  We have constructed a photoionization model, using the 3-D Monte Carlo code
MOCASSIN for one of the hydrogen-deficient knots (J3) of the born-again
planetary nebula Abell 30. The model consists of spherical knots, comprising a
cold, dense, hydrogen-deficient core with very high metal abundances. The inner
core is surrounded by a less dense hydrogen-deficient and metal-enriched gas
envelope, with less extreme abundances. The envelope of the knot might have
been formed by the mixing of the knot material with the surrounding nebular
gas. This bi-chemistry, bi-density model did not produce enough heating to
match the fluxes of the collisionally excited emission lines (CELs) and of the
optical recombination lines (ORLs) observed in the spectrum of the knot. We
therefore included heating by photoelectric emission from dust grains in the
thermal equilibrium calculations, and found that dust-to-gas ratios of 0.077
and 0.107 by mass for the central core and the envelope of the knot,
respectively, are sufficient to fit the spectrum. Surprisingly, photoelectric
emission from grains is the dominant source of heating in the hot envelope of
the knot, while heating by photoionization of helium and heavy elements
dominates in the cold core. The chemical abundances inferred from our modelling
indicate, in agreement with the empirical analysis of Wesson et al. (2003),
that the C/O ratio in the two regions of the knot is less than unity, contrary
to theoretical predictions for born-again nebulae.
