Macrophase versus Microphase Separation in Solutions of Block Copolymers: Lifshitz Line in the Energetic Parameter's Space

Abstract

AbstractThe aim of this work is an in‐depth study of the stability of solutions of block copolymers with respect to both micro‐ and macrophase separation. For this purpose the correlation functions of block copolymers of various architectures are calculated as well as the critical values ​​of the wave number and Flory Huggins parameter at which a certain type of separation are estimated. As the result, the Lifshitz lines are built. Unlike some preceding papers dealing with the Lifshitz lines in the space of some thermodynamic parameters like polymer volume fraction, temperature, and composition, this consideration here concerns the space of some energetic (molecular) parameters related to the Flory–Huggins interaction parameters. In other words, this study answers a non‐trivial problem in which repeated units are to be chosen to synthesize such a block copolymer of a given architecture that its phase separation in a prescribed (micro‐ or macro) way would be guaranteed. A method is proposed for calculating the Lifshitz lines delimiting the regions of macro‐ and microphase separation in solutions of both diblock copolymers and copolymers of a more complex architecture.