Often in real chemical reactors, a large number of distinct species interact through an intricate network of chemical reactions. Such complex systems can behave in unexpected ways, causing multiple steady states, instabilities, runaway reactions, explosions, etc. The goal of this research is the creation of theory that provides practicing engineers and chemists with readily applicable analytical tools to be used for: (1) the operation of reactors with complex but well understood chemistry (the theory would provide an indication of the stability problems that should be a source of concern), and (2) the study of reactors with poorly understood chemistry (the theory would provide means for the sensitive discrimination between rival mechanisms put forward to account for laboratory observations). The PI's chemical reaction theory is rooted in the idea that, however vast the territory of chemical reaction engineering might seem, the systems of differential equations that present themselves for study have a very special structure. At least when the kinetics is mass action, each system is determined (up to rate constant values) in a very precise way from the underlying network of chemical reactions, and so it becomes meaningful to ask questions about the relationship between reaction network structure and qualitative properties of the corresponding differential equations. Work under this grant will consist of three new projects: (1) unification of the PI's earlier deficiency-oriented theories with newer developments based on his Species-Complex-Linkage graph (SCL Graph) and application to more complex systems such as electrochemical reactions; (2) application of existing and newly developed theory to heterogeneous catalysis with special emphasis on the way in which the operative catalytic pathway reveals itself in multiple steady state data by way of a characteristic "mechanistic signature"; and (3) development of user-oriented personal computer software which would not require knowledge of the underlying complex mathematical analysis.
