  We explore the impact of three water-soluble polyelectrolytes (PEs) on the
flow of concentrated suspensions of poly(N-isopropylacrylamide) (PNIPAm)
microgels with thermoresponsive anionic charge density. By progressively adding
the PEs to a jammed suspension of swollen microgels, we show that the rheology
of the mixtures is remarkably influenced by the sign of the PE charge, PE
concentration and hydrophobicity only when the temperature is raised above the
microgel volume phase transition temperature $T_c$, namely when microgels
collapse, they are partially hydrophobic and form a volume-spanning colloidal
gel. We find that the original gel is strengthened close to the isoelectric
point, attained when microgels are mixed with cationic PEs, while PE
hydrophobicity rules the gel strengthening at very high PE concentrations.
Surprisingly, we find that polyelectrolyte adsorption or partial embedding of
PE chains inside the microgel periphery occurs also when anionic polymers of
polystyrene sulfonate with high degree of sulfonation are added. This gives
rise to colloidal stabilization and to the melting of the original gel network
above $T_c$. Contrastingly, the presence of polyelectrolytes in suspensions of
swollen, jammed microgels results in a weak softening of the original repulsive
glass, even when an apparent isoelectric condition is met. Our study puts
forward the crucial role of electrostatics in thermosensitive microgels,
unveiling an exciting new way to tailor the flow of these soft colloids and
highlighting a largely unexplored path to engineer soft colloidal mixtures.
