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Phase Diagram of Diblock Copolymer Melt in Dimension d = 5

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Dzięcielski M. , Lewandowski K. , Banaszak M.

Computational Methods in Science and Technology

2011

tom Vol. 17, No. 1-2

17-23

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 chi N. 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 chi, 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.

Simulation of Ionic Copolymers by Molecular Dynamics

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Dzięcielski M. , Knychała P. , Banaszak M.

Computational Methods in Science and Technology

2016

tom Vol. 22, No. 4

187--196

Using GROMACS (a molecular dynamics package) we simulate ionic copolymers and compare the numerical results with those obtained by the lattice Monte Carlo simulations. While the results are qualitatively similar for both methods, the simulation times are significantly longer for the molecular dynamics simulations than those for the corresponding Monte Carlo runs

Monte Carlo simulations and self-consistent field theory applied to calculations of density profiles in A1BA2 triblock copolymer melts

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Dzięcielski M. , Wołoszczuk S. , Banaszak M.

Polimery

2014

tom T. 59, nr 7-8

580--584

Using two complementary numerical methods, the lattice Monte Carlo simulations with parallel tempering and self-consistent field theory, we investigate the distribution of A1, B, and A2 segments in the lamellar nanostructure of A1BA2 triblock copolymer melts. While the lattice Monte Carlo method is in principle exact, it is limited by a variety of factors, such as finite size effects, long relaxation times required to reach the thermal equilibrium and geometry of the underlying lattice. It is also limited to chains consisting of relatively few segments. The self-consistent field theory, on the other hand, is free of the above limitations, but it is a mean-field approach which does not take into account the thermal fluctuations. Therefore we confront the results obtained from the two above methods and draw conclusions concerning both the comparison of the two methods and the localization of the A1 segments in the B domain with increasing length of the A1 block. For Monte Carlo simulations we employ two types of chains, 2-32-30 and 1-16-15, and for the self-consistent field theory we use the corresponding values of the thermodynamic incompatibility parameter, c/v.

Teorię samozgodnego pola średniego i symulacje Monte Carlo wykorzystano do oceny dystrybucji segmentów A1, B i A2 w strukturach warstwowych. Porównano wyniki uzyskane za pomocą tych dwóch metod i przedstawiono wnioski dotyczące zmian lokalizacji segmentów A1 w domenie B wraz ze zwiększaniem długości bloków A1.