We present a general principle of topography-directed (TD) inkjet printing for functional micro-tracks embedded in a flexible elastomer substrate. The essential features of the TD inkjet printing in a micro-structured substrate with periodic grooves and ridges are described in terms of the topographic parameters for the transformation from a single droplet to a filament or an edge-disjoint pattern of ink in the groove. Silver ink, being widely used for producing conductive wires by conventional inkjet printing, is utilized as a testbed in our study. The underlying mechanisms for the spreading and drying processes of ink drops under the topographic compartment can be understood in a two-dimensional parameter space of the aspect ratio of the groove and the contact angle of ink on the substrate. The wetting morphologies of ink droplets are described in an analytical model where the Laplace pressure and the mean curvature at the vapor/ink interface are taken into account. The first principle of the TD inkjet printing would be applicable for constructing a variety of functional micro-tracks with high pattern fidelity from different classes of solutions such as conducting polymers, organic semiconductors, and colloidal nanoparticles.

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