A dimensional regularization approach to the renormalization group treatment of polymer excluded volume is formulated in chain conformation space where monomers are specified by their spatial positions and their positions along the chain and the polymers may be taken to be monodisperse. The method utilizes basic scale invariance considerations. First, it is recognized that long wavelength macroscopic descriptions must be well defined in the limit that the minimum atomic or molecular scale Λ is set to zero. Secondly, the microscopic theory is independent of the conveniently chosen macroscopic scale of length κ. The freedom of choice of κ is exploited along with the assumed renormalizability of the theory to provide the renormalization group equations which directly imply the universal scaling laws for macroscopic properties. The renormalizability of the model implies the existence of the general relations between the basic macroparameters, such as chain length, excluded volume, etc., and their microscopic counterparts in the microscopic model for the system. These macro-micro relations are defined through the condition that macroscopic quantities be well defined for polymer chains for any spatial dimensionality. The method is illustrated by calculating the end vector distribution function for all values of end vectors R. The evaluation of this distribution function currently requires the use of expansions in ε=4-d. In this case our distribution reduces to known limits for R→0 or ∞. Subsequent papers will present calculations of the polymer coherent scattering function, the monomer spatial distribution function, and concentration dependent properties.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry