  Context. As revealed by high-resolution spectral investigations in the
wavelength range between 300 and 400 nm, the interstellar extinction curve does
not display any of the sharp electronic absorption bands that are
characteristic for large polyatomic molecules, such as polycyclic aromatic
hydrocarbons (PAHs), which belong to the most abundant interstellar molecules.
Aims. We aim to verify whether the absorption curves of mixtures of
medium-sized PAHs produced in the laboratory can explain the astronomical
observations. Methods. The PAH mixtures were synthesized by infrared laser
pyrolysis and subsequent chemical extraction and size separation. The matrix
isolation technique was used to study the absorption spectra of isolated
molecules at low temperature. Results. Our experimental results demonstrate
that the UV-visible absorption curves of PAH mixtures can be very smooth,
displaying no sharp bands, if the molecular diversity is sufficiently high.
Conclusions. In view of the absence of sharp electronic features on the
interstellar extinction curve for 300 < {\lambda} < 400 nm, we conclude from
our experimental findings that the interstellar PAH population must be very
diverse. The low fractional abundances of individual species prevent their
detection on the basis of spectral fingerprints in the UV.
