Fluctuation effects in blends of A + B homopolymers with AB diblock copolymer

Abstract

Field-theoretic simulations (FTSs) are performed on ternary blends of A- and B-type homopolymers of polymerization N and symmetric AB diblock copolymers of polymerization N. Unlike previous studies, our FTSs are conducted in three-dimensional space, with the help of two new semi-grand canonical ensembles. Motivated by the first experiment to discover bicontinuous microemulsion (BμE) in the polyethylene-polyethylene propylene system, we consider molecules of high molecular weight with size ratios of α ≡ N/N = 0.1, 0.2, and 0.4. Our focus is on the A + B coexistence between the two homopolymer-rich phases in the low-copolymer region of the phase diagram. The Scott line, at which the A + B phases mix to form a disordered melt with increasing temperature (or decreasing χ), is accurately determined using finite-size scaling techniques. We also examine how the copolymer affects the interface between the A + B phases, reducing the interfacial tension toward zero. Although comparisons with self-consistent field theory (SCFT) illustrate that fluctuation effects are relatively small, fluctuations do nevertheless produce the observed BμE that is absent in the SCFT phase diagram. Furthermore, we find evidence of three-phase A + B + BμE coexistence, which may have been missed in the original as well as subsequent experiments.

Instability of the Microemulsion Channel in Block Copolymer-Homopolymer Blends

“…This anomalous behavior, also encountered in Ref. [45], implies that we have overrun the end of the Scott line. We, therefore, conclude that it ends at an ordinary tricritical point near ϕ c ≈ 0.07.…”

“…The first application of FTS was by Düchs et al [33,34], but those studies were limited to 2D. More recently, Spencer and Matsen [45] performed Monte Carlo simulations of H½W − ; w þ in 3D. By adapting the FTS to a variety of different ensembles, they found evidence for A þ B þ BμE coexistence, but the high computational costs limited the size of their simulations boxes and resulted in significant metastability issues.…”

“…We first locate the Scott line separating A þ B coexistence from the DIS state, using the finite-size scaling method [47] detailed in Ref. [45]. This method calculates the fourth-order cumulant,…”

“…For our smallest ϕ c ¼ 0.085, the swelling of the LAM phase limited simulations to two periods, but nevertheless past studies have shown that finite-size effects remain modest even for two periods [49][50][51], and our current simulations support this. The transition between A þ B and LAM is located following a similar approach [45], but with grand-canonical FTS for replicas at different chemical potentials, μ c , spanning the transition. Parallel tempering was disabled because it becomes ineffective due to the large spacing between replicas.…”

Nanostructure stability and swelling of ternary block copolymer/homopolymer blends: A direct comparison between dissipative particle dynamics and experiment

“…In contrast to mean field theories (MFTs), which neglect thermal fluctuations, DPD simulations predict the formation of a βμE phase in symmetric ternary blends, consistent with the experimental observation. We note that field theoretic simulations also find a βμE phase in ternary blends, but always in coexistence with A and B homopolymer phases . Such three‐phase systems have not been observed experimentally for α < 1.…”