Unusual finite size effects in the Monte Carlo simulation of microphase formation of block copolymer melts

Abstract

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.