Solid-State Order and Charge Mobility in [5]- to [12]Cycloparaphenylenes

We report a computational study of mesoscale morphology and charge-transport properties of radially π-conjugated cycloparaphenylenes ([ n]CPPs) of various ring sizes ( n = 5-12, where n is the number of repeating phenyl units). These molecules are considered structural constituents of fullerenes and carbon nanotubes. [ n]CPP molecules are nested in a unique fashion in the solid state. Molecular dynamics simulations show that while intramolecular structural stability (order) increases with system size, intermolecular structural stability decreases. Density functional calculations reveal that reorganization energy, an important parameter in charge transfer, decreases as n is increased. Intermolecular charge-transfer electronic couplings in the solid state are relatively weak (due to curved π-conjugation and loose intermolecular contacts) and are on the same order of magnitude (∼10 meV) for each system. Intrinsic charge-carrier mobilities were simulated from kinetic Monte Carlo simulations; hole mobilities increased with system size and scaled as ∼ n⁴. We predict that disordered [ n]CPPs exhibit hole mobilities as high as 2 cm²/(V·s). Our computations show a strong correlation between reorganization energy and hole mobility (μ ∼ λ^-4). Quantum mechanical calculations were performed on cofacially stacked molecular pairs for varying phenyl units and reveal that orbital delocalization is responsible for both decreasing reorganization energies and electronic couplings as n is increased.