Mesoscopic Hamiltonian for the fluctuations of adsorbed Lennard-Jones liquid films

We use Monte Carlo simulations of a Lennard-Jones fluid adsorbed on a short-range planar wall substrate to study the fluctuations in the thickness of the wetting layer, and we get a quantitative and consistent characterization of their mesoscopic Hamiltonian, $\mathcal{H}\left[\xi \right]$. We have observed important finite-size effects, which were hampering the analysis of previous results obtained with smaller systems. The results presented here support an appealing simple functional form for $\mathcal{H}\left[\xi \right]$, close but not exactly equal to the theoretical nonlocal proposal made on the basis a generic density-functional analysis by Parry and coworkers. We have analyzed systems under different wetting conditions, as a proof of principle for a method that provides a quantitative bridge between the molecular interactions and the phenomenology of wetting films at mesoscopic scales.

Figure 1

Interfacial potential $\mathrm{\Phi }\left(\overline{\xi }\right)$ as a function of the mean thickness of the liquid film, for two strengths of the wall-fluid attraction: ${\epsilon }_{\mathrm{sf}}/\epsilon =0.81$ (top) and $0.77$ (bottom). The light (green) curves use $\overline{\xi }={\xi }_N$, from the total number of particles. The dark (black) curves use $\overline{\xi }={\xi }_{\mathrm{IS}}$ from the ISM position of the film edge. The dashed lines show the exponential fits [Eq. (4) with $\lambda =1.55/\sigma$] to $\mathrm{\Phi }\left({\xi }_{\mathrm{IS}}\right)$.

Figure 2

Wall damping effect on the inverse mean-square amplitude of the thickness fluctuations, $\mathrm{\Delta }\mathrm{\Gamma }(q,{\xi }_{\mathrm{IS}})$, Eq. (3), for the wave number $q\sigma =0.6$, with increasing thickness of the adsorbed liquid film, for the three values of the wall fluid attraction, ${\epsilon }_{\mathrm{sf}}/\epsilon =1.3$ (top), $0.81$ (central), and $0.77$ (bottom); and two lateral sizes of the simulation box: $L_x=10.3\sigma$ (left) and $L_x=31\sigma$ (central). Density profile (right) of ${\xi }_{\mathrm{IS}}\simeq 4.40\sigma$ (dark color) and ${\xi }_{\mathrm{IS}}\simeq 7.72\sigma$ (light color) films for $L_x\simeq 10.3\sigma$ (solid line) and ${\xi }_{\mathrm{IS}}\simeq 4.80\sigma$ (dark color) and ${\xi }_{\mathrm{IS}}\simeq 8.10\sigma$ (light color) for $L_x\simeq 31\sigma$ (dashed line).

Figure 3

Wall-damping effect on inverse mean-square amplitude of the film-thickness fluctuation, $\mathrm{\Delta }\mathrm{\Gamma }(q,{\xi }_{\mathrm{IS}})$ with increasing thickness of the adsorbed liquid film, for ${\epsilon }_{\text{sf}}/\epsilon =0.81$ and larger lateral size $L_x=31\sigma$. Circles, $q\sigma =0.21$; squares, $q\sigma =0.6$; diamonds, $q\sigma =0.85$; and triangles up, $q\sigma =1.22$. The full lines are the best fits to an exponential decay $\mathrm{\Delta }\mathrm{\Gamma }(q,{\xi }_{\mathrm{IS}})=\mathrm{\Delta }{\mathrm{\Gamma }}_0\left(q\right)\text{exp}(-1.55{\xi }_{\mathrm{IS}}/\sigma )$ for each $q$.

Figure 4

The adimensional $\mathrm{\Delta }{\mathrm{\Gamma }}_0\left(q\right)/A_0=\mathrm{\Delta }\mathrm{\Gamma }(q,{\xi }_{\mathrm{IS}})/\left[A_0\text{exp}(-\lambda {\xi }_{\mathrm{IS}})\right]$, with $\lambda \sigma =1.55$, versus $q$. The values are for the largest lateral sizes of the simulation box, $L_x=31\sigma$. The empty symbols show the $\mathrm{\Delta }{\mathrm{\Gamma }}_0\left(q\right)$ simulation results for the three values of ${\epsilon }_{\text{sf}}$: ${\epsilon }_{\text{sf}}=1.3\epsilon$ (top); ${\epsilon }_{\text{sf}}=0.81\epsilon$ (bottom, black squares); and ${\epsilon }_{\text{sf}}=0.77\epsilon$ (bottom, red triangles up). The full symbols are the theoretical prediction for $q=0$, $\mathrm{\Delta }{\mathrm{\Gamma }}_0(q=0)/A_0={\lambda }^2\beta {\mathrm{\Phi }}_0$. The full lines are the better fits to quadratic function: ${\lambda }^2\beta {\mathrm{\Phi }}_0+\mathrm{\Delta }{\gamma }_{\mathrm{FJ}}{q}^2$. The dashed line is a guide to the eye.

Figure 5

The function $\mathrm{\Delta }\mathrm{\Gamma }(q,{\xi }_{\mathrm{IS}}){\sigma }^4/A_0$ (as in Fig. 2, but in logarithmic scale), for $L_x=31\sigma$, ${\epsilon }_{\mathrm{sf}}=1.3\epsilon$, and two values of the wavevector $q\sigma =0.21$ (top) and $q\sigma =0.85$ (bottom). Black circles give the ISM results and gray (on line red) starts symbols show the results of the Gibbs surface (GS) film thickness; the lines are only to guide the eye. The inset shows the surface tension function ${\gamma }^{\mathrm{LV}}\left(q\right)$ for the liquid-vapor interface, ISM black line and GS gray (on line red) line.