Wetting behavior of nanodroplets: The limits of Young's rule validity

Abstract

We study the contact angle of polymer melt sessile droplets on a flat structureless substrate subject to long-range van der Waals forces when the droplet size is diminished. For this purpose, droplets containing 4096 to 512 monomers for chains of length N = 32 are carefully equilibrated at 80% of the Θ-temperature using a coarse-grained bead spring model of flexible polymers in a Monte Carlo computer experiment. The spherically averaged density profile of these droplets, both in the z-direction perpendicular to the substrate surface and in the radial direction, is obtained. At weak adhesion we find that the contact angle grows steadily with the decrease of drop size so that below a critical size these drops dewet the surface. This suggests a strong contribution of a positive line tension κ in the determination of the equilibrium drop shape. At much stronger adhesion, however, the contact angle does not change with drop size, indicating κ ≈ 0. In general, our simulational results outline the limits of validity of Young's relation for the contact angle of sessile nanodroplets and support the more general Gretz rule which takes into account the role of line tension in the balance of surface forces.

Drop size effect on contact angle explained by nonextensive thermodynamics. Young's equation revisited

“…This led several authors to investigate nanodrop behavior [53][54][55]. Gu's results particularly interested us.…”

As-placed contact angles for sessile drops

“…One can describe the force per length associated with this pinning, k/r, by Eq. (2) (see [8,33,[38][39][40][41]) (where r is the radius of the circle the drop makes with the surface). In this description k has opposite values, k A and k R corresponding to advancing and receding contact angles:…”

“…Equation (8) shows that the effect of finite hydrostatic force is to move the contact angle from its advancing to the apparent asplaced contact angle. Note that Eqs.…”

“…Absent from the above list is the Young equilibrium contact angle, θ Y . Though θ Y is theoretically better established than other contact angles, it is less commonly used experimentally [7][8][9], especially for θ > 10 • [10] due to the difficulty in determining its value within the spectrum between the advancing and receding angles. Instead, maximal advancing, θ A , and minimal receding, θ R , contact angles [11][12][13][14][15][16][17][18][19][20][21][22] and the as-placed contact angle [3,5,[23][24][25], θ AP , which is considered in this study, are more commonly reported.…”

Colloidal crystals and water: Perspectives on liquid–solid nanoscale phenomena in wet particulate media

“…The examination of small menisci has been so far elusive, although the precise knowledge their size and shape are critical (the more, the smaller the bridge) for calculation of the induced capillary forces (see Section 3.3.1). Furthermore, the bridge profile concerns the underlying YoungLaplace theory [86], whose validity may be questionable at small scales [87,88]. Figures 9a,b illustrates a fairly accurate description of the nanomeniscus formed between two silica spheres (in this case, they are not part of a CC).…”