Elastic properties of a confined fluid

Monte Carlo computer simulation is employed to determine the local, wave-number-dependent, high-frequency elastic properties of a Lennard-Jones fluid that is confined between two walls. In particular, the elastic constants are calculated from coarse-grained stress correlation functions and then related to the local fluid structure via planar radial distribution functions. We find that local fluid properties correlate with the inhomogeneous fluid density and the strength of the wall-fluid interaction. Finally, we discuss the utility of this analysis in the interpretation of experiments involving the characterization of confined fluids.

Figure 1

A graphical construction showing how to obtain the values ${\lambda }_1$ and ${\lambda }_2$ in Eq. (8). These values are determined by calculating the fraction of the line segment of length $Z_j-Z_i$ that lies within the averaging slab delimited by $z_1$ and $z_2$. The intercepts at $\lambda =0$ and $\lambda =1$ are $Z_i$ and $Z_j$, respectively. For the example illustrated here, ${\lambda }_1=(z_1-Z_i)/(Z_j-Z_i)$ and ${\lambda }_2=(z_2-Z_i)/(Z_j-Z_i)$.

Figure 2

The local average atomic number fraction $\langle \varphi \left(z\right)\rangle$ versus $z/a$, where $a=1.564\sigma$, for a confined fluids with ${\epsilon }_s=1$ (dotted line), ${\epsilon }_s=2$ (dashed line), and ${\epsilon }_s=3$ (solid line), respectively. The fluids are confined between walls located at $z=0$ and $z=10a$. In each case the average density $\rho {\sigma }^3=0.627$ and $T=0.95\epsilon /k_B$. The width of the averaging slab $\delta =0.2a$. Note the density oscillations induced by the wall.

Figure 3

The local, planar radial distribution function $g_{\left|\right|}\left(r\right)$ versus $r/\sigma$ for ${\epsilon }_s=1$ (dotted line) and ${\epsilon }_s=3$ (solid line) for the region $z=0.6a\pm \delta$. Note the larger height of the first peak for larger ${\epsilon }_s=3$.

Figure 4

The elastic constants $c_{11}\left(k\right)$ (circle), $c_{12}\left(k\right)$ (square), and $c_{44}\left(k\right)$ (diamond) versus $k\sigma$ for the bulk fluid as determined from stress correlations. In addition, $c_{11}\left(k\right)$ is calculated from the radial distribution function [Eq. (1)] (solid line) to check the results.

Figure 5

(a) The three nonlocal elastic constants $c_{11}\left(k\right)$ (circle), $c_{12}\left(k\right)$ (square), and $c_{44}\left(k\right)$ (diamond) versus $k\sigma$ for an inhomogeneous fluid near a wall ($0.5a\le z\le 1.0a$). For this case, ${\epsilon }_s=3.0$. (b) The elastic constant $c_{11}\left(k\right)$ versus $k\sigma$ in the near-wall regime for three different values of ${\epsilon }_s$, namely ${\epsilon }_s=3.0$ (circle), ${\epsilon }_s=2.0$ (square), and ${\epsilon }_s=1.0$ (diamond). Clearly, this elastic constant is larger for larger values of ${\epsilon }_s$. (c) The elastic constant $c_{11}\left(k\right)$ versus $k\sigma$ for $0.5a\le z\le 1.0a$ (circle), $1.0a\le z\le 1.5a$ (square), and $3.0a\le z\le 3.5a$ (diamond).