In particular, the search for an even buffer capacity across large pH ranges is primordial for the production of linear pH gradients. Mathematical optimization of such mixtures rests mostly on objective functions minimization, typically through least square methods, by adjusting the concentrations of known buffer substances . On the other hand, theoretical studies of pH mixtures that lead to real values prediction has mostly been conducted analytically, greatly limiting the situations that could be dealt with as the complexity of the system grows extremely rapidly with the composition . Such studies are not primarily interested with actual buffers but rather with the mathematical conditions that drive a buffer system. In this way, it is possible, for instance, to find the conditions in terms of dissociation constants (or pK a ) and concentrations that guarantee the largest possible pH range of even buffer index for a two weak acid mixture, provided that one can neglect the contribution of H 3 O + and OH -. One can, analytically, hardly go much further given the degree of the master polynomials that drive the more complicated systems-this is the case also for complexation equilibria where overlapping involving two steps already leads to intricate calculations , even though they do not involve formally an equilibrium with the solvent. Hence, it is hopeless to expect analytical solutions that could predict the best chemical properties to produce constant buffer index over large pH ranges-i.e. more than 1 pH unit, roughly, as going further necessarily involves using more than two chemical components. For that matter, it is even hard to guarantee finding the best mathematical conditions to reach the flattest possible index buffer curve for extreme pH, as then the contribution of H 3 O + or OH -cannot be neglected anymore, which renders the system impossible to solve analytically for two weak acid mixtures.