Dynamics of polymer chains confined into tubes: Scaling theory and Monte Carlo simulations

Abstract

The crossover from chain dynamics described by the Rouse model to reptation behavior is studied for chains confined into straight tubes. Scaling considerations are presented for mean‐square displacements parallel and perpendicular to the tube, for the static structure factor, and for dynamic coherent and incoherent structure factors, taking excluded‐volume interactions into account. Monte Carlo calculations of long chains (from N=100 up to N=800 links) on the tetrahedral lattice in tubes with diameters in the range from d_T=16 to d_T=32 lattice spacings are presented and analyzed in terms of the scaling picture. While the scaling predictions are nicely confirmed, the simulations also reveal additional interesting features: (i) For intermediate wave vectors the structure factor exhibits (damped) oscillations. This behavior is discussed in terms of the analogy with a one‐dimensional harmonic ‘‘crystal’’ composed of blobs, and differs from the behavior of a nonconfined chain stretched to the same length. (ii) In the center of gravity system of the chain, the monomer displacements along the tube axis for monomers near the chain ends are very much larger than those near the chain center. We also give a preliminary discussion of consequences for the dynamics of melts, if they are modeled in terms of tubes following a random‐walk contour.