Rubinovich Leonid, Polak Micha
Department of Chemistry, Ben-Gurion University of the Negev, Beer-Sheva 8410500, Israel.
Entropy (Basel). 2025 May 27;27(6):564. doi: 10.3390/e27060564.
By introducing the concept of nanoreaction-based fluctuating mixing entropy, the challenge posed by the smallness of a closed molecular system is addressed through equilibrium statistical-mechanical averaging over fluctuating reaction extent. Based on the canonical partition function, the interplay between the mixing entropy and fluctuations in the reaction extent in nanoscale environments is unraveled while maintaining consistency with macroscopic behavior. The nanosystem size dependence of the mixing entropy, the reaction extent, and a concept termed the "reaction extent entropy" are modeled for the combination reactions A+B↔2C and the specific case of H2+I2↔2HI. A distinct inverse correlation is found between the first two properties, revealing consistency with the nanoconfinement entropic effect on chemical equilibrium (NCECE). To obtain the time dependence of the instantaneous mixing entropy following equilibration, the Stochastic Simulation (Gillespie) Algorithm is employed. In particular, the smallest nanosystems exhibit a step-like behavior that deviates significantly from the smooth mean values and is associated with the discrete probability distribution of the reaction extent. As illustrated further for molecular adsorption and spin polarization, the current approach can be extended beyond nanoreactions to other confined systems with a limited number of species.
通过引入基于纳米反应的涨落混合熵概念，借助对涨落反应程度进行平衡统计力学平均，解决了封闭分子系统规模小所带来的挑战。基于正则配分函数，揭示了纳米尺度环境中混合熵与反应程度涨落之间的相互作用，同时保持与宏观行为的一致性。针对组合反应A + B ↔ 2C以及特定情况H₂ + I₂ ↔ 2HI，对混合熵、反应程度以及一个称为“反应程度熵”的概念的纳米系统尺寸依赖性进行了建模。在前两个属性之间发现了明显的负相关，这与纳米限域对化学平衡的熵效应（NCECE）一致。为了获得平衡后瞬时混合熵的时间依赖性，采用了随机模拟（吉莱斯皮）算法。特别地，最小的纳米系统呈现出阶梯状行为，与平滑平均值有显著偏差，且与反应程度的离散概率分布相关。如分子吸附和自旋极化的进一步说明所示，当前方法可扩展到纳米反应之外，应用于具有有限物种数的其他受限系统。
