Résumé : Context. The enrichment in s-process elements of barium stars is known to be due to pollution by mass transfer from a companion formerly on the thermally pulsing asymptotic giant branch (AGB), now a carbon-oxygen white-dwarf (WD). Aims. We are investigating the relationship between the s-process enrichment in the barium star and the mass of its WD companion. It is expected that helium WDs, which have masses lower than about 0.5 M⊙ and never reached the AGB phase, should not pollute their giant companion with s-process elements. Therefore the companion should never turn into a barium star. Methods. Spectra with a resolution of R ∼ 86 000 were obtained with the HERMES spectrograph on the 1.2 m Mercator telescope for a sample of 11 binary systems involving WD companions of various masses. We used standard 1D local thermodynamical equilibrium MARCS model atmospheres coupled with the Turbospectrum radiative-transfer code that is embedded in the BACCHUS pipeline to derive the atmospheric parameters through equivalent widths of Fe I and Fe II lines. Least-squares minimization between the observed and synthetic line shape was used to derive the detailed chemical abundances of CNO and s-process elements. Results. The abundances of s-process elements for the entire sample of 11 binary stars were derived homogeneously. The sample encompasses all levels of overabundances: from solar [s/Fe] = 0 to 1.5 dex in the two binary systems with S-star primaries (for which dedicated MARCS model atmospheres were used). The primary components of binary systems with a WD more massive than 0.5 M⊙ are enriched in s-process elements. We also found a trend of increasing [s/Fe] with [C/Fe] or [(C+N)/Fe]. Conclusions. Our results confirm the expectation that binary systems with WD companions less massive than 0.5 M⊙ do not host barium stars.