Weak segregation theory of microphase separation in associating binary homopolymer blends

In this paper we study the phase behavior of blends of associating homopolymers A and B in the weak segregation regime. The homopolymers are "associating" in the sense that hydrogen bonds are possible between the A chains and the B chains. Hydrogen bonds between two A chains, or between two B chains, are not possible. Each B chain can form at most one hydrogen bond, whereas each A chain might form bonds with several B chains, leading to the formation of block copolymer-like clusters. If the hydrogen bonds are strong enough, the system might undergo a microphase separation transition. However, due to the reversible nature of the hydrogen bonds, the system is in dynamic equilibrium, enabling it to adapt its cluster composition to changing conditions. Therefore, to construct the phase diagram, the free energy should be minimized simultaneously with respect to the cluster composition and the parameters describing the microstructure. We show that in the weak segregation regime this minimization can be split into two independent steps. In the first step, one determines what the cluster composition would have been if the system were homogeneous. In the second step, this composition is inserted into the expression for the Landau free energy without the nonlocal term. We show that the error made in the first step (neglecting the change in cluster composition due to the presence of the microstructure) exactly cancels the error made in the second step (omission of the nonlocal term from the Landau free energy). For the simplest associating homopolymer blend the phase diagram is presented.