2837
J . Phys. Chem. 1992, 96,2831-2843
Third-Order Nonlinear Optical Properties of Conjugated Rigid-Rod Polyquinollnes Asbwini K. Agrawal, Samson A. Jenekhe,* Department of Chemical Engineering and Center for Photoinduced Charge Transfer, University of Rochester, Rochester, New York 14627-0166
Herman Vanherzeele, and Jeffrey S. Meth Du Pont Central Research and Development Department, Wilmington, Delaware 19880-0356 (Received: September 18, 1991; In Final Form: December 2, 1991)
We have used picosecond third harmonic generation spectroscopy to investigate the third-order optical nonlinearities of a series of 12 systematically designed homopolymers and random copolymers in the class of conjugated rigid-rod polyquinolines and polyanthrazolines. The x(~)(-~w;w,o,w) spectra of these materials in the 0.9-2.4-~m wavelength (1.4-0.5 eV) range showed resonance peaks which were identified as the three-photon resonances. The magnitude of the three-photon resonance ) in the range 0.8 X 10-"-3.3 X lo-" esu with backbone structure of the polymers. Off-resonance at enhanced x ( ~varied ) for all the polymers were found to be very close to each other, ~ ( 2 . 5 0.5) X esu within 2.38 Nm, the x ( ~values ) not be correlated with the optical bandgap the experimental errors. The magnitude of the resonant or nonresonant x ( ~could of the series of polymers. A theoretical fit of the x(') dispersion data using a three-level model based on essential states mechanism suggested that more than one excited state is responsible for the observed third-order optical nonlinearity of the materials. The nonlinear optical properties of the random copolymers were, within experimental errors, the molar averages of those of the respective constituent homopolymers, suggestingthe absence of significant changes in the third-order optical nonlinearities with introduction of disorder in the copolymer backbone.
*
CHART I
Introduction
Conjugated polymers hold potential as third-order nonlinear optical materials.'-I6 The large nonresonant third-order sus-
* R
Ph 1
(1) (a) Prasad, P. N.; Williams, D. J. Introduction to Nonlinear Optical Effects in Molecules and Polymers; Wiley: New York, 1991. (b) Marder, S. R., Sohn, J. E., Stucky, G. D., Eds. Materials for Nonlinear Optics: Chemical Perspectiues; ACS Symposium Series No. 455; American Chemical Society: Washington, DC, 1991. (c) Chemla, D. S., Zyss, J., Eds. Nonlinear Optical Properties of Organic Molecules and Crystals; Academic Press: New York, 1987; Vol. 1 and 2. (d) Skotheim, T. A., Ed. Electroresponsiue Molecular and Polymeric Systems; Marcel Dekker: New York, 1991; Vol. 2. (e) Eaton, D. F. Science 1991, 253, 281-287. (f) B r a a s , J. L., Chance, R. R., Eds. Conjugated Polymeric Materials: Opportunities in Electronics, Optoelectronics, and Molecular Electronics; Kluwer Academic Publishers: Dordrecht, 1990. (2) (a) Vijaya, R.; Murti, Y. V. G. S.; Rao, T. A. P.; Sundararajan, G. J.Appl. Phys. 1991,69,3429-3431. (b) Drury, M. R. Solid State Commun. 1988, 68, 417. (c) Kajzar, F.; Etemad, S.; Baker, G. L.; Messier, J. Solid Stare Commun. 1987,63, 1 1 13. (d) Krausz, F.; Wintner, E.; Leising, G. Phys. Reu. B 1989, 39, 3701. (e) Sinclair, M.; Moses, D.; Heeger, A. J.; Vilhelmsson, K.; Valk, B.; Salour, M. Solid State Commun. 1987,61, 221. (f) Etemad, S.; Baker, G. L. Synrh. Mer. 1989, 28, D159. (9) Dorsinville, R.; Yang, L.; Alfano, R. R.; Tubino, R.; Destri, S.Solid State Commun. 1988, 68, 875. (h) Marder, S. R.; Perry, J. W.; Klavetter, F. L.; Grubbs, R. H. Chem. Mater. 1989, I , 171. (i) Neher, D.; Wolf, A.; Bubeck, C.; Wegner, G. Chem. Phys. Lett. 1989,163, 116. (j) Fann, W.-S.; Benson, S.; Madey, J. M. J.; Etemad, S.; Baker, G. L.; Kajzar, F. Phys. Rev. Lett. 1989,62, 1492. (3) Kanetake, T.; Ishikawa, K.; Hasegawa, T.; Koda, T.; Takeda, K.; Hasegawa, M.; Kubodera, K.; Kabayashi, H. Appl. Phy. Lett. 1989, 54, 2287-2289. (4) {a) Kaino, T.; Kobayashi, H.; Kobodera, K.-I.; Kurihara, T.; Saito, S.; Tsutsui, T.; Tokito, S. Appl. Phys. Lett. 1989,54, 1619. (b) McBranch, D.; Sinclair, M.; Heeger, A. J.; Patil, A. 0.; Shi, S.; Askari, S.; Wudl, F. Synth. Met. 1989, 29, E85. (c) Messier, J. In: Messier, J., et al., Eds. Nonlinear Optical Effects in Organic Polymers; 1989; p 47. (d) Rao, D. N.; Chopra, P.; Ghoshal, S.K.; Swiatkiewicz, J.; Prasad, P. N. J . Chem. Phys. 1986,84, 7049. (e) Sauteret, C.; Hermann, J. P.; Frey, R.; Pradere, F.; Ducuing, J.; Baughman, R. H.; Chance, R. R. Phys. Rev. Lett. 1976, 36, 956. (f) Tormellas, W. E.; Rochford, K. B.; Zanoni, R.; Aramaki, s.;Stegeman, G. I. Opt. Commun. 1991,82, 94-100. ( 5 ) (a) Swiatkiewicz, J.; Prasad, P. N.; Karasz, F. E.; Druy, M. A,; Glatkowski, P. Appl. Phys. Lert. 1990,56,892. (b) Sugiyama, T.; Wada, T.; Sasabe, H. Synrh. Met. 1989, 28, C323. (c) Dorsinville, R.; Yang, L.; Alfano, R. R.; Zamboni, R.; Danieli, R.; Ruani, G.; Taliani, C. Opt. Lett. 1989, 14, 1321. (d) Kajzar, F.; Messier, J.; Sentein, C.; Elsenbaumer, R. L.;Miller, G. G. SPIE, Nonlinear Optical Prop. Org. Mater. II 1989, 1147, 37. (e) Singh, B. P.; Samoc, M.; Nalwa, H. S.;Prasad, P.N. J . Chem. Phys. 1990, 92, 2756. (f) Kaino, T.; Kubodera, K.; Kobayashi, H.; Kurihara, T.; Saito, S.; Tsutsui, T.; Tokito, S.; Murata, H. Appl. Phys. Lett. 1988,53, 2002. (g) Kajzar, F.; Ruani, R.; Taliani, C.; Zamboni, R. Synth. Mer. 1990, 37, 223. (h) Torruellas, W. E.; Neher, D.; Zanoni, R.; Stegeman, G. I.; Kajzar, F.; Leclerc, M.Chem. Phys. Lett. 1990, 175, 11-16.
m
-o-=+-
m
b
bh
Ph' 2
Ph
C
Ph 3
d
G C H 4 - J 1 PPQ 2a PBPQ 2b PBAPQ 2c PSPQ 2d PPPQ 2e PDMPQ
e
3a 3b 3c 3d 3e
PBDA PBADA PSDA PPDA PDMDA
ceptibility x ( ~ )very , fast response time (subpicosecond), ease of fabrication, and the possibility of molecular engineering to modify (6) Houlding, V. H.; Nahata, A.; Yardley, J. T.; Elsenbaumer, R. L. Chem. Mater. 1990, 2, 169-172. (7) (a) Jenekhe, S. A.; Chen, W. C.; Lo, S. K.; Flom, S. R. Appl. Phys. Lett. 1990, 57, 126-128. (b) Jenekhe, S. A.; Lo, S. K.; Flom, S. R. Appl. Phys. Lett. 1989, 54, 2524. (8) Kaino, T.; Kubodera, K.-I.; Tomaru, S.; Kurihara, T.; Saito, S.; Tsutsui, T.; Tokito, S. Electron. Lett. 1987, 23, 1095. (b) Swiatkiewicz, J.; Prasad, P. N. Appl. Phys. Lett. 1990, 56, 892. (9) (a) Vanherzeele, H.; Meth, J. S.; Jenekhe, S. A,; Roberts, M. F. Appl. Phys. Lett. 1991, 58, 663-665. (b) Vanherzeele, H.; Meth, J. S.;Jenekhe, S. A,; Roberts, M. F. J. Opt. SOC.A m . B, in press. (10) Lee, C. Y.-C.; Swiatkiewicz, J.; Prasad, P. N.; Mehta, R.; Bai, S. J. Polymer 1991,32, 1195-1 199. (11) (a) Jenekhe, S. A.; Roberts, M. F.; Agrawal, A. K.; Meth, J. S.; Vanherzeele, H. Mater. Res. SOC.Symp. Proc. 1991, 214, 55-59. (b) Meth, J. S.; Vanherzeele, H.; Jenekhe, S. A.; Yang, C.-J.; Roberts, M. F.; Agrawal, A. K. SPIE Proc. 1991, 1560, 13-24. (12) (a) Lindle, J. R.; Bartoli, F. J.; Hoffman, C. A.; Kim, 0.-K.; Lee, Y. S.; Shirk, J. S.; Kafafi, 2. H. Appl. Phys. Lett. 1990, 56, 712. (b) Yu, L.; Chen, M.; Dalton, L. R. Chem. Muter. 1990, 2, 649. (13) (a) Yu, L. P.; Dalton, L. R. Synrh. Mer. 1989,29, E463. (b) Yu, L.; Dalton, L. R. Macromolecules 1990, 23, 3439. (14) (a) Prasad, P. N.; Reinhardt, B. A. Chem. Mater. 1990, 2,660-669. (b) Zhao, M.-T.; Samoc, M.; Prasad, P. N.; Reinhardt, B. A,; Unroe, M. R.; Prazak, M.; Evers, R. C.; Kane, J. J.; Jariwala, C.; Sinsky, M. Chem. Mater. i990,2,670-678.
0022-3654/92/2096-2837%03.00/0 0 1992 American Chemical Society
2838 The Journal of Physical Chemistry, Vol. 96, No. 7, 1992 electronic, optical, physical, and structural properties according to the requirements of application, are some of the advantages provided by conjugated polymers. In the past few years, substantial progress has been made in understanding the different routes of synthesis and processing of various classes of conjugated polymers. The third-order optical nonlinearities of many of them, including polyacetylene,2 p~lydiacetylenes,~~~ polythiophene~,~-~ poly(p-phenylenevinylene),s poly(benzobisthiazoles),9Jo poly(benzimidazobenzophenanthroline) type ladder (BBL) and semhave been iladder (BBB) polymers,11si2and polyquin~xalines,~~ investigated using various techniques. However, none of these polymers exhibit all the required properties for practical nonlinear optical applications. The magnitude of the nonresonant x ( ~is) still quite low, and optical losses are usually high. It is essential to understand the physical basis of the third-order nonlinear optical response in conjugated polymers and the underlying x ( ~structural ) properties in order to design and synthesize new materials with larger third-order optical nonlinearities and figure of merit. Although a large amount of data on the thirdorder susceptibility of polymers has been accumulated during the past decade, it is difficult to compare data or to elucidate x ( ~ ) structural properties from them. Different characterization techniques have been used, and data sets as a function of frequency are available only for very few polymers, for example, polyacetylene,2Jpolydiacetylene$‘ and polythi~phene.~~ As a result, the relative contributions of resonant and nonresonant processes and the real and imaginary contributions to the optical nonlinearity are not well defined. Consequently, systematic studies are required to investigate s t r u c t u r e ~ (relationships ~1 and for testing theoretical models. Recently, some systematic studies on benzimidazoles, benzothiazoles, benzoxazoles, and related small molecules were reported, providing some insight into the structure-y (second hyperpolarizability) re1ati0nships.l~ It was reported that y increases rapidly with increasing conjugation length and increasing a-electron density. It was also suggested that *-electron density could be increased by replacing hydrocarbon aromatic rings with heterocyclic rings or by placing electron-donating side groups in the molecules. However, relationships found in small molecules may not necessarily translate to macromolecular systems. Moreover, it is difficult to isolate and study one particular factor by changing structures in small molecules as such changes often result in simultaneous changes in more than one factor. Therefore, we recently started a systematic investigation of conjugated polymers in an effort to establish the structure-^(^) relationships and the physical nature of the ~ ( in~ these 1 materials.7*9,iiJ5J6 Our approach consists of five steps: ( 1 ) systematic design and synthesis of series of macromolecular structures within a single class of conjugated polymers; (2) development of thin-film processing approaches to control optical quality and morphology of the solid polymers and consequently optical losses; (3) measurement of wavelength dispersion of x ( ~in) polymer thin films using third harmonic generation (THG) spectroscopy, which probes only the electronic contribution to ~ ( ~ 1(4) ; theoretical modeling and understanding of the dispersion data using the essential states theory; (5) correlation of molecular structures to third-order nonlinear optical properties. In this paper, we report the third-order nonlinear optical properties of nine conjugated polyquinolines and polyanthrazolines . polymers, shown including the dispersion of ~ ( ~ ) ( - 3 w ; w , w , w )These in Chart I, were synthesized in order to understand the role of effective a-electron delocalization along the backbone of conjugated polymers on their third-order nonlinear optical properties. The conformation of the polymer chains and hence the *-electron (15) (a) Osaheni, J. A,; Jenekhe, S. A,; Vanherzeele, H.; Meth, J. S. Chem. Mafer. 1991, 3, 218-221. (b) Osaheni, J. A,; Jenekhe, S. A,; Vanherzeele, H.; Meth, J. S. Polym. Prepr. 1991, 32, 154. (c) Osaheni, J. A,; Jenekhe, S. A.; Vanherzeele, H.; Meth, J. S. J . Phys. Chem., this issue. (d) Jenekhe, S. A.; Yang, C.-J.; Vanherzeele, H.; Meth, J. S. Chem. Mafer. 1991, 3, 985-988. (e) Yang, C.-J.; Jenekhe, S. A,; Vanherzeele, H.; Meth, J. S. Polym. Prepr. 1991, 32, 165. (16) (a) Agrawal, A. K.; Jenekhe, S. A,; Vanherzeele, H.; Meth, J. S. Chem. Mafer. 1991, 3 , 765-768. (b) Agrawal, A. K.; Jenekhe, S. A,; Vanherzeele, H.; Meth, J. s. Polym. Prepr. 1991, 32, 124.
Agrawal et al. CHART 11
\
bh
Ph’
A\
bh
-lY
Ph‘
PSPQPBPQ (50:50)
P B W B A P Q (5O:SO)
’’ \
bh
Ph/
PSPQPBAPQ (50:50)
delocalization were altered by manipulating the steric hindrances on the backbone of the polymer chain by placing various linkages between the adjacent aromatic rings (structures a-d) or by fusing the quinoline rings together (2 3).’7a9bThe *-electron delocalization is inferred from the lowest energy peak (Amax) in the optical absorption spectrum: the larger the ,A, value, the more delocalized the electrons. Since the materials do not contain donor or acceptor groups which can shift the absorption, this correlation is expected to be valid. Two polymers, PDMPQ (Ze)and PDMDA (3e), with methylene linkage were synthesized to determine the effect of a-electron delocalization beyond the polymer repeat unit. A substantial blue shift of A,, (lowest energy maximum) in the nonconjugated polymers (PDMPQ, A- = 370 MI; PDMDA, A= 404 nm) compared to the conjugated polyquinolines and polyanthrazolines suggested effective *-electron delocalization over many repeat units. Further, the solution optical absorption spectra of these polymers in 0.1 mol % di-m-cresyl phosphatelm-cresol show trends in & similar to that in solid state ~pectra.”~These results suggest that the observed variations in A, are not merely a reflection of intermolecular interactions or packing but evidence of *-electron delocalization in these polymers. By restricting the structural changes to one class of polymers, the effect of *-electron delocalization was independently studied without the complications of overlapping effects of other factors, for example, electron density, changing substituents, intermolecular interactions, etc. It was hoped that this approach might also help in optimizing the conformation of polyquinolines for obtaining enhanced nonlinear optical properties. Another series of three random copolymers (Chart 11) was investigated in order to determine the effect of random disorder in the polymer backbone on third-order nonlinear optical properties. It was thought that by introducing random disorder in the backbone chain of the polymers, one might be able to affect the anharmonicity or asymmetry of the system and thereby enhance x ( ~ )Also, . copolymers constitute an important class of materials as they provide a means of obtaining amorphous materials with low optical losses and thus an overall improved figure of merit: Re ( ~ ( ~ ~ ( - w ; w , - w , w ) ) / c r . The processing and linear optical properties of all the homopolymers and copolymers in Charts I and I1 have previously been studied by us and are described in detail elsewhere.” Optical losses of the order of 1-10 cm-’ were determined in thin films of the polymers shown in Chart I.17aOur recent studies on waveguiding The cubic in PPPQ (2d) have shown similar optical nonlinear optical properties of Zb, ZC,and their random copolymer were previously discussed in a communication.16
-
Experimental Section Synthesis. The monomers, reaction medium, and polymers were successfully synthesized using procedures similar to those described in the literature.’* The details of the synthesis and structural (17) (a) Agrawal, A. K.; Jenekhe, S. A. Chem. Mafer. 1992,4, 95-104. (b) Agrawal, A. K.; Jenekhe, S. A., in preparation. (c) Otomo, A,; Mittler-Neher, s.;Stegeman. G . 1.; Mehta, R.; Lee, C. Y.-C.; Agrawal, A. K.; Jenekhe, S. A., to be presented at CLEO, 1992.
The Journal of Physical Chemistry, Vol, 96, No. 7, 1992 2839
Nonlinear Optics of Polyquinolines
TABLE I:,,,A the Resonant x ( ~ )and , Nonresonant x ( ~of) Conjugated Rigid-Rod Polyquinolines and Polyanthrazolines
h
c ._ C
~ ( ’ 1 , 10-’2 esu
t.
.-*e
poh
e
PPQ
v
w V
PBPQ
s
PBAPQ
z
[L
PSPQ as prepared (E)
-
4
WAVELENGTH, h (nm)
illuminated (Z) PPPQ
Figure 1. Optical absorption spectrum of rigid-rod polyquinoline: PBPQ.
PBDA PBADA PSDA PPDA PBPQIPBAPQ PSPQ/ PBAPQ as prepared (E)
h”
at 3Aa
(nm) [ev] 289 [4.29] 410 (3.021 (2)b 311 L3.991 (2) 394 i3.isj (1) 305 [4.07] (2) 399 [3.11] (1)
(pm) [eV]
resonant
nonresonant (2.38 pm)
1.2 [1.03]
11.2 f 2.2
2.3 f 0.5
1.2 [1.03]
19.2 f 3.8
2.1 f 0.4
1.2 [1.03]
26.6 f 5.3
2.2 f 0.4
1.2 [1.03]
8.1 f 1.6
2.2 f 0.4
1.2 [1.03]
33.3 f 6.6
3.2 f 0.6
1.32 [0.94] 1.05 [1.18] 1.32 [0.94] 1.05 [1.18] 1.32 [0.94] 1.05 [1.18] 1.32 [0.94]
15.0 f 3.0 31.5 f 6.3 19.3 f 3.8 13.8 f 2.7 13.4 f 2.7 17.7 f 3.5 10.9 f 2.2
2.0 f 0.4
1.2 [1.03]
26.4 f 5.2
2.0 f 0.4
1.2 [1.03]
17.8 f 3.6
2.2 f 0.4
1.2 [1.03]
18.8
* 3.8
1.8 f 0.4
284 [4.37] (2) 408 (3.041 ( I ) 289 [4.29] (1) 372 13.331 (2) 299 i4.1sj i2j 398 [3.12] (1) 338 L3.671 ( 1 ) 414 i3.OOj (2) 336 [3.69] (1) 426 (2.911 (2) 361 [3.43] ( I ) 448 [2.77] (2) 338 [3.67] ( I ) 443 [2.80] (2) 310 (4.00) (2) 397 [3.12] ( 1 )
2.8 f 0.6 2.2 f 0.4 1.8 f 0.4
280 [4.43] (2) 404 13.071 (1)
illumunated (Z) PSPQ/PBPQ as prepared (E) 1
300
400
500
600
700
I
WAVELENGTH, X (nm)
Figure 2. Optical absorption spectrum of rigid-rod polyanthrazoline:
PBDA.
characterization of the new polymers will be reported separately,17a.b
Sample Preparation. Thin films of the polymers were spin coated on fused silica substrate using the complexation-mediated solubilization and processing scheme described earlier.I’laqb Dilute solutions of the polymers were made in pure diphenyl phosphate (DPP) and spun at 100-120 “C or alternatively were made in DPP/nitromethane and spun at room temperature. Coatings of the polymer complex so obtained were regenerated to the pure polymers by precipitating them in triethylamine/ethanol for 24 h. The films were dried in vacuum at 70 OC for 4-6 h and shown by various techniques to be free of DPP.17a*bFigures 1 and 2 represent the typical optical absorption spectra of PBPQ of polyquinoline series (“PQ”series, l, 2) and PBDA of polyanthrazoline series (‘DA” series, 3), respectively. It is to be noted that the optical absorption spectrum of each member of this class of polymers has two bands with different oscillator strengths as exemplified in Figures 1 and 2. A summary of the optical absorption spectra of all the polymers studied is given in Table I, including the & and relative acillator strength of the two bands. Laser System. The laser system, which has been described in detail el~ewhere,’~ operates in two modes: continuous wave (100 MHz) and pulsed (10 Hz). The laser is continuously tunable from 0.6 to 4 pm in either of the two modes, and the pulse duration can be selected to be short (typically 5 ps) or long (typically 30-50 ps) independent of any other operating parameters. The average output power over the entire tuning range is at the miliwatt level for all modes of operation. The computer-controlled system is (18) (a) Pelter, M. W.; Stille, J. K. Macromolecules 1990, 23, 2418. (b) Sybert, P. D.; Beever, W. H.; Stille, J. K. Macromolecules 1981, 14,493. (c) Imai, Y.;Johnson, E. F.; Katto, T.; Kurihara, M.; Stille, J. K. J . Polym. Sci., Polym. Chem. Ed. 1975, 13, 2233-2249. (d) Ning, R. Y.; Madan, P. B.; Stembach, L. H. J. Heterocycl. Chem. 1974.11, 107-1 11. (e) Zimmermann, E. K.; Stille, J. K. Macromolecules 198S, 18, 321-327. (f) Sutherlin, D. M.; Stille, J. K. Macromolecules 1986, 19, 257-266. (g) Beever, W. H.; Stille, J. K. J . Polym. Sci., Polym. Symp. 1978, 65, 41-53. (h) Stille, J. K. Macromolecules 1981, 14, 870-880. (19) Vanherzeele, H. Appl. Opr. 1990, 29, 2246.
illuminated (Z)
280 402 290 390
[4.43] (2) [3.08] (1) [4.28] (1) I3.181 (2)
OValues in square brackets are in electronvolts. bNumbers in parentheses indicate the relative peak intensities: (1) > (2).
based on a high-power mode-locked Nd:YLF laser which synchronously pumps a dye laser and seeds a Nd:YLF regenerative amplifier. Frequency mixing and parametric generation/amplification in KTP crystals are used to obtain the large tunability. For x ( ~studies, ) the 10-Hz operation mode is used, and depending on the geometry of measurement (THG or DFWM) the pulse duration (respectively long or short) is selected. In this study, we have used the output of the parametric generator/amplifier consisting of a pair of single 35-45-ps pulses (signal and idler) each with energy >0.5 mJ anywhere in the tuning range. Pulse-to-pulse energy fluctuations were below 5%. THG Setup and Measurementof the Third-Order Swceptibility. The THG setup used in the measurement is as follows: A Glan Taylor polarizer is kept near the output of the laser system which rejects one of the orthogonally polarized output pulses (signal or idler). The remaining output beam is attenuated to 100 pJ/pulse, and its polarization direction is adjusted to vertical by means of a Soleil-Babinet compensator followed by a second Glan-Taylor polarizer. The energy per pulse is monitored by measuring a small fraction (4%) of the beam using a calibrated (cooled) Ge-detector. The remaining beam is split (90/10) into two separate beams. The weaker beam is used in a reference path and the stronger one in a sample path. The optics for focusing and collection as well as the equipment for THG detection (filters, monochromator, PMT, and boxcar integrator) are kept identical in both paths with the exception of a vacuum cell which is used only in the sample path. In the sample path, the sample is rotated about a vertical axis to generate a THG Maker fringe pattern. The vacuum cell removes undesirable contributions from air to the THG signal of the sample. In the reference path, a highly nonlinear (and stationary) polymer film on a silica substrate is used to generate the third harmonic. The thickness of this film is chosen so that it is smaller than the coherence length to avoid Maker fringes in the THG signal, and yet it is thick enough to give a THG signal that is 2 or more orders of magnitude larger than that from the substrate (to avoid interference). To improve signal-to-noise ratio (S/N), all laser shots are rejected for which either the energy of
2840 The Journal of Physical Chemistry, Vol. 96, No. 7, 1992
the fundamental or the third harmonic in the reference arm fall outside predetermined windows. In this way, the instabilities (both in energy per pulse and pulse width) of the laser source are effectively reduced to 1%. By the same token, any possible degradation of the sample in the reference arm can be monitored in real time. By taking the ratio of the THG signals in both arms, the effect of fluctuations in both power and pulse width of the fundamental beam are further eliminated. Finally, averaging this ratio of some 250 laser shots yields a precision of typically *OS%. The third-order susceptibility ~(~)(-3w;w,w,w) of the sample (thin polymer film on a fused silica substrate) is obtained relative to the fused silica in the following way: First, an approximate value for ~(~)(-3w;w,w,w) of the polymer is inferred using a procedure similar to that described in ref 3. The Maker fringe pattern of the sample is compared to the Maker fringe pattern of a blank substrate also placed in the sample arm. Since the thickness 1 of our polymer films is much less than their coherence length, the following approximation can be used:3
The subscripts s refers to the substrate (silica), I is the third harmonic signal, I , , represents the coherence length of the substrate, and f(al,a3,1)is defined by6 f(a,,a3,1) = 2 exp[-(3al + a3)l/2]{cosh [(a33a1)1/2] - COS ( A k l ) ] { [ ( a-j 3~~1)1/2]’ - (Akl)’]-I (2) where Ak = a/lc and a l , a3are standard Naperian absorption coefficients at the fundamental and third harmonic wavelength. Difference in the refractive indexes at both wavelengths between the polymer film and the substrate are neglected in eq 1. The third harmonic signals are obtained as follows: For a sample that gives a much stronger THG signal for the film than that of the substrate, no Maker fringes can be observed. In such a case, I is the THG signal near normal incidence and I, inferred from constructing the envelope of the Maker fringes of a blank fused silica plate (also obtained by placing the silica in the sample arm). The x ( ~value ) obtained from eq 1 is then the final value. In the other case, Le., when the THG signal from the film is comparable to that of the substrate, envelopes for the minima and maxima of the Maker fringes are constructed and both I and I, can be inferred from the minimum (m) and maximum (M) envelopes near the normal incidence:
I = dmM
(3a)
For the silica reference, a value of ~(~)(-3w;w,w,w)= 2.8 X esu at 1.9 pm was used.2oThis value was corrected for dispersion by using a simple approximation of Miller’s rule. The error for Ix(’)(-3w;w,w,w)I of the films was typically 20%, which reflects mostly the errors in measurements of the film thickness (up to f15%) and index of refraction.
Theory Many approaches have been developed to predict and fit the x(’) dispersion of conjugated molecules and polymers. For polymers, like polyacetylene and polydiacetylene, fits to the experimental data were obtained using band theory.*’ In this theory, only the valence band and the conduction band are thought to contribute to the optical nonlinearity. Another approach, which has been used to calculate the second hyperpolarizability in conjugated systems, is based on sum-over-states perturbation theory.*’ In this theory, the second-order hyperpolarizability is (20) Buchalter, B.; Meredith, G. R. Appl. Opt. 1982, 21, 3221. (21) Agrawal, G. P.; Cojan, C.; Flytzanis, C. Phys. Reu. B 1978, 17, 776. (22) (a) Smz, Z. G.;McWilliams, P. C. M.; Hayden, G.W. Chem. Phys. Lert. 1990,171, 14. (b) Dixit, S. N.; Guo, D.; Mazumdar, S. Mol. Crysr. Liq. Cryst. 1991, 194, 33. (c) Heflin, J. R.; Wong, K. Y . ;Zamani-Khamiri, 0.; Garito, A. F. Phys. Reu. B 1988, 38, 1573. (d) Kuzyk, M. G.;Dirk, C. W. Phys. Rev. A 1990, 41, 5098-5 109.
Agrawal et al.
Two -Level Model
Three-Level Model
Figure 3. Schematic diagram of two-level and three-level models of the essential states mechanism of the third-order NLO response.
calculated using the full perturbation expression and summed over all the excited states of the system. Recent calculations on finite length polyenes have shown that only a small number of states have large transition dipole moments connecting them to one another. These states, called essential states, contribute significantly to the observed optical nonlinearity of the system and can account for most of the nonlinear optical response. Recently, essential states models have been used to fit the x ( ~dispersion ) data of p~lydiacetylene~‘ and p o l y t h i ~ p h e n e . In ~ ~ the model presented here, we have used the second approach with the modification that the Lorentzian line shape has been replaced with a hyperbolic secant line shape. This modification accounts for the effects of inhomogeneous and vibronic broadenings in the systems that have been largely ignored in other models. The Lorentzian line shape decays very slowly in the wings and does not represent the linear absorption profile with suitable accuracy, while the hyperbolic secant (sech) line shape decays more rapidly in the wings and provides a better description of the linear absorption spectrum as well as the nonlinear dispersion. Several approximations have been used to simplify the mathematics involved. Although not every one of these approximations are ideal, the improvement obtained in fitting the nonlinear dispersion data supports the need of the proposed modifications in the model and its further development. A detailed description of the approximations used and the method of calculation of x ( ~have ) been given in ref 9b. Two different cases in the above model have been used. The first case, which is the two-level model, involves the ground state and the lowest lying transition dipole allowed excited state as the two essential states. This model is very similar to band theory in its predictions. In the second case, which is the three-level model, another essential state is introduced which has an energy greater than the first excited state and a large transition dipole moment connecting it to the first excited state, thus making this state an even parity state. The inclusion of this state provides an additional pathway for the nonlinear mechanism as shown in Figure 3. However, this second pathway contributes to the nonlinearity with a sign opposite to that of the first pathway. As a result, an interference can be expected between these two paths, which can lead to substantially different behavior of optical nonlinearity with changes in bandgap. First, we use the two-level model to fit the dispersion data. A third level is added only when the dispersion cannot be accurately fit using the two-level model. The second hyperpolarizability is calculated using the proper fitting parameters and is then used to derive the macroscopic x ( ~using ) the standard local field correction factors and the number density factor. The latter is calculated theoretically using atomic contributions to the density of the material and is generally found to be accurate to f5%. The polymers are assumed to be centrosymmetric, so no permanent dipoles exist. The absence of donor or acceptor groups in these materials make this a reasonable approximation.
Results and Discussion The wavelength dispersion of the magnitude of ~ ( ~ ) ( - 3 w ; w , o , w ) of the nine homopolymers and three copolymers in the 0.9-2.4-pm wavelength range are shown in Figures 4-7. As can be seen from ) of these polymers exhibit a resonance the figures, the x ( ~spectra peak a t about 3 times the wavelength of maximum absorption (3X,,,) and off-resonance values for wavelengths longer than 2.0 ) for these materials at 2.38 pm, pm. The off-resonant x ( ~values
The Journal of Physical Chemistry, Vol. 96, No. 7, 1992 2841
Nonlinear Optics of Polyquinolines 12,
301 -
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Figure 5. x(’) spectra of PBPQ, PBAPQ, PSPQ, and PPPQ. The solid lines are guides for the eye only.
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-
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Figure 6. x ( ~spectra ) of PBDA, PBADA, PSDA, and PPDA. The solid lines are guides for the eye only.
shown in Table I, vary marginally in the range (1.8-3.2) X esu. However, the variations in the resonant ~ 0values, ) also shown in Table I, are significantly larger ((0.8-3.3) X lo-” esu). The position of resonance peak in the xQ) spectra and the absence of linear absorption features in the wavelength range 0.7-2.4 km in their optical absorption spectra suggest that all of the observed resonance peaks are due to three-photon resonance. In some of the polymers, two such three-photon resonance peaks are observed in accord with the two strong transitions seen in their optical absorption spectra. In the polyquinoline (YPQ”) series (Figure 9,the nonresonant x ( ~values ) of different polymers lie very close to each other and are within the experimental error of *20%. However, the resonant x(’) values differ significantly from one polymer structure to another. The resonant x(’)depends on the oscillator strength and line width of the transition. If we try to explain the differences in the resonant x(’)based on the bandgap theory, which predicts a strong dependence of x ( ~on) bandgap,21we find that PBPQ, PBAPQ, and PSPQ seem to follow such bandgap dependence to ) of these polymers lie in the some extent. The resonant x ( ~values
X
2.000
2,400
(nm)
Figure 7. x(’) spectra of copolymers PSPQ/PBAPQ, PBPQ/PBAPQ, and PSPQ/PBPQ. The solid lines are guides for the eye only.
same order as that of *-electron delocalization: PSPQ(Z) < PBPQ < PBAPQ. The lower resonant x ( ~value ) of PSPQ compared to that of the other two polymers (PBPQ and PBAPQ) is due to the possible photoisomerization from trans to cis conformation of the stilbene linkage in PSPQ. This photoisomerization which seems to occur due to the multiphoton process of the intense picosecond near IR laser pulses, gives rise to cis conformation that has the lowest *-electron delocalization among the three polymers.I6 However, PPPQ which has & very close to PBPQ and less than that of PBAPQ has a resonant x ( ~value ) that is significantly superior to all of the other polymers (PBAPQ, PBPQ, PSPQ) in this series. This behavior of PPPQ suggests that our explanation of the x ( ~results ) based on bandgap and hence ?r-electron delocalization is probably insufficient and that we might have overlooked other changes in the electronic structure of these polymers, such as line width of the transition. The consistent trend of increasing resonant x ( ~value ) with increasing *-electron delocalization seen in PBPQ, PBAPQ, and PSPQ may be fortuitous. Also, the basic polyquinoline (PPQ, Figure 4) shows a resonant x ( ~of) 1.1 X 10-I2 esu, which is smaller than that of PBPQ and PBAPQ, even though PPQ exhibits a higher degree of *-electron delocalization compared to PBPQ and PBAPQ. These results of the THG spectroscopy of the PQ series of conjugated polymers thus strongly suggest that x ( ~does ) not always scale with bandgap or *-electron delocalization. On the other hand, the x(’)spectra of the corresponding polyanthrazoline (“DA”) series (Figure 6) show no correlation in x(’)with ?r-electron delocalization (h), even in part as observed in the PQ series. The order of the resonant x(’)values does not remain the same throughout the resonant region. The peak values of the x(’)spectra of the polymers in the DA series follow different orders in the two three-photon resonant regions. Even though the order of increasing *-electron delocalization is PBDA < PBADA < PPDA < PSDA, the order of increasing values of resonant x(’) at 1.32 pm is PPDA < PSDA < PBDA < PBADA and that at 1.05 pm is PBDA < PSDA < PPDA < PBADA (Figure 6). The nonresonant x ( ~values ) of polymers in the DA series at 2.38 km are again very close to each other, and the differences are within the experimental error (Table I). From these results, no specific trends can be established based solely on the degree of *-electron delocalization. When 2 (PQ series) and 3 (DA series) are compared, we find that the structural modifications in going from PQ polymers to DA polymers have resulted in the red shift of the lowest energy transition by 20-40 nm and consequent decrease in the bandgap by 0.15-0.3 eV. However, there is no evidence of any increase in the nonresonant or resonant x(’) of polymers in DA series compared to the polymers in PQ series with similar R linkages. The similar values of the nonresonant x(’)of both series, within experimental errors, suggest that there is no significant effect of the structural modifications, and hence *-electron delocalization (Amx), on off-resonance third-order optical nonlinearities in these polymers. In contrast, the three-photon resonant x(’) values corresponding to the lowest energy transitions in the two series
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2842 The Journal of Physical Chemistry, Vol. 96, No. 7. 1992
Agrawal et al.
TABLE 11: Three-Level Model Fitting Parameters for the Dispersion of Polyauinolines and Polyanthrazolines PlYm p , g/cm3 N, lo2’ cm-3 E,, eV pgo’ D S,,, eV E,, eV PPQ PBPQ PBAPQ PSPQ PPPQ PBDA PBADA PSDA PPDA
1.29 1.27 1.26 1.25 1.28 1.28 1.27 1.26 1.29
3.83 4.11 3.92 3.d 4.79 3.20 3.02 2.99 3.83
2.74 2.88 3.29 2.72 3.04 2.75 2.49 2.39 2.42
exhibit a different behavior. The resonant x ( ~values ) of polymers in the PQ series were, in general, higher than those of polymers in the DA series with similar R linkages. This trend in the third-order optical susceptibility corresponds to the differences seen in the optical absorption spectra of the two series. As can be seen from the representative optical absorption spectra of the two series (Figures 1 and 2), the polymers of DA series show a much weaker lowest energy transition compared to the other higher energy transitions, while polymers in PQ series show a stronger lowest energy transition compared to their higher energy transitions. This feature seems to suggest that the magnitude of the resonant x ( ~is)a function of the relative oscillator strength of the various transitions in the electronic structure of the polymer. Exception to this trend is seen in the case of stilbene-linked polymers PSPQ and PSDA, and this might be due to the difference in the degree of isomerization obtained from trans to cis conformation of the stilbene units in the two polymers upon exposure to the laser beam during the measurements. Another feature that relates the resonant x ( j )to the oscillator strength is seen in some polymers of the DA series. The relative magnitude of the two resonant peaks of x ( ~observed ) in these polymers (for example, PBADA, PPDA, and PSDA) at 1.32 and 1.05 pm correlates well with the relative strength of the two absorption peaks observed at 426-448 and 336-361 nm in their respective optical absorption spectra (Table I). In Figure 7, the ~ 0spectra ) of the three random copolymers show nonresonant x ( j )values similar to those of the constituent homopolymers, within experimental errors. The resonant x ( ~ ) values of the three copolymers lie in the order PBAPQ/PBPQ > PSPQIPBPQ PSPQ/PBAPQ. Copolymers containing stilbene moieties (PSPQ/PBAPQ, PSPQ/PBPQ) again show a lower degree of *-electron delocalization than PBAPQIPBPQ due to photoinduced isomerization from trans to cis conformation of the stilbene linkages similar to that seen in the case of the homopolymer PSPQ (Table I). The resonant x0) values follow the same trend as that of Lx in the copolymers, and the results may be interpreted in terms of the scaling of ~ 0with ) *-electron delocalization. However, such conclusions should be reached with utmost caution in the light of the other results discussed above. Theoretical Modeling. We have used a three-level model to fit the x ( j )dispersion of 10 polymers in the series. Figures 8 and 9 represent two of such cases where the fits have been obtained for the x ( ~spectra ) of PBDA and PPQ respectively, using the energies of two excited states (Eo, E,), the values of transition dipole moments (P,,,P,) connecting these states to one another, the widths of the hyperbolic secant functions (Sgo,Sm),and the number density (N) of polymer repeat unit. As can be seen from Figures 8 and 9, a reasonably good agreement was obtained between the theoretical fit and the experimental data. Similar fits were also obtained for the remaining homopolymers and the copolymer PSPQ/PBAPQ. The three-level model fitting parameters for all the homopolymers are summarized in Table 11. The energies (Eo,E,) and widths (Sgo,S,) model the linear absorption spectrum. It should be noted that the polymer repeat unit number density N and physical density p, shown in Table 11, are independently calculated quantities. We could not verify the calculated physical density by direct measurement. The only available data,Iah 1.174 g/cm3, which is 6-9% smaller than the calculated physical density in Table 11, is for an amorphous nonconjugated polyquinoline. The present polymers (Chart I)
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0.51 0.65 0.70 0.65
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x(’) values of PPQ using
are semicrystalline materials and hence would be expected to have higher densities that are much closer to the calculated values. We also note that when a two-level model was used in an attempt to fit the dispersion data, no reasonable fit could be obtained. This suggests that more than one excited state is significantly contributing to the observed optical nonlinearity and that band theoryz1is not sufficient to explain the nonlinear optical properties of the polymers. Our various c a l ~ u l a t i o n as s ~well ~ ~ as ~ ~those ~ by other based on the essential states model have shown ) different energy levels may add that the contribution to x ( ~from with different signs and could result in an overall reduction or enhancement of x ( ~without ) even changing the bandgap. These results are in contrast to prior theoretical calculations and ex-
J. Phys. Chem. 1992, 96, 2843-2848
’1 100 PURE POLYMER
50
COPOLYMER (5050)
100 PURE POLYMER
Figure 10. Resonant x ( ~ as ) a function of copolymer composition for PSPQ/PBAPQ,PBPQIPBAPQ,and PSPQIPBPQ.
perimental studies on oligomers and model compounds of conjugated molecules where the third-order susceptibility x(’) or second hyperpolarizability y has been shown to strongly depend on the A,- or optical bandgap.’4-2’ Therefore, it is essential that systematic studies aimed at elucidating the structured’) property relationships in polymers include high molecular weight polymer structures. Effects of Copolymerization. In Figure 10, the resonant x ( j ) is represented as a function of copolymer composition for all the three copolymers. The x ( j ) of copolymer PSPQ/PBAPQ (5050) lies on a straight line joining the x(’)values of the two constituent homopolymers, while in the case of copolymers PBAPQ/PBPQ (5050) and PSPQ/PBPQ (5050) a marginal enhancement in resonant x(’) values is observed compared to the respective molar averages of the x(’) values of the constituent homopolymers. In PBAPQ/PBPQ, an increase of 15% in resonant x(’) was observed esu calculated from compared to the molar average of 22.9 X the x(’) values of constituent homopolymers PBAPQ and PBPQ. Similarly, an incrtase of 38% was observed in copolymer PSPQ/PBPQ compared to the calculated molar average of 13.7 X esu. The THG spectroscopy results, both in the resonance and the nonresonance regions of the copolymers, suggest that the introduction of disorder in the copolymer backbone does not have a significant effect on the third-order optical nonlinearities.
Conclusions The third-order nonlinear optical properties of a series of systematically designed nine homopolymers and three random
2843
copolymers in the class of conjugated rigid-rod polyquinolines and polyanthrazolines have been studied using third harmonic generation (THG) spectroscopy. Three-photon resonance peaks at 3A- were observed in the x(’) spectra of the polymers. Although off-resonance a t 2.38 pm, the x(’) values were found to be very close to each other for all the polymers within the experimental errors, the peak value of the three-photon enhanced x(’)varied in the range 0.8 X 10-”-3.3 X 10-l’ esu with the backbone structure of the polymers. The results suggested that there was no significant dependence of the nonresonant ~ (values 9 on the molecular structure or degree of *-electron delocalization of the polymers. The resonant x(’) values, which varied significantly on the other hand, did not correlate well with the degree of a-electron delocalization of the polymers. A theoretical three-level model based on essential states mechanism was used to obtain a fit to the x(’)dispersion of the polymers. The superior fit obtained using a three-level model in constrast to a two-level model suggests that more than one excited state is responsible for the observed third-order optical nonlinearity of the materials. On the basis of the experimental and theoretical x(’) spectra of the series of systematically derived polymer structures, we can say that the magnitude of x(’) does not always scale with the *-electron delocalization of the conjugated polymers and that knowledge of the overall electronic excited-state structure is essential in determining the third-order nonlinear optical response of the materials. The results of the x(’)spectra of the three random copolymers showed that the x ( j ) values of the copolymers were the molar averages of the x ( ~values ) of the respective constituent homopolymers, suggesting the absence of significant enhancement or reduction in the third-order optical nonlinearities with the introduction of disorder in the copolymer backbone. Thus, random copolymerization provides one approach to tailoring the value of the third-order NLO susceptibility from known nonlinear optical polymers.
Acknowledgment. Work at University of Rochester was sup ported by the Amoco Foundation and the National Science Foundation (Grant CHE-88 1-0024). The nonlinear optical characterization was carried out at Du Pont. H.V. acknowledges the valuable technical assistance of J. Kelly. Registry No. 1, 139102-46-8; 2a, 75460-97-8;2b, 135614-64-1;2c, 86527-06-2; 2 4 76996-76-4; 3a, 59827-44-0 3b, 137091-74-8; 3c, 139102-47-9; 3d, 137091-72-6.
Theory of Anomalous Photon Echo Decays in Confined Excitonic Systems Frank C . Spano Department of Chemistry, Temple University. Philadelphia, Pennsylvania 191 22 (Received: September 3, 1991)
An analytical expression for the photon echo decay in a linear aggregate consisting of N coupled two-level molecules is derived
in the weak field limit. The expression has two terms: one which involves transitions between the ground state and the one-exciton state, and a second which involves two-photon absorption to the doubly excited states or two-excitons. For interpulse separation times Idwhich obey Y 1
