Abstract
Field-theoretic simulations (FTS) provide an efficient technique for investigating fluctuation effects in block copolymer melts with numerous advantages over traditional particle-based simulations. For systems involving two components (i.e., A and B), the field-based Hamiltonian, , depends on a composition field, , that controls the segregation of the unlike components and a pressure field, , that enforces incompressibility. This review introduces researchers to a promising variant of FTS, in which fluctuates while tracks its mean-field value. The method is described in detail for melts of AB diblock copolymer, covering its theoretical foundation through to its numerical implementation. We then illustrate its application for neat AB diblock copolymer melts, as well as ternary blends of AB diblock copolymer with its A- and B-type parent homopolymers. The review concludes by discussing the future outlook. To help researchers adopt the method, open-source code is provided that can be run on either central processing units (CPUs) or graphics processing units (GPUs).
Highlights
Block copolymers refer to polymeric molecules composed of two chemically-distinct segments, generally denoted as A and B, that are grouped together into separate sections or rather blocks [1,2]
The segments will differ in their interactions, usually resulting in an incompatibility characterized by a positive Flory–Huggins interaction parameter, χ
There is, some significant deviation at weak segregations, where the Field-theoretic simulations (FTS) results coincide with the mean-field or rather random-phase approximation (RPA) [22] as opposed to the more accurate renormalized one-loop calculation (ROL) theory
Summary
Block copolymers refer to polymeric molecules composed of two chemically-distinct segments, generally denoted as A and B, that are grouped together into separate sections or rather blocks [1,2]. The ODT is bounded by the spherical phase, whereas in experiments there is no critical point and instead all the ordered phases generally extend to the ODT [23] This qualitative shortcoming of SCFT occurs because it neglects composition fluctuations, which are important in the disordered phase [18]. Have predicted that the fluctuations destabilize the complex Fddd phase, which is contrary to experiments [27,28] This is not surprising given the significant approximations involved in the Fredrickson–Helfand theory, which cause the spherical phase to become unstable at experimentally relevant values of N. We provide open-source code for neat diblock copolymer melts that can be readily modified to handle more complex systems
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