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Multiscale Molecular Simulation of Solution Processing of SMDPPEH:PCBM Small Molecule Organic Solar Cells Cheng-Kuang Lee, and Chun-Wei Pao ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b05027 • Publication Date (Web): 20 Jul 2016 Downloaded from http://pubs.acs.org on July 24, 2016

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ACS Applied Materials & Interfaces

Multiscale

Molecular

Simulation

of

Solution

Processing of SMDPPEH: PCBM Small-Molecule Organic Solar Cells Cheng-Kuang Lee† and Chun-Wei Pao*,‡ †Material and Chemical Research Laboratories, Industrial Technology Research Institute, Hsinchu 31040, Taiwan ‡Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan *E-mail: [email protected]

ABSTRACT

Solution-processed small-molecule organic solar cells are a promising renewable energy source because of their low production cost, mechanical flexibility, and light weight relative to their pure inorganic counterparts. In this work, we developed a coarse-grained (CG) Gay-Berne ellipsoid molecular simulation model based on atomistic trajectories from all-atom molecular dynamics simulations of smaller system sizes to systematically study the nanomorphology of the SMDPPEH/PCBM/solvent ternary blend during solution processing, including the blade-coating process by applying external shear to the solution. With the significantly reduced overall system degrees of freedom and computational acceleration from GPU, we were able to go well beyond the limitation of conventional all-atom molecular simulations with a system size on the order of

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hundreds of nanometers with mesoscale molecular detail. Our simulations indicate that similar to polymer solar cells, the optimal blending ratio in small-molecule organic solar cells must provide the highest specific interfacial area for efficient exciton dissociation, while retaining balanced hole/electron transport pathway percolation. We also reveal that blade-coating processes have a significant impact on nanomorphology. For given donor/acceptor blending ratios, applying an external shear force can effectively promote donor/acceptor phase segregation and stacking in the SMDPPEH domains. The present study demonstrated the capability of an ellipsoid-based coarse-grained model for studying the nanomorphology evolution of small-molecule organic solar cells during solution processing/blade coating and provided links between fabrication protocols and device nanomorphologies. KEYWORDS

coarse-grained

molecular

simulation,

small-molecule

solar

cell,

bulk

heterojunction, nanomorphology, ellipsoids INTRODUCTION Organic photovoltaic cells (OPVs) have unique advantages, including a lower production cost, increased mechanical flexibility, and a lighter weight than their silicon-based counterparts.1-4 The photoactive layer of OPV, namely, the bulk heterojunction (BHJ) layer, comprises an interpenetrating network of two different materials, namely, an electron donor and an electron acceptor. Electron acceptor materials are usually fullerenes (C60 or C70) or their derivatives, such as [6,6]-phenyl-C61-butyric acid methyl ester (PCBM), whereas electron donor materials are usually conjugated semiconducting polymers such as poly(3-hexylthiophene) (P3HT).5 Currently, the power conversion efficiency of single-junction solution-processed BHJ polymer solar cells using conjugated polymers as electron donors can exceed 11%.6 However, despite these recent successes, polymer solar cells suffer from problems such as batch-to-batch


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variations in solubility, molecular weight, and polydispersity, which lead to inconsistencies in both processing conditions and performance and hinder their commercialization progresses. In contrast, solution-processed small-molecule (SM) BHJ solar cells comprise well-defined molecules with much higher molecular precision than synthetic polymers, thereby minimizing the batch-to-batch variations.2,4,7-9 However, the most critical drawback of SM BHJ solar cells is their lower efficiencies compared with their polymer counterparts. It was not until very recently that SM BHJ OPVs achieved efficiencies greater than 9%;9 therefore, further improving the device performance of the SM BHJ solar cell is a critical issue. The device efficiency of the SM BHJ solar cell is strongly correlated with the nanomorphology of the BHJ layer. The electron donor/acceptor interfacial area is directly correlated with exciton dissociation, and the percolation of the electron donor/acceptor domains toward the anode/cathode is vital for subsequent charge carrier transport to the electrodes for photocurrent generation. The BHJ layer nanomorphology is strongly correlated with the fabrication protocols of the BHJ layer, for example, the solvent additive and electron donor/acceptor blending ratio.13,10

Therefore, comprehensive insights into the correlations of macroscopic device performance,

nanoscale BHJ morphologies, and device fabrication protocols are important for promoting SM OPV device performance. However, such correlations are still difficult to reveal by current stateof-the-art experimental characterization tools. Conventional characterization tools such as TEM11 or AFM5 can only characterize the morphology of the surface of the BHJ layer. Novel techniques that have the potential of revealing three-dimensional structures, such as second-ion mass microscopy,12 XPS depth profiling,13 scanning electric potential microscopy,14 or electron tomography,15,16 have not yet been employed in investigating the three-dimensional morphologies of SM BHJ solar cells. Without the high-resolution, three-dimensional BHJ layer


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morphology, it is impossible to reveal the correlations between the device fabrication protocols and the device nanomorphology. Computer simulations are potentially valuable tools to complement experiments to fill the gap between the fabrication protocols and device performance of SM OPVs.17,18 Ab initio calculations are powerful tools in determining the electronic properties such as the HOMO LUMO levels. However, the system size that ab initio calculations can handle is limited to single or a few small molecules,19 which is too small for investigating the three-dimensional BHJ layer morphology. All-atom atomistic molecular dynamics (AMD) simulations can simulate the trajectories of a large number of atoms (of the order of millions) based on classical force fields,20,21 which is powerful in revealing the detailed atomistic structure of the PCBM and P3HT/PCBM interfaces;20 however, the maximum system size that AMD can handle is on the order of ten nanometers, which is still beyond the typical system size of the BHJ layer of SM BHJ solar cells. Continuum computational models such as the phase field method can model the morphological evolution of the BHJ layer with both length and time scales compatible with experiments;22 however, the phase field model fails to provide local order details such as the identification of local crystalline and amorphous regions. In this study, we constructed a coarse-grained (CG) model to simulate the nanomorphological evolution of the solution processing of SM OPV using 2,5-di-(2-ethylhexyl)-3,6-bis-(5"-n-hexy[2,2',5',2"]terthiophen-5-yl)-pyrrolo[3,4-c]pyrrolo-1,4-dione (SMDPPEH) as an electron donor and the fullerene derivative [6,6]-phenyl C61-butyric acid methyl ester (PCBM) as an electron acceptor.23-25 In this CG model, the SMDPPEH donor molecule (containing 140 atoms), PCBM electron acceptor (containing 88 atoms), and chlorobenzene solvent (CB, containing 12 atoms) are coarse-grained into ellipsoid and spheroid particles using the Gay-Berne potential,26 which


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has been widely employed to study the structural properties of liquid crystals.27,28 The Gay-Berne potential parameters were fitted based on molecular trajectories from AMD simulations of smaller systems of interest. With the significantly reduced overall system degrees of freedom from coarse-graining, the system length scale that CGMD can handle is compatible with the typical BHJ layer length scale in experiments. We systematically investigated the effects of the SMDPPEH:PCBM blending ratios on the BHJ nanomorphology. Furthermore, we were able to simulate the effects of external shear on the SMDPPEH:PCBM solution to mimic the bladecoating processes, one of the solution processing methods aiming to reduce material waste during device fabrication. Therefore, in the present study, we demonstrated that the CG model we constructed can successfully simulate the solution processing of the SMDPPEH:PCBM blend, thereby providing insights into BHJ nanomorphologies that are difficult to reveal from experiments. Furthermore, the CG scheme can be readily extended to other small-molecule OPVs or even solution-processed organic light-emitting diode (OLED) materials29 to help experimental teams to quickly optimize their device fabrication conditions for newly synthesized small-molecule donor materials. SIMULATION METHODOLOGY The scheme for the coarse-graining of SMDPPEH/PCBM/CB molecules is displayed in Figure 1a. From the AMD simulation of SMDPPEH molecules, we found that the SMDPPEH molecule is essentially planar with a rigid backbone; see Movie M1 in the Supporting Information. Hence, we coarse-grained one SMDPPEH molecule into one ellipsoid and coarse-grained both the PCBM and CB molecules into spheroids; see Figure 1a. Similar to our previous works on the CGMD simulation of polymer solar cells, we employed a structural-based scheme to fit the CG force field;30-32 that is, the CG force fields are fitted to reproduce the structural properties of the


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CG degrees of freedom of the blends (e.g., radial distribution function, probability distribution function) for analyzing the atomistic trajectories of the AMD simulations of smaller systems of interest. In the present study, the CG force fields were fitted into the Gay-Berne formulation for ellipsoids. The Gay-Berne ellipsoid potential is essentially an orientation-dependent LennardJones potential and is of the form26,28

U ( A1 , A 2 , r12 ) = U r ( A1 , A 2 , r12 , γ ) ⋅η12 ( A1 , A 2 ,υ ) ⋅ χ12 ( A1 , A 2 , r12 , µ )

(1)

where A1, A2, and r12 are the transformation matrices of the two ellipsoids and the respective center-to-center vector between them. Ur controls the shifted distance dependent Lennard-Jones interaction, based on the distance of closest approach between two ellipsoids h. Ur can be expressed as U r = 4ε ( ρ 12 − ρ 6 ) ,

(2)

where ρ can be expressed as

ρ=

σ , h + γσ

(3)

where ε , σ and γ are the shifted Lennard-Jones well depth, radius, and a user-specified shifted parameter, respectively. The inter-ellipsoid separation h can be approximated as

1  -1 h = r12 −  rˆ12T G 12 rˆ12  2  where r12 = r1 − r2 , and rˆ12 =

−

1 2

, (4)

r1 − r2 . G 12 can be written as r12

G12 = A1T S12 A1 + A 2T S 2 2 A 2 ,

(5)

where S i is the "shape" matrix of the ith ellipsoid, namely, S i = diag ( ai , bi , ci ) , where ai , bi , and ci are the semi-axes of the ellipsoid (see Figure 1c).


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η12 η12 and χ12 are ellipsoid orientation-dependent energy terms. η12 can be written as υ

 2s s  2 η12 =  1 2  ,  det(G ) 

(6)

where si = [ ai bi + ci ci ][ ai bi ] . The third term on the right side of Eq. 1, χ12 , can be expressed 1/2

as µ

χ12 =  2rˆ12T B12 −1rˆ12  ,

(7)

B12 = A1T E12 A1 + A 2T E2 2 A 2 ,

(8)

where B12 can be written as

where Ei is the relative energy matrix of the ith ellipsoid, defined as Ei = diag ( ε ia , ε ib , ε ic ) .


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Figure 1. (a) Coarse-grained (CG) scheme of SMDPPEH/PCBM/CB molecules in the present study; (b) fitting CG force field for SMDPPEH molecules; (c) illustration of the three principal axes of the ellipsoid representing the SMDPPEH molecule; and (d) relative orientations required to be taken into consideration when fitting Gay-Berne parameters for SMDPPEH molecules. Gay-Berne Parametrization for SMDPPEH Molecules There are many ways to fit the Gay-Berne potential parameters. Usually, the potential energy surfaces of two ellipsoids with several predefined orientations (e.g., end-to-end, face-to-face, or side-to-side) are chosen as the target function to fit the Gay-Berne potential parameters.33,34 In


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this work, the Gay-Berne potential parameters were fitted to reproduce the orientation-dependent probability distribution functions of the ellipsoid pairs from AMD simulations. As displayed in the left panel of Figure 1b, AMD simulations of a system with one thousand SMDPPEH molecules were carried out at T=300 K and P=1 atm. Next, the orientation-dependent probability distribution function P AMD ( Ω, r ) of two SMDPPEH molecules with a relative Euler angle

Ω (φ ,θ , ϕ ) and the separation r were computed by analyzing their atomistic trajectories. Then, the Gay-Berne potential parameter set { pGB } was obtained by minimizing the following penalty function using simplex optimization,

f = ∑∑  P AMD ( Ω, r ) − P GB ( Ω, r , { pn } )  , 2

Ω

r

(9)

where P GB ( Ω, r , { pn } ) is the probability distribution function of the ellipsoids (right panel of Figure 1b) computed from CGMD simulations with the Gay-Berne parameter set from the nth iteration,

{ pn } .

In the AMD calculations, we employed the LAMMPS molecular dynamics

simulation packages and the PCFF+ force field to describe the interactions between atoms. The AMD was computed by sampling the atomistic trajectories of probability distribution function P

twenty million MD steps. Figure 2 displays the probability distribution of the relative orientation of two SMDPPEH molecules from the all-atom atomistic MD (upper panels) and from CGMD using the Gay-Berne potential parametrized in the present study (lower panels). In Figure 2a, the Euler angle along the long axis a - namely, φ - is fixed at zero, and the probability distribution as a function of both the Euler angle (Euler angle of relative rotation along axis c; see the schematic displayed in Figure 2a) and the separation r between two SMDPPEH molecules was displayed. Note that we


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encapsulate the contribution from the Euler angle ϕ (rotation along axis b) to reduce the noise in the probability distribution function; see the inset in the upper panel of Figure 2a. This is a reasonable approximation because the largest contribution comes from ϕ = 0 , and the contribution from the rest of the values of angle ϕ is negligible. As displayed in the upper panel of Figure 2a, the primary contribution to the probability distribution function comes from θ = 0 , namely, the direct face-to-face configuration. Furthermore, we can also find that the most probable separation r between two ellipsoids is r=4.2 A; see the red arrow in the upper panel of Figure 2a. In addition to φ = 0 (face-to-face configuration), we also computed the probability distribution of φ = π , namely, face-to-side, as a function of the Euler angle θ and separation r; see the upper panel of Figure 2b. Note that once again, the contribution from the Euler angle ϕ was encapsulated to reduce the noise. The most probable Euler angle θ is θ=0 with r=4.2 A. The lower panels of Figure 2 display the probability distribution from the CGMD simulation based on the optimized Gay-Berne parameters in the present study. Our Gay-Berne parameters can successfully reproduce the location of the primary peak from the face-to-face configuration; see the lower panel of Figure 2a. Nevertheless, the peak is broader from our optimized Gay-Berne parameters, which can be attributed to the functional form of the Gay-Berne potential being “softer" compared with the actual interaction between SMDPPEH molecules, thereby leading to a broader peak from CGMD simulations relative to the AMD simulation. The “soft" interaction of the Gay-Berne parameterization can also be observed in the probability distribution from the broader peaks in the face-to-side configuration relative to those from AMD simulations; see the lower panel of Figure 2b. Nevertheless, the major contribution comes from the face-to-face configuration, and the Gay-Berne parameterization in the present study can successfully capture the relative orientation and separation that is the most probable.


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Figure 2. Probability distribution function of the relative orientation between two SMDPPEH

molecules from AMD (upper panels), and CGMD using the Gay-Berne potential parameters from the present study. (a) Probability distribution with Euler angle φ fixed at zero and (b) φ fixed at π. Gay-Berne Parametrization for PCBM and Chlorobenzene

Because both the PCBM and CB molecules were represented as spheroidal particles (Figure 1a), the anisotropic Gay-Berne potential reduces to the isotropic Lennard-Jones potential and can therefore be parameterized by fitting the radial distribution functions (RDFs), similar to our previous works in fitting CG force fields for polymer solar cell systems.31,32 The CG scheme of wrapping a whole PCBM molecule into one Lennard-Jones spheroid is distinct from other earlier


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studies in which each C60 molecules is treated as an individual sphere with finite size.35,36 Nevertheless, as will be shown below, such a CG scheme yields good agreement with the RDFs from the respective all-atom atomistic MD simulations, demonstrating that this CG scheme provides reasonable agreement in the morphology of the amorphous PCBM domains, which is the typical microstructure for PCBM in solution-processed OPVs. Furthermore, a significant computational speed-up can be obtained by coarse-graining the PCBM molecules into LennardJones spheroids, allowing us to explore the BHJ nanomorphology evolution of systems with larger spatial and temporal scales. It must be noted that to reproduce the crystal structures of fullerene derivatives with complicated molecular structures such as the di-mesogenic-C60,36 the fullerene cage itself must be treated individually as a sphere. Figures 3 a-e display the RDFs computed from the all-atom atomistic MD (symbols) and from the optimized Gay-Berne parameters (lines), respectively. The RDFs from CGMD based on Gay-Berne parametrization in the present work are in good agreement with those from AMD simulations. Note that the height of the first peak of the RDF of the PCBM pairs is lower than those from the all-atom atomistic MD based on PCBM crystals,37,38 because the RDF of the PCBM in the present study was computed in the amorphous phase. Furthermore, it is interesting to notice that for the RDFs of the SMDPPEH-PCBM (Figure 3d) and SMDPPEH-CB (Figure 3e) pairs, there exist three peaks (1, 2, and 3 in Figures 3d,e). These peaks correspond to the adsorption sites of the PCBM/CB molecules on the SMDPPEH molecules, namely, the face site, side site, and tail site, respectively. The RDFs from AMD indicate that PCBM molecules prefer adsorbing on the face site (Figure 3d), whereas CB molecules prefer adsorbing on the side sites (Figure 3e) because of the ethylhexyl group. Hence, the Gay-Berne potential parameters from the present study can


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reasonably reproduce the preferential adsorption sites of both PCBM and CB molecules on SMDPPEH molecules.


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Figure 3. Radial distribution functions (RDFs) of all molecular pairs computed from AMD

(symbols) and from CGMD simulations (lines); (a) PCBM-PCBM pair; (b) CB-CB pair; (c) PCBM-CB pair; (d) SMDPPEH-PCBM pair; (e) SMDPPEH-CB pair. In the present study, AMD simulations for sampling the ellipsoid orientational probability distribution and the RDFs were carried out using the LAMMPS molecular simulation package.39 The PCFF+ force field was employed to describe the interactions between atoms in the system. In the AMD simulations, the systems were first relaxed in the NPT ensemble with a system pressure and temperature of 1 atm and 300K. The subsequent sampling of the probability distribution was carried out in the NVT ensemble at 300 K for twenty million time steps. The CGMD simulations of Gay-Berne ellipsoids were carried out on a GPU workstation with four Nvidia GTX Titan X GPU cards installed using the LAMMPS package with GPU implementation to accelerate the CGMD simulations.40 The optimized Gay-Berne potential parameters in the present study are compiled in Table 1.

Table 1. Optimized Gay-Berne and Lennard-Jones Potential Parameters for SMDPPEH, PCBM,

and CB Molecules Employed in the Present Study. Pairs

Potential Forms

SMDPPEH-SMDPPEH SMDPPEH-PCBM SMDPPEH-CB PCBM-PCBM PCBM-CB CB-CB

Gay-Berne Gay-Berne Gay-Berne Lennard-Jones Lennard-Jones Lennard-Jones

σ (Å) ε (kcal/mol) 3.5 6.3 4.5 9.0 7.2 5.4

0.1 0.1 0.1 1.5 0.6 0.1

S a (Å)

Sb (Å)

Sc (Å)

εa

εb

εc

υ

µ

γ

33.0 21.0 19.2 -

16.0 12.5 10.7 -

3.5 6.3 4.5 -

2 2 2 -

2 3 6 -

10 4 3 -

1 1 1 -

1 1 1 -

1 1 1 -


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RESULTS AND DISCUSSION

With the CG force field based on the Gay-Berne ellipsoid model, we were able to investigate the nanomorphological evolution of the SMDPPEH:PCBM blend during solution processing in the CB solution. In the present study, we systematically explored the effects of the SMDPPEH:PCBM blending ratio and the external shear on the nanomorphology of SMDPPEH:PCBM blends to mimic the blade-coating processes. Effects of SMDPPEH:PCBM Blending Ratio

It has been reported that the performance of the SMDPPEH:PCBM OPV strongly depends on the blending ratio of SMDPPEH versus PCBM.23 Hence, we simulated the solvent evaporation processes of three SMDPPEH:PCBM solutions with three different weight blending ratios (namely, relative weight percentages of SMDPPEH and PCBM): 30%:70%, 50%:50%, and 70%:30%. The morphologies of the SMDPPEH:PCBM blends in CB solution are displayed in Figures 4a-c. The initial concentrations of the SMDPPEH:PCBM solutions were 41.45, 42.28, and 43.25 mg/ml for the 30%:70%, 50%:50%, and 70%:30% solutions. Note that the solubilities of SMDPPEH and PCBM in CB solution are 20 mg/ml41 and 59.5 mg/ml,42 respectively. Therefore, based on the SMDPPEH/PCBM solubilities reported from experiments, we would expect no PCBM dissolution in all three cases and possible SMDPPEH dissolution in the 50%:50% and 70%:30% solutions. From Figures 4a-c, we can find that there is no evident SMDPPEH/PCBM dissolution, demonstrating that the Gay-Berne parameters fitted in the present study for a ternary SMDPPEH/PCBM/CB system are in reasonable agreement with experiments. To simulate solvent evaporation processes, we employed a quasi-equilibrium approach that has been applied in studying the solvent evaporation processes of P3HT:PCBM blends.32 In this approach, we mimic the solvent evaporation by randomly removing 1% of the


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solvent molecules (ca. 7987 CB molecules) per 104 CGMD time steps (namely, 5x104 fs), corresponding to an evaporation rate on the order of 1.8x10 6 g/min after the time rescaling. Note that we assumed that the system quickly equilibrates itself during solvent evaporation, leading to a negligible solvent/SMDPPEH/PCBM concentration gradient along the z direction. A recent 1D phase field model study has revealed a negligible gradient in the concentration profile upon solvent evaporation, which validates our approximation.22 Note that in this random solvent removal process, we are studying the nanomorphological evolution in the bulk with no free surface or substrate involved. It is interesting to note that if the solvent evaporation rate is further reduced (namely, there is an increase in the time interval of solvent removal from our simulations), we would expect denser molecular packing because the SMDPPEH and PCBM molecules have more time to rearrange themselves based on our observations of the CGMD simulation of the solution processing of P3HT:PCBM blends.32 Denser films imply closer intermolecular separations, which can potentially increase the overlap integrals and charge carrier hopping rates. The nanomorphologies of the SMDPPEH:PCBM blends after CB solvent evaporation are displayed in Figures 4d-f. Throughout the blending ratios explored in the present study, we observed moderate phase segregation between SMDPPEH and PCBM molecules, which is in good agreement with both the AFM23 and TEM experiments.24


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Figure 4. Nanomorphologies of SMDPPEH:PCBM blends in solution (a-c), and dried film (d-f)

under different SMDPPEH:PCBM blending ratios. (a) and (d): 30%:70%; (b) and (e): 50%:50%; (c) and (f): 70%:30%. Note that in (a)-(c), only SMDPPEH and PCBM molecules are displayed. Next, we evaluate the nanomorphologies of the SMDPPEH:PCBM blends by computing the morphological properties of the blend using the spatial discretization scheme we employed for polymer solar cells.31 As illustrated in Figure 5a, in this scheme, we divided the entire simulation cell into small voxels of size close to that of a PCBM CG particle (1 nm); see the left panels of Figure 5a for the original system from the CGMD simulation (upper left panel) and the corresponding spatially discretized simulation cell (lower left panel). With this spatial discretization scheme, we can estimate the following morphological properties that are critical for the solar cell device performance:

Domain size/width. Specific interfacial area, which measures the SMDPPEH/PCBM interfacial area per unit volume.


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Domain percolation probability, which estimates the fraction of SMDPPEH/PCBM domains that can percolate through the simulation cell; see the right panels of Figure 5a. This

quantity is vital for charge transport to the respective electrodes. The domain width of the SMDPPEH/PCBM phases was estimated by computing the autocorrelation length (ACR).43 The details of the ACR calculation can be found in the Supporting Information. The domain widths of SMDPPEH and PCBM under different blending ratios are displayed by the red and blue lines in Figure 5b, respectively, showing that the domain widths of SMDPPEH/PCBM decrease with the decreasing SMDPPEH/PCBM relative concentration. The SMDPPEH/PCBM domain widths are the closest at 4-5 nm at a 50%:50% blending ratio. The specific interfacial area of SMDPPEH/PCBM with different blending ratios is displayed by the green line in Figure 5b. Note that the 50%:50% blend gives the maximum specific interfacial area, implying that the 50%:50% blend should give the highest exciton dissociation rate, which can promote the solar cell efficiency. Note that the optimal blending ratio of SMDPPEH:PCBM from experiments is 50%:50%,23 suggesting that the optimal blending ratio is that which yields the maximum specific interfacial area, which is similar for both polymer solar cells and polymer/inorganic nanocrystal hybrid solar cells.31,44 Finally, the percolation probabilities of the SMDPPEH/PCBM domains as functions of the blending ratio are displayed in Figure 5c, and we can find that they decrease with the decreasing relative concentration because of the increasing number of isolated domains. The SMDPPEH/PCBM domain percolation probabilities are the most similar at the 50%:50% blending ratio, suggesting that similar percolation probabilities between hole/electron transport pathway also plays an important role in device performance. Note that the method to estimate the percolation probability employed in the present study is valid only for bulk systems. For a system that does not contain periodicity, for example, the CGMD of the BHJ system including a cathode/anode, a different approach has to be employed to


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estimate the domain percolation.45 The charge carrier transport properties based on the BHJ nanomorphologies can potentially be extracted directly from charge carrier dynamics kinetic Monte Carlo simulations.46

Figure 5. (a) Schematics of the spatial discretization method employed in the present study; (b)

domain widths of SMDPPEH (red) and PCBM (blue), and specific interfacial area (green) under


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different SMDPPEH:PCBM blending ratios; and (c) percolation probabilities of SMDPPEH and PCBM domains with respect to SMDPPEH:PCBM blending ratios. Effects of Shearing Rate

The amount of material wasted during device fabrication is a critical issue in the large-scale fabrication of organic solar cells. In the conventional spin-casting process, a significant amount of material is wasted, thereby limiting the application of this process in commercial device fabrication. In contrast, blade-coating processes can be easily integrated into roll-to-roll fabrication with much less material wasted, making them ideal for the commercial production of OPVs. To mimic the blade-coating processes, an external shear force was applied to the SMDPPEH:PCBM solution. Two thin slabs of SMDPPEH:PCBM solution were fixed at the top and bottom of the simulation cells, and the slab at the bottom was moved with a predefined constant dragging velocity v. Note that upon applying external shear, the simulation cell in the z direction was not periodic, while the cell periodicities in the lateral dimensions (namely, x and y directions) were retained. The shear rate is defined as

v h

γ& = , (10)

where v and h are the dragging velocity of the top slab and the film thickness, respectively. To investigate the effect of the shearing rate, the nanomorphological evolution of the SMDPPEH:PCBM solution with a 50%:50% blending ratio was examined under three shear rates (after time rescaling), namely, low (4.2x107/s), intermediate (4.2x108/s), and high (4.2x109/s), along with a blend without shear forces applied (zero shear), namely, the 50%:50% blend displayed in Figures 4b,e. The typical shearing rates in the blade coating processes range between 103/s and 106/s;47 hence, the shearing rate in the present study was slightly on the high


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side relative to experiments. Here, we assume that the amount of solvent evaporation during the shearing process is negligible because 1) the duration of the shearing process is much shorter than that of the subsequent solution equilibration process and 2) during the shearing process, the upper surface (which the solvent molecules evaporate from) is covered by the blade or slot, thereby blocking solvent evaporation. Therefore, the solvent evaporation process started following the shearing process. Once again, during the solvent evaporation process, we randomly removed 1% of all solvent molecules every 5x104 fs. The nanomorphology of the 50%:50% SMDPPEH:PCBM solution under different shearing rates is displayed in Figures 6a-c. Note that only the SMDPPEH and PCBM molecules are displayed, while the empty space is filled with CB solvent molecules. It is evident that applying an external shear can effectively promote the aggregation of PCBM phases; see the large PCBM domains in Figure 6c. The aggregation of PCBM domains can be further manifested from the relative SMDPPEH/PCBM weight concentration profile along the z direction (see Figure S1 in the Supporting Information), which shows an increasing fluctuation in the relative concentration (a sign of domain formation) with the increasing shearing rate. Interestingly, we can observe that applying an external shear force leads to the segregation of CB molecules toward the bottom moving slab, and the higher the shearing rate, the more pronounced the CB solvent molecule segregation; see the large empty space at the top of Figures 6b,c. This solvent molecule segregation toward the bottom moving slab is highly likely because of the molecular size differences among the CB solvent, SMDPPEH and PCBM molecules. The small CB molecules can more easily to cope with the motion of the moving bottom slab, thereby leading to solvent molecule segregation. Hence, the precipitation of the PCBM domains under external shear can be attributed to the rise in the local SMDPPEH/PCBM concentration in the lower part of the


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solution beyond the solubility limit because of CB solvent molecule segregation toward the bottom moving slab. Figures 6d-f display the nanomorphologies of SMDPPEH:PCBM blends under low (Figure 6d), intermediate (Figure 6e), and high (Figure 6f) shear rates after solvent removal, which demonstrates that the degree of SMDPPEH:PCBM segregation increases with respect to increasing external shear rate during the shearing process. A similar effect of phase segregation promotion has also been revealed in solution-processed P3HT:PCBM blends from AFM images,48 demonstrating that this is a generic phenomenon for both solution-processed polymers and small-molecule organic solar cells. Furthermore, it appears that high shearing rates also promote stacking between SMDPPEH molecules; see the stacking between the ellipsoidal particles in Figures 6d-f. Nevertheless, further quantitative morphological analysis is required. Next, we will analyze the morphological properties of the SMDPPEH:PCBM blends after solvent removal.


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Figure 6. Nanomorphologies of 50%:50% SMDPPEH:PCBM blends under external shear (a-c)

and after solvent removal following the shearing process (d-f). The SMDPPEH:PCBM solution was subjected to a low shear rate (0.04/ns, a, d), intermediate shear rate (0.42/ns, b,e), and high shear rate (4.2/ns, c,f). Note that only the SMDPPEH and PCBM molecules are displayed for clarity; therefore, all empty spaces are filled with CB molecules. Figure 7 displays the morphological properties of SMDPPEH:PCBM blends under different shear rates. Figure 7a displays the RDFs of the SMDPPEH ellipsoidal particles under different shear rates, and the first peak corresponds to the stacking between SMDPPEH molecules. It is evident that applying a shear force can effectively promote SMDPPEH stacking. The enhancement of SMDPPEH stacking can potentially promote hole-hopping transport along the direction between neighboring SMDPPEH molecules, which is expected to improve the device performance. Nevertheless, other morphological properties that are also relevant to the device performance, namely, the aforementioned specific interfacial area and the percolation probabilities, must be evaluated as well. Figure 7b displays the SMDPPEH/PCBM domain widths (red and blue lines, respectively) and the specific interfacial area (green line) as functions of the external shear rate. Clearly, we can observe that under the same SMDPPEH:PCBM blending ratio, higher shear rates leads to coarser SMDPPEH:PCBM domains, which is consistent with the morphologies displayed in Figures 6d-f. However, the specific interfacial area (green line in Figure 7b) drops for blends subjected to a high shear rate process, indicating that blends with coarser domains are often accompanied by poorer specific interfacial areas, potentially lowering the exciton dissociation rates at the interface. Furthermore, from Figure 7c, we find that the PCBM domain percolation is poor relative to that at other shear rates, manifesting that a high shearing rate results in large, compact, and isolated PCBM domains,


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which is not good for electron transport due to the truncated electron transport pathway to the cathode. Hence, the effects of applying a shear force to SMDPPEH:PCBM solutions can be summarized in the following:

Promotion of

Promotion of segregation between SMDPPEH and PCBM phases; however, if the shear rate is

stacking of SMDPPEH molecules, which is good for hole transport.

too high, the PCBM domains will become large and compact, leading to a small specific interfacial area and isolated PCBM domains that potentially hinder exciton dissociation and subsequent electron transport.

Therefore, there exists an optimal external shear rate that can effectively promote SMDPPEH stacking, while preventing the formation of isolated PCBM domains. In the present study, from Figure 7, we can find that the specific interfacial area of the SMDPPEH:PCBM blend reaches a maximum at an intermediate shearing rate (Figure 7b), which also gives the most balanced hole/electron transport pathway percolations (Figure 7c), implying that a device fabricated under such an external shear rate should yield the optimal performance. Nevertheless, further multiscale calculations incorporating mesoscale charge carrier transport simulations are required for directly constructing morphologies with charge transport properties.


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Figure 7. Morphological properties of 50%:50% SMDPPEH:PCBM blends under different shear

rates: (a) RDFs of SMDPPEH molecules; (b) SMDPPEH:PCBM blend domain widths (red: SMDPPEH, blue:PCBM) and specific interfacial area (green); (c) domain percolation probabilities. CONCLUSIONS

In the present study, we developed a coarse-grained molecular dynamics simulation model to investigate the nanomorphologies of SMDPPEH:PCBM small-molecule organic solar cells during solution processing. We employed the Gay-Berne ellipsoid model, coarsened SMDPPEH, PCBM and CB solvent molecules into ellipsoidal/spheroidal particles, and parametrized the GayBerne potential by fitting the orientation-dependent probability functions or radial distribution functions computed from respective all-atom atomistic molecular dynamics simulations. Then, we carried out a series of large-scale coarse-grained MD simulations to study the morphological evolution of the SMDPPEH:PCBM blend during solution processing. We examined the effects of the SMDPPEH:PCBM blending ratios on the resultant blend morphologies, and we found that, similar to polymer solar cells and polymer/inorganic hybrid solar cells, the blends in smallmolecule organic solar cells with the optimal blending ratio yield the highest specific interfacial area and the most balanced donor/acceptor domain percolations. Next, to investigate the morphological evolution during the blade-coating process, we applied external shear to the SMDPPEH:PCBM solution and investigated the morphological evolution during the shearing and subsequent solvent evaporation. Our simulations indicate that, for the same blending ratio, differences in shear rates yield distinct nanomorphologies. Applying a shear force leads to CB solvent molecules segregating toward the moving slab, facilitating the segregation of SMDPPEH/PCBM domains. Furthermore, the shear force can also promote the formation of


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stacking between SMDPPEH molecules, thereby promoting hole transport. However, high shear rates result in a strong phase segregation, the formation of large, compact, and isolated PCBM domains with a low specific interfacial area and PCBM domain percolations. Our CGMD simulations indicate that there exists an optimal shearing rate that can maximize the SMDPPEH:PCBM specific interfacial area, while promoting stacking between SMDPPEH molecules. We envision that the ellipsoid model can be easily extended to modeling the morphologies of other small-molecule OPVs or small-molecule organic electronic materials, thereby helping experimental teams optimize device fabrication. Supporting Information Available

Animation of a single SMDPPEH molecule from all-atom atomistic molecular dynamics simulation

(Movie

M1);

method

for

computing

autocorrelation

length

(ACR);

SMDPPEH/PCBM relative weight percentage profile along the z direction (Figure S1). This material is available free of charge via the Internet at http://pubs.acs.org/. AUTHOR INFORMATION Corresponding author

*E-mail: [email protected] Conflict of Interest

The authors declare no competing financial interest. ACKNOWLEDGMENTS

We thank the Academia Sinica Thematic Project no. AS-103-SS-A02 and the Ministry of Science and Technology for their financial support of projects no. 102-2628-M-001-004-MY3 and 104-2911-1-001-508-MY2. We also thank the National Center for High-Performance


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Computing for their support in computational facilities. C.-K. Lee especially thanks Dr. T.-L. Huang and the JSOL Corporation for financial and technical support. REFERENCES

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