Architecture Effects in Complex Spherical Assemblies of (AB)_n-Type Block Copolymers

Abstract

Molecular architecture plays a key role in the selfassembly of block copolymers, but few studies have systematically examined the influence of chain connectivity on tetrahedrally close-packed (TCP) sphere phases. Here, we report a versatile material platform comprising two blocks with substantial conformational asymmetry, A = poly(trifluoroethyl acrylate) and B = poly(dodecyl acrylate), and use it to compare the phase behavior of AB diblocks, ABA triblocks, and (AB) n radial star copolymers with n = 3 or 4. Each architecture forms TCP sphere phases at minority A block compositions (f A < 0.5), namely, σ and A15, but with differences in the location of order−order phase boundaries that are not anticipated by mean-field self-consistent field theory simulations. These results expand the palette of polymer architectures that readily self-assemble into complex TCP structures and suggest important design considerations when targeting specific phases of interest.

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

“…Phase diagrams were constructed for FDF, F2DF, and F4DF using a combination of small-angle X-ray scattering (SAXS) to interrogate self-assembly (Figures S8–S14) and dynamic mechanical thermal analysis (DMTA, Figure S15) to measure order–disorder transition temperatures ( T ODT ) by monitoring changes in G ′ on slow heating (2 °C/min) at a fixed low frequency (ω = 1 rad/s). To map volumetric degree of polymerizations ( N ) onto segregation strength ( χN ), the Flory–Huggins interaction parameter χ = α/ T + β of each monomer pair was determined from experimentally measured T ODT values for a series of compositionally symmetric samples ( f F ≈ 0.5) using the mean-field result for symmetric triblock copolymers: ( χN ) ODT = 18.996. , See the Supporting Information (Figure S16) for details of our analysis by linear regression, which yielded the following expressions: χ FDF = (84 ± 1)/ T – (0.101 ± 0.003), χ F2DF = (77 ± 7)/ T – (0.06 ± 0.03), and χ F4DF = (59 ± 5)/ T + (0.02 ± 0.01). Note that the FDF expression was previously reported and is reproduced here for comparison …”

“…(We note in passing that samples at low f F show a reversible, temperature-dependent CPS−BCC order−order transition that is counter to theoretical predictions. 35 ) In contrast, F2DF and F4DF both form pure HCP but with different windows of stability. F2DF selfassembles into pure HCP at a single composition (f F = 0.23, Figure S9), as did four different F4DF samples spanning at least 5 volume percent (f F = 0.25−0.30, Figure S10).…”

“…Note that the FDF expression was previously reported and is reproduced here for comparison. 35 Figure 2 summarizes the phase behavior of FDF, F2DF, and F4DF at minority F-block volume fractions (f F < 0.5). A number of unique features are apparent, most notably regions of pure HCP found with F2DF and F4DF triblocks, which is also observed in 4DF diblocks (Figure S11).…”

“…We have previously estimated the conformational asymmetry of FDF as 43, where b i is the statistical segment length of block i as calculated from the entanglement plateau measured by rheology. 35 Here, we attempted to perform a similar analysis to estimate ε F2D and ε F4D but encountered difficulties synthesizing the homopolymers of 2-dodecyl acrylate and 4-dodecyl acrylate with sufficiently high molecular weight (>100 kDa) to show a prominent entanglement plateau. Nevertheless, the fact that A15 appears in the F2DF and F4DF phase diagrams strongly suggests ε F2D and ε F4D are comparable to ε FD , as the stabilization of the A15 phase requires even higher values of ε than σ.…”

Topological Defects, Inherent Structures, and Hyperuniformity

“…Given this difference, it would be interesting to explore the impact of topological defects on the large-scale structural features of crystals in three dimensions, and the potential findings may shed light on the emergence of hyperuniformity in certain disordered inherent structures. For example, there were theories [50] suggesting that MRJ packings (or random close packings as termed by many experimentalists) might be considered as disordered topological variants of the tetrahedral particle packings, just like that Frank-Kasper phases [50,60,61] are considered as ordered topological variants.…”