Structure and Dynamics of Hybrid Colloid-Polyelectrolyte Coacervates: Insights from Molecular Simulations.

Electrostatic interactions in polymeric systems are responsible for a wide range of liquid-liquid phase transitions that are of importance for biology and materials science. Such transitions are referred to as complex coacervation, and recent studies have sought to understand the underlying physics and chemistry. Most theoretical and simulation efforts to date have focused on oppositely charged linear polyelectrolytes, which adopt nearly ideal-coil conformations in the condensed phase. However, when one of the coacervate components is a globular protein, a better model of complexation should replace one of the species with a spherical charged particle or colloid. In this work, we perform coarse-grained simulations of colloid-polyelectrolyte coacervation using a spherical model for the colloid. Simulation results indicate that the electroneutral cell of the resulting (hybrid) coacervates consists of a polyelectrolyte layer adsorbed on the colloid. Power laws for the structure and the density of the condensed phase, which are extracted from simulations, are found to be consistent with the adsorption-based scaling theory of hybrid coacervation. The coacervates remain amorphous (disordered) at a moderate colloid charge, Q, while an intra-coacervate colloidal crystal is formed above a certain threshold, at Q > Q*. In the disordered coacervate, if Q is sufficiently low, colloids diffuse as neutral nonsticky nanoparticles in the semidilute polymer solution. For higher Q, adsorption is strong and colloids become effectively sticky. Our findings are relevant for the coacervation of polyelectrolytes with proteins, spherical micelles of ionic surfactants, and solid organic or inorganic nanoparticles.

Sorting of Cluster-Confined Metallic Single-Walled Carbon Nanotubes for Fabricating Atomically Vacant Uranium Oxide.

Single-walled carbon nanotube (SWCNT) heterostructures have shown great potential in catalysis, magnetism, and nanofluidics, in which host SWCNTs with certain conductivity (metallic or semiconducting) are highly required. Herein, inspired by the large molecular weight and redox properties of polyoxometalate (POM) clusters, we reported the selective separation of POM encapsulated metallic SWCNTs (POM@m-SWCNTs) with a uniform diameter through density gradient ultracentrifugation (DGU). The confined POMs increased the SWCNT density and amplified the nanotubes' density difference, thus greatly lowering the centrifugal force (70,000g) of DGU. With this strategy, a series of POM@m-SWCNTs of ∼1.2 nm with high purity were sorted. The mechanism supported by theoretical and experimental evidence showed that the separation of m-SWCNTs depended on not only nanotube/cluster size but also the conductivity of SWCNTs. The smallest 1.2 nm m-SWCNT that can exactly accommodate a 0.9 nm-{Mo6} cluster exhibited the maximum electron transfer to inner clusters; thus, intertube π-π stacking of such m-SWCNTs was greatly loosened, leading to the preferential dispersion into individual ones and partitioning in the uppermost layer after DGU. As a proof-of-concept application, this sorting strategy was extended to separate heavy-element 238U-encapsulated m-SWCNTs. The phase-pure, tiny (1-2.5 nm) U4O9 crystals with atomic vacancy clusters were fabricated on m-SWCNTs through growth kinetic control. This work may provide a general way to construct desired actinide materials on specific SWCNTs.

Accelerating First Principles Calculation of Multi-Component Alloy Steady-State Structure and Elastic Properties in Full Component Space.

The FeNiCrAlCoCuTi alloy system has great advantages in mechanical properties such as high hardness and toughness. It has high performance potential and research value and the key in research is designing alloy compositions with target properties. The traditional method, experimental analysis, is highly inefficient to properly exploit the intrinsic relationship between material characteristics and properties for multi-component alloys, especially in investigating the whole composition space. In this work, we present a research way that uses first principles calculation to obtain the properties of multi-component alloys and uses machine learning to accelerate the research. The FeNiCrAlCoCuTi alloy system with its elastic properties is used as an example to demonstrate this process. We specifically design models for each output, all of which have RMSE values of less than 1.1, and confirm their effectiveness through experimental data in the literature, showing that the relative error is below 5%. Additionally, we perform an interpretable analysis on the models, exposing the underlying relationship between input features and output. By means of spatial transformation, we achieve the prediction of the full-component spatial performance from binary to multiple components. Taking the FeNiCrAlM (M = Co, Cu, Ti) quinary alloy system as an example, we design a single-phase BCC structure composed of an Fe0.23Cr0.23Al0.23Ni0.03Cu0.28 alloy with a Young's modulus of 273.10 GPa, as well as a single-phase BCC structure composed of an Fe0.01Cr0.01Al0.01Ni0.44Co0.53 alloy with a shear modulus of 103.6 GPa. Through this research way, we use machine learning to accelerate the calculation, which greatly shortens research time and costs. This work overcomes the drawbacks of traditional experiments and directly obtains element compositions and composition intervals with excellent performance.

Anisotropic Growth of One-Dimensional Carbides in Single-Walled Carbon Nanotubes with Strong Interaction for Catalysis.

Tungsten and molybdenum carbides have shown great potential in catalysis and superconductivity. However, the synthesis of ultrathin W/Mo carbides with a controlled dimension and unique structure is still difficult. Here, inspired by the host-guest assembly strategy with single-walled carbon nanotubes (SWCNTs) as a transparent template, we reported the synthesis of ultrathin (0.8-2.0 nm) W2C and Mo2C nanowires confined in SWCNTs deriving from the encapsulated W/Mo polyoxometalate clusters. The atom-resolved electron microscope combined with spectroscopy and theoretical calculations revealed that the strong interaction between the highly carbophilic W/Mo and SWCNT resulted in the anisotropic growth of carbide nanowires along a specific crystal direction, accompanied by lattice strain and electron donation to the SWCNTs. The SWCNT template endowed carbides with resistance to H2O corrosion. Different from normal modification on the outer surface of SWCNTs, such M2C@SWCNTs (M = W, Mo) provided a delocalized and electron-enriched SWCNT surface to uniformly construct the negatively charged Pd catalyst, which was demonstrated to inhibit the formation of active PdHx hydride and thus achieve highly selective semihydrogenation of a series of alkynes. This work could provide a nondestructive way to design the electron-delocalized SWCNT surface and expand the methodology in synthesizing unusual 1D ultrathin carbophilic-metal nanowires (e.g., TaC, NbC, ß-W) with precise control of the anisotropy in SWCNT arrays.

Polyelectrolyte Complex Coacervation across a Broad Range of Charge Densities.

Polyelectrolyte complex coacervates of homologous (co)polyelectrolytes with a near-ideally random distribution of a charged and neutral ethylene oxide comonomer were synthesized. The unique platform provided by these building blocks enabled an investigation of the phase behavior across charge fractions 0.10 ≤ f ≤ 1.0. Experimental phase diagrams for f = 0.30-1.0 were obtained from thermogravimetric analysis of complex and supernatant phases and contrasted with molecular dynamics simulations and theoretical scaling laws. At intermediate to high f, a dependence of polymer weight fraction in the salt-free coacervate phase (w P,c) of w P,c ∼ f 0.37±0.01 was extracted; this trend was in good agreement with accompanying simulation predictions. Below f = 0.50, w P,c was found to decrease more dramatically, qualitatively in line with theory and simulations predicting an exponent of 2/3 at f ≤ 0.25. Preferential salt partitioning to either coacervate or supernatant was found to be dictated by the chemistry of the constituent (co)polyelectrolytes.

Neural Network Sampling of the Free Energy Landscape for Nitrogen Dissociation on Ruthenium.

In heterogeneous catalysis, free energy profiles of reactions govern the mechanisms, rates, and equilibria. Energetics are conventionally computed using the harmonic approximation (HA), which requires determination of critical states a priori. Here, we use neural networks to efficiently sample and directly calculate the free energy surface (FES) of a prototypical heterogeneous catalysis reaction-the dissociation of molecular nitrogen on ruthenium-at density-functional-theory-level accuracy. We find that the vibrational entropy of surface atoms, often neglected in HA for transition metal catalysts, contributes significantly to the reaction barrier. The minimum free energy path for dissociation reveals an "on-top" adsorbed molecular state prior to the transition state. While a previously reported flat-lying molecular metastable state can be identified in the potential energy surface, it is absent in the FES at relevant reaction temperatures. These findings demonstrate the importance of identifying critical points self-consistently on the FES for reactions that involve considerable entropic effects.

Spatiotemporal Formation and Growth Kinetics of Polyelectrolyte Complex Micelles with Millisecond Resolution.

We have directly observed the in situ self-assembly kinetics of polyelectrolyte complex (PEC) micelles by synchrotron time-resolved small-angle X-ray scattering, equipped with a stopped-flow device that provides millisecond temporal resolution. A synthesized neutral-charged diblock polycation and homopolyanion that we have previously investigated as a model charge-matched, core-shell micelle system were selected for this work. The initial micellization of the oppositely charged polyelectrolytes was completed within the dead time of mixing of 100 ms, followed by micelle growth and equilibration up to several seconds. By combining the structural evolution of the radius of gyration (Rg) with complementary molecular dynamics simulations, we show how the self-assemblies evolve incrementally in size over time through a two-step kinetic process: first, oppositely charged polyelectrolyte chains pair to form nascent aggregates that immediately assemble into spherical micelles, and second, these PEC micelles grow into larger micellar entities. This work has determined one possible kinetic pathway for the initial formation of PEC micelles, which provides useful physical insights for increasing fundamental understanding self-assembly dynamics, driven by polyelectrolyte complexation that occurs on ultrafast time scales.

Crossover from Rouse to Reptation Dynamics in Salt-Free Polyelectrolyte Complex Coacervates.

Considerable interest in the dynamics and rheology of polyelectrolyte complex coacervates has been motivated by their industrial application as viscosity modifiers. A central question is the extent to which classical Rouse and reptation models can be applied to systems where electrostatic interactions play a critical role on the thermodynamics. By relying on molecular simulations, we present a direct analysis of the crossover from Rouse to reptation dynamics in salt-free complex coacervates as a function of chain length. This crossover shifts to shorter chain lengths as electrostatic interactions become stronger, which corresponds to the formation of denser coacervates. To distinguish the roles of Coulomb interactions and density, we compare the dynamics of coacervates to those of neutral, semidilute solutions at the same density. Both systems exhibit a universal dynamical behavior in the connectivity-dominated (subdiffusion and normal diffusion) regimes, but the monomer relaxation time in coacervates is much longer and increases with increasing Bjerrum length. This is similar to the cage effect observed in glass-forming polymers, but the local dynamical slowdown is caused here by strong Coulomb attractions (ion pairing) between oppositely charged monomers. Our findings provide a microscopic framework for the quantitative understanding of coacervate dynamics and rheology.

Controlling Complex Coacervation via Random Polyelectrolyte Sequences.

The utilization of chemical sequence control in polymeric materials is key to enabling material design on par with biomacromolecular systems. One important avenue for scalable sequence-controlled polymers leverages the random copolymerization of distinct monomers, with the statistical distribution of the monomeric sequence arising from reaction kinetics following a first-order Markov process. Here we utilize the framework of the random phase approximation (RPA) to develop a theory for the phase behavior of symmetric polyelectrolyte coacervates whose chemical sequences are dictated by simple statistical distributions. We find that a high charge "blockiness" within the random sequences favors the formation of denser and more salt-resistant coacervates while simultaneously increasing the width of the two-phase region. We trace these physical effects to the increased cooperativity of Coulomb interactions that results from increased charge blockiness in oppositely charged polyelectrolytes.

[Analysis of the EEG information of rats epileptic model using unstable periodic orbits].

In order to further research into the EEG information of rats epileptic model, we applied different nonlinear dynamic methods. After having analyzed the EEG signal of rat falling sickness by means of approximate entropy and correlation dimension, we adopted a the new method, unstable periodic orbits, which was used to analyze complex activity of neurons system to look for the change regularity of change in the EEG signal in the whole course of rat's falling sickness. We found period 1 orbits and period 2 orbits to be statistically significant in the data of ictal time of epilepsy. At the same time, we found period 1 orbits to be statistically significant in the data of preictal time of epilepsy.