Reptation Dynamics of Semirigid Polymers in Porous Media

A theory of the dynamics of a semirigid polymer molecule in a porous medium is formulated on the basis of the reptation theory. The porous medium is assumed to be made up of a network of hollow cylinders of uniform radius, a model approximating the situation in controlled pore glasses. When the pores confine a long semirigid chain with a persistence length at least comparable to the pore radius, the chain takes an extended conformation, wiggling around the center line (primitive path) of the tube formed by the solid pore walls; this result is confirmed through a computer simulation. Because of the rigidity of the pore walls, the tube and the primitive path have the conformation of a wormlike chain with a persistence length (usually longer than that of the semirigid chain) determined by the pore structure. The computer simulation comparing chains of the same extension in the pore network and identical concentration in the fluid surrounding the porous material shows that a semirigid chain with a persistence length intermediate between the pore radius and the persistence length of the primitive path will be present in the largest concentration within the pore. When the primitive path moves its center of mass in the porous medium, the motion of the semirigid chain is restricted to travel along the pore and the tube. We notice that the restricted motion fulfills the basic assumption of the reptation theory of Doi and Edwards for entangled linear flexible chains but that the conformation of the primitive path is different here. Applying the formulation of the reptation theory to the dynamics of the primitive path, we obtain the long-time diffusion constant of the semirigid polymer as a function of the chain geometry and the pore geometry. For the short-time behavior of the chain dynamics in the pore network, we employ the normal-mode analysis for an isolated wormlike chain developed by Aragón and Pecora. Combining the two results, we obtain the mean-square displacement of monomers on a sufficiently long semirigid polymer chain as t^α, where α ≅¼ for the short-time wiggling motion inside the pore, α ≅1 for the translational motion along a pore within one pore branch, α ≅ ½ for the intermediate time region where the reptation mode along the tube dominates, and α = 1 for the long-time diffusion beyond the tube dimension. The intermediate region, however, is not distinctly observed unless the polymer chain is extremely long.