Percolating bulk heterostructures from neutron reflectometry and small-angle scattering data

We generate percolating fullerene-polymer bulk heterostructures that are consistent with the experimental characterization of a nanostructure, in particular neutron reflectometry and small-angle neutron scattering data from as-cast and annealed poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl C61-butyric acid methyl ester systems. Transport simulations correlate changes in exciton dissociation efficiency and charge collection efficiency with morphological features including characteristic domain size, fullerene concentration profile, degree of fullerene sequestration, and degree of P3HT crystallization.

Figure 1

(Left figure) As-cast and annealed PCBM density profiles extracted from neutron reflectometry data compared to PCBM density profiles of restrained Ising morphologies on cubic lattices of size ${400}^3$ [see Eq. (1)]. Morphologies without c-P3HT fibers and with 30$\%$ c-P3HT fibers fit the reflectometry data. (Right figure) Many model morphologies reproduce the neutron reflectometry data, as illustrated by cross sections of six examples encompassing as-cast and annealed (with and without c-P3HT) cases, where the light regions indicate P3HT, the dark regions represent PCBM, and the gray regions indicate c-P3HT fibers (the inset to Fig. 2 shows a top view of the c-P3HT fiber network).

Figure 2

Experimental and simulated SANS results of the best fit morphologies. Dotted lines are the results of fits to polydisperse sphere models [7]. The amplitude of the model results (solid lines) are scaled to fit the experimental data (squares, circles), and the lattice constant is extracted from the best fit to the data. Views of the relevant morphologies are also shown, colored as in Fig. 1. In the bottom figure the simulated SANS data (dashed green line) is for c-P3HT fraction 30$\%$. All 3D visualizations of model morphologies presented here were generated using vmd [41, 42].

Figure 3

Charge collection efficiencies ${\chi }_q$ and exciton dissociation efficiency ${\chi }_{\mathrm{diss}}$ (insets) as a function of charge and exciton recombination lengths ($L_q$, $L_x$), respectively. (Top figure) For systems with or without c-P3HT fibers. The hole hop rate on fibers in “fast” c-P3HT data is 100 times faster in-plane. (Bottom figure) For annealed morphologies with $0\%,10\%,15\%$, and $20\%$ sequestered PCBM. ${\chi }_q$: Solid (dashed) lines indicate electrons (holes).