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Volume 17 (1-2) 2011, 17-23

Phase Diagram of Diblock Copolymer Melt in Dimension d = 5

Dzięcielski Michał, Lewandowski Krzysztof, Banaszak Michał

Faculty of Physics, A. Mickiewicz University
ul. Umultowska 85, 61-614 Poznań, Poland
e-mail: mbanasz@amu.edu.pl

Received:

Received: 21 November 2011; revised: 05 December 2011; accepted: 09 December 2011; published on-line: 15 December 2011

DOI:   10.12921/cmst.2011.17.01.17-23

OAI:   oai:lib.psnc.pl:735

Abstract:

Using the self-consistent field theory (SCFT) in spherical unit cells of various dimensionalities, D, a phase diagram of a diblock, A-b-B, is calculated in 5 dimensional space, d = 5. This is an extension of a previuos work for d = 4. The phase diagram is parameterized by the chain composition, f, and incompatibility between A and B, quantified by the product χN. We predict 5 stable nanophases: layers, cylinders, 3D spherical cells, 4D spherical cells, and 5D spherical cells. In the strong segregation limit, that is for large χN, the order-order transition compositions are determined by the strong segregation theory (SST) in its simplest form. While the predictions of the SST theory are close to the corresponding SCFT extrapolations for d = 4, the extrapolations for d = 5 significantly differ from them. We find that the S5 nanophase is stable in a narrow strip between the ordered S4 nanophase and the disordered phase. The calculated orderdisorder transition lines depend weakly on d, as expected

Key words:

diblock copolymer melt, field theory, order-disorder transition, order-order transition, phase diagram

References:

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