Polymers and Random Walks-Renormalization Group Description and Comparison With Experiment

Although real polymers involve the sequential addition of monomers having fixed bond lengths, fixed bond angles and some freedom of rotation about single bond, the properties of polymers aver large length scales can be modeled by treating the polymer configuration as that of a random walk formed by the monomer units. Serious complications arise in the theoretical description of these polymers because of excluded volume constraints which prohibit different monomers from occupying the same position in space. This polymer excluded volume problem has been modeled in terms of a simple continuous random walk with short range repulsive interactions. The expansion of polymer properties in this repulsive interaction can readily be shown by dimensional analysis to involve an expansion in a large parameter, in the limit of long polymers. The renormalization group method is utilized as a systematic means for resuming this divergent perturbation expansion. The theory proceeds by analytically continuing the treatment to continuous range of spatial dimensionalities to expose and regularize the singularities in the analytically continued theory. The renormalization group approach is described from a heuristic physical standpoint and extensive comparisons are provided to show how it quantitatively reproduces vast amounts of dilute solution polymer properties with no adjustable parameters.