Thin films, a whisper-thin veil of liquid, so delicate it is often overlooked, yet crucial to everything from the vitreous humor in our eyes to the lubrication in high-speed engines. Despite such omni-presence, the behavior of thin films, and especially their rupture mechanism puzzled scientists for decades.
How does a film break? Is there a warning before it breaks?
These are the questions we set out to answer. Investigating these details experimentally can be challenging, if not impossible. Traditional theoretical methods also fall short at this small scale. To overcome these challenges, we used large-scale non-equilibrium molecular dynamics simulations (NEMD), with attention to the inhomogeneous nature of the liquid-vapor surface of the film. Pure Lennard-Jones particles were used to model the film to eliminate the variables of gravity, impurities, and surfactants. This allowed to observe the film’s entire life-cycle: from hydrodynamic drainage and fluctuation-driven black film formation to stochastic nucleation, geometrical frustration, and deterministic coarsening.

Bridging the Breaks: Unifying Rupture Modes

Traditionally, there are two major modes of film rupture. The first is spinodal-like disintegration, usually occurs in relatively thinner  films. These films are so unstable that multiple sites throughout the film break almost simultaneously, and one would observe irregularly shaped holes. The second mode is heterogeneous rupture, which occurs mostly in thicker films, often arising from defects or impurities. In this latter mode, holes are sparsely distributed, and are circular in shape. 

Results from our MD simulations suggest that the reason behind the morphological differences exhibited by these modes is rooted in the ease with which the film breaks. For thinner films, it is much easier to rupture, leading to many sites breaking simultaneously. The presence of multiple neighboring rupture sites disrupts their growth, causing them to take on irregular shapes due to space constraints as they expand. Conversely, in thicker films, rupturing a site is more difficult, and the right perturbation or thermal fluctuation is rare. When it does occur, not many sites achieve this. Therefore, only a few sites break, and they can grow uninterrupted for a much longer period allowing them to form circular shapes. It is only when these holes grow large enough to encounter neighboring holes that their shapes become irregular, similar to the very early stages of spinodal-like rupture in thinner films.Thus, the rupture modes are manifestations of similar events, sharing similar molecular origins, occurring over different length and time scales.

The Precursor of the Future

One unexpected and intriguing discovery was the identification of a 'memory window' - a finding that emerged after a long and winding investigative process. Despite employing numerous methods (including wavelet and superlet transform, random forest model, nearest-neighbors) to examine the variations in the local density, temperature, or energy of the rupture sites, we found no warning of the rupture, nor did we find any consistent patterns in their temporal evolution. However, by saving the state of the film at regular intervals, and restarting multiple independent simulations from these points, we found a time window within which the film always ruptured at the same location, even upon the application of external perturbations. This observation suggests that a deterministic hole formation process precedes stochastic rupture, adding a new layer of understanding to the spontaneous rupture of thin films - we invoke the concept of liquid's inherent structure to explain this transition.

Beyond Thin Films

The implications of the existence of the rupture memory extend far beyond the realm of thin films. This suggests that in many systems, deterministic processes can set the stage for seemingly random events. In social dynamics, for example, certain conditions might predetermine the occurrence of major societal changes or upheavals. In financial markets, underlying deterministic factors could foreshadow seemingly random market crashes or booms. Understanding these deterministic precursors could significantly change how we analyse such events.

Once a thin film entered the memory window, its fate was sealed. This finding challenges the traditional view that stochastic events are entirely unpredictable and without precursors. Instead, it opens up the possibility that with the right tools and understanding, we might predict and even prevent undesirable outcomes in various fields.  By uncovering the hidden order within seemingly random events, observations made in this study pave the way for new approaches to prediction and intervention.

Co-authors: Li Shen, James P Ewen, David M Heyes, Daniele Dini, and Edward R Smith. 
Full paper: https://doi.org/10.1038/s42005-024-01745-z