Ultrafast Charge Separation from a âColdâ Charge-Transfer State

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C: Energy Conversion and Storage; Energy and Charge Transport

Ultrafast Charge Separation from a “Cold” Charge-Transfer State Driven by Nonuniform Packing of Polymers at Donor/Acceptor Interfaces Chong Li, Yuan Li, Maomao Zhang, Lingxia Xu, Wei Qin, and Kun Gao J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10585 • Publication Date (Web): 10 Jan 2019 Downloaded from http://pubs.acs.org on January 11, 2019

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The Journal of Physical Chemistry

Ultrafast Charge Separation from a “Cold” Charge-Transfer State Driven by Nonuniform Packing of Polymers at Donor/Acceptor Interfaces Chong Li,† Yuan Li,‡ Maomao Zhang,† Lingxia Xu,† Wei Qin† and Kun Gao*,† †

School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100,

China ‡School

of Information Science and Engineering, Shandong University, Qingdao 266237, China

ABSTRACT: Understanding the mechanism of how a “cold” charge-transfer (CCT) state is dissociated into free charges and how morphologies of bulk heterojunction thin films affect such a process is of critical importance for improving the overall efficiency of polymer solar cells (PSCs). Here, by modeling a polymer/fullerene-based donor/acceptor interface in the transition region from an intermixed polymer/fullerene phase to a pure polymer phase, we demonstrate that the nonuniform packing of polymers can provide a driving force to dissociate the CCT state in a time scale of no more than 200 fs. Importantly, charge separation is shown to be achieved by two successive processes, i.e., “charge delocalization process between polymers” and “charge migration process along polymers”, and there exists an optimal packing of polymers that is most efficient for charge separation. Also, we demonstrate that the charge separation process can be further promoted by aggregation or crystallinity of fullerenes as a result of charge delocalization. These findings are in agreement with the morphology-dependent ultrafast charge separation phenomena reported experimentally in numerous high-performance PSCs.

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KEYWORDS: polymer solar cells, donor/acceptor interface, charge separation, charge-transfer state, morphology

1. INTRODUCTION Over the past few decades, polymer solar cells (PSCs) have attracted intense interest for their potential applications in low-cost, large-area and flexible photovoltaic modules.1-3 Although an encouraging power conversion efficiency (PCE) of 17.3% for PSCs has been reported,4 the understanding of the underlying mechanisms for the operations of PSCs still remains incomplete. One crucial issue is the lack of thorough clarification about the mechanism by which charge separation is achieved at polymer-based donor/acceptor (D/A) interfaces. As we know, strongly bound electron-hole pairs (i.e., Frenkel excitons) can be generated in polymers right after photon absorption due to the presence of strong electron-lattice (e-l) interactions and low dielectric constant in these materials.5-6 To realize efficient charge separation, prototypical PSCs are usually employed on the basis of bulk heterojunction (BHJ) architectures, in which polymers are used as electrondonor (D) and fullerene derivatives (or other small molecules) as electron-acceptor (A), respectively. In such systems, charge separation requires that the initially generated excitons can arrive at the D/A interfaces via different migration processes,7-9 which usually needs a time scale exceeding 1 ps due to the speed limitation of exciton migration.10 During this process, the large binding energy of excitons is generally considered to be overcome by a positive energetic offset between the lowest unoccupied molecular orbitals (LUMOs) [or the highest occupied molecular orbitals (HOMOs)] of the donor and acceptor,2 although some recent researches have suggested that the energetic offset is not an important criterion for efficient charge separation.11-12 2


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Furthermore, in the past few years, benefiting from the development of ultrafast technologies, ultrafast charge separations within 1 ps have received great interest and also brought new challenges to the theoretical interpretations.10,13-15 In 2012, by using the transient absorption spectroscopy (TAS) to probe the charge-carrier dynamics of different polymer-based BHJ materials, Kaake et al. found that ~70% of charges are created within 100 fs, while the remaining ~30% are generated by exciton migration to D/A interfaces within 1-500 ps after photon absorption.10 A natural question in this regard arises: how are free charges generated within such an ultrafast time scale and what are the key factors responsible for the ultrafast charge separations? In addition to the roles of quantum coherence,16-17 quantum resonance,18 and ultrafast exciton migration,19 the effects of BHJ microstructures or morphologies have also attracted widespread attention in recent studies.20-23 A growing consensus is that the contribution of ultrafast charge separation to the total charge separation (including ultrafast charge separation and via exciton migration) can be explicitly affected by BHJ morphologies.24-25 As we know, the morphologies of BHJ are usually very complicated in polymer/fullerene blends and generally have a microstructure of three phases, i.e., pure polymer phase, pure fullerene phase, and their intimately intermixed phase. When an exciton is directly generated in the intermixed phase, its migration to D/A interfaces is unnecessary. As such, the fraction of intermixed phase in polymer/fullerene blends is expected to play an important role in the ultrafast charge separation. No matter how these charge separations are achieved, the charge transfer process at D/A interfaces is inevitable and an instantaneous intermediate state is consequently created, known as a charge-transfer (CT) state.26-28 Up to now, most experimental observations about charge separation at D/A interfaces are interpreted either as a “cold” CT state (CCT state) or a “hot” CT state (HCT 3



state) mediated process, referred to as “cold-mechanism”29-31 and “hot-mechanism”,32-33 respectively. The “hot-mechanism” states that the excess energy of a HCT state can lead to efficient charge separation via electron delocalization or lattice vibrations.34-35 In contrast, the “coldmechanism” states that the excess energy plays a negligible role in charge separation.30, 36-37 For instance, Vandewal et al. investigated the role of the CCT state in charge separation in a number of D/A combinations.30 They found that the quantum yield of charge separation for all the studied systems has little dependence on whether or not the initially generated CT state has energy in excess of the energy of the CCT state. What is the driving force for helping the opposite charges in a CCT state overcome the binding barrier? To date, several mechanisms have been proposed to clarify the possible contributions, and the most representative ones include: (1) beneficial role of the high local charge-carrier mobility in charge separation dynamics;38 (2) impact of charge delocalization along the donor chains,39-40 in the acceptor aggregations,41-42 or over the D/A interfaces, on lowering the electron-hole binding barrier; (3) entropic contribution in the presence of disorder intrinsically existing near the D/A interfaces;31, 43 (4) contribution of a local nonuniform electric field to the charge separation, which are also intrinsically present and/or artificially created or modulated near the D/A interfaces.44 In this study, we will demonstrate the crucial role of BHJ morphologies in impacting the ultrafast charge separation from a CCT state. In PSCs with polymer/fullerene blends, polymers tend to partly crystallize into pure phase such that an amorphous polymer phase is present and mixes with fullerenes near the D/A interfaces, known as intermixed polymer/fullerene phase.45 In the past few years, the impact of intermixed phase on the photovoltaic process in PSCs has attracted increasing attention,46 and most high-performance devices have been made by using 4


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polymer/fullerene blends consisting of both pure phases and intermixed phases.47-49 A general conclusion is that, for optimized morphologies, intermixed phases are conductive to improving the device performance by promoting the charge separation and suppressing the geminate charge recombination.45-46,

49-50

For instance, by using an electro-absorption (stark effect) probe,

Scarongella et al. directly visualized the ultrafast migration of transferred charges along chains extending from intermixed phase to pure phase, by which the charge separation is achieved.21 As such, amorphous blends with intermixed phase are expected to have a larger band gap than their pure phase,22 and the energy cascade along polymers consequently creates an energetic driving force for charge migration away from the intermixed phase.51-52 Most recently, the impact of BHJ morphologies on the photovoltaic process of PSCs was systematically reviewed by Yi and Shuai.53 They outlined that both charge separation and charge recombination are closely related to the intermolecular packing structures at the D/A interfaces. In spite of these progresses, however, the charge separation dynamics at D/A interfaces is still not clear when the intermixed phase is included to describe the morphologies of the polymer/fullerene blends. Most importantly, it is necessary to give a reliable description of the correlation between charge separation dynamics and blend morphologies of PSCs in order to provide useful information for improving the device performance. Here, we address these issues by simulating the charge separation dynamics in a transition region from the intermixed polymer/fullerene phase to the pure polymer phase, as shown schematically in Figure 1a.

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Figure 1. (a) Schematic illustration of a transition region from the intermixed polymer/fullerene phase to the pure polymer phase, where a CCT state is initially generated at a polymer/fullerene interface. (b) A model description for the local region (highlighted by a square in Figure 1a), which only consists of two polymers (denoted as D1-chain and D2-chain, respectively) and a fullerene (denoted as A-chain). For simplicity, a linear interchain packing configuration between D1 and D2 chains is employed. d DL1 ,D2 and d DR ,D separately indicate the interchain distance between the left 1

2

and right ends of D1/D2 chains. The interchain packing between D2 and A chains is assumed to be parallel with an interchain distance of dD2 ,A .

2. MODEL AND METHOD It is noted that the transition region from the intermixed phase to the pure polymer phase features an interchain distance between polymers in the intermixed phase (where the polymers are intercalated by fullerenes) larger than that in the pure phase. As a result, the interchain packing of polymers are usually nonuniform at the D/A interface. For simplicity, we consider the local region (highlighted by a square in Figure 1a) as the model system, which consists of only two polymer chains and one fullerene molecule. To model this system, we employ an extended version of the one-dimensional Su-Schrieffer-Heeger (SSH) tight-binding model,54 which highlights both the 6


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electron-lattice (e-l) interactions and the electron-electron (e-e) interactions. Within this framework, the two polymers can be renormalized as two long chains, denoted as D1-chain (with the sites labeled as n=1-100) and D2-chain (with the sites labeled as n=101-200), respectively. In the case of fullerene, we use a short chain to describe its electronic and lattice structures, denoted as A-chain (with the sites labeled as n=201-220). The model system employed in this work has been shown in Figure 1b. The interchain packing between D1 and D2 chains is constructed in a nonuniform manner and a L

R

linear packing configuration is employed for simplicity. d D1 ,D 2 and d D1 ,D 2 separately indicate the interchain distance between the left and right ends of D1/D2 chains. The interchain packing between D2 and A chains is assumed to be parallel with an interchain distance of dD2 ,A . As such, the overall Hamiltonian of the D1/D2/A system includes two parts: H  H intra  H inter

(1)

H intra describes the intrachain part for an isolated chain, which can be written as a sum of Hi，int ra by introducing the chain index i (including D1-chain, D2-chain and A-chain): H intra   H i ,intra    H i ,elec  H i ,latt  i

(2)

i

Here, H i ,ele shows the electronic part of the i-th chain:



H i ,ele    i , n Ci, n , s Ci , n , s   ti ,n ,n 1 Ci,n 1, s Ci ,n , s  Ci,n , s Ci ,n 1, s n,s



n,s

1  1  +U   Ci, n , s Ci , n , s   Ci,n ,  s Ci , n,  s   2  2 n 





(3)



+V  Ci, n Ci , n  1 Ci,n 1Ci ,n 1  1 n

i ,n denotes the on-site energy of an electron at site n, and C i,n,s  C i ,n,s  is the creation





(annihilation) operator of an electron at site n with spin s s ,  . The second term shows the electron hopping between the nearest-neighbor sites along the i-th chain, and the transfer integral

ti ,n ,n 1

between sites n and n+1 is written as: 7



ti ,n,n 1  t0  i  ui ,n 1  ui ,n    1 te n

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(4)

t0 represents the nearest-neighbor transfer integral for a uniform bond structure,  i the e-l

ui , n

interaction constant,

the displacement of a unit at site n, and te the symmetry-breaking

parameter introduced to describe a system with a non-degenerate ground state character. The last two terms in equation 3 represent the e-e interactions, which are treated with the Hartree-Fock approximation for simplicity. U represents the strength of the on-site Coulomb interactions and V the strength of the nearest-neighbor Coulomb interactions.

Hi,latt in equation 2 describes the lattice part of the i-th chain, which includes the elastic potential and kinetic energy of the lattice and is treated classically as follows: H i ,latt 

K 2

 u

i , n 1

 ui , n   2

n

M 2

u

2

(5)

i ,n

n

K is the elastic constant between the nearest-neighbor sites, and M the mass of a site. The second term in equation 1 shows the interchain interactions between any two chains of the D1/D2/A system: H inter 

1  H i, j 2 i , j i

(6)

Here, H i , j represents the interchain interaction between the i-th chain and the j-th chain, written as:

H i , j  t i , j  n   C i ,n,sC j ,n,s  C j ,n,sC i ,n,s  



(7)

n

where ti , j  n   t0 exp 1  di , j  n  / 5 denotes the interchain transfer integral between the   10 vertical-neighbor sites of the i-th chain and the j-th chain, and is determined by the interchain distance d i , j  n  . As shown in Figure 1b, di , j  n  can be expressed as:

d  n  dDL1 ,D2  k  n  D1 ,D2  d D2 ,A  n  d D2 ,A  L d D1 ,A  n  d D1 ,D2  d D2 ,A  k  n



(8)



where k is a coefficient describing the linear packing configuration between D1 and D2 chains. It is 8


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noted that the value of k is dependent on the values of d DL1 ,D2 and d DR1 ,D2 . In such a model system, when a CCT state is initially generated at the D2/A interface, the linear packing between D1 and D2 chains is expected to provide a driving force to dissociate the CCT state. By employing a quantum nonadiabatic evolution method, we can separately obtain the temporal evolution of the lattice displacement ui , n   (i.e., nuclear motion) and the electronic state  i , ,s   . The nuclear motion is classically described by the Newtonian equation of motion:

Mui ,n  K  2ui ,n  ui ,n1  ui ,n1   2i  i ,n,n1  i ,n,n 1    Mui ,n

(9)

where i ,n,m  m  n  1 denotes the density matrix and is defined as:

 i ,n,m   i ,  , s  n,  f  , s i ,  , s  m, 

(10)

 ,s

 i , ,s  n,   n  i , ,s   is the projection of the electronic state  i , ,s   on the Wannier state of site n. f  , s   0,1 is a time-independent distribution function and determined by the initial occupation of the electronic state  i ,  , s   . The evolution of  i ,  , s  n,  follows the timedependent Schrödinger equation:

i

   1   i ,  , s  n,     i ,n  U   i ,n ,n ,  s    V   i ,n 1,n 1   i ,n 1,n 1  2   i ,  , s  n,  t 2     ti ,n ,n 1 i ,  , s  n  1,   ti ,n ,n 1 i ,  , s  n  1,    ti , j i  n   j ,  , s  n, 

(11)

j

It is important to note from equations 9 and 11 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 dynamical processes, which guarantees the nonadiabatic nature of the quantum dynamics approach used in our simulations. Here, equations 9 and 11 can be numerically solved by the Runge-Kutta method of order eight with step-size control. In addition, a damping force  Mui ,n is introduced in equation 9 to describe the energy dissipation into the 9



surrounding medium by a tuning parameter λ, the value of which is determined by the external environment.55

3. RESULTS AND DISCUSSION To obtain a D/A electronic structure, we set different values of on-site energies to the D-chains and A-chain: D,n  0.3 eV and A,n  0 . In addition, in view of the fact that, in an actual PSC, different molecular materials are usually employed as the donor and acceptor (e.g. polymer/fullerene-type and polymer/nonfullerene-type PSC), we set different e-l interactions to the D-chains and A-chain. For the D-chains, we refer to the cis-polyacetylene and set  D  4.1 eV/Å, while for the A-chain we set  A  3.9 eV/Å. The rest parameters in the Hamiltonian are separately set as t0  2.5 eV , te  0.05 eV , K = 21 eV/Å2, M = 1.35 × 104 eV·fs2/Å2, λ = 0.05 fs-1, U = 1.5 eV, V = 0.5 eV, dDL1 ,D2  6 Å, dDR1 ,D2  2 Å and d D2 ,A  5 Å. Before the dynamical simulations, we assume that a CCT state has already been generated at the D/A interface, either by exciton dissociation or direct below-gap excitation.29, 56 To obtain such an initial state, we assume that D1-chain is far away from the D2/A interface at the initial stage. It means that, before the dynamical simulations, the D1-chain does not have any effect on the CCT state. The net charge distribution qn  e   n ,n  1 of the D1/D2/A system has been presented in Figure 2. We can see that some charges (~0.5 e) are transferred from the D2-chain to the A-chain and, notably, the transferred charges are spatially localized. In fact, the localization effect can significantly strengthen the interaction between the transferred charges and thus result in a strong binding energy of the CCT state. Referring to the method used in our previous work,57 the binding energy of the CCT state is calculated to be about 0.1 eV for the present parameters, which value is 10


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far above the thermal energy at room temperature and consistent with the experimental results.58-60 Thus, charge separation cannot be directly achieved from the CCT state without the assistance of other perturbations.

Figure 2. Net charge distribution

qn

of the D1/D2/A system with a CCT state initially generated at

D2/A interface.

We now turn to consider the effect of a perturbation applied by turning on the interactions between D1-chain and D2/A interface. To avoid numerical errors, the corresponding

ti , j  n  is

turned on smoothly with time τ, which is chosen in the form of a half Gaussian function: 2 2 t   D1 ,D2  A   n  exp      c  /  w  tD1 ,D2  A   n,    tD1 ,D2  A   n 

 c  c

For all the following simulations, we choose  c  50 fs and  w  25 fs , respectively. After an ultrafast switch-on time of 50 fs, the interchain packing configuration of the D1/D2/A system reaches stability. We then take the CCT state as the initial state and simulate its evolution dynamics in the D1/D2/A system. The results of time evolution of the net charge distribution qn have been presented in Figure 3a. It is seen that the evolution of the CCT state experiences two successive 11



processes immediately after the interactions between D1-chain and D2/A interface is switched on. In the first stage (during the time period of 50≤ τ ≤180 fs), the positive charges initially localized on D2-chain gradually extend to D1-chain. However, the spatial position of the positive charges on D1/D2 chains keeps nearly unchanged relative to the negative charges on A-chain. It means that these opposite charges still spatially overlap and are bound together. As such, we refer to the first stage of the evolution as the “charge delocalization process between D1 and D2 chains”. In the following stage (during the time period of 180˂ τ ≤220 fs), we can see that the positive charges undergo an ultrafast migration process along D1/D2 chains until they arrive at their right-ends, while the negative charges remain in the A-chain all the time. The different behaviors between the positive and negative charges in the CCT state remarkably increase their spatial distance, and we refer to this stage as the “charge migration process along D1 and D2 chains”.

Figure 3. (a) Time evolution of the net charge distribution

qn in the D1/D2/A system with the CCT

state initially generated at D2/A interface. (b) The charges transferred to the i-th chain Qi ,T as a function of time.

To determine whether charge separation has been achieved after the two successive stages, we 12


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separately calculate the total charges transferred to the i-th chain [i.e., Qi ,T     qi , n   ] as a n

function of time, and the results have been shown in Figure 3b. We can see that the charges transferred to A-chain QA,T are remarkably increased during the period of τ ≤220 fs, except for the initially slight oscillations due to the switch-on of the interactions between D1-chain and D2/A interface. Specifically, during the “charge delocalization process” when the positive charges tend to delocalize along the vertical direction of D1/D2 chains, the spatial distance between the positive charges and the negative charges transferred to A-chain is increased. Accordingly, the overlap or binding between these opposite charges is reduced, and the amount of charges transferred to Achain QA,T is also increased in this process. When it is in the “charge migration process”, however, the positive charges begin to quickly migrate along the direction parallel to D1/D2 chains, by which the spatial distance between the positive charges and the negative charges is further increased. The charges transferred to A-chain QA,T continue to increase during the evolution and finally, at about τ =220 fs, the amount of transferred charges reaches QA,T  e . It indicates that the overlap or binding between the positive charges on D1/D2 chains and the negative charges on A-chain have been completely eliminated via experiencing the two successive processes, and the charge separation is thus realized on an ultrafast time scale of ~170 fs (excluding the initial switch-on time of 50 fs). However, why can the CCT state be dissociated into free charges by the nonuniform packing of polymers? As reported previously, the creation energy of a charged state in strong coupled polymers is expected to be smaller than that in weak coupled polymers.24, 57 In this study, since the packing between D1 and D2 chains is in a linear form, the interchain coupling is increasingly strengthened from the left to the right ends. As a result, there should exist an energy gradient for the creation of a charged state along the D1/D2 chains, which thus induces an energetic driving force for 13



the positive charges transferred into D1/D2 chains to migrate towards their right ends. In Figure 4, we present the total energy E as a function of the time during the evolution of the CCT state (50≤ τ ≤220 fs). In the time period of 50≤ τ ≤180 fs, since the positive charges on D1/D2 chains only migrate a short distance along the right direction (see the “charge delocalization process” in Figure 3a), the total energy of the system accordingly presents a slight decrease as a function of time. However, in the time period of 180˂ τ ≤220 fs, we can see that the total energy of the system decreases remarkably with time because the positive charges on D1/D2 chains experience an ultrafast migration process until they arrive at the right chain-ends (see the “charge migration process” in Figure 3a). Here, for the convenience of analysis, we assume that the induced driving force along the D1/D2 chains remains unchanged with the charge migration. Thus, the charge separation process from the CCT state is determined by whether the driving force can overcome the binding barrier between the opposite charges in the CCT state. At the beginning, the binding barrier between the opposite charges in the CCT state (i.e., the binding energy of 0.1 eV) is so high that the driving force only plays a negligible role in the charge separation. However, by experiencing the “charge delocalization process”, the binding barrier between the opposite charges is effectively reduced. It can be confirmed by the increase of the charges transferred to A-chain QA,T (see the time period of 50≤ τ ≤180 fs in Figure 3b). Once the binding barrier falls to a critical value comparable to the strength of the induced driving force, charge separation takes place by experiencing an ultrafast charge migration process shown above.

14


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Figure 4. The total energy E of the D1/D2/A system as a function of time during the charge separation process (50≤ τ ≤220 fs).

The driving force induced along the D1/D2 chains can be modulated by varying the linear packing configuration between D1 and D2 chains. Here, the linear packing configuration between D1 and D2 chains (i.e., the linear coefficient k) can be varied by changing the value of d DL1 ,D2 while fixing the value of d DR1 ,D2 (see Figure 1b). Through systematic simulations, we find that there exists a very small numerical range for d DL1 ,D2 (i.e., 5.5  d DL1 ,D2  6.5 Å), in which the charge separation can be achieved. A larger value of d DL ,D (> 6.5 Å) means a higher energy gradient for the creation 1

2

of a charge state along D1/D2 chains, and a stronger driving force is consequently induced for charge separation. However, the charge delocalization between D1 and D2 chains is also accordingly suppressed during the “charge delocalization process” due to the weaker interchain interaction. Thus, the binding barrier between the opposite charges in the CCT state cannot be effectively reduced to the critical value matching the driving force, and the charge separation cannot be achieved in the L case of d DL1 ,D2  6.5 Å. Instead, a smaller value of d D1 ,D2 (< 5.5 Å) favors the charge delocalization

between D1 and D2 chains such that the binding barrier between the opposite charges in the CCT state can be effectively reduced. However, the driving force induced by the linear packing 15



configuration between D1 and D2 chains is not strong enough to overcome the binding barrier between the opposite charges. In view of this, the competition between the induced driving force and the modulated binding barrier in different cases can lead to an optimal packing configuration between D1 and D2 chains for the charge separation. For the present model parameters, the optimal configuration corresponds to a value of d DL1 ,D2  6 Å, by which the charge separation from the initial CCT state can be achieved on the shortest time scale of 170 fs. From the above simulations, we have obtained the ultrafast charge separation from the CCT state driven by a linear packing of polymers. On the one hand, the time scale of the charge separation reaches 170 fs. On the other hand, the charge separation can be obtained only in a very small range of linear packing configuration between D1 and D2 chains. In contrast, in a number of D/A combinations, the experimental works have reported that charge separation can take place with a time scale less than 100 fs.20-22 It seems that, in actual conditions, charge separation from the CCT state might take place more efficiently. The reason for the difference should be attributed to the simplified model description employed in this study. In actual photovoltaic D/A systems, fullerenes as common-used acceptor materials tend to aggregate and form small clusters. Up to now, there is a growing consensus that aggregation between fullerenes facilitates the charge delocalization and thus promote the charge separation.41-42 In this regard, we need to extend our model system to include one more A-chain (denoted as A2-chain with the sites labeled as n =221-240). For simplicity, the packing between A1 and A2 chains is assumed to be parallel with a fixed interchain distance

d A1 ,A2  5 Å, as shown schematically in Figure 5a. The values of all other parameters are the same as those in the previous model.

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Figure 5. (a) A model description for the extended D1/D2/A1/A2 system, where the packing between A1 and A2 chains is parallel with an interchain distance of d A1 ,A2 . (b) Net charge distribution qn of the D1/D2/A1/A2 system with a CCT state initially generated at the D2/A1/A2 interface.

For the extended D1/D2/A1/A2 system, we assume that a CCT state has been initially generated at the D2/A1/A2 interface before the dynamical simulations with similar method used above. Figure 5b shows the net charge distribution

qn of the D1/D2/A1/A2 system. It is seen that charge transfer

takes place between D2-chain and A1/A2 chains. The binding energy between the opposite charges is calculated to be 0.08 eV, which is smaller than that obtained in the previous model. Thus, the binding barrier between the opposite charges in the initial CCT state is effectively reduced due to the delocalization of the negative charges over A1 and A2 chains. It is expected that charge separation from the CCT state should be more efficient than the previous case when the linear packing configuration between D1 and D2 chains is switched on. The results of time evolution of the net charge distribution

qn have been presented in Figure 6. Compared with the results shown in

Figure 3a, we find that the “charge delocalization process between D1 and D2 chains” is not obvious after the switch-on of the linear packing configuration. Instead, the ultrafast charge migration process directly takes place along D1/D2 chains until they arrive at their right-ends at about τ =130 17



fs. It means that, due to the delocalization of negative charges over A1 and A2 chains, the binding barrier between the opposite charges in the initial CCT state has been reduced such that the driving force is strong enough to overcome it. Thus, in the extended model system, charge separation can be achieved from the CCT state only through the ultrafast “charge migration process along D1 and D2 chains”. As a result, charge separation can be realized on a time scale less than 100 fs, in consistent with the time scale reported in experiments.20-22 In addition, we also systematically simulate the impact of the linear packing configuration between D1 and D2 chains on the charge separation in the extended model system. We find a relatively large range of linear packing configuration (i.e., 5  d DL1 ,D2  7 Å) for the charge separation. This result further confirms that aggregation between fullerenes can promote the charge separation process in PSCs.

Figure 6. Time evolution of the net charge distribution qn in the D1/D2/A1/A2 system with the CCT state initially generated at the D2/A1/A2 interface.

Notably, in some polymer-based D/A systems with low weight ratio of polymer donors, the polymers are diluted in fullerenes or other acceptor molecules, that is, the polymer chains tend to be isolated. In this regard, charge separation should be inefficient due to the lack of the nonuniform packing of polymers. However, many studies have verified that some PSCs with low concentration 18


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polymer donors still present high external quantum efficiency (EQE) and PCE, which means that charge separation and migration in these systems are still efficient.61-64 As stated above, this result might be attributed to the delocalization of the transferred negative charges over acceptor molecules. Here, what we need to emphasize is that the nonuniform packing of acceptor molecules away from the D/A interface might play a more important role in the efficient charge separation. In the D/A system with low concentration polymer donors, since the polymer chains are dispersed in the aggregates of acceptor molecules, the packing of acceptor molecules away from the D/A interface tend to be more ordered than that near the D/A interface. It means that the inter-molecular distance between acceptors tends to decrease towards the direction away from the D/A interface. Similar to the picture presented above, the nonuniform packing of acceptor molecules should also induce an energetic driving force for the transferred negative charges to migrate towards the direction away from the D/A interface. To further verify this picture, we should rebuild a model system consisting of a polymer as the donor and several small molecules as the acceptor, in which the packing of acceptor molecules is nonuniform away from the D/A interface, and present a dynamical simulation to the charge separation process.

4. CONCLUSIONS In summary, we have demonstrated the crucial role of the nonuniform packing of polymers in the ultrafast charge separation in photovoltaic PSCs by a model study of the dissociation dynamics of a CCT state. We considered a linear configuration of the polymer packing at the D/A interfaces from intermixed phase to pure phase, which provides a driving force to dissociate the CCT state on a time scale of ~200 fs or less. In particular, the simulations demonstrated that charge separation from the CCT state is achieved by two successive processes, including the “charge delocalization process 19



between polymers” and the “charge migration process along polymers”. To obtain charge separation, the binding barrier between the opposite charges in the CCT state has to be reduced to a critical value that the driving force can reach. In addition, we also investigated the impact of the linear packing configuration of polymers on the charge separation and found that there exists an optimal packing of polymers that is most efficient for charge separation. Finally, we demonstrated that aggregation or crystallinity between fullerenes can further promote the charge separation process due to the charge delocalization between them. These results provide an insight into both the charge separation dynamics at polymer-based D/A interfaces and how BHJ morphologies affect the dynamical processes, which are helpful for interface engineering and performance improvement of PSCs.

AUTHOR INFORMATION Corresponding Author *E-mail:

[email protected]

ORCID Chong Li : 0000-0001-7934-3417 Maomao Zhang: 0000-0003-3891-7220 Wei Qin: 0000-0003-4579-0061 Kun Gao: 0000-0002-9146-0090 Notes The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors appreciate the financial support from the National Natural Science Foundation of China (Grant Nos. 11674195 and 21473102), and the Fundamental Research Funds of Shandong University.

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Kemerink, M., Charge Transport in Pure and Mixed Phases in Organic Solar Cells. Adv. Energy Mater. 2017, 7, 1700888. (64) Spoltore, D., et al., Hole Transport in Low-Donor-Content Organic Solar Cells. J. Phys. Chem. Lett. 2018, 9, 5496-5501.

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