Chemical modification of the surface of a sulfonated membrane by formation of a sulfonamide bond

This paper describes a novel approach for the surface modification of a cation-exchange membrane, bearing sulfonate groups, by a cationic layer. The modification procedure involved the chlorosulfonation of the sulfonate groups of the base membrane with thionyl chloride, followed by a reaction with a diamine to yield a sulfonamide bond and a terminal amine. The latter could be quaternized by reaction with methyl iodide or protonated by soaking in acidic media. The membranes were characterized in detail by attenuated total reflectance Fourier transform infrared and X-ray photoelectron spectroscopies as well as elemental analysis to confirm that the above reactions occurred. The selectivity of these membranes toward the electrochemically assisted transport of protons versus Zn2+ metallic cations was determined during an electrodialysis in a two-compartment electrochemical cell. The data indicate a significant decrease of the transport of the metallic cations following modification of the membrane with the cationic layer. The later allows for the transport of protons from the catholyte to the anolyte compartment with much improved selectivity since the divalent cations are excluded from the membrane due to the electrostatic barrier of the cationic layer.     

Modification of ion-exchange membrane used for separation of protons and metallic cations and characterization of the membrane by current-voltage curves

The ionic transport properties of several cations (H(+), Na(+), and Zn(2+)) across sulfonated ion-exchange membranes modified with an amine were investigated by the measurement of current-voltage curves to determine the effect of the surface modification of the membrane. The membrane was modified by chlorosulfonation and amination with a diamine (N,N-dimethylethylenediamine) and an amine (isoamylamine) to form a sulfonamide bond between amine groups and the surface layer. In the case of the modification with the diamine, the terminal amine was protonated in acidic media or quaternized with methyl iodide. The presence of a positively charged layer on the two sides of the membrane strongly decreased the limiting current flowing across the membrane in the presence of a 1:1 electrolyte such as HCl or HNO(3) due to an increase of the resistance of the membrane. In the case of divalent cations such as Na(+) and Zn(2+), electrostatic repulsion also contributes to the decrease of the limiting current. The presence of divalent anions seems to increase the limiting current somewhat due to their preconcentration within the cationic layer, which facilitates their subsequent transport across the membrane. When only one face of the membrane was modified, the current-voltage measurements showed that the membrane did not behave like a bipolar membrane. For one-side (under forward polarization) and two-side modified membranes, counterions are slightly blocked in the membrane by the cationic layer, which led to a decrease of the membrane conductivity during electrodialysis.     

On the Dimension of Posets with Cover Graphs of Treewidth 2

In 1977, Trotter and Moore proved that a poset has dimension at most 3 whenever its cover graph is a forest, or equivalently, has treewidth at most 1. On the other hand, a well-known construction of Kelly shows that there are posets of arbitrarily large dimension whose cover graphs have treewidth 3. In this paper we focus on the boundary case of treewidth 2. It was recently shown that the dimension is bounded if the cover graph is outerplanar (Felsner, Trotter, and Wiechert) or if it has pathwidth 2 (Biró, Keller, and Young). This can be interpreted as evidence that the dimension should be bounded more generally when the cover graph has treewidth 2. We show that it is indeed the case: Every such poset has dimension at most 1276.     

A Note on the Cops and Robber Game on Graphs Embedded in Non-Orientable Surfaces

We consider the two-player, complete information game of Cops and Robber played on undirected, finite, reflexive graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if, after a move, a cop and the robber are on the same vertex. The minimum number of cops needed to catch the robber on a graph is called the cop number of that graph. Let c(g) be the supremum over all cop numbers of graphs embeddable in a closed orientable surface of genus g, and likewise ${\tilde c(g)}$ for non-orientable surfaces. It is known (Andreae, 1986) that, for a fixed surface, the maximum over all cop numbers of graphs embeddable in this surface is finite. More precisely, Quilliot (1985) showed that c(g) ≤ 2g + 3, and Schröder (2001) sharpened this to ${c(g)\le \frac32g + 3}$ . In his paper, Andreae gave the bound ${\tilde c(g) \in O(g)}$ with a weak constant, and posed the question whether a stronger bound can be obtained. Nowakowski & Schröder (1997) obtained ${\tilde c(g) \le 2g+1}$ . In this short note, we show ${\tilde c(g) \leq c(g-1)}$ , for any g ≥ 1. As a corollary, using Schröder’s results, we obtain the following: the maximum cop number of graphs embeddable in the projective plane is 3, the maximum cop number of graphs embeddable in the Klein Bottle is at most 4, ${\tilde c(3) \le 5}$ , and ${\tilde c(g) \le \frac32g + 3/2}$ for all other g.     

Boxicity of Graphs on Surfaces

The boxicity of a graph G = (V, E) is the least integer k for which there exist k interval graphs G _i  = (V, E _i ), 1 ≤ i ≤ k, such that ${E = E_1 \cap \cdots \cap E_k}$ . Scheinerman proved in 1984 that outerplanar graphs have boxicity at most two and Thomassen proved in 1986 that planar graphs have boxicity at most three. In this note we prove that the boxicity of toroidal graphs is at most 7, and that the boxicity of graphs embeddable in a surface Σ of genus g is at most 5g + 3. This result yields improved bounds on the dimension of the adjacency poset of graphs on surfaces.     

Thermodynamic Properties of Polymorphs of Fluorosulfate Based Cathode Materials with Exchangeable Potassium Ions

FeSO₄F‐based frameworks have recently emerged as attractive candidates for alkali insertion electrodes. Mainly owing to their rich crystal chemistry, they offer a variety of new host structures with different electrochemical performances and physical properties. In this paper we report the thermodynamic stability of two such K‐based “FeSO₄F” host structures based on direct solution calorimetric measurements. KFeSO₄F has been reported to crystallize in two different polymorphic modifications—monoclinic and orthorhombic. The obtained enthalpies of formation from binary components (KF plus FeSO₄) are negative for both polymorphs, indicating that they are thermodynamically stable at room temperature, which is very promising for the future exploration of sulfate based cathode materials. Our measurements show that the low‐temperature monoclinic polymorph is enthalpically more stable than the orthorhombic phase by ≈10 kJ mol^?1, which is consistent with the preferential formation of monoclinic KFeSO₄F at low temperature. Furthermore, observed phase transformations and difficulties in the synthesis process can be explained based on the obtained calorimetric results. The KMnSO₄F orthorhombic phase is more stable than both polymorphs of KFeSO₄F.     

Analysis of the local structure of phosphorus-substituted LAMOX oxide ion conductors

The effect of partial substitution of molybdenum by phosphorus on the global and local structural arrangement of the fast oxide-ion conductor La(2)Mo(2)O(9) (LAMOX) has been studied by X-ray powder diffraction as well as (139)La and (31)P solid state NMR. The diffraction patterns show that La(2)Mo(2-y)P(y)O(9-y/2) forms a solid solution at low phosphorus concentrations, and that there is a structural phase transition upon increasing phosphorus concentration. This phase transition is also reflected in (139)La and (31)P NMR spectra. The possibility to excite (31)P multiple-quantum coherences of one of the (31)P NMR signals gives evidence of an accumulation of phosphorus atoms on neighbouring Mo-type sites already before formation of three-dimensional precipitates. On the basis of our X-ray and NMR results we propose a possible structural arrangement of the compound La(2)Mo(2-y)P(y)O(9-y/2) that explains the experimental observations by crystal twinning.     

Trees with Given Stability Number and Minimum Number of Stable Sets

We study the structure of trees minimizing their number of stable sets for given order n and stability number α. Our main result is that the edges of a non-trivial extremal tree can be partitioned into n ? α stars, each of size \({\lceil\frac{n-1}{n-\alpha}\rceil}\) or \({\lfloor\frac{n-1}{n-\alpha}\rfloor}\) , so that every vertex is included in at most two distinct stars, and the centers of these stars form a stable set of the tree.     

High density amorphous ices: disordered water towards close packing

The structure of amorphous ice under pressure has been studied by molecular dynamics at 160 K. The starting low-density phase undergoes significant changes as the density increases, and at rho=1.51 g/cm(3) our calculated g(OO)(r) is in excellent agreement with in situ neutron diffraction data obtained at 1.8 GPa and 100 K on very high density amorphous ice made at 150 K. As the system is further compressed, in the theoretical simulations, up to rho=1.90 g/cm(3), the structural modifications are continuous up to the highest density. The analysis of orientational distributions reveals that dense amorphous ice is characterized by major distortions of the tetrahedral geometry, and that the pressure structural changes, already observed experimentally at lower densities, can be interpreted as a trend towards a disordered closed-packed structure.     

Degenerations of cubic threefolds and matroids

We present a surprising connection between cubic threefolds and the well-known regular matroid by making use of intermediate Jacobians of cubic threefolds realized as Prym varieties. As a corollary we obtain a new proof of the nonrationality of generic cubic threefolds.