Self-avoiding lattice walk confined between two planes interacting with them

Abstract

Self-avoiding walk on a lattice is investigated as a model of dilute polymer solutions in a narrow slit between plates. The limiting free energy is estimated as a function of interplate distance and temperature from the exact enumeration for up to 20 steps on the tetrahedral lattice. If the walk interacts with both plates with an attractive potential, there is a threshold value which coincides with the adsorption temperature Tc for the single plane. As the interplate distance decreases, a repulsive force between plates increases for T>Tc while an attractive force increases for T<Tc. If the walk interacts with only one of the plates, there is always a repulsive force. The results are in qualitative agreement with the theory of DiMarzio and Rubin for the random walk model. Analogical relationship between the constrained walk and the critical behavior of magnetic film is also discussed.