Segment diffusion and nuclear magnetic resonance spin-lattice relaxation of polymer chains confined in tubes: Analytical treatment and Monte Carlo simulation of the crossover from Rouse to reptation dynamics

Abstract

The frequency and molecular mass dependences of nuclear magnetic resonance spin-lattice relaxation and the time dependence of the mean-squared segment displacement of Kuhn segment chains confined in static straight and randomly coiled tubes with “soft” and “hard” walls were studied. “Soft” walls were modeled in the form of a cylindrical distribution of a harmonic radial potential. This scenario is analytically solvable in contrast to the situation of “hard” (reflecting) walls corresponding to an infinitely deep square-well radial potential. In the latter case, we have therefore employed Monte Carlo simulations using a modified Stockmayer chain model. In both situations, qualitatively equivalent results were obtained. Depending on the effective tube diameter (or width of the potential well) a crossover from Rouse to reptation behavior occurs which sets on already far beyond the Flory radius of the polymer. In terms of the spin-lattice relaxation dispersion, reptation reveals itself by T1∝M0ω3/4 in the chain mode regime, in good agreement with experimental data for polymers in artificial tubes reported in our previous paper by Kimmich et al. [Chem. Phys. Lett. 307, 147 (1999)].