Ultrafast Exciton Migration and Dissociation in π-Conjugated Polymers

Article pubs.acs.org/JPCC

Ultrafast Exciton Migration and Dissociation in π‑Conjugated Polymers Driven by Local Nonuniform Electric Fields Ruixuan Meng,† Yuan Li,‡ Kun Gao,*,† Wei Qin,† and Luxia Wang§ †

School of Physics, State Key Laboratory of Crystal Materials and ‡School of Information Science and Engineering, Shandong University, Jinan 250100, China § Department of Physics, University of Science and Technology Beijing, Beijing 100083, China ABSTRACT: Experimental verification for ultrafast charge generations is a significant advancement in recent studies of polymer solar cells, but its underlying mechanism still remains unclear. In this paper, a new mechanism of ultrafast charge generation is proposed, where a local nonuniform electric field plays a vital role. We systematically simulate the exciton dissociation dynamics along a polymer chain with electric field linearly distributed. The polymer chain can be divided into two regions according to the exciton dissociation degree, i.e., complete dissociation region and partial dissociation region. In the former, a photogenerated exciton can dissociate directly and completely into free charges. In the latter, however, a photogenerated exciton first experiences an ultrafast migration process toward the complete dissociation region and then partially dissociates with fractional free charge generation. In most of our simulations, the exciton dissociation can take place within a time scale of 1 ps, contributing to the ultrafast charge generation.

spectroscopy (TAS).17,20−26 In 2012, by using TAS to monitor the dynamics of charge carriers in different polymer-based BHJ materials,23 Kaake et al. found that ∼70% of charges separate within 100 fs, while the remaining ∼30% are generated by exciton migration to D/A interfaces within 1−500 ps after photon absorption. Up to now, ultrafast charge separation has been verified in a wide range of high-performing BHJ materials.17,21−24,26−28 To reveal the possible mechanisms, most researches focused on the BHJ microstructure or morphology.17,29,30 As we know, the BHJ microstructure is very complicated in polymer/fullerene blends, which generally have a three-phase microstructure comprised of pure polymer regions, pure fullerene regions, and their intimately intermixed regions, respectively.17,31 When an exciton is directly photogenerated in the intermixed regions, its migration to the D/A interface is unnecessary. In this regard, the fraction of intermixed regions in BHJ materials has been demonstrated to play an important role in the ultrafast charge generation.31−35 However, by performing a transient absorption experiment on a bilayer sample with only pure polymer and fullerene regions, Kaake et al. further concluded that the intermixed regions of polymer/fullerene should not be the reason for the dominance of ultrafast charge generation.36 As such, how do these free charges generate within such an ultrafast time scale and what are the key factors responsible for the ultrafast charge generation? These questions are critical to a complete understanding of the operational mechanism of PSCs, and several potential solutions have been recently proposed in the literature. For instance, Kaake et al. claimed that the initial

1. INTRODUCTION Over the past few decades, polymer solar cells (PSCs) have attracted intense interest because of their potential applications in large-area and flexible photovoltaic modules.1−6 Although encouraging power conversion efficiencies of ∼13% have been reported,7−9 the mechanism by which free charges are generated remains unclear. Since the 1990s, the problem of charge photogeneration in polymers has attracted a great deal of interest. For instance, by transient-photoconductivity measurements on film of poly(p-phenylenevinylene) (PPV),10 Moses and Heeger identified a fast component (∼100 ps) and a slow component (∼600 ps) of the transient photocurrent and attributed them to polaron and bipolaron generation, respectively. In addition, by steady state photoconduction experiments on thin films of PPV derivatives, contacted in a sandwich configuration, Barth and Bässler presented evidence for intrinsic charge photogeneration.11 Up to now, we have known that, due to strong electron−lattice interaction and low dielectric constant in polymers, a strongly bound electron−hole pair (i.e., an exciton) primarily generates in these materials after photon absorption.12,13 To realize efficient charge generation, a prototypical PSC is generally fabricated by a blend of polymer donors (D) and fullerene acceptors (A), known as a bulk heterojunction (BHJ) architecture.14−17 In such a system, a general picture of charge separation requires that the exciton must migrate to a D/A interface.18 However, due to the fact that the exciton migration speed is limited by disorders in polymers, efficient charge separation in BHJ materials usually takes place with a time scale on the order of >1 ps.18,19 In recent years, ultrafast charge generation within 1 ps or less has received great interest, benefiting from the development of ultrafast technologies, such as the transient absorption © XXXX American Chemical Society

Received: August 16, 2017 Published: August 30, 2017 A

DOI: 10.1021/acs.jpcc.7b08198 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C photoexcited state should be highly delocalized or coherent at early times (∼100 fs) due to the uncertainty associated with its position,20,36 which thus results in a higher probability for charge transfer taking place at D/A interfaces. Smith and Chin investigated the ultrafast charge generation in phenyl-C71butyric acid methyl ester (PCBM) within a simple tight-binding Hamiltonian and suggested that hot electronic states can provide a resonant escape pathway for the electron away from the interface within 100 fs.37 In addition, by employing a full quantum dynamics method, Yao et al. speculated that the ultrafast charge generation should be mainly ascribed to the quantum resonance between local excitons and a broad array of long-range charge transfer (CT) states assisted by the moderate off-diagonal vibronic couplings.28 In this paper, we propose a new mechanism of ultrafast charge generation, in which local nonuniform electric fields play a vital role. It is known that, in PSCs, the difference in the work function of electrode materials induces an internal electric field of only 104−105 V/cm,38 which is too small to dissociate a photogenerated exciton into free charges. To obtain efficient charge generations in PSCs, an additional electric field is then required, of which the strength usually needs to reach a value of 105−106 V/cm. In actual applications, the additional electric field can be temporarily produced by applying a reverse bias on the device39,40 and permanently ensured by incorporating a ferroelectric blend layer into the device41−45 or by embedding a fixed charge layer at the D/A interface.46 Up to now, most researches regarded these electric fields as uniform forms (such as the well-known Onsager−Braun model39,47,48), although lots of evidence for the importance of electric field in improving the charge generation49−51 as well as suppressing the charge recombination46 has been presented. However, an actual electric field in PSCs might be spatially localized and has a nonuniform distribution owning to various factors, such as charge screening and in particular the complex morphology of polymer-based BHJ materials.44 Orientation disorders of polymer chains29,52,53 and various defects54−58 inevitably exist in actual materials. On the one hand, these disorders and defects destroy the uniformity of an applied electric field; on the other hand, they lead to charge trapping, and some nonuniform electric fields can thus be created around these trapping charges.

Figure 1. Schematic of the distribution of a local nonuniform electric field En along a polymer chain induced by a trapping positive charge, where a linear electric field is assumed, as presented by the black solid line. In region I, a photogenerated exciton can be dissociated directly and completely into free charges with unity charge on an ultrafast time scale of tc. For all the following simulations, we choose tc = 30 fs and tw = 15 fs, respectively. Once the linear electric field is turned on, a photogenerated exciton in the polymer will undergo a dynamic evolution. By B

DOI: 10.1021/acs.jpcc.7b08198 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

such that, when a polymer is photoexcited by absorbing a single phonon, the strong interaction between the excited electron− hole pair and bond lattice causes self-trapping and consequently produces a self-trapped or spatially localized exciton.65 Referring to the method used in our previous work,64 we calculate the exciton binding energy in the polymer and get a value of EB = 0.26 eV in the present parameters. To overcome such a binding energy and realize the exciton dissociation, we can apply a strong enough electric field to the polymer, which is calculated to be E > 7 × 105 V/cm. In this work, we will focus on the exciton dissociation dynamics by a nonuniform electric field, as described in Figure 1. We note that the exciton dissociation dynamics in our model system is closely related to its initial generating position ng in the polymer chain. According to the degree of exciton dissociation, the polymer chain can be divided into two different regions: complete dissociation region (see region I of Figure 1) and partial dissociation region (see region II of Figure 1) with the region boundary at n = 60 for the present parameters. When an exciton is initially photogenerated in region I, where the electric field is strong enough (>7 × 105 V/ cm), the bound electron and hole in the exciton can be separated directly and completely. The result of exciton dynamics in the case of ng = 70 is displayed in Figure 2,

employing a nonadiabatic evolution method, we can separately obtain the temporal evolution of the lattice displacement un(t) (i.e., nuclear motion) and electronic state |ψμ(t)⟩. Here, the nuclear motion is classically described by the Newtonian equation of motion Mun̈ = K (un + 1 + un − 1 − 2un) + 2α[ρn , n + 1(t ) − ρn , n − 1(t )] − eEn[ρn , n (t ) − 1]

(6)

where the density matrix ρn,n′ (n′ = n ± 1) is defined as ρn , n ′(t ) =

∑ ψμ*(n , t )fμ ψμ(n′, t ) μ

(7)

fμ is a time-independent distribution function, which is set as 0, 1, or 2 depending on the initial occupation of the electronic state |ψμ(t)⟩. ψμ(n, t) is the projection of the electronic state |ψμ(t)⟩ on the Wannier state of site n (i.e., ψμ(n, t) = ⟨n|ψμ(t)⟩). The evolution of ψμ(n, t) depends on the time-dependent Schrödinger equation iℏ

∂ ψ (n , t ) = −tn , n + 1ψμ(n + 1, t ) − tn − 1, nψμ(n − 1, t ) ∂t μ 1 + eEn(na + un)ψμ(n , t ) (8) 2

It is important to note from eqs 6 and 8 that the nuclear motions and electronic states are coupled together all through the evolutions. As a result, the nuclear motions can evolve on multiple potential energy surfaces in the dynamic processes, which guarantees the nonadiabatic nature of the quantum dynamics approach used in our simulations. Here, eqs 6 and 8 can be numerically solved by the Runge−Kutta method of order eight with step-size control, which has been widely used and proven to be an effective approach in the study of dynamic processes in polymers.60,61 Values of the model parameters are set according to those generally used for cis-polyacetylene, that is, t0 = 2.5 eV, α = 41 eV/nm, K = 2100 eV/nm2, M = 13.5 × 105 eV·fs2/nm2, a = 0.122 nm, and te = 0.05 eV. Despite that the model is built for a specific polymer, the obtained results are expected to be qualitatively valid for other conjugated polymers. In addition, according to the typical size of a pure polymer region (10−20 nm) in BHJ materials,32 the total sites of the polymer chain are chosen as N = 120. The coefficient of the linear electric field is set as w = −1.0 × 10−2 V/nm2 such that the absolute value of the electric field strength En ranges from 0 to 1.5 × 106 V/cm along the polymer chain, consistent with an actual case stated above.39−45

Figure 2. Time evolution of the net charge density distribution ρn during the exciton dissociation dynamics, in which the exciton is initially generated at ng = 70.

which shows the time evolution of the net charge density distribution ρn(t) = ∑μψ*μ (n, t)fμψμ(n, t) − 1. We can see that the exciton directly dissociates into free charges shortly after the beginning of the evolution. Also, the separated positive and negative charges transport to the opposite ends of the polymer chain. Further calculations of the separated charges QS(t) [QS(t) = ∑Nn=ndρn(t), where nd corresponds to the exciton dissociating position in the polymer chain] during the exciton dissociation dynamics show that the separated charges can nearly reach QS = e after the stability of the evolution (see the black solid line in Figure 3). It means that the exciton can be completely dissociated, yielding free charges with unity charge. In particular, the results show that the exciton dissociation takes place within an ultrafast time scale of 100 fs. In fact, the exciton dissociation is much faster when the exciton generating position is closer to the right end of the polymer chain. For example, the red dashed line in Figure 3 also shows the time evolution of the separated charges QS in the case of ng = 80. Apparently, the separated charge quantity increases more rapidly than that in the case of ng = 70. Thus, when excitons are initially

3. RESULT AND DISCUSSION At the beginning of the simulations, we assume that an exciton has been generated by a photoexcitation in the polymer chain, which can be obtained by minimizing the total energy of the system. As is well-known, in usual inorganic materials an exciton is an excited electron−hole pair confined by the Coulomb interaction. In polymers, the Coulomb interaction will also play an important role in any theoretical description of excitons.62 However, the fact is that the exciton binding energy in prototypical polymers is usually in the range of 0.2−1.0 eV,63,64 which is much stronger than that in usual inorganic materials. Such a result should be ascribed to the strong electron−lattice interaction and low electric dielectric constant in polymers. In the current SSH model, the strong electron− lattice interaction is highlighted by employing the constant α, C

DOI: 10.1021/acs.jpcc.7b08198 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

apparent charge separation after 400 fs during the exciton migration. Why is the exciton dynamics in a nonuniform electric field so different from that in a uniform one? As stated above, an exciton will be polarized under a relatively weak electric field.66,67 The red solid line in Figure 5 shows the instantaneous

Figure 3. Time evolution of the separated charges QS during the exciton dissociation dynamics, where the exciton is initially generated at ng = 70 and ng = 80, respectively.

photogenerated in region I of the current model system, they can be directly dissociated by the strong electric field into free charges with unity charge on an ultrafast time scale of 0, by which the exciton will be driven to migrate from left to right along the polymer chain, just as described in Figure 4a. As the exciton migrates, the electric field acting on the exciton turns to be stronger and stronger. At about t = 400 fs, the exciton center breaks through the region boundary and enters region I. As a result, the electric field acting on the exciton becomes strong enough to dissociate the exciton into free charges. However, the charge separation is found to be quite different from the case of direct exciton dissociation presented in Figure 2. To give a clearer description, the blue dashed line in Figure 5 shows the instantaneous net charge distribution ρn of the exciton at t = 400 fs. The charge distribution includes three parts, that is, the polarized positive charges QP, polarized negative charges QP′ , as well as the separated charges QS. According to the charge conservation, there exists the relation QP = −(Q′P + QS). At about t = 400 fs, the absolute value of the separated charges |QS| quickly rises with the exciton migration (see the red solid line in Figure 6). As a result, the driving force F = −QP[E(n−c ) − E(n+c )] −

Figure 4. Time evolution of the net charge density distribution ρn during the exciton dynamics, where the exciton is initially generated at different positions of the polymer chain, that is, (a) ng = 40, (b) ng = 30, and (c) ng = 60, respectively.

the polymer chain, which actually experiences two different processes. In the initial 400 fs period, the exciton migrates from its initial position to the strong field region. At about t = 400 fs, the exciton center breaks through the region boundary (i.e., n = 60). After that, the exciton returns back and migrates in the opposite direction of the polymer chain until it arrives at the left chain end. In addition, we note that there also appears D

DOI: 10.1021/acs.jpcc.7b08198 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

Therefore, a local nonuniform electric field in PSCs should play a vital role in the ultrafast charge generation. In actual operation of a PSC with BHJ architecture, the total charge yield might be also determined by other mechanisms, especially the charge transfer following the exciton migration to a D/A interface.18,19 In general, charge generation in many highperforming PSCs indeed takes place with a very high efficiency since the fact is that the internal quantum efficiency obtained from these devices can approach and even exceed 90%. However, it should be stressed that the time scales of different charge generation processes are quite different. For instance, by using TAS to monitor the dynamics of charge carriers in different polymer-based BHJ materials,23 Kaake et al. found that ∼70% of charges are generated within 100 fs (known as the ultrafast charge generation), while the remaining ∼30% are generated by exciton migration to D/A interfaces within 1−500 ps after photon absorption. Here, let us briefly analyze the contribution of the ultrafast charge generation determined by nonuniform electric fields to the total charge yield. In order to compare with the actual situations, we have tried to choose appropriate parameters for our model system, including the chain length of N = 120 (that is, a molecular length of 15 nm according to the typical size of a pure polymer region 10−20 nm in BHJ materials32), the coefficient of the linear electric field w = −1.0 × 10−2 V/cm2 (such that the absolute value of the electric field strength En ranges from 0 to 1.5 × 106 V/cm along the polymer chain, consistent with an actual case39−45), as well as a prototypical exciton binding energy of EB = 0.26 eV in polymers. In such a framework, we find that, as long as an exciton is generated in the range of 20 < ng ≤ 120, the exciton can be dissociated on a time scale of 7 × 105 V/cm in present parameters), a photogenerated exciton can be directly dissociated into free charges with unity charge on an ultrafast time scale of