Relaxation of a Polymer Chain Confined in a Tube

Abstract

Relaxation modes and rates of a single polymer chainconfined in a straight tube by repulsive wallsare studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account.The relaxation modes and rates are estimatedby solving generalized eigenvalue problems forthe equilibrium time correlation matrices C^//_{i, j}(t) = ‹ (z_i(t) - z_c(t)) (z_j(0) - z_c(0)) ›_c and C^⊥_{i, j}(t) = ½‹ r_i^⊥ (t) · r_j^⊥ (0) ›_c, where z_i and r_i^⊥ are the components of the position vector of the ith segmentparallel and perpendicular to the tube axis, respectively, and z_c is the parallel component of the center of mass of the polymer chain.For the parallel component, the behavior of the pth slowest relaxation rateλ^//_p of a polymer chain of N segments agrees with the scaling prediction λ^//_p ~= λ_b (gp/N)²for gp/N << 1, where λ_b and g arethe slowest relaxation rate within each blob andthe number of segments per blob, respectively.The corresponding relaxation modes show the Rouse-like behavior.For the perpendicular components, the behavior of the pth slowest relaxation rate λ^⊥_pis consistent with the scaling prediction{λ}^⊥_p ~= λ_b for gp/N < 1.The behavior of the corresponding relaxation modes is consistent with the blob picture.