Classification of precursors in nanoscale droplets

Molecular precursors, ultrathin films that precede spreading droplets, are still far from being understood, despite intensive study. The inherent microscopic length scales make small-scale experimental techniques and molecular simulation ideal methods to study this phenomenon. Previous work on molecular precursors using nanoscale droplets, however, consistently suffers from incorrect measurement of the dimensions of the precursor film. An alternative method to accurately characterize the precursor film is presented here. In contrast to previous measures, this method (i) allows for easy detection and characterization of precursors and (ii) yields wetting dynamics that agree with experimental observations. Finally, we briefly comment on previous studies whose conclusions may merit reconsideration in light of the present work.

Figure 1

Sketch of a liquid droplet with a precursor film (blue/dark gray) on a solid substrate (gray/light gray). The distance $l$, from the edge of the main droplet to the leading edge of the precursor, is the correct measure for characterizing the precursor length. Previous studies have instead used the distance $r$ from the leading edge of the precursor to the center of the droplet.

Figure 2

Number count of liquid particles as a function of $z$. Close to the substrate, there is a natural layering of the atoms, each corresponding to one molecular layer.

Figure 3

Characterization of the precursor: (a) Snapshot from a simulation with a thin precursor. The inset shows a selected area of the precursor. From the image, it is difficult to judge if the change in the precursor height is continuous or stepwise. (b) Histogram of the density of the droplet. The blue (dark gray) points denote the position of the interface. The red (medium gray) line is the circular arc fitted to the data points. (c) Close-up of the precursor with unequal scaling in $x$ and $z$ direction for clarity. $l_1, l_2$, and $l_3$ are the length of the first three precursor layers. (d) The black points denote the effective height of the droplet as obtained from ellipsometry measurements. The red (medium gray) line is the circular arc obtained from a fit to the measured interface positions. The light-gray line corresponds to the base position of the surface. (e) Close-up to the contact line region with unequal scaling in $x$ and $z$ directions for clarity. The measurement reveals that the precursor is continuously growing and not terraced [as might be inferred from (a)].

Figure 4

Spreading of the liquid droplet (blue/dark gray) on the substrate (light gray) with ${\epsilon }_{sl}=1.5\epsilon$ at times (from top to bottom) $0\tau , 4550\tau$, and $10500\tau$. A thin precursor evolves.

Figure 5

Left: Visualization of the final snapshots from simulations. Center: Evolution of the length of the first four $r_i$. Right: Evolution of the length of the first four $l_i$. Rows correspond to different values of ${\epsilon }_{sl}$, as given in the upper left of each row.

Figure 6

Effective thickness of the droplet of chain molecules for different values of ${\epsilon }_{sl}$. Top: entire droplet with equal scaling in $x$ and $z$ directions. Bottom: selected region with alternate scaling. The snapshots correspond to the final snapshot from each simulation. Multiple distinct layers do not occur in any simulations. While it seems from Fig. 5 that multiple distinct layers separate, results in these images show that the precursor is continuously growing and not terraced.

Figure 7

Top: Measured values of $r_1$ and fitted functions. Scatter points (that almost look like lines because of their large number): measured data. Continuous lines: fitted functions. Middle: same data in log-log representation. The thin, light-gray lines have a slope of 0.5. Bottom: Spreading exponents ${\alpha }_r$ of the first layer as determined from the fit. The spreading exponent for ${\alpha }_r$ is smaller than the expected value of 0.5 and not constant.

Figure 8

Analysis of the spreading exponent from the correct measure of the precursor length $l_1$. Top: log-log plot of measured data with the ideal slope of 0.5 that matches the diffusive spreading exponent. The measured data approach the diffusive behavior for long simulation times. Bottom: Attempts to measure the spreading exponent from linear fits to the log-log representation. The desired plateau is only observed for ${\epsilon }_{sl}=1.5\epsilon$ and is located at $\alpha \approx 0.55$.