Evaluation of the degree of cross-linking of cellulose-based superabsorbent hydrogels: a comparison between different techniques

Three different techniques have been applied to the evaluation of the degree of cross-linking of superabsorbent cellulose-based hydrogels obtained from water solutions of carboxymethylcellulose sodium salt (CMCNa) and hydroxyethylcellulose (HEC), chemically cross-linked with divinyl sulfone. These polyelectrolyte hydrogels are biodegradable and have the same sorption capacity as acrylate-based superabsorbents on the market. A ¹³C solid state NMR analysis was carried out on dry samples of hydrogel to obtain the degree of cross-linking, an important parameter that affects the swelling and mechanical properties of a hydrogel. Dynamic mechanical analysis was performed during the hydrogel cross-linking using a parallel plate rheometer under oscillatory deformations in order to monitor the evolution of the hydrogel viscoelastic properties during the synthesis. The value of |G*| and the slope of the stress-deformation ratio plots from uniaxial compression tests were used to evaluate the elastically effective degree of cross-linking according to classical rubber elasticity theory. Moreover, a dynamic mechanical analysis was carried out on cross-linked hydrogels at different degrees of swelling in order to investigate the influence of the swelling on the mechanical properties and the application of rubber elasticity theory to swollen hydrogels.     

Copper Oxide-Based Photocatalysts and Photocathodes: Fundamentals and Recent Advances

This work aims at reviewing the most impactful results obtained on the development of Cu-based photocathodes. The need of a sustainable exploitation of renewable energy sources and the parallel request of reducing pollutant emissions in airborne streams and in waters call for new technologies based on the use of efficient, abundant, low-toxicity and low-cost materials. Photoelectrochemical devices that adopts abundant element-based photoelectrodes might respond to these requests being an enabling technology for the direct use of sunlight to the production of energy fuels form water electrolysis (H₂) and CO₂ reduction (to alcohols, light hydrocarbons), as well as for the degradation of pollutants. This review analyses the physical chemical properties of Cu₂O (and CuO) and the possible strategies to tune them (doping, lattice strain). Combining Cu with other elements in multinary oxides or in composite photoelectrodes is also discussed in detail. Finally, a short overview on the possible applications of these materials is presented.     

Structural study of hyaluronic acid oligomers and their complexes with copper in water by NMR and IR and molecular dynamics calculations

The hexasaccharide (trimer) and tetrasaccharide (dimer) oligomers of hyaluronic acid were investigated by ¹H and ¹³C high resolution Nuclear Magnetic Resonance. The dynamic behavior of the molecules and their complexation with copper(II) were analysed by ¹H NMR relaxation studies. A specific site for the complexation of the tetrasaccharide with Cu²⁺ was demonstrated by analysis of the paramagnetic effect of the metal on non-selective proton relaxation rates. A model for the complex involving two molecules of the tetrasaccharide is proposed.     

Travelling Waves in a SI Endemic Model

In this paper we consider an endemic SI model with standard incidence and prove the existence of monotone and unimodal travelling waves with large velocity. The birth and death rates can be quite general. When the birth rate is constant we prove the existence of two kinds of travelling waves and give the minimal velocity of one of the types.     

Entire Solutions of Superlinear Problems with Indefinite Weights and Hardy Potentials

We provide the structure of regular/singular fast/slow decay radially symmetric solutions for a class of superlinear elliptic equations with an indefinite weight. In particular we are interested in the case where such a weight is positive in a ball and negative outside, or in the reversed situation. We extend the approach to elliptic equations in presence of Hardy potentials, i.e. to

$$\begin{aligned} \varDelta u +\frac{h(|\text {x}|)}{|\text {x}|^2} u+ f(u, |\text {x}|)=0 \end{aligned}$$

where h is not necessarily constant. By the use of Fowler transformation we study the corresponding dynamical systems, presenting the construction of invariant manifolds when the global existence of solutions is not ensured.

     

A Nonlinear Korn Inequality Based on the Green-Saint Venant Strain Tensor

A nonlinear Korn inequality based on the Green-Saint Venant strain tensor is proved, whenever the displacement is in the Sobolev space \(W^{1,p}\), \(p\geq 2\), under Dirichlet conditions on a part of the boundary. The inequality can be useful in proving the coercivity of a nonlinear elastic energy.     

Concurrent factors determine toughening in the hydraulic fracture of poroelastic composites

Brittle materials fail catastrophically. In consequence of their limited flaw-tolerance, failure occurs by localized fracture and is typically a dynamic process. Recently, experiments on epithelial cell monolayers have revealed that this scenario can be significantly modified when the material susceptible to cracking is adhered to a hydrogel substrate. Thanks to the hydraulic coupling between the brittle layer and the poroelastic substrate, such a composite can develop a toughening mechanism that relies on the simultaneous growth of multiple cracks. Here, we study this remarkable behaviour by means of a detailed model, and explore how the material and loading parameters concur in determining the macroscopic toughness of the system. By extending a previous study, our results show that rapid loading conveys material toughness by promoting distributed cracking. Moreover, our theoretical findings may suggest innovative architectures of flaw-insensitive materials with higher toughness.     

Fast Drift and Diffusion in a Class of Isochronous Systems with the Windows Method

The aim of the paper is to deal with some peculiar difficulties arising from the use of the geometrical tool known as windows method in the context of the well known problem of Arnold’s diffusion for isochronous nearly-integrable Hamiltonian systems. Despite the simple features of the class of systems at hand, it is possible to show how the absence of an anisochrony term leads to several substantial differences in the application of the method, requiring some additional devices, such as non-equally spaced transition chains and variable windows. As a consequence, we show the existence of a set of unstable orbits, whose drifting time matches, up to a constant, the one obtained via variational methods.