Dresden 2009 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 24: Pattern formation in colloidal and granular systems I

DY 24.7: Talk

Thursday, March 26, 2009, 16:15–16:30, ZEU 255

Fractionation in random symmetric A-B block copolymers — •Alice von der Heydt and Annette Zippelius — Institut für Theoretische Physik, Göttingen, Germany

Starting from a mean-field free energy based on a microscopic model, we investigate the coexistence of homogeneous and structured phases of a triblock copolymer melt with an incompatibility χ∝ 1/T between A- and B-blocks. The natural random block sequence distribution is generated by a Markov process with an overall A-probability p=1/2 and a correlation parameter λ. The latter determines the structure of the ordered phases which the initially disordered melt forms on increasing χ: lamellae with wave number k(λ) appear for λ < λ_c, two homogeneous A- and B-rich phases for λ > λ_c [1].

An explicit fractionation ansatz takes into account the exchange of individual sequences between coexisting lamellar and homogeneous phases: higher χ give rise to two additional homogenous phases for λ < λ_c, and to a third lamellar phase with an increased content of alternating sequences for λ > λ_c. The new phases emerge with zero volume fraction, but with a finite deviation from the natural sequence distribution, and, for the fractionated lamellae, with finite k. Reliable results can be obtained especially in the vicinity of the tricritical point (λ_c, χ_c), where other methods encounter difficulties.

[1] G. H. Fredrickson, S. T. Milner, and L. Leibler, Multicritical Phenomena and Microphase Ordering in Random Block Copolymer Melts, Macromol. 25 (1992), 6341