Coexistence of Polymeric Microemulsion with Homopolymer-Rich Phases

Bicontinuous microemulsion in binary blends of complementary diblock copolymers

The phase behavior of binary blends of AB diblock copolymers of compositions f and 1 - f is examined using field-theoretic simulations. Highly asymmetric compositions (i.e., f ≈ 0) behave like homopolymer blends macrophase separating into coexisting A- and B-rich phases as the segregation is increased, whereas more symmetric diblocks (i.e., f ≈ 0.5) microphase separate into an ordered lamellar phase. In self-consistent field theory, these behaviors are separated by a Lifshitz critical point at f = 0.2113. However, its lower critical dimension is believed to be four, which implies that the Lifshitz point should be destroyed by fluctuations. Consistent with this, it is found to transform into a tricritical point. Furthermore, the highly swollen lamellar phase near the mean-field Lifshitz point disorders into a bicontinuous microemulsion (BμE), consisting of large interpenetrating A- and B-rich microdomains. BμE has been previously reported in ternary blends of AB diblock copolymer with its parent A- and B-type homopolymers, but in that system the homopolymers have a tendency to macrophase separate. Our alternative system for creating BμE is free of this macrophase separation.

Phase Separation, Reaction Equilibrium, and Self-Assembly in Binary Telechelic Homopolymer Blends

We study a binary blend of telechelic homopolymers that can form reversible AB-type bonds at the chain ends. Reversibly bonding polymers display novel material properties, including thermal tunability and self-healing, that are not found in conventional covalently bonded polymers. Previous studies of reversibly bonding polymer systems have been limited by the computational demand of accounting for an infinite number of possible reaction products in a spatially inhomogeneous, self-assembled structure. We demonstrate that newly developed theoretical models and numerical methods enable the simultaneous computation of phase equilibrium, reaction equilibrium, and self-assembly via self-consistent field theory. Phase diagrams are computed at a variety of physically relevant conditions and are compared with nonreactive analogues as well as previous experimental studies of telechelic polymer blends.

Assessment of the partial saddle point approximation in field-theoretic polymer simulations

Field-theoretic simulations are numerical treatments of polymer field theory models that go beyond the mean-field self-consistent field theory level and have successfully captured a range of mesoscopic phenomena. Inherent in molecularly-based field theories is a "sign problem" associated with complex-valued Hamiltonian functionals. One route to field-theoretic simulations utilizes the complex Langevin (CL) method to importance sample complex-valued field configurations to bypass the sign problem. Although CL is exact in principle, it can be difficult to stabilize in strongly fluctuating systems. An alternate approach for blends or block copolymers with two segment species is to make a "partial saddle point approximation" (PSPA) in which the stiff pressure-like field is constrained to its mean-field value, eliminating the sign problem in the remaining field theory, allowing for traditional (real) sampling methods. The consequences of the PSPA are relatively unknown, and direct comparisons between the two methods are limited. Here, we quantitatively compare thermodynamic observables, order-disorder transitions, and periodic domain sizes predicted by the two approaches for a weakly compressible model of AB diblock copolymers. Using Gaussian fluctuation analysis, we validate our simulation observations, finding that the PSPA incorrectly captures trends in fluctuation corrections to certain thermodynamic observables, microdomain spacing, and location of order-disorder transitions. For incompressible models with contact interactions, we find similar discrepancies between the predictions of CL and PSPA, but these can be minimized by regularization procedures such as Morse calibration. These findings mandate caution in applying the PSPA to broader classes of soft-matter models and systems.

Emergence of a Spin Microemulsion in Spin-Orbit Coupled Bose-Einstein Condensates

We report the first numerical prediction of a "spin microemulsion"-a phase with undulating spin domains resembling classical bicontinuous oil-water-surfactant emulsions-in two-dimensional systems of spinor Bose-Einstein condensates with isotropic Rashba spin-orbit coupling. Using field-theoretic numerical simulations, we investigated the melting of a low-temperature stripe phase with supersolid character and find that the stripes lose their superfluidity at elevated temperature and undergo a Kosterlitz-Thouless-like transition into a spin microemulsion. Momentum distribution calculations highlight a thermally broadened occupation of the Rashba circle of low-energy states with macroscopic and isotropic occupation around the ring. We provide a finite-temperature phase diagram that positions the emulsion as an intermediate, structured isotropic phase with residual quantum character before transitioning at higher temperature into a structureless normal fluid.

Photocrosslinkable Polymeric Bicontinuous Microemulsions

We present an approach to photocrosslink bicontinuous microemulsions derived from ternary blends of poly(methoxyethyl acrylate) (PM, Mn = 4200 g/mol), poly(hexyl methacrylate-co-coumarin methacrylate) (PHC, Mn = 6800 g/mol), and PM-b-PHC diblock polymer (Mn = 19,400 g/mol) in a phase-selective manner, enabling structural characterization at an unprecedented level of detail. This strategy utilizes the [2 + 2] photodimerization reaction of coumarin derivatives to covalently crosslink blends without the use of harsh reagents or disruptive thermal treatment, thus preserving the intricate network structure throughout curing. The resulting crosslinked bicontinuous microemulsions exhibited rubbery behavior at elevated temperatures, achieving an elastic shear modulus of nearly 1 MPa at 70 °C, owing to the presence of the three-dimensional co-continuous network morphology. The dimensional stabilization afforded by crosslinking further allowed the microstructure to be directly imaged by scanning electron microscopy and atomic force microscopy. Contrary to recent theoretical findings, the BμE appears in a wide temperature and compositional window, suggesting that it is a robust feature of these blends. As a proof of concept demonstrating both the utility of bicontinuous microemulsion-derived materials and versatility of this strategy toward broader applications in energy storage and transport, the uncrosslinked portion of a cured blend was extracted by washing and replaced with an ionic liquid; the resultant heterogeneous solid electrolyte exhibited a room-temperature conductivity of 2 mS/cm, approximately one-quarter that of the pure ionic liquid.

Nonequilibrium Processes in Polymer Membrane Formation: Theory and Experiment

Porous polymer and copolymer membranes are useful for ultrafiltration of functional macromolecules, colloids, and water purification. In particular, block copolymer membranes offer a bottom-up approach to form isoporous membranes. To optimize permeability, selectivity, longevity, and cost, and to rationally design fabrication processes, direct insights into the spatiotemporal structure evolution are necessary. Because of a multitude of nonequilibrium processes in polymer membrane formation, theoretical predictions via continuum models and particle simulations remain a challenge. We compiled experimental observations and theoretical approaches for homo- and block copolymer membranes prepared by nonsolvent-induced phase separation and highlight the interplay of multiple nonequilibrium processes─evaporation, solvent-nonsolvent exchange, diffusion, hydrodynamic flow, viscoelasticity, macro- and microphase separation, and dynamic arrest─that dictates the complex structure of the membrane on different scales.

Field-Theoretic Simulations for Block Copolymer Melts Using the Partial Saddle-Point Approximation

Field-theoretic simulations (FTS) provide an efficient technique for investigating fluctuation effects in block copolymer melts with numerous advantages over traditional particle-based simulations. For systems involving two components (i.e., A and B), the field-based Hamiltonian, Hf[W-,W+], depends on a composition field, W-(r), that controls the segregation of the unlike components and a pressure field, W+(r), that enforces incompressibility. This review introduces researchers to a promising variant of FTS, in which W-(r) fluctuates while W+(r) tracks its mean-field value. The method is described in detail for melts of AB diblock copolymer, covering its theoretical foundation through to its numerical implementation. We then illustrate its application for neat AB diblock copolymer melts, as well as ternary blends of AB diblock copolymer with its A- and B-type parent homopolymers. The review concludes by discussing the future outlook. To help researchers adopt the method, open-source code is provided that can be run on either central processing units (CPUs) or graphics processing units (GPUs).

Field-theoretic simulations beyond δ-interactions: Overcoming the inverse potential problem in auxiliary field models

Modern field-theoretic simulations of complex fluids and polymers are constructed around a particle-to-field transformation that brings an inverse potential u^-1 in the model equations. This has restricted the application of the framework to systems characterized by relatively simple pairwise interatomic interactions; for example, excluded volume effects are treated through the use of δ-function interactions. In this study, we first review available nonbonded pair interactions in field-theoretic models and propose a classification. Then, we outline the inverse potential problem and present an alternative approach on the basis of a saddle-point approximation, enabling the use of a richer set of pair interaction functions. We test our approach by using as an example the Morse potential, which finds extensive applications in particle-based simulations, and we calibrate u^-1 with results from a molecular dynamics simulation. The u^-1 thus obtained is consistent with the field-theoretic model equations, and when used in stand-alone self-consistent field simulations, it produces the correct fluid structure starting from a random initial state of the density field.