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Unusual finite size effects in the Monte Carlo simulation of microphase formation of block copolymer melts
Author(s) -
Micka Uwe,
Binder Kurt
Publication year - 1995
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.1995.040040303
Subject(s) - monte carlo method , radius of gyration , periodic boundary conditions , copolymer , gyration , scaling , statistical physics , physics , materials science , lattice (music) , polymer , thermodynamics , condensed matter physics , boundary value problem , mathematics , geometry , quantum mechanics , nuclear magnetic resonance , statistics , acoustics
Abstract Extensive Monte Carlo simulations are presented for the Fried‐Binder model of block copolymer melts, where polymer chains are represented as self and mutually avoiding walks on a simple cubic lattice, and monomer units of different kind (A, B) repel each other if they are nearest neighbors (ε AB > 0). Choosing a chain length N = 20, vacancy concentration Φ v = 0,2, composition ƒ = 3/4, and a L × L × L geometry with periodic boundary conditions and 8 ≤ L ≤ 32, finite size effects on the collective structure factor S ( q ) and the gyration radii are investigated. It is shown that already above the microphase separation transition, namely when the correlation length ξ( T ) of concentration fluctuations becomes comparable with L , a nonmonotonic variation of both S ( q ) and the radii with L sets in. This variation is due to the fact that the wavelength λ * ( T ) of the ordering (defined from the wavenumber q * where S ( q ) is maximal at λ * = 2 π/ q * ) in general is incommensurable with the box. The competition of two nontrivial lengths ξ( T ), λ * ( T ) with L makes the straigthforward application of finite size scaling techniques impossible, unlike the case of polymer blends. Since also the specific heat is found to have a broad rounded peak near the transition only, locating the transition accurately from Monte Carlo simulations remains an unsolved problem.