Thermodynamics Predicts How Confinement Modifies the Dynamics of the Equilibrium Hard-Sphere Fluid

We study how confining the equilibrium hard-sphere fluid to restrictive one- and two-dimensional channels with smooth interacting walls modifies its structure, dynamics, and entropy using molecular dynamics and transition-matrix Monte Carlo simulations. Although confinement strongly affects local structuring, the relationships between self-diffusivity, excess entropy, and average fluid density are, to an excellent approximation, independent of channel width or particle-wall interactions. Thus, thermodynamics can be used to predict how confinement impacts dynamics.

Figure 1

Self-diffusivity $D$ vs the negative of excess entropy per particle $-s^{\mathrm{ex}}/k_{\mathrm{B}}$ for the bulk HS fluid (solid curve) and for the HS fluid in 2D channels (symbols). The symbols correspond to $h_z=2.5$ (circle), 5 (square), 7.5 (plus), 10 (triangle up), and 15 (cross). The color codes are ${ϵ}_{\mathrm{w}}=1$ (blue), 0.5 (cyan), 0 (red), $-0.5$ (yellow), and $-1$ (green). Inset is the same plot with added points for the 1D channels: $5\times 5$, $7.5\times 7.5$, and $5\times 7.5$ shown by red diamonds.

Figure 2

Self-diffusivity $D$ and excess entropy per particle $s^{\mathrm{ex}}/k_{\mathrm{B}}$ vs average density $\rho =N/V^{\prime }$ based on the total system volume $V^{\prime }$. Systems shown include the bulk HS fluid (solid curve) and the HS fluid confined to the 1D and 2D channels (symbols) discussed in the text. Symbols are identical to those given in Fig. 1.

Figure 3

Density profiles $\rho (z)$ for HS fluids confined to a 2D channel of width $h_z=2.5$. Although each system has different particle-wall interaction strengths ${ϵ}_{\mathrm{w}}$, they share a common average density $\rho$ (dashed) and self-diffusivity $D$.

Figure 4

Self-diffusivity $D$ vs average density ${\rho }_h=N/V$ based on the total particle-center-accessible volume $V$. Systems shown include the bulk HS fluid (solid curve) and the HS fluid confined to the 2D channels between hard walls.