The application of the principle of least action to some self-organized chemical reactions

Abstract

In contrast to the traditional viewing of reaction mechanism as a time-continuous progress of sequent intermediate states the feedback oscillatory self-organisation is investigated. Some cases of solid-state reactions are analyzed but main interest is directed to the “principle of the least action”, introduced into the science by P.L.M. Maupertuis in 1744. It is used for the evaluation of diffusion action of propagating Belousov–Zhabotinsky (BZ) waves where the diffusion action is calculated as the product: K× κ× m× λ× u, K is the diffusivity factor ( K=1 for one-dimensional space, K=2 for two-dimensional space, K=4 π for three-dimensional space), κ is the tortuosity factor ( κ=1 for water non-restricted solutions, κ>1 for gels, membranes, glasses, etc.), m is the mass of H + cations creating the propagating osmotic wave, λ represents a path necessary for the accumulation of H + in order to overcome the opposing pressure of the surroundings and u is the propagation speed of BZ waves. The examination of data available from literature revealed a strong tendency of successive target and spiral waves in water solutions ( κ=1) to minimize their action to a characteristic value h=6.63±0.06×10 −34 J s, having a striking coincidence with the Planck constant of microcosms.