How and why nanoparticle's curvature regulates the apparent pKa of the coating ligands

Dissociation of ionizable ligands immobilized on nanopaticles (NPs) depends on and can be regulated by the curvature of these particles as well as the size and the concentration of counterions. The apparent acid dissociation constant (pK(a)) of the NP-immobilized ligands lies between that of free ligands and ligands self-assembled on a flat surface. This phenomenon is explicitly rationalized by a theoretical model that accounts fully for the molecular details (size, shape, conformation, and charge distribution) of both the NPs and the counterions.     

Aggregation and self-assembly of amphiphilic block copolymers in aqueous dispersions of carbon nanotubes

The self-assembly (SA) of amphiphilic block copolymers (poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide)) was investigated in dispersions of single-walled and multiwalled carbon nanotubes (SWNT and MWNT, respectively) as a function of temperature. Differential scanning calorimetry (DSC) was used for characterization of the thermal behavior of the combined polymers-nanostructures system, and spin-probe electron paramagnetic resonance (EPR) was employed for probing the local dynamic and polarity of the polymer chains in the presence of nanostructures. It was found that SWNT and MWNT modify the temperature, enthalpy, and dynamic behavior of polymer SA. In particular, SWNT were found to increase the cooperativity of aggregating chains and dominate aggregate dynamics. MWNT reduced the cooperativity, while colloidal carbon black additives, studied for comparison, did not show similar effects. The experimental observations are consistent with the suggestion that dimensional matching between the characteristic radius of the solvated polymer chains and the dimensions of additives dominate polymer SA in the hybrid system.     

Long-lasting dashed waves in a reactive microemulsion

In the Belousov-Zhabotinsky (BZ) reaction carried out in a reverse microemulsion with Aerosol OT as surfactant, the existence of two different sizes of droplets containing the BZ reactants leads to the emergence of segmented (dashed) waves. This bimodal distribution of sizes is stabilized by adding small amounts of the homopolymer poly(ethylene oxide) (PEO). Addition of PEO lengthens the period during which these patterns are observed, so that dashed waves can persist for 12-14 h, in contrast to the 2-3 h found in earlier studies without added polymer.     

Chiral separation: mechanism modeling in two-dimensional systems

Fluid phase separations of racemates are difficult because the subtle, short-ranged differences in intermolecular interactions of like and unlike pairs of chiral molecules are typically smaller than the thermal energy. A surface restricts the configurational space available to the pair of interacting molecules, thus changing the effective interactions between them. Because of this restriction, a surface can promote chiral separation of mixtures that are racemic in bulk. In this paper, we investigate chiral symmetry breaking induced by an achiral surface in a racemate. A parallel tempering Monte Carlo algorithm with tempering over the temperature domain is used to examine the interplay between molecular geometry and energetics in promoting chiral separations. The system is restricted to evolve in two dimensions. By controlling the balance between electrostatic and steric interactions, one can direct the surface assembly of the chiral molecules toward formation of small clusters of identical molecules. When molecular shape asymmetry is complemented by dipolar alignment, chiral micellar clusters of like molecules are assembled on the surface. We examine the case of small model molecules for which the two-dimensional restriction of the pair potential is sufficient to induce chiral segregation. An increase in molecular complexity can change the balance of intermolecular interactions to the point that heterochiral pairs are energetically more favored. In this case, we find conditions in which formation of homochiral micelles is still achieved, due to a combination of multibody and entropic effects. In such systems, an examination of the pair potential alone is insufficient to predict whether the multimolecular racemate will or will not segregate.     

Effects of block copolymer's architecture on its association with lipid membranes: experiments and simulations

Triblock copolymers of the form poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) have been shown to effectively interact with and restore activity of damaged cell membranes. To better understand the interaction between these polymers and cell membranes, we have modeled the outer leaflet of a cell membrane with a lipid monolayer spread at the air-water interface and injected poloxamers of varying architectures into the subphase beneath the monolayer. Subsequent interactions of the polymer with the monolayer upon compression were monitored with concurrent Langmuir isotherm and fluorescence microscopy measurements. Monte Carlo simulations were run in parallel using a coarse-grained model to capture interactions between lipids and poloxamers. Changing the ratio of the PEO to PPO block lengths (NPEO:NPPO) affects the equilibrium spreading pressure of the polymer. Poloxamers with a relatively longer central hydrophobic block are less soluble, resulting in more polymer adsorbed to the interface and therefore a higher equilibrium spreading pressure. Simulation results show that changing the poloxamer structure effectively affects its solubility. This is also reflected in the degree of lipid corralling as poloxamers with a higher chemical potential (and resulting higher equilibrium spreading pressure) cause the neighboring lipid domains to be more ordered. Upon lateral compression of the monolayers, the polymer is expelled from the film beyond a certain squeeze-out pressure. A poloxamer with a higher NPEO:NPPO ratio (with either NPEO or NPPO held constant in each series) has a lower squeeze-out pressure. Likewise when the total size of the polymer is varied with a constant hydrophilic:hydrophobic ratio, smaller poloxamers are squeezed out at a lower pressure. Our simulation results capture the trends of our experimental observations, both indicating how the interactions between lipids and poloxamers can be tuned by the polymer architecture.     

A Generalized Information-Theoretic Approach for Bounding the Number of Independent Sets in Bipartite Graphs

This paper studies the problem of upper bounding the number of independent sets in a graph, expressed in terms of its degree distribution. For bipartite regular graphs, Kahn (2001) established a tight upper bound using an information-theoretic approach, and he also conjectured an upper bound for general graphs. His conjectured bound was recently proved by Sah et al. (2019), using different techniques not involving information theory. The main contribution of this work is the extension of Kahn’s information-theoretic proof technique to handle irregular bipartite graphs. In particular, when the bipartite graph is regular on one side, but may be irregular on the other, the extended entropy-based proof technique yields the same bound as was conjectured by Kahn (2001) and proved by Sah et al. (2019).     

Halide affinity for the water-air interface in aqueous solutions of mixtures of sodium salts

The water-air interface plays a critical role in many physical and chemical processes of the Earth's atmosphere. In particular, heavy halide ions are strongly involved in processes of fundamental importance in determining the prevalence of many atmospheric components through heterogeneous reactions at the water-air interface. In this work, molecular dynamics simulations are used to study the halide enhancements at the water-air interface in the case of mixtures of Cl(-), Br(-), and I(-) ions. The results show a pattern of enhancement directly correlated to the anion polarizability. This effect is explained in terms of the charge distribution across the slab resembling an electrical double layer. As a result, the anions with higher polarizability lower the system's potential energy by enhancing their presence at the interface.     

Tunable diacetylene polymerized shell microbubbles as ultrasound contrast agents

Monodisperse gas microbubbles, encapsulated with a shell of photopolymerizable diacetylene lipids and phospholipids, were produced by microfluidic flow focusing, for use as ultrasound contrast agents. The stability of the polymerized shell microbubbles against both aggregation and gas dissolution under physiological conditions was studied. Polyethylene glycol (PEG) 5000, which was attached to the diacetylene lipids, was predicted by molecular theory to provide more steric hindrance against aggregation than PEG 2000, and this was confirmed experimentally. The polymerized shell microbubbles were found to have higher shell-resistance than nonpolymerizable shell microbubbles and commercially available microbubbles (Vevo MicroMarker). The acoustic stability under 7.5 MHz ultrasound insonation was significantly greater than that for the two comparison microbubbles. The acoustic stability was tunable by varying the amount of diacetylene lipid. Thus, our polymerized shell microbubbles are a promising platform for ultrasound contrast agents.     

Representation of finite games as network congestion games

Weighted network congestion games are a natural model for interactions involving finitely many non-identical users of network resources, such as road segments or communication links. However, in spite of their special form, these games are not fundamentally special: every finite game can be represented as a weighted network congestion game. The same is true for the class of (unweighted) network congestion games with player-specific costs, in which the players differ in their cost functions rather than their weights. The intersection of the two classes consists of the unweighted network congestion games. These games are special: a finite game can be represented in this form if and only if it is an exact potential game.     

Pattern formation in a reaction-diffusion-advection system with wave instability

In this paper, we show by means of numerical simulations how new patterns can emerge in a system with wave instability when a unidirectional advective flow (plug flow) is added to the system. First, we introduce a three variable model with one activator and two inhibitors with similar kinetics to those of the Oregonator model of the Belousov-Zhabotinsky reaction. For this model, we explore the type of patterns that can be obtained without advection, and then explore the effect of different velocities of the advective flow for different patterns. We observe standing waves, and with flow there is a transition from out of phase oscillations between neighboring units to in-phase oscillations with a doubling in frequency. Also mixed and clustered states are generated at higher velocities of the advective flow. There is also a regime of "waving Turing patterns" (quasi-stationary structures that come close and separate periodically), where low advective flow is able to stabilize the stationary Turing pattern. At higher velocities, superposition and interaction of patterns are observed. For both types of patterns, at high velocities of the advective field, the known flow distributed oscillations are observed.