Thickness-Dependent Phase Transition Drives Nanoridge-to-Mesa Instability in Micellar Freestanding Films

Abstract

Understanding fluxes and instabilities within freestanding ultrathin films is necessary for a better understanding of, and control over, the stability and lifetime of foams and emulsions. In micellar foam films, confinement-induced layering of micelles leads to stepwise thinning or stratification that occurs by the expansion of thinner, darker domains. Often, because of a nanoridge-to-mesa instability, one or more brighter white spots or "mesas" appear at the circular moving front between thinner domains and the thicker (less dark) surrounding film. Previous studies assume that the instability and the appearance of white spots are similar to the capillarity-driven Rayleigh instability that leads to the breakup of a coherent liquid jet. Using the IDIOM (interferometry digital imaging optical microscopy) protocols we recently developed, we characterize the nanoridge-to-mesa instability with exquisite spatiotemporal resolution (thickness <1 nm, time <1 ms). The instability could be classified as a Rayleigh instability if a similar sequence of thick and thin undulations is visualized around the expanding domains. However, quantitative analysis reveals that only mesas grow in size after the instability, whereas the rest of the nanoridge preserves its shape. By analogy to the phase separation into compositionally distinct regions, we show that the spontaneous nucleation of thicker mesas in stratifying films is a phase transition driven by the oscillatory nature of the free-energy functional.

Foam film stratification studies probe intermicellar interactions

“…The ID-IOM setup, shown schematically in Fig. 1A, is utilized for visualization of a single foam film undergoing drainage and simultaneously for quantitative analysis of thickness variations and transitions (15)(16)(17)(48)(49)(50). A high-speed camera attached to a microscope captures the pixel-wise reflected light intensity that is determined by interference between light reflected from the two liquid-air interfaces of a single foam film, as sketched in Fig.…”

“…2 (and in movies included as supplementary information). In addition to the snapshots that show the contrast in grayscale intensity, here we include representative thickness maps obtained by converting intensity into pixel-wise thickness using IDIOM protocols, as detailed elsewhere (16,48,49). Even though the measurements of step size are routinely carried out by using monochromatic light sources and photodiodes as detectors that measure the average reflected light intensity (27), the visualization and analysis of nanoscopic topographical features shown in Fig.…”

“…Even though the measurements of step size are routinely carried out by using monochromatic light sources and photodiodes as detectors that measure the average reflected light intensity (27), the visualization and analysis of nanoscopic topographical features shown in Fig. 2 only began with the advent of IDIOM protocols (15)(16)(17)(48)(49)(50).…”

“…2H turns out to be a chain of mesas in the corresponding thickness map whose the in-plane dimensions are in microns (see scale bar), and thickness is in nm (see colormap). Even though the hydrodynamic mechanisms predict the formation of nanoridge around a growing domain due to local volume conservation, the direct experimental evidence was lacking before Zhang and Sharma used IDIOM protocols and analysis based on thin-film equation to capture the shape evolution of nanoridges and nanoridge-to-mesa instability (15,16,48,49). Zhang and Sharma (48) also showed that the nanoridge in the build-up region (going outwards from the thinner domain) exhibits a quasi-steady shape.…”

“…Even though the hydrodynamic models assume or predict that nanoridge forms around a growing domain, characterization and analysis of such nonflat structures began after the introduction of IDIOM protocols (15,16,48,49). The "micelle-vacancy diffusion" or "colloidal crystal" mechanism does not explain the appearance of ridges, observed as brighter halos around growing domains in greyscale images obtained using reflected light microscopy, or in some instances, subsequent appearance of bright circular spots at moving front between expanding domain and its thicker surroundings, identified to be relatively flat, pancake-like structures we called mesas.…”