Hidden Confinement Induced by Charged Excitons: External Electric

Aug 13, 2015 - State Key Laboratory for Surface Physics, Fudan University, Shanghai 200433, China ... University of Missouri−St. Louis, St. Louis, M...
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Hidden Confinement Induced by Charged Excitons: External Electric Field Adjustment to Achieve Highly Efficient Fluorescence in PLEDs Renai Chen,†,‡ Weikang Chen,† Deyao Jiang,† Sheng Li,*,†,‡,§ and Thomas F. George*,§ †

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

ABSTRACT: Experiments have shown that intensive charge injections are able to greatly enhance the efficiency of polymer light emitting diodes (PLEDs). Yet, under strong external electric filed/high voltages, there is a certain degree of efficiency roll-off. For this paradox, this article reveals the following underlying mechanism: Under a low electric field, a charged polaron is driven to the potential well created by an exciton, where they fuse together to form a “charged exciton”. The carrier fusion induces the triplet state to fluoresce, which greatly enhances the performance of the device (ideally, the internal quantum efficiency can exceed 95%). As long as the external field continues to increase and surpasses 4.5 × 104 V/cm, the above confinement is broken, and the polaron also steps out of the potential well, which leads to a major setback of the overall device efficiency. Then, when the electric field reaches as high as 0.8 MV/cm, the original exciton is dissociated. For achieving highly efficient fluorescent PLEDs, it is seen that the appropriate electric field magnitude ranges from 5 × 102 to 2 × 104 V/cm.

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INTRODUCTION

Basically, the simplest single-layer polymer LED has a sandwich-like structure, where a thin luminescent conjugated polymer layer is embedded between two electrodes. When electrons and holes are injected, excitons are soon formed, and later their radiative decay emits light.17 However, when HTL/ HIL (ETL/EIL) is inserted into the diode, the injected charge carriers are very likely to form quasiparticles, like polarons and bipolarons, transporting in the polymer, because of the unique one-dimensional structural property that conjugated polymers mostly inherit. Due to the transfer of charged carriers, polarons, either delocalized or localized, play a crucial role in efficient charge carrier transport in polymers,18 which means the charged carriers are destined to interact frequently with neutral excitons (singlet or triplet) during the transfer driven by the external electric field. To understand the interaction between a charged polaron and neutral exciton, the first step is to delineate the dynamics of charged carriers in a conjugated polymer, which has been thoroughly studied by Xie and An.19,20 Although a high electric field is able to efficiently inject and accelerate charged carriers in a conjugated polymer, Devizis et al. also observed that once electric field reaches a certain threshold, fluorescence in poly(spirobifuorene-co-benzothiadiazole) is soon quenched.21 Here, some experiments provide a possible mechanism for the

The promising advantages of ultralow-cost, lightweight and flexible polymer light emitting diodes (PLEDs)1 have attracted lots of research attention since the first prototype was invented based on poly(p-pheylene vinylene) (PPV) in the 1990s.2 Modified and optimized PPV derivatives have been prepared to enhance the light emitting properties.3−5 Pyridine-containing, thiophene-based conjugated polymers have been utilized to fabricate new PLEDs,6,7 and fluorene-based copolymers have been tested to show orange- and red-light-emitting devices.8 In order to improve the performance and stability of the PLED devices, researchers have started to modify the structure of the diodes. Toward this end, Cao et al. have found that by blending electron transport materials with the conjugated polymer, the electroluminescence of the device is greatly enhanced.9 Also, it has been observed that PLEDs with an electron transport layer (ETL) possess significantly lower turnon voltages, higher brightness, and better luminous efficiency than whose without.10 Further, Friend and co-workers have reported high efficiency polymer electroluminescent devices by employing a compact ZnO electron transport and injection layer (EIL).11 Compared with inserting ETL/EIL into the devices, it is more favorable for PLEDs’ electroluminescence efficiency to embed a hole transport layer (HTL)/hole injection layer(HIL).12−14 Recently, researchers have even used graphene oxide as a HTL to create highly efficient PLEDs.15,16 © XXXX American Chemical Society

Received: June 30, 2015 Revised: August 12, 2015

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DOI: 10.1021/acs.jpcc.5b06260 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C light quenching that a high electric field dissociates the neutral exciton and sharply decrease the electroluminescence of a PLED.22−24 Mostly, it has been illustrated that in highly efficient metalfree organic electroluminescent diodes,25,26 there exists a channel where triplet excitons undergo slow radiative decay to fluoresce, thereby increasing the device internal quantum efficiency over 90%. Prior to exploring the underlying mechanism, two aspects have to be considered. First, the small energy difference between the lowest singlet (S1) and triplet (T1) in the given sample may not facilitate the production of the singlet exciton through the fusion of two triplets. Second, if even all the triplets are presumptively turned into singlets, the highest theoretical internal efficiency through triplet−triplet annihilation (TTA) channel is 62.5% (25% + 1/2 × 75%); this is far lower than the reported value, which indicates that the fluorescence decay channel cannot be attributed to triplet−triplet annihilation (TTA). Therefore, it is highly possible that there exists other underlying channels to enable/utilize the triplet exciton to emit delayed fluorescence. In addition, Zhang’s recent research has demonstrated that low (rather than high) driving voltage can help improve the efficiency of organic light-emitting diodes and reduce efficiency roll off.27 A critical question is whether there exists a possible mechanism that, besides injection and transport of charge carriers, given a low electric field, the interaction between a charged carrier and neutral exciton is able to enhance the efficiency of a PLED. The experiments reported by Tamura et al. that the dissociation of excitons in a polymeric heterojunction is driven by phonons28,29 suggest that strong electron−phonon interactions in a quasi-one-dimensional polymer structure can play a key role in exciton dynamics under an external electric field. In order to clarify the above questions and underlying mechanism behind the phenomenon, in this present work we want to illustrate the collision− transition process between certain confined states of polarons and excitons, as well as depict the dynamics as the electric field is increased. For this purpose, we employ nonadiabatic quantum molecular dynamics to investigate polaron transportation and its interaction with excitons under an external electric field. We focus on the collision between a polaron and an exciton in order to determine the limiting external energy for electroluminescence quenching, as well as the range of the magnitude of the electric field that is favorable for highly efficient PLEDs.

Here, t0 is a hopping constant, 2.5−5.0 eV; α is an electron− lattice coupling constant, 4.5 eV/Å; cl,s+ (cl,s) denotes the electron creation (annihilation) operator at cluster l with spin s; ul is the displacement of cluster l; te is the Brazovskii−Kirova term,31 0.05−0.12 eV; K is an elastic constant, 21 eV/Å2; U(2.0−5.0 eV) and V(0.5−2.0 eV) are the on-site and nearestneighbor Coulomb interactions, respectively; a (0.12−0.50 nm) is the lattice constant; HE is the interaction of the electrons with the external electric field along the polymer chain; E (the unit is V/cm) is the electric field strength; and N is the number of lattice sites. For nonadiabatic dynamics, the time-dependent Schrödinger equation is employed directly: iℏ

HE =

l ,s,s′

⎛

∑ Ee⎝l − ⎜

l ,s

N + 1 ⎞⎟ anl , s 2 ⎠

(6)

where μ is the number of electron eigenstates. The electron−electron interaction is treated in the Hartree− Fock approximation as He =

⎧ ⎛ occ ⎪

∑ ⎨⎪U ⎜⎜∑ |Zl−,μs|2 − l ,s

⎩ ⎝

μ

⎞ 1⎟ 2 ⎟⎠

occ

+ V [∑ (∑ s′

−

⎫ ⎪

occ

|Zl−−s1,′ μ|2

μ occ

+

∑ |Zl−+s1,′ μ|2 − 2)]⎬cl+,scl ,s ⎪

⎭

μ

∑ (V ∑ Zls,μZls+ 1,μ)(cl+,scl ,s + H . c. ) l ,s

(7)

μ

where occ stands for the electron occupation or population. Then, the wave function with different spin takes a new form as ⎡ ⎛ 1⎞ εμZls, μ = ⎢U ⎜ρl−s − ⎟ + V (∑ ρl −s ′ 1 + ⎣ ⎝ 2⎠ s′

∑ ρl+s ′ 1 − 2) s′ occ

⎛ N + 1 ⎞⎟ ⎤ s a⎥Zl , μ − [V ∑ Zls, μZls− 1, μ + t0 + Ee⎜l − ⎝ 2 ⎠ ⎦ μ

(1)

+ α(ul − 1 − ul) + ( −1)l − 1te]Zls− 1, μ

He = U ∑ nl , ↑nl , ↓ + V ∑ nl , snl + 1, s ′ l

(5)

H Φμ = εμΦμ

l ,s

l

}

Beginning with t1,t2 (until tN), the electronic wave function of the later time is the time evolutional result of the wave function at the earlier time. As long as the interval is short enough (for example, 0.01 fs), the wave function at any time can be obtained. As functionals of the lattice displacement ul, the eigenenergy εμ and eigenwave function Φμ = {Zsl,μ} are determined by the eigenequation of the above Hamiltonian

H = −∑ [t0 + α(ul + 1 − ul) + ( −1)l te] × [cl++ 1, scl , s

∑ (ul+ 1 − ul)2 + He + HE

iH (t f − ti) Ψ(ti) ℏ

{

Ψ(t f ) = exp −

METHODS For the investigation of a quasi-one-dimensional conjugated polymer system, a valid methodology begins with the extended Su−Schreiffer−Heeger−Hubbard (SSSH) Hamiltonian:30,31

K 2

(4)

If the initial electronic wave function is Ψ(ti) and the final is Ψ(tf), the Hamiltonian is time-independent during a very short time interval (tf − ti), whereby we can write

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+ H . c. ] +

∂ Ψ = HΨ ∂t

occ

(2)

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

+ ( −1)l + 1te]Zls+ 1, μ

(3) B

(8) DOI: 10.1021/acs.jpcc.5b06260 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Figure 1. Dynamic evolution of a negative polaron and triplet exciton moving left to right under two different external electric fields strengths −2.5 × 103 V/cm for (a,b) and 5.5 × 104 V/cm for (c,d), where the direction of the field along the polymer chain is opposite that of the polaron evolution. (a) and (c) are for the lattice configuration evolution in 5 ps and 500 fs, respectively, and (b) and (d) for the charge density evolution in 5 ps and 500 fs, respectively.

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2 where the charge distribution is defined as ρl = ∑occ μ |Ψl,μ| − n0, and n0 is the density of the positively charged background. After the eigenfunction is obtained, the electronic wave function at a given instant is manifested by a linear combination of the eigenfunctions

Ψ(t ) =

RESULTS AND DISCUSSION After electrons and holes are injected into a PLED from electrodes, they transport through ETL/HTL and enter into the polymer/emitting layer. Then the formation of self-trapped quasiparticles, i.e., polarons and excitons, are described by the distortion of alternating bond as mentioned above, which is due to the strong electron−phonon coupling in a one-dimensional polymer chain. Here, we choose the polymer chain consisting of 200 lattice sites, where the triplet exciton is localized in the middle of the chain, and a negative polaron is located just on the left after it is injected by the external electric field, which is in keeping with a reported experimental observation of organic molecular wires.33 As a low external electric field of 2.5 × 103 V/cm is applied along the polymer chain, shown in Figure 1a,b, the negative polaron moves comparatively slow, approaching and meeting the triplet exciton at 2 ps. Then, the polaron fuses with the exciton, leading to the formation of an intermediate state called a “charged triplet exciton.”34 Regarding the charge distribution during the whole dynamics as illustrated in Figure 1b, the exciton is neutral at the beginning but is partially charged after it collides and fuses with the polaron. Apparently, after exciton absorbs the charge carrier, the “absorption” of an exciton brings additional mass to the resultant charged exciton. Meanwhile, its speed is slowed down significantly. In contrast, when the electric field is tuned to a higher value, 5.5 × 104 V/cm as shown in Figure 1c,d, the field drives the polaron to move much more quickly, meeting the electric-immobile exciton within just 300 fs (Figure 1c). What happens is quite interesting! The polaron does not bind itself with the exciton anymore, but instead passes straight through, with the exciton still existing. The charge distribution diagram

∑ cμ(t )Φμ (9)

μ

Taking advantage of the orthonormality of the eigenfunctions, the expansion coefficients are easily obtained cμ(t ) = ⟨Φμ|Ψ(t )⟩

(10)

Therefore, we have clarified the relationship between the electronic wave functions of the system and the eigenfunctions of the instantaneous Hamiltonian. Coupled with the Feynman−Hellmann theorem Fl = − Ψ

∂H Ψ ∂ul

(11)

under an external field, the ultrafast dynamical process of quasiparticles, like polarons and excitons, in a conjugated polymer chain can be well described. At the point where an emissive transition occurs, we need the transition rate equation32 γab =

where p formulas coupling polarons

4(Ea − Eb)3 3ℏ4c 3

|⟨a|r |b⟩|2 =

4(Ea − Eb)3 3ℏ4c 3

p2

(12)

= e⟨a|r|b⟩ is the transition dipole moment. These together provide a complete description of transport, and transition processes of quasiparticles (including and excitons) in conjugated polymer system. C

DOI: 10.1021/acs.jpcc.5b06260 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C also shows the same phenomenon: the charge of the negative polaron does not infect the exciton at all. What then is the mechanism behind this scenario? To answer this question, we should first know the physical nature of these quasiparticles in the conjugated polymer. The real particles, like electrons/holes, unite together with the distorted lattice as one entity, i.e., they not only behave like normal particles but also inherit the properties the phonon possess in organic conducting materials.35 Therefore, when two quasiparticles are in different excited states and one is accelerated to a sufficiently large velocity, they can traverse across each other like two colliding waves, as seen in Figure 1c. Although the collision does not affect the overall attributes of the polaron and the exciton, their displacements both shift by tens of lattice sites from their original direction, which resembles what happens when two mechanical wave packets meet each other. The cause of this shift is the sudden change of atomic force of the system during collision, which we call a “phase shift.” It is still a puzzle as to why the quasiparticles do not pass through each other and fuse together as depicted in Figure 1a,b. To discover the underlying mechanism, let us turn to Figure 2.

Figure 3. Lattice energy at different times of 0.1, 1, 2, and 4 ps under an external electric field of 2.5 × 103 V/cm.

field, the newly formed potential well also moves slowly to the right. When the field value is raised to 5.5 × 104 V/cm, the confinement effect is broken, as shown in Figure 1c,d. The question arises as to what the breaking energy is and where it comes from. Figure 4 describes the evolution of the electron

Figure 2. Schematic drawing of the confinement effect caused by the polaron and exciton. The fusion between the polaron and exciton produces a potential valley in potential surface. The length scale of the potential well is just the scale of the triplet exciton, about seven lattice sites. Figure 4. Evolution of the total electron energy under an external electric field of 5.5 × 104 V/cm.

The exciton has a larger potential defect, while both the polaron and the exciton are “trapped” by their own surrounding distorted lattice potential. The length scale of the potential well is just the scale of the triplet exciton, about seven lattice sites. Thus, under a low electric field, the overall physical picture can be seen as when the charge polaron is approaching the neutral exciton driven by the field, the polaron looks like falling into the potential well created by the exciton, as shown in Figure 2. After fusion between the polaron and exciton, in the potential surface there occurs a valley that is induced by the intermediate charged exciton. Let us consider the evolution of the lattice energy, consisting of the elastic potential energy and the kinetic energy. Figure 3 shows that, at the beginning, there are two major lattice energy potentials corresponding to the polaron (left) and exciton (in the middle), where the lattice energy surrounding the exciton is apparently lower and deeper than that of the polaron. As time goes along, the electric field drives the charged polaron to move to the exciton at the center of the polymer chain. Just within the time of 2 ps, when the charged polaron approaches the exciton, the polaron not only falls into the deeper potential well of the exciton but also fuses with the exciton, finally forming a larger potential well. The electric field of 2.5 × 103 V/cm is not enough to drive the polaron to escape the potential well. Up to 4 ps, the confinement of the polaron and exciton continues and leads to a new confined state called the “charged exciton.” Thus, given the charge of the exciton and the external electric

energy over 500 fs under an electric field of 5.5 × 104 V/cm. Within 100 fs, the strong electron−phonon interaction induces the electron energy to oscillate, leading to electron relaxation. After the electron energy stabilizes, it gradually rises due to the continuous driving by the electric field. Yet, once time reaches 250 to 300 fs, the electron energy rises sharply. At this point, the confinement is broken, which also can be seen from Figure 1c where the polaron is passing through the exciton. Therefore, the sudden rise of the electron energy can be explained as follows: after the charged quasiparticle, i.e., polaron, has been absorbing and accumulating momentum from the external field, it breaks the lattice confinement and escapes from the exerted potential well, as mentioned above. From Figure 4, the confinement barrier that the polaron needs to overcome is concluded to be 0.05 eV. So far, we have a clear understanding of the distinctive behaviors of the polaron and exciton interactions under different electric fields. We now want to illustrate why the breaking of the confinement effect would eliminate a potential highly efficient fluorescent channel. As shown in Figure 5, when a low external electric field is applied (opposite direction) along the polymeric chain, called channel (1), the negative polaron travels to couple with the triplet exciton into a confinement state, i.e., negatively charged exciton. Through the exciton’s high energy level C, the electron D

DOI: 10.1021/acs.jpcc.5b06260 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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population ceases at 0.9989, which means that both the electron transition and fluorescence emission is forbidden. For clarification of the halting of the electron population change, the evolution of the transition dipole offers the answer in Figure 7. It is shown that the transition dipole moment starts to rise at

Figure 5. Schematic drawing of the energy occupation structure and transport dynamics of the polaron and exciton along the polymer chain. P− and T represent negative polaron and triplet exciton, respectively, and T− denotes the negatively charged triplet exciton. A− D represent the higher and lower energy levels of the polaron and exciton. (a) Energy structure before the electric field is applied. (b) A low voltage of 2.5 × 103 V/cm is applied, and the polaron is confined with the exciton. (c) A high voltage 5.5 × 104 V/cm is applied, and the polaron and exciton separate.

Figure 7. Time evolution of the square of the transition dipole moment between the upper energy level of the polaron and upper energy level of the exciton (energies A and C in Figure 5) within 1000 fs (the unit of the vertical axis is e2·Å2).

in the high energy level A of the polaron can transit to the lower energy level without violating the Pauli exclusion principle. Thus, a photon is emitted (albeit often delayed), and the polymer returns to the negative polaron configuration, which means the triplet exciton is utilized purposely for fluorescence. However, in channel (2) for a strong external electric field, the polaron collides with the triplet exciton inelastically, breaking the weak confinement state, and passes through to the other end of the exciton, by which the fluorescence channel is quickly quenched. Based on the physical picture given above, using the transition dynamics, some essential quantities can be extracted when the higher field of 5.5 × 104 V/cm is applied along the polymer chain, which provides insight as to why and how the fluorescence is quenched. Figure 6 demonstrates the electron

200 fs, reaching a peak at around 300 fs. During this time span, the growth of the transition dipole moment also triggers the light emission. Beyond 300 fs, dipole moment begins to decay. Up to 400 fs, it falls to zero where, actually, the polaron is just apart from the potential well created by exciton due to the driving high electric field. Because of the polaron leaving from the exciton, the overlap of the wave functions of the two carriers also disappears, which directly leads to the dipole moment dying out. What should be noted here is that we still do not exclude the ultrafast nonadiabatic electron transfer process that might happen in the energy structure because it usually happens at the donor/acceptor interface of different materials (note the fusion is an intrachain process), and the acceptor should have a strong electron affinity (like C60). More importantly, the exciton is often dissociated during the nonradiative transfer process,35−37 quenching the fluorescence. Here, if the external electric voltage is tuned to an extremely high value, what happens to the polaron and exciton on the chain? Both of them (see Figure 8a,b) collapse and dissociate to charge carriers, which agrees with the experimental observation.21 When the electric field of 5.5 × 103 V/cm is changed to 8 × 105 V/cm at 300 fs, the quenching of the exciton appears to be an ultrafast process that is below several femtoseconds. Also, it is observed that while the high field needed for exciton dissociation is over 2.0 MV/cm or more for some organic materials,22−24 the obtained value in our research is somehow lower, slightly below 1 MV/cm, which is due to the electromagnetic shieldings. Reviewing our results, we see that the low electric field is beneficial for taking advantage of the hidden confinement effect to greatly increase the efficiency of the fluorescent device. However, considering the fact that too low a voltage would not be favorable for electron/hole injection and transport, the appropriate proper choice of the electric field ranges from 0.5 to 20 kV/cm. However, in other works in the literatures,38,39 the hole polaron quenches the singlet exciton. Although it is a different mechanism, it still can be illustrated as follows: Once Förster energy transfer of the singlet exciton causes the hole polaron to transit to the excited state, it actually induces the

Figure 6. Time evolution of the electron population of the upper energy level (A in Figure 5) of the original polaron within 1000 fs.

population in the upper occupied energy level of the original polaron, namely, energy level A as depicted in Figure 5a, up to 1 ps. It can be seen that, between about 200 and 400 fs, the electron population in the upper occupied energy level of the polaron has a comparatively sharp decrease. Near the 300 fs, the polaron moves close to the exciton and collides with it. After the polaron is driven out of the potential well by the higher electric field of 5.5 × 104 V/cm, the change of E

DOI: 10.1021/acs.jpcc.5b06260 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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ACKNOWLEDGMENTS This work was supported by the National Science Foundation of China under Grant 21374105, the Zhejiang Provincial Science Foundation of China under Grant R12B040001, and the public project of Zhejiang province under Grant 2014C31135.

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Figure 8. Dynamic evolution of the negative polaron and triplet exciton when the external electric field is tuned from 5.5 × 103 to 8 × 105 V/cm suddenly at 300 fs. (a) Configuration evolution and (b) charge density evolution.

excitation of multiple new phonons, which leads to nonradiative emission, also quenching the singlet exciton.

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CONCLUSIONS While the transport ability of charge carriers in polymer emitting diodes is greatly enhanced and the efficiency considerably upgraded by adding ETL/EIL or HTL/HIL to the sample device structure, charge carriers, like polarons, as driven by a low electric field, move and fall into the potential well of an exciton to form a confinement intermediate state with the exciton, which is called a charged exciton. This new state favorably induces a triplet exciton to fluoresce. However, since the confinement energy barrier is quite small, around 0.05 eV, even a slight gain in the voltage can easily break the coupling between charge carriers and excitons. Based on the above mechanism and our developed nonadiabatic molecular dynamics, we determine that an electric field range of 5 × 102t o 2 × 104 V/cm should be appropriate for realizing highly efficient fluorescent polymeric devices. Further, our calculations indicate that once the external field exceeds a threshold of 8× 105 V/cm, the excitons are dissociated, thus quenching the light emission, which agrees with experimental results.22−24,27

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REFERENCES

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Phone: 1-314-516-5252. Notes

The authors declare no competing financial interest. F

DOI: 10.1021/acs.jpcc.5b06260 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.5b06260 J. Phys. Chem. C XXXX, XXX, XXX−XXX