When moist air encounters a cold surface, it condenses into a collection of droplets, forming what are commonly known as "breath figures". Dew formation has been extensively studied on a variety of surfaces, including rough, chemically heterogeneous, patterned, polymeric, liquid-infused and pure liquid substrates. Despite the sensitivity to the substrate nature, common features for condensation include the primary and continued nucleation of nanodroplets, their diffusive growth and their coalescence to a more advanced stage. The collected droplets typically evolve towards scale-free polydisperse size distributions, ranging from freshly nucleated nanodroplets to millimetre sizes. Remarkably, on atomically smooth liquid substrates, dew droplets exhibit a 2D crystalline order with high monodispersity.
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(a) Schematic of the controlled humidity chamber. (b) Breath figures imaged from above using a microscope, on substrates of increasing elastic modulus G for a relative humidity ρ/ρsat = 1.22 ± 0.11, and Ts = 5˚C.
In this seminar, I will discuss the condensation dynamics on soft, smooth, crosslinked polymer gels. We conduct condensation experiments in a chamber with controlled humidity [Fig. (a)] onto PDMS gels, whose elastic modulus is varied between 10 and 106 Pa, on uncross-linked PDMS liquid as well as on stiff PDMS brushes. Although elasticity should be marginal at the nanometric scale at which drops form, we report that the nuclei density is highly sensitive to the substrate softness, which suggests that nucleation follows a low-energy pathway sensitive to the degree of cross-linking.
A central question is how the water vapor flux allocates between the generation of new droplets and the enlargement of existing ones. Once droplets enter the visible range (R ~ 1 µm), the number of droplets remains constant (until they start to touch and coalesce). The absence of further nucleation, and hence the selection of droplet density, is attributed to the formation of a saturated vapor boundary layer near the substrate. This layer significantly raises the energy barrier for additional nucleation, effectively suppressing it. As a result, monodisperse breath figures can persist on soft PDMS gels.
Later, when neighboring drops get closer, they attract each other due to the so-called Cheerios interactions mediated by substrate deformations. Drops then gather into clusters that exhibit a reluctance to coalesce. The delay in coarsening is found to be a decreasing function of the substrate elastic modulus. This ultimately results in the formation of a persistent bidimensional quasi-crystal of droplets, that coarsens according to a universal law akin to Oswald ripening.
Breath figures offer a macroscopic approach to probe the molecular characteristics of the polymer interface, challenge the elastocapillarity theory at small scales and raise the question of multiple Cheerios interactions between a large set of drops.