Addressing complexity in catalyst design: From volcanos and scaling to more sophisticated design strategies

Volcano plots and scaling relations are commonly used to design catalysts and understand catalytic behavior. These plots are a useful tool due to their robust and simple analysis of catalysis; however, catalysts that follow the volcano plot paradigm have an inherent limit to their performance. Scaling and Brønsted-Evans-Polanyi (BEP) relations, which are linear correlations in reaction energetics, force tradeoffs when optimizing catalysts, which leads to this limit on performance. Therefore, materials and design strategies that are not limited by volcano plots and scaling relations are of high interest, and this is the focus of this Report. We first give an overview of volcano plots and scaling relations. Deviations from scaling relations and the volcano plot and their causes are discussed in more detail. Finally, design strategies that do not rely on the volcano plot paradigm are reviewed.     

Introduction to focus issue: design and control of self-organization in distributed active systems

Spatiotemporal self-organization is found in a wide range of distributed dynamical systems. The coupling of the active elements in these systems may be local or global or within a network, and the interactions may be diffusive or nondiffusive in nature. The articles in this focus issue describe biological and chemical systems designed to exhibit spatiotemporal dynamics and the control of such dynamics through feedback methods.     

Field theoretical approach to inhomogeneous ionic systems: thermodynamic consistency with the contact theorem,Gibbs adsorption and surface tension

Using a statistical field approach we investigate the structure of an electrolyte solution in contact with a neutral impenetrable wall. The Hamiltonian contains the Coulomb interaction and the ideal entropy. At the level of the quadratic approximation, the Hamiltonian yields the Debye-Hückel theory in the bulk. Analytic expressions of the charge-charge and potential-potential inhomogeneous correlation functions are obtained. Exact asymptotic results for point ion charge correlation functions are obtained and the profile for the fluctuation of the electric potential is calculated. We also consider the term beyond the quadratic expansion of the ideal entropy in the Hamiltonian. With this term a higher order coupling between charge density and number density produces a non-trivial profile for the total ion density. This density profile is consistent with the contact theorem and the related surface tension calculated from the Gibbs adsorption isotherm.     

One-dimensional Ising-like systems: an analytical investigation of the static and dynamic properties, applied to spin-crossover relaxation

We investigate the dynamical properties of the 1-D Ising-like Hamiltonian taking into account short and long range interactions, in order to predict the static and dynamic behavior of spin crossover systems. The stochastic treatment is carried out within the frame of the local equilibrium method [1]. The calculations yield, at thermodynamic equilibrium, the exact analytic expression previously obtained by the transfer matrix technique [2]. We mainly discuss the shape of the relaxation curves: (i) for large (positive) values of the short range interaction parameter, a saturation of the relaxation curves is observed, reminiscent of the behavior of the width of the static hysteresis loop [3]; (ii) a sigmoidal (self-accelerated) behavior is obtained for large enough interactions of any type; (iii) the relaxation curves exhibit a sizeable tail (with respect to the mean-field curves) which is clearly associated with the transient onset of first-neighbor correlations in the system, due to the effect of short-range interactions. The case of negative short-range interaction is briefly discussed in terms of two-step properties. Received 29 October 1999 and Received in final form 30 December 1999     

An expansion of the field modulus suitable for the description of strong field gradients in axisymmetric magnetic fields: application to single-sided magnet design, field mapping and STRAFI

Mapping (or plotting) the magnetic field has a critical importance for the achievement of the homogeneous magnetic field necessary to standard MR experiments. A powerful tool for this purpose is the Spherical Harmonic Expansion (SHE), which provides a simple way to describe the spatial variations of a field in free space. Well-controlled non-zero spatial variations of the field are critical to MRI. The resolution of the image is directly related to the strength of the gradient used to encode space. As a result, it is desirable to have strong variations of the field. In that case, the SHE cannot be used as is, because the field modulus variations are affected by the variations of all components of the field. In this paper, we propose a method based on the SHE to characterize such variations, theoretically and experimentally, in the limit of an axisymmetric magnetic field. Practical applications of this method are proposed through the examples of single-sided magnet design and characterization, along with Stray-Field Imaging (STRAFI).