Conducting polyfurans by electropolymerization of oligofurans

Polyfurans have never been established as useful conjugated polymers, as previously they were considered to be inherently unstable and poorly conductive. Here, we show the preparation of stable and conducting polyfuran films by electropolymerization of a series of oligofurans of different chain lengths substituted with alkyl groups. The polyfuran films show good conductivity in the order of 1 S cm^–1, good environmental and electrochemical stabilities, very smooth morphologies (roughness 1–5 nm), long effective conjugation lengths, well-defined spectroelectrochemistry and electro-optical switching (in the Vis-NIR region), and have optical band-gaps in the range of 2.2–2.3 eV. A low oxidation potential needed for polymerization of oligofurans (compared to furan) is a key factor in achievement of improved properties of polyfurans reported in this work. DFT calculations and experiments show that polyfurans are much more rigid than polythiophenes, and alkyl substitution does not disturb backbone planarity and conjugation. The obtained properties of polyfuran films are similar or superior to the properties of electrochemically prepared poly(oligothiophene)s under similar conditions.     

Enhanced Electrochemical Performance of Supercapacitors via Atomic Layer Deposition of ZnO on the Activated Carbon Electrode Material

Fabricating electrical double-layer capacitors (EDLCs) with high energy density for various applications has been of great interest in recent years. However, activated carbon (AC) electrodes are restricted to a lower operating voltage because they suffer from instability above a threshold potential window. Thus, they are limited in their energy storage. The deposition of inorganic compounds’ atomic layer deposition (ALD) aiming to enhance cycling performance of supercapacitors and battery electrodes can be applied to the AC electrode materials. Here, we report on the investigation of zinc oxide (ZnO) coating strategy in terms of different pulse times of precursors, ALD cycles, and deposition temperatures to ensure high electrical conductivity and capacitance retention without blocking the micropores of the AC electrode. Crystalline ZnO phase with its optimal forming condition is obtained preferably using a longer precursor pulse time. Supercapacitors comprising AC electrodes coated with 20 cycles of ALD ZnO at 70 °C and operated in TEABF₄/acetonitrile organic electrolyte show a specific capacitance of 23.13 F g⁻¹ at 5 mA cm⁻² and enhanced capacitance retention at 3.2 V, which well exceeds the normal working voltage of a commercial EDLC product (2.7 V). This work delivers an additional feasible approach of using ZnO ALD modification of AC materials, enhancing and promoting stable EDLC cells under high working voltages.     

Convex feasibility modeling and projection methods for sparse signal recovery

A computationally-efficient method for recovering sparse signals from a series of noisy observations, known as the problem of compressed sensing (CS), is presented. The theory of CS usually leads to a constrained convex minimization problem. In this work, an alternative outlook is proposed. Instead of solving the CS problem as an optimization problem, it is suggested to transform the optimization problem into a convex feasibility problem (CFP), and solve it using feasibility-seeking sequential and simultaneous subgradient projection methods, which are iterative, fast, robust and convergent schemes for solving CFPs. As opposed to some of the commonly-used CS algorithms, such as Bayesian CS and Gradient Projections for sparse reconstruction, which become inefficient as the problem dimension and sparseness degree increase, the proposed methods exhibit robustness with respect to these parameters. Moreover, it is shown that the CFP-based projection methods are superior to some of the state-of-the-art methods in recovering the signal’s support. Numerical experiments show that the CFP-based projection methods are viable for solving large-scale CS problems with compressible signals.     

Anionic graft polymerization of propylene sulfide on cellulose. I

The anionic graft polymerization of propylene sulfide on cellulose membrane was studied. Alkali cellulosates were used to initiate graft polymerization, and graft polymers of high polypropylene sulfide content were obtained in good yields. The graft polymerization was accompanied by a certain extent of homopolymerization. The effects of reaction solvent, monomer concentration, cellulosate degree of substitution, and type of the alkali metal cellulosate on the graft polymer composition, yield, and on the molecular weight of the grafted side chains were investigated.     

Galvanostatic Fast Charging of Alkali-Ion Battery Materials at the Single-Particle Level: A Map-Driven Diagnosis

In this work, we develop a new tool to provide a diagnostic map for alkali-ion intercalation materials under galvanostatic conditions. These representations, stated in the form of capacity level diagrams, are built from hundreds of numerical simulations representing different experimental conditions, summarized in two dimensionless parameters: a kinetic parameter denominated Ξ and a finite diffusion parameter l. To lay the theoretical and methodological foundations, a general model is used here. This model can be adapted to the thermodynamic and kinetic framework of specific systems. We provide two representative examples.     

Cohomology of the hyperelliptic Torelli group

Let SI(S _g ) denote the hyperelliptic Torelli group of a closed surface S _g of genus g. This is the subgroup of the mapping class group of S _g consisting of elements that act trivially on H ₁(S _g ; ?) and that commute with some fixed hyperelliptic involution of S _g . We prove that the cohomological dimension of SI(S _g ) is g ? 1 when g ≥ 1. We also show that H _g?1(SI(S _g ); ?) is infinitely generated when g ≥ 2. In particular, SI(S ₃) is not finitely presentable. Finally, we apply our main results to show that the kernel of the Burau representation of the braid group B _n at t = ?1 has cohomological dimension equal to the integer part of n/2, and it has infinitely generated homology in this top dimension.     

Magidor–Malitz reflection

In this paper we investigate the consistency and consequences of the downward Löwenheim–Skolem–Tarski theorem for extension of the first order logic by the Magidor–Malitz quantifier. We derive some combinatorial results and improve the known upper bound for the consistency of Chang’s conjecture at successor of singular cardinals.     

From single- to multiple-soliton solutions of the perturbed KdV equation

The solution of the perturbed KdV equation (PKDVE), when the zero-order approximation is a multiple-soliton wave, is constructed as a sum of two components: elastic and inelastic. The elastic component preserves the elastic nature of soliton collisions. Its perturbation series is identical in structure to the series-solution of the PKDVE when the zero-order approximation is a single soliton. The inelastic component exists only in the multiple-soliton case, and emerges from the first order and onwards. Depending on initial data or boundary conditions, it may contain, in every order, a plethora of inelastic processes. Examples are given of sign-exchange soliton-anti-soliton scattering, soliton-anti-soliton creation or annihilation, soliton decay or merging, and inelastic soliton deflection. The analysis has been carried out through third order in the expansion parameter, exploiting the freedom in the expansion to its fullest extent. Both elastic and inelastic components do not modify soliton parameters beyond their values in the zero-order approximation. When the PKDVE is not asymptotically integrable, the new expansion scheme transforms it into a system of two equations: The Normal Form for ordinary KdV solitons, and an auxiliary equation describing the contribution of obstacles to asymptotic integrability to the inelastic component. Through the orders studied, the solution of the latter is a conserved quantity, which contains the dispersive wave that has been observed in previous works.