Critical exponents for surface interacting self-avoiding lattice walks. I. Three-dimensional lattices

Self-avoiding lattice walks interacting with an interface are investigated as a model of polymer adsorption. The value of a critical exponent δa is estimated at 1.7±0.3 from the exact enumeration data up to 20 and 14 steps for the tetrahedral and simple cubic lattices, respectively; δa is defined from the dependence of the free energy of an adsorbed polymer chain on the interaction with interface. The value differs from the scaling prediction δa = 5/2 of de Gennes. An assumption involved in the scaling treatment is examined by using the enumerations of self-avoiding walks confined between two planes in order to explain the disagreement.