  We study the changes in the conformations of brushes upon the addition of
crosslinks between the chains using the bond fluctuation model. The
Flory-Rehner model applied to uni-axially swollen networks predicts a collapse
for large degrees of crosslinking $q$ proportional to $q^{-1/3}$ in
disagreement with our simulation data. We show that the height reduction of the
brushes is driven by monomer fluctuations in direction perpendicular to the
grafting plane and not due to network elasticity. We observe that the impact of
crosslinking is different for reactions between monomers of the same or on
different chains. If the length reduction of the effective chain length due to
both types of reactions is accounted for in a function $\beta(q)$, the height
of the brush can be derived from a Flory approach for the equilibrium brush
height leading to $H(q)\approx H_{b}\beta(q)^{1/3}$, whereby $H_{b}$ denotes
the height of the non-crosslinked brush.
