Some new concepts on the complexity of catalytic systems
As a whole, a catalyst acts as a hyperoperator computing a non-linear combination of several complexity structures; then, the overall complexity can be described through a non-linear combination of chemical and structural complexity. The latter is characterized through the fractal dimension and depends on the geometric and electronic factors.
Therefore, it has been observed that catalytic processes can be either well or ill-conditioned systems, depending on the condition number (k). A system with a low k value is well-conditioned, while a system with a high k appears ill-conditioned. Thus, structure-sensitive reactions can be classified as ill-conditioned systems, since small variations on the catalyst surface produce large effects on the catalytic activity. Finally, it has been proved that the overall complexity of a catalytic system is a state function and there is an inverse correlation between entropy and complexity.
The catalyst surface is structurally and compositionally complex, exposing adsorption/reaction centres that act either singularly (single sites) or in group (cluster of sites); in fact, it can have a fractal texture. These catalytic active sites behave as dynamic entities in the space-time domain and then their physico-chemical properties strongly depend on the operating conditions (1-4). During catalytic reaction, the solid surface typically receives a mixture of reactant molecules and often has to carry on intricate reaction networks with multiple steps and pathways in a general graph (5,6). Therefore, the catalyst operates through complex self-organizing phenomena, in which both the geometric and electronic factors play a key role on the chemical kinetics (7,8). Open systems, far from the equilibrium - reactions at steady-state flow conditions - can be described by a set of non-linear partial differential equations, combining the chemical kinetics with the diffusive phenomena of the adsorbed species, as follows: