Critical exponents for surface interacting selfhyphen;avoiding lattice walks. II. The square lattice

摘要

Critical exponents for the twohyphen;dimensional version of adsorption of a polymer chain at an interface are estimated asdgr;asime;1.9andzgr;sime;1.5from the exact enumeration of selfhyphen;avoiding walks up to 21 terms on the square lattice, wheredgr;aand zgr; are defined from the respective dependences of the free energy and the thickness of adsorption layer on monomerndash;surface interaction; zgr; is to be estimated to be about unity for threehyphen;dimensional lattices. These values are different from the scaling predictions of de Gennes:dgr;a=4andzgr;=3in two dimensions, andzgr;=1.5in three dimensions. An assumption in the scaling treatment is examined by using the exact enumeration data in order to explain the discrepancy.