Density profile of a polymer in a slab
Departamento de Física, Universidade Federal de Santa Catarina,
88.040-900 Florianópolis, SC Brazil
Corresponding author: firstname.lastname@example.org
Accepted: 18 August 1997
We consider the problem of a polymer, modelled as a self-avoiding walk on a square lattice on the semi-plane, which is confined between walls located at and x=m. For each monomer incorporated into the walk and located at one of the walls the partition function is multiplied by a Boltzmann factor , so that the walls may be attractive () or repulsive (). The activity of a monomer will be denoted by z. Using a recursive procedure which allows us to obtain the partition function of the problem for values of m up to 4, we calculated the fraction of monomers in each column x of the slab, at the critical value of the activity zc, where the mean value of the number of monomers diverges. As expected, this density profile is convex for sufficiently attracting walls and concave for repulsive walls. For m>1, there exists an interval of values for ω in which the profile is neither convex nor concave.
PACS: 05.50.+q – Lattice theory and statistics; Ising problems / 61.41.+e – Polymers, elastomers, and plastics
© EDP Sciences, 1997