Phase diagrams block copolymers

To estabhsh relationships between different block copolymer phase diagrams and also to facilitate comparison with theory, it is necessary to specify parameters in addition to yN and/. First, asymmetry of the conformation... 

For most BC the phase diagram is characterized by the presence of an upper critical solution temperature, UCST, also known as an order-disorder transition temperature or a microphase separation temperature. Below UCST the block copolymers phase separate, while above it, an isotropic melt is obtained. Owing to the chemical... 

Fig. 4.4 Theoretical diblock copolymer phase diagrams for different levels of polydispersity. a An increase of the overall PDI with identical block PDIs results in a shift towards lower xA values while the phase diagram stays symmetrical (Adapted with permission from Cooke et al. [20]. Copyright 2013 American Chemical Society), b An asymmetrical increase of PDI with PD/a > PDIs shifts the phase boundaries towards decreasing xA and increasing /a values, and creates biphasic regions 2-4>. Note that the phase space of the pure gyroid morphology is even narrower for asymmetric block polydispersities (Reprinted with permission from Matsen et al. [21]. Copyright 2013 by the American Physical Society)...

In a solvent, block copolymer phase behavior is controlled by the interaction between the segments of the polsrmers and the solvent molecules as well as the interaction between the segments of the two blocks. If the solvent is unfavorable for one block, this can lead to micelle formation in dilute solution. The phase behavior of concentrated solutions can be mapped onto that of block copolymer melts (97). Lamellar, hexagonal-packed cylinder, micellar cubic, and bicontinu-ous cubic structures have all been observed (these are all lyotropic liquid crystal phases, similar to those observed for nonionic surfactants). This is illustrated by representative phase diagrams for Pluronic triblocks in Figure 6. 

In a dilute solution, blends of homopolymers A and B equivalent to the two blocks of the copolymers are compatible in a common good solvent contrary to what happens in a highly selective solvent, we do not expect mesophases to form in a dilute solution but only in semidilute and concentrated solutions. Mesophases formed by block copolymers in nonselective solvents have been studied many experimental groups, perhaps most recently bv Hashimoto et al. and Williams et al. The usual interpretation of experiments is based on the "dilution approximation" in which the phase diagram of a solution can be obtained from the corresponding pure copolymer phase diagram by replacing Xab AB where is the monomer volume fraction. We have seen in section... 

An-Chang Shi is a professor of physics at the McMaster Univereity, Hamilton, Ontario, Canada. He received his BSc in physics from Fudan Univereity in 1982 and obtained his PhD in physics from Univereity of Illinois at Urbana-Champaign in 1988. From 1988 to 1892 he was a Post-Doctoral Fellow and Research Associate at McMaster University. He joined Xerox Research Centre of Canada as a Member of Research Staff in 1992, and moved to the Department of Physics and Astronomy at McMaster Univereity in 1999. His main research area concerns the theory of phases and phase transitions in block copolymers. Over the last years, An-Chang Shi has worked on a number of problems in theoretical polymer physics, including the development of statistical mechanics theory for polymeric s) tem the investigation of phase diagrams of block copolymer melts, blends and solutions as well as block copolymers tmder confinement and the study of kinetic pathways of order-order transitions of block copolymer phases. 

Phase Diagrams of Various Block Copolymer Systems Theory. 131... 

Fig. 59 Phase diagram for blend consisting of two symmetric PS-6-PI block copolymers of different molecular weights in parameter space of temperature and fraction of higher molecular weight copolymer, . disordered state lamella A PS cylinder. From [179]. Copyright 2001 American Chemical Society... 

Fig. 61 a Schematic representation of phase diagram of blend of PS-rich (a) with Pi-rich (/S) PS-fc-PI block copolymer in parameter space of a, and T. Expected morphologies of blend specimen are also sketched at b low and c high temperatures. Note phase diagram is effective only for American Chemical Society... 

---