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Register a new userRole of Thermal Fluctuations in Nonlinear Thin Film Dewetting
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The spontaneous formation of droplets via dewetting of a thin fluid film from a solid substrate allows for materials nanostructuring, under appropriate experimental control. While thermal fluctuations are expected to play a role in this process, their relevance has remained poorly understood, particularly during the nonlinear stages of evolution. Within a stochastic lubrication framework, we show that thermal noise speeds up and substantially influences the formation and evolution of the droplet arrangement. As compared with their deterministic counterparts, for a fixed spatial domain, stochastic systems feature a smaller number of droplets, with a larger variability in sizes and space distribution. Finally, we discuss the influence of stochasticity on droplet coarsening for very long times.
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We study the dewetting of liquid films capped by a thin elastomeric layer. When the tension in the elastomer is isotropic, circular holes grow at a rate which decreases with increasing tension. The morphology of holes and rim stability can be controlled by changing the boundary conditions and tension in the capping film. When the capping film is prepared with a biaxial tension, holes form with a non-circular shape elongated along the high tension axis. With suitable choice of elastic boundary conditions, samples can even be designed such that square holes appear.
We investigate the effect of short chains on slip of highly entangled polystyrenes (PS) during thin film dewetting from non-wetting fluorinated surfaces. Binary and ternary mixtures were prepared from monodisperse PS with weight average molecular weights $5 < M_textrm{w} < 490$ kg/mol. Flow dynamics and rim morphology of dewetting holes were captured using optical and atomic force microscopy. Slip properties are assessed in the framework of hydrodynamic models describing the rim height profile of dewetting holes. We show that short chains with $M_textrm{w}$ below the polymer critical molecular weight for entanglements, $M_textrm{c}$, can play an important role in slip of highly entangled polymers. Among mixtures of the same $M_textrm{w}$, those containing chains with $M<M_textrm{c}$ exhibit larger slip lengths as the number average molecular weight, $M_textrm{n}$, decreases. The slip enhancement effect is only applicable when chains with $M<M_textrm{c}$ are mixed with highly entangled chains such that the content of the long chain component, $phi_textrm{L}$, is dominant ($phi_textrm{L}<0.5$). These results suggest that short chains affect slip of highly entangled polymers on non-wetting surfaces due to the physical or chemical disparities of end groups, and any associated dynamical effect their presence may have, as compared to the backbone units. The enhanced slip in this regard is attributed to the impact of chain end groups or short chain enrichment on the effective interfacial friction coefficient. Accordingly, for entangled PS, a higher concentration of end groups or short chains at the interface results in a lower effective friction coefficient which consequently enhances the slip length.
Experiments on dewetting thin polymer films confirm the theoretical prediction that thermal noise can strongly influence characteristic time-scales of fluid flow and cause coarsening of typical length scales. Comparing the experiments with deterministic simulations, we show that the Navier-Stokes equation has to be extended by a conserved bulk noise term to accomplish the observed spectrum of capillary waves. Due to thermal fluctuations the spectrum changes from an exponential to a power law decay for large wavevectors. Also the time evolution of the typical wavevector of unstable perturbations exhibits noise induced coarsening that is absent in deterministic hydrodynamic flow.
The effect of thermal fluctuations near a contact line of a liquid interface partially wetting an impenetrable substrate is studied analytically and numerically. Promoting both the interface profile and the contact line position to random variables, we explore the equilibrium properties of the corresponding fluctuating contact line problem based on an interfacial Hamiltonian involving a contact binding potential. To facilitate an analytical treatment we consider the case of a one-dimensional interface. The effective boundary condition at the contact line is determined by a dimensionless parameter that encodes the relative importance of thermal energy and substrate energy at the microscopic scale. We find that this parameter controls the transition from a partially wetting to a pseudo-partial wetting state, the latter being characterized by a thin prewetting film of fixed thickness. In the partial wetting regime, instead, the profile typically approaches the substrate via an exponentially thinning prewetting film. We show that, independently of the physics at the microscopic scale, Youngs angle is recovered sufficiently far from the substrate. The fluctuations of the interface and of the contact line give rise to an effective disjoining pressure, exponentially decreasing with height. Fluctuations therefore provide a regularization of the singular contact forces occurring in the corresponding deterministic problem.
The objective of this work is to study the role of shear on the rupture of ultrathin polymer films. To do so, a finite-difference numerical scheme for the resolution of the thin film equation was set up taking into account capillary and van der Waals (vdW) forces. This method was validated by comparing the dynamics obtained from an initial harmonic perturbation to established theoretical predictions. With the addition of shear, three regimes have then been evidenced as a function of the shear rate. In the case of low shear rates the rupture is delayed when compared to the no-shear problem, while at higher shear rates it is even suppressed: the perturbed interface goes back to its unperturbed state over time. In between these two limiting regimes, a transient one in which shear and vdW forces balance each other, leading to a non-monotonic temporal evolution of the perturbed interface, has been identified. While a linear analysis is sufficient to describe the rupture time in the absence of shear, the nonlinearities appear to be essential otherwise.
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