of trimer of corresponding PIs, simulated variations in the differential and first derivative of Gaussian function in the case of the increase in fwhm, and TDDFT calculation results of model compounds. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Sroog, C. E. J. Polym. Sci., Part D: Macromol. ReV. 1976, 11, 161. (2) St. Clair, A. K.; St. Clair, T. L.; Shevket, K. I. L. Polym. Mater. Sci. Eng. 1984, 51, 62. (3) Reuter, H.; Franke, H.; Feger, C. Appl. Opt. 1988, 27, 4565. (4) Jin, Q.; Yamashita, T.; Horie, K.; Yokota, R.; Mita, I. J. Polym. Sci., Part A: Polym. Chem. 1993, 31, 2345. (5) Takanari, I.; Matsushita, J.; Yamada, M.; Fukai, H.; Nishioka, Y. Mol. Cryst. Liq. Cryst. 2007, 471, 195. (6) Matsuura, T.; Ando, S.; Sasaki, S.; Yamamoto, F. Macromolecules 1994, 27, 6665. (7) Dien-Hart, R.; Wright, W. W. Macromol. Chem. 1971, 143, 189. (8) Ishida, H.; Wellinghoff, S. T.; Baer, E.; Koenig, J. L. Macromolecules 1980, 13, 826. (9) Erskine, D.; Yu, P. Y.; Freimanis, S. C. J. Polym. Sci., Part C: Polym. Lett. 1988, 26, 465.

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