Temperature Dependence of the Diffusion Coefficient of PCBM in Poly

and Biochemistry, and ∥Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, United Stat...
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Temperature Dependence of the Diffusion Coefficient of PCBM in Poly(3-hexylthiophene) Neil D. Treat,†,‡ Thomas E. Mates,‡ Craig J. Hawker,†,‡,§ Edward J. Kramer,†,‡,∥ and Michael L. Chabinyc*,†,‡ †

Materials Department, ‡Materials Research Laboratory, §Department of Chemistry and Biochemistry, and ∥Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, United States S Supporting Information *

ABSTRACT: Interest in new functional small molecule and polymer blends, such as polymer−fullerene bulk heterojunction (BHJ) organic solar cells motivates the development of new methods to measure the diffusion coefficient of molecular species (e.g., PCBM) in polymers. The aim of this study is to systematically improve our understanding of the relevant material and processing parameters needed to control the microstructure of BHJ organic solar cells in order to develop a more complete understanding of how to improve its power conversion efficiency. Here, we fabricate a terraced monolayer−bilayer sample of P3HT and P3HT/PCBM and use this structure to quantify both the volume fraction of miscible PCBM in P3HT and the diffusion coefficient of disordered PCBM in disordered P3HT. Our findings reveal that the diffusion coefficient for disordered PCBM in P3HT is strongly dependent on the annealing temperature (i.e., increasing by 3 orders of magnitude when doubling the annealing temperature) and weakly dependent on the PCBM concentration. The temperature-dependent diffusion coefficients were fit with an Arrhenius relationship to determine an activation energy for the diffusion of disordered PCBM through P3HT. Ultimately, this report demonstrates that the self-assembly of the P3HT:PCBM BHJ solar cell during annealing and cooling is not limited by the diffusion of deuterated PCBM in P3HT with the nanostructure of PCBM being controlled by the relative volume fractions of ordered and disordered P3HT.

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INTRODUCTION Diffusion of molecules in polymers is a subject that has been studied in a variety of contexts including drug delivery,1 nanolithography,2 permeation through membranes,3 polymerization reaction kinetics,4 and organic photovoltaics.5−7 The most efficient organic photovoltaics comprise a phaseseparated, bicontinuous blend of an electron-donating polymer and an electron-accepting fullerene; this structure is referred to as a bulk heterojunction (BHJ).8−12 However, due to the nanoscale structures in polymer:fullerene BHJs, it has been difficult to determine the role that diffusion of the fullerene within the polymer has on their morphology and stability. A number of approaches have been developed to study the diffusion kinetics of small molecules within molecule−polymer blends.13−17 Many of these methods, particularly those based on fluorescence, are difficult to perform on BHJs. Therefore, there is a need to develop new analytical methods to determine the solid-state diffusion characteristics of small molecules within polymer matrices. This study reports the development of a general methodology to measure lateral diffusion in thin films, which is used here to examine the diffusion process of a fullerene in a semiconducting polymer. We focus on one of the most extensively characterized BHJ systems: a blend of poly(3hexylthiophene) (P3HT) and [6,6]-phenyl-C61-butyric acid methyl ester (PCBM).18−20 Efficient solar cells fabricated from this system comprise a multiphase system of pure P3HT © 2013 American Chemical Society

crystallites, mixed disordered P3HT and PCBM, and disordered PCBM-rich phases.5−7,21−24 The complex microstructure of the photoactive layer is thermodynamically controlled by the material properties (e.g., polymer−fullerene miscibility) and kinetically controlled by the processing parameters (e.g., film drying times) and subsequent thermal annealing conditions. To understand the formation of this microstructure, one must first develop an understanding of the characteristics that control its evolution. An important processes that governs the morphology is how rapidly PCBM diffuses through the disordered domains of P3HT during thermal annealing, i.e., the concentration dependent diffusion coefficient of PCBM in P3HT. The miscibility and diffusion of PCBM within P3HT has been a topic of increased interest, which is due, in part, to the complex microstructure of ordered and disordered domains of P3HT that have been observed in the blend.5−7,18,21−24 Initial work in this area focused on measuring the depletion of PCBM from a P3HT:PCBM BHJ in the vicinity of a PCBM crystallite as a function of annealing time.5 The concentration profile of the remaining PCBM in the P3HT was fit with Fick’s second law and resulted in an estimate of the diffusion coefficient of PCBM in P3HT of 2.5 × 10−10 cm2/s at a temperature of 140 Received: November 13, 2012 Revised: December 17, 2012 Published: January 24, 2013 1002

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Figure 1. (a) (top) DSIMS image of the monolayer−bilayer interface after heating at 110 °C for 5 s, which is defined as t = 0 for the lateral diffusion. The green areas correspond to areas of high 2H counts, i.e., regions with high concentrations of dPCBM; the dark regions are devoid of dPCBM. (bottom) A schematic representation of the side view of the terranced monolayer−bilayer sample geometry with annotated scale. The bright green dots in the P3HT layer correspond to the initial volume fraction of dPCBM in the P3HT layer. (b) (top) DSIMS image of the lateral diffusion of dPCBM after annealing at 110 °C for 120 min and (bottom) corresponding schematic representation to scale.

P3HT after heating at 50 and 70 °C for different amounts of time were fit with a 1D solution to Fick’s second law and yielded a diffusion coefficient of 2.2 × 10−11 and 5.7 × 10−11 cm2/s, respectively. The diffusion profiles of dPCBM in P3HT measured at 90 and 110 °C exhibited a weak concentration dependence, and thus, a Boltzmann−Matano analysis was utilized to elucidate a diffusion coefficient. Our findings reveal that the diffusion of disordered dPCBM in P3HT is strongly dependent on temperature, varying over 2 orders of magnitude between 50 and 110 °C and weakly dependent on dPCBM concentration, varying by a factor of 2.5 for ϕ = 0.001−0.06 at 110 °C. Finally, these diffusion data were used to estimate the activation energy of diffusion of PCBM through P3HT at ϕ = 0.01, which is within the expected values for the diffusion of molecular species through polymer matrices. Ultimately, the rapid diffusion of disordered dPCBM in P3HT indicates that, during typical solar cell annealing times (e.g., 10 min) and cooling rates (e.g., 125 °C/s), the self-assembly of the P3HT:PCBM BHJ is not kinetically limited by the diffusion of PCBM through P3HT.

°C. Building on these initial studies, we decoupled the diffusion of the PCBM in the P3HT from its crystallization by investigating the temperature-dependent miscibility and interdiffusion of disordered PCBM in P3HT in a bilayer of disordered PCBM and P3HT. Upon annealing, the bilayer rapidly mixed, reaching a temperature-dependent equilibrium concentration of disordered PCBM in P3HT.5−7 Also, from these diffusion data, we estimated that the diffusion coefficient of disordered PCBM in P3HT must be larger than 3 × 10−10 cm2/s, but due to the rapid diffusion, a precise value could not be determined. These initial studies reveal that disordered PCBM is miscible and rapidly diffuses within disordered P3HT, but the concentration and temperature dependence of the diffusion coefficient and their potential impact on the selfassembly of the BHJ have not been reported. We focus here on quantifying the concentration- and temperature-dependent diffusion coefficient of disordered PCBM in P3HT by studying its lateral diffusion. Toward this goal, we developed a method to fabricate a terraced monolayer−bilayer sample geometry with overlapping strips of P3HT and disordered PCBM. Our sample geometry is similar to recent work using photolithographically defined structures made by solution casting where scanning X-ray transmission microscopy (SXTM) was used for imaging.25 Our work differs from that work because we can quantify the diffusion of disordered deuterated (d)PCBM in P3HT over large diffusion distances (i.e., ∼ 100 μm) without the possible effects of residual casting solvent. Additionally, the experimental conditions were chosen here such that the dPCBM remained disordered, which decouples the effects that crystallization may have on the diffusion of dPCBM through P3HT. In this study, the temperature-dependent volume fraction of miscible dPCBM in P3HT (ϕ0) was quantified in the area of the terraced structure analogous to a P3HT/dPCBM bilayer using dynamic secondary ion mass spectrometry (DSIMS) depth profiles and represented these data as the miscibility− immiscibility phase diagram of disordered dPCBM and P3HT. Next, the lateral diffusion of disordered dPCBM within the portion of the terraced film analogous to a monolayer film of P3HT was measured using DSIMS imaging as a function of annealing time and temperature, which enabled quantification of the temperature-dependent diffusion coefficient of disordered dPCBM in P3HT. The diffusion profiles of dPCBM in

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EXPERIMENTAL SECTION

Materials. P3HT (Sepiolid P200, BASF, Mw = 20K−30K, RR > 95%, PDI = 2.0) and dPCBM (Sigma-Aldrich, 99.5%) were purchased and used as received. Terraced P3HT/dPCBM Monolayer−Bilayer Sample Fabrication. P3HT was dissolved in chlorobenzene at a concentration of 15 mg/mL and stirred overnight at 90 °C in a N2-filled glovebox. Silicon substrates coated with 150 nm of thermal oxide were cleaned by ultrasonication in acetone, 2 wt % soap:DI H2O, DI H2O, and isopropanol for 15 min, and dried in a stream of N2 gas. The P3HT solution was spin-coated in a N2-filled glovebox at 2000 rpm for 40 s and thermally annealed at 150 °C for 10 min. The dPCBM films were thermally evaporated on separate cleaned SiO2/Si substrates at a pressure of ∼10−7 Torr at a rate of 0.3 Å/s through a solar cell electrode shadow mask (1.5 mm wide by 4 mm long) to produce a patterned substrate with a final dPCBM film thickness of 60 nm. The P3HT film was then transferred onto a water interface by sequential immersion in dilute HF and DI H2O and removed from the water interface with the evaporated dPCBM film supported on a SiO2/Si substrate. The final film structure consisted of patterned areas of P3HT/dPCBM/SiO2 (bilayer) and P3HT/SiO2/Si (monolayer). Dynamic Secondary Ion Mass Spectrometry. A Physical Electronics 6650 Quadrapole dynamic SIMS was used to obtain depth and lateral profiles of the films on SiO2/Si substrates. For this, a highly focused (i.e., ∼5 μm in diameter for DSIMS imaging and ∼30 1003

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μm for DSIMS depth profile) 2 kV O2+ beam operating at ∼45 nA was rastered across a 300 μm × 300 μm area, and negative secondary ions were collected. Additional information about signal analysis and fitting can be found in the Supporting Information.

and 110 °C for various amounts of time (analogous to the lateral diffusion experiments), and then a 110 nm thick polystyrene film was transferred on top of the annealed samples (representative DSIMS profiles Figures S4−S7). Note that, in all cases, the annealing conditions were chosen such that the dPCBM remained disordered. The temperature-dependent ϕ0 of dPCBM in the P3HT layer was quantified by averaging the ϕ of dPCBM in the P3HT layer as a function of depth. The ϕ0 of disordered dPCBM in P3HT was found to be independent of the annealing time and to increase with increasing annealing temperature with the ϕ0 data, plotted in Figure 2 corresponding to the metastable miscibility−

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RESULTS AND DISCUSSION The concentration- and temperature-dependent diffusion of disordered dPCBM in P3HT was quantified using a terraced monolayer−bilayer sample geometry. This sample geometry enables the study of the diffusion of any chemically distinct species within a matrix over distances up to ∼1 mm and volume fractions (ϕ) as low as 0.001. As illustrated in Figure 1a, this sample geometry first requires the formation of a relatively sharp interface between the P3HT and dPCBM, which was achieved by thermally evaporating a 60 nm film of disordered dPCBM through a shadow mask (fabrication and characterization details are reported in the Experimental Section and Supporting Information, respectively) on a SiO2(150 nm)/Si substrate. Next, a 50 nm thick P3HT sample was spin-coated on a separate SiO2(150 nm)/Si substrate, annealed at 150 °C for 10 min to increase the crystallinity of P3HT (these conditions are similar to the annealing process in most studies of P3HT:PCBM BHJ solar cells18,19) and to remove any residual solvent, and then transferred on top of the evaporated dPCBM by sequential immersion in dilute HF and DI H2O. The resulting samples were characterized with cross-section scanning electron microscopy, and these images are presented in the Supporting Information (Figure S3). In this sample geometry, the P3HT is semicrystalline and the dPCBM is disordered, which is the typical microstructure of these components in the most efficient P3HT:PCBM solar cells.5−7,18,21−24,26,27 The lateral diffusion process in this terraced monolayer− bilayer sample can be broken down into two steps: (1) establishing a local equilibrium volume fraction of dPCBM (ϕ0) in the portion of the P3HT film directly above the dPCBM strips (i.e., the bilayer); (2) lateral diffusion of miscible disordered dPCBM in the neat semicrystalline P3HT monolayer. Given the relatively small polymer film thickness (50 nm), the dPCBM rapidly diffuses into the P3HT film and equilibrates to ϕ0 for each annealing temperature. The disordered dPCBM then diffuses laterally into the portion of the pure P3HT (distances of x > 0 in Figure 1a), depleting dPCBM in the P3HT:dPCBM, which is replenished by the pure dPCBM film underneath (evidence detailed below). Thus, this geometry can be thought of as an infinite reservoir of miscible dPCBM in P3HT with a volume fraction of ϕ0 for x < 0 (i.e., in the bilayer portion of the film) at all annealing times. Note that the diffusion medium is isotropic in plane, and therefore the diffusion of the dPCBM in disordered P3HT must also be isotropic in plane. In theory, this terraced monolayer−bilayer sample could be utilized to determine the diffusion coefficient of virtually any chemically distinct, isotropic material that can be evaporated or float cast and is analogous to lateral diffusion measurements in inorganic semiconductors.28 Temperature-Dependent Miscibility of Disordered dPCBM in P3HT. The equilibrium volume fraction of miscible dPCBM in P3HT (ϕ0) was measured using DSIMS depth profiles in the portion of the P3HT film directly above the neat dPCBM layer, i.e., the portion of the terraced film analogous to a P3HT/dPCBM bilayer film. For these experiments, the terrace monolayer−bilayer samples were annealed at 50, 70, 90,

Figure 2. Metastable phase diagram for the volume fraction of miscible disordered dPCBM in P3HT as a function of annealing temperature for BASF P3HT (Sepiolid P200, black circles).

immiscibility phase diagram for disordered dPCBM in P3HT. It was found that as the annealing temperature increased from 50 to 110 °C, the ϕ0 for disordered dPCBM in the P3HT increased from 0.006 to 0.06. Reduced values for the temperature dependent ϕ0 relative to previous reports were observed and this reduction in ϕ0 is likely due to the absence of solvent in dPCBM films (Figure S9). Most importantly, the ϕ0 was independent of the annealing time at a given annealing temperature (Figure S8), which indicates that the neat underlayer of dPCBM maintains an ϕ0 of disordered dPCBM in P3HT during the extent of the lateral diffusion process, an assumption that is of critical importance for the lateral diffusion in these samples is to be accurately modeled. A significant outcome of this work is the observation that the ϕ0 for disordered dPCBM in P3HT increases with increasing annealing temperature and maintains a constant value with annealing time. Lateral Diffusion of Disordered dPCBM in P3HT. The diffusion of disordered dPCBM in P3HT as a function of distance from the dPCBM interface was quantified using DSIMS imaging. For these experiments, a 300 μm square crater was etched with a highly focused O2+ ion beam (giving a lateral resolution of ∼5 μm) with the use of a 2H-labeled PCBM species yielding images with typical signal-to-noise ratios of 250:1 and a 2H detection limit of ϕ = 0.001 (Figure S10). The initial interface of the dPCBM film (x = 0) was defined to be the point at which the signal was one standard deviation less than the ϕ0 of disordered dPCBM in P3HT. The interfacial width was characterized with DSIMS images collected after samples were heated for 5 s at 110 °C (Figure 1a). These 1004

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results indicate that ϕ0 has been established with in the P3HT film with a negligible amount of lateral diffusion and is defined as t = 0 for the lateral diffusion experiments. It was observed that the lateral interfacial between the dPCBM strips and P3HT film has a width of ∼5 μm, which is likely due to a combination of the resolution of the DSIMS imaging and the interfacial width of the evaporated dPCBM film. The lateral dPCBM concentration profiles in a P3HT/ dPCBM terraced monolayer−bilayer sample were measured after annealing at 50, 70, 90, and 110 °C for various times, t. Line averages of the images (three different 20 × 300 μm areas) were taken as a function of distance, and the average 2H signal at x < 0 was normalized to the temperature-dependent ϕ0 previously quantified with the DSIMS depth profiles (Figure 1b). Representative plots of the ϕ of dPCBM as a function of distance from the dPCBM interface (x = 0) when heated at 110 °C for 30, 60, and 120 min are presented in Figure 3a. As the annealing time increases from 30 to 120 min, the disordered dPCBM diffuses greater distances in the P3HT, which results in

an increased ϕ of dPCBM measured at x > 0. After applying the Boltzmann transformation29−31 (i.e., where x is normalized by t1/2), the resulting ϕ’s collected at different times form a single profile at each annealing temperature (Figure 3b and Figure S11), indicating that the dPCBM diffusion mechanism does not change as a function of annealing time (i.e., absence of dPCBM crystallization). Next, the dPCBM concentration profiles measured at 50 and 70 °C were fit with a one-dimensional solution to Fick’s second law of diffusion to yield a value for the diffusion coefficient of disordered dPCBM in P3HT. Note that the 1D solution of Fick’s second law (detailed in the Supporting Information) assumes the diffusion coefficient D is independent of the dPCBM concentration. However, as indicated by the χ2 goodness-of-fit test (Figure S13), this was only found to be true for samples annealed at 50 and 70 °C. Thus, by using Fick’s second law, it was possible to determine that the D for disordered dPCBM in P3HT is 2.2 × 10−11 and 5.7 × 10 −11 cm2/s at 50 and 70 °C, respectively (Figure 4). Note that in all

Figure 4. Plot of the diffusion coefficient, D(ϕ), of disordered PCBM in P3HT as a function of dPCBM volume fraction, ϕ, at various annealing temperatures. Note that the size of the data point is equivalent to the error of the measurement. The values of D(ϕ) at 50 °C (black diamonds) and 70 °C (green triangles) are the concentration-independent diffusion coefficients of dPCBM in P3HT determined from the 1D solution of Fick’s second law. The values of D(ϕ) at 90 °C (orange circles) and 110 °C (blue squares) are determined from the Boltzmann−Matano analysis (see Supporting Information for derivation). The temperature-dependent equilibrium concentration of dPCBM in P3HT is denoted as ϕ0.

cases the errors associated with the values for D(T) are less than 10%. As alluded to above, the data collected at 90 and 110 °C are not well fit by the 1D solution to Fick’s second law, suggesting that the D varies as a function of dPCBM concentration. To test this hypothesis, the ϕ of dPCBM versus x was fit with an empirical function, and the Boltzmann−Matano analysis (see Supporting Information for more details) was used to determine D(ϕ), the concentration-dependent diffusion coefficient of disordered dPCBM in P3HT. Figure 4 plots the D(ϕ) as a function of ϕ at 90 and 110 °C; a more extensive list of data collected at 90 and 110 °C can be found in Table S1. These data reveal that the D(ϕ) for disordered dPCBM in P3HT is strongly temperature dependent, increasing from 2.2 × 10−11 cm2/s at 50 °C to 1.0 × 10−9 cm2/s at 110 °C measured at ϕ = 0.01. Furthermore, the D(ϕ) of dPCBM in

Figure 3. (a) Plot of the empirical fit of the dPCBM volume fraction after annealing at 110 °C for t = 0 min (black), 30 min (orange), 60 min (blue), and 120 min (green) as a function of distance from the P3HT/PCBM bilayer interface (x = 0). The green open circles are the experimental data that were fit with the empirical exponential function. (b) Plot of the exponential fit of the d-PCBM volume fraction as a function of distance normalized by the square root of annealing time at 110 °C. The error bars are generated from the standard deviation of the fit parameters. 1005

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P3HT was found to be weakly dependent on the ϕ of dPCBM in the P3HT layer, decreasing by 2.5 times when the ϕ increased from 0.001 to 0.06 (measured at 110 °C). It is plausible that this inverse relationship of D(ϕ) to ϕ is due to the increasing probability for disordered dPCBM to form aggregates (i.e., clusters of two or more disordered PCBM molecules), which are likely less mobile relative to the molecularly dispersed dPCBM. By utilizing data collected from a simple terraced monolayer−bilayer sample geometry, the Boltzmann−Matano analysis demonstrates that the diffusion of disordered dPCBM in P3HT is strongly dependent on annealing temperature and weakly dependent on the dPCBM concentration. Assuming that the diffusion of dPCBM in P3HT can be modeled by an Arrhenius relationship, these data allow the determination of an activation energy for the diffusion of disordered dPCBM in P3HT (see Supporting Information). To obtain the activation energy, the D of disordered dPCBM in P3HT at ϕ = 0.01 was collected as a function of annealing temperature and plotted as the logarithm of D(ϕ = 0.01) versus 1000/T (Figure 5). Fitting with an Arrhenius relationship gives

equilibrium dispersion in P3HT at elevated temperature. The mass diffusion of PCBM is still ∼3 orders of magnitude slower than the diffusion of charge carriers even at 150 °C, and as evident from previous results, the mass diffusion should have little influence on the transit of a mobile carrier during operation of a P3HT:PCBM solar cells at elevated temperatures.26 Cooling to room temperature will decrease the miscibility of the PCBM in the P3HT, which causes the dispersed PCBM to precipitate, forming PCBM-rich domains. Typical cooling rates from 150 °C to room temperature can be estimated to be between 250 °C/s and 125 °C/s (i.e., 0.5−1.0 s). Assuming a constant cooling rate yields an average diffusion coefficient of 9.8 × 10−10 cm2/s and an approximate diffusion distance of disordered PCBM in P3HT between 440 and 620 nm. Again, these large diffusion distances (relative to the BHJ microstructure) indicate that the self-assembly process of a P3HT:PCBM BHJ is not limited by the diffusion of PCBM. Therefore, the observed P3HT:PCBM BHJ microstructure must be governed by other processes. It is plausible that the resulting dimensions of the PCBM domains are controlled by the volume fractions of disordered P3HT domains (i.e., the phase of P3HT that is miscible with disordered PCBM).

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CONCLUSIONS Through the fabrication and analysis of annealed terraced monolayer−bilayer samples with DSIMS depth profiles and imaging, we were able to quantify both the equilibrium miscibility and the lateral diffusion profile of disordered dPCBM into P3HT. The lateral dPCBM concentration profiles collected at 50 and 70 °C were fit by a 1D solution to Fick’s second law and yielded diffusion coefficients of 2.2 × 10−11 and 5.7 × 10 −11 cm2/s, respectively. The concentration profiles of dPCBM measured at 90 and 110 °C were fit by Boltzmann− Matano analysis and were found to be weakly dependent on dPCBM concentration (i.e., decreasing by 2.5 times when the ϕPCBM increased from 0.001 to 0.1 measured at 110 °C). Most importantly, it was found that the diffusion of dPCBM was strongly temperature dependent, varying from 2.2 × 10−11 cm2/ s at 50 °C to 1.0 × 10−9 cm2/s at 110 °C measured at ϕ = 0.01. This temperature-dependent diffusion at ϕdPCBM = 0.01 yielded an activation energy for the diffusion of disordered dPCBM in P3HT of 65.5 kJ/mol, which is within the typical range for diffusion of a small molecule in a polymer. The key finding in this study is that the rapid diffusion of PCBM in P3HT indicates that the self-assembly of the P3HT:PCBM BHJ is not limited by the diffusion of PCBM in P3HT. It is likely that the formation of the phase-separated nanostructure is governed by the dimensions of the disordered P3HT domains.

Figure 5. Concentration-dependent diffusion coefficient, D(ϕ = 0.01), of disordered dPCBM in P3HT versus inverse temperature. The slope provides the activation energy of 65.5 kJ/mol (15.6 kcal/mol) for the diffusion of disordered dPCBM through a P3HT:PCBM BHJ.

an activation energy of 65.5 kJ/mol (15.6 kcal/mol) for the diffusion of disordered dPCBM in a P3HT:PCBM blend with a ϕPCBM = 0.01. This activation energy is within the range of that expected for the diffusion of a small molecule through a polymer, i.e., 50−80 kJ/mol,14,32 and indicates that disordered PCBM diffuses in P3HT as a molecular species. Relationship of PCBM Diffusion to the Self-Assembly of the P3HT:PCBM BHJ. Quantifying the diffusion rate of PCBM within a P3HT:PCBM blend gives insights into the selfassembly of BHJs. When heated to 150 °C, we can estimate from the fit of the temperature-dependent D(ϕ = 0.01) that the diffusion coefficient of disordered dPCBM in P3HT is 5.0 × 10−9 cm2/s. Typical annealing times of 10 min18,26,33 would give PCBM diffusion distances of up to 35 μm (distance = 2(Dt)1/2), which is more than 3 orders of magnitude larger than the typical length scales of phase separation observed in P3HT:PCBM BHJs at room temperature (i.e., ∼20 nm).27,34 These large diffusion distances indicate that PCBM reaches an

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ASSOCIATED CONTENT

* Supporting Information S

Experimental details; ATR-FTIR and 2D GIWAXS data of evaporated films of PCBM; bilayer cross-section SEM; details of DSIMS image fitting and associated errors; specifics of the Boltzmann−Matano analysis; table and plots of dPCBM concentration-dependent diffusion coefficient. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 1006

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Author Contributions

(25) He, X.; Collins, B. A.; Watts, B.; Ade, H.; McNeill, C. R. Small 2012, 8, 1920−1927. (26) Treat, N. D.; Shuttle, C. G.; Toney, M. F.; Hawker, C. J.; Chabinyc, M. L. J. Mater. Chem. 2011, 21, 15224−15231. (27) Kozub, D. R.; Vakhshouri, K.; Orme, L. M.; Wang, C.; Hexemer, A.; Gomez, E. D. Macromolecules 2011, 44, 5722−5726. (28) Suzuki, K.; Horie, H.; Yamashita, Y.; Kataoka, Y. Appl. Phys. Lett. 1990, 57, 1018−1021. (29) Boltzmann, L. Ann. Phys. 1894, 289, 955−958. (30) Matano, C. Jpn. J. Phys. 1933/34, 8, 109−113. (31) Shewmon, P. G. Diffusion in Solids; McGraw-Hill: New York, 1963. (32) Diffusion in Polymers; Neogi, P., Ed.; Marcel Dekker, Inc.: New York, 1996. (33) Gomez, E. D.; Barteau, K. P.; Wang, H.; Toney, M. F.; Loo, Y. L. Chem. Commun. 2010, 47, 436−438. (34) van Bavel, S. S.; Sourty, E.; de With, G.; Loos, J. Nano Lett. 2008, 9, 507−513.

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

We thank the NSF SOLAR program for partial support of this work (CHE-1035292). N.D.T. acknowledges support from the ConvEne IGERT Program (NSF-DGE 0801627) and NSF Graduate Research Fellowship. Portions of this work were carried out using the MRL Central Facilities, which are supported by the MRSEC Program of the NSF under Award DMR-1121053; a member of the NSF funded Materials Research Facilities Network.

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dx.doi.org/10.1021/ma302337p | Macromolecules 2013, 46, 1002−1007