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1 Supporting Information Role of Molecular Weight Distribution on Charge Transport in Semiconducting Polymers Scott Himmelberger, Koen Vandewal, Zhuping Fei, Martin Heeney, Alberto Salleo* Mobility Model Derivation Below, we derive the simple mobility model described in the text: The charge carrier mobility µ is defined as the drift velocity v d in the presence of an electric field E = (1) For a given electric field, (2) Assuming the charge travels some arbitrary distance d in time t (3) We assume inter-molecular charge transport (pi-hopping) is rate limiting. Thus, the time is a function of the total number of hops taken N t as well as the time per hop t h (4) The number of hops depends on the number of short n L chains (low MW) and long n H chains (high MW) traversed by the charge = + (5) We assume that charges on long chains travel β times further than charges on short chains. This gives for the total distance d travelled: + (6)
2 We assume the number of short and long chains a charge traverses is proportional to the low MW mol fraction χ L and high MW mol fraction χ H respectively = (7) Combining (5)-(7), and solving for N t, (8) Therefore, (9) In order to relate the mass fractions of high w H and low w L MW materials to their mol fractions, we define α as the molar mass ratio of the high MW sample relative to the low MW sample. = (10) Substituting and solving in terms of the fraction of the high MW material, we obtain: (11) Simplifying, we are left with: (12)
3 Polymer Synthesis and Separation P3HT Synthesis and Fractionation: In a 3-necked flask, a solution of 2, 5- dibromohexylthiophene (3.26 g, 10 mmol) in anhydrous tetrahydrofuran (THF) (45 ml) was cooled to 0 o C. A solution of n-butylmagnesium bromide (4.8 ml of a 2.0 M solution in THF, 9.6 mmol) was added via syringe and the cooling bath was removed. After stirring for 30 min, the reaction was heated to reflux for 30 min. The heating bath was lowered so that the temperature dropped just below reflux, and the catalyst Ni(dppp)Cl 2 (54 mg) was added all at once as a solid. The reaction was refluxed for 4 h, and allowed to cool to RT. The solution was precipitated into a well stirred solution of methanol (80 ml)/25%. HCl (20 ml) and stirred for 1h. The resulting suspension was filtered directly into a soxhlet thimble. This was extracted (soxhlet) with methanol (12 h), acetone (12 h) and hexane (12 h). The solid in the soxhlet thimble was dried to afford a dark purple P3HT (1.26 g, yield: 75 %, Mn = 30 Kda, Mw = 52 Kda, PDI = 1.7). The crude P3HT was fractionated by preparative gel permeation chromatography (GPC) in chlorobenzene at 80 C, using a loading of ca. 100 mg of P3HT in hot chlorobenzene (5 ml). Fractions were collected manually and analysed by analytical GPC. Several preparative runs were performed, and fractions of similar Mn and polydispersity were combined, concentrated and re-precipated into methanol. Gel Permeation Chromatography: Number-average (Mn) and weight-average (Mw) were determined on an Agilent Technologies 1200 series GPC running in chlorobenzene at 80 C, using two PL mixed B columns in series, and calibrated against narrow polydispersity polystyrene standards. P3HT was fractionated on a preparative Shimadzu SEC system. The system comprises a DGU-20A3 degasser, an LC-20A pump, a CTO-20A column oven, an
4 Agilent PLgel 10 µm MIXED-D column and a SPD-20A UV detector. Fractions were collected manually. As the P3HT has a semistiff backbone and hence an increased hydrodynamic radius, the molecular weight is an overestimate relative to the polystyrene standard. By comparing MALDI-TOF-MS and GPC data, others have shown the GPC derived MW to be overestimated by a factor of (Fibonacci) Hovever, we reference the GPC derived MW in this manuscript to provide consistency with existing reports. All final fractions had a polydispersity (PDI) of 1.2. Figure S1. GPC elution traces of P3HT with different M n in chlorobenzene at 80 o C.
5 Paracrystalline Disorder The paracrystalline disorder (g) is defined as the variance of interplanar spacing (d) (Equation SI1). For relatively disordered systems, such as pi-stacked P3HT,it is related to the width of the pi-stacking peak ( q ) at q z ~1.7 (Equation SI2). = (S1) = (S2) Mobility Model Fit The model shows qualitatively the same trend as the measured mobility values (Figure 3). The hopping time t h was chosen to be a constant with blend ratio as the exact functional form of t h versus disorder is not known. The goodness of fits of the model with constant hopping time suggest that this factor does not significantly affect carrier mobility. As paracrystalline disorder increases linearly with % HMW however, introducing trap states into the polymer bandgap, we would expect the inter-chain hopping time t h to increase. The ratio of distance traveled on long chains relative to short chains β was allowed to vary in the fit and take on any value less than the ratio of molecular weights α. A significant portion of the films is composed of extended aggregated material (~45%) and the direction of the polymer backbone in the crystalline and amorphous regions is expected to be correlated due to the continuity of tie-chains from aggregates into the amorphous regions. In other semicrystalline semiconducting polymers the average polymer backbone orientation was found to differ on the order of ~10-15 over a ~40 nm length scale for polymers similar to P3HT. 1,2 Due to the large fraction of material in aggregates as well as the moderately high persistence length of P3HT,
6 which has been measured to be ~3.3 nm in a good solvent, 3 we assume the low MW P3HT (8 kda) is nearly fully extended. The values we find for β (Table 1) suggest that chains are fully extended in the 29 kda samples as well, with the extension beginning to saturate in the higher MW (42, 61 kda) fractions. This is in good agreement with studies on P3HT films and nanowires which have shown domain sizes to increase linearly before leveling off at ~30 kda as chain folds and entanglement begin to dominate. 4,5
7 Grazing Incidence X-ray Diffraction Images Figure S2. Grazing incidence X-ray diffraction images of P3HT blends
8 PESA measurements Figure S3. Photoelectron spectroscopy in air (PESA) measurements of high (42kDa) (a) and low (8kDa) (b) molecular weight P3HT. The ionization potential does not vary significantly for the low and high molecular weight P3HT films studied in this work.
9 Absorption Coefficient Spectra Shape Analysis Absorption coefficients were measured by performing transmission and reflection experiments with the aid of an integrating sphere. The spectral shape analysis developed by FC Spano was implemented by fitting the vibronic progression using Equation SI3 6 : 1!! exp (S3) where A is the absorbance as a function of the photon energy (E), S is the Huang-Rhys factor, m and n are differing vibrational levels, E 0-0 is the 0-0 transition energy, E p is the intermolecular vibrational energy, W is the excitonic bandwidth which is related to intra-chain disorder, and σ is the Gaussian linewidth which is related to inter-chain disorder.
10 Figure S4. Absorption coefficient spectra shape analysis for P3HT blends.
11 Activation Energy The activation energy of the high MW P3HT is not significantly different than that of the low MW P3HT. Figure S5. Activation energy extracted from temperature dependent mobility measurements for low (8kDa) and high (42kDa) P3HT
12 Figure S6. AFM phase and topography images respectively of 8kDa (a-b), 29 kda (c-d), 61 kda (e-f), kda (g-h), and kda (i-j) P3HT
13 References (1) Watts, B.; Schuettfort, T.; McNeill, C. R. Adv. Funct. Mater. 2011, 21, (2) Schuettfort, T.; Watts, B.; Thomsen, L.; Lee, M.; Sirringhaus, H.; McNeill, C. R. ACS Nano 2012, 6, (3) Cesar, B.; Rawiso, M.; Mathis, A.; François, B. Synthetic Metals 1997, 84, (4) Zhang, R.; Li, B.; Iovu, M. C.; Jeffries-EL, M.; Sauvé, G.; Cooper, J.; Jia, S.; Tristram- Nagle, S.; Smilgies, D. M.; Lambeth, D. N.; McCullough, R. D.; Kowalewski, T. J. Am. Chem. Soc. 2006, 128, (5) Liu, J.; Arif, M.; Zou, J.; Khondaker, S. I.; Zhai, L. Macromolecules 2009, 42, (6) Turner, S. T.; Pingel, P.; Steyrleuthner, R.; Crossland, E. J. W.; Ludwigs, S.; Neher, D. Advanced Functional Materials 2011, 21,
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