PATTERN-RECOGNITION AND ALTERNATIVE PHYSICAL-CHEMISTRY METHODOLOGIES

Alternative formalisms for two different domains in physical chemistry are considered here: thermodynamics and chemical kinetics. In thermod ynamics the performance of a diagrammatic method based on geometric an d algebraic considerations is illustrated here. This method based on t he particular symmetry of a thermodynamic diagram allows one to obtain the most important thermodynamic expressions of a simple system and t o solve thermodynamic problems strictly related to these expressions. The different thermodynamic expressions can be developed with the appl ication of various geometric patterns to the proposed diagram. Further more, the particular structure of this diagram allows one to develop a matrix formulation of the pattern formalism. The matrix formalism req uires one to recast the thermodynamic parameters of the diagram into a vectorial form. The number of thermodynamic relations that can? thus, be ''discovered'' is enormous. In chemical kinetics, two new approach es for writing kinetic equations in matrix form or directly in the int egrated form are introduced here. The first method is based on the der ivation of the rate K matrix of a kinetic systems of any order in a di rect and straightforward way. This method, which allows one to solve f irst-order and some second-order kinetics with the normal matrix algeb ra methods, is mainly based on rate matrices which show interesting '' patterns'' due to their internal structure, which can further be used to check their validity and help to construct more complicated rate ma trices. In fact, it is possible to derive a set of rules, which offers the possibility to construct rate matrices in a total mechanical way. The convolution approach to chemical kinetics applies to species that are consumed solely through first-order steps, regardless of the comp lexity of its formation pathways. This last method offers the possibil ity to formulate the rate equation directly in the integrated form, a form which shows an interesting structure, especially in the case of c onsecutive reaction schemes. A careful lecture of the different topics of this paper will not overlook the fact that the real subject of the proposed formalisms is the detection and recognition of patterns and to show that, sometimes, behind impressive relations or matrices a ver y ''unimpressive'' pattern is hiding.