Control of Refractive Indices of Optical Polymers: Theoretical Prediction and Molecular Design Method Shinji ANDO The fundamental theory and a method to predict the refractive indices and dispersions of organic molecules and optical polymers were outlined. The e ects of substituents exerting on the refractive index of organic molecules are quantified from an analysis of the empirical molecular refractions and molar volumes of mono-substituted benzenes. When density of an organic molecule is known, its refractive index and the wavelength dispersion can be predicted with a high accuracy based on the Lorentz-Lorenz formula because the wavelength dispersion of molecular polarizabilities are well reproduced by the density functional theory DFT. A series of thermally stable sulfur-containing polyimides with high refractive indices and low dispersion were newly designed and synthesized based on the above method. It was confirmed that DFT calculation is a useful tool to design new optical polymers with controlled refractive indices and dispersions. Key words: refractive index, dispersion, polymer, DFT calculation, high refractive index polymer l 400 800 nm n 1.8 D n 1. 1 5 n C V n C/V a n a L L 2 n 1 4π 4π ρn N 2 α A α n 2 3 3 M R V 0 φ 1 152 8552 2 12 1 E4 5 E-mail: sando@polymer.titech.ac.jp 298 2
1 6 7 R H 1.100 N C 2.418 N C C 1.733 N C C 2.398 N C 6 H 5 25.463 N C 10 H 7 43.00 N O C O 2.211 N OO H 1.525 N O, C O 1.643 N F 0.95 N Cl 5.967 N Br 8.865 N I 13.90 NC N S C S 7.97 N S S H 7.69 NO 2 S S S 8.11 NO 2 0.71 NO 2 0.48 NO 2 R 2.322 2.499 2.840 3.21 3.59 4.36 2.65 2.27 2.71 3.46 2.48 2.47 3.05 3.79 7.59 7.44 6.72 7.30 1 2φ n 2 1 φ N r N A M V 0 M/r r R 1 6 7 a a 2 3 n a K K 8 n n nm n589 1 ν 3 n486 n656 n n 1 2 4 44 8 2015 80 70 60 50 40 30 20 1.3 1.4 1.5 1.6 1.7 n 1 2. L L R /V 0 V int V 0 /N A a /V int 1 n R /V 0 a /V int V vdw a V vdw V int K p R /V 0 a /V vdw S Br, I K p 299 3
SC 6 H 5 COC 6 H 5 OC 6 H 5 C 6 H 5 NH 2 NO 2 OH CN OCH 3 IBr Cl SC 6 H 5 F 2 a R /V 0 b R /V 0 11 9 K p 10 14 l 589 nm R /V 0 2 11 R 1 V 0 M r 2 2 300 4 3. 1 TD-DFT 12 16 PI l 850 1550 nm l 140 200 nm n a Gaussian 09 Rev.C-01 functional a 2 V int L L DFT CAM B3LYP 6 31G d 10 6 31+G 2d,p 15 16 n 3
3 5 n n 4ab DFT 500 nm 6 101 l 44 8 2015 486, 589, 656 nm a l L L 589 nm n 589 n 4 Br DFT n n n DFT n 589 n 5 n DFT 301 5
6 8 7 18 27 R R' Bicerano 17 1 4. PMMA PSt PC n DFT 6 n n 302 6 PSt PC n S SO 2 18 27 DFT S c PI 7 1.7 PI PI s-bpda 7 APTT PI l 633 850 1310 nm n l 8 n S c SO 2 BADPS
n VIS n 633 9 b n 633 1.7 PI PI n 1.75 DFT 9 a b n CT S c n CHDA, CBDA CT n 1.72 PI n l n D/l 2 n D 9 a PI n D PI D ODPA mdpsda PI PI CBDA CHDA 3SDEA s-bpda PI l 633, 845, 1324 nm 44 8 2015 1 33 1984 266 273. 2 1987 3 1994 4 1998 520 2008 170 176. 6 3 1984 7 J. A. Dean: Lange s Handbook of Chemistry, 15th ed. McGraw- Hill, 1998. 8 M. Fox: Optical Properties of Solids Oxford Univ. Press, 2001. 9 M. Schmidt, A. Brodin, P. Jacobsson and F. H. J. Maurer: J. Chem. Phys., 112 2000 1020 1028. 10 G. L. Slonimskii, A. A. Askadskii and A. I. Kitaigotodskii: Polym. Sci. USSR, A12 1970 556 577. 11 A. Javadi, A. Shockravi, A. Rafieimanesh, A. M. Malek and S. Ando: Polym. Int., 64 2015 486 495. 12 S. Ando: J. Photopolym. Sci. Technol., 19 2006 351 360. 13 S. Ando, T. Fujigaya and M. Ueda: J. Photopolym. Sci. Technol., 15 2002 559 568. 14 S. Ando and M. Ueda: J. Photopolym. Sci. Technol., 16 2003 537 544. 15 Y. Terui and S. Ando: J. Polym. Sci. Part B: Polym. Phys., 43 2005 2109 2120. 16 S. Ando: in preparation. 17 J. Bicerano: Prediction of Polymer Properties CRC Press, 2002. 18 J.-G. Liu, Y. Nakamura, Y. Suzuki, Y. Shibasaki, S. Ando and M. Ueda: Macromolecules, 40 2007 4614 4620. 19 J.-G. Liu, Y. Nakamura, Y. Shibasaki, S. Ando and M. Ueda: J. Polym. Sci. Part A: Polym. Chem., 45 2007 5606 5617. 20 J.-G. Liu, Y. Nakamura, Y. Suzuki, Y. Shibasaki, S. Ando and M. Ueda: Macromolecules, 40 2007 7902 7909. 21 J-G. Liu, Y. Nakamura, T. Ogura, Y. Shibasaki, S. Ando and M. Ueda: Chem. Mater., 20 2008 273 281. 22 R. Okutsu, S. Ando and M. Ueda: Chem. Mater., 20 2008 4017 4023. 23 R. Okutsu, Y. Suzuki, S. Ando and M. Ueda: Macromolecules, 41 2008 6165 6168. 24 N.-H. You, Y. Suzuki, D. Yorifuji, S. Ando and M. Ueda: Macromolecules, 41 2008 6361 6366. 25 C. A. Terraza, J.-G. Liu, Y. Nakamura, Y. Shibasaki, S. Ando and M. Ueda: J. Polym. Sci. Part A: Polym. Chem., 46 2008 1510 1520. 26 N.-H. You, Y. Suzuki, T. Higashihara, S. Ando and M. Ueda: Polymer, 50 2009 789 795. 27 Y. Suzuki, T. Higashihara S. Ando and M. Ueda: Eur. Polym. J., 46 2010 34 41. 2015 2 19 303 7