Cation exchange membranes by pre-irradiation grafting of styrene into FEP films. II. Properties of copolymer membranes

The structure and some physico-chemical properties of radiation grafted FEP-g-polystyrenesulfonic acid proton exchange membranes were studied as a function of the degree of grafting. The distribution of grafted polymer across the membrane thickness was obtained from microprobe measurements. It was found that for low levels of grafting (ca. 3%), polystyrene chains are located near the membrane surface only, and the interior of the membrane remains ungrafted. With the increasing degree of grafting, polystyrene chains were incorporated into the interior of the membrane as well. An almost homogeneous distribution of grafts in the membrane was obtained at a graft level of > 13%. The influence of the degree of grafting on membrane properties, such as ion exchange capacity, swelling, and specific resistivity was studied. Three different states of water, viz., freezing free, freezing bound, and nonfreezing water have been identified in noncrosslinked membranes. However, the nature and the amount of crosslinker had a profound influence on the states of water in a membrane. © 1996 John Wiley & Sons, Inc.     

Metal‐Free Catalyst for the Chemoselective Methylation of Amines Using Carbon Dioxide as a Carbon Source

N‐methylation of amines is an important step in the synthesis of many pharmaceuticals and has been widely applied in the preparation of other key intermediates and chemicals. Therefore, the development of efficient methylation methods has attracted considerable attention. In this respect, carbon dioxide is an attractive C₁ building block because it is an abundant, renewable, and nontoxic carbon source. Consequently, we developed a highly chemoselective, metal‐free catalytic system that operates under ambient conditions for the N‐methylation of amines.     

Catalytic Generation and Chemoselective Transfer of Nucleophilic Hydrides from Dihydrogen

Copper(I)–N-heterocyclic-carbene (NHC) complexes enabled the catalytic generation of nucleophilic hydrides from dihydrogen (H₂) and their subsequent transfer to allylic chlorides. The highly chemoselective catalyst displayed no concomitant hydrogenation reactivity; in fact, the terminal double bond formed in the hydride transfer remained intact. Switching to deuterium gas (D₂) allowed for regioselective monodeuteration with excellent isotope incorporation.     

A higher-order large-scale regularity theory for random elliptic operators

We develop a large-scale regularity theory of higher order for divergence-form elliptic equations with heterogeneous coefficient fields a in the context of stochastic homogenization. The large-scale regularity of a-harmonic functions is encoded by Liouville principles: The space of a-harmonic functions that grow at most like a polynomial of degree k has the same dimension as in the constant-coefficient case. This result can be seen as the qualitative side of a large-scale C^k,α-regularity theory, which in the present work is developed in the form of a corresponding C^k,α-“excess decay” estimate: For a given a-harmonic function u on a ball B_R, its energy distance on some ball B_r to the above space of a-harmonic functions that grow at most like a polynomial of degree k has the natural decay in the radius r above some minimal radius r₀.

Though motivated by stochastic homogenization, the contribution of this paper is of purely deterministic nature: We work under the assumption that for the given realization a of the coefficient field, the couple (φ, σ) of scalar and vector potentials of the harmonic coordinates, where φ is the usual corrector, grows sublinearly in a mildly quantified way. We then construct “kth-order correctors” and thereby the space of a-harmonic functions that grow at most like a polynomial of degree k, establish the above excess decay, and then the corresponding Liouville principle.