Becker T, Nelissen K, Cleuren B, Partoens B, Van den Broeck C
Hasselt University, B-3590 Diepenbeek, Belgium.
Hasselt University, B-3590 Diepenbeek, Belgium and Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Nov;90(5-1):052139. doi: 10.1103/PhysRevE.90.052139. Epub 2014 Nov 18.
We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.110601]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their behavior is similar to that of interacting particles in porous materials. Different expressions for the particle jump rates are derived from transition-state theory. Which expression should be used depends on the strength of the interparticle interactions. Analytical expressions for the self- and transport diffusion are derived when correlations, caused by memory effects in the environment, are neglected. The diffusive behavior is studied numerically with kinetic Monte Carlo (kMC) simulations, which reproduces the diffusion including correlations. The effect of correlations is studied by comparing the analytical expressions with the kMC simulations. It is found that the Maxwell-Stefan diffusion can exceed the self-diffusion. To our knowledge, this is the first time this is observed. The diffusive behavior in one-dimensional and higher-dimensional systems is qualitatively the same, with the effect of correlations decreasing for increasing dimension. The length dependence of both the self- and transport diffusion is studied for one-dimensional systems. For long lengths the self-diffusion shows a 1/L dependence. Finally, we discuss when agreement with experiments and simulations can be expected. The assumption that particles in different cavities do not interact is expected to hold quantitatively at low and medium particle concentrations if the particles are not strongly interacting.
我们拓展了最近一项关于相互作用粒子晶格模型的研究[《物理评论快报》111, 110601 (2013年) PRLTAO0031 - 900710.1103/PhysRevLett.111.110601]。讨论了吸附等温线以及粒子数的平衡涨落作为相互作用的函数。它们的行为类似于多孔材料中相互作用粒子的行为。从过渡态理论推导出了粒子跳跃速率的不同表达式。应使用哪种表达式取决于粒子间相互作用的强度。当忽略由环境中的记忆效应引起的相关性时，推导出了自扩散和输运扩散的解析表达式。用动力学蒙特卡罗（kMC）模拟对扩散行为进行了数值研究，该模拟再现了包括相关性的扩散。通过将解析表达式与kMC模拟进行比较来研究相关性的影响。发现麦克斯韦 - 斯蒂芬扩散可以超过自扩散。据我们所知，这是首次观察到这种情况。一维和高维系统中的扩散行为在定性上是相同的，相关性的影响随维度增加而减小。研究了一维系统中自扩散和输运扩散的长度依赖性。对于长长度，自扩散表现出1/L的依赖性。最后，我们讨论了何时可以预期与实验和模拟达成一致。如果粒子之间没有强相互作用，那么在低和中等粒子浓度下，不同腔室中的粒子不相互作用的假设预计在定量上成立。
