Excess-entropy scaling of dynamics for a confined fluid of dumbbell-shaped particles

We use molecular simulation to study the ability of excess entropy scaling relationships to describe the kinetic properties of a confined molecular system. We examine a model for a confined fluid consisting of dumbbell-shaped molecules that interact with atomistically detailed pore walls via a Lennard-Jones potential. We obtain kinetic, thermodynamic, and structural properties of the system at three wall-fluid interaction strengths and over a temperature range that includes sub- and super-critical conditions. Four dynamic properties are considered: translational and rotational diffusivities, a characteristic relaxation time for rotational motion, and a collective relaxation time stemming from analysis of the coherent intermediate scattering function. We carefully consider the reference state used to define the excess entropy of a confined fluid. Three ideal-gas reference states are considered, with the cases differentiated by the extent to which one-body spatial and orientational correlations are accounted for in the reference state. Our results indicate that a version of the excess entropy that includes information related to the one-body correlations in a confined fluid serves as the best scaling variable for dynamic properties. When adopting such a definition for the reference state, to a very good approximation, bulk and confined data for a specified dynamic property at a given temperature collapse onto a common curve when plotted against the excess entropy.

Figure 1

(Color online) Laterally averaged density profiles $\rho \left(z\right)$. (a) $H=10$, ${\epsilon }_{\text{sf}}=1.0$, and $T=2.0$. Curves from bottom to top (center of the pore) correspond to $\rho =0.2$ (red), 0.3 (green), 0.4 (blue), and 0.5 (brown). (b) $H=5$, ${\epsilon }_{\text{sf}}=1.0$, and $T=2.0$. Curves from bottom to top (center of the pore) correspond to $\rho =0.2$ (red), 0.3 (green), 0.4 (blue), and 0.5 (brown). (c) $H=5$, ${\epsilon }_{\text{sf}}=1.0$, and $\rho =0.45$. Curves from bottom to top (center of the pore) correspond to $T=5.0$ (blue), 2.0 (green), and 1.0 (red). (d) $H=5$, $T=2.0$, and $\rho =0.45$. Curves from bottom to top (peaks closest to the wall) correspond to ${\epsilon }_{\text{sf}}=0.2$ (red), 1.0 (green), and 3.0 (blue).

Figure 2

(Color online) Lateral density profile $\rho \left(x,y\right)$ at $z=0.83$ for the $H=5$, ${\epsilon }_{\text{sf}}=1.0$ pore at $T=2.0$, $\rho =0.45$. The figure spans one square unit cell of the fcc lattice. The gray circle and quarter circles show the location of atoms in the outermost layer of the 100 face of the fcc crystal.

Figure 3

(Color online) Conditional orientational distribution function $\alpha \left(\text{cos}\theta ,\varphi \mid \mathbf{r}\right)$ at $x/a=y/a=0.25$ and $z=0.83$ for the $H=5$, ${\epsilon }_{\text{sf}}=1.0$ pore at $T=2.0$, $\rho =0.45$.

Figure 4

(Color online) Ideal-gas entropies for the (a) $H=5$ and (b) $H=10$ pores with ${\epsilon }_{\text{sf}}=1.0$ at $T=2.0$. Symbols represent different versions of the reference state entropy as denoted within the legend.

Figure 5

(Color online) (a) translational and (b) rotational diffusion coefficients. Symbols represent different pore width and wall strength combinations as denoted within the legend. Solid lines represent the bulk fluid. Data are grouped from bottom to top as $T=1.0$ (blue), $T=2.0$ (black), and $T=5.0$ (red).

Figure 6

(Color online) Relationship between translational diffusivity and various versions of the excess entropy at $T=5.0$. Symbol shape is consistent with the definition adopted in Fig. 5. Solid lines represent the bulk fluid.

Figure 7

(Color online) Relationship between translational diffusivity and excess entropy. Symbol shape is consistent with the definition adopted in Fig. 5. Solid lines represent the bulk fluid. Data are grouped from bottom to top as $T=1.0$ (blue), $T=2.0$ (black), and $T=5.0$ (red).

Figure 8

(Color online) Relationship between (a) rotational diffusivity, (b) rotational relaxation time, and (c) collective relaxation time and excess entropy. Symbol shape is consistent with the definition adopted in Fig. 5. Solid lines represent the bulk fluid. Data are grouped from bottom to top as $T=1.0$ (blue), $T=2.0$ (black), and $T=5.0$ (red).