MC simulation results

The MC simulations were able to reproduce experimental data presented in fig. 3.2 (symbols) reasonably well. The simulation results shown in fig. 3.2 as solid lines demonstrate that the large PC71BM domains contribute negligible response (no exciton lifetime rise of the response is observed) and their surface indeed can be neglected, which means that these domains are spectroscopically invisible. The fact that the large PC71BM domains are spectroscopically invisible allows the detection of the volume fraction of large and small PC₇₁BM clusters, which was used as a fitting parameter in order to reproduce the amplitudes of the transients in fig. 3.2 (see S3.2 for more details).

The results of the simulations are summarized in fig. 3.5 as solid lines – the PC₇₁BM cluster sizes. The estimated PC₇₁BM cluster size varies from 2 nm to 7 nm. The global fit parameters resulted in energy disorder meV (consistent with other report³⁹) and exo-energetic exciton hopping rate ps^-1. Both parameters represent a statistical average value of the whole ensemble. The energy disorder σ determines the time delay position when the response starts to saturate because the further arrival of excitons becomes

a) b)

78

much less probable when these excitons are trapped. The exo-energetic exciton hopping rate k₀ determines how fast the excitons arrive at the interface, therefore, changing has a very similar effect to the change of the size of PC71BM cluster. The strong variation of does not make sense because PC₇₁BM exciton diffusion length has to be realistic (~5-6 nm^{40, 41}).

0 Monte Carlo simulations while the symbols represent estimates made from surface volume / total volume ratio. (a) represents RRa-P3HT blends, (b) MDMO-PPV blends, (c) RRe-P3HT blends.

Summarizing the results, the PC71BM load can be ascribed to three main categories: 1) the low PC71BM load – w ≤ 0.11; 2) the average PC71BM load – w = 0.25 ÷ 1.5; 3) the high PC71BM load – w ≥ 2. The low PC71BM load blends of RRa-P3HT and MDMO-PPV exhibit the steep growth of small PC71BM clusters up to the size of ~3 nm. Similar PC71BM content dependence should be present in RRe-P3HT blends¹⁴, however, experimental data does not exhibit growth of small PC71BM clusters up to w = 1 due to limited experimental accuracy as the PC₇₁BM excitation selectivity was too low (part of the absorption goes to the charge transfer state excitation as explained in Chapter 2). The growth of small PC₇₁BM clusters with further PC₇₁BM load appears to be rather slow in RRa-P3HT and MDMO-PPV blends as compared to low PC₇₁BM loads. On the other hand, the growth of PC₇₁BM clusters with increasing w of RRe-P3HT blends becomes comparable to that of RRa-P3HT. Note that the previously discussed disruption of nanocrystals of RRe-P3HT is reflected as the disappearance of the large PC71BM domains, shown in fig. 3.6a w = 1.5 ÷ 2.3.

The shortcoming of using the response from dissociated PC71BM excitons is that MC simulations cannot extract the particular size of large PC71BM domains where excitons do not reach the interface. The size of large PC71BM domains was obtained from the AFM for the

a)

b)

c)

spectroscopy

79 MDMO-PPV blends (fig. S3.8) and from STEM for the RRe-P3HT blends (fig. S3.9); the results are shown in fig. 3.6b.

Fig. 3.6 Simulated volume fraction and size of large the PC₇₁BM domains where most excitons do not reach the interface with a polymer. The top panel (a) represents the volume fraction while the bottom panel (b) shows the size of large PC₇₁BM domains (obtained from AFM and STEM measurements).

The large (> 15 nm) PC71BM domains start to appear in the MDMO-PPV and the RRe-P3HT blends for w > 0.5. Coincidently, the small clusters of PC71BM do not exhibit significant growth with an increase of w. It may seem that with increasing PC71BM load not only the size and density of the large (> 15 nm) PC71BM domains should increase but also that the small (≤ 7 nm) PC71BM clusters should grow in size substantially, especially for the MDMO-PPV blends with high PC₇₁BM loads. This unanticipated behavior can be explained in the following terms: when the PC₇₁BM load increases, the density of small PC₇₁BM clusters should increase; hence, these clusters would start to merge at some point forming large PC₇₁BM domains. Consequently, the size of small PC₇₁BM clusters would not increase substantially with the addition of extra PC₇₁BM but the density of large PC₇₁BM domains would definitely increase.

Another explanation for the slow growth of the small (≤ 7 nm) PC71BM clusters is that, in fact, these clusters are percolated with polymer chains or segments, therefore, effectively reducing their size. This effect is expected to be slightly more pronounced in the PC71BM:polymer blends as compared to the PC61BM:polymer because the PC71BM (unlike PC61BM) is a mixture of three isomers and hence, the PC71BM is expected to exhibit higher solubility and lower crystallinity, which consequently leads to higher spatial disorder.

Alternatively, it is possible that two PC71BM molecules might prefer to stick to each other a)

b)

80

entwining with their side chains already within a solution, before the drop-casted solution dries. Consequently, as PC71BM concentration in the solution would increase with an increase of PC₇₁BM, the probability of PC₇₁BM aggregation would also increase. This increasing probability of aggregation could account for the faster growth of PC₇₁BM clusters up to w = 0.25. As soon as w would become larger than 0.25, the growth of the small PC₇₁BM clusters would saturate, which could be caused by saturation of aggregation in the solutions used in this work (i.e. most PC₇₁BM molecules are paired). Formation of larger PC₇₁BM aggregates in the solution is not very likely. Therefore, further growth of PC₇₁BM clusters would be driven by aggregation during solution drying process, which would not be as steep as the initial aggregation occurring already in the solution.

It cannot be entirely excluded that excitons are delocalized over two or more isoenergetic PC71BM molecules (i.e. PC71BM nanocrystal³²) and dissociate immediately via hole transfer to the polymer. Therefore, the actual size of PC71BM clusters may be slightly larger than estimated. Referring to Kim et al.³² formation of PC61BM nanocrystals is not very pronounced with w ≤ 1 for MDMO-PPV and for RRa/RRe-P3HT blends. As was already indicated, the PC71BM is expected to be less likely to form nanocrystals as compared to PC61BM. Therefore, exciton delocalization should not play a significant role in underestimation of PC71BM cluster size at least for the relatively low PC71BM loads of w ≤ 1.

Moreover, due to the disappearance of the RRe-P3HT nanocrystals for w ≥ 1.5, RRe-P3HT becomes more amorphous, whereas PC₇₁BM molecules are highly soluble in the amorphous regions of P3HT as compared to the nanocrystalline regions.