  Polymers confined to a narrow channel are subject to strong entropic forces
that tend to drive the molecules apart. In this study, we use Monte Carlo
computer simulations to study the segregation behavior of two flexible
hard-sphere polymers under confinement in a cylindrical channel. We focus on
the effects of using polymers of different lengths. We measure the variation of
the conformational free energy, $F$, with the center-of-mass separation
distance, $\lambda$. The simulations reveal four different separation regimes,
characterized by different scaling properties of the free energy with respect
to the polymer lengths and the channel diameter, $D$. We propose a regime map
in which the state of the system is determined by the values of the quantities
$N_2/N_1$ and $\lambda/(N_1+N_2)D^{-\beta}$, where $N_1$ and $N_2$ are the
polymer lengths, and where $\beta\approx 0.64$. The observed scaling behavior
of $F(\lambda)$ in each regime is in reasonable agreement with predictions
using a simple theoretical model. In addition, we use MC dynamics simulations
to study the segregation dynamics of initially overlapping polymers by
measurement of the incremental mean first-passage time with respect to
$\lambda$. For systems characterized by a wide range of $\lambda$ in which a
short polymer is nested within a longer one, the segregation dynamics are close
to that expected for two noninteracting 1D random walkers undergoing unbiased
diffusion. When the free energy gradient is large segregation is rapid and
characterized by out-of-equilibrium effects.
