Dynamics of Nonequilibrium Single-Chain Conformations in Triblock Copolymers

Abstract

Using self-consistent field theory (SCFT) and Monte-Carlo simulations, we study the structure and dynamics of loops and bridges in the lamellar phase of symmetric ABA triblock copolymers at χN = 80. The bridge fraction, ν B , linearly correlates with the average variance, X 1 2 = ⟨X ̂1i 2 ⟩, of the first Rouse mode. Using SCFT with constraint X 1 2 , we calculate the free-energy landscape, F(L,X 1 2), and observe a nonmonotonic variation of the optimal lamellar spacing, L*, with X 1 2 . SCFT also provides information about the distribution, P(X ̂1i ), of Rouse modes of individual chains. In the lamellar phase, P exhibits two pronounced peaks, corresponding to the single-chain loop and bridge states. This suggests that the system can be conceived as a mixture of noninteracting loops and bridges with a two-state Markov dynamics, yielding a dynamic equation for the relaxation of the nonconserved, collective order parameter, X 1 2 . These findings are corroborated by multichain simulations of a soft, coarse-grained model. We observe an extremely long relaxation time, 4 × 10 5 τ R , compared to the Rouse time, τ R , in the disordered state. This timescale is the inverse of the conversion rates from loops to bridges and vice versa, which we obtain by single-chain simulations in conjunction with forward-flux sampling. These results suggest that the multichain simulations can be significantly accelerated by the heterogeneous multiscale method (HMM).

Phase Separation of Regular, Quasi-Two-Dimensional AB Copolymer Networks

“…Thus on the scale of a single mesh cell, there exist two distinct mesh-cell configurations, loops and bridges, by analogy to the behavior of multiblock copolymers, ,− and the system can adjust the lamellar period, l *, by changing the statistical weight of loops and bridges. For highly crumpled networks, l u / R db ≪ 1, also l u ≪ l *, and the networks predominately form loops.…”

“…For and moderate incompatibility, the lamellar spacing l * may be smaller than the average mesh-cell size. This results in a bimodal distribution of mesh-cell lengths, by analogy to the formation of loops and bridges in multiblock copolymers. ,− The mesh cells may additionally deform into a rectangle and rotate to reconcile the lamellar spacing, l *, with the average mesh-cell size, l u , giving rise to a multigrain morphology where the lamellar normals make an angle with the global orientation that is dictated by the periodic boundary conditions (or fixing the boundary nodes of the network). This behavior resembles that of nematic or smectic elastomers. − , …”

Stress Chain Analysis for an ABA Triblock Copolymer Using Principal Component Scores

“…Different from an AB diblock copolymer, an ABA triblock copolymer can take bridge conformation in which both of the A blocks are in different A domains, and loop conformation in which both of the A blocks are in the same A domain. The ratio of these chains depends on various structural factors such as chain length, molecular composition, segregation level, and phase-separated structure as well as the process by which the phase-separated structure has been fabricated, − and greatly affects the physical properties under deformation. , In particular, the bridge chains affect the mechanical stress under deformation, and some loop chains also contribute to the stress through entanglements between those chains. ,, Takano et al determined the bridge fraction for seven styrene-based copolymers with similar subchain lengths and different components using the dynamic Young’s modulus measured by dynamic viscoelastic measurements, and then discussed the relationship between the mechanical strength and bridge fractions. They confirmed that the breaking stress in the uniaxial deformation is proportional to the effective bridge fraction, including the stretched loop chains, because of the entanglement of the B block.…”