Nanoscale memory provided by thermoreversible stochastically structured polymer aggregates on mica

Stimuli-responsive polymers are used in a large variety of applications due to the controlled manner in which their physical properties can be reversibly altered. In this study, we demonstrate the thermoreversible structuring of poly(N-isopropylacrylamide)-based polymer. By temperature-controlled atomic force microscopy, we demonstrate that polymer aggregates form on mica above the polymer lower critical solution temperature and disperse below it, and in so doing, display positional "memory" in that the nanodomains are retained in the same positions and with the same shapes during repeated cooling/heating cycles. Such positional "memory" may be useful for multiple applications in nano-microscale devices.     

On the correspondence between fermion and boson states and operators

Mapping of shell-model (fermion) Hamiltonians onto boson Hamiltonians which underly the interaction boson model ^1–5) is investigated. A simple correspondence is defined and a sufficient condition given for shell-model Hamiltonians to simply correspond to finite hermitian boson Hamiltonians. A special case is discussed where diagonalization of a shell-model Hamiltonian for valence protons and neutrons can be exactly carried out in an equivalent (but different) boson space. If, however, the proton Hamiltonian and neutron Hamiltonian are diagonal in the seniority scheme, mapping of fermion states onto orthogonal boson states cannot be a simple correspondence. In that case the boson quadrupole operators equivalent to fermion guadrupole operators cannot be single-boson operators but must be more complicated, ones.     

Implementability of correlated and communication equilibrium outcomes in incomplete information games

In a correlated equilibrium, the players’ choice of actions is directed by correlated random messages received from an outside source, or mechanism. These messages allow for more equilibrium outcomes than without any messages (pure-strategy equilibrium) or with statistically independent ones (mixed-strategy equilibrium). In an incomplete information game, the messages may also reflect the types of the players, either because they are affected by extraneous factors that also affect the types (correlated equilibrium) or because the players themselves report their types to the mechanism (communication equilibrium). Mechanisms may be further differentiated by the connections between the messages that the players receive and their own and the other players’ types, by whether the messages are statistically dependent or independent, and by whether they are random or deterministic. Consequently, whereas for complete information games there are only three classes of equilibrium outcomes, with incomplete information the corresponding number is 14 or 15 for correlated equilibria and even larger—15, 16 or 17—for communication equilibria. For both solution concepts, the implication relations between the different kinds of equilibria form a two-dimensional lattice, which is considerably more intricate than the single-dimensional one of the complete information case.     

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.