Theory for the effect of polydispersity on the phase behaviour of diblock copolymers

Abstract

<P> Polymers are one of the most prevalent types of molecules in modern life. These long macromolecules make up everything from DNA to plastics to Jell-0™. An interesting class of polymers are block copolymers, which are composed of two (or more) chains, or blocks, of chemically distinct monomers covalently bonded end-to-end to form a single polymer. Different types of polymers tend to avoid each other, but since block copolymers are joined together the polymer species can not macroscopically phase separate. Instead, they separate on the scale of the size of the polymers, forming nanostructures. For a diblock copolymer melt, which is made from two types of polymers, these nanostructures can be, depending on the ratio of the length of one block to the other, spheres, cylinders, lamellae, or the more bizarre gyroid phase. </p> <P> Self-consistent field theory (SCFT) as formulated by Helfand in 1975 has in recent years been successfully applied to the study of the phase behaviour of diblock copolymers. However, most of the studies assume that the polymers are monodisperse, while almost all polymer melts are polydisperse. This work examines the effect of polydispersity in the block lengths on phase behaviour of diblock copolymer melts, by developing the SCFT for polydisperse block copolymers. The theory is examined using a perturbation method, as well as the random-phase approximation (RPA). The perturbation parameter is the ratio K of the weight-averaged molecular weight and the number-averaged molecular weight, which is a common measure of polydispersity. </p> <P> The results show polydispersity shifts the transition from a disordered phase to an ordered phase to a higher temperature, and increases the period of the nanostructures. It is also observed that polydispersity leads to larger non-lamellar phase regions in the phase diagrams. Results from the RPA also suggest that macrophase separation occurs for large polydispersities. </p>