驱动自催化反应混合物的群体动力学
Population dynamics of driven autocatalytic reactive mixtures
摘要：
受基于非平衡态热力学的反应动力学理论和驱动反应扩散的线性稳定性的启发，我们应用Fokker-Planck方程来描述与化学库接触的反应性粒子系综的群体动力学。我们通过比较具有相同热力学但不同反应动力学的系统来说明自催化对种群动力学的影响。系统的动态相行为可能完全不同于其热力学所暗示的。通过定义相分离的粒子系综时的概率分布是双峰，我们发现，热力学相分离可能会被抑制的自抑制反应，而自催化增强相分离，并在某些情况下诱导系综，由philically单相系统分离成两个不同的群体，我们称之为虚拟相分离。不对称反应动力学也导致在反转反应方向时在性质上不同的群体动力学。在可忽略涨落的极限下，我们用特征线法和线性化方法研究了浓度标准偏差的演化以及相分离的条件，与完全数值解符合得很好。讨论了锂离子电池和{ \it原位} X射线衍射的应用。
英文摘要：
Motivated by the theory of reaction kinetics based on nonequilibrium thermodynamics and the linear stability of driven reaction-diffusion, we apply the Fokker-Planck equation to describe the population dynamics of an ensemble of reactive particles in contact with a chemical reservoir. We illustrate the effect of autocatalysis on the population dynamics by comparing systems with identical thermodynamics yet different reaction kinetics. The dynamic phase behavior of the system may be entirely different from what its thermodynamics may suggest. By defining phase separation for a particle ensemble to be when the probability distribution is bimodal, we find that thermodynamic phase separation may be suppressed by autoinhibitory reactions, while autocatalysis enhances phase separation and in some cases induce the ensemble that consists of thermodynamically single-phase systems to segregate into two distinct populations, which we term fictitious phase separation. Asymmetric reaction kinetics also results in qualitatively different population dynamics upon reversing the reaction direction. In the limit of negligible fluctuations, we use method of characteristics and linearization to study the evolution of the standard deviation of concentration as well as the condition for phase separation, in good agreement with the full numerical solution. Applications are discussed to Li-ion batteries and {\it in situ} x-ray diffraction.
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