S2.1.1. Calculation of transient PIA anisotropy dependence on fullerene load The anisotropy is defined by Eq. 2.9, though, if the system under investigation consists of two materials the anisotropy cannot be recalculated as the sum of the anisotropies of the two components because anisotropy is not an additive quantity. Here we aim to verify if a simple approach of the two-component model (i.e. absorption fractions of the two materials) to describe the anisotropy, such as was used by Bakulin et al.31, is valid.
Let us define that PC71BM fraction in polymer:fullerene blends is equal to x. The value of x can range between 0 to 1, where 1 corresponds to 100%. Then the remaining fraction of the polymer is equal to 1-x. Let us assume that only the polymer provides the PIA response because the PC71BM response is negligibly small in the majority of blends, and was subtracted from the parallel and perpendicular components, respectively. Then the parallel component of the response (polarization of the response parallel with respect to polarization of the excitation pulse) is described by the following equation:
, (S2.1)
where and – are both parallel components of PIA coming from charges (positive charges) residing on the polymer. The difference between the and is that the former represents PIA response when charges appear after direct polymer photoexcitation while the latter represents the appearance of charge after the hole transfer from fullerene when the PC71BM is directly photoexcited. Similarly, perpendicular component of PIA polarization with respect to excitation polarization can be described the following way:
, (S2.2)
where and – are perpendicular components of PIA after photoexcitation of the polymer and PC71BM respectively.
The anisotropy dependence on the PC71BM fraction can be described in the following way based on equation 2.9:
(S2.3)
50
There are two boundary conditions: and . The boundary condition of gives the anisotropy value of pristine polymer . The two components of PIA, either parallel or perpendicular, are related and, therefore, one of them can be expressed through another. was expressed:
(S2.4)
An additional boundary condition that needs to be exploited, is the following equation which describes the PC71BM to polymer absorption contrast k by:
, (S2.5)
where the sum of parallel and perpendicular components and represent the isotropic response of PIA coming from a direct polymer excitation ( ) or after a PC71BM excitation ( ), respectively, referring to equation 2.8. eq. S2.5 essentially represents that isotropic component of fullerene absorption is equal to the isotropic component of polymer absorption multiplied by the PC71BM excitation selectivity k.
The eq. S2.5 was used to express :
. (S2.7)
Finally, the boundary condition of gives the anisotropy retained after the hole transfer (when the direct polymer excitation is negligibly small) , assuming that it is not exactly equal to 0. This boundary condition was used to express :
. (S2.8)
After substitution of , and the anisotropy is reduced to the following equation:
, (S2.9)
Direct photoexcitation of PC71BM followed by hole transfer to polymer results in the PIA response, which has hardly any correlation with the excitation polarization, therefore anisotropy is either equal to 0 or very small and the term Bkx can be neglected:
, (S2.9)
51 If anisotropy is normalized to 1 (by making A = 1) then it should strictly follow the polymer absorption fraction (eq. 2.3 and 2.4). This justifies the use of anisotropy as a measure to identify the share of photons, which are absorbed by the polymer.
S2.1.1.1. Compensation of high anisotropy effect due to partial exciton dissociation The anisotropy was used as a measure of the fraction of absorbed photons, which end up with the hole transfer process using eq. 2.4. We point out that eq. 2.4 is correct only when all PC71BM excitons have dissociated via hole transfer within the given pump-probe time delay. This conclusion implies that one should measure anisotropy at the longest possible pump-probe delay, however, the initial anisotropy of pristine polymer decreases with time.
Therefore, the contrast between the anisotropy of polymer and PC71BM excitation decreases with the delay and consequently the accuracy of the estimate decreases as well.
There is a much better approach to make the correct estimate without losing the accuracy. At short pump-probe delay, only the interfacial fraction of PC71BM excitons is dissociated at the donor-acceptor interface while the bulk excitons need some time to reach the interface. Therefore, effectively the polymer contribution to the anisotropy is exaggerated.
The blends with low PC71BM fraction (2-5%) are expected to have mostly dispersed PC71BM molecules. In such case majority of PC71BM excitons are located at the interface with polymer and the response is delayed only by the hole transfer time.
Ultrafast hole transfer time indicates extremely efficient exciton dissociation process.
Therefore, within 0.5 ps we can assume that all PC71BM excitons are dissociated in the blends with 2-5% of PC71BM. The PIA of these low PC71BM blends normalized to the total absorption gives the relative number, which corresponds to 100% efficiency of exciton dissociation. When the same normalization is applied to other blends the efficiency of exciton dissociation at 0.5 ps per absorbed photon can be estimated. Application of this procedure to parallel and perpendicular components of PIA allows recalculating the overall fraction of dissociated excitons using eq. 2.2. The remaining fraction of the response corresponds to the fraction of excitons which did not reach interface yet. This response of none-dissociated excitons can be added as a fixed value to the parallel component and perpendicular component of PIA at 0.5 ps (the value is the same for both the parallel and perpendicular components because the hole transfer results in zero anisotropy):
, (S2.10)
52 and
, (S2.11) where ΔISO is the remaining fraction of the response corresponding to none-dissociated excitons, and are modified parallel and perpendicular components. The corrected anisotropy is presented in the following equation:
. (S2.12)
Photoinduced anisotropy at 0.5 ps was calculated using the eq. S2.12 as an average between 0.25 ps and 0.75 ps and then presented in fig. 2.4.
S2.1.2. Spectroscopy details S2.1.2.1. Optical absorption
The pump-probe (nonlinear) spectroscopy begins with the analysis of the linear absorption data. The absorption spectra were measured for different polymer:PC71BM blends in order to retrieve information about the wavelength range where the PC71BM photoexcitation has significant excitation selectivity. The lowest PC71BM transition available can be seen in all absorption spectra as a bump at 680 nm (fig. S2.1). Fig. S2.1e inset demonstrates disappearance of red absorption shoulder (620 nm), which was attributed to RRe-P3HT nanocrystals26, 67, 68
, when PC71BM load changes from 60% to 70% (note that transition at 680 nm remains unchanged).
Drop casting method resulted in the dispersion of optical densities caused by the variation of film thicknesses (fig. S2.1 and S2.2). Pristine RRe-P3HT film exhibits higher measured OD (with absorption spectrometer) than blends with <20% of PC71BM (fig. S2.1g full squares). To prove that such overestimated OD is due to the scattering, an additional measurement was performed with the laser pointer with 660 nm wavelength. The laser beam passed the sample and the intensity was registered in silicon detector (fig. S2.1g open squares). The sample was placed next to the detector window to reduce light scattering. The measurement with the reduced scattering effect demonstrates that OD of pristine RRe-P3HT film is indeed lower than any blends with PC71BM.
53
OD Absorption spectrometer = 680 nm
RRe-P3HT
Fig. S2.1 Summary of linear absorption measurements of polymer:PC71BM blends:
a)-b) RRa-P3HT:PC71BM c)-d) MDMO-PPV:PC71BM e)-f) RRe-P3HT:PC71BM. Absorption spectra are represented in a), c) and e). Optical density: b) and f) at 680 nm; d) at 630 nm. The optical density of
54 b) MDMO-PPV:PC71BM and c) RRe-P3HT:PC71BM. Lines are guidelines for the eye.
There is a general tendency for the film thickness of the polymer:PC71BM blends prepared by drop casting method to decrease with the PC71BM load (fig. S2.2). RRa-P3HT demonstrates the sudden decrease of thickness when a small amount of PC71BM is added.
This behavior can be reasoned by the low substrate wetting effect (observed when the solution was drop cast) towards the pristine RRa-P3HT solution, whereas addition of PC71BM gradually increases substrate wetting. Due to the low substrate wetting effect the solution, which was initially evenly distributed across the whole surface of the substrate, collects in the center when the solvent evaporates. The further decrease of the film thickness of RRa-P3HT blends with an addition of PC71BM has a more gradual nature, similar to the MDMO-PPV and RRe-P3HT blends. The gradual decrease of the film thickness can be explained by the decrease of the viscosity of the solution when PC71BM is added. The change of the solution viscosity was intuitively expected since the PC71BM molecules are smaller than that of the polymer and have a round shape. Whereas polymer chains may entangle with each other in the solution and, therefore, the free movement in the solution is hindered. The thickness of the films has also a certain variation across the film (especially RRa-P3HT with small loads of PC71BM) and dispersion, which can be seen in fig. S2.2 as the scattering of the data points.
S2.1.2.2. Verification of a pump-probe overlap time-delay position
The hole transfer process was expected to be ultrafast (~30 fs)31 and, therefore, posed a tough requirement to control and characterize the pump-probe time-overlap position
a
55 accurately. Measurement of pump-probe time-overlap position was realized with a reference sample MEH-PPV:TNF, where the actual delay position of pump-probe time-overlap was estimated by the delay of the rising flank of the PIA response (fig. S2.3a). These two materials prepared by solution processing are known to form CT complex50, 61, 62, 64
. The pump pulse of the laser directly photoexcites the bound CT state between MEH-PPV and TNF. This CT state has an immediate response (within experimental time resolution). The pump-probe time-overlap was measured on MEH-PPV:TNF before and after each measurement of polymer:PC71BM blend, where the actual overlap position was taken as an average of these two measurements (“before” and “after”). Typically, the two measurements (“before” and “after”) of MEH-PPV:TNF exhibited pump-probe time-overlap drift by no more than 5 fs. Note that the resolvable delay of the half maximum amplitude of the response is not limited by the Gaussian width of the convoluted pump-probe overlap but by the signal to noise ratio (fig. S2.3a). This fact allowed observing the hole transfer time below the convoluted pump-probe overlap time-width. The measured PIA transients of polymer:PC71BM blends were corrected by the variation of pump-probe overlap positions.
The long-term time-overlap positions of pump-probe measurements are shown in fig. S2.3b.
The fluctuations of pump-probe time-overlap did not exceed ±15 fs within 14 hours of
Fig. S2.3 PIA transient (-ΔT/T) of MEH-PPV:TNF (symbols) and fits with different Gaussian widths of convoluted pump-probe overlap (lines) (a) and the variation of fitted zero position depending on the pump-probe measurement time in hours (b)
a)
b)
56
S2.1.2.3. PC71BM background response
Excitation of pristine PC71BM films resulted in weak but still detectable IR response (fig. S2.4). This response was subtracted from the PIA transients (fig. 2.2).This small response originated either from IR absorption of PC71BM anions generated by dissociation of excitons delocalized between two adjacent PC71BM molecules, or exciton dissociation at local (energetic) traps. Alternatively, the response might originate from the charge transfer excitons (see more detailed discussion in Chapter 4).
The PC71BM contribution to the response is negligibly small at small loads of PC71BM.
However, the PC71BM response has to be accounted for blends with higher PC71BM loads as it begins to interfere with the blend response, especially around zero delays. The PC71BM response can be described as a step-like function (within experimental time resolution). As the blends with higher PC71BM load exhibit a more delayed response dominated by the hole-transfer(consult fig. 2), the pristine PC71BM response pulls the initial rising flank of transients to the zero time thereby introducing systematic errors in the hole-transfer time. In addition, the PC71BM background response changes the transient amplitudes, albeit not very significantly.
0.0 0.5 1.0
Delay (ps)
0.0 0.5 1.0
0 1 2 3
-T/T/Absorbed_photon (arb. u.)
Delay (ps)
0.0 0.5 1.0
Delay (ps)
Fig. S2.4 The PIA transient of 100% PC71BM normalized to absorption and excitation density: parallel component (left), perpendicular component (middle) and isotropic component (right).
IR spectrum of the PC71BM response (Chapter 4, fig. 4.12) is clearly distinguishable from charge-induced absorption of, for instance, RRa-P3HT (see the discussion about PIA spectra in Chapter 4 and fig. 4.8) that potentially allows for their deconvolution in the frequency domain. However, a simpler method can be used if one realizes that PC71BM background has a non-negligible contribution only with high loads of PC71BM, and this background decreases with the decrease of PC71BM amount in the blend.
ISO
57 Based on the aforementioned observation, the following procedure was applied to account for the PC71BM IR response in the transients. The 100% PC71BM transients for parallel and perpendicular components were normalized by the number of absorbed photons and then were fitted with a step function. The share of PC71BM absorption of the excitation beam was calculated using the following relation:
(S2.13) where k is the already-known absorption contrast of PC71BM equal to 70 and 25 for RRa-P3HT and MDMO-PPV, respectively, 3 and 18 for RRe-RRa-P3HT blends with PC71BM loads of 0-60% and 70-90% respectively (k = 3 in 0-60% PC71BM blends is due to the CT state absorption as explained in section 2.5), x is the weight fraction of PC71BM, and is absorption of a particular blend. The normalized in such manner PC71BM background was subtracted separately for parallel and perpendicular components of the transients. After this, both isotropic and anisotropic components were calculated according to eq. 2.8 and 2.9 (parallel components in fig. S2.5 and perpendicular components in fig. S2.6).
The PC71BM background response, shown in fig. S2.5, demonstrates that this background is very likely overestimated for RRa-P3HT blends with a PC71BM load below 10%. We performed the measurement of PC71BM background response in diluted solution with OD ~0.3 (PC71BM molecules are isolated) and did not observe any resolvable response, i.e. the response is, at least, 2-orders of magnitude weaker than in the films (not shown). This measurement confirmed the assumption that only PC71BM aggregates give a response at our probe frequency. Since the blends of RRa-P3HT with low PC71BM load (< 10%) are expected to form mostly isolated islands of PC71BM molecules, therefore the PC71BM background is hardly expected to be present and we did not subtract it for these blends.
58 black lines represent the PC71BM background response.
59 black lines represent the PC71BM background response.
S2.1.2.4. Zero-time artifact
The nature of 30 fs decay in the PIA response (attributed to the zero-time spike) was investigated in order to find out if it can be avoided, for instance, by reducing the excitation intensity if the exciton annihilation occurs. This artifact was pronounced only for pristine MDMO-PPV polymer, whereas RRe-P3HT:PC71BM blends exhibited the presence of zero-time spike with PC71BM fractions 0÷5% (fig. 2.2, fig. 2.3, and fig. S2.7).
Fig. S2.7 demonstrates that the zero-time artifact does not influence the PIA response at delays longer than 250 fs. fig. S2.8 shows examples of the response of the RRe-P3HT:PC71BM blends. The response is shown as a dependence on excitation density at the maximum amplitude and at 3 ps pump-probe delay. It is clear that maximum amplitude and amplitude at 3 ps, both exhibit a linear dependence on excitation intensity up to the value of intensity that was chosen as measurement condition for pump-probe measurements of hole transfer. The linear dependence of the response amplitude on excitation intensity disapproves the presence of exciton annihilation process, which would have exhibited quadratic
60
dependence. The nonlinear dependence of the response appears at excitation densities
> 100 µJ/cm2 for maximum amplitude and at 3 ps delay.
Fig. S2.7 A demonstration of the influence of the zero-delay spike on the PIA response of MDMO-PPV, RRe-P3HT polymers and their blends with PC71BM –Symbols represent measured data points, solid black lines are fits composed of "slowly" ( > 1ps) decaying component (dashed blue lines) and 30 fs decaying component (dotted dark red lines).
0.00 0.01
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 0.00
0.08
-T/T
RRe-P3HT:PC71BM 5%
Max amplitude 3 ps
3 ps Max amplitude
RRe-P3HT:PC71BM 20%
Excitation density (J/cm2)
Fig. S2.8 The maximum amplitude of the RRe-P3HT:PC71BM response and the amplitude of this response at 3 ps as a dependence on excitation density: a) 5% of PC71BM and b) 20% of PC71BM.
Symbols are experimental data, lines represent the linear fits of the data.
The appearance of the zero-delay spike also known as “coherent artifact”85 can be explained using Feynman diagrams (fig. S2.9). The normal pump-probe measurement
b )
a )
a)
b)
61 involves the positive delay between the pump and the probe pulses: the molecule is photoexcited first and afterward it is probed for the change in absorption. This time gap between the pump and probe is depicted as the horizontal line in the fig. S2.9a and clearly separated Vis and IR transitions in fig. S2.9c. When the pump and probe pulses overlap, the regular pump-probe scheme depicted in fig. S2.9a and S2.9c is no longer valid, instead, the
“inverted” pulse sequence becomes possible. Here the pump and probe pulses create a two-photon coherence (virtual) state that is projected by the second interaction with the pump pulse onto the observed transient polarization (fig. S2.1b and S2.1d). As the two-photon coherence is extremely short-lived, the inverted pulse sequence does not survive longer than the pulse overlap region. Because the inverted process possesses the same χ3 origin as the pump-probe one, the linear excitation intensity dependence is maintained.
When the excitation density exceeds 100 µJ/cm2 the response becomes nonlinear in RRe-P3HT:PC71BM blends (fig. S2.8). One of the explanations for this saturation could be the appearance of exciton annihilation. The dependency of the response upon the excitation density at 100 ps for several RRe-P3HT:PC71BM blends (not shown) was checked, but saturation up to 75 µJ/cm2 (experimental conditions for measurement of hole transfer process) was not observed. Exciton annihilation probability increases with the delay time up to the lifetime of excitons because they have a chance to diffuse and meet each other.
Therefore, diffusion-mediated exciton annihilation should appear at significantly lower excitation intensity as compared to the annihilation that occurs immediately after exciton generation. In contrast to these expectations, the saturation appears for both the short and long pump-probe delays at similar excitation intensities, therefore rejecting the possibility of exciton annihilation. There is another possibility: a two-photon absorption, which can be a combination of two pump photons or pump and probe photons because both options give the total energy above the bandgap of the polymer. Although, considering the higher intensity of the pump pulse it is more likely that two photons from the pump pulse photoexcite the polymer.
62
Fig. S2.9 Feynman (a and b) and ladder (c and d) diagrams for pump-probe process (a and c), coherent spike (b and d).
S2.1.3. Global fit details
The global fit allows to model the experimental data assuming that some physical phenomena are not changing across the entire variation of PC71BM loads (fixed time constants), but only the contributions of each phenomenon change when PC71BM is added (variable amplitudes). Global fit revealed that ultrafast growth component, with a time constant of 30 fs, is present with the lowest PC71BM loads and its contribution to the overall
The global fit allows to model the experimental data assuming that some physical phenomena are not changing across the entire variation of PC71BM loads (fixed time constants), but only the contributions of each phenomenon change when PC71BM is added (variable amplitudes). Global fit revealed that ultrafast growth component, with a time constant of 30 fs, is present with the lowest PC71BM loads and its contribution to the overall