Beyond the Young-Laplace model for cluster growth during dewetting of thin films: Effective coarsening exponents and the role of long range dewetting interactions

Abstract

Long range dewetting forces acting across thin films, such as the fundamental van der Waals interactions, may drive the formation of large clusters (tall multilayer islands) and pits, observed in thin films of diverse materials such as polymers, liquid crystals, and metals. In this study we further develop the methodology of the nonequilibrium statistical mechanics of thin films coarsening within continuum interface dynamics model incorporating long range dewetting interactions. The theoretical test bench model considered here is a generalization of the classical Mullins model for the dynamics of solid film surfaces. By analytic arguments and simulations of the model, we study the coarsening growth laws of clusters formed in thin films due to the dewetting interactions. The ultimate cluster growth scaling laws at long times are strongly universal: Short and long range dewetting interactions yield the same coarsening exponents. However, long range dewetting interactions, such as the van der Waals forces, introduce a distinct long lasting early time scaling behavior characterized by a slow growth of the cluster height/lateral size aspect ratio (i.e., a time-dependent Young angle) and by effective coarsening exponents that depend on cluster size. In this study, we develop a theory capable of analytically calculating these effective size-dependent coarsening exponents characterizing the cluster growth in the early time regime. Such a pronounced early time scaling behavior has been indeed seen in experiments; however, its physical origin has remained elusive to this date. Our theory attributes these observed phenomena to ubiquitous long range dewetting interactions acting across thin solid and liquid films. Our results are also applicable to cluster growth in initially very thin fluid films, formed by depositing a few monolayers or by a submonolayer deposition. Under this condition, the dominant coarsening mechanism is diffusive intercluster mass transport while the cluster coalescence plays a minor role, both in solid and in fluid films.

Molecular simulation of thin liquid films: Thermal fluctuations and instability

“…The current work reveals the effects of thermal fluctuations on the initial stages of instability growth; however, there are also abundant interesting flow dynamics in the later stages of the process where thermal fluctuations could play a role. For example, future research could consider the coarsening dynamics after the film has ruptured into droplets [41,42].…”

Solid-state wetting at the nanoscale

“…Ref. [9]), one can still describe a film or adsorbate with a coverage lower than a monolayer within the same freeenergy framework. In the sub-monolayer regime, the variable h represents the surface coverage.…”

“…However, interactions with a longer range, such as those discussed below in Section 3, can give rise to larger values of λ line . In this case, line effects are the leading order corrections, but as the size of the islands approaches the range of the interaction potential, the equilibrium shape may exhibit strong scale-dependent deviations [9].…”

Triple-line kinetics for solid films

“…Such a wetting potential has been used to enforce the presence of a continuous wetting layer in the case of unstable films with a destabilization originating from faceting instabilities [23] or heteroepitaxial elastic strain [24]. The case of partial wetting, where the wetting potential exhibits a negative minimum, has also been studied in solid films to describe the formation of holes [25] or Ostwald ripening of solid nanoislands [26].…”