Abstract

Theoretical and experimental studies of molecular photodegradation in π-conjugated chromophores with resonant and nonresonant excitation relative to the lowest-energy electronic transition of the chromophore are performed. The limitations of previous photodegradation models are discussed, and new models that overcome these limitations and provide more accurate estimates of chromophore photostability are presented. In particular, the necessity of considering multiple degradation pathways in the analysis of photobleaching studies is shown. Photostability studies of a dihydrofuran thiophene-bridged dicyanomethylene based chromophore (FTC) employing 1.55-μm excitation reveal that the photoinitiated decay kinetics are biphasic. We present what we believe to be a new, double-pathway photodegradation model capable of describing this behavior. Through investigations employing the singlet-oxygen quencher bis(dithiobenzil)nickel, photooxidation is shown to be one of the photodegradation pathways, and the ability of a quencher to inhibit chromophore photooxidation is quantified. The studies presented here provide insight into the mechanism of photochemical degradation of π-conjugated chromophores for devices operating in the visible and at telecommunication wavelengths.

© 2007 Optical Society of America

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References

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  1. Ch. Bosshard, M. Bösch, I. Liakatas, M. Jäger, and P. Günter, "Second-order nonlinear optical organic materials: recent developments," in Nonlinear Optical Effects and Materials, Vol. 72 of Optical Sciences, P.Günter, ed. (Springer, 2000), pp. 163-299.
  2. H. Ma, A. K. Y. Jen, and L. R. Dalton, "Polymer-based optical waveguides: materials, processing, and devices," Adv. Mater. 14, 1339-1365 (2002).
    [CrossRef]
  3. S. R. Marder, W. E. Torruellas, M. Blanchard Desce, V. Ricci, G. I. Stegeman, S. Gilmour, J. L. Bredas, J. Li, G. U. Bublitz, and S. G. Boxer, "Large molecular third-order optical nonlinearities in polarized carotenoids," Science 276, 1233-1236 (1997).
    [CrossRef] [PubMed]
  4. M. Jazbinsek, P. Rabiei, Ch. Bosshard, and P. Günter, "Nonlinear organic materials for VLSI photonics," AIP Conf. Proc. 709, 187-213 (2004).
    [CrossRef]
  5. P. Rabiei, W. H. Steier, Z. Cheng, and L. R. Dalton, "Polymer microring filters and modulators," J. Lightwave Technol. 20, 1968-1975 (2002).
    [CrossRef]
  6. O. P. Kwon, B. Ruiz, A. Choubey, L. Mutter, A. Schneider, M. Jazbinsek, V. Gramlich, and P. Günter, "Organic nonlinear optical crystals based in configurationally locked polyene for melt growth," Chem. Mater. 18, 4049-4054 (2006).
    [CrossRef]
  7. A. Schneider, M. Neis, M. Stillhart, B. Ruiz, R. U. A. Khan, and P. Günter, "Generation of terahertz pulses through optical rectification in organic DAST crystals: theory and experiment," J. Opt. Soc. Am. B 23, 1822-1835 (2006).
    [CrossRef]
  8. C. Zhang, L. R. Dalton, M. C. Oh, H. Zhang, and W. H. Steier, "Low V-pi electrooptic modulators from CLD-1: chromophore design and synthesis, material processing, and characterization," Chem. Mater. 13, 3043-3050 (2001).
    [CrossRef]
  9. T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen,"Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore systems," Adv. Mater. 18, 3038-3042 (2006).
    [CrossRef]
  10. M. Stähelin, C. A. Walsh, D. M. Burland, R. D. Miller, R. J. Twieg, and W. Volksen, "Orientational decay in poled 2nd-order nonlinear-optical guest-host polymers--temperature-dependence effects of poling geometry," J. Appl. Phys. 73, 8471-8479 (1993).
    [CrossRef]
  11. P. Pretre, U. Meier, U. Stalder, Ch. Bosshard, P. Günter, P. Kaatz, C. Weder, P. Neuenschwander, and U. W. Suter, "Relaxation processes in nonlinear optical polymers: a comparative study," Macromolecules 31, 1947-1957 (1998).
    [CrossRef]
  12. C. Zhang, C. Wang, L. R. Dalton, H. Zhang, and W. H. Steier, "Progress toward device-quality second-order nonlinear optical materials. 4. A trilink high μβ NLO chromophore in thermoset polyurethane: a "guest-host" approach to larger electrooptic coefficients," Macromolecules 34, 253-261 (2001).
    [CrossRef]
  13. Y. H. Kuo, J. D. Luo, W. H. Steier, and A. K. Y. Jen, "Enhanced thermal stability of electrooptic polymer modulators using the Diels-Alder crosslinkable polymer," IEEE Photon. Technol. Lett. 18, 175-177 (2006).
    [CrossRef]
  14. A. Dubois, M. Canva, A. Brun, F. Chaput, and J. P. Boilot, "Photostability of dye molecules trapped in solid matrices," Appl. Opt. 35, 3193-3199 (1996).
    [CrossRef] [PubMed]
  15. A. Galvan-Gonzalez, K. D. Belfield, G. I. Stegeman, M. Canva, S. R. Marder, K. Staub, G. Levina, and R. J. Twieg, "Photodegradation of selected π-conjugated electro-optic chromophores," J. Appl. Phys. 94, 756-763 (2003).
    [CrossRef]
  16. A. Galvan-Gonzalez, G. I. Stegeman, A. K. Y. Jen, X. Wu, M. Canva, A. C. Kowalczyk, X. Q. Zhang, H. S. Lackritz, S. Marder, S. Thayumanavan, and G. Levina, "Photostability of electro-optic polymers possessing chromophores with efficient amino donors and cyano-containing acceptors," J. Opt. Soc. Am. B 18, 1846-1853 (2001).
    [CrossRef]
  17. A. Galvan-Gonzalez, M. Canva, G. I. Stegeman, L. Sukhomlinova, R. J. Twieg, K. P. Chan, T. C. Kowalczyk, and H. S. Lackritz, "Photodegradation of azobenzenes nonlinear optical chromophores: the influence of structure and environment," J. Opt. Soc. Am. B 17, 1992-2000 (2000).
    [CrossRef]
  18. A. Galvan-Gonzalez, M. Canva, and G. I. Stegeman, "Effect of temperature and atmospheric environment on the photodegradation of some disperse red 1-type polymers," Opt. Lett. 24, 1741-1743 (1999).
    [CrossRef]
  19. M. Bösch, C. Fischer, C. Cai, I. Liakatas, Ch. Bosshard, and P. Günter, "Photochemical stability of highly nonlinear optical bithiophene chromophores," Synth. Met. 124, 241-243 (2001).
    [CrossRef]
  20. M. E. DeRosa, M. Q. He, J. S. Cites, S. M. Garner, and Y. R. Tang, "Photostability of high μβ electro-optic chromophores at 1550 nm," J. Phys. Chem. B 108, 8725-8730 (2004).
    [CrossRef]
  21. J. Vydra, H. Beisinghoff, T. Tschudi, and M. Eich, "Photodecay mechanisms in side chain nonlinear optical polymethacrylates," Appl. Phys. Lett. 69, 1035-1037 (1996).
    [CrossRef]
  22. L. Mutter, M. Jazbinsek, M. Zgonik, U. Meier, Ch. Bosshard, and P. Günter, "Photobleaching and optical properties of organic crystal 4-N, N-dirnethylamino-4′-N′-methyl stilbazolium tosylate," J. Appl. Phys. 94, 1356-1361 (2003).
    [CrossRef]
  23. J. W. Martin, J. W. Chin, and T. Nguyen, "Reciprocity law experiments in polymeric photodegradation: a critical review," Prog. Org. Coat. 47, 292-311 (2003).
    [CrossRef]
  24. H. Shiozaki, H. Nakazumi, Y. Takamura, and T. Kitao, "Mechanism and rate constants for the quenching of singlet oxygen by nickel complexes," Bull. Chem. Soc. Jpn. 63, 2653-2658 (1990).
    [CrossRef]
  25. K. M. Sung and R. H. Holm, "Functional analogue reaction systems of the DMSO reductase isoenzyme family: probable mechanism of S-oxide reduction in oxo transfer reactions mediated by bis(dithiolene)-tungsten(IV,VI) complexes," J. Am. Chem. Soc. 124, 4312-4320 (2002).
    [CrossRef] [PubMed]
  26. B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Zhang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, "The molecular and supramolecular engineering of polymeric electro-optic materials," Chem. Phys. 245, 35-50 (1999).
    [CrossRef]
  27. D. Briers, G. Koeckelberghs, I. Picard, T. Verbiest, A. Persoons, and C. Samyn, "Novel chromophore-functionalized poly[2(trifluoromethyl) adamantyl acrylate-methyl vinyl urethane]s with high poling stabilities of the nonlinear optical effect," Macromol. Rapid Commun. 24, 841-846 (2003).
    [CrossRef]
  28. E. K. L. Yeow, S. M. Melnikov, T. D. M. Bell, F. C. De Schryver, and J. Hofkens, "Characterizing the fluorescence intermittency and photobleaching kinetics of dye molecules immobilized on a glass surface," J. Phys. Chem. A 110, 1726-1734 (2006).
    [CrossRef] [PubMed]

2006 (5)

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen,"Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore systems," Adv. Mater. 18, 3038-3042 (2006).
[CrossRef]

Y. H. Kuo, J. D. Luo, W. H. Steier, and A. K. Y. Jen, "Enhanced thermal stability of electrooptic polymer modulators using the Diels-Alder crosslinkable polymer," IEEE Photon. Technol. Lett. 18, 175-177 (2006).
[CrossRef]

E. K. L. Yeow, S. M. Melnikov, T. D. M. Bell, F. C. De Schryver, and J. Hofkens, "Characterizing the fluorescence intermittency and photobleaching kinetics of dye molecules immobilized on a glass surface," J. Phys. Chem. A 110, 1726-1734 (2006).
[CrossRef] [PubMed]

O. P. Kwon, B. Ruiz, A. Choubey, L. Mutter, A. Schneider, M. Jazbinsek, V. Gramlich, and P. Günter, "Organic nonlinear optical crystals based in configurationally locked polyene for melt growth," Chem. Mater. 18, 4049-4054 (2006).
[CrossRef]

A. Schneider, M. Neis, M. Stillhart, B. Ruiz, R. U. A. Khan, and P. Günter, "Generation of terahertz pulses through optical rectification in organic DAST crystals: theory and experiment," J. Opt. Soc. Am. B 23, 1822-1835 (2006).
[CrossRef]

2004 (2)

M. E. DeRosa, M. Q. He, J. S. Cites, S. M. Garner, and Y. R. Tang, "Photostability of high μβ electro-optic chromophores at 1550 nm," J. Phys. Chem. B 108, 8725-8730 (2004).
[CrossRef]

M. Jazbinsek, P. Rabiei, Ch. Bosshard, and P. Günter, "Nonlinear organic materials for VLSI photonics," AIP Conf. Proc. 709, 187-213 (2004).
[CrossRef]

2003 (4)

L. Mutter, M. Jazbinsek, M. Zgonik, U. Meier, Ch. Bosshard, and P. Günter, "Photobleaching and optical properties of organic crystal 4-N, N-dirnethylamino-4′-N′-methyl stilbazolium tosylate," J. Appl. Phys. 94, 1356-1361 (2003).
[CrossRef]

J. W. Martin, J. W. Chin, and T. Nguyen, "Reciprocity law experiments in polymeric photodegradation: a critical review," Prog. Org. Coat. 47, 292-311 (2003).
[CrossRef]

A. Galvan-Gonzalez, K. D. Belfield, G. I. Stegeman, M. Canva, S. R. Marder, K. Staub, G. Levina, and R. J. Twieg, "Photodegradation of selected π-conjugated electro-optic chromophores," J. Appl. Phys. 94, 756-763 (2003).
[CrossRef]

D. Briers, G. Koeckelberghs, I. Picard, T. Verbiest, A. Persoons, and C. Samyn, "Novel chromophore-functionalized poly[2(trifluoromethyl) adamantyl acrylate-methyl vinyl urethane]s with high poling stabilities of the nonlinear optical effect," Macromol. Rapid Commun. 24, 841-846 (2003).
[CrossRef]

2002 (3)

P. Rabiei, W. H. Steier, Z. Cheng, and L. R. Dalton, "Polymer microring filters and modulators," J. Lightwave Technol. 20, 1968-1975 (2002).
[CrossRef]

K. M. Sung and R. H. Holm, "Functional analogue reaction systems of the DMSO reductase isoenzyme family: probable mechanism of S-oxide reduction in oxo transfer reactions mediated by bis(dithiolene)-tungsten(IV,VI) complexes," J. Am. Chem. Soc. 124, 4312-4320 (2002).
[CrossRef] [PubMed]

H. Ma, A. K. Y. Jen, and L. R. Dalton, "Polymer-based optical waveguides: materials, processing, and devices," Adv. Mater. 14, 1339-1365 (2002).
[CrossRef]

2001 (4)

C. Zhang, L. R. Dalton, M. C. Oh, H. Zhang, and W. H. Steier, "Low V-pi electrooptic modulators from CLD-1: chromophore design and synthesis, material processing, and characterization," Chem. Mater. 13, 3043-3050 (2001).
[CrossRef]

C. Zhang, C. Wang, L. R. Dalton, H. Zhang, and W. H. Steier, "Progress toward device-quality second-order nonlinear optical materials. 4. A trilink high μβ NLO chromophore in thermoset polyurethane: a "guest-host" approach to larger electrooptic coefficients," Macromolecules 34, 253-261 (2001).
[CrossRef]

M. Bösch, C. Fischer, C. Cai, I. Liakatas, Ch. Bosshard, and P. Günter, "Photochemical stability of highly nonlinear optical bithiophene chromophores," Synth. Met. 124, 241-243 (2001).
[CrossRef]

A. Galvan-Gonzalez, G. I. Stegeman, A. K. Y. Jen, X. Wu, M. Canva, A. C. Kowalczyk, X. Q. Zhang, H. S. Lackritz, S. Marder, S. Thayumanavan, and G. Levina, "Photostability of electro-optic polymers possessing chromophores with efficient amino donors and cyano-containing acceptors," J. Opt. Soc. Am. B 18, 1846-1853 (2001).
[CrossRef]

2000 (1)

1999 (2)

A. Galvan-Gonzalez, M. Canva, and G. I. Stegeman, "Effect of temperature and atmospheric environment on the photodegradation of some disperse red 1-type polymers," Opt. Lett. 24, 1741-1743 (1999).
[CrossRef]

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Zhang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, "The molecular and supramolecular engineering of polymeric electro-optic materials," Chem. Phys. 245, 35-50 (1999).
[CrossRef]

1998 (1)

P. Pretre, U. Meier, U. Stalder, Ch. Bosshard, P. Günter, P. Kaatz, C. Weder, P. Neuenschwander, and U. W. Suter, "Relaxation processes in nonlinear optical polymers: a comparative study," Macromolecules 31, 1947-1957 (1998).
[CrossRef]

1997 (1)

S. R. Marder, W. E. Torruellas, M. Blanchard Desce, V. Ricci, G. I. Stegeman, S. Gilmour, J. L. Bredas, J. Li, G. U. Bublitz, and S. G. Boxer, "Large molecular third-order optical nonlinearities in polarized carotenoids," Science 276, 1233-1236 (1997).
[CrossRef] [PubMed]

1996 (2)

J. Vydra, H. Beisinghoff, T. Tschudi, and M. Eich, "Photodecay mechanisms in side chain nonlinear optical polymethacrylates," Appl. Phys. Lett. 69, 1035-1037 (1996).
[CrossRef]

A. Dubois, M. Canva, A. Brun, F. Chaput, and J. P. Boilot, "Photostability of dye molecules trapped in solid matrices," Appl. Opt. 35, 3193-3199 (1996).
[CrossRef] [PubMed]

1993 (1)

M. Stähelin, C. A. Walsh, D. M. Burland, R. D. Miller, R. J. Twieg, and W. Volksen, "Orientational decay in poled 2nd-order nonlinear-optical guest-host polymers--temperature-dependence effects of poling geometry," J. Appl. Phys. 73, 8471-8479 (1993).
[CrossRef]

1990 (1)

H. Shiozaki, H. Nakazumi, Y. Takamura, and T. Kitao, "Mechanism and rate constants for the quenching of singlet oxygen by nickel complexes," Bull. Chem. Soc. Jpn. 63, 2653-2658 (1990).
[CrossRef]

Adv. Mater. (2)

H. Ma, A. K. Y. Jen, and L. R. Dalton, "Polymer-based optical waveguides: materials, processing, and devices," Adv. Mater. 14, 1339-1365 (2002).
[CrossRef]

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen,"Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore systems," Adv. Mater. 18, 3038-3042 (2006).
[CrossRef]

AIP Conf. Proc. (1)

M. Jazbinsek, P. Rabiei, Ch. Bosshard, and P. Günter, "Nonlinear organic materials for VLSI photonics," AIP Conf. Proc. 709, 187-213 (2004).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. Vydra, H. Beisinghoff, T. Tschudi, and M. Eich, "Photodecay mechanisms in side chain nonlinear optical polymethacrylates," Appl. Phys. Lett. 69, 1035-1037 (1996).
[CrossRef]

Bull. Chem. Soc. Jpn. (1)

H. Shiozaki, H. Nakazumi, Y. Takamura, and T. Kitao, "Mechanism and rate constants for the quenching of singlet oxygen by nickel complexes," Bull. Chem. Soc. Jpn. 63, 2653-2658 (1990).
[CrossRef]

Chem. Mater. (2)

C. Zhang, L. R. Dalton, M. C. Oh, H. Zhang, and W. H. Steier, "Low V-pi electrooptic modulators from CLD-1: chromophore design and synthesis, material processing, and characterization," Chem. Mater. 13, 3043-3050 (2001).
[CrossRef]

O. P. Kwon, B. Ruiz, A. Choubey, L. Mutter, A. Schneider, M. Jazbinsek, V. Gramlich, and P. Günter, "Organic nonlinear optical crystals based in configurationally locked polyene for melt growth," Chem. Mater. 18, 4049-4054 (2006).
[CrossRef]

Chem. Phys. (1)

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Zhang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, "The molecular and supramolecular engineering of polymeric electro-optic materials," Chem. Phys. 245, 35-50 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Y. H. Kuo, J. D. Luo, W. H. Steier, and A. K. Y. Jen, "Enhanced thermal stability of electrooptic polymer modulators using the Diels-Alder crosslinkable polymer," IEEE Photon. Technol. Lett. 18, 175-177 (2006).
[CrossRef]

J. Am. Chem. Soc. (1)

K. M. Sung and R. H. Holm, "Functional analogue reaction systems of the DMSO reductase isoenzyme family: probable mechanism of S-oxide reduction in oxo transfer reactions mediated by bis(dithiolene)-tungsten(IV,VI) complexes," J. Am. Chem. Soc. 124, 4312-4320 (2002).
[CrossRef] [PubMed]

J. Appl. Phys. (3)

L. Mutter, M. Jazbinsek, M. Zgonik, U. Meier, Ch. Bosshard, and P. Günter, "Photobleaching and optical properties of organic crystal 4-N, N-dirnethylamino-4′-N′-methyl stilbazolium tosylate," J. Appl. Phys. 94, 1356-1361 (2003).
[CrossRef]

M. Stähelin, C. A. Walsh, D. M. Burland, R. D. Miller, R. J. Twieg, and W. Volksen, "Orientational decay in poled 2nd-order nonlinear-optical guest-host polymers--temperature-dependence effects of poling geometry," J. Appl. Phys. 73, 8471-8479 (1993).
[CrossRef]

A. Galvan-Gonzalez, K. D. Belfield, G. I. Stegeman, M. Canva, S. R. Marder, K. Staub, G. Levina, and R. J. Twieg, "Photodegradation of selected π-conjugated electro-optic chromophores," J. Appl. Phys. 94, 756-763 (2003).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (3)

J. Phys. Chem. A (1)

E. K. L. Yeow, S. M. Melnikov, T. D. M. Bell, F. C. De Schryver, and J. Hofkens, "Characterizing the fluorescence intermittency and photobleaching kinetics of dye molecules immobilized on a glass surface," J. Phys. Chem. A 110, 1726-1734 (2006).
[CrossRef] [PubMed]

J. Phys. Chem. B (1)

M. E. DeRosa, M. Q. He, J. S. Cites, S. M. Garner, and Y. R. Tang, "Photostability of high μβ electro-optic chromophores at 1550 nm," J. Phys. Chem. B 108, 8725-8730 (2004).
[CrossRef]

Macromol. Rapid Commun. (1)

D. Briers, G. Koeckelberghs, I. Picard, T. Verbiest, A. Persoons, and C. Samyn, "Novel chromophore-functionalized poly[2(trifluoromethyl) adamantyl acrylate-methyl vinyl urethane]s with high poling stabilities of the nonlinear optical effect," Macromol. Rapid Commun. 24, 841-846 (2003).
[CrossRef]

Macromolecules (2)

P. Pretre, U. Meier, U. Stalder, Ch. Bosshard, P. Günter, P. Kaatz, C. Weder, P. Neuenschwander, and U. W. Suter, "Relaxation processes in nonlinear optical polymers: a comparative study," Macromolecules 31, 1947-1957 (1998).
[CrossRef]

C. Zhang, C. Wang, L. R. Dalton, H. Zhang, and W. H. Steier, "Progress toward device-quality second-order nonlinear optical materials. 4. A trilink high μβ NLO chromophore in thermoset polyurethane: a "guest-host" approach to larger electrooptic coefficients," Macromolecules 34, 253-261 (2001).
[CrossRef]

Opt. Lett. (1)

Prog. Org. Coat. (1)

J. W. Martin, J. W. Chin, and T. Nguyen, "Reciprocity law experiments in polymeric photodegradation: a critical review," Prog. Org. Coat. 47, 292-311 (2003).
[CrossRef]

Science (1)

S. R. Marder, W. E. Torruellas, M. Blanchard Desce, V. Ricci, G. I. Stegeman, S. Gilmour, J. L. Bredas, J. Li, G. U. Bublitz, and S. G. Boxer, "Large molecular third-order optical nonlinearities in polarized carotenoids," Science 276, 1233-1236 (1997).
[CrossRef] [PubMed]

Synth. Met. (1)

M. Bösch, C. Fischer, C. Cai, I. Liakatas, Ch. Bosshard, and P. Günter, "Photochemical stability of highly nonlinear optical bithiophene chromophores," Synth. Met. 124, 241-243 (2001).
[CrossRef]

Other (1)

Ch. Bosshard, M. Bösch, I. Liakatas, M. Jäger, and P. Günter, "Second-order nonlinear optical organic materials: recent developments," in Nonlinear Optical Effects and Materials, Vol. 72 of Optical Sciences, P.Günter, ed. (Springer, 2000), pp. 163-299.

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Figures (9)

Fig. 1
Fig. 1

Representation of a general photodegradation process [15]. An incoming photon strikes a chromophore and excites it to a higher energy state with the probability P ( σ ) . Following excitation, the molecule repopulates the ground state in average B times before reacting to form a stable byproduct(s). The quantum probability for this process, referred to as photodegradation, is 1 B .

Fig. 2
Fig. 2

Illustration of resonant and nonresonant excitation regimes. The resonant case is indicated by the dark shaded area, and the nonresonant case by the light shaded area. The solid curve represents the absorption spectrum of the unbleached chromophore, while the dotted curve illustrates the spectrum of the bleached chromophore.

Fig. 3
Fig. 3

Resonant excitations: comparison between the photodegradation model with Ω = 1 as reported previously [14] (dashed curve) and the emended model with Ω = T presented here (dotted curve). The triangles represent a set of simulated data. The assumed figure-of-merit is B σ = 10 28 m 2 , while the photon flux is n 0 = 5 × 10 23 m 2 s 1 at a 633 nm wavelength. A lower limit of the chromophore photochemical stability is obtained considering T Ω = T ( t ) for the parameters T R = 1 , T 0 = 0.25 , and T = 0.85 . Forcing T Ω = 1 ( t ) to match the simulated data results in an overestimation of the chromophore figure-of-merit.

Fig. 4
Fig. 4

Possible representations of a biphasic photodegradation process. Left, the chromophores are stimulated into two possible excitation bands and can decay to a single bleached state b through two different pathways with their specific probabilities and therefore figure-of-merits ( B σ e ) 1 and ( B σ e ) 2 . Right, following irradiation, the chromophores are excited to a single, broadened band of excited states and can react either to the bleached state b 1 (with probability 1 B 1 ) or to another bleached state b 2 (probability 1 B 2 ).

Fig. 5
Fig. 5

Left, absorption spectra of FTC (squares, 20 wt % ), Ni-complex (crosses, 5 wt % ), and both quencher and chromophore (circles, 1:4 ratio), respectively, dispersed in amorphous polycarbonate. Right, structures of the FTC-type dihydrofuran thiophene-bridged dicyanomethylene-based chromophore (2-[4-(2-{5-[2-(4-{Bis-[2-(tert-butyl-dimethyl-silanyloxy)-ethyl]-amino}-phenyl)-vinyl]-thiophen-2-yl}-vinyl)-3-cyano-5,5-dimethyl-5H-furan-2-ylidene]-malononitrile) and the singlet-oxygen quencher Ni-complex (bis(dithiobenzil)nickel).

Fig. 6
Fig. 6

Schematic diagram of the photostability apparatus.

Fig. 7
Fig. 7

Photodegradation of FTC chromophores at a 1.55 μ m wavelength. The shaded zone refers to the 300   min representing the initial decay as measured in previous studies [20]. Such a time frame restriction allows for a reasonable use of the previous model as in Eq. (25). The calculated initial evolution of this model is shown as the dashed–dotted curve, while the dashed curve stands for its behavior along the entire measurement. The dotted curve represents the single-pathway photodegradation model (SPM), and the solid curve shows the evolution of the double-pathway photodegradation model (DPM). Notice that the DPM follows the data better than the SPM (minimal sum of the squared deviations χ 2 reduced by one order of magnitude), consistently with a double-pathway degradation process. The amount of chromophores undergoing rapid photooxidation is quantified to about 40% by means of the DPM. The parameters for the theoretical curves are presented in Fig. 9 (blank columns).

Fig. 8
Fig. 8

Photodegradation of the chromophore species FTC in the presence of the singlet-oxygen quencher bis(dithiobenzil)nickel (Ni-complex) with excitation at a 1.55 μ m wavelength. The degradation is that slow, that the entire data set is well matched by all models and no restricted time frame is necessary to use the model of Eq. (25). The figure-of-merit obtained by the previous model is approximatively twice as large as that by the SPM (dashed and dotted curves, respectively). The analysis of the DPM curve shows that the quencher inhibits photooxidation for about 95% of the chromophores. The parameters for the theoretical curve are summarized in Fig. 9 (shaded columns).

Fig. 9
Fig. 9

Comparison of the figure-of-merits B σ determined using the different photodegradation models for FTC irradiated at 1.55 μ m with the quencher bis(dithiobenzil)nickel (Ni-complex, shaded columns) and without (blank columns). For the case of the double-pathway degradation model (DPM), the figure-of-merits for the two processes are marked by 1 and 2, respectively. The percentages indicated in the picture refer to the amount of chromophores degrading through the related pathway. The values and errors reported here present averages over several photostability measurements weighted by 1 χ 2 . Fitting parameters for the previous model are given for the initial evolution only in case of FTC alone ( * ) and for the full time frame for all other measurements.

Equations (27)

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N 0 = N u ( t , z ) + N b ( t , z ) .
J i ( t , z ) = 0 z N i ( t , z ̃ ) d z ̃ , i = u , b .
n ( t , z ) = n 0 e σ u J u ( t , z ) e σ b J b ( t , z ) .
d d t N u ( t , z ) = 1 B n ( t , z ) × σ u N u ( t , z ) .
d d t J u ( t , d ) = σ u B n 0 × 0 d N u ( t , z ) e σ u J u ( t , z ) e σ b J b ( t , z ) d z .
d d t J u ( t , d ) σ u B n 0 × Ω 0 d N u ( t , z ) e σ u J u ( t , z ) d z 1 B n 0 Ω 0 d z ( σ u J u ( t , z ) ) e σ u J u ( t , z ) d z .
d d t J u ( t , d ) 1 B n 0 Ω × ( e σ u J u ( t , d ) 1 ) ,
1 e σ u J u ( t , d ) 1 d J u ( t , d ) 1 B n 0 Ω d t .
d ln ( w ( t ) 1 w ( t ) ) σ u B n 0 Ω d t .
w ( t ) 1 w ( t ) A exp ( σ u B Ω n 0 t ) , A w 0 1 w 0 = T 0 1 T 0 .
e σ u J u ( t , d ) A exp ( σ u B Ω n 0 t ) 1 + A exp ( σ u B Ω n 0 t ) .
T ̃ ( t ) = e σ u J u ( t , d ) e σ b J b ( t , d ) e σ u J u ( t , d ) Ω .
T Ω ( t ) T R T 0 Ω T 0 + ( 1 T 0 ) exp ( σ u B Ω n 0 t ) .
τ Ω = ( B σ u 1 n 0 ) 1 Ω .
T = e σ b N 0 d < Ω < 1 .
T Ω = T ( t ) T actual ( t ) T Ω = 1 ( t ) , t .
d d t N u ( t , z ) = 1 B n ( t , z ) × σ e N u ( t , z ) .
d d t N u ( t ) = σ e n 0 B × N u ( t ) .
N u ( t ) = N 0 exp ( σ e n 0 B t ) , N b ( t ) = N 0 ( 1 exp ( σ e n 0 B t ) ) .
T ̃ ( t ) = e σ u N u ( t ) d e σ b N b ( t ) d = e σ u N 0 exp [ ( σ e B ) n 0 t ] d e σ b N 0 ( 1 exp [ ( σ e B ) n 0 t ] ) d .
T 0 T ̃ ( 0 ) = e σ u N 0 d , T e σ b N 0 d .
T ( t ) = T R T 0 exp [ ( σ e B ) n 0 t ] T ( 1 exp [ ( σ e B ) n 0 t ] ) .
τ = B σ e 1 n 0 .
ln α ( t ) α 0 = σ e B n 0 t .
T ( t ) = T 0 exp [ ( σ e B ) n 0 t ] .
N u ( t ) = f × N 0 exp [ ( σ e B ) 1 n 0 t ] + ( 1 f ) N 0 exp [ ( σ e B ) 2 n 0 t ] ,
T ( t ) = T R T 0 f exp [ ( σ e B ) 1 n 0 t ] T f ( 1 exp [ ( σ e B ) 1 n 0 t ] ) × T 0 ( 1 f ) exp [ ( σ e B ) 2 n 0 t ] T ( 1 f ) ( 1 exp [ ( σ e B ) 2 n 0 t ] ) .

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