  The statistical theory of polymers tethered around the inner surface of a
cylindrical channel has traditionally employed the assumption that the
equilibrium density of the polymers is independent of the azimuthal coordinate.
However, simulations have shown that this rotational symmetry can be broken
when there are attractive interactions between the polymers. We investigate the
phases that emerge in these circumstances, and we quantify the effect of the
symmetry assumption on the phase behavior of the system. In the absence of this
assumption, one can observe large differences in the equilibrium densities
between the rotationally symmetric case and the non-rotationally symmetric
case. A simple analytical model is developed that illustrates the driving
thermodynamic forces responsible for this symmetry breaking. Our results have
implications for the current understanding of the polymer behavior in
cylindrical nanopores.
