Inkjet printing of precisely defined features using contact-angle hysteresis.

Motivated by the process of inkjet printing of electronics, we study experimentally and theoretically the processes limiting the printing of sharply defined, equilibrium corners. Using a non-volatile ionic liquid, we inkjet print squares with rounded corners on a substrate of roughened, display-grade glass. We show experimentally that with increasing roughness, corner radius decreases, allowing more precisely defined features to be printed. To interpret these results in terms of contact-angle hysteresis (difference between the advancing and retreating contact angles θA and θR), we implement the following model with the Surface Evolver program. With drop volume fixed, we minimize drop surface energy subject to a prescribed contact line. We identify θA and θR as the minimum and maximum contact angles around the drop perimeter. We find that with decreasing corner fidelity, contact-angle hysteresis also decreases. We are thus able to infer θR from the corner radius of printed features. We conclude that increasing contact-angle hysteresis allows the printing of more precisely defined features.

Femtoliter-scale patterning by high-speed, highly scaled inverse gravure printing.

Pattern printing techniques have advanced rapidly in the past decade, driven by their potential applications in printed electronics. Several printing techniques have realized printed features of 10 µm or smaller, but unfortunately, they suffer from disadvantages that prevent their deployment in real applications; in particular, process throughput is a significant concern. Direct gravure printing is promising in this regard. Gravure printing delivers high throughput and has a proven history of being manufacturing worthy. Unfortunately, it suffers from scalability challenges because of limitations in roll manufacturing and limited understanding of the relevant printing mechanisms. Gravure printing involves interactions between the ink, the patterned cylinder master, the doctor blade that wipes excess ink, and the substrate to which the pattern is transferred. As gravure-printed features are scaled, the associated complexities are increased, and a detailed study of the various processes involved is lacking. In this work, we report on various gravure-related fluidic mechanisms using a novel highly scaled inverse direct gravure printer. The printer allows the overall pattern formation process to be studied in detail by separating the entire printing process into three sequential steps: filling, wiping, and transferring. We found that pattern formation by highly scaled gravure printing is governed by the wettability of the ink to the printing plate, doctor blade, and substrate. These individual functions are linked by the apparent capillary number (Ca); the printed volume fraction (φ(p)) of a feature can be constructed by incorporating these basis functions. By relating Ca and φ(p), an optimized operating point can be specified, and the associated limiting phenomena can be identified. We used this relationship to find the optimized ink viscosity and printing speed to achieve printed polymer lines and line spacings as small as 2 µm at printing speeds as high as ∼1 m/s.

Methodology for inkjet printing of partially wetting films.

Inkjet printing of precisely defined structures is critical for the realization of a range of printed electronics applications. We develop and demonstrate a methodology to optimize the inkjet printing of two-dimensional, partially wetting films. When printed inks have a positive retreating contact angle, we show that any fixed spacing is ineffective for printing two-dimensional features. With fixed spacing, the bead contact angle begins large, leading to a bulging overflow of its intended footprint. Each additional line reduces the bead contact angle, eventually leading to separation of the bead. We propose a printing scheme that adjusts the line-to-line spacing to maintain a bead's contact angle between its advancing and retreating values as it is printed. Implementing this approach requires an understanding of the two-dimensional bead surface and compensation for evaporation during the print. We derive an analytic equation for the bead's surface with pinned contact lines and use an empirical fit for mass loss due to evaporation. Finally, we demonstrate that enhanced contact angle hysteresis, achieved by preprinting a feature's border, leads to better corner definition.

Dynamic response of geometrically constrained vapor bubbles.

We consider a two-dimensional model of a vapor bubble between two horizontal parallel boundaries held at different temperatures. When the temperatures are constant, a steady state can be achieved such that evaporation near the contact lines at the hot bottom plate is balanced by condensation in colder areas of the interface near the top. The dynamic response of the bubble is probed by treating the case of time-dependent wall temperatures. For periodic modulations of the wall temperature the bubble oscillates about the steady state. In order to describe such time-dependent behavior we consider the limit of small capillary number, in which the effects of heat and mass transfer are significant only near the contact lines at the bottom plate and in a small region near the top. When the bottom temperature is modulated and the top temperature is held fixed, the amplitude of forced oscillations is constant for low-frequency modulations and then rapidly decays in the high-frequency regime. When the top temperature is modulated with fixed bottom temperature, the dynamic-response curve is flat in the low-frequency regime as well, but it also flattens out when the frequency is increased. This shape of the response curve is shown to be the result of the nonmonotonic behavior of the thickness of the liquid film between the bubble interface and the top plate: when the temperature is decreased, the film thickness increases rapidly, but then slowly decays to a value which is smaller than the initial thickness. The dynamic response is also studied as a function of the forcing amplitude.