Formation of Hot Excitons, Annealing, and Relaxation in Conjugated

Article pubs.acs.org/JPCC

Formation of Hot Excitons, Annealing, and Relaxation in Conjugated Polymers under an External Optical Pulse Yu-song Zhang,†,‡ Wei-kang Chen,† Zhe Lin,† Deyao Jiang,†,‡ Sheng Li,*,†,‡,§ and Thomas F. George*,§ †

Department of Physics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China Department of Physics and Key State Laboratory of Surface Physics, Fudan University, Shanghai 200433, China § Office of the Chancellor and Center for Nanoscience, Departments of Chemistry & Biochemistry and Physics & Astronomy, University of Missouri−St. Louis, St. Louis, Missouri 63121, United States ‡

ABSTRACT: With an optical pulse focusing on a typical semiconducting conjugated polymer, PPV, the resultant electron transition induces an oscillation of the band gap. The gap varies with a period of 50 fs and acts like a comb, filtering the original optical pulse to become an effective light pulse that has a period of 50 fs as well. The effective optical pulse thereby localizes the electron in the first 50 fs, yielding a hot exciton within 100 fs, which is in agreement with experimental results. Because of the prominent electron−lattice coupling of the conjugated polymer, the effective light field not only triggers lattice vibrations but also drives the hot exciton to undergo relaxation. During the relaxation over 1000 fs, the hot exciton loses its excess energy, finally completing its annealing process.

1. INTRODUCTION For progress on research on high-performance polymeric solar cells1−8 and lasers,9−20 understanding and controlling the hot carrier dynamics in conjugated polymers is an essential step to optimize the optoelectronic performance of organic semiconductors. There is, however, a lack of accurate, quantitative, and precise investigations for the dynamical process of excited states, such as hot excitons. In particular, much less is known about the nature of hot electron−hole pairs in a conjugated polymer, which results from optical excitation just within the band gap. Taking a simple chain-like structure for the conjugated polymer, low dimensionality can provide an appropriate window to explore the properties of excited states via the change of symmetry. Actually, for a quantum dot of zero dimension, it has been found that once a hot electron−hole pair, namely, “hot” exciton, is created by external optical excitation, there is an accompanying transient Stark effect. As the exciton cools down, the magnitude of symmetry breaking diminishes and eventually disappears as the hot electron−hole pair becomes a normal exciton.21 Given the dynamical effects induced by a hot exciton in a zero-dimensional quantum dot,21 in this paper we will focus on the dynamical process of the hot carrier in a 1D conjugated © XXXX American Chemical Society

polymer. Previous theoretical research has demonstrated that excitons dissociate, via the hot carrier transfer states, to effectively form mobile charge carriers,22 where the excess energy of the excited state has been seen to drive the geminate electron and hole to separate at the donor/acceptor interface of a DTDCTB/C60 complex. It is essential to unveil the underlying mechanism with respect to the hot carrier transfer and its mobility, where the annealing of the hot exciton is crucial for the polymeric solar cells. Toward this end, femtosecond stimulated Raman spectroscopy (FSRS) has been applied to disentangle the signatures of the bulk and interfacial donor response in the bulk heterojunction of MDMO-PPV and PCBM.23 On the basis of this, an accurate measurement reveals the whole ultrafast process of the exciton, and the dynamical property of excitons in conjugated polymers is furthermore found to be strongly related to the relaxation. What is the role of relaxation during the dynamical process of the hot exciton? To understand this, one can consider the quantum dot of inorganic materials, such as CdSe, where an Received: January 26, 2017 Revised: March 15, 2017 Published: April 7, 2017 A

DOI: 10.1021/acs.jpcc.7b00863 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

turn, triggers lattice vibrations. Such vibrations make it highly possible to drive the hot exciton into relaxation, where the excitons lose their excess energy and finish their annealing process. To prove this assumption is another task of this article.

ultrafast dynamical probe experimentally demonstrates that the relaxation largely contributes to the localization of the exciton,24 yet for chain-like polymers the evolution of the hot exciton involves intrachain and interchain exciton transitions, which raises a question as to which type of transitions makes a meaningful contribution to the relaxation. In solution aggregates of a low-band gap donor−acceptor polymer PBDTTT, the hot intrachain excitons play the main role in the relaxation, directly inducing the generation of stabilized interchain charge-separated states in the bulk heterojunctions.25 Meanwhile, on the basis of inorganic semiconductor quantum wells, the initial formation of the hot carrier is in the femtosecond time domain; then, decreasing the excess energy is completed within 2 ps.26 Within the π-electron system of low dimension, such as a semiconducting single-walled carbon nanotube, time-resolved two-photon photoemission spectroscopy (TR-TPPE) illustrates that due to the photons with energies above the band gap the hot excitons are not only populated but also lose most of their excess energy within the first 100 fs after photoexcitation. After undergoing relaxation, the hot excitons are either annihilated or trapped within a few picoseconds.27 What is the core factor that drives the relaxation during of the hot exciton? In colloidal lead chalcogenide nanocrystals, it has been demonstrated that the dynamics of hot charge carriers is closely related to lattice vibrations, and the cooling of charge carriers is attributed to phonon scattering.28 Furthermore, the investigation of a blend of semiconducting poly(3-hexylthiophene) (P3HT), via a ultrahigh-molecular-weight polyethylene (UHMW-PE) matrix, has shown that the lattice vibrational relaxation has an influence on and even modifies the formation of an aggregate excited state in conjugated polymers.29 A series of theoretical methods have been developed to explore the dynamical process of the hot exciton, including diabatized time-dependent density functional theory (DTDFT) to analyze exciton transfer and related conical intersections.30 On the basis of the framework of the self-consistent charge density functional tight binding (SCC-DFTB) method, nonadiabatic molecular dynamics (NA-MD) of large systems has been introduced to uncover the details of excited-state dynamics on the nanoscale.31 The recent theoretical research regarding the ultrafast dynamics furthermore reported that in conjugated polymers like those in the PPV family these conformational subunits electronically couple to neighboring subunits. During the relaxation, the resultant subtly delocalized collective states of nanoscale excitons will determine the polymer optical properties.32 Although these methods not only include multiple transfer processes consisting of the Förster and Dexter process but also explore the details of intraband carrier relaxation and nonradiative electron−hole recombination, it is still difficult to combine the electron−lattice coupling, which is due to the one dimensionality of the conjugated polymer, with the dynamics during the annealing of the hot exciton. Besides, how to reveal the linking between dynamics and external optical fields presents another barrier to describe the annealing of the hot exciton, relaxation, and phonon coupling. Thus it is one of the missions of this article to develop a valid approach that not only is able to describe the evolution of the electron population for external optical excitation but also can involve the relaxation of hot excitons. On the basis of the presentation above, an assumption with respect to the annealing of hot excitons is also proposed as follows: The external optical field yields hot excitons, which, in

2. METHODS Recently, it has been demonstrated that once external light excites a conjugated polymer, such as PBDTTT and poly(3hexylthiophene) (P3HT), to yield an exciton, the evolution of the fluorescence spectrum within 1 ns reveals the details of the evolution for lasers with different wavelengths and provides the time scale of the exciton formation, relaxation, and radiative decay.33,34 Furthermore, researchers have combined experimental and theoretical studies of excitation relaxation in (MEH-PPV), where the paradigm is based on the basic characteristics of conjugated polymers that are decided by conformational subunits.32 To clarify the mechanism regarding the relaxation of the exciton, it becomes necessary to consider the quasi-1D structure of conjugated polymers for the modeling of the Hamiltonian that is used to describe the polymeric properties. Thus the Hamiltonian has to include both the electron−lattice and electron−electron interactions. On the basis of previous research with respect to the semiconducting conjugated polymer poly(p-phenylenevinylene) (PPV),35−37 we select PPV to be a model for the calculation, where the related Hamiltonian, starting with the typical 1D model, can be constructed. We start with the extended Su−Schreiffer−Heeger−Hubbard Hamiltonian H = He + HL

(1)

where He is the electronic component and H3L is the lattice component He =

∑ [t0 − α(μl+ 1 − μl ) + (−1)l te](cl†+ 1,scl ,s + H.c.) l ,S

(2)

+ H′

H′ = U ∑ nl ,↑nl , ↓ + V l

HL =

K 2

∑

nl , Snl + 1, s (3)

l ,S ,S′

∑ (μl+ 1 − μl )2 + l

M 2

·2

∑ ul l

(4)

Here H′ is the term describing the electron−electron interaction, t0 is the hopping constant (2.5 eV), α is the electron−lattice coupling constant (4.78 eV/Å), te is the Brazovskii−Kirova term (0.06 eV), K is the elastic constant, c†l,s (cl,s) denotes the electron creation (annihilation) operator at cluster l with spin s and corresponding electron occupation number nl,s = c†l,scl,s, K is an elastic constant (21 eV/Å2), U (3.0 eV) and V (1.0 eV) are on-site and nearest-neighbor Coulomb interactions, and ul is the displacement of cluster l. The electron−electron interaction can be treated with the Hartree−Fock approximation, and the above eigenequation can be rewritten as follows B


Article

The Journal of Physical Chemistry C ⎛ 1⎞ εμZls, μ = [U ⎜ρl−s − ⎟ + V (∑ ρl −s ′ 1 + ⎝ 2⎠ s′

3. RESULTS AND DISCUSSION When the conjugated polymer is stimulated by external light to create an exciton, it recently has been seen that the dynamical evolution of the fluorescence spectrum is within 1 ns once the conjugated polymer is stimulated by a laser with wavelength 500 nm. Related experimental research reveals the details of the evolution for lasers with different wavelengths and provides the time scale of the exciton formation, relaxation, the radiative decay.27,32,33 3.1. External Laser Pulse. Let us choose a laser beam with pulse width of 20 fs as the external optical source, where the functional relationship between the light intensity and time is shown as Figure 1A. On the basis of the discrete Fourier

∑ ρl+s ′ 1 − 2)]Zls,μ s′

occ

− [V ∑ Zls, μZls− 1, μ + t0 + α(ul − 1 − ul) μ occ

+ ( −1)l − 1te]Zls− 1, μ − [V ∑ Zls, μZls+ 1, μ + t0 μ l+1

+ α(ul + 1 − ul) + ( −1)

te]Zls+ 1, μ

(5)

Here we also defined the charge distribution as occ ρl s = ∑μ |Zls, μ|2 − n0, where n0 is the density of the positively charged background. Because the electronic energy spectrum and its quantum states are functionals of the lattice displacement, the displacement of the unit is obtained via the conventional dynamical equation that is coupled with the Feynman−Hellmann theorem Fl = − Ψ

M

d 2ul dt

2

∂H Ψ ∂ul

(6)

⎫ ⎧ occ ∂E = −⎨∑ ν + K (2ul − ul + 1 − ul − 1)⎬ ⎩ ν ∂ul ⎭ ⎪

⎪

⎪

⎪

Figure 1. (A) Light intensity−time domain. (B) Light intensity− wavelength. (7)

transformation, the relationship between light intensity and time domain figure can be transformed into the new one between light intensity and frequency domain. Then, the relationship between the light intensity and the wavelength is obtained, as illustrated in Figure 1B, where the light intensity is distributed within a limited range of wavelengths. The intensity reaches its maximum value at the wavelength of 1027 nm. In Figure 1B, we have provided a blue dot that indicates the intensity and wavelength of the external optical pulse, 0.939 μJ/ s·cm2 and 677 nm. Once the conjugated polymer undergoes the excitation due to the external optical field, an electron in the HOMO transits into the LUMO through absorbing a photon, forming the socalled electron−hole pair, that is, exciton, which can be simply described schematically, as in Figure 2. Owing to the excitation driven by external optical pulse (Figure 1), the details at beginning of the excitation can be exhibited as follows. When the conjugated polymer macromolecule is excited by the external laser pulse as mentioned, the localization of the

If a conjugated PPV undergoes external photoexcitation, then an electron transits from a lower level Γd to an upper level Γu. In regard to Γu, |u⟩ represents its wave function, Eu its energy value, and Pu its electron population. Correspondingly, for Γd, there are |d⟩, Ed, and Pd. Within the time span Δt, the change of population ΔPu is composed of two parts: One is ascribed to a stimulated transition, ΔPd→u, and the other is ascribed to a spontaneous transition, ΔPu→d ΔPu = ΔPd → u + ΔPu → d

(8)

Without the restriction of Pauli repulsion, the dipole moment between Γu and Γd can be written as p = ⟨u|r|d⟩, where r is the dipole operator in the polymer chain. Then, the stimulated transition rate can be expressed as a function of the light-field frequency ω, and ρ(ω) is the energy density of the external photoelectric field Wd → u =

⎛ E − Ed ⎞ 4π 2 2 ⎟ p ρ(ω)δ ⎜ω − u 2 ⎝ ℏ ⎠ 3ℏ

(9)

As for spontaneous emission, the spontaneous transition rate γu→d between these states is determined by γu → d =

4(Eu − Ed)3 3ℏ4c 3

p2

(10)

Here ℏ is Planck’s constant, c is the speed of light in vacuum, ε0 is the permittivity of vacuum, and p = ⟨u|r|d⟩ denotes the dipole moment of the two energy levels.35 At time t, the energy spectrum, the wave function, and the electron occupation number can be obtained according to nonadiabatic molecular dynamics. On the basis of this, we can theoretically present the dynamic fluorescence spectrum along with the variation of the electron occupation number in the process of the hot exciton formation and its annealing in the conjugated polymer.

Figure 2. Electronic structure of an electron−hole pair induced by optical excitation. C


Article


LUMO. Meanwhile, considering the electron−lattice coupling in the conjugated polymer, the electronic structure changes as conjugated polymer undergoes the external excitation. As depicted in Figure 5, both the band gap and the energy level of

electron occurs within 80 fs, as shown in Figure 3, which is in agreement with the previous experimental research. Once the

Figure 5. (A) Time-dependent evolution of the bandwidth between HOMO and LUMO. (B) Time-dependent evolution of the energy gap width. Figure 3. Localization of the electron in the HOMO induced by the external laser pulse with 30 μJ/cm2.

original HOMO/LUMO oscillate sharply in the first 200 fs. In particular, at 50 fs, the difference between HOMO and LUMO is narrowest (∼0.6 eV). After that, the difference reaches 1.2 eV at 80 fs, whose period is estimated at ∼50 fs. After multiple oscillations of the electronic structure, the difference gradually reaches a certain value of 0.92 eV, while the gap is still 1.83 eV. Given that the difference between the HOMO and LUMO matches the wavelength of the optical pulse illustrated in Figure 1B, the electron in the HOMO mainly absorbs the photon and transits to LUMO. Meanwhile, the oscillation of the difference between the HOMO and LUMO, as shown in Figure 5A, causes the oscillation of the absorption spectrum, thus forming a new effective light pulse whose intensity varies with a certain period, which eventually settles in by 600 fs, as illustrated in Figure 6. Ultimately, it is the effective light pulse, not the original external light intensity, that is the key factor in affecting the transition rate.

hot exciton is formed in the polymer molecule, the localization of electron cloud of hot exciton just appears within 100 fs after the excitation.27,32,33 With the formation of the hot exciton, the electron in the HOMO will transit into the LUMO, thereby leading to the change of the electron occupation number in the HOMO and the LUMO. Thus it becomes necessary to move our focus to the evolution of the electron population in the LUMO and HOMO. As demonstrated in Figure 4A, the electron occupation in the LUMO increases slowly in the initial 20 fs with the optical

Figure 4. (A) Evolution of the electron occupation number in the LUMO in the initial 120 fs. (B) Evolution of the transition rate in the initial 120 fs.

excitation. From 20 to 40 fs, the electron occupation number in LUMO increases rapidly. However, it increases slowly again between 40 and 80 fs. After 80 fs, the electron occupation number of each energy level becomes steady. It is obvious that in Figure 4 the evolution of the electron occupation number in LUMO is not smooth. There exist two inflection points at the times of 27 and 68 fs during the evolution of the electron occupation in the LUMO, which is marked by circles in Figure 4A. Figure 4B presents the whole transition process, which tightly links the inflection points at times 27 and 68 fs, when the transition rate rises to the highest peak of 0.08 fs−1 at 27 fs, while it reaches the second peak of 0.006 fs−1 at 68 fs. To clarify the underlying mechanism that induces the appearance of inflection points, we have to investigate the factors influencing the electron transition. In light of the selection rule with respect to the electron transition, the transition rate is determined by the intensity of the exciting light and the energy gap between the molecular orbitals as eq 9. Therefore, the concentration can be moved to the energy gap and the difference between the HOMO and

Figure 6. Time variation of effective light pulse.

The existence of two steps during the evolution of electron population in the initial 120 fs, as seen in Figure 4A, is due to the oscillation of the effective light pulse shown in Figure 6. Because of eq 9, the transition rate is determined by the energy density of the external optical pulse. Thus in the first 50 fs (namely, the first oscillation period of the effective light pulse) the transition rate decreases to 0 when the effective light pulse decreases to 0 from 25 to 50 fs. Actually, in the first oscillation period of the effective light pulse as Figure 6, the external optical field still has not fully stimulated an electron to move from the HOMO into the LUMO, where the formation of electron−hole pair is ∼95% with “5% electron” remaining in the HOMO. In the second oscillation period, the rest of the electron is promoted to the LUMO, while the transition rate D


Article

The Journal of Physical Chemistry C increases to 0.006 fs−1 at 80 fs. With the formation of the hot exciton, the electron transition rate decreases to 0, which finally leads to the second peak in the evolution of the transition rate in the initial 120 fs, as seen in Figure 4B. 3.2. Formation and Annealing of Hot Excitons. With excitation by the external light of intensity as Figure 1, Figure 7

form the localized distortion. When time reaches 140 fs, the lattice configuration is completely locally distorted. Because of the permanent aspect of the electron−phonon interaction, the local distortion of the lattice configuration influences the electron structure. Figure 9A shows the evolution

Figure 7. (A) Total energy of the polymer chain in 200 fs. (B) Total energy of polymer chain from 200 to 1600 fs.

Figure 9. (A) Electron energy over 200 fs. (B) Time-dependent distribution of the electron cloud over 100 fs.

presents the evolution of the total energy of the polymer chain system over 1600 fs. The energy increases rapidly reaches its maximum value at 60 fs. Referring to the evolution of the electron population in the LUMO in Figure 4A, we see that at 60 fs the electron−hole pair−hot exciton−is formed. However, at this point in time, the total energy still does not reach a stable value. As shown in Figure 7B, the total energy of the whole polymer chain undergoes an oscillation of ∼850 fs and then reaches a stable value, which is also the process of annealing of the hot exciton. Thus the excitation of the exciton in a conjugated polymer can be divided into two steps: one is the formation of the photoinduced hot exciton and the other is the annealing of the hot exciton. 3.2.1. Photoinduced Hot Excitons. During the first 80 fs, because of the effective external optical field, the electron in the HOMO transits into the LUMO, leading to the formation of the hot exciton, as depicted in Figure 4A. Actually, within the first 60 fs, the total energy of the system has rapidly increased from −644.3 to −642.5 eV and triggers the oscillation of energy with the period of 50 fs, as shown in Figure 7A. Besides the total energy of the polymer chain, the lattice energy that involves the kinetic energy and the potential energy also has undergone a similar evolution. This is described in Figure 8A, where the lattice energy begins to oscillate with the

of the electron energy over the same time span. In the initial 80 fs, the oscillation of the lattice energy with the period of 50 fs triggers the oscillation of the electron energy with the period of 40 fs. We observe in Figure 9B that the electron cloud starts to localize in the middle of the polymer chain within the initial 20 fs. As time reaches 80 fs, the localization of the electron cloud has been formed along the polymer chain. 3.2.2. Annealing. During the time span from 80 to 1600 fs, it is found, as seen in Figure 10, that the localization of the lattice

Figure 10. (A) Time-dependent evolution of lattice configuration over 1600 fs. (B) Time-dependent distribution of the exciton electron cloud over 1600 fs.

configuration accompanies and is consistent with the localization of the electron cloud along with the formation of the hot exciton. We raise a question: Does both the localization of the electron cloud and the locally distorted lattice configuration imply the formation of a stable exciton? To respond to this question, let us look at the energy evolution after the formation of the hot exciton, as shown in Figure 11A over the time span from 80 to 1600 fs, where the total energy starts to oscillate with the period of 50 fs near the energy of −645.7 eV. The amplitude of oscillation gradually becomes smaller as time increases. Furthermore, the electron energy and the lattice energy oscillate with the period of ∼50 fs over the whole process, tending toward stability at ∼850 fs, as shown in Figure 11B,C. The evolution of the energy of the whole system, including the total, lattice, and electron energies, from 80 to 1600 fs, exactly constitutes the relaxation of the hot excitons. Considering the evolution of lattice and electron cloud and the lattice, as depicted in Figure 10, it demonstrated that the

Figure 8. (A) Lattice energy over 200 fs. (B) Evolution of the lattice configuration over 140 fs.

period of 50 at 80 fs, consistent with the behavior of the total energy. Thus we can say that the oscillation of lattice energy with the large amplitude of 3.5 eV not only directly induces the lattice to seriously vibrate but also destroys the original lattice configuration of dimerization, finally resulting in the lattice distortion. It can be seen from Figure 8B that the original lattice configuration of dimerization is broken within the first 100 fs to E



■

Article

AUTHOR INFORMATION

Corresponding Authors

*S.L.: E-mail: [email protected]. Phone: 86-579-8228-2424. *T.F.G.: E-mail: [email protected]. Phone: 1-314-516-5252. ORCID

Thomas F. George: 0000-0003-1225-6778 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Science Foundation of China under grant 21374105 and the Zhejiang Provincial Science Foundation of China under grant R12B040001.

■

REFERENCES

(1) Brabec, C. J.; Sariciftci, N. S.; Hummelen, J. C. Plastic Solar Cells. Adv. Funct. Mater. 2001, 11, 15−26. (2) Nelson, J. Organic Photovoltaic Films. Curr. Opin. Solid State Mater. Sci. 2002, 6, 87−95. (3) Li, Y.; Zou, Y. Conjugated Polymer Photovoltaic Materials with Broad Absorption Band and High Charge Carrier Mobility. Adv. Mater. 2008, 20, 2952−2958. (4) Dennler, G.; Scharber, M. C.; Brabec, C. J. Polymer-Fullerene Bulk-Heterojunction Solar Cells. Adv. Mater. 2009, 21, 1323−1338. (5) Li, C.; Liu, M.; Pschirer, N. G.; Baumgarten, M.; Müllen, K. Polyphenylene-Based Materials for Organic Photovoltaics. Chem. Rev. 2010, 110, 6817−6855. (6) Facchetti, A. π-Conjugated Polymers for Organic Electronics and Photovoltaic Applications. Chem. Mater. 2011, 23, 733−758. (7) Piliego, C.; Loi, M. A. Charge Transfer State in Highly Efficient Polymer-Fullerene Bulk Heterojunction Solar Cells. J. Mater. Chem. 2012, 22, 4141−4150. (8) Winder, C.; Sariciftci, N. S. Low Bandgap Polymers for Photon Harvesting in Bulk Heterojunction Solar Cells. J. Mater. Chem. 2004, 14, 1077−1086. (9) Akselrod, G. M.; Young, E. R.; Bradley, M. S.; Bulović, V. Lasing Through a Strongly-Coupled Mode by Intra-Cavity Pumping. Opt. Express 2013, 21, 12122−12128. (10) Kéna-Cohen, S.; Forrest, S. Room-Temperature Polariton Lasing in an Organic Single-Crystal Microcavity. Nat. Photonics 2010, 4, 371−375. (11) Yoon, J.; Lee, W.; Caruge, J. M.; Bawendi, M.; Thomas, E. L.; Kooi, S.; Prasad, P. N. Defect-Mode Mirrorless Lasing in Dye-Doped Organic/Inorganic Hybrid One-Dimensional Photonic Crystal. Appl. Phys. Lett. 2006, 88, 091102−091103. (12) Kowalsky, W.; Rabe, T.; Schneider, D.; Johannes, H.-H.; Karnutsch, C.; Gerken, M.; Lemmer, U.; Wang, J.; Weimann, T.; Hinze, P.; Riedl, T. Organic Semiconductor Distributed Feedback Lasers. Proc. SPIE 2005, 6008, 60080Z. (13) Schneider, D.; Rabe, T.; Riedl, T.; Dobbertin, T.; Kröger, M.; Becker, E.; Johannes, H.-H.; Kowalsky, W.; Weimann, T.; Wang, J.; et al. Laser Threshold Reduction in an All-Spiro Guest-Host System. Appl. Phys. Lett. 2004, 85, 1659−1661. (14) Rose, A.; Zhu, Z.; Madigan, C. F.; Swager, T. M.; Bulović, V. Sensitivity Gains in Chemosensing By Lasing Action In Organic Polymers. Nature 2005, 434, 876−879. (15) Kushida, S.; Braam, D.; Pan, C.; Dao, T. D.; Tabata, K.; Sugiyasu, K.; Takeuchi, M.; Ishii, S.; Nagao, T.; Lorke, A.; Yamamoto, Y. Whispering Gallery Resonance From Self-Assembled Microspheres Of Highly Fluorescent Isolated Conjugated Polymers. Macromolecules 2015, 48, 3928−3933. (16) Wang, X.; Liao, Q.; Li, H.; Bai, S.; Wu, Y.; Lu, X.; Hu, H.; Shi, Q.; Fu, H. Near-Infrared Lasing from Small-Molecule Organic Hemispheres. J. Am. Chem. Soc. 2015, 137, 9289−9295. (17) Shapira, O.; Kuriki, K.; Orf, N. D.; Abouraddy, A. F.; Benoit, G.; Viens, J. F.; Rodriguez, A.; Ibanescu, M.; Joannopoulos, J. D.; Fink, Y.;

Figure 11. (A) Total energy, (B) lattice energy, and (C) electron energy from 80 to 1600 fs.

relaxation of the hot exciton, from 80 to 1600 fs, does not destroy the localization of the resultant exciton. Mostly, the relaxed exciton still keeps the perfect character of the localization as the hot exciton at 80 fs, not only in the lattice structure but also in the electron cloud. Thus the whole process of relaxation, within the time span from 80 to 1600 fs, is actually the annealing of the hot exciton.

4. CONCLUSIONS After an optical pulse is applied to a conjugated polymer, the resultant electron transition induces oscillation of the gap width. Such oscillation changes the absorption of the external optical field inversely, forming an effective optical pulse whose intensity varies with a period of 50 fs, which is totally different from the original optical pulse. For the effective light pulse, the electron is localized in the first 50 fs, and the excited polymer yields the hot exciton within 100 fs, which is in agreement with experimental results.27,32,33 Owing to the prominent electron− lattice coupling of the conjugated polymer, the effective light field furthermore triggers the lattice vibration that drives the hot exciton to undergo relaxation. Accounting for the relaxation over 1000 fs, the hot exciton loses the excess energy that involves the electronic energy and lattice energy, finally completing its annealing. F


Article

The Journal of Physical Chemistry C et al. Surface-Emitting Fiber Lasers. Opt. Express 2006, 14, 3929− 3935. (18) Gourdon, F.; Chakaroun, M.; Fabre, N.; Solard, J.; Cambril, E.; Yacomotti, A.-M.; Bouchoule, S.; Fischer, A.; Boudrioua, A. Optically Pumped Lasing from Organic Two-Dimensional Planar Photonic Crystal Microcavity. Appl. Phys. Lett. 2012, 100, 213304−213307. (19) Riechel, S.; Kallinger, C.; Lemmer, U.; Feldmann, J.; Gombert, A.; Wittwer, V.; Scherf, U. A Nearly Diffraction Limited Surface Emitting Conjugated Polymer Laser Utilizing a Two-Dimensional Photonic Band Structure. Appl. Phys. Lett. 2000, 77, 2310−2312. (20) Chen, R.; Ta, V. D.; Sun, H. Bending-Induced Bidirectional Tuning of Whispering Gallery Mode Lasing From Flexible Polymer Fibers. ACS Photonics 2014, 1, 11−16. (21) Trinh, M. T.; Sfeir, M. Y.; Choi, J. J.; Owen, J. S.; Zhu, X. A Hot Electron−Hole Pair Breaks the Symmetry of a Semiconductor Quantum Dot. Nano Lett. 2013, 13, 6091−6097. (22) Shen, X.; Han, G.; Fan, D.; Xie, Y.; Yi, Y. Hot Charge-Transfer States Determine Exciton Dissociation in the DTDCTB/C60 Complex for Organic Solar Cells: A Theoretical Insight. J. Phys. Chem. C 2015, 119, 11320−11326. (23) Hoffman, D. P.; Leblebici, S. Y.; Schwartzberg, A. M.; Mathies, R. A. Exciton Mobility in Organic Photovoltaic Heterojunctions from Femtosecond Stimulated Raman. J. Phys. Chem. Lett. 2015, 6, 2919− 23. (24) Kambhampati, P. Hot Exciton Relaxation Dynamics in Semiconductor Quantum Dots: Radiationless Transitions on the Nanoscale. J. Phys. Chem. C 2011, 115, 22089−22109. (25) Guo, Z.; Lee, D.; Gao, H.; Huang, L. Exciton Structure and Dynamics in Solution Aggregates of a Low-Bandgap Copolymer. J. Phys. Chem. B 2015, 119, 7666−72. (26) Sippel, P.; Albrecht, W.; van der Bok, J. C.; Van Dijk-Moes, R. J.; Hannappel, T.; Eichberger, R.; Vanmaekelbergh, D. Femtosecond Cooling of Hot Electrons in CdSe Quantum-Well Platelets. Nano Lett. 2015, 15, 2409−16. (27) Kafle, T. R.; Wang, T.; Kattel, B.; Liu, Q.; Gong, Y.; Wu, J. Z.; Chan, W. L. Hot Exciton Relaxation and Exciton Trapping in SingleWalled Carbon Nanotube Thin Films. J. Phys. Chem. C 2016, 120, 24482−24490. (28) Geiregat, P.; Delerue, C.; Justo, Y.; Aerts, M.; Spoor, F.; Van Thourhout, D.; Siebbeles, L. D.; Allan, G.; Houtepen, A. J.; Hens, Z. A Phonon Scattering Bottleneck for Carrier Cooling in Lead Chalcogenide Nanocrystals. ACS Nano 2015, 9, 778−88. (29) Parkinson, P.; Müller, C.; Stingelin, N.; Johnston, M. B.; Herz, L. M. Role of Ultrafast Torsional Relaxation in the Emission from Polythiophene Aggregates. J. Phys. Chem. Lett. 2010, 1, 117−118. (30) Tamura, H. Diabatization for Time-Dependent Density Functional Theory: Exciton Transfers and Related Conical Intersections. J. Phys. Chem. A 2016, 120, 9341−9347. (31) Pal, S.; Trivedi, D. J.; Akimov, A. V.; Aradi, B.; Frauenheim, T.; Prezhdo, O. V. Nonadiabatic Molecular Dynamics for Thousand Atom Systems: A Tight-Binding Approach towards PYXAID. J. Chem. Theory Comput. 2016, 12, 1436−1448. (32) Dykstra, T. E.; Hennebicq, E.; Beljonne, D.; Gierschner, J.; Claudio, G.; Bittner, E. R.; Knoester, J.; Scholes, G. D. Conformational Disorder and Ultrafast Exciton Relaxation in PPV-Family Conjugated Polymers. J. Phys. Chem. B 2009, 113, 656−667. (33) Banerji, N.; Cowan, S.; Leclerc, M.; Vauthey, E.; Heeger, A. J. Exciton Formation, Relaxation, and Decay in PCDTBT. J. Am. Chem. Soc. 2010, 132, 17459−17470. (34) Banerji, N.; Cowan, S.; Vauthey, E.; Heeger, A. J. Ultrafast Relaxation of the Poly(3-hexylthiophene) Emission Spectrum. J. Phys. Chem. C 2011, 115, 9726−9739. (35) Choi, H. Y.; Rice, M. J. Excited Polarons in Poly(Phenylene Vinylene) and Poly(Diacetylene). Phys. Rev. B: Condens. Matter Mater. Phys. 1991, 44, 10521−10524. (36) Gao, K.; Liu, X. J.; Liu, D. S.; Xie, S. J. Charge Carrier Generation Through Reexcitations of an Exciton in Poly(p-phenylene vinylene) Molecules. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 75, 205412−205417.

(37) Wang, C.; Zhuang, L. Q.; Chen, R. A.; Li, S.; George, T. F. Localization and Relaxation of Singlet Exciton Formation in Conjugated Polymers under Photoexcitation. J. Phys. Chem. B 2013, 117, 3258−3263.

G


Formation of Hot Excitons, Annealing, and Relaxation in Conjugated

Recommend Documents