Kinetic Pattern Formation with Intermolecular Interactions: A Modified Brusselator Model

A systematic study on immiscible binary systems undergoing thermal/photo reversible chemical reactions

In this work, we systematically study an immiscible binary system undergoing thermal/photo reversible reactions in theory. For the thermal reaction case, no dissipative structures can be formed and only uniform equilibrium states are observed but the dynamical evolution to these trivial states witnesses a new type of sophisticated phase amplification phenomenon-temporary phase separation (TPS). Linear analysis and light-scattering calculations confirm that TPS is predominated either by spinodal decomposition or nucleation and growth mechanism, or by both successively. For the photo reaction case, steady dissipative patterns exist and are maintained by the external energy input of lights. Linear analysis together with simulations reveals that the characteristic wavelength (ξ) of these structures shortens as the input energy density increases and they obey the relation of ln ξ∝ 1/T_b with T_b the effective temperature of lights. The TPS phenomenon and length-scale dependency of dissipative patterns observed in this simple binary system might have rich implications for the non-equilibrium thermodynamics of biological systems.

A Feynman Path Integral-like Method for Deriving Reaction-Diffusion Equations

This work is devoted to deriving a more accurate reaction-diffusion equation for an A/B binary system by summing over microscopic trajectories. By noting that an originally simple physical trajectory might be much more complicated when the reactions are incorporated, we introduce diffusion-reaction-diffusion (DRD) diagrams, similar to the Feynman diagram, to derive the equation. It is found that when there is no intermolecular interaction between A and B, the newly derived equation is reduced to the classical reaction-diffusion equation. However, when there is intermolecular interaction, the newly derived equation shows that there are coupling terms between the diffusion and the reaction, which will be manifested on the mesoscopic scale. The DRD diagram method can be also applied to derive a more accurate dynamical equation for the description of chemical reactions occurred in polymeric systems, such as polymerizations, since the diffusion and the reaction may couple more deeply than that of small molecules.