Order–disorder transition of polystyrene-block-polyisoprene Part II. Characteristic length as a function of polymer concentration, molecular weight, copolymer composition, and χ parameter

A series of polystyrene-block-polyisoprene diblock copolymers having various degrees of polymerization Nn and composition fPS were studied as a function of temperature T and polymer concentration φp by means of in situ small-angle X-ray scattering methods. The results indicated that the characteristic length D as evaluated from D=2π/qm with qm being the wave number of the first-order scattering maximum was found to obey the following scaling law: D∼(φp/T)1/3Nn2/3 for φp/T≥(φp/T)MF∼Nn−1/2, and D∼(φp/T)0Nn1/2 for φp/T≤(φp/T)MF for the copolymer systems covered in this work. Here (φp/T)MF is a crossover value of φp/T from the mean-field disordered state to the non-mean-field disordered state. These results are consistent with our previous experimental observations [Hashimoto et al., Macromolecules 16 (1983) 1093]. The results obtained here together with our previous results of χeff∼(φp/T)Nn−1/2 and D0∼Nn1/2 (Mori et al., J Chem Phys, 104 (1996) 7765) give the following scaling law:D/D0∼(χeffNn)1/3 for (χeffNn)≥(χeffNn)MFandD/D0∼(χeffNn)0 for (χeffNn)≤(χeffNn)MFwhere χeff is an effective segmental interaction parameter between polystyrene and polyisoprene segments at a given φp and T for a given copolymer, and D0 is the wavelength of the dominant mode of the concentration fluctuations of the copolymer systems in the mean-field disordered state. (χeffNn)MF is the crossover value of χeffNn at the mean-field disordered state to the non-mean-field disordered state, which depends on fPS.