Enhancing the Water Stability of Al‐MIL‐101‐NH2 via Postsynthetic Modification

The resistance of metal–organic frameworks towards water is a very critical issue concerning their practical use. Recently, it was shown for microporous MOFs that the water stability could be increased by introducing hydrophobic pendant groups. Here, we demonstrate a remarkable stabilisation of the mesoporous MOF Al‐MIL‐101‐NH₂ by postsynthetic modification with phenyl isocyanate. In this process 86 % of the amino groups were converted into phenylurea units. As a consequence, the long‐term stability of Al‐MIL‐101‐URPh in liquid water could be extended beyond a week. In water saturated atmospheres Al‐MIL‐101‐URPh decomposed at least 12‐times slower than the unfunctionalised analogue. To study the underlying processes both materials were characterised by Ar, N₂ and H₂O sorption measurements, powder X‐ray diffraction, thermogravimetric and chemical analysis as well as solid‐state NMR and IR spectroscopy. Postsynthetic modification decreased the BET equivalent surface area from 3363 to 1555 m² g^?1 for Al‐MIL‐101‐URPh and reduced the mean diameters of the mesopores by 0.6 nm without degrading the structure significantly and reducing thermal stability. In spite of similar water uptake capacities, the relative humidity‐dependent uptake of Al‐MIL‐101‐URPh is slowed and occurs at higher relative humidity values. In combination with ¹H‐²⁷Al D ‐HMQC NMR spectroscopy experiments this favours a shielding mechanism of the Al clusters by the pendant phenyl groups and rules out pore blocking.     

The complexity of cutting complexes

This paper investigates the combinatorial and computational aspects of certain extremal geometric problems in two and three dimensions. Specifically, we examine the problem of intersecting a convex subdivision with a line in order to maximize the number of intersections. A similar problem is to maximize the number of intersected facets in a cross-section of a three-dimensional convex polytope. Related problems concern maximum chains in certain families of posets defined over the regions of a convex subdivision. In most cases we are able to prove sharp bounds on the asymptotic behavior of the corresponding extremal functions. We also describe polynomial algorithms for all the problems discussed.Bernard Chazelle wishes to acknowledge the National Science Foundation for supporting this research in part under Grant No. MCS83-03925. Herbert Edelsbrunner is pleased to acknowledge the support of Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862.     

Rotating Charge Coupled to the Maxwell Field: Scattering Theory and Adiabatic Limit

We consider a spinning charge coupled to the Maxwell field. Through the appropriate symmetry in the initial conditions the charge remains at rest. We establish that any time-dependent finite energy solution converges to a sum of a soliton wave and an outgoing free wave. The convergence holds in global energy norm. Under a small constant external magnetic field the soliton manifold is stable in local energy seminorms and the evolution of the angular velocity is guided by an effective finite-dimensional dynamics. The proof uses a non-autonomous integral inequality method.     

Neighborhood Complexes and Generating Functions for Affine Semigroups

Given a₁,a₂,...,a_n ∈ ℤ^d$, we examine the set, G, of all non-negative integer combinations of these a_i. In particular, we examine the generating function f(z) = ∑_{b ∈ G}z_b. We prove that one can write this generating function as a rational function using the neighborhood complex (sometimes called the complex of maximal lattice-free bodies or the Scarf complex) on a particular lattice in ℤ_n. In the generic case, this follows from algebraic results of Bayer and Sturmfels. Here we prove it geometrically in all cases, and we examine a generalization involving the neighborhood complex on an arbitrary lattice.     

Variant superfield representations

We discuss some variant superfield representations which can arise by the replacement of some of the usual fields in a multiplet with p-form gauge fields.     

Corn stover fractions and bioenergy

Information is presented on structure, composition, and response to enzymes of corn stover related to barriers for bioconversion to ethanol. Aromatic compounds occurred in most tissue cell walls. Ferulic acid esterase treatment before cellulase treatment significantly improved dry weight loss and release of phenolic acids and sugars in most fractions over cellulase alone. Leaf fractions were considerably higher in dry weight loss and released sugars with esterase treatment, but stem pith cells gave up the most phenolic acids. Results help identify plant fractions more appropriate for coproducts and bioconversion and those more suitable as residues for soil erosion control.