Quantitative insights into the phase behaviour and miscibility of organic photovoltaic active layers from the perspective of neutron spectroscopy

We present a neutron spectroscopy based method to study quantitatively the partial miscibility and phase behaviour of an organic photovoltaic active layer made of conjugated polymer:small molecule blends, presently illustrated with the regio-random poly(3-hexylthiophene-2,5-diyl) and fullerene [6,6]-Phenyl C$_{61}$ butyric acid methyl ester (RRa-P3HT:PCBM) system. We perform both inelastic neutron scattering and quasi-elastic neutron scattering measurements to study the structural dynamics of blends of different compositions enabling us to resolve the phase behaviour. The difference of neutron cross sections between RRa-P3HT and PCBM, and the use of deuteration technique, offer a unique opportunity to probe the miscibility limit of fullerene in the amorphous polymer-rich phase and to tune the contrast between the polymer and the fullerene phases, respectively. Therefore, the proposed approach should be universal and relevant to study new non-fullerene acceptors that are closely related - in terms of chemical structures - to the polymer, where other conventional imaging and spectroscopic techniques present a poor contrast between the blend components.


Introduction
Excitons, generated upon light absorption in conjugated polymers, are known to dissociate into free charges in the presence of an electron acceptor material. Bulk heterojunctions made of polymer donor and small-molecule acceptor materials constitute the active layer of organic solar cells. The microstructure of such blends is complex with most likely three phases, a small-molecule rich phase, an amorphous polymer-rich phase and if the polymer is semi-crystalline, a pure crystalline polymer phase. 1 Only few polymers such as poly [2,5-bis(3-tetradecylthiophen-2-yl)thieno [3,2-b]thiophene] (PBTTT) 2 are known to co-crystallise with fullerene acceptors. Because of the asymmetry of the donor and acceptor molecular weights, the small molecule rich phase is nearly pure. The amorphous polymer-rich phase is beneficial for charge separation 3 while the presence of nearly pure percolated donor and acceptor domains are beneficial for the transport of charges generated at the donor:acceptor heterojunction to the electrodes.
If crystallinity is relatively simple to monitor by methods such as X-Ray diffraction, the composition of the amorphous mixture of the blends 4,5 as well as changes in conformation with respect to the neat materials is more difficult to access. 6,7 Although crystallinity has been shown to improve charge transport 8 and potentially lead to extra driving force for charge separation by lowering the electronic energy levels, 2 a spinodal-type decomposition emerged as a new picture for phase separation at length scales directly relevant to the operation of the devices, [9][10][11] with the coarsening of this phase separation directly linked to burn in degradation mechanisms. 10 The crucial role of the Flory-Huggins interaction parameter (χ) in controlling phase behaviour, i.e. miscibility in the amorphous phase has been emphasised and related to solar cell efficiency. 11,12 χ is both composition-and temperature-dependent, and is related to the thermodynamical stability of the blend. However, the formation of the bulk heterojunction proceeds through solution processing. 13 Thus, the final microstructure is not thermodynamically stable but kinetically trapped. Crystal seeds of small molecules and more or less large crystals of the polymer may form in the solution depending on the quality of the solvent for each component of the blend. 14-16 Moreover, liquid-liquid demixing may occur during solvent evaporation which could contribute to enhance phase separation. Figure 1: (a) Schematic illustration of the quantities extracted from the neutron spectroscopic measurements. From the measured dynamical structure function, S(Q, E) (color coded map), at 360 K using IN6, the diffraction pattern (left), QENS spectrum, and low-energy INS spectrum (bottom) are obtained. The mid-to-high energy vibrational spectrum (bottom right) was measured at 10 K using IN1-Lagrange. (b) Total, incoherent and coherent macroscopic neutron cross-sections (Σ) as a function of h-PCBM concentration in the presently studied samples. The samples represented by scatter points are h-RRa-P3HT:h-PCBM at 296 K (0 wt%, 20 wt%, 75 wt% and 100 wt% h-PCBM) and d-RRa-P3HT:h-PCBM at 360 K (0 wt%, 35 wt%, 50 wt%, 100 wt% h-PCBM). The macroscopic neutron cross-sections are extracted from the QENS data as explained in Supporting Information.
Previously, we used a combination of quasi-elastic neutron scattering (QENS) measurements 17 and molecular dynamics (MD) simulations 18 to investigate the impact of each com-ponent of a blend of regio-regular poly(3-hexylthiophene-2,5-diyl) (RR-P3HT) and fullerene [6,6]-Phenyl C 61 butyric acid methyl ester (PCBM) on their respective dynamics. We observed that, upon blending with PCBM, the QENS signal of P3HT is narrowing, while upon blending with RR-P3HT, the QENS signal of PCBM is broadening. We did interpret these observations as a signature of the frustration of RR-P3HT and plasticization of PCBM upon blending, respectively. The frustration of RR-P3HT was also observed by other groups on a different time scale. [19][20][21] Our MD simulations suggested that these changes were due to the partial miscibility of P3HT:PCBM, in particular the formation of an amorphous mixture of P3HT:PCBM. MD simulations further revealed a conformational change of P3HT chain to accommodate PCBM with enhanced cofaciality between the polymer thiophene rings and the PCBM cage. This has further been supported by Zheng et al., whose MD simulations pointed towards the same cofaciality between P3HT and PCBM. They calculated the transfer integrals between P3HT and PCBM in such arrangement, 22 concluding that the enhanced cofaciality was beneficial for the charge separation processes in organic solar cells. To gain deeper insights, we use the deuteration technique to vary the contrast between the polymer and the fullerene. In the following, hydrogenated and deuterated materials will be labeled with the prefix h-and d-, respectively. The different sample compositions and their neutron cross sections are presented in Figure 1 b. We propose to take advantage of the difference of neutron cross sections between conjugated polymer and fullerene to evaluate the miscibility limit of fullerene within the amorphous polymer-rich phase. The neutron spec-troscopy based method presently described should be universal and relevant to study blends with new non-fullerene acceptors that are closely related in terms of chemical structures to the polymer, which otherwise lead to a poor contrast between the blend components when using conventional imaging and optical spectroscopy techniques. 23

Results and discussion
Evaluating the phase composition of the blends Having determined the macroscopic densities (see Supporting Information) of the neat polymer and fullerene phases, Σ RRa−P 3HT and Σ P CBM (Figure 1 b), respectively, we can proceed with modelling the QENS data to gain quantitative insights into the concentrationdependent phase behaviour, as shown in Figure 3 a and b. RRa-P3HT is fully amorphous and thus, it is reasonable to assume that the studied samples with an overall PCBM concentration higher than the miscibility limit, µ, exhibit two phases; a nearly pure h-PCBM phase and an amorphous RRa-P3HT rich phase. The QENS signal can, therefore, be expressed for an overall h-PCBM concentration c 0 larger than µ as follow: where S(c 0 , E, Q) is the concentration-dependent total dynamical scattering function, S P CBM (E, Q) is the dynamical scattering function of the PCBM phase and S mix (µ, E, Q) is the mixedphase dynamical scattering function at the miscibility limit. Below the miscibility limit µ, it is reasonable to assume that we have a solid solution (amorphous mixture) and we assume that: where S mix (c 0 , E, Q) is the concentration-dependent dynamical scattering function of the mixed-phase below the miscibility limit and S RRa−P 3HT (E, Q) is the dynamical scattering function of the RRa-P3HT phase. In order to describe continuously the change and evolution in phase behaviour, we use logistic functions with a large k parameter to approximate step functions, so the previous equation becomes: The two quantities to fit are the miscibility µ and the scattering intensity at the miscibility limit S mix (µ, E, Q). We fit successfully the QENS spectra using this model ( Figures 3 a   and  Furthermore, we found that as expected and supported by other techniques, the miscibility is increasing slightly with temperature. 1 The observed difference in the miscibility limits obtained at 296K for h-RRa-P3HT:h-PCBM and d-RRa-P3HT:h-PCBM can be attributed to factors like deuteration, difference in molecular weight of the two polymers and the difference in regioregularity (Table 1). Interestingly, this simple model assuming two phases above the miscibility limit captures well the microstructure of the blends, hence allowing us to extract the QENS spectra at the miscibility limit for each blend at different temperatures ( Figures   3 c and d). The further narrowing of the QENS spectra of h-P3HT:h-PCBM for overall PCBM concentrations larger than the miscibility limit is not due to an extra frustration of the RRa-P3HT but to the presence of the almost neat crystalline PCBM phase.

Monitoring simultaneously miscibility and microstructure
The phase separation can be enhanced by the crystallisation of one of the blend components; here, the PCBM phase. By averaging the S(Q, E) signal in energy, we can extract the neutron diffractograms of the samples, therefore allowing us to study miscibility and crystallisation of PCBM simultaneously (Figure 4). The background in the diffractograms presented in    The neutron spectroscopy measurements were performed using the direct geometry, cold neutron, time-of-flight, time-focusing spectrometer IN6, and the hot-neutron, inverted geometry spectrometer IN1-Lagrange at the Institut Laue-Langevin (ILL, Grenoble, France).
Data were reduced, treated and analysed in a similar way as was done in our previous related works. 17,26 DFT-based quantum chemical isolated molecule and solid-state periodic calculations were performed using Gaussian 16 27 and Castep, 28 respectively. For the isolated molecules, the functional/basis-set b3lyp/6-311g(d,p) was chosen. 29 For the solid-state periodic calculations, the functional PBE 30 with van der Waals corrections 31 were used. Full computational details can be found in reference. 26

Conclusions
We presented a neutron spectroscopy based methodology to study phase behavior and morphology of the blend system P3HT:PCBM. We used a variable PCBM composition approach and deuteration technique for P3HT to determine the miscibility limits of the fullerene within the regio-random (amorphous) form of P3HT (RRa-P3HT). Temperature-dependent and composition-dependent quasi-elastic neutron scattering and inelastic neutron scattering measurements were performed to evaluate the phase composition and behaviour of the blends, to monitor simultaneously their miscibility and microstructure evolution and to probe changes in their morphology. This approach enabled us to resolve the evolution of the microstructure and morphology that are correlated with changes in structural dynamics of the polymer and fullerene upon blending. Our approach using single-molecule and solid-state periodic DFT calculations could reproduce the differences in INS spectra between crystalline neat h-PCBM and the more disordered h-PCBM rich phase. However, no clear evidences of P3HT conformational changes over blending could be concluded. It should be reminded though that neutrons probe an ensemble of conformations of both neat d-RRa-P3HT phase and d-RRa-P3HT rich phase. Therefore, our approach might be limited in the capture of morphological changes that will affect only chains that are in close contact with the PCBM.