Controlling Exciton Diffusion and Fullerene Distribution in Photovoltaic Blends by Side Chain Modification

The influence of crystallinity on exciton diffusion and fullerene distribution was investigated by blending amorphous and semicrystalline copolymers. We measured exciton diffusion and fluorescence quenching in such blends by dispersing fullerene molecules into them. We find that the diffusion length is more than two times higher in the semicrystalline copolymer than in the amorphous copolymer. We also find that fullerene preferentially mixes into disordered regions of the polymer film. This shows that relatively small differences in molecular structure are important for exciton diffusion and fullerene distribution.


Calculation of fraction of ordered phase (crystallinity fraction)
For estimating the fraction of aggregated polymer phase compared to amorphous polymer phase we analyzed the absorption spectra of blends with different ratios of amorphous polymer. Here we assumed isotropic distribution of polymer crystallites. Furthermore the amorphous polymer fraction in blends as well as for the pristine semicrystalline polymer (AnE-PVab) is assumed to have the same properties as the amorphous polymer (AnE-PVba). Hence the absorption spectrum of AnE-PVba is fitted onto the absorption spectra of all samples by stretching and compressing the spectra, matching a uniform shared slope at around 460 nm, see Figure S1 (left panel). 1 After fitting the spectra we subtracted the spectrum of amorphous AnE-PVba from the other spectra, revealing the absorption spectra of the polymer aggregates only, see Figure S1 (right panel). To finally estimate the crystalline polymer fraction, the integral intensities of absorption spectra Figure S1 left panel) were calculated. Subtracting the integral intensity of the pristine AnE-PVba absorption spectrum from the integral intensities of all other sample absorption spectra and dividing those values by the appropriate integral intensities of the sample absorption spectra revealed the fraction of aggregated polymer phase for all samples. The integral intensities and evaluated percentage crystallinity is given in Table S1. Figure S2 shows the crystalline polymer fraction as a function of AnE-PVba concentration. 24.0 0 Table S1: Calculated integral intensities of absorption spectra (see Figure S1 left) and the evaluated crystalline fraction of samples.

Calculation of quenching efficiency from PLQY ratio
The photoluminescence quantum yield (PLQY) of neat samples and samples containing 1 wt% PCBM were measured using a Hamamatsu integrating sphere C9920-02 luminescence measurement system using a excitation wavelength of 400 nm. The values of PLQY obtained are given in table S2 Then quenching efficiency was obtained

Time-resolved fluorescence quenching of mixed blends of amorphous, semicrystalline polymers with PCBM
The time-resolved fluorescence of mixed blends with different ratios of amorphous and semicrystalline polymers with small, known quantities of fullerene (PCBM) was measured and is shown in Figure S3. In all investigated blends, more fluorescence quenching is observed for higher concentration of the quencher. Furthermore, quenching in the pristine semicrystalline (AnE-PVab) polymer is more than in the pristine amorphous (AnE-PVba) polymer and blends of these two materials.
where is excited state lifetime, is diffusion coefficient. is Fӧrster radius and can be calculated from spectral overlap of absorption of acceptor and emission of donor as follows 2 = 0.2108 × [ 2 × × −4 × ] 1/6 ( 2) where is fluorescence quantum yield of donor (given above), 2 is orientation factor representing relative orientation of two dipoles, is refractive index of medium and is the spectral overlap factor and can be calculated from spectral overlap integral of normalized fluorescence intensity of donor and normalized absorption of the acceptor as follows where ( ) is the normalized fluorescence intensity of the donor, ( ) is the molar extinction coefficient of the acceptor and is the wavelength. By assuming = 0.67 for randomly oriented chromophores and = 1.49, we obtained = 2.02 ± 0.11 for semicrystalline (0% amorphous) and = 1.64 ± 0.09 for amorphous (100% amorphous) polymer using equation S2. where is total number of quenching sites 3 and is excited state lifetime. We know all parameters in equation S4 except . Hence by fitting experimental data after 350 ps with equation S4 (shown in Figure S5), we obtained a value of diffusion coefficient of (5.9 ± 0.6) × 10 −4 2 / for AnE-PVab (0% amorphous) and (2.6 ± 0.3) × 10 −4 2 / for AnE-PVba (100% amorphous). Then by using the value of , the value of quenching radius ( ) of 0.9 ± 0.2 nm is obtained for amorphous and 0.8 ± 0.2 nm for semicrystalline polymer using equation S1.

Determination of number of quenching sites in amorphous region of blends
The number of quenching sites in the amorphous region is calculated as where is total number of quenching sites 3 and is number of quenching sites in the semicrystalline region.
where is the volume of semicrystalline region and is concentration of quencher in the semicrystalline region. The value of is determined by experimental data after 150 ps (see Figure 4).
By combining the equation S5 and S6, the value of is determined for each blend and is given in table S3.

Determination of concentration of quencher in amorphous region for blend of 90% amorphous polymer
In order to verify the quantitative information about the concentration of quencher in the amorphous region, we measured time-resolved fluorescence in blends of 90 % amorphous polymer with small, known quantities of fullerene (PCBM) by selecting an emission window from 600 to 611 nm (where most of the emission is coming from the amorphous polymer). The resulting natural logarithm of ratio of PL obtained from emission of blue side for the blends of 90% amorphous polymer is plotted in Figure S6. We selected this blend for investigation because the energy transfer from amorphous to semicrystalline in other blends is very fast (see  Table S3).