Various Low-Symmetry Phases in High-χ and Conformationally Asymmetric PDMS-b-PTFEA Copolymers

Abstract

Since the discovery of the Frank−Kasper (FK) phase a decade ago, single-component block copolymer systems have offered unique opportunities to explore the structural and phase-transition properties of topologically close-packed FK phases composed of point-particle motifs. Here, we present the formation of complex low-symmetry phases and their thermodynamic stability using high-χ and high-ε linear diblock copolymers, where χ and ε are the Flory−Huggins interaction parameter and conformational asymmetry between the two blocks, respectively. A series of polydimethylsiloxane-b-poly(2,2,2-trifluoroethyl acrylate) (PDMS-b-PTFEA) copolymers are prepared by tuning the volume fraction (f PTFEA ) of a minor PTFEA block. The packing structures of PDMS-b-PTFEAs are mapped in the space of temperature versus f PTFEA using X-ray scattering measurements. In addition to the packing structures reported earlier, we identify another A15 phase at higher f PTFEA close to a hexagonally packed cylinder (HEX) phase and establish the phase sequence of HEX−A15−σ−C14−BCC with decreasing f PTFEA . Theoretical calculation of relative freeenergy densities confirms the experimental phase sequence of the composition-dependent sphere-packing structures. Interestingly, the domain sizes of three-dimensional (3D) sphere-packing structures are nearly temperature-invariant compared to that of a twodimensional HEX structure, and we attribute this dimensional stability to the strong enthalpic effects in the formation of 3D packing structures and the geometrical characteristics of spherical domains. Our results demonstrate that the interaction parameter χ, together with the known role of conformational asymmetry ε, serves as the primary thermodynamic parameter for selecting and stabilizing various low-symmetry packing structures in sphere-forming linear diblock copolymer systems.

Frank–Kasper Phases of Diblock Copolymer Melts Studied with the DPD Model: SCF Results

“…While this is the first time C14 is predicted to be stable in SCF calculations of neat DBC melts, and our ε-range includes that of PF-PDMS for which stable C14 is found by Ryu et al, they also reported σ and A15 formed in this DBC. 33,34 Given the many differences (in, for example, polydispersity, χ-value, etc.) between experimental and model systems, the aforementioned direct comparison between the SCF and simulation results based on exactly the same model system is the only way to unambiguously quantify the fluctuation/correlation effects inherently neglected by the SCF theory, but important in the low-molecular-weight DBC melts forming FK phases in experiments; this will be reported in future publications.…”

“…44,45 While SCF theory 46 can be considered as the most successful molecular-level theory for BCP assembly partly due to its well-developed numerical calculations, 45,47−54 as a mean-field theory, it neglects the effects of system fluctuations/correlations, thus corresponding to the limit of , where the invariant degree of polymerization 55 nR V ( / ) e 3 2 controls the fluctuations/correlations in a melt of n DBC chains in volume V with R e being the root-mean-square chain end-to-end distance. In comparison, all neat DBC melts forming FK phases in experiments to date 12,14,16,17,21,[29][30][31][32][33][34][35]37,38 have 25 385 < < , with only one exception 36 of 520. We also note that the aforementioned SCF calculations show that σ is unstable for ε < 2.1, 14,16,39 thus overestimating the ε-value needed for obtaining σ and A15 in experiments.…”

“…36 Similarly, A15 has been found in PLA-PDDA, 14,32 PF-PDDA, 37 and PF-PDMS. 34 In comparison, other FK phases have been much less studied. Kunieda and co-workers suggested C15 formed in PEO-PDMS, 17 Bates and co-workers studied metastable C14 and C15 formed in PLA-PI, 16,38 and very recently, Ryu and coworkers reported stable C14 formed in PF-PDMS.…”

“…Their stability can be attributed to the conformational asymmetry between the two blocks, characterized by ε ≡ ( a A / a B ) 2 , where a P (P = A,B) denotes the statistical segment length of the P block calculated using the same reference volume for A- and B-segments. To date, several experimental groups have reported σ in poly­(lactide)-poly­(isoprene) (PLA-PI with ε = ( a PLA / a PI ) 2 ≈ 1.32), ,,− PLA-poly­(ethylethylene) (PLA-PEE with ε = ( a PLA / a PEE ) 2 ≈ 1.68), PLA-poly­(dodecyl acrylate) (PLA-PDDA with ε = ( a PLA / a PDDA ) 2 ≈ 3.4), , poly­(trifluoroethyl acrylate)-PDDA (PF-PDDA with ε ≡ ( a PF / a PDDA ) 2 ≈ 2.0), PF-poly­(dimethylsiloxane) (PF-PDMS with ε = ( a PF / a PDMS ) 2 ≈ 2.2), , poly­(ethylene oxide)-poly­(2-ethyl hexylacrylate) (PEO-PA with ε ≡ ( a PEO / a PA ) 2 ≈ 3.5), and PEP-PDMS (with ε ≡ ( a PEP / a PDMS ) 2 ≈ 1.6) . Similarly, A15 has been found in PLA-PDDA, , PF-PDDA, and PF-PDMS …”

“…To date, several experimental groups have reported σ in poly­(lactide)-poly­(isoprene) (PLA-PI with ε = ( a PLA / a PI ) 2 ≈ 1.32), ,,− PLA-poly­(ethylethylene) (PLA-PEE with ε = ( a PLA / a PEE ) 2 ≈ 1.68), PLA-poly­(dodecyl acrylate) (PLA-PDDA with ε = ( a PLA / a PDDA ) 2 ≈ 3.4), , poly­(trifluoroethyl acrylate)-PDDA (PF-PDDA with ε ≡ ( a PF / a PDDA ) 2 ≈ 2.0), PF-poly­(dimethylsiloxane) (PF-PDMS with ε = ( a PF / a PDMS ) 2 ≈ 2.2), , poly­(ethylene oxide)-poly­(2-ethyl hexylacrylate) (PEO-PA with ε ≡ ( a PEO / a PA ) 2 ≈ 3.5), and PEP-PDMS (with ε ≡ ( a PEP / a PDMS ) 2 ≈ 1.6) . Similarly, A15 has been found in PLA-PDDA, , PF-PDDA, and PF-PDMS …”