Anomalous diffusion of lithium-anion clusters in ionic liquids

Lithium-ion transport is significantly retarded in ionic liquids (ILs). In this work, we performed extensive molecular dynamics simulations to mimic the kinetics of lithium ions in ILs using [N-methyl-N-propylpyrrolidium (pyr[Formula: see text])][bis(trifluoromethanesulfonyl)imide (Ntf[Formula: see text])] with added LiNtf[Formula: see text] salt. And we analyzed their transport, developing a two-state model and comparing it to the machine learning-identified states. The transport of lithium ions involves local shell exchanges of the Ntf[Formula: see text] in the medium. We calculated train size distributions over various time scales. The train size distribution decays as a power law, representing non-Poissonian bursty shell exchanges. We analyzed the non-Poissonian processes of lithium ions transport as a two-state (soft and hard) model. We analytically calculated the transition probability of the two-state model, which fits well to the lifetime autocorrelation functions of LiNtf[Formula: see text] shells. To identify two states, we introduced the graph neutral network incorporating local molecular structure. The results reveal that the shell-soft state mainly contributes to the transport of the lithium ions, and their contribution is more important in low temperatures. Hence, it is the key for enhanced lithium ion transport to increase the fraction of the shell-soft state.

Universality, Scaling, and Collapse in Supercritical Fluids

Supercritical fluid (SCF) is known to exhibit salient dynamic and thermodynamic crossovers and an inhomogeneous molecular distribution. However, the question as to what basic physics underlies these microscopic and macroscopic anomalies remains open. Here, using an order parameter extracted by machine learning, the fraction of gas-like (or liquid-like) molecules, we find simplicity and universality in SCF: First, all isotherms of a given fluid collapse onto a single master curve described by a scaling relation. The observed power law holds from the high-temperature and -pressure regime down to the critical point where it diverges. Second, phase diagrams of different compounds collapse onto their master curves by the same scaling exponent, thereby demonstrating a putative law of corresponding supercritical states in simple fluids. The reported results support a model of the SCF as a mixture of two interchangeable microstates, whose spatiotemporal dynamics gives rise to unique macroscopic properties.

Cation-π Interactions and Their Contribution to Mussel Underwater Adhesion Studied Using a Surface Forces Apparatus: A Mini-Review

Mussel underwater adhesion is a model phenomenon important for the understanding of broader biological adhesion and the development of biomimetic wet adhesives. The catechol moiety of 3,4-dihydroxyphenyl-l-alanine (DOPA) is known to be actively involved in the mechanism of mussel underwater adhesion; however, other underwater adhesion mechanisms are also crucial. The surface forces apparatus (SFA) has often been used to explore the contributions of other mechanisms to mussel underwater adhesion; e.g., recent SFA-based nanomechanical studies have revealed that cation-π interactions, one of the strongest intermolecular interactions in water, are the pivotal interactions of adhesive proteins involved in underwater mussel adhesion. This mini-review surveys recent research on cation-π interactions and their contributions to strong mussel underwater adhesion, shedding light on some biological processes and facilitating the development of biomedical adhesives.

Upper Critical Solution Temperature (UCST) Behavior of Coacervate of Cationic Protamine and Multivalent Anions

Complex coacervation is an emerging liquid/liquid phase separation (LLPS) phenomenon that behaves as a membrane-less organelle in living cells. Yet while one of the critical factors for complex coacervation is temperature, little analysis and research has been devoted to the temperature effect on complex coacervation. Here, we performed a complex coacervation of cationic protamine and multivalent anions (citrate and tripolyphosphate (TPP)). Both mixtures (i.e., protamine/citrate and protamine/TPP) underwent coacervation in an aqueous solution, while a mixture of protamine and sodium chloride did not. Interestingly, the complex coacervation of protamine and multivalent anions showed upper critical solution temperature (UCST) behavior, and the coacervation of protamine and multivalent anions was reversible with solution temperature changes. The large asymmetry in molecular weight between positively charged protamine (~4 kDa) and the multivalent anions (<0.4 kDa) and strong electrostatic interactions between positively charged guanidine residues in protamine and multivalent anions were likely to contribute to UCST behavior in this coacervation system.

Salt Triggers the Simple Coacervation of an Underwater Adhesive When Cations Meet Aromatic π Electrons in Seawater

Adhesive systems in many marine organisms are postulated to form complex coacervates (liquid-liquid phase separation) through a process involving oppositely charged polyelectrolytes. Despite this ubiquitous speculation, most well-characterized mussel adhesive proteins are cationic and polyphenolic, and the pursuit of the negatively charged proteins required for bulk complex coacervation formation internally remains elusive. In this study, we provide a clue for unraveling this paradox by showing the bulky fluid/fluid separation of a single cationic recombinant mussel foot protein, rmfp-1, with no additional anionic proteins or artificial molecules, that is triggered by a strong cation-π interaction in natural seawater conditions. With the similar condition of salt concentration at seawater level (>0.7 M), the electrostatic repulsion between positively charged residues of mfp-1 is screened significantly, whereas the strong cation-π interaction remains unaffected, which leads to the macroscopic phase separation (i.e., bulky coacervate formation). The single polyelectrolyte coacervate shows interesting mechanical properties including low friction, which facilitates the secretion process of the mussel. Our findings reveal that the cation-π interaction modulated by salt is a key mechanism in the mussel adhesion process, providing new insights into the basic understanding of wet adhesion, self-assembly processes, and biological phenomena that are mediated by strong short-range attractive forces in water.

Molecular and structural basis of low interfacial energy of complex coacervates in water

Complex coacervate refers to a phase-separated fluid, typically of two oppositely charged polyelectrolytes in solution, representing a complex fluid system that has been shown to be of essential interest to biological systems, as well as for soft materials processing owing to the expectation of superior underwater coating or adhesion properties. The significance and interest in complex coacervate fluids critically rely on its low interfacial tension with respect to water that, in turn, facilitates the wetting of macromolecular or material surfaces under aqueous conditions, provided there is attractive interaction between the polyelectrolyte constituents and the surface. However, the molecular and structural bases of these properties remain unclear. Recent studies propose that the formation of water-filled and bifluidic sponge-like nanostructured network, driven by the tuning of electrostatic interactions between the polyelectrolyte constituents or their complexes may be a common feature of complex coacervate fluids that display low fluid viscosity and low interfacial tension, but more studies are needed to verify the generality of these observations. In this review, we summarize representative studies of interfacial tension and ultrastructures of complex coacervate fluids. We highlight that a consensus property of the complex coacervate fluid is the observation of high or even bulk-like water dynamics within the dense complex coacervate phase that is consistent with a low cohesive energy fluid. Our own studies on this subject are enabled by the application of magnetic resonance relaxometry methods relying on spin labels tethered to polyelectrolyte constituents or added as spin labeled probe molecules that partition into the dense versus the equilibrium coacervate phase, permitting the extraction of information on local polymer dynamics, polymer packing and local water dynamics. We conclude with a snapshot of our current perspective on the molecular and structural bases of the low interfacial tension of complex coacervate fluids.

Bundling in semiflexible polymers: A theoretical overview

Supramolecular assemblies of polymers are key modules to sustain the structure of cells and their function. The main elements of these assemblies are charged semiflexible polymers (polyelectrolytes) generally interacting via a long(er)-range repulsion and a short(er)-range attraction. The most common supramolecular structure formed by these polymers is the bundle. In the present paper, we critically review some recent theoretical and computational advances on the problem of bundle formation, and point a few promising directions for future work.

Bicontinuous Fluid Structure with Low Cohesive Energy: Molecular Basis for Exceptionally Low Interfacial Tension of Complex Coacervate Fluids

An exceptionally low interfacial tension of a dense fluid of concentrated polyelectrolyte complexes, phase-separated from a biphasic fluid known as complex coacervates, represents a unique and highly sought-after materials property that inspires novel applications from superior coating to wet adhesion. Despite extensive studies and broad interest, the molecular and structural bases for the unique properties of complex coacervates are unclear. Here, a microphase-separated complex coacervate fluid generated by mixing a recombinant mussel foot protein-1 (mfp-1) as the polycation and hyaluronic acid (HA) as the polyanion at stoichiometric ratios was macroscopically phase-separated into a dense complex coacervate and a dilute supernatant phase to enable separate characterization of the two fluid phases. Surprisingly, despite up to 4 orders of magnitude differing density of the polyelectrolytes, the diffusivity of water in these two phases was found to be indistinguishable. The presence of unbound, bulk-like, water in the dense fluid can be reconciled with a water population that is only weakly perturbed by the polyelectrolyte interface and network. This hypothesis was experimentally validated by cryo-TEM of the macroscopically phase-separated dense complex coacervate phase that was found to be a bicontinuous and biphasic nanostructured network, in which one of the phases was confirmed by staining techniques to be water and the other polyelectrolyte complexes. We conclude that a weak cohesive energy between water-water and water-polyelectrolytes manifests itself in a bicontinuous network, and is responsible for the exceptionally low interfacial energy of this complex fluid phase with respect to virtually any surface within an aqueous medium.

Complexation and coacervation of like-charged polyelectrolytes inspired by mussels

It is well known that polyelectrolyte complexes and coacervates can form on mixing oppositely charged polyelectrolytes in aqueous solutions, due to mainly electrostatic attraction between the oppositely charged polymers. Here, we report the first (to the best of our knowledge) complexation and coacervation of two positively charged polyelectrolytes, which provides a new paradigm for engineering strong, self-healing interactions between polyelectrolytes underwater and a new marine mussel-inspired underwater adhesion mechanism. Unlike the conventional complex coacervate, the like-charged coacervate is aggregated by strong short-range cation-π interactions by overcoming repulsive electrostatic interactions. The resultant phase of the like-charged coacervate comprises a thin and fragile polyelectrolyte framework and round and regular pores, implying a strong electrostatic correlation among the polyelectrolyte frameworks. The like-charged coacervate possesses a very low interfacial tension, which enables this highly positively charged coacervate to be applied to capture, carry, or encapsulate anionic biomolecules and particles with a broad range of applications.

Entangled polymer complexes as Higgs phenomena

We derive an effective Maxwell-London equation for entangled polymer complexes under topological constraints, borrowing the theoretical framework from topological field theory. We find that the transverse current flux of a test polymer chain, surrounded by entangled chains, decays exponentially from its centerline position with a finite penetration depth, which is analogous to the magnetic-field decay in a superconductor (SC), referred to as the Meissner effect. Just as the mass acquirement of photons in a SC is the origin of the magnetic-field decay, the polymer obtains uncrossable intersections along the chain due to the preservation of the linking number, which restricts the deviation of the transverse polymer current in the normal direction. The underlying physics is as follows: less flexible polymers have stronger current-current correlations, giving rise to a heavier effective mass of the gauge fields and resulting in a shorter decay length. Interestingly, this picture is well incorporated within the most successful phenomenological theory of the, so called, tube model, the microscopic origins of which researchers have long pursued. The correspondence of our equation of motion to the tube model claims that the confining tube potential is a consequence of the topological constraint (linking number). The tube radius is attributed to the decay length. On increasing the effective mass (by strengthening the interaction at an uncrossable intersection or a number of intersections), the tube becomes narrower. Using this argument, the exponential decay of the chain leakage out of the tube is well understood.

General Differential Contact Identities for Macromolecules

We discuss general Maxwell identities relating a macromolecule's charge, the forces acting at its surface, and the osmotic pressure of the solution in which it sits. The identities are closely related to the contact value relations that hold for certain special geometries, but are more general. In particular, the Maxwell identities can be applied to any macromolecule geometry, and they hold both within and outside of mean-field theory. Examples illustrate that combining the identities with approximate treatments of screening can often return simple, accurate osmotic pressure estimates.

Charge Renormalization for Ellipsoidal Macroions

We study the problem of counterion condensation for ellipsoidal macroions, a geometry well-suited for modeling liquid crystals, anisotropic vesicles, and polymers. We find that the ions within an ellipsoid's condensation layer are relatively unrestricted in their motions, and consequently work to establish a quasi-equipotential at its surface. This simplifies the application of Alexander et al.'s procedure, enabling us to obtain accurate analytic estimates for the critical valence of a general ellipsoid in the weak screening limit. Interestingly, we find that the critical valence of an eccentric ellipsoid is always larger than that of the sphere of equal volume, implying that counterion condensation provides a force resisting the deformation of spherical macroions. This contrasts with a recent study of flexible spherical macroions, which observed a preference for deformation into flattened shapes when considering only linear effects. Our work suggests that the balance of these competing forces might alter the nature of the transition.

Electrostatic interaction between nonuniformly charged colloids: experimental and numerical study

The influence of the surface charge distribution on the interaction between nanosized particles in water is reported. The distribution of charges at the surface of initially neutral microemulsion droplets has been modulated by additions of various oligomeric cationic surfactants. The osmotic compressibility of the doped microemulsions was measured by light and small-angle neutrons scattering and reveals that the overall effective interaction induced by the ionic groups is repulsive. However, particular charge distributions decrease the osmotic compressibility much less than others. Independent measurements of the activity of the bromide counterions with specific electrodes evidence a significant decrease in the effective charge, which, however, cannot account for the osmotic compressibility in the framework of the primitive model. The q dependence of the structure factor reveals an attractive contribution over a short distance. Numerical studies assign this attractive contribution to the overlap of hydration shells that are extended as a result of the charge localization.

Cation–π interaction in DOPA-deficient mussel adhesive protein mfp-1

Deployment of cation–π interactions can be a complementary strategy for the successful underwater adhesion of mussels.

Contact time- and pH-dependent adhesion and cohesion of low molecular weight chitosan coated surfaces

Low molecular weight chitosan (LMW chitosan, ∼5 kDa) potentially has many desirable biomedical applications such as anti-microbial, anti-tumor, and anti-diabetes. Unlike high molecular weight chitosan, LMW chitosan is easily dissolvable in aqueous solutions even at neutral and basic pH, but its dissolution mechanism is not well understood. Here, we measured adhesion and cohesion of molecularly thin LMW chitosan films in aqueous solutions in different buffer pHs (from 3.0 to 8.5) using a surface forces apparatus (SFA). Interestingly, significantly lower adhesion force was measured for LMW chitosan films compared to the high molecular weight chitosan (∼150 kDa) films. Not only the strength of adhesion is lower, but also the critical contact time where adhesion starts to increase with contact time is longer. The results from both the SFA and atomic force microscopy (AFM) indicate that, in physiological and basic conditions, the low cohesion of LMW chitosan due to the stiffness of the chain which cause strong electrostatic correlation energy penalty when they are aggregated. Here, we propose the reduction in cohesion for shorter chitosan (LMW chitosan) as an explanation of its high solubility of LMW chitosan in physiological pHs.

Limiting law excess sum rule for polyelectrolytes

We revisit the mean-field limiting law screening excess sum rule that holds for rodlike polyelectrolytes. We present an efficient derivation of this law that clarifies its region of applicability: The law holds in the limit of small polymer radius, measured relative to the Debye screening length. From the limiting law, we determine the individual ion excess values for single-salt electrolytes. We also consider the mean-field excess sum away from the limiting region, and we relate this quantity to the osmotic pressure of a dilute polyelectrolyte solution. Finally, we consider numerical simulations of many-body polymer-electrolyte solutions. We conclude that the limiting law often accurately describes the screening of physical charged polymers of interest, such as extended DNA.

Repulsion between oppositely charged planar macroions

The repulsive interaction between oppositely charged macroions is investigated using Grand Canonical Monte Carlo simulations of an unrestricted primitive model, including the effect of inhomogeneous surface charge and its density, the depth of surface charge, the cation size, and the dielectric permittivity of solvent and macroions, and their contrast. The origin of the repulsion is a combination of osmotic pressure and ionic screening resulting from excess salt between the macroions. The excess charge over-reduces the electrostatic attraction between macroions and raises the entropic repulsion. The magnitude of the repulsion increases when the dielectric constant of the solvent is lowered (below that of water) and/or the surface charge density is increased, in good agreement with experiment. Smaller size of surface charge and the cation, their discreteness and mobility are other factors that enhance the repulsion and charge inversion phenomenons.