Inhomogeneous Substrates

Similar results were obtained in a study of dodecane droplets wetting a chemically inhomogeneous substrate made of an incomplete OTS monolayer on oxidized silicon (see Fig. 6.7a). In this case the droplet contact line is quite irregular (see Fig. 6.7c) even 

Other studies have aimed at controlling the inhomogeneity of the substrate to probe the fundamental properties of nanodroplets. Herminghaus eto/. have patterned a silicon surface with 

Checco et al. have studied the morphology of ethanol and octane droplets condensed on chemically nanopatterned 

These results are described quantitatively by the augmented Young equation model of droplet morphology  

This equation relates the droplet capillary pressure (left-hand side where K (x) is the local curvature of the liquid surface at a specific coordinate x normal to the striped pattern) to the chemical potential difference A p(a A T) between the substrate and the liquid reservoir (at T = To) and the partial derivative of the effective interface potential co with respect to the liquid thickness /(x) (often referred to as the disjoining pressure, see also chapter 3). 

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Numerical solution of Eq. (51) was carried out for a nonlocal effective Hamiltonian as well as for the approximated local Hamiltonian obtained by applying a gradient expansion. It was demonstrated that the nonlocal effective Hamiltonian represents quite well the lateral variation of the film density distribution. The results obtained showed also that the film behavior on the inhomogeneous substrate depends crucially on the temperature regime. Note that the film exhibits different wetting temperatures on both parts of the surface. For chemical potential below the bulk coexistence value the film thickness on both parts of the surface tends to appropriate assymptotic values at x cx) and obeys the power law x. Such a behavior of the film thickness is a consequence of van der Waals tails. The above result is valid when both parts of the surface exhibit either continuous (critical) or first-order wetting. 

McKee, C. F. and Ostriker, J. P. (1977) A theory of the interstellar medium three components regulated by supernova explosions in an inhomogeneous substrate. Astrophysical Journal, 218, 148-169. 

Fig. 2. Schematic of microelectrochemical measurements on inhomogeneous substrates using various capillary sizes.

Planar but chemically inhomogeneous substrates are encountered in various practical application, in particular those related to open nanofluidics. One tries to understand the wetting and adsorption properties of such systems in terms of the wetting properties of separate, chemically homogeneous regions. A simple chemical step consists of two semi-infinite planes, each composed of a different material, say, (1) for x < 0 and (2) for... 

Fig. 1. Snapshot configuration of adsorbate on geometrically inhomogeneous substrate and elementary processes at interphase boundary S - direct scattering, including reactive one A - eidsorption channel D - desorption channel M - migration channel wave line is the sketch of the potential relief for LG model dSs, dSa - filled areas in layers 3 and 2 of total area dS that are open to the gas phase T, Ts - gas and surface temperatures, respectively.

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