A New Principal Curve Algorithm for Nonlinear Principal Component Analysis

This paper emerged from work supported by EPSRC grant GR/S84354/01 and proposes a method of determining principal curves, using spline functions, in principal component analysis (PCA) for the representation of non-linear behaviour in process monitoring. Although principal curves are well established, they are difficult to implement in practice if a large number of variables are analysed. The significant contribution of this paper is that the proposed method has minimal complexity, assuming simple spline geometry, thus enabling efficient computation. The paper provides a foundation for further work where multiple curves may be required to represent underlying non-linear information in complex data.

Some Understanding of Fischer-Tropsch Synthesis from Density Functional Theory Calculations

The combination of density functional theory (DFT) calculations and kinetic analyses is a very useful approach to study surface reactions in heterogeneous catalysis. The present paper reviews some recent work applying this approach to Fischer-Tropsch (FT) synthesis. Emphasis is placed on the following fundamental issues in FT synthesis: (i) reactive sites for both hydrogenation and C-C coupling reactions; (ii) reaction mechanisms including carbene mechanism, CO-insertion mechanism and hydroxyl-carbene mechanism; (iii) selectivity with a focus on CH(4) selectivity, alpha-olefin selectivity and chain growth probability; and (iv) activity.

Density Functional Theory Study of Iron and Cobalt Carbides for Fischer-Tropsch Synthesis

Carbides are important phases in heterogeneous catalysis. However, the understanding of carbide phases is inadequate: Fe and Co are the two commercial catalysts for Fischer-Tropsch (FT) synthesis, and experimental work showed that Fe carbide is the active phase in FT synthesis, whereas the appearance of Co carbide is considered as a possible deactivation cause, TO understand very different catalytic roles of carbides, all the key elementary steps in FT synthesis, that is, CO dissociation, C(1) hydrogenation, and C(1)+C(1) coupling, are extensively investigated on both carbide surfaces using first principles calculations. In particular, the most important issues in FT synthesis, the activity and methane selectivity, on the carbide surfaces are quantitatively determined and analyzed. They are also discussed together with metallic Fe and Co surfaces. It is found that (i) Fe carbide is more active than metallic Fe and has similar methane selectivity to Fe, being consistent with the experiments; and (ii) Co carbide is less active than Co and has higher methane selectivity, providing evidence on the molecular level to support the suggestion that the formation of Co carbide is a cause of relatively high methane selectivity and deactivation on Co catalysts.

Possibility of designing catalysts beyond the traditional volcano curve: A theoretical framework for multi-phase surfaces

The current theory of catalyst activity in heterogeneous catalysis is mainly obtained from the study of catalysts with mono-phases, while most catalysts in real systems consist of multi-phases, the understanding of which is far short of chemists' expectation. Density functional theory (DFT) and micro-kinetics simulations are used to investigate the activities of six mono-phase and nine bi-phase catalysts, using CO hydrogenation that is arguably the most typical reaction in heterogeneous catalysis. Excellent activities that are beyond the activity peak of traditional mono-phase volcano curves are found on some bi-phase surfaces. By analyzing these results, a new framework to understand the unexpected activities of bi-phase surfaces is proposed. Based on the framework, several principles for the design of multi-phase catalysts are suggested. The theoretical framework extends the traditional catalysis theory to understand more complex systems.

Catalyst screening: Refinement of the origin of the volcano curve and its implication in heterogeneous catalysis

Understanding the overall catalytic activity trend for rational catalyst design is one of the core goals in heterogeneous catalysis. In the past two decades, the development of density functional theory (DFT) and surface kinetics make it feasible to theoretically evaluate and predict the catalytic activity variation of catalysts within a descriptor-based framework. Thereinto, the concept of the volcano curve, which reveals the general activity trend, usually constitutes the basic foundation of catalyst screening. However, although it is a widely accepted concept in heterogeneous catalysis, its origin lacks a clear physical picture and definite interpretation. Herein, starting with a brief review of the development of the catalyst screening framework, we use a two-step kinetic model to refine and clarify the origin of the volcano curve with a full analytical analysis by integrating the surface kinetics and the results of first-principles calculations. It is mathematically demonstrated that the volcano curve is an essential property in catalysis, which results from the self-poisoning effect accompanying the catalytic adsorption process. Specifically, when adsorption is strong, it is the rapid decrease of surface free sites rather than the augmentation of energy barriers that inhibits the overall reaction rate and results in the volcano curve. Some interesting points and implications in assisting catalyst screening are also discussed based on the kinetic derivation. Moreover, recent applications of the volcano curve for catalyst design in two important photoelectrocatalytic processes (the hydrogen evolution reaction and dye-sensitized solar cells) are also briefly discussed.