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共轭聚合物链中光激发过程的无序效应

傅聪 叶梦浩 赵晖 陈宇光 鄢永红

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共轭聚合物链中光激发过程的无序效应

傅聪, 叶梦浩, 赵晖, 陈宇光, 鄢永红

Effects of intrachain disorder on photoexcitation in conjugated polymer chains

Fu Cong, Ye Meng-Hao, Zhao Hui, Chen Yu-Guang, Yan Yong-Hong
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  • 应用包含链内无序和电子关联的Su-Schriffer-Heeger模型, 研究了共轭聚合物链中无序效应在光激发演化过程中的作用, 尤其是对激子产率的影响. 采用multi-configurational time-dependent Hartree–Fock方法处理电子部分的含时Schrödinger方程, 而晶格部分的运动则由经典的牛顿方程决定. 研究发现, 加入无序后, 光激发弛豫后的产物与纯净聚合物链中有着定性的不同. 相比于纯净聚合物中光激发下会有一定的概率直接生成极化子对, 考虑无序效应后则更趋向于生成激子, 并且激子的产率很大程度上依赖于无序的类型和强度. 另外还研究了电子-电子相互作用和共轭链长度对激子产率的影响.
    The luminescence efficiency of conjugated polymers has been a central topic in the study of light emitting. The effect of disorder plays an important role in generating excitons after the conjugated polymers have been excited by photons. In this paper, by using the Su-Schriffer-Heeger model, which has been modified to include intrachain disorder and electron correlation, we investigate the effects of disorder on the photoexcitation, especially on the yield of excitons in a conjugated polymer chain. We adopt the multi-configurational time-dependent Hartree–Fock method to solve the multi-electron time-dependent Schrödinger equation and the Newtonian equation of motion for the lattice vibration. The results show that after the photoexcitation relaxation process, the products of the disordered polymer chain are qualitatively distinct from those of the pure polymer chain. While the pairs of polarons can be generated directly after the photoexcitation in a pure polymer chain, the disorder favors excitons as the products of the photoexcitation, and the yield of excitons depends crucially on the kind and strength of the disorder. Furthermore, the influences of the electron correlation and the conjugation length on the yield of excitons are also discussed. Specifically, we find that in the case of diagonal disorder, when the conjugation length is short and the diagonal disorder is weak, the excitons are mainly generated by the recombination of two lattice defects with a high yield of excitons which will be reduced as the conjugation length increases. The excitons tend to be generated directly with a low yield of excitons which is enlarged as the disorder gets stronger when the conjugation length is long or the diagonal disorder is strong. The on-site Coulomb repulsion favors the generation of excitons as well. The case of off-diagonal disorder is similar to that of diagonal disorder except that the on-site Coulomb potential favors the generation of excitons in the weak disorder regime but depresses the generation of excitons in the strong disorder regime. When both diagonal and off-diagonal disorders are considered, the yield of excitons is dominated by the off-diagonal disorder. We hope that our investigations can provide useful guidance and help for designing organic photoelectric materials and devices.
      通信作者: 赵晖, zhaoh@fudan.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11474218, 11575116)资助的课题
      Corresponding author: Zhao Hui, zhaoh@fudan.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11474218, 11575116)
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    Shirakawa H, Louis E J, MacDiarmid A G, Chiang C K, Heeger A J 1977 J. Chem. Soc. Chem. Commun. 16 578

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    Heeger A J 2001 Rev. Mod. Phys. 73 681Google Scholar

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    Friend R H, Gymer R W, Holmes A B, Burroughes J H, Marks R N, Taliani C, Dos Bradley D C, Santos D A D, Brédas J L, Lögdlund M, Salaneck W R 1999 Nature 397 121Google Scholar

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    Dodabalapur A, Katz H E, Torsi L, Haddon R C 1995 Science 269 1560Google Scholar

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    Yu G, Gao J, Hummelen J C, Wudl F, Heeger A J 1995 Science 270 1789Google Scholar

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    Onsager L 1938 Phys. Rev. 54 554Google Scholar

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    Scher H, Rackovsky S 1984 J. Chem. Phys. 81 1994Google Scholar

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    Leng J M, Jeglinski S, Wei X, Benner R E, Vardeny Z V, Guo F, Mazumdar S 1994 Phys. Rev. Lett. 72 156Google Scholar

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    Kersting R, Lemmer U, Deussen M, Bakker H J, Mahrt R F, Kurz H, Arkhipov V I, Bässler H, Göbel E O 1994 Phys. Rev. Lett. 73 1440Google Scholar

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    Barth S, Bässler H 1997 Phys. Rev. Lett. 79 4445Google Scholar

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    Graupner W, Cerullo G, Lanzani G, Nisoli M, List E J W, Leising G, De Silvestri S 1998 Phys. Rev. Lett. 81 3259Google Scholar

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    Clarke T M, Durrant J R 2010 Chem. Rev. 110 6736Google Scholar

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    Sariciftci N S 1998 Primary Photoexcitations in Conjugated Polymers: Molecular Exciton Versus Semiconductor Band Model (Singapore: World Scientific) pp20−50

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    Moses D, Okumoto H, Lee C H, Heeger A J, Ohnishi T, Noguchi T 1996 Phys. Rev. B 54 4748

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    Moses D, Dogariu A, Heeger A J 2000 Chem. Phys. Lett. 316 356Google Scholar

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    Ruseckas A, Theander M, Andersson M R, Svensson M, Prato M, Inganäs O, Sundström V 2000 Chem. Phys. Lett. 322 136Google Scholar

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    Miranda P B, Moses D, Heeger A J 2001 Phys. Rev. B 64 081201(RGoogle Scholar

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    Moses D, Dogariu A, Heeger A J 2000 Phys. Rev. B 61 9373Google Scholar

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    De Sio A, Troiani F, Maiuri M, Réhault J, Sommer E, Lim J, Huelga S F, Plenio M B, Rozzi C A, Cerullo G, Molinari E, Lienau C 2016 Nat. Comm. 7 13742Google Scholar

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    Wang R, Yao Y, Zhang C F, Zhang Y D, Bin H J, Xue L W, Zhang Z G, Xie X Y, Ma H B, Wang X Y, Li Y F, Xiao M 2019 Nat. Commun. 10 398Google Scholar

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    Dong Y F, Nikolis V C, Talnack F, Chin Y C, Benduhn J, Londi G, Kublitski J, Zheng X J, Mannsfeld S C B, Spoltore D, Muccioli L, Li J, Blase X, Beljonne D, Kim J S, Bakulin A A, D′Avino G, Durrant J R, Vandewal K 2020 Nat. Commun. 11 4617Google Scholar

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    An Z, Wu C Q, Sun X 2004 Phys. Rev. Lett. 93 216407Google Scholar

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    Coropceanu V, Cornil J, da Silva Filho D A, Olivier Y, Silbey R, Brédas J L 2007 Chem. Rev. 107 926Google Scholar

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    Shinar J, Shinar R 2008 J. Phys. D: Appl. Phys. 41 133001Google Scholar

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    Sun Z, Li S, Xie S J, An Z 2019 J. Chem. Phys. C 123 21336Google Scholar

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    Menon A, Dong H P, Niazimbetova Z I, Rothberg L J, Galvin M E 2002 Chem. Mater. 14 3668Google Scholar

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    Konezny S J, Rothberg L J, Galvin M E, Smith D L 2010 Appl. Phys. Lett. 97 143305Google Scholar

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    Yuan X J, Dong X F, Li D M, Liu D S 2011 J. Chem. Phys. 134 244901Google Scholar

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    Yuan X J, Li D M, Yin S, Gao K, Cui B, Liu D S 2012 Org. Electron. 13 2094Google Scholar

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    Sariciftci N S, Heeger A J 1997 Handbook Organic Conductive Molecules Polymers (New York: Wiley) pp413–455

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    Li X X, Hou D, Chen G 2018 Org. Electron. 54 245Google Scholar

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    Wang Y D, Liu J J, Wang X R, Di B, Meng Y 2018 Europhys. Lett. 123 37003Google Scholar

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    Miranda R P, Fisher A J, Stella L, Horsfield A P 2011 J. Chem. Phys. 134 244101Google Scholar

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    Su W P, Schrieffer J R, Heeger A J 1979 Phys. Rev. Lett. 42 1698Google Scholar

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    Su W P, Schrieffer J R, Heeger A J 1980 Phys. Rev. B 22 2099Google Scholar

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    Brazovskii S A, Kirova N N 1981 Sov. Phys. JETP Lett. 33 4

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    Heeger A J, Kivelson S, Schrieffer J R, Su W P 1988 Rev. Mod. Phys. 60 781Google Scholar

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    Meng Y, Liu X J, Di B, An Z 2009 J. Chem. Phys. 131 244502Google Scholar

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    Sun Z, Li Y, Xie S J, An Z, Liu D S 2009 Phys. Rev. B 79 201310(RGoogle Scholar

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    Sun Z, Li Y, Gao K, Liu D S, An Z, Xie S J 2010 Org. Electron. 11 279Google Scholar

  • 图 1  加入对角无序后, 电子$ \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $激发后晶格交错序参量$ \delta_i = (-1)^i(u_{i+1}-u_i)/2 $随时间的演化 (a) $ L = 64, \; \sigma_\varepsilon = 0.01 $ eV; (b) $ L = 128, \; \sigma_\varepsilon = 0.10 $ eV, 插图显示了$ \varepsilon_2^{\rm v} $上一个电子激发到导带$ \varepsilon_2^{\rm c} $后, 电子初始占据状态的示意图

    Fig. 1.  Dynamical evolution of the staggered bond order parameter $ \delta_{i} = (-1)^{i}(u_{i+1}-u_{i})/2 $ with time for photoexcitation $ \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $: (a) $ L = 64, \; \sigma_\varepsilon = 0.01 $ eV; (b) $ L = 128, \; \sigma_\varepsilon = 0.10 $ eV. The inset shows the initial electronic levels for a photoexcitation process of $ \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $.

    图 2  激子的产率在不同链长和电子关联下随着对角无序强度的变化 (a) $ L = 64, \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $; (b) $ L = 96, \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $; (c) $L = $$ 128, \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c}$; (d) $ L = 64, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $; (e) $ L = 96, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $; (f) $ L = 128, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $

    Fig. 2.  Dependence of the yield of the exciton on the strength of diagonal disorder: (a) $ L = 64, \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $; (b) $ L = 96, \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $; (c) $ L = 128, \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $; (d) $ L = 64, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $; (e) $ L = 96, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $; (f) $ L = 128, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $.

    图 3  激子的产率在不同链长和电子关联下随着非对角无序强度的变化 (a) $ L = 64, \; \varepsilon_2^{\upsilon}\rightarrow\varepsilon_2^c $; (b) $ L = 96, \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $; (c) $L = 128, $$ \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c}$; (d) $ L = 64, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $; (e) $ L = 96, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $; (f) $ L = 128, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $

    Fig. 3.  Dependence of the yield of the exciton on the strength of off-diagonal disorder: (a) $ L = 64, \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $; (b) $L = $$ 96, \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c}$; (c) $ L = 128, \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $; (d) $ L = 64, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $; (e) $ L = 96, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $; (f) $ L = 128, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $.

    图 4  两种无序同时存在时, 激子的产率在不同链长和电子关联下随着无序强度的变化 (a) $ L = 64, \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $; (b) $L = 96, $$ \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c}$; (c) $ L = 128, \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $; (d) $ L = 64, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $; (e) $ L = 96, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $; (f) $ L = 128, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $

    Fig. 4.  Dependence of the yield of the exciton on the strength of both diagonal and off-diagonal disorder: (a) $ L = 64, \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $; (b) $ L = 96, \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $; (c) $ L = 128, \; \varepsilon_2^{\rm v}\rightarrow\varepsilon_2^{\rm c} $; (d) $ L = 64, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $; (e) $ L = 96, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c} $; (f) $L = 128, \; \varepsilon_4^{\rm v}\rightarrow\varepsilon_4^{\rm c}$.

  • [1]

    Shirakawa H, Louis E J, MacDiarmid A G, Chiang C K, Heeger A J 1977 J. Chem. Soc. Chem. Commun. 16 578

    [2]

    Heeger A J 2001 Rev. Mod. Phys. 73 681Google Scholar

    [3]

    Friend R H, Gymer R W, Holmes A B, Burroughes J H, Marks R N, Taliani C, Dos Bradley D C, Santos D A D, Brédas J L, Lögdlund M, Salaneck W R 1999 Nature 397 121Google Scholar

    [4]

    Dodabalapur A, Katz H E, Torsi L, Haddon R C 1995 Science 269 1560Google Scholar

    [5]

    Yu G, Gao J, Hummelen J C, Wudl F, Heeger A J 1995 Science 270 1789Google Scholar

    [6]

    Onsager L 1938 Phys. Rev. 54 554Google Scholar

    [7]

    Scher H, Rackovsky S 1984 J. Chem. Phys. 81 1994Google Scholar

    [8]

    Leng J M, Jeglinski S, Wei X, Benner R E, Vardeny Z V, Guo F, Mazumdar S 1994 Phys. Rev. Lett. 72 156Google Scholar

    [9]

    Kersting R, Lemmer U, Deussen M, Bakker H J, Mahrt R F, Kurz H, Arkhipov V I, Bässler H, Göbel E O 1994 Phys. Rev. Lett. 73 1440Google Scholar

    [10]

    Barth S, Bässler H 1997 Phys. Rev. Lett. 79 4445Google Scholar

    [11]

    Graupner W, Cerullo G, Lanzani G, Nisoli M, List E J W, Leising G, De Silvestri S 1998 Phys. Rev. Lett. 81 3259Google Scholar

    [12]

    Clarke T M, Durrant J R 2010 Chem. Rev. 110 6736Google Scholar

    [13]

    Sariciftci N S 1998 Primary Photoexcitations in Conjugated Polymers: Molecular Exciton Versus Semiconductor Band Model (Singapore: World Scientific) pp20−50

    [14]

    Moses D, Okumoto H, Lee C H, Heeger A J, Ohnishi T, Noguchi T 1996 Phys. Rev. B 54 4748

    [15]

    Moses D, Dogariu A, Heeger A J 2000 Chem. Phys. Lett. 316 356Google Scholar

    [16]

    Ruseckas A, Theander M, Andersson M R, Svensson M, Prato M, Inganäs O, Sundström V 2000 Chem. Phys. Lett. 322 136Google Scholar

    [17]

    Miranda P B, Moses D, Heeger A J 2001 Phys. Rev. B 64 081201(RGoogle Scholar

    [18]

    Moses D, Dogariu A, Heeger A J 2000 Phys. Rev. B 61 9373Google Scholar

    [19]

    De Sio A, Troiani F, Maiuri M, Réhault J, Sommer E, Lim J, Huelga S F, Plenio M B, Rozzi C A, Cerullo G, Molinari E, Lienau C 2016 Nat. Comm. 7 13742Google Scholar

    [20]

    Wang R, Yao Y, Zhang C F, Zhang Y D, Bin H J, Xue L W, Zhang Z G, Xie X Y, Ma H B, Wang X Y, Li Y F, Xiao M 2019 Nat. Commun. 10 398Google Scholar

    [21]

    Dong Y F, Nikolis V C, Talnack F, Chin Y C, Benduhn J, Londi G, Kublitski J, Zheng X J, Mannsfeld S C B, Spoltore D, Muccioli L, Li J, Blase X, Beljonne D, Kim J S, Bakulin A A, D′Avino G, Durrant J R, Vandewal K 2020 Nat. Commun. 11 4617Google Scholar

    [22]

    An Z, Wu C Q, Sun X 2004 Phys. Rev. Lett. 93 216407Google Scholar

    [23]

    Jaiswal M, Menon R 2006 Polym. Int. 55 1371Google Scholar

    [24]

    Coropceanu V, Cornil J, da Silva Filho D A, Olivier Y, Silbey R, Brédas J L 2007 Chem. Rev. 107 926Google Scholar

    [25]

    Shinar J, Shinar R 2008 J. Phys. D: Appl. Phys. 41 133001Google Scholar

    [26]

    Wang Y D, Zhang X G, Meng Y, Di B, Zhang Y L, An Z 2017 Org. Electron. 49 286Google Scholar

    [27]

    Sun Z, Li S, Xie S J, An Z 2019 J. Chem. Phys. C 123 21336Google Scholar

    [28]

    Menon A, Dong H P, Niazimbetova Z I, Rothberg L J, Galvin M E 2002 Chem. Mater. 14 3668Google Scholar

    [29]

    Konezny S J, Rothberg L J, Galvin M E, Smith D L 2010 Appl. Phys. Lett. 97 143305Google Scholar

    [30]

    Yuan X J, Dong X F, Li D M, Liu D S 2011 J. Chem. Phys. 134 244901Google Scholar

    [31]

    Yuan X J, Li D M, Yin S, Gao K, Cui B, Liu D S 2012 Org. Electron. 13 2094Google Scholar

    [32]

    Sariciftci N S, Heeger A J 1997 Handbook Organic Conductive Molecules Polymers (New York: Wiley) pp413–455

    [33]

    Li X X, Hou D, Chen G 2018 Org. Electron. 54 245Google Scholar

    [34]

    Wang Y D, Liu J J, Wang X R, Di B, Meng Y 2018 Europhys. Lett. 123 37003Google Scholar

    [35]

    Miranda R P, Fisher A J, Stella L, Horsfield A P 2011 J. Chem. Phys. 134 244101Google Scholar

    [36]

    Miranda R P, Fisher A J, Stella L, Horsfield A P 2011 J. Chem. Phys. 134 244102Google Scholar

    [37]

    Su W P, Schrieffer J R, Heeger A J 1979 Phys. Rev. Lett. 42 1698Google Scholar

    [38]

    Su W P, Schrieffer J R, Heeger A J 1980 Phys. Rev. B 22 2099Google Scholar

    [39]

    Brazovskii S A, Kirova N N 1981 Sov. Phys. JETP Lett. 33 4

    [40]

    Heeger A J, Kivelson S, Schrieffer J R, Su W P 1988 Rev. Mod. Phys. 60 781Google Scholar

    [41]

    Meng Y, Liu X J, Di B, An Z 2009 J. Chem. Phys. 131 244502Google Scholar

    [42]

    Sun Z, Li Y, Xie S J, An Z, Liu D S 2009 Phys. Rev. B 79 201310(RGoogle Scholar

    [43]

    Sun Z, Li Y, Gao K, Liu D S, An Z, Xie S J 2010 Org. Electron. 11 279Google Scholar

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  • 被引次数: 0
出版历程
  • 收稿日期:  2020-10-30
  • 修回日期:  2021-01-15
  • 上网日期:  2021-05-20
  • 刊出日期:  2021-06-05

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