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Enhanced two-photon absorption properties of weakly conjugated oligomers
Optical Materials 21 (2002) 555–557 www.elsevier.com/locate/optmat
Enhanced two-photon absorption properties of weakly conjugated oligomers C. Martineau, G. Lemercier, C. Andraud
*
Ecole Normale Sup erieure de Lyon (ENS-Lyon), St er eochimie et Interactions Mol eculaires (STIM), UMR CNRS no. 5532, 69364 Lyon C edex 07, France
Abstract The theoretical study of two-photon absorption (TPA) properties of a non-conjugated dimer is related to cooperative effects between monomers. This effect leads to a strong increase of the TPA cross-section. This phenomenon is studied in the case of the three-level model. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 78.66.Q; 82.50.P; 42.70.M,N Keywords: Two-photon absorption; Oligomers; CNDO/S calculations
1. Introduction Two-photon absorption (TPA) properties of organic compounds were shown to be relevant for many applications [1]. Several organic molecules consisting in substituted systems were optimized for these applications by studying the influence of the conjugated path and of substituents [2–4]. Recently, we developed a new strategy involving organic oligomers for TPA applications in the visible range, in which the N-oligomer is considered as constituted of N monomers in excitonic coupling. This strategy was found to be efficient in unsubstituted conjugated dimers, i.e. a bistilbene molecule (the stilbene-3) [5], and the bifluorene [6].
*
Corresponding author. Tel.: +33-4-7272-8398; fax: +33-47272-8483. E-mail address: [email protected] (C. Andraud).
Theoretical studies showed also the interest of longer oligomers, such as polyphenyls and polyfluorenes, corroborating our model of excitonic interactions for conjugated systems [7]. An experimental work on a polyfluorene also confirmed this trend [8]. In this paper, we present the theoretical TPA properties of a weakly conjugated dimer, (the molecule IIn of Fig. 1). This molecule is a system of type D–p–A–p–D, in which D is the vanillyl donor group, p the conjugated path consisting in a polyenic chain with n double bonds and A the ketone acceptor group. The molecule IIn can be considered as constituted of two monomers In of type D–p–A, in which the acceptor group is an aldehyde (the efficiency of acceptor groups can be considered as similar in both cases). Calculated TPA properties of II2 were dissected using the three-level model and were related to those of I2 from an excitonic coupling model.
0925-3467/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 3 4 6 7 ( 0 2 ) 0 0 1 9 9 - 4
556
C. Martineau et al. / Optical Materials 21 (2002) 555–557 O MeO
( H
) n In
MeO
O MeO
(
( n
) n
)
II n
MeO
OMe
OMe
Fig. 1. Molecular structures of the dimer IIn and of its monomer parent In .
2. Calculations procedure Fig. 2. TPA spectra of I2 and II2 .
The TPA cross-section rTPA is proportional to the imaginary part of the average second hyperpolarizability (Eqs. (1) and (2)): rTPA ¼
3 x2 h 2 2 f 4 Imhcðx; x; x; xÞi 10 n c e0
1 hci ¼ ðcxxxx þ cyyyy þ czzzz þ cxxyy þ cyyxx þ cyyzz 5 þ czzyy þ cxxzz þ czzxx Þ
ð1Þ
ð2Þ
The calculation of rTPA was performed using the same procedure than in Ref. [4] from the Orr and WardÕs equation [9]. Theoretical results were interpreted on the basis of the three-level model following Eq. (3) [10]: 1 c/ ð3Þ l201 ðl212 þ Dl21 Þ 2 ðE01 ðE02 =2ÞÞ C where l01 and l12 are the transition moments between the ground state S0 and the lowest charge transfer excited-state S1 , and between S1 and the lowest two-photon excited state S2 , respectively. Dl1 is the dipole moment difference between S0 and S1 ; this feature, which is generally neglected in symmetric molecules, does not vanish in I2 and II2 as will be seen below on Table 1. E01 and E02 are respectively the energies of S1 and S2 .
3. Results and discussion The spectral TPA distribution of II2 is displayed on Fig. 2 with that of I2 for comparison. The TPA spectrum of II2 consists in several bands between 450 and 650 nm at respectively 465, 518 and 579 nm, while the TPA spectrum of I2 is only composed in this wavelength range of a well-defined band at 524 nm. The analysis of rTPA of II2 in terms of dipolar coupling consists to consider II2 as a dimer of two monomers I2 in coupling interactions. In this assumption, we used the exciton model of aggregates to interpret the electronic states parameters of II2 . In this model, the transition moments lij ðIIÞ (l01 and l12 ) of the dimer are defined as a function of those of their parent monomer lij ðIÞ following Eq. (4): pffiffiffi ð4Þ lij ðIIÞ ¼ 2 cos hlij ðIÞ in which the angle h is related to geometry of the dimer [11]; in the case of II2 , h ¼ 24°. The exciton coupling analysis of rTPA of II2 was performed on the 518 nm TPA band (Fig. 2); this band is the analog of the 524 nm band of I2 , since
Table 1 One-photon and TPA parameters of I2 and II2 I2 II2
k01 (nm)
kTPA (nm)
l01 (D)
Dl1 (D)
l12 (D)
rTPA (cm4 s/photon)
287 319
524 518
7.4 12.5
4.7 2.6
6.8 11.1
1:7 1048 5:4 1048
C. Martineau et al. / Optical Materials 21 (2002) 555–557
both bands appear at similar wavelengths in similar charge transfer systems with a weak further conjugation process in II2 . TPA parameters (rTPA , kTPA and l12 ) and one-photon absorption features (k01 , l01 and Dl1 ) were reported on Table 1. The ratios aij (aij ¼ lij ðIIÞ=lij ðIÞ) between lij ðIIÞ and lij ðIÞ are respectively 1.7 and 1.6 for l01 and l12 ; these values are relatively close of the ratio of 1.3 predicted by the relationship (4), validing our coupling model. The difference could arise from the slightly different acceptor efficiencies of the ketone and of the aldehyde in II2 and I2 respectively. The dipolar coupling leads to enhanced rTPA values in II2 , since a ratio of 3.2 is obtained between the TPA cross-sections of II2 and I2 for the considered band. It is relevant to note that these enhanced values of rTPA are mainly due to the large increase of dipole moments transitions following Eq. (4). In the case of II2 Eq. (3) reduces to (5), since for this molecule the ratio l201 l212 =l201 Dl21 is nearly equal to 10; this is not true for I2 , in which this parameter is close to 1. Due to this behavior, no relationship between rTPA ðIIÞ and rTPA ðIÞ could be established on the basis of the three-level model. c/
l201 l212 2
ðE01 ðE02 =2ÞÞ C
ð5Þ
Studies of further systems, in which the influence of the donor group D and of the length of the polyenic chain n are investigated (Fig. 1), are currently in progress. References [1] B.A. Reinhardt, Photon. Sci. News 4 (1999) 21.
557
[2] (a) J.E. Ehrlich, X.L. Wu, I.-Y.S. Lee, Z.-Y. Hu, H. R€ ockel, S.R. Marder, J.W. Perry, Opt. Lett. 22 (1997) 1843; (b) J.W. Perry, S. Barlow, J.E. Ehrlich, A.A. Heikal, Z.-Y. Hu, I.-Y.S. Lee, K. Mansour, S.R. Marder, H. R€ ockel, M. Rumi, S. Thayumanavan, X.-L. Wu, Nonlinear Opt. 21 (1999) 225; (c) S. Delysse, P. Filloux, V. Dumarcher, C. Fiorini, J.-M. Nunzi, Opt. Mater. 9 (1998) 347; (d) C. Nguefack, T. Zabulon, R. Anemian, C. Andraud, A. Collet, S. Topcßu, P.L. Baldeck, Nonlinear Opt. 21 (1999) 309. [3] M. Albota, D. Beljonne, J.L. Bredas, J.E. Ehrlich, J.-Y. Fu, A.A. Heikal, S.E. Hess, T. Kogej, M.D. Levin, S.R. Marder, D. McCord-Maughon, J.W. Perry, H. R€ ockel, M. Rumi, G. Subramaniam, W.W. Webb, X.-L. Wu, C. Xu, Science 281 (1998) 1653. [4] (a) C. Andraud, R. Anemian, A. Collet, J.-M. Nunzi, Y. Morel, P.L. Baldeck, J. Opt. A: Pure Appl. Opt. 2 (2000) 284; (b) R. Anemian, C. Andraud, A. Collet, J.-M. Nunzi, Y. Morel, P.L. Baldeck, Nonlinear Opt. 25 (2000) 145. [5] (a) P.-A. Chollet, V. Dumarcher, J.-M. Nunzi, P. Feneyrou, P. Baldeck, Nonlinear Optics 21 (1999) 299; (b) P.-A. Chollet, A. Sornin, B. Paci, V. Hully, J.-M. Nunzi, Y. Morel, P.L. Baldeck, in: K. Nashimoto, B.W. Wessels, J. Shmulovich, A.K.-Y. Jen, K. Lewis, R. Pachter, R. Sutherland, J. Perry (Eds.), Mat. Res. Soc. Symp. Proc., Thin Films for Optical Waveguide Devices and Materials for Optical Limiting, vol. 597, MRS, Boston, in press. [6] Y. Morel, A. Irimia, P. Najechalski, Y. Kervella, O. Stephan, P.L. Baldeck, C. Andraud, J. Chem. Phys. 114 (2001) 5391. [7] C. Andraud, P.L. Baldeck, Nonlinear Opt. 25 (2000) 133. [8] P. Najechalski, Y. Morel, O. Stephan, P.L. Baldeck, Chem. Phys. Lett. 343 (2001) 44. [9] B.J. Orr, J.F. Ward, Mol. Phys. 20 (1971) 513. [10] A.F. Garito, J.R. Heflin, K.Y. Wong, O. Zamani-Khamiri, in: R.A. Hann, D. Bloor (Eds.), Organic Materials for Nonlinear Optics, Royal Society of Chemistry, London, 1989, p. 16. [11] E.G. McRae, M. Kasha, J. Chem. Phys. 28 (1958) 721.
Enhanced two-photon absorption properties of weakly conjugated oligomers C. Martineau, G. Lemercier, C. Andraud
*
Ecole Normale Sup erieure de Lyon (ENS-Lyon), St er eochimie et Interactions Mol eculaires (STIM), UMR CNRS no. 5532, 69364 Lyon C edex 07, France
Abstract The theoretical study of two-photon absorption (TPA) properties of a non-conjugated dimer is related to cooperative effects between monomers. This effect leads to a strong increase of the TPA cross-section. This phenomenon is studied in the case of the three-level model. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 78.66.Q; 82.50.P; 42.70.M,N Keywords: Two-photon absorption; Oligomers; CNDO/S calculations
1. Introduction Two-photon absorption (TPA) properties of organic compounds were shown to be relevant for many applications [1]. Several organic molecules consisting in substituted systems were optimized for these applications by studying the influence of the conjugated path and of substituents [2–4]. Recently, we developed a new strategy involving organic oligomers for TPA applications in the visible range, in which the N-oligomer is considered as constituted of N monomers in excitonic coupling. This strategy was found to be efficient in unsubstituted conjugated dimers, i.e. a bistilbene molecule (the stilbene-3) [5], and the bifluorene [6].
*
Corresponding author. Tel.: +33-4-7272-8398; fax: +33-47272-8483. E-mail address: [email protected] (C. Andraud).
Theoretical studies showed also the interest of longer oligomers, such as polyphenyls and polyfluorenes, corroborating our model of excitonic interactions for conjugated systems [7]. An experimental work on a polyfluorene also confirmed this trend [8]. In this paper, we present the theoretical TPA properties of a weakly conjugated dimer, (the molecule IIn of Fig. 1). This molecule is a system of type D–p–A–p–D, in which D is the vanillyl donor group, p the conjugated path consisting in a polyenic chain with n double bonds and A the ketone acceptor group. The molecule IIn can be considered as constituted of two monomers In of type D–p–A, in which the acceptor group is an aldehyde (the efficiency of acceptor groups can be considered as similar in both cases). Calculated TPA properties of II2 were dissected using the three-level model and were related to those of I2 from an excitonic coupling model.
0925-3467/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 3 4 6 7 ( 0 2 ) 0 0 1 9 9 - 4
556
C. Martineau et al. / Optical Materials 21 (2002) 555–557 O MeO
( H
) n In
MeO
O MeO
(
( n
) n
)
II n
MeO
OMe
OMe
Fig. 1. Molecular structures of the dimer IIn and of its monomer parent In .
2. Calculations procedure Fig. 2. TPA spectra of I2 and II2 .
The TPA cross-section rTPA is proportional to the imaginary part of the average second hyperpolarizability (Eqs. (1) and (2)): rTPA ¼
3 x2 h 2 2 f 4 Imhcðx; x; x; xÞi 10 n c e0
1 hci ¼ ðcxxxx þ cyyyy þ czzzz þ cxxyy þ cyyxx þ cyyzz 5 þ czzyy þ cxxzz þ czzxx Þ
ð1Þ
ð2Þ
The calculation of rTPA was performed using the same procedure than in Ref. [4] from the Orr and WardÕs equation [9]. Theoretical results were interpreted on the basis of the three-level model following Eq. (3) [10]: 1 c/ ð3Þ l201 ðl212 þ Dl21 Þ 2 ðE01 ðE02 =2ÞÞ C where l01 and l12 are the transition moments between the ground state S0 and the lowest charge transfer excited-state S1 , and between S1 and the lowest two-photon excited state S2 , respectively. Dl1 is the dipole moment difference between S0 and S1 ; this feature, which is generally neglected in symmetric molecules, does not vanish in I2 and II2 as will be seen below on Table 1. E01 and E02 are respectively the energies of S1 and S2 .
3. Results and discussion The spectral TPA distribution of II2 is displayed on Fig. 2 with that of I2 for comparison. The TPA spectrum of II2 consists in several bands between 450 and 650 nm at respectively 465, 518 and 579 nm, while the TPA spectrum of I2 is only composed in this wavelength range of a well-defined band at 524 nm. The analysis of rTPA of II2 in terms of dipolar coupling consists to consider II2 as a dimer of two monomers I2 in coupling interactions. In this assumption, we used the exciton model of aggregates to interpret the electronic states parameters of II2 . In this model, the transition moments lij ðIIÞ (l01 and l12 ) of the dimer are defined as a function of those of their parent monomer lij ðIÞ following Eq. (4): pffiffiffi ð4Þ lij ðIIÞ ¼ 2 cos hlij ðIÞ in which the angle h is related to geometry of the dimer [11]; in the case of II2 , h ¼ 24°. The exciton coupling analysis of rTPA of II2 was performed on the 518 nm TPA band (Fig. 2); this band is the analog of the 524 nm band of I2 , since
Table 1 One-photon and TPA parameters of I2 and II2 I2 II2
k01 (nm)
kTPA (nm)
l01 (D)
Dl1 (D)
l12 (D)
rTPA (cm4 s/photon)
287 319
524 518
7.4 12.5
4.7 2.6
6.8 11.1
1:7 1048 5:4 1048
C. Martineau et al. / Optical Materials 21 (2002) 555–557
both bands appear at similar wavelengths in similar charge transfer systems with a weak further conjugation process in II2 . TPA parameters (rTPA , kTPA and l12 ) and one-photon absorption features (k01 , l01 and Dl1 ) were reported on Table 1. The ratios aij (aij ¼ lij ðIIÞ=lij ðIÞ) between lij ðIIÞ and lij ðIÞ are respectively 1.7 and 1.6 for l01 and l12 ; these values are relatively close of the ratio of 1.3 predicted by the relationship (4), validing our coupling model. The difference could arise from the slightly different acceptor efficiencies of the ketone and of the aldehyde in II2 and I2 respectively. The dipolar coupling leads to enhanced rTPA values in II2 , since a ratio of 3.2 is obtained between the TPA cross-sections of II2 and I2 for the considered band. It is relevant to note that these enhanced values of rTPA are mainly due to the large increase of dipole moments transitions following Eq. (4). In the case of II2 Eq. (3) reduces to (5), since for this molecule the ratio l201 l212 =l201 Dl21 is nearly equal to 10; this is not true for I2 , in which this parameter is close to 1. Due to this behavior, no relationship between rTPA ðIIÞ and rTPA ðIÞ could be established on the basis of the three-level model. c/
l201 l212 2
ðE01 ðE02 =2ÞÞ C
ð5Þ
Studies of further systems, in which the influence of the donor group D and of the length of the polyenic chain n are investigated (Fig. 1), are currently in progress. References [1] B.A. Reinhardt, Photon. Sci. News 4 (1999) 21.
557
[2] (a) J.E. Ehrlich, X.L. Wu, I.-Y.S. Lee, Z.-Y. Hu, H. R€ ockel, S.R. Marder, J.W. Perry, Opt. Lett. 22 (1997) 1843; (b) J.W. Perry, S. Barlow, J.E. Ehrlich, A.A. Heikal, Z.-Y. Hu, I.-Y.S. Lee, K. Mansour, S.R. Marder, H. R€ ockel, M. Rumi, S. Thayumanavan, X.-L. Wu, Nonlinear Opt. 21 (1999) 225; (c) S. Delysse, P. Filloux, V. Dumarcher, C. Fiorini, J.-M. Nunzi, Opt. Mater. 9 (1998) 347; (d) C. Nguefack, T. Zabulon, R. Anemian, C. Andraud, A. Collet, S. Topcßu, P.L. Baldeck, Nonlinear Opt. 21 (1999) 309. [3] M. Albota, D. Beljonne, J.L. Bredas, J.E. Ehrlich, J.-Y. Fu, A.A. Heikal, S.E. Hess, T. Kogej, M.D. Levin, S.R. Marder, D. McCord-Maughon, J.W. Perry, H. R€ ockel, M. Rumi, G. Subramaniam, W.W. Webb, X.-L. Wu, C. Xu, Science 281 (1998) 1653. [4] (a) C. Andraud, R. Anemian, A. Collet, J.-M. Nunzi, Y. Morel, P.L. Baldeck, J. Opt. A: Pure Appl. Opt. 2 (2000) 284; (b) R. Anemian, C. Andraud, A. Collet, J.-M. Nunzi, Y. Morel, P.L. Baldeck, Nonlinear Opt. 25 (2000) 145. [5] (a) P.-A. Chollet, V. Dumarcher, J.-M. Nunzi, P. Feneyrou, P. Baldeck, Nonlinear Optics 21 (1999) 299; (b) P.-A. Chollet, A. Sornin, B. Paci, V. Hully, J.-M. Nunzi, Y. Morel, P.L. Baldeck, in: K. Nashimoto, B.W. Wessels, J. Shmulovich, A.K.-Y. Jen, K. Lewis, R. Pachter, R. Sutherland, J. Perry (Eds.), Mat. Res. Soc. Symp. Proc., Thin Films for Optical Waveguide Devices and Materials for Optical Limiting, vol. 597, MRS, Boston, in press. [6] Y. Morel, A. Irimia, P. Najechalski, Y. Kervella, O. Stephan, P.L. Baldeck, C. Andraud, J. Chem. Phys. 114 (2001) 5391. [7] C. Andraud, P.L. Baldeck, Nonlinear Opt. 25 (2000) 133. [8] P. Najechalski, Y. Morel, O. Stephan, P.L. Baldeck, Chem. Phys. Lett. 343 (2001) 44. [9] B.J. Orr, J.F. Ward, Mol. Phys. 20 (1971) 513. [10] A.F. Garito, J.R. Heflin, K.Y. Wong, O. Zamani-Khamiri, in: R.A. Hann, D. Bloor (Eds.), Organic Materials for Nonlinear Optics, Royal Society of Chemistry, London, 1989, p. 16. [11] E.G. McRae, M. Kasha, J. Chem. Phys. 28 (1958) 721.