Quantum Physics Division

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Phase diagram of diblock copolymer melt in dimension d=5

M. Dzięcielski^{1}
,
K. Lewandowski^{1}
,
M. Banaszak^{1}

^{1} Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614, Poznan, Poland

**Computational Methods in Science and Technology, 17(1), 17-23 (2011)**

Abstract:

Using 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 S_{5} nanophase is stable in a narrow strip between ordered S_{4} nanophase and the disordered phase. The calculated order-disorder transition lines depend weakly on d, as expected.

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