Liquid meniscus condensation in dip-pen nanolithography

Abstract

The condensation of a liquid meniscus between a curved tip and a completely wetting substrate is theoretically studied in the context of dip-pen nanolithography (DPN). Utilizing the grand canonical Monte Carlo simulation of a two-dimensional lattice gas model, we studied the onset and broadening of menisci by tips with a range of curvatures. The tip–liquid interaction is characterized in terms of the wettability of the tip, and both wetting and drying tips are considered to mimic the various (hydrophilic and hydrophobic) ink molecule–water interactions possible in DPN. We study the microscopic details of the meniscus formation and examine the thermodynamic stability of the meniscus by focusing on the fluctuation in its width. After its initial formation, a meniscus grows continuously with increasing saturation (relative humidity), but the meniscus is typically wider than 10 molecular diameters until the saturation is sufficiently high that the entire interfacial region frills with liquid. For large tip–substrate distances, meniscus formation only occurs in the high saturation limit where conventional capillary condensation occurs. A general trend is that a sharp (small radius of curvature), dry tip results in a smaller meniscus width which further shrinks upon shortening the tip–substrate distance and/or raising temperature. At very short tip–substrate distances, the nascent meniscus is unstable and its width is independent of the tip curvature and wettability. The minimum width corresponds to a physical dimension of about 2.5 nm.