Polymer knot confined in a tube: statics and relaxation dynamics

The statics and relaxation dynamics of a polymer knot confined in a cylindrical tube of diameter D are investigated by Monte Carlo simulations. The prime knots with crossings varying from 3(1) to 7(1) are considered. The equilibrium radius of gyration along the axial direction is scaled as R(parallel) approximately R(F)(R(F)/D)(m), where R(F) is the Flory radius of a knotted polymer. Our simulation results suggest that m=0.95, which is different from the value for a linear chain, m=2/3. The relaxation behavior of the knotted polymer is studied after the tubular constraint is removed. The relaxation time can be scaled as tau(parallel) approximately NR(1+1/m)(F)R(1-1/m)(parallel), which is confirmed by simulations. The effect of topological complexity on both properties is manifested through the Flory radius.