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.
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