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Self-consistent mean field theory of the lamellar morphology of binary copolymer-homopolymer blends Vavasour, Jeffrey David

Abstract

The mean field theory of neat copolymers [1] has been extended to consider binary copolymer-homopolymer blends. A set of self-consistent equations was derived describing the most-probable configuration of the system for a given set of parameters. Numerical techniques yielded the density distributions of the copolymer blocks and homopolymer. The lamellar microphase-separated state of the copolymer-homopolymer blend was probed over a wide range of system parameters. For blends in which the ratio of homopolymer molecular volume to copolymer molecular volume, fH, was negligible, the system was found to mimic a copolymer-solvent blend, [2] with a reduction in the domain thickness analogous to that seen in the dilution approximation of neutral solvents. When fH ≅ 0.5, the homopolymer was found to reside preferentially at the centre of the copolymer's subdomain of like-species. This localisation enlarged the subdomain appropriately for the homopolymer volume and, as a by-product, enlarged the total domain thickness of the lamellar unit cell relative to the neat case. At intermediate fH, a balance was struck in which the domain thickness was largely unaffected by the addition of homopolymer. Unlike the prior fourth-order Many-Wave Approximation (MWA) result, [3] this effect seemed to manifest after an initial stabilising quantity of homopolymer localised at the interphase. The value of fH at which the domain thickness was most stable was roughly 4.50(xTc)~1.36, where xTc is the product of the Flory parameter and the copolymer molecular volume in appropriate dimensionless units. As expected, the MWA and the current result's weak-segregation limit were in agreement. Our results suggest that an experimental investigation into homopolymer localisation is warranted. [Scientific formulae used in this abstract could not be reproduced.]

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