POLYMER IN A STRIP - PROFILE OF THE MONOMER DENSITY

We study a model of self-avoiding walks (SAWs) on a square lattice in the (x, y greater than or equal to 0) semiplane, which are confined be tween two impenetrable walls located at x = 0 and x = m greater than o r equal to 0. Such a model may describe polymers inside a strip. The a ctivity of a monomer (site of the lattice incorporated into the walks) is denoted by z = exp(-beta mu), mu being the chemical potential, and monomers located at the walls interact with them, so that the energy of the system is increased by epsilon for each monomer located at x = 0 or x = m. Using a transfer matrix formalism for the partition functi on of the model, we calculate the fraction of monomers in each column 0 less than or equal to x less than or equal to m at the activity z(c) corresponding to the polymerization transition, where the number of m onomers diverge, for 0 less than or equal to m less than or equal to 8 . We find convex density profiles for sufficiently attracting walls an d concave profiles when the walls are repulsive. The transition betwee n these two regimes takes place in an interval of values for epsilon, in which the density profile is neither convex nor concave, a more com plex behavior being observed. (C) 1998 Elsevier Science B.V. All right s reserved.