Tunability of Self-Organized Structures Based on Thermodynamic Flux

Abstract

Nature establishes structures and functions via self-organization of constituents, including ions, molecules, and particles. Understanding the selection rule that determines the self-organized structure formed from many possible alternatives is fundamentally and technologically important. In this study, the selection rule for the self-organization associated with a reaction−diffusion system was explored using the Liesegang phenomenon, by which a periodic precipitation pattern is formed as a model system. Experiments were conducted by systematically changing the mass flux. At low mass fluxes, a vertically periodic pattern was formed, whereas at high mass fluxes, a horizontally periodic pattern was formed. The results inferred that a structural vertical-to-horizontal periodicity transition occurred in the selforganized periodic structure at the crossover flux at which the entropy production rate reversed. Numerical analyses attributed the as-observed flux-dependent structural transition to the selection of the self-organized pattern with a higher entropy production rate. These findings contribute to our understanding of how nature controls self-organized structures and geometry, potentially facilitating the development of novel designs, syntheses, and fabrication processes for well-controlled organized functional structures.

Role of Stochasticity in Helical Self-Organization during Precipitation

“…On the contrary, we have recently explained the switching behavior between band and dendritic structures for Liesegang phenomena in terms of the entropy production rate. 42 Therefore, we will also discuss the switching between band and helix according to the entropy production rate.…”

Momentum transport of morphological instability in fluid displacement with changes in viscosity

“…Previous studies have experimentally and theoretically demonstrated that the local thermodynamic flux is proportional to the global driving force. 38,49,56,[58][59][60][61] If the thermodynamic flux is linearly related to the thermodynamic force, entropy production can be re-expressed as a quadratic function of F as follows:…”

“…Previous studies have experimentally and theoretically demonstrated that the local thermodynamic flux is proportional to the global driving force. 38,49,56,58–61 If the thermodynamic flux is linearly related to the thermodynamic force, entropy production can be re-expressed as a quadratic function of F as follows: σ = J ( F ) X ( F ) = L ( F − θ ) 2 ,where L , and θ are phenomenological coefficients that vary with the system state. Coefficient θ is related to the free energy required for transitioning from one state to another or the interference intensity with other irreversible processes.…”

“…The principle using the thermodynamic flux expressed as a function of the global driving force has already been utilized to employ entropy production as a selection rule between various crystal morphologies in a resting fluid. 38,55,56 Among the possible formation patterns, the actual pattern formed requires the diffusion flux to evolve such that entropy production is maximized. In this study, we analyzed the interfacial instability with molecular diffusion exhibiting the transition from normal VF to tip-splitting instability using thermodynamic flux and energy dissipation.…”