Influence of Nanocellulose Structure on Paper Reinforcement

This article describes how crystalline or fibrous nanocellulose influences the mechanical properties of paper substrate. In this context, we used commercially available cellulose nanocrystals, mechanically prepared cellulose nanofibers dispersed in water or ethanol, and carboxy cellulose nanofibers. Selective reinforcement of the paper treated with the nanocellulose samples mentioned above was observed. The change in the fibre structure was assessed using scanning electron microscopy, roentgenography, and spectroscopy techniques. In addition, the effect of nanocellulose coating on physical properties was evaluated, specifically tensile index, elongation coefficient, Elmendorf tear resistance, Bendtsen surface roughness, Bendtsen air permeability, and bending strength. It can be concluded that the observed decrease in the strength properties of the paper after applying some NC compositions is due to the loss of potential disturbances in hydrogen bonds between the nanocellulose dispersed in ethanol and the paper substrate. On the other hand, significantly increased strength was observed in the case of paper reinforced with nanocellulose functionalized with carboxyl groups.     

Dynamical Coulomb blockade observed in nanosized electrical contacts

Electrical contacts between nanoengineered systems are expected to constitute the basic building blocks of future nanoscale electronics. However, the accurate characterization and understanding of electrical contacts at the nanoscale is an experimentally challenging task. Here, we employ low-temperature scanning tunneling spectroscopy to investigate the conductance of individual nanocontacts formed between flat Pb islands and their supporting substrates. We observe a suppression of the differential tunnel conductance at small bias voltages due to dynamical Coulomb blockade effects. The differential conductance spectra allow us to determine the capacitances and resistances of the electrical contacts which depend systematically on the island-substrate contact area. Calculations based on the theory of environmentally assisted tunneling agree well with the measurements.     

13C-NMR studies of polyfluorinated hydrocarbons,carboxylic acid derivatives,alcohols and ethers

δ¹³C values and coupling constants (¹J(¹³C¹H), ¹J(¹³C¹³C), ⁿJ(¹⁹F¹³C) are reported for 19 polyfluorinated organic compounds. It is shown that the shielding of carbon depends upon the number of fluorine atoms in α -position. If the R_F-group is linked to a π -system hyperconjugative $\text{and}$ η-π interaction accounts for the δ¹³C data. The values ¹J(¹³C¹H) and ¹J(¹³C¹³C) are in qualitative agreement with changes of the s-character of the respective bonds.     

A Hilbert Space Approach to Fractional Differential Equations

Journal of Dynamics and Differential Equations - We study fractional differential equations of Riemann–Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of...     

Filling the complexity gaps for colouring planar and bounded degree graphs

A colouring of a graph is a function such that for every . A -regular list assignment of is a function with domain such that for every , is a subset of of size . A colouring of respects a -regular list assignment of if for every . A graph is -choosable if for every -regular list assignment of , there exists a colouring of that respects . We may also ask if for a given -regular list assignment of a given graph , there exists a colouring of that respects . This yields the -Regular List Colouring problem. For , we determine a family of classes of planar graphs, such that either -Regular List Colouring is -complete for instances with , or every is -choosable. By using known examples of non--choosable and non--choosable graphs, this enables us to classify the complexity of -Regular List Colouring restricted to planar graphs, planar bipartite graphs, planar triangle-free graphs, and planar graphs with no -cycles and no -cycles. We also classify the complexity of -Regular List Colouring and a number of related colouring problems for graphs with bounded maximum degree.     

Maximal Equilateral Sets

A subset of a normed space $X$ X is called equilateral if the distance between any two points is the same. Let $m(X)$ m ( X ) be the smallest possible size of an equilateral subset of $X$ X maximal with respect to inclusion. We first observe that Petty’s construction of a $d$ d - $X$ X of any finite dimension $d\ge 4$ d ≥ 4 with $m(X)=4$ m ( X ) = 4 can be generalised to give $m(X\oplus _1\mathbb R )=4$ m ( X ⊕ 1 R ) = 4 for any $X$ X of dimension at least $2$ 2 which has a smooth point on its unit sphere. By a construction involving Hadamard matrices we then show that for any set $\Gamma $ Γ , $m(\ell _p(\Gamma ))$ m ( ? p ( Γ ) ) is finite and bounded above by a function of $p$ p , for all $1\le p<2$ 1 ≤ p < 2 . Also, for all $p\in [1,\infty )$ p ∈ [ 1 , ∞ ) and $d\in \mathbb N $ d ∈ N there exists $c=c(p,d)>1$ c = c ( p , d ) > 1 such that $m(X)\le d+1$ m ( X ) ≤ d + 1 for all $d$ d - $X$ X with Banach–Mazur distance less than $c$ c from $\ell _p^d$ ? p d . Using Brouwer’s fixed-point theorem we show that $m(X)\le d+1$ m ( X ) ≤ d + 1 for all $d$ d - $X$ X with Banach–Mazur distance less than $3/2$ 3 / 2 from $\ell _\infty ^d$ ? ∞ d . A graph-theoretical argument furthermore shows that $m(\ell _\infty ^d)=d+1$ m ( ? ∞ d ) = d + 1 . The above results lead us to conjecture that $m(X)\le 1+\dim X$ m ( X ) ≤ 1 + dim X for all finite-normed spaces $X$ X .     

Equiframed Curves – A Generalization of Radon Curves

Equiframed curves are centrally symmetric convex closed planar curves that are touched at each of their points by some circumscribed parallelogram of smallest area. These curves and their higher-dimensional analogues were introduced by Peczynski and Szarek (1991, Math Proc Cambridge Philos Soc 109: 125–148). Radon curves form a proper subclass of this class of curves. Our main result is a construction of an arbitrary equiframed curve by appropriately modifying a Radon curve. We give characterizations of each type of curve to highlight the subtle difference between equiframed and Radon curves and show that, in some sense, equiframed curves behave dually to Radon curves.Research supported by a grant from a cooperation between the Deutsche Forschungsgemeinschaft in Germany and the National Research Foundation in South Africa. Parts of this paper were written during a visit to the Department of Mathematics, Applied Mathematics and Astronomy of the University of South Africa.     

Energy Consumption During Nanoparticle Production: How Economic is Dry Synthesis?

The production of oxide nanoparticles by selected wet-chemistry or dry processes is compared in terms of energy requirements. Clear differences arise for production using electricity-intensive plasma processes, organic- or chloride-derived flame synthesis and liquid based precipitation processes. In spite of short process chains and elegant reactor design, many dry methods inherently require vastly bigger energy consumption than the multi-step wet processes. Product composition strongly influences the selection of the preferred method of manufacturing in terms of energy requirement: Metal oxide nanoparticles of light elements with high valency, e.g. titania demand high volumes of organic precursors and traditional processes excel in terms of efficiency. Products with heavier elements, more complex composition and preferably lower valency such as doped ceria, zirconia, and most mixed oxide ceramics may be readily manufactured by recently developed dry processes.