Polymer Semiflexibility Induces Nonuniversal Phase Transitions in Diblock Copolymers

Abstract

The order-disorder phase transition and the associated phase diagrams of semiflexible diblock copolymers are investigated using the wormlike chain model, incorporating concentration fluctuations. The free energy up to quartic order in concentration fluctuations is developed with chain-rigidity-dependent coefficients, evaluated using our exact results for the wormlike chain model, and a one-loop renormalization treatment is used to account for fluctuation effects. The chain length N and the monomer aspect ratio α directly control the strength of immiscibility (defined by the Flory-Huggins parameter χ) at the order-disorder transition and the resulting microstructures at different chemical compositions f_{A}. When monomers are infinitely thin (i.e., large aspect ratio α), the finite chain length N lowers the χN at the phase transition. However, fluctuation effects become important when chains have a finite radius, and a decrease in the chain length N elevates the χN at the phase transition. Phase diagrams of diblock copolymers over a wide range of N and α are calculated based on our fluctuation theory. We find that both finite N and α enhance the stability of the lamellar phase above the order-disorder transition. Our results demonstrate that polymer semiflexibility plays a dramatic role in the phase behavior, even for large chain lengths (e.g., N≈100).

100th Anniversary of Macromolecular Science Viewpoint: Opportunities in the Physics of Sequence-Defined Polymers

“…Related single-chain in mean field (SCMF) simulations have demonstrated the importance of addressing these limitations for copolymers, [121][122][123] for example showing that semiflexible random copolymers exhibit non-trivial phase behavior due to how molecular packing and monomer-level structure relate to monomer sequence (Figure 3a). 97,98,124 There is evidence that detailed models, that specifically resolve monomer length-scales, are indeed a crucial aspect for studying sequence-defined polymers. Particle-based computational models have demonstrated sequence-specific effects in compatibilization, 125 where highly non-regular sequences decrease the interfacial tension between two species beyond regular blocky or alternating sequences.…”

“…Complex Langevin (i.e., numerical field theory) calculations can address the limitations of RPA, and has also been used to consider sequence-specificity in charged polymer phase behavior. − However, all of these approaches rely on coarse-grained chain representations (e.g., Gaussian segments) that do not fully resolve the packing and organization of monomer sequences. Related single-chain in mean field (SCMF) simulations have demonstrated the importance of addressing these limitations for copolymers, − for example, showing that semiflexible random copolymers exhibit nontrivial phase behavior due to how molecular packing and monomer-level structure relate to monomer sequence (Figure a). ,, …”

Fluctuation Effects in Semiflexible Diblock Copolymers

“…One source of nonuniversality is the finite polymer flexibility at low molecular weights. Recently, we developed a theory that accounts for polymer semiflexibility and fluctuation effects using the wormlike chain model . We show that phase transitions of semiflexible diblock copolymers with finite aspect ratios strongly deviate from the Gaussian chain theory at molecular weights lower than N ≈ 100.…”

Biology and Physics of Heterochromatin-Like Domains/Complexes

“…A more accurate description is that HP1-containing heterochromatin fibres behave like semi-flexible worm-like chains [ 193 , 221 ]. Semi-flexibility would mean that domains/complexes have their own values for χN ODT distinct from ≈10.5 for bulk di-BCPs that behave as flexible chains governed by Gaussian statistics [ 159 , 222 ]. Accordingly, for the discussion below, the values for the order–disorder transition of heterochromatin- like and Pc-G domains/complexes are termed χN ODT_HC and χN ODT_PC , respectively.…”