Phase behavior of homopolymer/diblock blends
Janert, Philipp Klaus, 1970-
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We study the micro- and macrophase behavior of symmetric AB-diblock copolymers in binary and ternary blends with corresponding homopolymers in mean field theory and for weak to intermediate segregation. We employ the standard Gaussian chain model and numerically solve the mean field equation in Fourier space. Besides homogeneous phases, we consider the following ordered morphologies: sheetlike lamellae, hexagonally arranged cylinders, and spheres on a body-centered-cubic lattice. We consider only symmetric diblocks, but vary the chain length of the homopolymers from 0.1 to 1.5 the length of the copolymer. For the ternary systems, we produce several constant temperature cuts through the Gibbs phase prism. For the binary system, we also study the temperature dependence of the phase diagram. For the symmetric system, in which both homopolymers are of equal length with the diblock, we consider the temperature dependence at all compositions of the ternary mixture. We find the following general trends: homopolymers, longer than the copolymer are expelled from the microstructure and phase separate. Homopolymers comparable to or shorter than the diblock, swell the microstructure, whereas very short homopolymers tend to destroy any ordered phase. For a narrow region in the weak to intermediate segregation regime, homopolymers comparable in length to the diblock can swell the microstructure indefinitely, leading to a complete unbinding of the ordered phase. The transition from bound to unbound as temperature is varied can be either continuous or first-order. In the latter case, the expected preunbinding line is found as a coexistence region between two different ordered phases with the same symmetry, but of different periodicity. For the symmetric system, in which all chains are of equal length, we find a multicritical Lifshitz point within mean field theory. All these results can be understood in terms of simple brush- and stretching arguments. A comprehensive overview over the statistical theory of flexible chain molecules has been provided, as well as a review over previous experimental and theoretical investigations of self-assembly in block copolymers systems.
- Physics