New Fast SCFT Algorithm Applied to Binary Diblock Copolymer/Homopolymer Blends

Abstract

We present an efficient strategy for mapping out the classical phase behavior of block copolymer systems using self-consistent-field theory. With our new algorithm, the complete solution of a classical block copolymer phase can be evaluated typically in a fraction of a second on a single-processor computer, even for highly segregated melts. This is accomplished by implementing the standard unitcell approximation for the cylindrical and spherical phases and solving the resulting equations using a Bessel function expansion. Here the method is used to investigate blends of AB diblock copolymer and A homopolymer, concentrating on the situation where the two molecules are of similar size.

Nanoparticle-regulated phase behavior of ordered block copolymers

“…This attribute, which distinguished such nanoparticles from small nanoparticles or simple low molar mass molecules that interact only by van der Waals forces, is experimentally observed and theoretically predicted. In this spirit, we note that independent studies have shown that the stability of block copolymer nanostructures can likewise be enhanced through the incorporation of selective 37 or functional 38 homopolymers that remain mixed within (and do not macrophase-separate from) the copolymer nanostructure. Addition of selective nanoparticles to ordered block copolymers may therefore not only yield novel, spatially-modulated hybrid materials via nanoparticle assembly 39 for a wide variety of growing nanotechnologies, but also provide an alternative physical means by which to promote polymeric nanostructure development.…”

A multi-species exchange model for fully fluctuating polymer field theory simulations

“…In contrast to microscopic simulation methods like molecular dynamics 3 or coarse-grained Monte Carlo 4 , partition functions containing particle-particle interactions are transformed mathematically such that the fundamental objects in SCFT are auxiliary chemical potential fields and their conjugate monomer species densities. While the field theories underpinning SCFT are formulated in continuous space, a range of numerical methods are available including projection of the fields onto a finite set of basis functions 5,6 , real-space solutions via finite differences on a computational lattice 7 , or pseudo-spectral solutions on a collocation grid invoking fast Fourier Transforms (FFTs) 8,9 . In all of these techniques the continuum SCFT equations are transformed into a large but finite set of non-linear equations that are solved iteratively by relaxation methods.…”

A theoretical and simulation study of the self-assembly of a binary blend of diblock copolymers

“…9 Later studies on blends over a wide range of compositions have mapped out macrophase separation and two-phase coexistence, but they were restricted to the cylinder, lamellar, micellar, and disordered phases only, and did not consider the gyroid phase or other bicontinuous and cocontinuous phases. 10,11 Experiments have shown that it is possible to obtain bicontinuous and cocontinuous phases by blending suitable DBCs-typically an asymmetric copolymer and a symmetric copolymer. [12][13][14] It was also shown that blending two symmetric DBCs does not always lead to a lamellar phase, but also to a spongy phase.…”