Metal‐Supported Aluminosilicate Ultrathin Films as a Versatile Tool for Studying the Surface Chemistry of Zeolites

The application of a variety of “surface‐science” techniques to elucidate surface structures and mechanisms of chemical reactions at zeolite surfaces has long been considered as almost impossible because of the poor electrical and thermal conductivity of those materials. Here, we show that the growth of a thin aluminosilicate film on a metal single crystal under controlled conditions results in adequate and well‐defined model systems for zeolite surfaces. In principle, silicate films that contain metals other than Al (e.g. Ti, Fe, etc) may be prepared in a similar way. We believe that this approach opens up a new playground for experimental and theoretical modeling of zeolites, aimed at a fundamental understanding of structure–reactivity relationships in such materials.     

A variational approach to nonlinear dynamics of nanoscale surface modulations

In this paper, we propose a variational formulation to study the singular evolution equations that govern the dynamics of surface modulations on crystals below the roughening temperature. The basic idea of the formulation is to expand the surface shape in terms of a complete set of basis functions and to use a variational principle equivalent to the continuum evolution equations to obtain coupled nonlinear ordinary differential equations for the expansion coefficients. Unlike several earlier approaches that rely on ad hoc regularization procedures to handle the singularities in the evolution equations, the only inputs required in the present approach are the orientation dependent surface energies and the diffusion constants. The method is applied to study the morphological equilibration of patterned unidirectional and bidirectional sinusoidal modulations through surface diffusion. In the case of bidirectional modulations, particular attention is given to the analysis of the profile decay as a function of ratio of the modulating wavelengths in the coordinate directions. A key question that we resolve is whether the one-dimensional decay behavior is recovered as one of the modulating wavelengths of the two-dimensional profiles diverges, or whether one-dimensional decay has qualitatively distinct features that cannot be described as a limiting case of the two-dimensional behavior. In contrast to some earlier suggestions, our analytical and numerical studies clearly show that the former situation is true; we find that the one-dimensional profiles, like the highly elongated two-dimensional profiles, decay with formation of facets. While our results for the morphological equilibration of symmetric one-dimensional profiles are in agreement with the free-boundary formulation of Spohn, the present approach can also be used to study the evolution of asymmetric profile shapes where the free-boundary approach is difficult to apply. The variational method is also used to analyze the decay of unidirectional modulations in the presence of steps that arise in most experimental studies due to a small misorientation from the singular surface.     

Photoinduced processes on alkali covered surfaces: NO desorption from K/Cr2O3(0001)

We have studied the ultraviolet laser induced desorption of NO/Cr₂O₃(0001), K/Cr₂O₃(0001) and the coadsorbate system NO/K/Cr₂O₃(0001) using resonance enhanced multiphoton ionization spectroscopy for state selective detection of the desorbing species after excitation with nanosecond laser pulses. The goal of our experiments was to study the influence of surface electronic modifications via alkali adsorption on the photodynamics of a simple molecule. The photochemistry of the isolated and the coadsorbate systems is strongly dependent on the coverage of the diverse components. In this paper we shall mainly focus on data for the low coverage regime of potassium. From the two adsorbate species of NO, a chemisorbed and a physisorbed species, we present data of the chemisorbed species. The velocity distributions show a strong dependence on the excitation energy which we interpret on the basis of electron energy loss spectra as being due to surface charge transfer states. This is corroborated with our coadsorption experiments with low coverages of potassium which alter the velocity distributions.     

On some approximation problems for complex polynomials

We consider weighted complex approximation problems of the form $$\mathop {\min }\limits_{p:p(a) = 1} \mathop {\min }\limits_{z \in \left[ { - 1,1} \right]} \left| {w(z)p(z)} \right|$$ withp ranging over all polynomials of degree ≤n anda purely imaginary. Recent results by Ruscheweyh and Freund forw(z) = 1 and \(w(z) = \sqrt {z + 1}\) are extended to more general weight functions. Moreover, the solution of a complex Zolotarev type problem is given.