Structure formation in films of weakly charged block polyelectrolyte solutions

Physics-based computational and theoretical approaches to intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) are an important class of proteins that do not fold to a well-defined three-dimensional shape but rather adopt an ensemble of inter-converting conformations. This feature makes their experimental characterization challenging and invites a theoretical and computational approach to complement experimental studies. In this review, we highlight the recent progress in developing new computational and theoretical approaches to study the structure and dynamics of monomeric and order higher assemblies of IDPs, with a particular emphasis on their phase separation into protein-rich condensates.

Self-assembled morphologies of an amphiphilic Y-shaped weak polyelectrolyte in a thin film

Different from the self-assembly of neutral polymers, polyelectrolytes self-assemble into smaller aggregates with a more loosely assembled structure, which results from the repulsive forces acting between similar electrical compositions with the introduction of ions. The Y-shaped weak polyelectrolytes self-assemble into a core-shell type cylindrical structure with a hexagonal arrangement in a thin film, whose thickness is smaller than the gyration radius of the polymer chain. The corresponding formation mechanism consists of enrichment of the same components, adjustment of the shape of the aggregate, and the subsequent separation into individual aggregates. With the increase in the thickness of the thin film until it exceeds the gyration radius of the polymer chain, combined with the greater freedom of movement along the direction of thin film thickness, the self-assembled structure changes into a micellar structure. Under confinement, the repulsive force to the polymeric components is weakened by the repulsive forces among polyelectrolyte components with like charges, and this helps in generating aggregates with more uniform size and density distribution. In particular, when the repulsive force between the walls and the core forming components is greater than that between the walls and the shell forming components, such asymmetric confinement produces a crossed-cylindrical structure with nearly perpendicular arrangement of two cylinder arrays. Similarly, a novel three-crossed cylinder morphology is self-assembled upon removal of confinement.

Morphology of lipid-like structured weak polyelectrolyte poly(ethylene oxide)-block-poly(methyl methacrylate) diblock copolymers induced by confinements

Combined with quantum calculations and mesoscale simulations, the self-assembly of twelve lipid-structured PEO-b-PMMA copolymers (BCPs) with six types of molecular topologies was investigated. The BCPs with MMA species as the connecting center of the other arms present ample mesoscale structures, such as micelles and lamellae or curved lamellar phases, and even macrophase separation occurs for the long-chained BCPs. The excluded volume effect of confinements helps form vesicle-like structures, which proved to be a possible method of confinement to regulate phase morphologies or segment distributions and, ultimately, the properties of materials. An analysis of the phase formation process of short-chained BCP with two hydrophilic EO segments and one hydrophobic MMA segment indicated that four stages were found in both neutral and non-neutral wall confinement, all of which present a hexagonal columnar phase. Surprisingly, when the repulsion effect of the wall to the EO segment is greater than that of the MMA segment, such BCP self assembles into a crossed columnar phase, and the intersection angle of the orientation of these two sets of cylinder arrays is 75 degrees, which can be used to produce heterogeneous nanotube arrays. For the short-chained BCP with four arms joined at MMA species and EO segments in the outer region, we found a novel method of exchanging the repulsive preference of the wall to the EO or MMA species that can control the adsorption or desorption of the lamellar phase with the interval of EO or MMA segments.

Mesoscopic simulation of the self-assembly of the weak polyelectrolyte poly(ethylene oxide)-block-poly(methyl methacrylate) diblock copolymers

We designed twelve types of weak polyelectrolytes (i.e., PEO-b-PMMA copolymers (BCP) in multi-arm structures, where six include EO blocks as joint points and the other six have MMA blocks as joint points). All of the BCPs with EO as the joint points form disordered phases with the exception of long-chained and four-armed BCP. The main mesophases of all of the BCPs with MMA as joint points are micelle-like and bicontinuous phases. In particular, the short-chained BCP with four-arms and EO segments outside form a new phase type (i.e., crossed lamellar phase). Using MesoDyn, we provide a comprehensive representation of the micelle and crossed lamellar phase formation mechanisms based on both thermodynamic and dynamic analyses. A shear force on a micelle-like phase could promote a hexagonal columnar phase, which is a good technique for generating an ordered arrangement of nanotube arrays. Blending homopolymers with the same constituents could promote uniformity of the micelle size and decrease the polydispersity, especially for blends with a high BCP concentration, which may provide a new approach for regulating the properties of materials.

Self-assembly in Nafion membranes upon hydration: water mobility and adsorption isotherms

By means of dissipative particle dynamics (DPD) and Monte Carlo (MC) simulations, we explored geometrical, transport, and sorption properties of hydrated Nafion-type polyelectrolyte membranes. Composed of a perfluorinated backbone with sulfonate side chains, Nafion self-assembles upon hydration and segregates into interpenetrating hydrophilic and hydrophobic subphases. This segregated morphology determines the transport properties of Nafion membranes that are widely used as compartment separators in fuel cells and other electrochemical devices, as well as permselective diffusion barriers in protective fabrics. We introduced a coarse-grained model of Nafion, which accounts explicitly for polymer rigidity and electrostatic interactions between anionic side chains and hydrated metal cations. In a series of DPD simulations with increasing content of water, a classical percolation transition from a system of isolated water clusters to a 3D network of hydrophilic channels was observed. The hydrophilic subphase connectivity and water diffusion were studied by constructing digitized replicas of self-assembled morphologies and performing random walk simulations. A non-monotonic dependence of the tracer diffusivity on the water content was found. This unexpected behavior was explained by the formation of large and mostly isolated water domains detected at high water content and high equivalent polymer weight. Using MC simulations, we calculated the chemical potential of water in the hydrated polymer and constructed the water sorption isotherms, which extended to the oversaturated conditions. We determined that the maximum diffusivity and the onset of formation of large water domains corresponded to the saturation conditions at 100% humidity. The oversaturated membrane morphologies generated in the canonical ensemble DPD simulations correspond to the metastable and unstable states of Nafion membrane that are not realized in the experiments.

Microphase separation in polyelectrolytic diblock copolymer melt: Weak segregation limit

The authors present a generalized theory of microphase separation for charged-neutral diblock copolymer melt. The stability limit of the disordered phase for salt-free melt has been calculated using random phase approximation (RPA) and self-consistent-field theory (SCFT). Explicit analytical free energy expressions for different classical ordered microstructures (lamellar, cylinder, and sphere) are presented. The authors demonstrate that the chemical mismatch required for the onset of microphase separation (chi*N) in charged-neutral diblock melt is higher and the period of ordered microstructures is lower than those for the corresponding neutral-neutral diblock system. Theoretical predictions on the period of ordered structures in terms of Coulomb electrostatic interaction strength, chain length, block length, and chemical mismatch between blocks are presented. SCFT has been used to go beyond the stability limit, where electrostatic potential and charge distribution are calculated self-consistently. Stability limits calculated using RPA are in perfect agreement with the corresponding SCFT calculations. Limiting laws for the stability limit and the period of ordered structures are presented and comparisons are made with an earlier theory. Also, transition boundaries between different morphologies have been investigated.