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1. Mapping the phase behavior of coacervate-driven self-assembly in diblock copolyelectrolytes

   https://doi.org/10.1039/c9sm00741e  

   Ong, Gary M.; Sing, Charles E. (June 2019, Soft Matter)

   Oppositely-charged polymers can undergo an associative phase separation process known as complex coacervation, which is driven by the electrostatic attraction between the two polymer species. This driving force for phase separation can be harnessed to drive self-assembly, via pairs of block copolyelectrolytes with opposite charge and thus favorable coulombic interactions. There are few predictions of coacervate self-assembly phase behavior due to the wide variety of molecular and environmental parameters, along with fundamental theoretical challenges. In this paper, we use recent advances in coacervate theory to predict the solution-phase assembly of diblock polyelectrolyte pairs for a number of molecular design parameters (charged block fraction, polymer length). Phase diagrams show that self-assembly occurs at high polymer, low salt concentrations for a range of charge block fractions. We show that we qualitatively obtain limiting results seen in the experimental literature, including the emergence of a high polymer-fraction reentrant transition that gives rise to a self-compatibilized homopolymer coacervate behavior at the limit of high charge block fraction. In intermediate charge block fractions, we draw an analogy between the role of salt concentration in coacervation-driven assembly and the role of temperature in χ -driven assembly. We also explore salt partitioning between microphase separated domains in block copolyelectrolytes, with parallels to homopolyelectrolyte coacervation. 

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2. Fluctuations, structure, and size inside coacervates

   https://doi.org/10.1140/epje/s10189-023-00335-1  

   Muthukumar, Murugappan (September 2023, The European Physical Journal E)

   Aqueous solutions of oppositely charged macromolecules exhibit the ubiquitous phenomenon of coacervation. This subject is of considerable current interest due to numerous biotechnological applications of coacervates and the general premise of biomolecular condensates. Towards a theoretical foundation of structural features of coacervates, we present a field-theoretic treatment of coacervates formed by uniformly charged flexible polycations and polyanions in an electrolyte solution. We delineate different regimes of polymer concentration fluctuations and structural features of coacervates based on the concentrations of polycation and polyanion, salt concentration, and experimentally observable length scales. We present closed-form formulas for correlation length of polymer concentration fluctuations, scattering structure factor, and radius of gyration of a labelled polyelectrolyte chain inside a concentrated coacervate. Using random phase approximation suitable for concentrated polymer systems, we show that the inter-monomer electrostatic interaction is screened by interpenetration of all charged polymer chains and that the screening length depends on the individual concentrations of the polycation and the polyanion, as well as the salt concentration. Our calculations show that the scattering intensity decreases monotonically with scattering wave vector at higher salt concentrations, while it exhibits a peak at intermediate scattering wave vector at lower salt concentrations. Furthermore, we predict that the dependence of the radius of gyration of a labelled chain on its degree of polymerization generally obeys the Gaussian chain statistics. However, the chain is modestly swollen, the extent of which depending on polyelectrolyte composition, salt concentration, and the electrostatic features of the polycation and polyanion such as the degree of ionization. 

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3. Microstructural Organization in α-Synuclein Solutions

   https://doi.org/10.1021/acs.macromol.1c02550  

   Das, Shibananda; Muthukumar, Murugappan (June 2022, Macromolecules)

   We have investigated the structural evolution in solutions of the intrinsically disordered protein, α-synuclein, as a function of protein concentration and added salt concentration. Accounting for electrostatic and excluded volume interactions based on the protein sequence, our Langevin dynamics simulations reveal that α-synuclein molecules assemble into aggregates and percolated structures with a spontaneous selection of a dominant structure characteristic of microphase separation. This microphase assembly is mainly driven by electrostatic interactions between the residues in N-terminal and C-terminal of the protein molecules, and presence of salt loosens the compactness of the microstructures. We have quantified the features of the spontaneously formed microstructures using interchain radial distribution functions, and experimentally measurable inter-residue contact maps and static structure factors. Our results are in contrast to the commonly hypothesized mechanism of liquid–liquid phase separation (LLPS) for the formation of droplets in solutions of intrinsically disordered proteins, opening a new paradigm to understand the birth and structure of membraneless organelles. In general, construction of phase diagrams of intrinsically disordered proteins and other biomacromolecular systems needs to incorporate features of microphase separation into other mechanisms of macrophase separation and percolation. 

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4. Tuning chain interaction entropy in complex coacervation using polymer stiffness, architecture, and salt valency

   https://doi.org/10.1039/c7me00108h  

   Lytle, Tyler K.; Sing, Charles E. (January 2018, Molecular Systems Design & Engineering)

   Oppositely-charged polyelectrolytes can undergo a liquid–liquid phase separation in a salt solution, resulting in a polymer-dense ‘coacervate’ phase that has found use in a wide range of applications from food science to self-assembled materials. Coacervates can be tuned for specific applications by varying parameters such as salt concentration and valency, polyelectrolyte length, and polyelectrolyte identity. Recent simulation and theory has begun to clarify the role of molecular structure on coacervation phase behavior, especially for common synthetic polyelectrolytes that exhibit high charge densities. In this manuscript, we use a combination of transfer matrix theory and Monte Carlo simulation to understand at a physical level how a range of molecular features, in particular polymer architecture and stiffness, and salt valency can be used to design the phase diagrams of these materials. We demonstrate a physical picture of how the underlying entropy-driven process of complex coacervation is affected by this wide range of physical attributes. 

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5. Ion transport mechanisms in lamellar phases of salt-doped PS–PEO block copolymer electrolytes

   https://doi.org/10.1039/c7sm01345k  

   Sethuraman, Vaidyanathan; Mogurampelly, Santosh; Ganesan, Venkat (January 2017, Soft Matter)

   We use a multiscale simulation strategy to elucidate, at an atomistic level, the mechanisms underlying ion transport in the lamellar phase of polystyrene–polyethylene oxide (PS–PEO) block copolymer (BCP) electrolytes doped with LiPF 6 salts. Explicitly, we compare the results obtained for ion transport in the microphase separated block copolymer melts to those for salt-doped PEO homopolymer melts. In addition, we also present results for dynamics of the ions individually in the PEO and PS domains of the BCP melt, and locally as a function of the distance from the lamellar interfaces. When compared to the PEO homopolymer melt, ions were found to exhibit slower dynamics in both the block copolymer (overall) and in the PEO phase of the BCP melt. Such results are shown to arise from the effects of slower polymer segmental dynamics in the BCP melt and the coordination characteristics of the ions. Polymer backbone-ion residence times analyzed as a function of distance from the interface indicate that ions have a larger residence time near the interface compared to that near the bulk of lamella, and demonstrates the influence of the glassy PS blocks and microphase segregation on the ion transport properties. Ion transport mechanisms in BCP melts reveal that there exist five distinct mechanisms for ion transport along the backbone of the chain and exhibit qualitative differences from the behavior in homopolymer melts. We also present results as a function of salt concentration which show that the mean-squared displacements of the ions decrease with increasing salt concentration, and that the ion residence times near the polymer backbone increase with increasing salt concentration. 

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