Stark Spectroscopy of Rubrene. I. Electroabsorption Spectroscopy and

Jun 3, 2016 - The origin of the nonzero difference in the electric dipole moment is argued. Stark fluorescence spectroscopy investigation is reported ...
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Stark Spectroscopy of Rubrene. I. Electroabsorption Spectroscopy and Molecular Parameters Toshifumi Iimori,*,† Ryuichi Ito,† Nobuhiro Ohta,‡ and Hideyuki Nakano† †

Department of Applied Chemistry, Muroran Institute of Technology, Muroran 050-8585, Japan Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, 1001 Ta-Hsueh Rd., Hsinchu 30010, Taiwan

‡

ABSTRACT: Electroabsorption spectroscopy investigation and the determination of molecular parameters for rubrene dispersed in a poly(methyl methacrylate) (PMMA) matrix are reported. The features of the band system in the absorption spectrum in PMMA are analogous to those in solutions. The changes in the electric dipole moment and the polarizability between the excited and ground states are determined from analysis of the Stark effect in the absorption band. The change in the transition dipole moment in the presence of an external electric field is also observed. Although rubrene is predicted to be classified as a nonpolar molecule, there is a contribution of the difference in the electric dipole moment between the excited and ground states to the electroabsorption spectrum. The origin of the nonzero difference in the electric dipole moment is argued. Stark fluorescence spectroscopy investigation is reported in Part II of this series.

I. INTRODUCTION

of our knowledge, despite the emergent interest in the rubrene molecule due to the above-mentioned functionality. One of the most powerful methods to obtain information on the molecular parameters is Stark spectroscopy. By using Stark spectroscopy technique, we can determine the molecular parameters such as the electric dipole moment and the polarizability for the excited and ground states. These molecular parameters are closely related to the shape of MOs in molecules, and therefore, Stark spectroscopy investigation can provide fundamental information on the electronic states of rubrene. Moreover, the experimentally determined molecular parameters can be a benchmark to test the accuracy of the results obtained by quantum chemical calculations of MOs and electronic states. Here, we report Stark spectroscopy investigation of rubrene dispersed in a polymer matrix. In Stark spectroscopy, we measure the electric-field-induced changes in absorbance and photoluminescence intensity, and difference spectra between the spectra measured in the presence and absence of an external electric field are obtained. For the absorption spectrum, the difference spectrum is called electroabsorption (EA) spectrum or Stark absorption spectrum. For the photoluminescence or fluorescence spectrum, the difference spectrum is called electrophotoluminescence spectrum or Stark fluorescence (SF) spectrum. As Part I of a series of papers, we show the EA spectroscopy investigation for rubrene here. The polarizability difference between the Franck−Condon (FC) excited state and the ground state is determined from the Stark shift of

Rubrene had been one of the important model systems used to best understand the photophysics of photoexcited aromatic molecules.1−3 Recently, rubrene has been regaining the spotlight because of intriguing properties for the application to organic electronic devices. In single crystals of rubrene, an excellent hole mobility reaching to 20 cm2 V−1 s−1 has been reported, and rubrene is under intense investigation as a promising organic semiconductor for the application to organic field-effect transistors in the field of organic electronics.4 Photophysics in single crystals of rubrene has also attracted considerable interest because photoexcitation of single crystals results in singlet fission in which a photoexcited singlet molecule can generate two molecules in triplet excited states.5,6 Such a multiple exciton generation due to the singlet fission can be applied to material engineering of photovoltaic cells.7 As the basis for understanding of the mechanism of the high hole mobility and the singlet fission, investigation to characterize the electronic state of rubrene has been spurred recently. Quantum chemical calculations of molecular orbitals (MOs), intermolecular interaction, the stable structure, and the vibrational modes both in isolated condition and in single crystals have been performed to gain an insight into the emergence of the hole mobility and singlet fission.8−10 The calculations for the MO of rubrene have shown that the S1−S0 electronic transition of rubrene can be ascribed to the transition between the highest occupied MO (HOMO) and the lowest unoccupied MO (LUMO).11,12 A variety of spectroscopic techniques have also been used to study the electronic states of rubrene so far.2,3,6,13−16 However, there appears to be no experimental study on molecular parameters such as polarizability to the best © XXXX American Chemical Society

Received: March 14, 2016 Revised: May 31, 2016

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The optical path length across the film is dependent on the angle χ. Due to the path length variation, the absorbance should increase by a factor of 1/sin χ = 1.22 at χ = 55° compared to that at χ = 90°. This effect was taken into account in the fitting of the EA spectra. It is well-known that rubrene is prone to readily photooxidize in atmospheric conditions.20 In our experiments, we paid attention to circumvent bleaching and quenching caused by photo-oxidation. In the EA measurements, the wavelength scan was repeated several times over a fixed wavelength range of interest. We did not observe significant change of the EA spectra for the initial two scans, and thus, we took an average of the two spectra to obtain one EA spectrum. Fitting of the EA spectra was performed by using the IGOR program (Wavemetrics). In an ab initio calculation of the structure of rubrene with the minimum energy, the GAMESS package program was used.

the absorption band. In the presence of an external electric field, the absorption band shows the broadening, from which we can determine the difference in electric dipole moment between the FC excited and ground states. The change in the transition dipole moment in the presence of an external electric field is also characterized. SF spectroscopy investigation is presented in a companion paper.17

II. EXPERIMENTAL METHODS Rubrene (Tokyo Chemical Industry, purified by sublimation) was used without further purification. Poly(methyl methacrylate) (PMMA, Aldrich, average molecular weight of 120000) was purified by a precipitation using benzene and methanol. A mixture of rubrene and PMMA was stirred in benzene (Kanto chemical, spectroscopy grade) until completely dissolved. The molar ratio of rubrene to PMMA monomer units was 1%. Thin films of PMMA containing rubrene (rubrene/PMMA) were prepared using a spin-coating technique on quartz substrates that were partially coated with a conductive indium tin oxide (ITO) layer. A semitransparent aluminum (Al) film was prepared on the surface of the rubrene/PMMA film by vacuum deposition. The substrate having the layered structure of quartz/ITO/(rubrene/PMMA)/Al was prepared thus and used as the sample. The ITO and Al films were used as electrodes. A part of the rubrene/PMMA film was masked in the vacuum deposition process, and the absorption spectrum of the area, which was uncoated by Al and ITO was measured by using a spectrophotometer (Hitachi U4100). The measurements of the absorption spectra were performed after the deposition of the Al film electrode. The absorption spectrum of the rubrene/ PMMA film was obtained by subtracting the absorption spectrum of the bare quartz substrate from the absorption spectrum of the sample. The thickness of the rubrene/PMMA films was measured using optical interferometry [NanoSpec (Nanometrics) and FilmTek (Scientific Computing International)]. The typical thickness of the rubrene/PMMA films was ca. 1 μm. EA spectra were measured using a home-built electric field modulation spectroscopy system. A Xe lamp was used as the light source, and the monochromatic light beam was linearly polarized with a polarizer and detected by a photomultiplier tube. Modulation of the intensity of the transmitted light (ΔI(2f 0)) was induced by application of an AC voltage with a frequency f 0 = 333 Hz to the electrodes of the sample and detected using a lock-in amplifier (LI5640, NF Corporation). The modulation at the second harmonic (2f 0) of the frequency of the applied voltage was monitored. The intensity of the DC component of the transmitted light (I) was recorded by an analog-to-digital converter. The EA spectrum (ΔA) was calculated from ΔI(2f 0) and I using the relation ΔA = −(2 2 /ln 10)ΔI(2f0 )/I

III. THEORETICAL BACKGROUND The Stark effect in electronic spectra depends on the changes Δμ = μe − μg and Δα = αe − αg, where μe, μg, αe, and αg are the permanent electric dipole moments and the polarizability tensors for the FC excited and ground states, respectively. The field-induced change in absorbance as a function of the frequency ν is given by21−28 ⎡ d ⎧ A (ν ) ⎫ ⎬ ΔA(ν) = (fF )2 ⎢A χ Α(ν) + Bχ ν ⎨ dν ⎩ ν ⎭ ⎣ + Cχ ν

d2 ⎧ A(ν) ⎫⎤ ⎨ ⎬⎥ dν 2 ⎩ ν ⎭⎦

(2)

where F is the electric field externally applied to the film, F = |F|, f is the internal field factor, χ is the angle between the electric field of the light and F, and Aχ, Bχ, and Cχ are, respectively, coefficients of the zeroth, first, and second derivatives of the unperturbed absorption spectrum, A(ν). The coefficients can be expressed as

A χ = a1 Bχ =

(3)

Δα̅ 1 + (3 cos2 χ − 1)(Δαm − Δα̅ ) + b1 2h 10h

⎧ 5 + (3 cos2 χ − 1)(3 cos2 η − 1) ⎫ ⎬ Cχ = (Δμ)2 ⎨ 30h2 ⎭ ⎩

(4)

(5)

where h is the Planck’s constant, η is the angle between Δμ and the transition dipole moment (m), Δμ = |Δμ|, and Δα̅ is given by the diagonal components of the polarizability tensor change: Δα̅ =

(1)

1 Tr(Δα) 3

(6)

Δαm is a component of the polarizability tensor change along the direction of m:

The voltage applied to the film was monitored with a voltmeter. The field strength was calculated from the voltage divided by the thickness of the rubrene/PMMA layer. In the EA measurement, the angle (χ) between the electric field of light and the externally applied electric field in PMMA films was controlled as one of the experimental parameters. The angle χ was varied by changing the angle of incidence of the light beam to the surface of the sample substrate and was calculated according to the Snell’s law of refraction.18,19 A rotary stage was used to change the angle of incidence.

Δαm = m·Δα ·m/|m|2

(7)

a1 and b1 in eqs 3 and 4 represent the terms arising from field effects on m: m(F ) = m + A·F + F ·B·F

(8)

where m(F) is the transition dipole moment in the presence of an external electric field, and tensors A and B represent the transition polarizability and transition hyperpolarizability, B

DOI: 10.1021/acs.jpca.6b02625 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A respectively. The explicit forms of a1 and b1 at the magic angle χ = 55° are24,25 a1 =

b1 =

1 3 |m|2

∑ Aij 2 +

2 3 |m|2

∑ miAijΔμj

i,j

i,j

2 3 |m|2

∑ miBijj i,j

(9)

(10)

where the indices i and j represent the molecule fixed axes and are used to represent individual components of the vectors and the tensors. In many cases, these two terms make negligibly small contributions to EA spectra. Some assumptions are made to obtain the expressions of the coefficients represented as eqs 3−5: (1) The orientation distribution in a molecular ensemble is isotropic in the absence of an external electric field. (2) Field-induced orientation and/or alignment of molecules are negligibly small, and we can consider that molecules are immobilized in a rigid polymer matrix. (3) The absorption band is much broader than the Stark shift. If the second assumption was not true and molecules were not immobilized, the terms that depend on μg and αgm − α̅g should contribute to the coefficients Aχ and Bχ.18,23,26 Here, αgm = m·αg·m/|m|2 is the component of the ground-state polarizability along the direction of m, and α̅g = 1/3Tr(αg). The terms containing μg originate from the field-induced orientation of polar molecules, and the terms containing αgm − α̅g originate from the field-induced alignment due to the polarizability anisotropy of molecules. In the case of nonpolar molecules, such as rubrene, all terms containing μg should be nearly zero. Moreover, the effect due to the field-induced alignment is generally negligible. Therefore, the second assumption can be rationalized. For the determination of the molecular parameters, we must know the internal field factor f, which represents a factor to convert the externally applied electric field to the local electric field acting on molecules in dielectric materials. Although a value of f is, in general, assumed to be in the range from 1.1 to 1.3 for frozen solvent matrices, the estimation of f in condensed phase systems is actually known as one of the difficult problems in Stark spectroscopy.28 If we can know an accurate value of f for PMMA films, the proper values of Δα̅ and Δμ would be given by the uncorrected values divided by f 2 and f, respectively. In actual data analyses, the spectra are plotted as a function of wavenumber ν̃ (in cm−1), and the converted form of eq 2 is then used according to the relation ν = cν̃, where c is the speed of light.

Figure 1. Absorption spectrum of rubrene (open circle) in PMMA and the result of fitting (solid line) with a sum of Gaussian line shapes (broken lines).

absorption maximum in a PMMA film is close to those in cyclohexane (ns = 1.42) and toluene (ns = 1.49). For analysis of EA spectra, we have to numerically calculate the derivative line shapes of the absorption spectrum. Actually, the absorbance was small, and the direct calculation of the derivative line shapes from the absorption spectrum resulted in too noisy line shapes. For the improvement of the quality of the data analysis of EA spectra, we performed the fitting of the absorption spectrum with a sum of Gaussian line shapes. The center wavenumbers of the Gaussian line shapes for the four vibronic progressions are 1.90 × 104, 2.04 × 104, 2.17 × 104, and 2.31 × 104 cm−1. The frequency of the progression is thus ca. 1.35 × 103 cm−1, which is in agreement with the vibronic progression observed in single crystals (0.17 eV) and in solution (0.165 eV).14,15 This progression can be assigned to a symmetric normal mode, which is correlated to a symmetric C−C stretching mode of the tetracene backbone.10,16 The absorption band centered at ∼2.42 × 104 cm−1 and a broad background absorption were also present in the absorption spectrum. The origin of the latter broad band might come from the incompleteness in the subtraction process of the absorption spectra described in the Experimental Methods. However, because of the weakness and broadness, the latter absorption band hardly affected the result of the analysis of EA spectra. The direction of the transition dipole moment m has been identified by the polarized spectroscopic study of rubrene single crystals. The m for the majority of the absorption studied in this work lies parallel to the M-axis of rubrene (Figure 2).14 As described in Part II of the series of the papers, dominant bands in the fluorescence spectrum are also polarized along the Maxis.17 In single crystals, much weaker absorption bands for which the polarization directions are not parallel to the M-axis also contribute to the spectrum in the wavenumber region higher than ∼20000 cm−1.14 This band having the different transition character is probably stemming from vibronic interaction with other electronic states.14 IV.B. Electroabsorption Spectrum. Figure 3 shows the EA spectrum recorded at χ = 55°, where the field strength was |F| = 0.7 MV cm−1. We observed a derivative-type line shape for the two lowest energy vibronic bands, and a field-induced increase of absorbance is observed in the wavenumber region lower than the position of the band maximum. This result indicates that the red-shift of the absorption band is induced by an external electric field. At χ = 90°, an analogous spectrum was obtained. The result of the fitting according to eq 2 is also shown in Figure 3. As described in Section IV.A, a sum of the Gaussian line shapes was used to fit the whole absorption

IV. RESULTS IV.A. Absorption Spectrum. Figure 1 shows the absorption spectrum for rubrene/PMMA. The observed vibronic transition is assigned to the S1 (π−π*) − S0 transition of rubrene,13 and the absorption maximum is located at 1.90 × 104 cm−1 (525 nm). The spectral shape is similar to those observed in solution and in amorphous film.6,14 In solution, the absorption maximum of rubrene shows a linear dependence on the so-called solvent polarizability function f(ns2) = (ns2 − 1)/ (2ns2 + 2), where ns is the refractive index of solvent.2 The C

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Figure 4. Contributions of the zeroth (dash-dot line), first (solid line), and second derivative (broken line) components in the fitting curves of the electroabsorption spectra. (a) χ = 55°. (b) χ = 90°.

Figure 2. (a) Chemical structure of rubrene. L, M, and N represent the molecule fixed axes. The L- and M-axes are parallel to the long and short axes of the tetracene backbone, respectively. (b) Structure of rubrene having a planar tetracene backbone determined by the X-ray crystallography of single crystals. (c) Structure of rubrene having a twisted tetracene backbone predicted by an ab initio quantum chemical calculation. See the text about the calculation method.

Table 1. Parameters Determined from the Fitting of Electroabsorption Spectrum for the S1−S0 Transition of Rubrene parameters

valuesa

Δα̅ Δμ Aχb

85 ± 10 Å 2.0 ± 0.1 D (−3.6 ± 0.4) × 10−20 m2 V−2 3

a The reported values are not corrected for the internal field factor f. See Section III and Section V.C about the corrected values. bAχ is the coefficient for the zeroth derivative component in the electroabsorption spectrum observed at χ = 55°.

The first derivative line shape is predominant in the EA spectrum. The first derivative coefficient Bχ (eq 4) is composed of the contributions from the polarizability difference Δα̅, Δαm − Δα̅, and the b1 term originating from the transition polarizability A (eq 10). In analysis, we assume that the contribution of the b1 term can be neglected approximately. This assumption is, in general, made for optically allowed transitions. Moreover, in the b1 term, the components of A are multiplied by the components of Δμ (eq 10). In nonpolar molecules, such as rubrene, Δμ is expected to be zero or small. Thus, the b1 term is also expected to be small. In addition, the relatively small contribution of A has been argued in the above discussion on the zeroth derivative coefficient. This is also reconciled with the assumption. For the further separation of the contributions of the first and second terms in the right-hand side of eq 4, the examination of the dependence of Bχ on the angle χ is necessary. In Figure 4a,b, the contribution of the first derivative component apparently decreases with the change from χ = 55° to 90°. However, a significant change of Bχ between χ = 55° and 90° was not seen after the correction due to the difference in optical path length. This result indicates that Δαm − Δα̅ is nearly zero. The contributing component to Bχ is, therefore, only a change in polarizability Δα̅. The fitting parameter yields Δα̅ = 85 ± 10 Å3, if the correction for f is not made (Table 1). Moreover, Δαm − Δα̅ ≅ 0 shows that the direction of the main component in Δα̅ is along the direction of the transition dipole moment m, i.e., the short axis of the tetracene backbone.

Figure 3. Electroabsorption spectrum obtained with χ of 55° and the result of fitting.

spectrum, and the derivative line shapes were numerically calculated from the fitting curve. The whole EA spectrum was fitted by using a single set of the coefficients Aχ, Bχ, and Cχ as the fitting parameters. The contributions of the each derivative line shapes to the fitting curve are shown in Figure 4a. The result of the fitting for the spectrum at χ = 90° is also shown in Figure 4b. The contribution of the zeroth derivative component is relatively small in comparison with the first derivative component, but it is non-negligible. This component is ascribed to the field-induced change in the transition dipole moment (eq 8). We observed a negative zeroth derivative component Aχ = (−3.6 ± 0.4) × 10−20 m2 V−2 at χ = 55° (Table 1). In the a1 term giving rise to Aχ (eq 9), the contribution from the transition polarizability A should be positive, while the transition hyperpolarizability B can make both positive and negative contributions depending on the sign and the magnitude of the components.24 We observed the negative value for the Aχ, and this result implies that the transition hyperpolarizability B is a dominant factor in the Aχ coefficient. D

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with the 6-31G basis set was used. The reduction of the repulsive interaction among the side phenyl groups is considered to play a major role in the stabilization of the twisted structure.8 While the planarization of the tetracene backbone found in single crystals is energetically unfavorable, the energetic cost can be compensated by the lattice energy gained by the efficient packing of the molecules in the planar structure.32 The importance of intermolecular interaction for the stabilization of the planar structure was also indicated by a quantum chemical calculation.8 For rubrene in solution, an experimental result of 13C NMR spectroscopy was in agreement with the twisted structure.33 In our experimental conditions, the contributions of molecular aggregates and intermolecular interaction to spectroscopic results are minor. Hence, we can assume the twisted structure belonging to the point group D2 for rubrene dispersed in a PMMA film. Theoretically, molecules belonging to the point group D2 must be classified as nonpolar.34 For nonpolar molecules, permanent electric dipole moments in both the ground and FC excited states are naively expected to become zero. However, the contribution of Δμ was not negligible in the EA spectra. Actually, the observations of nonzero Δμ have been reported for a number of nominally nonpolar molecules.26,35−39 As an explanation of the nonzero Δμ, it has been proposed that inhomogeneous local interactions between solute molecules and matrices may be symmetry breaking perturbations for the solutes.35 A similar mechanism has been discussed in the study of the Stark effect on hole-burning spectra.40,41 In these studies, a variety of matrices including solvents, frozen solvents, and polymers were used. This fact shows that the observation of nonzero Δμ for nominally nonpolar molecules is not a special case, and the inhomogeneous local interactions producing symmetry breaking perturbations are not ascribed to a specific interaction between the solute molecule and the matrix. Thus, it is likely that the nonzero Δμ for rubrene dispersed in a PMMA film is also explained by this mechanism. V.C. Comparison of Electronic Structure with Tetracene. The structure of rubrene in a PMMA film is predicted to be twisted. Quantum chemical calculations for the twisted rubrene have shown that the wave functions, which correspond to the HOMO and the LUMO, are largely localized on the tetracene backbone, and the orbitals on the side phenyl groups make only a minor contribution to them.10,16 Moreover, the positions of nodes and the distributions of electron density in these MOs for rubrene are similar to those for tetracene monomer, and the S1−S0 transitions for the two molecules are well described by a single electron excitation from the HOMO to the LUMO.10,12 Although the optimized structure of tetracene monomer is perfectly planar,9,10 the results of the quantum chemical calculations imply that the molecular parameters for the two molecules may also be comparable to each other despite the difference in the planarity of the structure. For tetracene, the data for Δα̅ reported in some classical works using Stark spectroscopy are scattered in the range from 15 to 43 Å3, whereas theoretical calculations have predicted somewhat larger values that range from 20 to 57 Å3.42 The value of Δα̅ for rubrene (Table 1) has the same order of magnitude to these values but is larger than those for tetracene, unless the correction for the internal field factor f is made. In EA measurements in condensed phase systems, an estimation of the internal field is often an annoying problem in

The second derivative line shape also makes some contribution to the EA spectra. A change in dipole moment evaluated from the coefficient Cχ at χ = 55° and eq 5 is Δμ = 2.0 ± 0.1 D. In addition, from the difference between the coefficients Cχ at χ = 55° and 90°, we can obtain the molecular parameter cos2 η ≅ 0.73 ± 0.10, where η is the angle between m and Δμ. This leads to η of ∼35° or ∼145°. Further selection between the two values cannot be made from the experimental data.

V. DISCUSSION V.A. Possible Contribution of Different Band Systems to Electroabsorption Spectra. We argue the possibility of the contribution of much weaker absorption bands having the different transition characters. Polarized spectroscopy investigation of rubrene single crystals has shown that different band systems having different polarization directions are superimposed in the absorption and fluorescence spectra.14,29 Rubrene single crystals are orthorhombic, and there are four molecules per unit cell.14 If we adopt the labeling of the crystallographic axes a, b, and c given in ref 14, the c-axis is parallel to the M-axes of molecules in the crystal (Figure 2). The L- and N-axes are parallel to the ab plane of the crystal. The main band system that shows the strongest absorption is c‑polarized, and the origin band of the progression of this main band system matches the origin band in the unpolarized absorption spectrum (Figure 1). The progressions of the other systems, which are a- and b-polarized, begin at nearly the same wavenumber as the second vibronic band of the main band system.14 The a- and b-polarized band systems are much weaker than the c-polarized main band system. The strongest cpolarized band system is coupled to the electronic transition for which m is along the M-axis in the molecule fixed axes (Figure 2), and the other band systems are coupled to the L- and Npolarized transitions. If the band systems that are characterized by different molecular parameters are superimposed on the absorption spectrum, we usually need to separate the overlapping band systems by using appropriate methods such as the fitting with a sum of Gaussian line shapes.30 Unless their individual contributions to EA spectra are taken into account, trials of the fitting will end in the results of poor quality or provide with physically unacceptable molecular parameters. In such cases, an individual set of the fitting parameters is necessary for each of the separated band systems in the fitting of EA spectra. However, as shown in Figure 3, the EA spectrum could be reasonably fitted by using the derivative line shapes of the whole absorption spectrum without band separation, and the corresponding single set of the coefficients. This result clearly corroborates that the molecular parameters elucidated in this work can definitely be ascribed to the S1−S0 electronic transition for which m is parallel to the M-axis. V.B. Nonzero Difference in Dipole Moment. Rubrene is formally expected to belong to the point group D2h. In single crystals, X-ray crystallography study has revealed a planar tetracene backbone, and the molecule belongs to the point group C2h (Figure 2b).31 However, quantum chemical calculations have predicted that, in isolated condition or solution, the most stable structure has a nonplanar and twisted tetracene backbone, and the two outermost C−C bonds on the tetracene backbone make an angle of ca. 40°.8,10,15 The structure has been predicted to belong to the point group D2. In Figure 2c, we show the twisted structure optimized by an ab initio calculation in which the density functional B3LYP method E

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The Journal of Physical Chemistry A quantitative discussions of the experimental data.28 In a simple model to calculate the internal field, it is assumed that the molecule resides in a spherical cavity in a dielectric medium, and then f is given by f = 3ε/(2ε + 1), where ε is the dielectric constant.43 If we use the literature value of ε ≅ 3.1 at frequencies below 1 kHz for PMMA,44 f is 1.3. The Δα̅ for rubrene after the correction with this internal field factor becomes 50 Å3. If we apply the range of the values of f between 1.1 and 1.3 that are calculated for frozen solvents,28 the values of Δα̅ are between 50 and 70 Å3. We believe that a proper value of Δα̅ for rubrene is between 50 and 85 Å3. Although there is an uncertainty that stems from the internal field factor, this range of values for rubrene overlaps with the values that have been reported for tetracene. Thus, it is likely that the result of the EA spectroscopy investigation for rubrene is not quite different from the theoretical prediction that the characteristics of the S1−S0 electronic transition and the MOs are nearly identical with each other for rubrene and tetracene. Although the estimated ranges of Δα̅ for the two molecules overlap, there is a difference between the mean values for them. This result might show that the Δα̅ for rubrene is larger than that for tetracene. The difference in the molecular parameter may be explained by invoking the contributions of both the MO on the side phenyl groups and the difference in the planarity of the tetracene backbone.

Chitose Institute of Science and Technology with the support by Nanotechnology Platform Program (Synthesis of Molecules and Materials) of MEXT, Japan. T.I. acknowledges CASIO science promotion foundation, and the cooperative research program of Network Joint Research Center for Materials and Devices.

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VI. CONCLUSIONS For rubrene dispersed in a polymer matrix, the observed absorption spectrum can be assigned to the S1−S0 electronic transition for which the transition dipole moment lies along the short axis of the tetracene backbone. Some molecular parameters were determined from analysis of the EA spectrum. The change in the polarizability upon the photoexcitation was evaluated to be f 2Δα̅ = 85 ± 10 Å3, where f is the internal field factor. The direction of the main component in Δα̅ is along the direction of the short axis of the tetracene backbone. The contribution of the field-induced change in the transition dipole moment was also non-negligible. Although rubrene was expected to be nonpolar, we observed a contribution of Δμ to the EA spectra. In solutions or isolated conditions, quantum chemical calculations have predicted that the most stable structure of rubrene has the twisted tetracene backbone and belongs to the point group D2. Molecules that belong to the point group D2 must be nonpolar, and thus, the nonzero value of Δμ can plausibly be understood as the manifestation of the symmetry-breaking perturbations from surrounding matrix molecules. The quantum chemical calculations have predicted that both the HOMO and the LUMO for rubrene are similar to those for tetracene monomer, and the result of the EA spectroscopy investigation is likely not to be quite different from this prediction.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81-143-465767. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partly supported by MEXT KAKENHI Grant Number 25870018. A part of this work was performed in F

DOI: 10.1021/acs.jpca.6b02625 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

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DOI: 10.1021/acs.jpca.6b02625 J. Phys. Chem. A XXXX, XXX, XXX−XXX