  We calculated theoretical evolutionary sequences of asymptotic giant branch
(AGB) stars, including formation and evolution of dust grains in their
circumstellar envelope. By considering stellar populations of the Large
Magellanic Cloud (LMC), we calculate synthetic colour-colour and
colour-magnitude diagrams, which are compared with those obtained by the
Spitzer Space Telescope. The comparison between observations and theoretical
predictions outlines that extremely obscured carbon-stars and oxygen-rich
sources experiencing hot bottom burning (HBB) occupy well defined, distinct
regions in the colour-colour ($[3.6]-[4.5]$, $[5.8]-[8.0]$) diagram. The C-rich
stars are distributed along a diagonal strip that we interpret as an
evolutionary sequence, becoming progressively more obscured as the stellar
surface layers enrich in carbon. Their circumstellar envelopes host solid
carbon dust grains with size in the range $0.05 < a < 0.2 \mu m$. The presence
of SiC particles is expected only in the more metal-rich stars. The reddest
sources, with $[3.6]-[4.5] > 2$, are the descendants of stars with initial mass
$M_{in} \sim 2.5 - 3 M_{\odot}$ in the very latest phases of the AGB life. The
oxygen-rich stars with the reddest colours ($[5.8]-[8.0] > 0.6$) are those
experiencing HBB, the descendants of $\sim 5 M_{\odot}$ objects formed $10^{8}$
yr ago; alumina and silicates dust start forming at different distances from
the central star. The overall dust production rate in the LMC is $\sim 4.5
\times 10^{-5} M_{\odot}/yr$, the relative percentages due to C- and M- star
being respectively 85$%$ and 15 $%$.
