Two-variable quasi-scaling for three-dimensional lattice polymers in a poor solvent regime

Abstract

The context of the renormalization group applied to the lattice polymer statistical mechanics with the nearest-neighbour triplet interaction in addition to the usual nearest-neighbour pair interaction yields a two-variable quasi-scaling relation. It asserts that a reduced moment is described by two arbitrary reduced moments. The validity of the two-variable quasi-scaling has been examined for lattice polymers with polymerization degree up to 1000 in the poor solvent regime and was confirmed. It is well known that single-variable scaling fails in this solvent regime. Linear relations connecting three reduced moments which are valid near the respective Gaussian points and considered to be universal are presented. The results, however, are not consistent with the premise employed in the continuous polymer model. The working RG is nonlinear. The consistency may be attained by polymers with polymerization degree much larger than 1000 for which the linearized RG will work. The authors' basic equation involves no particular reference point such as the Theta -point. This is in contrast to previous scaling simulations and experiments.