Evolved low-mass stars of a wide range of metallicity bear signatures of a non-standard mixing event in their surface abundances of Li, C, and N, and in their 12C/13C ratio. A Na overabundance has also been reported in some giants of open clusters but remains controversial. The cause of the extra-mixing has been attributed to thermohaline convection that should take place after the RGB bump for low-mass stars and on the early-AGB for more massive objects. To track the occurrence of this process over a wide mass range, we derive in a homogeneous way the abundances of C, N, O, and Na, as well as the 12C/13C ratio in a sample of 31 giants of 10 open clusters with turn-off masses from 1.7 to 3.1 Msun. A group of first ascent red giants with M/Msun leq 2.5 exhibits lower [N/C] ratios than those measured in clump giants of the same mass range, suggesting an additional increase in the [N/C] ratio after the first dredge-up. The sodium abundances corrected from NLTE are found to be about solar. [Na/Fe] shows a slight increase of 0.10 dex as a function of stellar mass in the 1.8 to 3.2 Msun range covered by our sample, in agreement with standard first dredge-up predictions. Our results do not support previous claims of sodium overabundances as high as +0.60 dex. An anti-correlation between 12C/13C and turn-off mass is identified and interpreted as being caused by a post-bump thermohaline mixing. Moreover, we find low 12C/13C ratios in a few intermediate-mass early-AGB stars, confirming that an extra-mixing process also operates in stars that do not experienced the RGB bump. In this case, the extra-mixing possibly acts on the early-AGB, in agreement with theoretical expectations for thermohaline mixing. [abridged]
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