  Polyelectrolyte (PE) brushes are widely used in biomaterials and
nanotechnology to regulate surface properties and interactions. Here, we apply
the electrostatic correlation augmented self-consistent field theory to
investigate the interactions between opposing PE brushes in a mixture of 1:1
and 3:1 salt solutions. Our theory predicts hysteretic feature of the normal
stress induced by strong ion correlations. In the presence of trivalent ions,
the force profile is discontinuous: repulsive in the compression branch and
adhesive in the separation branch. The molecular origin of the hysteretic force
is the coexistence of two collapsed modes: two separated condensed layer on
each surface in the compression and a single bundled condensed layer in the
separation. With the systematic inclusion of ion correlations, our theory fully
captures the hysteretic force, adhesive separation, ``jump-in'' and
``jump-out'' features, and the ``specific ion effect'', all in good agreement
with the reported experimental results.
