Theory of interfacial charge-transfer complex photophysics in $\pi$-conjugated polymer-fullerene blends

We present a theory of the electronic structure and photophysics of 1:1 blends of derivatives of polyparaphenylenevinylene and fullerenes. Within the same Coulomb-correlated Hamiltonian applied previously to interacting chains of single-component $\pi$-conjugated polymers, we find an exciplex state that occurs below the polymer’s optical exciton. Weak absorption from the ground state occurs to the exciplex. We explain transient photoinduced absorptions in the blend, observed for both above-gap and below-gap photoexcitations, within our theory. Photoinduced absorptions for above-gap photoexcitation are from the optical exciton as well as the exciplex while for below-gap photoexcitation induced absorptions are from the exciplex alone. In neither case are free polarons generated in the time scale of the experiment. Importantly, the photophysics of films of single-component $\pi$-conjugated polymers and blends can both be understood by extending Mulliken’s theory of ground-state charge transfer to the case of excited-state charge transfer.

Figure 1

(Color online) Top view of the relative locations of the 8-unit PPV oligomer and the ${\text{C}}_{60}$ molecule assumed in our calculations for three different geometries I, II, and III. In geometry I, the topmost pentagon of ${\text{C}}_{60}$ is parallel to PPV plane and located symmetrically below an ethylenic bond of the 8-unit PPV oligomer. In geometry II, the same pentagon of ${\text{C}}_{60}$ is located symmetrically below a phenyl ring of the PPV oligomer. In geometry III, the central ethylenic bond of the PPV oligomer is parallel to the common bond between two hexagons in ${\text{C}}_{60}$.

Figure 2

(Color online) The highest bonding and lowest antibonding Hartree-Fock MOs of the 8-unit PPV oligomer (left) and ${\text{C}}_{60}$ (right) within $H_{intra}$. The HOMOs of PPV and ${\text{C}}_{60}$ are at 2.18 and 1.80 eV, respectively. The corresponding LUMOs are at 5.82 and 5.18 eV, respectively.

Figure 3

(Color online) Below-gap electronic structure of the ${\text{PPV-C}}_{60}$ blend for (a) ${\kappa }_{\perp }=1.3$ and (b) ${\kappa }_{\perp }=2.0$ (geometry I). The dashed lines correspond to exciplexes with the numbers against them giving their ionicities. The hatched regions are occupied by fifteen discrete ${\text{PPV-C}}_{60f}^{\ast }$ states with tiny energy gaps between them.

Figure 4

(Color online) Main panel: optical absorption to the lowest exciton in pure PPV and ${\text{PPV-C}}_{60}$ blend with ${\kappa }_{\perp }=1.3$ and 2.0 (geometry I). The inset shows the subgap difference absorptions, normalized to the absorption at the peak of the exciton for both ${\kappa }_{\perp }$.

Figure 5

(Color online) Calculated PAs for photoexcitations above (red dot-dashed) and below (black solid) the optical exciton ${\text{PPV}}^{\ast }{\text{-C}}_{60}$ for ${\kappa }_{\perp }=1.3$ (geometry I). In panel (b), the calculated ${\text{PA}}_1$ has been rigidly blueshifted to its experimental location.

Figure 6

(Color online) Calculated PAs originating from (a) the exciplex and (b) the exciton for the three different geometries in Fig. 1. Adjustments of ${\kappa }_{\perp }$ values are done to achieve ionicity of $\sim 0.95$ for the exciplex in ${\text{PPV-C}}_{60}$.

Figure 7

(Color online) Schematic of the consequences of above- and below-gap photoexcitations. Vertical straight arrows pointing up denote absorptions; curly arrows pointing down denote nonradiative relaxations.

Figure 8

(Color online) Relative locations of the ${\text{P}}_1$ and ${\text{PA}}_1$ bands, calculated using SCI and QCI.