Hexagonal Close-Packed Sphere Phase of Conformationally Symmetric Block Copolymer

Abstract

The self-consistent field theory (SCFT) predicted the existence of a close-packed sphere phase over a narrow window in the phase diagram of a block copolymer (bcp). It however remains unclear whether the face-centered cubic (FCC) or hexagonal close-packed (HCP) lattice represents the more stable close-packed lattice of the spherical micelles formed by the neat bcp in the quiescent melt. Here, we revisited this problem by exploring the stable close-packed lattice of conformationally symmetric poly(ethylene oxide)-block-poly(1,2-butadiene) (PEOb-PB). We disclosed that an HCP structure eventually formed in the ordered phase upon cooling from the micellar liquid phase. The micelle ordering was found to follow the Ostwald's step rule of the Alexander−McTague type, where a metastable BCC phase first developed followed by a transformation into the stable HCP structure. The higher thermodynamic stability of HCP relative to that of FCC was consistent with the prediction of a later SCFT calculation by Matsen and also demonstrated the generic difference between soft colloids and hard colloids in selecting their stable close-packed lattices.

Small‐Angle X‐Ray Scattering Studies of Block Copolymer Nano‐Objects: Formation of Ordered Phases in Concentrated Solution During Polymerization‐Induced Self‐Assembly

“…The first three peaks are closely spaced (around 0.03 Å −1 ) and resemble the peak pattern expected for hexagonally close‐packed (HCP) spheres. This phase has been previously observed on numerous occasions for both block copolymers [57, 77] and surfactant lyotropic liquid crystals [78, 79] . Data analysis using peak‐indexing protocols available within DataSqueeze ® 3.0 software [76] confirmed that all SAXS peaks observed on cooling from 90 °C (Figure 4 A) to 25 °C were consistent with an HCP phase (see Figure 4 C for experimental vs. theoretical peak indexing).…”

Emergence of Hexagonally Close-Packed Spheres in Linear Block Copolymer Melts

“…18 (We note that the original publication identified this CPS phase as FCC, the purity of which was later called into question. 19,20 ) Hsu recently reexamined the phase behavior of PEO-b-PBD with a significantly lower molecular weight (M n = 3 kDa, Đ = 1.04, f PEO = 0.167) and identified a slow transformation from BCC to HCP spheres over the course of 120 h at 27 °C, which persisted across a slightly larger temperature range to ∼40 °C. 20 This result is rather surprising; even though SCFT calculations indicate HCP is globally stable, conventional wisdom suggests experimentalists are unlikely to find pure FCC or HCP because the free energy difference separating them is vanishingly small.…”

“…19,20 ) Hsu recently reexamined the phase behavior of PEO-b-PBD with a significantly lower molecular weight (M n = 3 kDa, Đ = 1.04, f PEO = 0.167) and identified a slow transformation from BCC to HCP spheres over the course of 120 h at 27 °C, which persisted across a slightly larger temperature range to ∼40 °C. 20 This result is rather surprising; even though SCFT calculations indicate HCP is globally stable, conventional wisdom suggests experimentalists are unlikely to find pure FCC or HCP because the free energy difference separating them is vanishingly small. 19 The formation of close-packed spheres at extreme compositions near the order−disorder transition is related to chain pullout, which relieves packing frustration by filling the far reaches of Wigner−Seitz cells with compositionally asymmetric chains that approximate homopolymer.…”

“…In pioneering work, Huang and co-workers provide a sense of how limiting these constraints are: a single poly­(ethylene oxide)- b -poly­(1,4-butadiene) (PEO- b -PBD) diblock copolymer ( M n = 14.7 kDa, Đ = 1.05, f PEO = 0.18) self-assembled into coexisting CPS and disordered micelles over a temperature range of about 4 °C . (We note that the original publication identified this CPS phase as FCC, the purity of which was later called into question. , ) Hsu recently reexamined the phase behavior of PEO- b -PBD with a significantly lower molecular weight ( M n = 3 kDa, Đ = 1.04, f PEO = 0.167) and identified a slow transformation from BCC to HCP spheres over the course of 120 h at 27 °C, which persisted across a slightly larger temperature range to ∼40 °C . This result is rather surprising; even though SCFT calculations indicate HCP is globally stable, conventional wisdom suggests experimentalists are unlikely to find pure FCC or HCP because the free energy difference separating them is vanishingly small …”

Small‐Angle X‐Ray Scattering Studies of Block Copolymer Nano‐Objects: Formation of Ordered Phases in Concentrated Solution During Polymerization‐Induced Self‐Assembly

“…Thefirst three peaks are closely spaced (around 0.03 À1 ) and resemble the peak pattern expected for hexagonally close-packed (HCP) spheres.T his phase has been previously observed on numerous occasions for both block copolymers [57,77] and surfactant lyotropic liquid crystals. [78,79] Data analysis using peak-indexing protocols available within Data-Squeeze 3.0 software [76] confirmed that all SAXS peaks observed on cooling from 90 8 8C( Figure 4A)t o2 5 8 8Cw ere consistent with an HCP phase (see Figure 4C for experimental vs.t heoretical peak indexing).…”