Constrained Gibbs energy minimisation

Computation of chemical equilibria and phase diagrams for multi-phase and non-ideal systems by the material-balance constrained Gibbs free energy minimisation is a modern application of the thermodynamic theory with increasing practical uses. However, in many prospective applications, the behaviour of matter is influenced by additional constraining factors, such as kinetic inhibitions, or electrochemical, charge transport and surface phenomena. For those situations, an extended Gibbs energy method can be applied. In this technique, the supplementary work-coefficient or affinity related condition is introduced to the Gibbs energy calculation as an additional undetermined Lagrange multiplier, which represents the constraint potential. A number of new phenomena can thus be included in Gibb- sian calculations. The extended Gibbs energy method is illustrated with some very basic examples.