DENSITY PROFILE OF A POLYMER IN A SLAB

We consider the problem of a polymer, modelled as a self-avoiding walk on a square lattice on the (x,y greater than or equal to 0) semi-plan e, which is confined between walls located at x = -m and x = m. For ea ch monomer incorporated into the walk and located at one of the walls the partition function is multiplied by a Boltzmann factor w = exp[-ep silon/k(B)T], so that the walls may be attractive (epsilon < 0) or rep ulsive (epsilon > 0). The activity of a monomer will be denoted by z. Using a recursive procedure which allows us to obtain the partition fu nction of the problem for values of m up to 4, we calculated the fract ion of monomers in each column x of the slab, at the critical value of the activity z(c), where the mean value of the number of monomers div erges. As expected, this density profile is convex for sufficiently at tracting walls and concave for repulsive walls. For m > 1, there exist s an interval of values for w in which the profile is neither convex n or concave.