Block copolymer molecular weight determination via gel permeation chromatography: Choosing a combining rule

We present a method for accurately determining the true molecular weights of narrow-distribution block copolymers, using only a basic gel permeation chromatograph (GPC) equipped with a refractive index detector and calibrated with polystyrene standards. Our approach is based on the well-known observation that GPC calibration curves for different homopolymers in good solvents are essentially parallel, allowing the curves for different polymers to be described by simple hydrodynamic equivalence ratios r_B versus polystyrene. We present values of r_B, in both toluene and tetrahydrofuran, for various polydiene and hydrogenated polydiene homopolymers commonly incorporated into commercial styrenic block copolymers. These values of r_B must be combined to yield the hydrodynamic equivalence ratio of the block copolymer, from which the block copolymer's true molecular weight can be determined. Three combining rules proposed in the literature are tested against a series of symmetric polystyrene-polybutadiene diblock copolymers of varying molecular weight. A simple linear combining rule accurately represents the results.