Collective diffusion coefficient in limited channel: two methods for fluid particles

Molecular dynamics and Monte Carlo methods are common measurements to study the diffusion coefficients of the fluid particles under restricted conditions. Here, the collective diffusion coefficient will be obtained through two methods: the one is Fick’s first law (direct mode), and the other is the relationship between collective diffusion coefficient and self-diffusion coefficient (indirect mode). A comparison between two methods is also discussed. The ways of calculation, which are applied for the self-diffusion coefficient and collective diffusion coefficient, are helpful for studying transport characteristics of various molecules in defined space. Graphical abstract In this manuscript, we have reported the collective diffusion coefficient obtained through two methods: Fick’s first law (direct mode, as shown in Fig. 1) and the relationship between collective diffusion coefficient and self-diffusion coefficient (indirect mode, as shown in Fig. 2). It is shown that the two methods are accessible and each has their advantages and disadvantages.