Capillary Fluctuations and Film-Height-Dependent Surface Tension of an Adsorbed Liquid Film

Our understanding of both structure and dynamics of adsorbed liquids heavily relies on the capillary wave Hamiltonian, but a thorough test of this model is still lacking. Here we study the capillary wave fluctuations of a liquid film with short-range forces adsorbed on a solid exhibiting van der Waals interactions. We show for the first time that the measured capillary wave spectrum right above the first order wetting transition provides an interface potential consistent with independent calculations from thermodynamic integration. However, the surface tension exhibits an oscillatory film thick dependence which reveals a hitherto unnoticed capillary wave broadening mechanism beyond mere interfacial displacements.

Figure 1

Density profiles for adsorbed layers of thickness $\ell$ of (full lines, from left to right) 1.9, 3.0, 4.1, 5.3, 6.5, 7.3, and $8.5\sigma$. The symbols depict the function $A_w\cos (k_{o}z+\theta )\exp (-b_{o}z)$ with $k_o$ and $b_l$ obtained from the bulk correlation function, and $A_w$, $\theta$ obtained from a fit to an adsorbed layer of thickness $\ell$ ca. $35\sigma$. Dashed lines are predictions from the superposition model, Eq. (6). Inset: Interface potential as a function of average film thickness, $\ell$ (symbols). Expectations from the Hamaker model are shown as a dark line.

Figure 2

Second derivative of the interface potential (full line) compared with expectations from the CWS, $g_{\mathrm{cws}}^{\prime \prime }$ (green circles) and from the Hamaker model (dashed line). Notice almost perfect match of $g^{\prime \prime }$ with $g_{\mathrm{cws}}^{\prime \prime }$ up to $\ell =2\sigma$. Inset: Enlarged view of $g^{\prime \prime }$ (full line), as compared with $g_V^{\prime \prime }$ (dashed line) and ${\gamma }_{\mathrm{cws}}-{\gamma }_{\infty }$ (symbols).

Figure 3

Film-thick-dependent surface tension, ${\gamma }_{\mathrm{cws}}(\ell )$ (circles, left axis) and bending rigidity ${\kappa }_{\mathrm{cws}}$ (squares, right axis) as obtained from the CWS. The full lines are predictions from the model ${\gamma }_{\infty }+g^{\prime \prime }(\ell )/b^2$, with $b=0.85{\sigma }^{-1}$. The thick arrow points to the value of ${\gamma }_{\infty }$ as obtained independently for the free interface.