Local Mode Overtone Spectra

theory is based on simple physical considerations that large length scale polymer properties must provide universal laws embodying the long chainlike character of polymers. These laws are represented in terms of scaling laws and their generalization to the important regions of intermediate excluded volume where the power law exponents are no longer universal constants. A motivation is provided for the eexpansion methods. The procedures for performing the eexpansion calculations, evaluating the renormalization constants, and determining the generalized scaling functions are beyond the scope of this article. However, we summarize some of the major results for the excluded volume dependence of a variety of equilibrium and dynamic properties of polymers at infinite dilution in terms of the same variables employed to analyze experimental data. The agreement between theory and experiment is very good especially for the crossover regime which is inaccessible to previous theories. It wil l be of interest to extend these theoretical methods to more complicated polymer s y ~ t e m s ~ * ~ l where there are too many relevant parameters for simple scaling13b arguments to provide an adequate zeroth order description.