Temperature Dependence of the Diffusion. Coefficient of PCBM in Poly(3-hexylthiophene)

Transcription

1 Supporting Information Temperature Dependence of the Diffusion Coefficient of PCBM in Poly(3-hexylthiophene) Neil D. Treat,, Thomas E. Mates,, Craig J. Hawker,,, Edward J. Kramer,,, Michael L. Chabinyc, Materials Department, Materials Research Laboratory, Department of Chemistry and Biochemistry, Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States Organic solar cells; fullerene-polymer miscibility; poly(3-hexyl thiophene); diffusion coefficient Fabrication and Characterization of Evaporated dpcbm P3HT (BASF, Sepiolid P200) was dissolved in chlorobenzene at a concentration of 15 mg/ml and stirred overnight at 90 C in a N 2 filled glove box. Silicon substrates coated with 150 nm of thermal oxide were sequentially cleaned by ultrasonication in acetone, 2% wt soap:di H 2 O, DI H 2 O, and isopropanol for 15 min respectively and dried in a stream of N 2 gas. The P3HT solution was spin coated on these substrates in a N 2 filled glovebox at 2000 rpm for 40 s and were thermally annealed at 150 C for 20 min. The dpcbm films were thermally evaporated on cleaned SiO 2 /Si substrates at a pressure of ~ 10-7 torr and rate of 0.3 Å/s to produce a final thickness of 60 nm. Powder and evaporated samples of PCBM were characterized with ATR- FTIR and the ester stretch from the PCBM at 1736 cm -1 and 1733 cm -1 for the powder and thin film respectively were observed (Figure S1) signifying no observable degradation occurred during the evaporation. This conclusion also agrees with other reports showing that the electronic properties and optical absorption of PCBM is unchanged by thermal evaporation. 1, 2 Grazing 1

2 incidence wide angle X-ray scattering from the PCBM film showed only a diffuse, isotropic scattering ring centered at ~1.4 Å -1 (Figure S2) characteristic of disordered PCBM. The P3HT film was floated off the SiO 2 -coated substrate onto the surface of a dilute HF bath which was then exchanged with DI water and the P3HT film was finally lifted off the water surface by the PCBM/SiO 2 /Si film on substrate creating the final terraced monolayer-bilayer structure (Figure S3). The samples were then thermally annealed in a N 2 filled glove box on a preheated hotplate (which had been calibrated with an IR thermometer and thermal probe) at various temperatures and times and were cooled rapidly by placing these on a room temperature metal surface. Figure S1. Attenuated total reflectance Fourier transformed infrared (ATR-FTIR) spectrographs of a PCBM powder (black trace) and evaporated PCBM thin film (red trace). 2

3 Figure S2. 2D grazing-incidence wide-angle X-ray scattering of a representative sample of evaporated dpcbm. Figure S3. Schematic representation of the terraced monolayer-bilayer sample (bottom) and corresponding cross-section scanning electron microscopy images corresponding to the P3HT:PCBM/PCBM bilayer (top left) and P3HT:PCBM region of a sample heated at 110 C for 120 min. 3

4 DSIMS Depth Profiles Figure S4. 2 H depth profiles collected with DSIMS in the bilayer portion of a terraced monolayer-bilayer P3HT/dPCBM films annealed at 50 C, 70 C, 90 C and 110 C for 255 min, 242 min, 180 min, and 120 min respectively. The annealing times were selected such that the dpcbm remained disordered. Figure S5. Depth profiles collected with DSIMS in the bilayer portion of a terraced monolayerbilayer P3HT/dPCBM films annealed at 110 C for 30 min. 4

5 Figure S6. Depth profiles collected with DSIMS in the bilayer portion of a terraced monolayerbilayer P3HT/dPCBM films annealed at 110 C for 60 min. Figure S7. Depth profiles collected with DSIMS in the bilayer portion of a terraced monolayerbilayer P3HT/dPCBM films annealed at 110 C for 120 min. 5

6 Figure S8. 2 H depth profiles collected with DSIMS in the bilayer portion of a terraced monolayer-bilayer P3HT/dPCBM films annealed at 110 C for 30 min (orange circles), 60 min (blue squares), and 120 min (green triangles). Figure S9. Phase diagram for the volume fraction of disordered dpcbm miscible in P3HT as a function of annealing temperature for this report (orange squares) and previous report (blue circles). 6

7 Fit of 2 H Signal from DSIMS Image A DSIMS instrument (Physical Electronics 6650) equipped with an O + 2 ion beam and a quadrupole mass analyzer was used to quantify the 2 H concentration in a 300 x 300 µm area (Figure S9). The DSIMS images were collected over a depth of approximately 5 nm (i.e. 50 s etch time with an average etch rate of 0.1 nm/sec). These images were subdivided into 20 µm x 300 µm areas and the pixels summed to give a plot of counts with respect to distance, and averaged over three areas (Figure S10). The counts were then normalized to volume fraction by normalizing counts corresponding to the pure PCBM film to unity. Figure S10. DSIMS image of a 300 x 300 µm area of a sample heated at 110 C for 120 min. The dashed box represents an area of 20 x 300 µm used to determine the 2 H counts verses distance. 7

8 Figure S11. Plot of normalized d-pcbm volume fraction versus distance normalized by the square root of time (µm/s1/2) (i.e. the Boltzmann transformation) at a) 50 C, b) 70 C, c) 90 C, and d) 110 C for various amounts of time. 8

9 1D Solution to Fick s Second Law The case of diffusion in one dimension was used to model the lateral diffusion in the terrace monolayer-bilayer samples at 50 C and 70 C. This 1D solution to Fick s second law is expressed as: C x, t = C 0 erfc x 2 Dtπ where C is concentration, D is the diffusion coefficient that in this case is independent of composition, x is distance, and t is time. Figure S12 represents the raw data and the 1D solution for Fick s 2 nd law for lateral diffusion profiles collected from the terraced monolayer-bilayer samples annealed at 50 C and 70 C for 255 min and 242 min respectively. These solutions give a concentration independent diffusion coefficient of dpcbm in P3HT of 2.2 x and 5.7 x cm 2 /s at 50 C and 70 C. Figure S12. Plot of d-pcbm volume fraction versus distance for samples annealed at 50 C (black diamonds) for s and 70 C (green triangles) for s. The concentration profiles given by the 1D solution to Fick s 2 nd Law with D = cm 2 /s at 50 C and cm 2 /s at 70 C are represented by the solid lines. 9

10 χ 2 Goodness-of-fit Test The χ 2 goodness-of-fit test was used to determine the most accurate fitting expression, specifically, comparing between the 1D solution to Fick s second law and the empirical exponential fit function used for the Boltzmann-Matano analysis. This test is given by the following expression: χ! =! (O! E! )! E!!!! where O i is the measured 2 H counts and E i is the value given by the fit. Lower values for χ 2 indicate more accurate fits. The summary of the χ 2 goodness-of-fit test as a function of annealing temperature can be found in Figure S13. The samples annealed at 90 C and 110 C exhibited lower values for χ 2 for the exponential fit revealing a concentration dependent diffusion for PCBM at these annealing temperatures. Figure S13. Plot of the χ 2 goodness-of-fit test as a function of annealing temperature. Note that lower values of χ 2 indicate a more acceptable fit. 10

11 Boltzmann-Matano Analysis The dpcbm volume fraction as a function of distance was collected at 90 C and 110 C were fit empirically with an exponential form: C = A e!!" where C is the dpcbm volume fraction, x is distance, and A and I are the fit parameters. All fits had a coefficient of determination (R 2 ) with a value greater than The raw data normalized by the square root of the annealing time for all annealing times and temperatures comprise a single master curve (Figure S11), which signifies that the diffusion coefficient is only a function of volume fraction. Therefore, the Boltzmann-Matano analysis 4, 5 can be used to determine to concentration dependent diffusion coefficient. Presented below is the derivation of the Boltzmann-Matano analysis for the specific case used in this study, which allows for the quantification of the temperature dependent diffusion coefficient as a function of dpcbm volume fraction. For our sample geometry, the boundary conditions are that C = C 0 at all distances of x < 0 at all annealing times. The raw data were fit by an empirical exponential expression: rearranged to give: C! = Ae!!" x = ln C A I The Boltzmann-Matano Analysis is given by: thus, D C! = 1 2t d dc x d dc x = 1 C! I!! x dc! and 11

12 !! x dc! = C 1 ln C A I Therefore, the Boltzmann-Matano analysis for an exponential fit is: D C! = 1 2t 1 C! I C 1 ln C A I The diffusion coefficient as a function of d-pcbm volume fraction from all annealing times and temperatures is tabulated in Table S1. Table S1. Tabulated diffusion coefficients averaged over three annealing times as a function of volume fraction and annealing temperature. The composition independent diffusion coefficient Volume Fraction Diffusion Coefficient (cm 2 /s) 90 C 110 C x x x x x x x x x Composition Independent D 1.7 x x

13 Activation Energy Calculation It was assumed that the diffusion process could be modeled by an Arrhenius equation given by: D = D! exp E! RT where D is the diffusion coefficient, D 0 is the maximum diffusion coefficient at infinite temperature, E A is the activation energy for diffusion, T is the temperature, and R is the gas constant. References 1. Labram, J. G.; Kirkpatrick, J.; Bradley, D. D. C.; Anthopoulos, T. D., Physical Review B 2011, 84 (7). 2. Chu, C. W.; Shrotriya, V.; Li, G.; Yang, Y., Applied Physics Letters 2006, 88 (15). 3. Treat, N. D.; Brady, M. A.; Smith, G.; Toney, M. F.; Kramer, E. J.; Hawker, C. J.; Chabinyc, M. L., Advanced Energy Materials 2011, 1 (1), Boltzmann, L., Annalen der Physik 1894, 289 (13), Matano, C., Jpn. J. Appl. Phys , 8,