Weak segregation theory of microphase separation in associating binary homopolymer blends

In this paper we study the phase behavior of blends of associating homopoly mers A and B in the weak segregation regime. The homopolymers are "associat ing" 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, wherea s each A chain might form bonds with several B chains, leading to the forma tion of block copolymer-like clusters. If the hydrogen bonds are strong eno ugh, the system might undergo a microphase separation transition. However, due to the reversible nature of the hydrogen bonds, the system is in dynami c equilibrium, enabling it to adapt its cluster composition to changing con ditions. 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 segrega tion regime this minimization can be split into two independent steps. In t he first step, one determines what the cluster composition would have been if the system were homogeneous. In the second step, this composition is ins erted into the expression for the Landau free energy without the nonlocal t erm. We show that the error made in the first step (neglecting the change i n cluster composition due to the presence of the microstructure) exactly ca ncels the error made in the second step (omission of the nonlocal term from the Landau free energy). For the simplest associating homopolymer blend th e phase diagram is presented.