POLYMERS IN PERIODIC AND APERIODIC POTENTIALS - LOCALIZATION EFFECTS

We investigate the behavior of polymer chains embedded in a lamellar m atrix by considering both a regular periodic environment and the effec t of disturbances. By using the Green's function formalism and an attr active Kronig-Penney model, we obtain analytically exact results. For the case of a regular lamellar matrix of period xi a long polymer chai n is characterized by an effective segment length l(eff), in analogy t o the effective mass of electrons in solids, For potential wells deep enough there appears a gap of forbidden states which separates the low -lying, adsorption band from the higher lying, desorption band. Due to the ground-state dominance, for polymers only the lowest lying states are of physical relevance. Isolated defects of the periodic structure may localize the polymer, in the sense that infinitely long chains ar e confined inside a region of finite extent L around the defect. For a single defect we find L=1/(epsilon Delta xi), where epsilon is the st rength of the periodic potential and Delta xi is the deviation from th e periodicity. This is also valid for finite chains when their number of segments exceeds the cross-over value N-L=2L(2)/l(eff)(2). (C) 1996 American Institute of Physics.