An approximation for the intrinsic viscosity of brush-shaped polymers

The dependence of the intrinsic viscosity [eta] on molecular weight and side-chain length for brush-shaped polymers is analyzed using a simplified expression for [eta], in which a brush-shaped polymer is modeled as a linear chain with a contour length equal to that of the backbone of the brush-shaped chain and a repeat unit molar mass that includes the molar mass of the side chain. The treatment is used to estimate the ratio (a) over cap/(a) over cap (ref) of the persistence length (a) over cap of the brush-shaped chain relative to a reference cham as a function of side-chain molecular weight. Values of (a) over cap/(a) over cap (ref) deduced for data on a series of brush-shaped polymers are found to be in good accord with values derived in a more complete treatment of the dependence of [eta] on M based on the wormlike chain model. Estimates of (a) over cap/(a) over cap (ref) are also given for a series Of poly(alkyl methacrylate) chains as a function of the alkyl chain length, and the approximate expression is applied to the evaluation of the true molecular weight from the apparent molecular weight determined in a size exclusion chromatography analysis based on the calibration of the columns in terms of the molecular weight of a standard polymer.