  It is well known that the dust properties of the diffuse interstellar medium
exhibit variations towards different sight-lines on a large scale. We have
investigated the variability of the dust characteristics on a small scale, and
from cloud-to-cloud. We use low-resolution spectro-polarimetric data obtained
in the context of the Large Interstellar Polarisation Survey (LIPS) towards 59
sight-lines in the Southern Hemisphere, and we fit these data using a dust
model composed of silicate and carbon particles with sizes from the molecular
to the sub-micrometre domain. Large (> 6 nm) silicates of prolate shape account
for the observed polarisation. For 32 sight-lines we complement our data set
with UVES archive high-resolution spectra, which enable us to establish the
presence of single-cloud or multiple-clouds towards individual sight-lines. We
find that the majority of these 35 sight-lines intersect two or more clouds,
while eight of them are dominated by a single absorbing cloud. We confirm
several correlations between extinction and parameters of the Serkowski law
with dust parameters, but we also find previously undetected correlations
between these parameters that are valid only in single-cloud sight-lines. We
find that interstellar polarisation from multiple-clouds is smaller than from
single-cloud sight-lines, showing that the presence of a second or more clouds
depolarises the incoming radiation. We find large variations of the dust
characteristics from cloud-to-cloud. However, when we average a sufficiently
large number of clouds in single-cloud or multiple-cloud sight-lines, we always
retrieve similar mean dust parameters. The typical dust abundances of the
single-cloud cases are [C]/[H] = 92 ppm and [Si]/[H] = 20 ppm.
