  We explore the effect of an attractive interaction between parallel-aligned
polymers, which are perpendicularly grafted on a substrate. Such an attractive
interaction could be due to, e.g., reversible cross-links. The competition
between permanent grafting favoring a homogeneous state of the polymer brush
and the attraction, which tends to induce in-plane collapse of the aligned
polymers, gives rise to an instability of the homogeneous phase to a bundled
state. In this latter state the in-plane translational symmetry is
spontaneously broken and the density is modulated with a finite wavelength,
which is set by the length scale of transverse fluctuations of the grafted
polymers. We analyze the instability for two models of aligned polymers:
directed polymers with a line tension and weakly bending chains with a bending
stiffness.
