Design of ABC triblock copolymers near the ODT with the random phase approximation

Leibler's random phase approximation for block copolymers, modified so as to be applicable to linear multiblock copolymers, has been quantitatively compared to data from three linear ABC/ACB triblock copolymer melts: poly(cyclohexylethylene-b-ethylene-b-ethylethylene) (CEE_E)/CE_EE, poly(styrene-b-isoprene-b-ethylene oxide) (SIO)/ISO (Macromolecules 2001, 34, 6994,-7008;Macromolecules 2002, 35, 7007-7017), and poly(styrene-b-isoprene-b-dimethylsiloxane) (SID)/ISD (Macromolecules 2002, 35, 3189-3197). The RPA calculation provides the mean-field static structure factor for a disordered block copolymer melt, which can be used to anticipate the scattering behavior and spinodal stability limit temperature (T_s); in the context of mean-field theory, the spinodal should lie near the order-disorder-transition temperature (T_ODT). We find that the RPA spinodal temperature semiquantitatively matches the magnitude and temperature dependence of the ODT as a function of molecular weight (in CE_EE/CEE_E) and composition (SIO/ISO). Furthermore, the structure factor also reproduces scattering phenomena in ABC triblock copolymers (ISD/SID) such as the two-peak profile observed in disordered ISD with X-ray scattering. The results show that the RPA is a useful tool in the design of multiblock copolymers without reliance on existing experimental data or cumbersome numerical self-consistent field calculations.