Influence of substitution on the optical properties of functionalized pentacene monomers and crystals: Experiment and theory
Y. Saeed, K. Zhao, N. Singh, R. Li, J. E. Anthony, A. Amassian, U. Schwingenschlögl
aa r X i v : . [ c ond - m a t . m t r l - s c i ] N ov Influence of substitution on the optical properties offunctionalized pentacene monomers and crystals: Experiment andtheory
Y. Saeed , K. Zhao , N. Singh , , R. Li , J. E.Anthony , A. Amassian , and U. Schwingenschl¨ogl KAUST, Physical Science & Engineering division,Thuwal 23955-6900, Kingdom of Saudi Arabia Solar and Photovoltaic Energy Research Center, KAUST,Thuwal 23955-6900, Kingdom of Saudi Arabia and Department of Chemistry, University of Kentucky, Lexington, Kentucky 40506-0055
Abstract
The influence of solubilizing substitutional groups on the electronic and optical properties offunctionalized pentacene molecules and crystals have been investigated. Density functional theoryis used to calculate the electronic and optical properties of pentacene, TIBS-CF -pentacene, andTIPS-pentacene. The results are compared with experimental absorption spectra of solutions andthe complex dielectric function of thin films in the 1 eV to 3 eV energy range. In all cases, the bandgaps of the isolated molecules are found to be smaller than those of the crystals. The absorptionspectra and dielectric function are interpreted in terms of the transitions between the highestoccupied molecular orbitals and lowest unoccupied molecular orbitals. The bands associated toC and Si atoms connecting the functional side group to the pentacene in the (6,13) positions arefound to be the main contributors to the optical transitions. The calculated dielectric functions ofthin films agree with the experimental results. A redshift is observed in crystals as compared tomolecules in experiment and theory both, where the amplitude depends on the packing structure. . INTRODUCTION The design of molecular semiconductors is increasingly important for the development oforganic electronics and organic photovoltaics (OPV) [1–3]. Early on pentacene had proven tobe one of the best performing molecular semiconductors, as vacuum-deposited organic thinfilm transistors have achieved a mobility as high as 6 cm V − s − [4–6]. However, it did notlend itself well to solution processing, which is believed to be key for low-cost manufacturingof organic semiconductors. In recent years, chemical modification of the acene has made itpossible to overcome the low solubility and poor stability in solution, whilst maintaining orenhancing the inter-molecular orbital overlap [7, 8].Functional substitution of pentacene has been shown to induce favorable crystal packingmotifs for both electronic and OPV applications [8, 9]. For example, pentacene withoutsubstitution shows a two-dimensional (2D) herringbone packing motif (see Fig. 1a), whilethe popular compound (6,13)-bis(tri-iso-propyl-silyl-ethynyl)-pentacene (TIPS-Pn) shows abrickwork 2D crystal packing (see Fig. 1c) [10]. The latter is currently one of the organicsemiconductors exhibiting the highest field-effect mobility [11], with recent carrier mobilityreports exceeding 4 cm V − s − [12]. When changing substitution from tri-iso-propyl-silyl-ethynyl to tri-iso-butyl-silyl-ethynyl and introducing a tri-fluoro-methyl group on the acenebackbone to modify the energy levels, to get 2-tri-fluoro-methyl-(6, 13)-bis-(tri-iso-butyl-silyl-ethynyl)-pentacene (TIBS-CF -Pn), the crystal packing changes to one-dimensional(1D) sandwich herringbone (see Fig. 1b). This molecule is found to perform as one of thebest non-fullerene acceptor molecules when mixed with P3HT donor polymer, yielding apower conversion efficiency of 1.28% [9].The substitutional chemistry employed affects the electronic properties of the monomeras well as of the solid state material itself. Meng et al. [13] have demonstrated that adjust-ing the alkyl substitution to the four terminal positions (2, 3, 9, and 10) of the pentacenechromophore shifts the energies of both the highest occupied molecular orbital (HOMO)and lowest unoccupied molecular orbital (LUMO) without significantly changing the gapbetween these two. When substituting all hydrogen atoms of pentacene with fluorine atomssome interesting changes of the extinction coefficient are found as the optical band gap isredshifted [14]. Recently, Lim et al. [15] have shown that the HOMO–LUMO energy lev-els can be tuned by varying the number of nitrile groups in cyano-pentacene substitution.2rom the above reports, a close relationship appears to exist between the substitution onthe pentacene chromophore and its electronic and optical properties. To tailor and improvethese properties, one should first understand the correlation between the chemical modifica-tion (like silyl-ethynyl substitution as in the cases of TIPS-Pn and TIBS-CF -Pn) and thephysical properties of the derivatives both in monomer and in crystalline states.The electronic and optical properties of pentacene in solution have been previously calcu-lated using first principles methods [16]. The calculated optical spectra of the vapor phaseare found to be in agreement with the measurements performed on the thin film phase ofpentacene. Doi et al. [17] have calculated the electronic band structures for both the singlecrystal and thin film polymorphs of pentacene and concluded that the effective mass of theelectrons or holes is larger in the single crystal. A first principles simulation of the thinfilm phase of pentacene shows a crucial dependence of the bandwidths of the HOMO andLUMO and of the band gap on the molecular stacking angles [18]. The electronic structuresof iodine- and rubidium-doped pentacene molecular crystals have also been investigated byab-initio calculations based on the ultrasoft pseudopotential method, predicting a metallicbehavior [19]. Recently, the structural and electronic properties of pentacene multilayers onthe Ag(111) surface have been studied, revealing that pentacene has no electronic contribu-tion at the Fermi level [20].Despite several experimental and theoretical investigations, the influence of the solubiliz-ing chemical substitutions and the resulting changes of the crystal packing on the electronicand optical properties of pentacene have not been reported. In this work, we study and com-pare the theoretical (single molecule and single crystal) and experimental (dissolved and thinfilm polycrystal) optical properties of pentacene, TIPS-Pn, and TIBS-CF -Pn. The resultsare analyzed in light of the calculated density of states (DOS) to see the influence of differentalkyl-silyl groups on the electronic and optical properties of both monomer and crystal ofthese materials useful to in electronic and OPV applications. II. EXPERIMENTS AND CHARACTERIZATION
Pentacene, toluene (anhydrous 99.8%) and 1,3,5-trichlorobenzene (anhydrous 99%) werepurchased from Sigma Aldrich and used without further purification. TIPS-Pn and TIBS-CF -Pn were synthesized [21] and purified by multiple recrystallization from acetone (TIPS-3 IG. 1: Molecular structure (top) and crystal packing (bottom) of (a) pentacene, (b) TIBS-CF -Pn,and (c) TIPS-Pn . Pn) or ethanol (TIBS-CF -Pn). Pentacene was dissolved in 1,3,5-trichlobenzene at 100 ◦ Cwith a concentration of 0.5 wt.% and stirred overnight in the dark. TIPS-Pn and TIBS-CF -Pn were dissolved in toluene at room temperature and stirred overnight in the dark.The solutions were filled in a 1 mm thick quartz cuvette and loaded in a Cary 5000 (Varian)instrument to aquire UV-vis absorption spectra. The measurements were performed overa spectral range from 300 nm to 2000 nm with a 2.0 nm slit width. Single crystal Si(100)wafers with a thermal oxide layer of 100 nm thickness were used as substrate for the thin filmdeposition. Prior to deposition, the substrates were cleaned in amonium hydroxide (30%NH OH), hydrogen peroxide (30% H O ) and Milli Q (1:1:5 ratio) for 15 min at 70 ◦ C. Thin4lms of TIPS-Pn and TIBS-CF -Pn were spin cast at 1000 rpm for 30 seconds in a N -filledglove-box and left to dry in inert atmosphere at room temperature. The optical properties ofthe spin-coated films were measured using variable angle spectroscopic ellipsometry (VASE)based on the M-2000XI rotating compensator configuration (J. A. Woollam Co. Inc). VASEspectra ranging from 0.734 eV to 5.895 eV were recorded at a 18 ◦ angle of incidence withrespect to the substrate normal from 45 ◦ to 80 ◦ with 2 ◦ increment. In the paper, we focuson the spectral range from 1 eV to 3 eV. Optical analysis of VASE data was performedusing the EASETM and WVASE32 software packages (J. A. Woollam Co. Inc). Opticalmodeling was performed assuming a homogeneous thin film exhibiting uniaxial anisotropy.To describe the dielectric behavior, a general oscillator approach consisting of Gaussianpeaks in the imaginary part of the dielectric function ε ( E ) was applied (more detailedinformation about the fitting procedure and the Gaussian parameters can be found in thesupporting information). All optical measurements were performed at room temperature inambient air. III. SIMULATIONS
Our calculations are based on density functional theory, using the full-potential linearizedaugmented plane wave (FP-LAPW) approach as implemented in the WIEN2k code [22].This approach describes the ground state of the present compound with high accuracy [23].On the other hand, calculation of optical spectra, in principle, involves excited states. Thus,additional approximations have to be introduced, which, however, do not compromise thefollowing line of reasoning [24]. Exchange and correlation effects are treated within thelocal density approximation [25]. In the FP-LAPW method, the unit cell is divided into twoparts: non-overlapping atomic spheres centered at the atomic sites and the interstitial region.The convergence parameter R mt · K max , where K max is the plane wave cut-off and R mt is thesmallest of the atomic sphere radii, controls the size of the basis set. It is set to R mt · K max = 5with G max = 24. A mesh of 48 uniformly distributed k -points in the irreducible wedge of theBrillouin zone is used for calculating the electronic properties and a dense mesh of 112 k -points is used to calculate the optical properties. A total energy convergence of at least 10 − Ry is achieved. The experimental lattice parameters of pentacene ( a = 5 .
959 ˚A, b = 7 . c = 15 .
610 ˚A, α = 81 . ◦ , β = 86 . ◦ , and γ = 89 . ◦ ), TIPS-Pn ( a = 7 .
565 ˚A, b = 7 . DO S ( s t a t e s / e V / m o l ec u l e ) SiC -3 -2 -1 0 1 2 3E-E F (eV)-3 -2 -1 0 1 2 3E-E F (eV)00.20.40.60.8 DO S ( s t a t e s / e V / m o l ec u l e ) -3 -2 -1 0 1 2 3E-E F (eV) M o l ec u l e D F T C r y s t a l D F T SiC______
Pentacene TIBS-CF -Pn TIPS-Pn _ _ __ _ _ _ _ FIG. 2: Comparison of the pentacene DOS with TIBS-CF -Pn and TIPS-Pn in both molecularand crystalline forms. ˚A, c = 16 .
835 ˚A, α = 89 . ◦ , β = 78 . ◦ , and γ = 83 . ◦ ), and TIBS-CF -Pn ( a = 17 . b = 16 .
552 ˚A, c = 18 .
168 ˚A, α = 90 ◦ , β = 113 . ◦ , and γ = 90 ◦ ) are used. IV. RESULTS AND DISCUSSION
In Fig. 1, we show the molecular and single crystal packing structures of pentacene,TIPS-Pn, and TIBS-CF -Pn. Pentacene (C H ) and TIPS-Pn (C H Si ) both exhibittriclinic ( P ¯1) crystal symmetries, while TIBS-CF -Pn (C H F Si ) has monoclinic ( P /c )symmetry.In Fig. 2, we show the calculated projected DOS for pentacene, TIBS-CF -Pn, andTIPS-Pn for the molecule and crystal in the energy range ± . -Pn and TIPS-Pn are6 ε ε α ( ω ) Molecule Cal.Crystal Calc.Molecule Exp.Crystal Exp. ε ε α ( ω ) ε ε α ( ω ) P e n t ace n e T I B S - C F - P n T I PS - P n (i)(d) (g)(a)(b) (e) (h)(c) (f) FIG. 3: Spectra of α , ε , and ε for pentacene, TIBS-CF -Pn, and TIPS-Pn in both molecule(monomer) and crystal form (experiment and simulation). found to be 1 eV and 0.85 eV, respectively, in the monomer phases, and 0.80 eV and 0.45eV, respectively, in the single crystal phases. The band gap of the TIPS-Pn single crystalis the lowest amongst these molecules owing to the largest LUMO bandwidth amongst thematerials investigated. The calculated band gaps are lower than in experiments, due to thewell known drawback of the local density approximation. The DOS shows more localizedpeaks for the pentacene molecule than its derivatives (Fig. 2). Due to the increase ofthe HOMO and LUMO bandwidths from monomers to crystals, the bands overlap (below E F ) in agreement with previous calculations for pentacene [17]. The HOMO and LUMOconsist mainly of bands belonging to the C and Si atoms which connect the side groupto the pentacene chromophore. The H bands appear 3.5 eV below E F for pentacene andits derivatives, while the F bands in TIBS-CF -Pn lie between − . − . α ( E ) as well as the photon energy-dependent complex dielectricfunction, e ε = ε ( E ) − iε ( E ). An average of the computed optical spectra along the threecoordinate axes is taken and compared with the average of the experimental optical spec-tra along the axes parallel and perpendicular to the plane of substrate. The absorptioncoefficients, α ( E ), of pentacene and its derivatives are calculated for a single molecule andcompared with experimental data of a dilute solution (see Figs. 3(a,b,c)). In the case of thepentacene solution, the experimental absorption spectrum shows several peaks at 2.13 eV,2.30 eV, 2.47 eV, and 2.86 eV. TIBS-CF -Pn and TIPS-Pn monomers exhibit peaks at 1.94eV, 2.10 eV, 2.26 eV, 2.45 eV and 2.82 eV. The first absorption peak in pentacene (2.13eV) is more intense than the other three peaks, while the first two peaks in TIBS-CF -Pnand TIPS-Pn are more intense than the others. A red shift of 0.22 eV between the firstabsorption peak of pentacene and of both TIBS-CF -Pn and TIPS-Pn, may be due to theeffect of the substitutional groups in the latter two derivatives.The absorption spectrum of pentacene for the thin film exhibits four absorption peaks at1.82 eV, 2.13 eV, 2.30 eV, and 2.86 eV which are redshifted as compare to the monomer. Inthe case of TIBS-CF -Pn, the HOMO-LUMO absorption bands are shifted to lower energieswith respect to the monomer spectrum, having peaks at 1.87 eV, 2.04 eV, 2.22 eV, and 2.81eV. A similar phenomenon is observed for TIPS-Pn thin films which show peaks at 1.78eV, 1.92 eV, 2.08 eV, and 2.76 eV. The shifts of the HOMO-LUMO absorption band aredifferent in thin films of these materials with respect to the monomers, namely 0.20 eV forpentacene, 0.07 eV for TIBS-CF -Pn, and 0.16 eV for TIPS-Pn. The different shifts maybe attributed to the different crystalline packing structures. The CF group does not haveany contribution because the C and F states (see the DOS) are well below the Fermi level.The calculated and experimental absorption coefficients also show a redshift between themonomer and the crystal. The calculations for monomers exhibit a single absorption peak,while the experiment shows more than one peak which is consistent with the DOS. The DOS8f monomers shows the single sharp LUMO and HOMO bands (allow only one transitionpeak) while that of for thin film have wider LUMO and HOMO bands, which can have moretransitions in absorption spectra. This may be due to the complete isolation of the moleculein the calculation, which may not be the case in solutions.The calculated ε ( E ) spectra along with their experimental counterparts for thin filmpentacene and its derivatives are presented in Figs. 3(d,e,f). The experimental ε ( E ) spectraof TIBS-CF -Pn and TIPS-Pn show two initial peaks at 1.85 eV and 1.91 eV, respectively,reflecting the optical band gap. The optical band gap is redshifted by 0.06 eV in TIPS-Pn as compared to TIBS-CF -Pn. The third peak is situated at 2.26 eV and 2.19 eV forTIBS-CF -Pn and TIPS-Pn, respectively. Another significant difference is the intensity ofthe third peak, which dominates in the ε ( E ) spectrum of TIBS-CF -Pn while in TIPS-Pnthe first peak is most prominent. The ε ( E ) spectrum changes dramatically by introducinga Si-branch in TIBS-CF -Pn and TIPS-Pn, which is due to the modified crystal packing.The calculated ε ( E ) spectra of TIBS-CF -Pn and TIPS-Pn are in qualitative agreementwith our experiments.The experimental ε ( E ) spectra of TIBS-CF -Pn and TIPS-Pn thin films show the firsttransition peaks at energies of 1.80 eV and 1.86 eV, respectively, while second and thirdpeaks position remain at the same energies in both crystals. This reflects that the alky-silyl length results in changes of the energy state of the first transition peak in ε ( E ). Thesubsequent peaks at 2.18 eV might be associated with a vibronic energy state between the SiHOMO and C LUMO. The calculated ε ( E ) spectra of crystals and monomers of pentacene,TIBS-CF -Pn, and TIPS-Pn show similar characteristics. The ε ( E ) spectra of the TIBS-CF -Pn and TIPS-Pn crystals demonstrate three peaks similar to the experimental results.Overall, the calculated ε ( E ) spectra of single crystals of TIBS-CF -Pn and TIPS-Pn are inagreement with our experimental thin film results.In conclusion, the effects of substitution on the electronic and optical properties havebeen discussed based on experiments and theoretical results. In the monomer state, thealkyl-silyl substitutions result in an energy shift of 0.22 eV (experimental) in TIBS-CF -Pnand TIPS-Pn as compared to pentacene. In the crystal state, the alkyl-silyl substitutioncontributes to different packing structures, which leads to a redshift by 0.09 eV in TIPS-Pnas compared to TIBS-CF -Pn. The HOMO-LUMO absorption band in thin films is shiftedtowards lower energies as compared to the monomer, by 0.07 eV and 0.16 eV for TIBS-CF -9n and TIPS-Pn, respectively. Our first principles calculation of optical spectra have beenanalyzed in terms of the calculated DOS. The optical transitions originate primarily from Cand Si bands. A redshift is observed from monomer to crystal for all compounds, where theextent of redshift depends on the packing structure. Overall, experiment and theory showa reasonable agreement for the optical spectra. [1] Z. Zaumseil and H. Sirringhaus, Chem. Rev. 107, 1296 (2007).[2] H. Wang and D. Yan, NPG Asia Mater. 2, 69 (2010).[3] A. Dodabalapor, H. E. Katz, L. Torsi, and R. C. Haddon, Science 269, 1560 (1995).[4] X. Li, B. K. C. Kjellander, J. E. Anthony, C. W. M. Bastiaansen, D. J. Broer, and G. H.Gelinck, Adv. Funct. Mater. 19, 3610 (2009).[5] O. D. Jurchescu, S. Subramanian, R. J. Kline, S. D. Hudson, J. E. Anthony, T. N. Jackson,and D. J. Gundlach, Chem. Mater. 20, 6733 (2008).[6] S. H. Kim, M. Jang , H. Yang, J. E. Anthony, and C. E. Park, Adv. Funct. Mater. 21, 2198(2011).[7] J. E. Anthony, J. Gierschner, C. A. Landis, S. R. Parkin, J. B. Sherman, and R. C. Bakus,Chem. Commun. 45, 4746 (2007).[8] S. Subramanian, S. K. Park, S. R. Parkin, V. Podzorov, T. N. Jackson, and J. E. Anthony, J.Am. Chem. Soc. 123, 9482 (2001).[9] Y. Shu, PhD thesis, University of Kentucky (2011).[10] O. Ostroverkhova, D. G. Cooke, F. A. Hegmann, R. R. Tykwinski, S. R. Parkin, and J. E.Anthony, Appl. Phy. Lett. 89, 192113 (2006).[11] S. K. Park, T. N. Jackson, J. E. Anthony, and D. A. Mourey, Appl. Phys. Lett. 91, 063514(2007).[12] G. Giri, E. Verploegen, S. C. B. Mannsfeld, S. A. Evrenk, D. H. Kim, S. Y. Lee, H. A. Becerril,A. A. Guzik, M. F. Toney, and Z. Bao, Nature 480, 504 (2011).[13] H. Meng, M. Bendikov, G. Mitchell, R. Helgeson, F. Wudl, Z. Bao, T. Siegrist, C. Kloc, andC. H. Chen, Adv. Mater. 15, 1090 (2003).[14] A. Hinderhofer, U. Heinemeyer, A. Gerlach, S. Kowarik, R. M. J. Jacobs, Y. Sakamoto, T.Suzuki, and F. Schreiber, J. Chem. Phys. 127, 194705 (2007).
15] Y.-F. Lim, Y. Shu, S. R. Parkin, J. E. Anthony, and G. G. Malliaras, J. Mater. Chem. 19,3049 (2009).[16] M. L. Tiago, J. E. Northrup, and S. G. Louie, Phys. Rev. B 67, 115212 (2003).[17] K. Doi, K. Yoshida, H. Nakano, A. Tachibana, T. Tanabe, Y. Kojima, and K. Okazaki, J.Appl. Phys. 98, 113709 (2005).[18] P. Parisse, L. Ottaviano, B. Delley, and S. Picozzi, J. Phys.: Condens. Matter 19, 106209(2007).[19] Y. Shichibu and K. Watanabe, Jpn. J. Appl. Phys. 42, 5472 (2003).[20] E. Mete, I. Demiroglu, M. F. Danisman, and S. Ellialtioglu, J. Phys. Chem. C 114, 2724(2010).[21] Y. S. Chung, N. Shin, J. Kang, Y. Jo, V. M. Prabhu, S. K. Satija, R. J. Kline, D. M.DeLongchamp, M. F. Toney, M. A. Loth, B. Purushothaman, J. E. Anthony, and D. Y. Yoon,J. Am. Chem. Soc., 133, 412 (2011).[22] P. Blaha, K. Schwarz, G. Madsen, D. Kvasicka, and J. Luitz, WIEN2k, An Augmented PlaneWave + Local Orbitals Program for Calculating Crystal Properties (TU Vienna, Vienna,2001).[23] U. Schwingenschl¨ogl and C. Schuster, Phys. Rev. Lett. 99, 237206 (2007); EPL 79, 27003(2007).[24] N. Singh and U. Schwingenschl¨ogl, Chem. Phys. Lett. 508, 29 (2011).[25] J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).[26] R. D. McCullough, Adv. Mater. 10, 93 (1998) . SUPPORTING INFORMATION The complex dielectric function e ε = ε − iε is related to the complex refraction index e n = n − ik by the following equations: ε = n − k and ε = 2 nk . Here, n and k are therefractive index and extinction coefficient, respectively. Kramers-Kronig transformation wasused during the model fitting as a constraint: ε ( ω ) = 1 + 2 π P Z ∞ ω ′ ǫ ( ω ′ ) ω ′ − ω dω ′ (1) ε ( ω ) = − ωπ P Z ∞ ǫ ( ω ′ ) − ω ′ − ω dω ′ (2)The mean square error was used to quantify the difference between experimental andmodel-generated data: M SE = vuut n − m n X i =1 [( N E i − N G i ) + ( C E i − C G i ) + ( S E i − S G i ) ] × n is the number of wavelengths, m is the number of fit parameters, and N = cos(2Ψ), C = sin(2Ψ) cos(∆), S = sin(2Ψ) sin(∆). Where, Ψ and ∆ are the amplitude ratio andphase shift, respectively.The M SE generated is 12.12 and 15.5 for TIPS-Pn and TIBS-CF -Pn with all anglesvariable from 45 ◦ to 80 ◦ , with 2 ◦ increment, respectively.Gaussian oscillators produce a Gaussian line shape in ε : ε = n X i A n (cid:20) Γ( E − E n σ n ) + Γ( E + E n σ n ) (cid:21) + i · (cid:18) exp (cid:20) − ( E − E n σ n ) (cid:21) + exp (cid:20) − ( E + E n σ n ) (cid:21)(cid:19) ! (4)where σ n = B n / (2 p ln(2)) and n is the oscillator number, A n = ε ( E n ) is the amplitude, E n (eV) is the center energy and B n (eV) is the full width at half maximum of the peak.The function Γ is a convergence series that produces a Kramers-Kronig consistent line shapefor ε . 12 ABLE I: Parameters of the modified Gaussian model obtained by fitting the imaginary part ofdielectric function ε ( E ) of TIBS-CF -Pn. ε xx ( E )= ε yy ( E ) ε zz ( E ) ε ∞ =1.901 ± ε ∞ =2.052 ± ± ± ± ± =0.887 ± =0.125 ± =1.868 ± =0.285 ± =0.159 ± =1.872 ± =0.395 ± =0.115 ± =2.040 ± =0.255 ± =0.127 ± =2.050 ± =0.156 ± =0.137 ± =2.204 ± =0.563 ± =0.155 ± =2.244 ± =0.123 ± =0.206 ± =2.368 ± =3.225 ± =0.670 ± =3.873 ± =0.133 ± =0.510 ± =2.838 ± =2.177 ± =0.125 ± =3.795 ± =0.110 ± =0.119 ± =3.304 ± =0.252 ± =0.337 ± =4.569 ± =0.453 ± =0.119 ± =3.744 ± =0.308 ± =0.657 ± =4.993 ± =0.629 ± =0.989 ± =4.187 ± =0.605 ± =0.975 ± =5.847 ± =0.235 ± =0.814 ± =5.076 ± =0.082 ± =0.145 ± =5.416 ± =0.617 ± =0.531 ± =5.649 ± ABLE II: Parameters of the modified Gaussian model obtained by fitting the imaginary part ofdielectric function ε ( E ) of TIPS-Pn. ε xx ( E )= ε yy ( E ) ε zz ( E ) ε ∞ =2.012 ± ε ∞ =2.251 ± ± ± ± ± =0.830 ± =0.080 ± =1.906 ± =1.087 ± =0.105 ± =1.891 ± =0.353 ± =0.080 ± =2.069 ± =0.666 ± =0.111 ± =2.053 ± =0.266 ± =0.497 ± =2.223 ± =1.566 ± =0.154 ± =3.503 ± =0.508 ± =0.198 ± =4.139 ± =2.709 ± =0.132 ± =3.886 ± =1.232 ± =0.204 ± =4.236 ± =1.532 ± =0.159 ± =4.256 ± =2.963 ± =0.467 ± =5.666 ± =1.344 ± =0.234 ± =4.132 ± =0.396 ± =0.963 ± =3.506 ± =0.467 ± =1.954 ± =5.419 ± =0.939 ± =0.586 ± =3.868 ± =0.400 ± =0.160 ± =5.737 ± =0.835 ± =0.453 ± =4.088 ±0.008