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Monte Carlo simulations are used to study the behavior of two polymers underconfinement in a cylindrical tube. Each polymer is modeled as a chain of hardspheres. We measure the free energy of the system, F, as a function of thedistance between the centers of mass of the polymers, lambda, and examine theeffects on the free energy functions of varying the channel diameter D andlength L, as well as the polymer length N and bending rigidity, kappa. Forinfinitely long cylinders, F is a maximum at lambda=0, and decreases withlambda until the polymers are no longer in contact. For flexible chains, thepolymers overlap along the cylinder for low lambda, while above some criticalvalue of lambda they are longitudinally compressed and non-overlapping whilestill in contact. We find that the free energy barrier height, scales as DeltaF/k_BT~ND^{-1.93+/-0.01}. In addition, the overlap free energy scales asF/k_BT=Nf(lambda/N;D), where f is a function parameterized by D. For channelsof finite L, the free energy barrier height increases with increasingconfinement aspect ratio L/D at fixed volume fraction phi, and it decreaseswith increasing phi at fixed L/D. Increasing the polymer bending rigidity kappamonotonically reduces the overlap free energy. For strongly confined systems, Fvaries linearly with lambda with a slope that scales as F'(lambda)~-k_BTD^{-beta} P^{-alpha}, where beta approx 2 and alpha approx 0.37 for N=200chains. These exponent values deviate slightly from those predicted using asimple model, possibly due to insufficiently satisfying the conditions definingthe Odijk regime. Finally, we use Monte Carlo dynamics simulations to examinepolymer segregation dynamics for fully flexible chains and observe segregationrates that decrease with decreasing entropic force magnitude. The polymers arenot conformationally relaxed at later times during segregation.

Polymer segregation under confinement: Free energy calculations and segregation dynamics simulations