  In this paper we aim to constrain for the first time the dust emission in the
mid-to-far infrared domain, in the LMC, with the use of the Spitzer IRS and
MIPS SED data, combined with Herschel data. We also consider UV extinction
predictions derived from modeling. We selected 10 regions observed as part of
the SAGE-Spec program, to probe dust properties in various environments
(diffuse, molecular and ionized regions). All data were smoothed to the
40arcsec angular resolution. The SEDs were modeled with DustEM models, using
the standard Mathis RF, as well as three additional RFs, with stellar clusters
ages ranging from 4 Myr to 600 Myr. Standard dust models used to reproduce the
Galactic diffuse medium are clearly not able to reproduce the dust emission in
the MIR wavelength domain. This analysis evidences the need of adjusting
parameters describing the dust size distribution and shows a clear distinct
behavior according to the type of environments. In addition, whereas the small
grain emission always seems to be negligible at long wavelengths in our Galaxy,
the contribution of this small dust component could be more important than
expected, in the submm-mm range, in the LMC averaged SED. Properties of the
small dust component of the LMC are clearly different from those of our Galaxy.
Its abundance, significantly enhanced, could be the result of large grains
shattering due to strong shocks or turbulence. In addition, this grain
component in the LMC systematically shows smaller grain size in the ionized
regions compared to the diffuse medium. Predictions of extinction curves show
significantly distinct behaviors depending on the dust models but also from one
region to another. Comparison of model predictions with the LMC mean extinction
curve shows that no model gives satisfactory agreement using the Mathis
radiation field while using a harder radiation field tends to improve the
agreement
