Data analysis 1. Charge yield

Fig. 3.3 shows the PC₇₁BM exciton dissociation to charges yield obtained from the maximal amplitudes of charge-induced response (fig. 3.2). Blends with the low PC₇₁BM/polymer weight ratio w, for instance, w ≤ 0.4, exhibit a high yield because PC₇₁BM clusters are either small or not present at all (i.e. there are only isolated PC₇₁BM molecules dispersed in the polymer). Taking into consideration ultrafast hole-transfer (HT) time (~30 fs)²⁵ (see also Chapter 2), we can assume that most excitons, very close to 100%, dissociate into charges for the blends with low PC₇₁BM content, e.g. w = 0.02. The charge yield (fig. 3.3) remains constant within experimental accuracy up to w = 0.4 for all PC71BM:polymer blends. Therefore, we assign the signal at low PC71BM content to the exciton-to-charges yield of unity, taking the average amplitude (shown in fig. S3.2) for blends with w = 0.02 ÷ 0.4 as the normalization factor.

Fig. 3.3 PC₇₁BM charge yield calculated from the amplitudes of the pump-probe transients (fig. 3.2) for the blends of (a) PC₇₁BM:RRa-P3HT, (b) PC₇₁BM:MDMO-PPV and (c) PC₇₁BM:RRe-P3HT. Symbols represent the experimental data, the lines present the results of the Monte-Carlo simulations. The red open symbols represent amplitudes at 1 ps, which are assigned to dissociation of the interface excitons, the green closed symbols are the maximal amplitudes, associated with all excitons that have reached interface, and the blue semi-closed symbols are the difference of the two, i.e. the excitons which originate from the bulk (i.e. outside the interface) of the PC71BM clusters.

b) a)

c)

spectroscopy

73 Further increase of w results in a decrease of the overall charge yield due to the growth of PC71BM clusters, which prevents a significant number of excitons from reaching an interface. The dependence of the yield on w for the three polymers blended with the PC₇₁BM is noticeably different. The RRa-P3HT blends (fig. 3.3a) do not exhibit clearly observable exciton losses even with the highest content of PC₇₁BM (green closed symbols in fig. 3.3a).

High charge yields in the RRa-P3HT blends signify good intermixing between the PC₇₁BM and the RRa-P3HT with mostly small PC₇₁BM clusters forming up to w = 9. In contrast, the MDMO-PPV blends (fig. 3.3b) demonstrate a significant loss of exciton dissociation efficiency already at the PC71BM content of w~1.5. This is not surprising since MDMO-PPV blends with fullerene derivatives are known to form large fullerene domains above certain acceptor weight fraction (fig. S3.8), depending on the preparation method^{7, 25-28} (e.g. w = 1 to 4).

The PC71BM:RRe-P3HT blends (squares in fig. 3.3c) exhibit a decrease of the yield at w = 0.67 ÷ 1.5 similarly to the MDMO-PPV blends but to a significantly smaller extent. The observed difference of charge yield between the RRa-P3HT and the RRe-P3HT was expected because the morphology of the films that are formed by these two polymers is very different:

the film of RRa-P3HT is completely amorphous, but the film of RRe-P3HT forms semi-crystalline domains. The molecules of RRe-P3HT form nanocrystals prior to the aggregation of PC71BM during solution drying process²⁹. Hence, most of the PC71BM molecules can only be dispersed in the disordered regions outside the nanocrystals of the RRe-P3HT film³⁰. Consequently, PC₇₁BM molecules have less volume to be dispersed within and, as a result, the PC₇₁BM is pushed to aggregate into the clusters. Therefore, we assign exciton losses (fig.

3.3c) in the blends of RRe-P3HT with w = 0.67 ÷ 1.5 to the formation of the PC₇₁BM cluster sizes comparable or larger than the exciton diffusion length.

Extrapolating this trend, one would expect the charge yield from the RRe-P3HT blends to further decrease above w = 1.5, however, the yield suddenly increases at w = 2.3. This unexpected and significant turn indicates an abrupt change in the nanostructure. The confirmation of this comes from the fact that linear absorption spectra demonstrate the disappearance of the red absorption shoulder of the RRe-P3HT near these blend compositions (fig. S2.2e in Chapter 2) associated with the absorption by the RRe-P3HT nanocrystals³¹. Others have also observed disruption of the RRe-P3HT nanocrystal at similar donor:acceptor compositions^{32, 33}. Hence, the morphology of the RRe-P3HT blends becomes more similar to

74

that of the RRa-P3HT blends for w ≥ 2.3 because most of the nanocrystals are no longer present.

Summarizing the discussion above the three PC₇₁BM:polymer blends exhibit very different charge yield as a function of the blend composition, which is reflected in the amplitude of the charge-induced response. Interestingly enough, the charge yield is sensitive to subtle changes in the morphology like the disappearance of nanocrystals in RRe-P3HT. To analyze the particular characteristic size of PC₇₁BM domains, the dynamics of exciton diffusion should be considered.

3.2.2.2. Exciton dissociation represents their diffusion

The characteristic size of the PC71BM cluster can be estimated on the basis of excitons that dissociate via HT almost immediately after photoexcitation as they are generated at the interface with polymer (see also Chapter 2), and excitons, which are delayed because they are generated in the bulk of PC71BM and, therefore, have to diffuse prior to the dissociation.

These two very different time-scales, namely the HT (< 1 ps²⁵) and the exciton diffusion (10-100 ps^{20, 34}), allow calculation of the fraction of excitons, which are generated at the interface with respect to the total number of excitons, by simply comparing the transient amplitudes at the respective times. This, in turn, provides a unique opportunity to make an estimate of the characteristic PC71BM cluster size as the ratio between the surface (interfacial) excitons and the entirety of (surface plus bulk) excitons through the surface-to-volume ratio. This ratio is inversely proportional to the linear size of the PC₇₁BM cluster.

This idea is illustrated in fig. 3.3. The charge yield at 1 ps (red open symbols) and 100 ps (green closed symbols) delays is related to the interfacial and all harvested excitons, respectively. The difference between the two represents the bulk excitons (semi-open blue symbols in fig. 3.3). The general observation of all blends studied in this work is a decrease of the share of interfacial excitons when PC₇₁BM content increases, which is assigned to a larger number of excitons harvested from the bulk of PC₇₁BM clusters.

RRa-P3HT blends show the increasing percentage of the dissociated bulk excitons when w increases: the increase is steep for low w = 0.02 ÷ 0.43, while the increase becomes slower with larger w > 0.5. MDMO-PPV blends (triangles in fig. 3.3b) exhibit the steep increase of the bulk exciton fraction only in the range of w = 0.02 ÷ 0.05 when PC71BM content is low. These blends with further increase of PC71BM content w = 0.05 ÷ 1 show an almost constant share of dissociated bulk excitons while the portion of excitons created at the

spectroscopy

75 interface as well as the total dissociation yield decrease. Fig. 3.3c shows the charge yield for RRe-P3HT blends (fig. 3.3c). The share of excitons created at the interface in these blends follows similar dependence on PC₇₁BM load as the total yield of dissociated excitons. The dissociated bulk exciton fraction increases with the amount of PC₇₁BM for w > 1 similarly to RRa-P3HT.

The RRe-P3HT blends, unlike the RRa-P3HT and the MDMO-PPV, do not show discernible dissociation of bulk excitons with w < 1.5 despite the fact that the overall charge yield decreases. When excitons are lost in the diffusion process, the appearance of extra charges is limited by the lifetime of excitons. Therefore, with the decrease of overall response the rise of the response limited by the finite (singlet) exciton lifetime (~500 ps in fig. S3.4, which is also consistent with fig. 4.6 in Chapter 4 and other reports^{20, 35}) is also expected.

However, the experimental data presented in fig. 3.2 clearly exhibit charge-induced response saturation within the first 100 ps, which is much shorter than the exciton lifetime. This observation poses a question: why does the response saturate much earlier than exciton lifetime limitation?

This seemingly contradictory observation can be resolved in the following way. The majority of PC71BM clusters that produce charges are smaller than the exciton diffusion length so that the leveling-off of the experimental transients is limited by the cluster size but not the exciton lifetime. In turn, the loss of charge yield is caused by the PC71BM domains, which are so large that they contribute a negligible number of bulk excitons to the overall charge yield. Such a situation is only possible with a bimodal distribution of the characteristic PC₇₁BM cluster sizes that are very different from each other. The bimodality can be explained by the concept of hierarchical morphology, present in the BHJ. The concept of hierarchical morphology is based on large phase separated fullerene domains that are surrounded by the polymer matrix, which contains dispersed fullerene molecules and small clusters30, 36, 37

. This argument is also applicable for the MDMO-PPV blends, which also exhibit a saturation of charge-induced response (charge yield) together with the decreasing overall amplitude. A more detailed analysis will be presented below.

3.2.3. Size of PC71BM aggregates