  Monte Carlo computer simulations are used to study the segregation behaviour
of two polymers under cylindrical confinement. Using a multiple-histogram
method, the conformational free energy, F, of the polymers was measured as a
function of the centre-of-mass separation distance, \lambda. We examined the
scaling of the free energy functions with the polymer length, the length and
diameter of the confining cylinder, the polymer topology (i.e. linear vs ring
polymers), and the packing fraction and size of mobile crowding agents. In the
absence of crowders, the observed scaling of F(\lambda) is similar to that
predicted using a simple model employing the de~Gennes blob model and the
approximation that the free energy of overlapping chains in a tube is equal to
that of two isolated chains each in a tube of half the cross-sectional area.
Simulations were used to test the latter approximation and reveal that it
yields poor quantitative predictions. This, along with generic finite-size
effects, likely gives rise to the discrepancies between the predicted and
measured values of scaling exponents for F(\lambda). For segregation in the
presence of crowding agents, the free energy barrier generally decreases with
increasing crowder packing fraction, thus reducing the entropic forces driving
segregation. However, for fixed packing fraction, the barrier increases as the
crowder/monomer size ratio decreases.
