skip to main content

Title: The C36 Laves phase in diblock polymer melts
The C14 and C15 Laves phases form as micelle packing structures in many types of soft matter, but the related C36 phase, which consists of alternating C14-type and C15-type layers, has not been observed in any such system. To understand this absence in the context of diblock polymers, we used self-consistent field theory to relate the morphology and energetics of C36 to other known mesophases. Two case studies were conducted: blends of AB diblock polymers with A homopolymers (where A forms the micelle core), in which C14 and C15 have stability windows, and neat AB diblock melts, in which Laves phases are metastable. Laves phases exhibit nearly identical micelle morphologies and nearly degenerate free energies, with the free energy of C36 being a near-perfect bisector of the C14 and C15 free energies in all cases, revealing an intrinsic symmetry in free energy that is attributed solely to the structural relationship between the phases in which the packing of C36 is intermediate between C14 and C15. Based on this connection between structure and free energy, C36 is thus not expected to form in flexible diblock polymers, since C14 and C15 can always form instead via facile mass transfer.  more » « less
Award ID(s):
Author(s) / Creator(s):
Date Published:
Journal Name:
Soft Matter
Page Range / eLocation ID:
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. We have combined a neural network formalism with metaheuristic structural global search algorithms to systematically screen the Mg–Ca binary system for new (meta)stable alloys. The combination of these methods allows for an efficient exploration of the potential energy surface beyond the possibility of the traditional searches based on ab initio energy evaluations. The identified pool of low-enthalpy structures was complemented with special quasirandom structures (SQS) at different stoichiometries. In addition to the only Mg–Ca phase known to form under standard synthesis conditions, C14-Mg 2 Ca, the search has uncovered several candidate materials that could be synthesized under elevated temperatures or pressures. We show that the vibrational entropy lowers the relative free energy of several phases with magnesium kagome layers: C15 and C36 Laves structures at the 2 : 1 composition and an orthorhombic oS36 structure at the 7 : 2 composition. The estimated phase transition temperatures close to the melting point leave open the possibility of synthesizing the predicted materials at high temperatures. At high pressures up to 10 GPa, two new phases at the 1 : 1 and 3 : 1 Mg : Ca stoichiometries become thermodynamically stable and should form in multi-anvil experiments. 
    more » « less
  2. Compositionally asymmetric diblock copolymers provide an attractive platform for understanding the emergence of tetragonally close-packed, Frank–Kasper phases in soft matter. Block-polymer phase behavior is governed by a straightforward competition between chain stretching and interfacial tension under the constraint of filling space at uniform density. Experiments have revealed that diblock copolymers with insufficient conformational asymmetry to form Frank–Kasper phases in the neat-melt state undergo an interconversion from body-centered cubic (bcc) close-packed micelles to a succession of Frank–Kasper phases (σ to C14 to C15) upon the addition of minority-block homopolymer in the dry-brush regime, accompanied by the expected transition from bcc to hexagonally packed cylinders in the wet-brush regime. Self-consistent field theory data presented here qualitatively reproduce the salient features of the experimental phase behavior. A particle-by-particle analysis of homopolymer partitioning furnishes a basis for understanding the symmetry breaking from the high-symmetry bcc phase to the lower-symmetry Frank–Kasper phases, wherein the reconfiguration of the system into polyhedra of increasing volume asymmetry delays the onset of macroscopic phase separation.

    more » « less
  3. Self-consistent field theory is employed to compute the phase behavior of binary blends of conformationally asymmetric, micelle-forming diblock copolymers with miscible corona blocks and immiscible core blocks (a diblock copolymer “alloy”). The calculations focus on establishing conditions that promote the formation of Laves phases by tuning the relative softness of the cores of the two different Laves phase particles via independent control of their conformational asymmetries. Increasing the conformational asymmetry of the more spherical particles of the Laves structure has a stabilizing effect, consistent with the expectations of increased imprinting of the Wigner–Seitz cells on the core/corona interface as conformational asymmetry increases. The resulting phase diagram in the temperature-blend composition space features a more stable Laves phase field than that predicted for conformationally symmetric systems. The phase field closes at low temperatures in favor of macrophase separation between a hexagonally-packed cylinder (hex) phase and a body-centered cubic phase. Companion calculations, using an alloy whose components do not produce a hex phase in the neat melt state, suggest that the Laves phase field in such a blend will persist at strong segregation. 
    more » « less
  4. The interaction in aqueous solutions of surfactants with amphiphilic polymers can be more complex than the surfactant interactions with homopolymers. Interactions between the common ionic surfactant sodium dodecyl sulfate (SDS) and nonionic amphiphilic polymers of the poly(ethylene oxide)–poly(propylene oxide)–poly(ethylene oxide) (PEO-PPO-PEO) type have been probed utilizing a variety of experimental techniques. The polymer amphiphiles studied here are Pluronic F127 (EO100PO65EO100) and Pluronic P123 (EO19PO69EO19), having the same length PPO block but different length PEO blocks and, accordingly, very different critical micellization concentrations (CMC). With increasing surfactant concentration in aqueous solutions of fixed polymer content, SDS interacts with unassociated PEO-PPO-PEO molecules to first form SDS-rich SDS/Pluronic assemblies and then free SDS micelles. SDS interacts with micellized PEO-PPO-PEO to form Pluronic-rich SDS/Pluronic assemblies, which upon further increase in surfactant concentration, break down and transition into SDS-rich SDS/Pluronic assemblies, followed by free SDS micelle formation. The SDS-rich SDS/Pluronic assemblies exhibit polyelectrolyte characteristics. The interactions and mode of association between nonionic macromolecular amphiphiles and short-chain ionic amphiphiles are affected by the polymer hydrophobicity and its concentration in the aqueous solution. For example, SDS binds to Pluronic F127 micelles at much lower concentrations (~0.01 mM) when compared to Pluronic P123 micelles (~1 mM). The critical association concentration (CAC) values of SDS in aqueous PEO-PPO-PEO solutions are much lower than CAC in aqueous PEO homopolymer solutions. 
    more » « less
  5. Abstract

    Designed multiblock copolymers with complex architectures offer unlimited opportunities to obtain novel nanostructured phases, however, their synthesis could be challenging and expensive. An alternative approach to access desired nanostructures is to use blends of block copolymers with simple chain architectures and designed block‐block interactions. We use binary blends composed of AB and CD diblock copolymers as a model system to establish design principles of polymeric blends containing block copolymers. Specifically, we explore the phase behavior of AB/CD blends by using the polymeric self‐consistent field theory to construct phase diagrams of the blends focusing on the sphere‐forming regions in the phase space. We predict the formation of various spherical packing phases composed of either core‐shell‐structured spheres or binary spheres resembling metallic alloys. We demonstrate that the equilibrium morphology can be regulated by adjusting the blend composition and molecular parameters such as block fractions, conformational asymmetry, and segment‐segment interactions. The strategy of using secondary interaction in polymeric blends to control the phase behavior explored in the current study can also be generalized to other soft matter systems.

    more » « less