# Crystallinity and Molecular Packing of Small Molecules in Bulk-Heterojunction Organic Solar Cells
## 4 Crystallinity and Crystalline Packing in SM-BHJ
Figure 4: (**a**) Stacked diffractograms of SQ: PC\({}_{70}\)BM active layers spin-coated from different solvents and on the top of different substrates, with thermal annealing (Th. A.) or solvent vapour annealing (SVA) post-deposition treatments. (**b**) GIWAXS diffraction image of a typical active layer; (**c**) Single-crystal X-ray diffraction structure of SQ crystallised in the P21/n space group. Adapted with permission from the Royal Society of Chemistry, copyright 2014 [63]. A subsequent extensive study from our group allowed application of the above method to a library of related donors [64]. The determination of the crystalline phase adopted by two donors in active layers of OSCs allowed an attempt of a qualitative analysis of the thermodynamics of the formation of crystallites in such active layers, in turn establishing a link between the latter parameters with the \(J\)-\(V\) characteristics of the devices. According to empirical evidence, it was assumed that the crystallisation of donor molecules from the amorphous active layer would then occur via homogeneous or heterogeneous nucleation and growth mechanisms. \[\Delta G(r)=\frac{1}{3}\pi r^{3}\Delta G_{V}+\frac{4}{3}\pi r^{3}\Delta G_{E} +4\pi r^{2}\gamma\]  
The free energy change for a classical homogenous nucleation process implying spherical nuclei of radius \(r\) is described by equation 1. Accordingly, \(\Delta G(r)\) is seen to be dependent on three energy parameters: \(\Delta G_{V}\) corresponding to the bulk free energy difference of crystal formation (energy/unit volume) intrinsic to each polymorphic crystalline phase; \(\gamma\) corresponding to the interfacial energy (i.e., energy arising from the interface between the nucleus composed of pure donor molecules and the D/A amorphous matrix the nucleus is growing from); and \(\Delta G_{E}\) the elastic free energy change due to the strain arising from the growth of a particle in the solid matrix. The latter two energy terms act as a barrier to nucleation. The profile shape of the free energy change of the transformation for a given system is seen to proceed through a maximum value (activation energy), determining the critical nucleus size (\(r^{\star}\), critical radius) to be achieved for crystallite growth to become favourable (when d\(\Delta G(r)\)/d\(r\) = 0; \(\Delta G^{\star}\)) [65]. Consequently, for a given active layer, \(r^{\star}\) and \(\Delta G^{\star}\) will be determined by the intrinsic ability of the donor molecule to arrange in a thermodynamically stable crystalline phase (maximising \(\Delta G_{V}\) and minimising \(\gamma\)) in the amorphous D/A blend. The interfacial contribution to nucleus growth dominates at small nucleus sizes, while the volumetric ones (\(\Delta G_{V}+\Delta G_{E}\)) dominate at large nucleus sizes. Figure 5: **(a)** Pristine PC\({}_{70}\)BM powdered layer diffractogram; **(b)** SQ: PC\({}_{70}\)BM “powdered” active layer diffractogram (black line) and refined diffractogram from the P21/n crystal structure of SQ (red line). The cell parameters, profile shape and scale factor were accounted for in the refinement routine, while all structural parameters (atomic positions and temperature factors) were kept constant. The Rietveld R factors provide clear evidence of structural agreement between the single crystal and the “powdered” layer; **(c)** calculated powder diffractogram of SQ from the P21/n X-ray single crystal structure (143 K). Adapted with permission from the Royal Society of Chemistry, copyright 2014 [63]. In order to provide an insight into the energetics of the crystallites' growth, relative quantification of the interfacial energy \(\gamma\) of the amorphous fraction of the active layers in the early stage of crystalline growth (\(r=0\)) was carried out [64].