We present new optical broad-band (UBVRI) aperture polarimetric observations of 53 post-asymptotic giant branch (AGB) stars selected to exhibit a large near-infrared excess. 24 out of the 53 stars (45% of our sample) are presented for the first time. A statistical analysis shows four distinctive groups of polarized post-AGB stars: unpolarized or very lowly polarized (degree of polarization or DoP < 1%), lowly polarized (1% < DoP < 4%), moderately polarized (4% < DoP < 8%) and highly polarized (DoP > 8%). 23 out of the 53 (66%) belong to the first group, 10 (19%) to the second, five (9%) to the third and only three (6%) to the last group. Approximately, 34% of our sample was found to be unpolarized objects, which is close to the percentage of round planetary nebulae. On average, the low and moderate groups show a wavelength-dependent polarization that increases towards shorter wavelength, implying an intrinsic origin of the polarization, which signifies a Rayleigh-like scattering spectrum typical for non-symmetrical envelopes composed principally of small dust grains. The moderately polarized stars exhibit higher K-W3 and W1-W3 colour indices compared with the group of lowly polarized stars suggesting a possible relation between DoP and mass-loss rate. Moreover, they are found to be systematically colder (redder in B-V), which may be associated with the condensation process close to these stars that results in higher degree of polarization. We also provide evidence that multiple scattering in optically thin polar outflows is the mechanism that gives high DoP in post-AGB stars with a bipolar or multi-polar envelopes.
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