TY - JOUR

T1 - A rigorous derivation of mean-field models describing 2D micro phase separation

AU - Niethammer, Barbara

AU - Oshita, Yoshihito

N1 - Publisher Copyright:
© 2020, The Author(s).
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/4/1

Y1 - 2020/4/1

N2 - We study the free boundary problem describing the micro phase separation of diblock copolymer melts in the regime that one component has small volume fraction ρ such that the micro phase separation results in an ensemble of small disks of one component. We consider the two dimensional case in this paper, whereas the three dimensional case was already considered in Niethammer and Oshita (Calc Var PDE 39:273–305, 2010). Starting from the free boundary problem restricted to disks we rigorously derive the heterogeneous mean-field equations on a time scale of the order of R3ln (1 / ρ) , where R is the mean radius of disks. On this time scale, the evolution is dominated by coarsening and stabilization of the radii of the disks, whereas migration of disks becomes only relevant on a larger time scale.

AB - We study the free boundary problem describing the micro phase separation of diblock copolymer melts in the regime that one component has small volume fraction ρ such that the micro phase separation results in an ensemble of small disks of one component. We consider the two dimensional case in this paper, whereas the three dimensional case was already considered in Niethammer and Oshita (Calc Var PDE 39:273–305, 2010). Starting from the free boundary problem restricted to disks we rigorously derive the heterogeneous mean-field equations on a time scale of the order of R3ln (1 / ρ) , where R is the mean radius of disks. On this time scale, the evolution is dominated by coarsening and stabilization of the radii of the disks, whereas migration of disks becomes only relevant on a larger time scale.

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U2 - 10.1007/s00526-020-1706-x

DO - 10.1007/s00526-020-1706-x

M3 - Article

AN - SCOPUS:85079716917

VL - 59

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

SN - 0944-2669

IS - 2

M1 - 54

ER -