  We present deep high-resolution (R~15,000) and high-quality UVES optical
spectrophotometry of nine planetary nebulae with dual-dust chemistry. We
compute physical conditions from several diagnostics. Ionic abundances for a
large number of ions of N, O, Ne, S, Cl, Ar, K, Fe and Kr are derived from
collisionally excited lines. Elemental abundances are computed using
state-of-the-art ionization correction factors. We derive accurate C/O ratios
from optical recombination lines. We have re-analyzed additional high-quality
spectra of 14 PNe from the literature following the same methodology.
Comparison with asymptotic giant branch models reveals that about half of the
total sample objects are consistent with being descendants of low-mass
progenitor stars (M < 1.5 Msun). Given the observed N/O, C/O, and He/H ratios,
we cannot discard that some of the objects come from more massive progenitor
stars (M > 3--4 Msun) that have suffered a mild HBB. None of the objects seem
to be a descendant of very massive progenitors. We propose that in most of the
planetary nebulae studied here, the PAHs have been formed through the
dissociation of the CO molecule. The hypothesis of a last thermal pulse that
turns O-rich PNe into C-rich PNe is discarded, except in three objects, that
show C/O > 1. We also discuss the possibility of a He pre-enrichment to explain
the most He-enriched objects. We cannot discard other scenarios like extra
mixing, stellar rotation or binary interactions to explain the chemical
abundances behaviour observed in our sample.
