Hybrid energy-minimization simulation of equilibrium droplet shapes on hydrophilic/hydrophobic patterned surfaces

Wetting Behavior of Inkjet-Printed Electronic Inks on Patterned Substrates

In inkjet printing technology, one important factor influencing the printing quality and reliability of printed films is the interaction of the jetted ink with the substrate surface. This short-range interaction determines the wettability and the adhesion of the ink to the solid surface and is hence responsible for the final shape of the deposited ink. Here, we investigate wetting morphologies of inkjet-printed inks on patterned substrates by carefully designed experimental test structures and simulations. The contact angles, the surface properties, and drop shapes, as well as their influence on the device variability, are experimentally and theoretically analyzed. For the simulations, we employ the phase-field method, which is based on the free energy minimization of the two-phase system with the given wetting boundary conditions. Through a systematic investigation of printed drops on patterned substrates consisting of hydrophilic and hydrophobic areas, we report that the printed morphology is related not only to the designed layout and the drop volume but also to the printing strategy and the wettability. Furthermore, we show how one can modify the intrinsic wettability of the patterned substrates to enhance the printing quality and reliability. Based on the present findings, we cast light on the improvement of the fabrication quality of thin film transistors.

Wicking assisted condenser platform with patterned wettability for space application

Vapor condensation is extensively used in applications that demand the exchange of a substantial amount of heat energy or the vapor-liquid phase conversion. In conventional condensers, the condensate removal from a subcooled surface is caused by gravity force. This restricts the use of such condensers in space applications or horizontal orientations. The current study demonstrates proof-of-concept of a novel plate-type condenser platform for passively removing condensate from a horizontally oriented surface to the surrounding wicking reservoir without gravity. The condensing surface is engineered with patterned wettabilities, which enables the continuous migration of condensate from the inner region of the condenser surface to the side edges via surface energy gradient. The surrounding wicking reservoir facilitates the continuous absorption of condensate from the side edges. The condensation dynamics on different substrates with patterned wettabilities are investigated, and their condensation heat transfer performance is compared. The continuous migration of condensate drops from a superhydrophobic to a superhydrophilic area can rejuvenate the nucleation sites in the superhydrophobic area, resulting in increased heat transport. The proposed condenser design with engineered wettability can be used for temperature and humidity management applications in space.

Inkjet printing on hydrophobic surfaces: Controlled pattern formation using sequential drying

Inkjet-printed micro-patterns on hydrophobic surfaces have promising applications in the fabrication of microscale devices such as organic thin-film transistors. The low wettability of the surface prevents the inkjet-printed droplets from spreading, connecting to each other, and forming a pattern. Consequently, it is challenging to form micro-patterns on surfaces with low wettability. Here, we propose a sequential printing and drying method to form micro-patterns and control their shape. The first set of droplets is inkjet-printed at a certain spacing and dried. The second set of droplets is printed between these dry anchors on the surface with low wettability. As a result, a stable bridge on the surface with low wettability forms. This printing method is extended to more complicated shapes such as triangles. By implementing an energy minimization technique, a simple model was devised to predict the shape of the inkjet-printed micro-patterns while confirming that their equilibrium shape is mainly governed by surface tension forces. The gradient descent method was utilized with parametric boundaries to emulate droplet pinning and wettability of the anchors and to prevent convergence issues from occurring in the simulations. Finally, the energy minimization based simulations were used to predict the required ink to produce dry lines and triangles with smooth edges.

Rupture of Liquid Bridges on Porous Tips: Competing Mechanisms of Spontaneous Imbibition and Stretching

Liquid bridges are commonly encountered in nature and the liquid transfer induced by their rupture is widely used in various industrial applications. In this work, with the focus on the porous tip, we studied the impacts of capillary effects on the liquid transfer induced by the rupture through numerical simulations. To depict the capillary effects of a porous tip, a time scale ratio, R_T, is proposed to compare the competing mechanisms of spontaneous imbibition and external drag. In terms of R_T, we then develop a theoretical model for estimating the liquid retention ratio considering the geometry, porosity, and wettability of tips. The mechanism presented in this work provides a possible approach to control the liquid transfer with better accuracy in microfluidics or microfabrications.

Fine printing method of silver nanowire electrodes with alignment and accumulation

One-dimensional metal nanowires offer great potential in printing transparent electrodes for next-generation optoelectronic devices such as flexible displays and flexible solar cells. Printing fine patterns of metal nanowires with widths <100 μm is critical for their practical use in the devices. However, the fine printing of metal nanowires onto polymer substrates remains a major challenge owing to their unintended alignment. This paper reports on a fine-printing method for transparent silver nanowires (AgNWs) electrodes miniaturized to a width of 50 μm on ultrathin (1 μm) polymer substrate, giving a high yield of >90%. In this method, the AgNW dispersion, which is swept by a glass rod, is spontaneously deposited to the hydrophilic areas patterned on a hydrophobic-coated substrate. The alignment and accumulation of AgNWs at the pattern periphery are enhanced by employing a high sweeping rate of >3.2 mm s^-1, improving electrical conductivity and pattern definition. The more aligned and more accumulated AgNWs lower the sheet resistance by a factor of up to 6.8. In addition, a high pattern accuracy ≤ 3.6 μm, which is the deviation from the pattern designs, is achieved. Quantitative analyses are implemented on the nanowire alignment to understand the nanowire geometry. This fine-printing method of the AgNW electrodes will provide great opportunities for realizing flexible and high-performance optoelectronic devices.

Pinning-Depinning Mechanism of the Contact Line during Evaporation of Nanodroplets on Heated Heterogeneous Surfaces: A Molecular Dynamics Simulation

Droplet evaporation on heterogeneous or patterned surfaces has numerous potential applications, for example, inkjet printing. The effect of surface heterogeneities on the evaporation of a nanometer-sized cylindrical droplet on a solid surface is studied using molecular dynamics simulations of Lennard-Jones particles. Different heterogeneities of the surface were achieved through alternating stripes of equal width but two chemical types, which lead to different contact angles. The evaporation induced by the heated substrate instead of the isothermal evaporation is investigated. It is found that the whole evaporation process is generally dominated by the nonuniform evaporation effect. However, at the initial moment, the volume expansion and local evaporation effects play important roles. From the nanoscale point of view, the slow movement of the contact line during the pinning process is observed, which is different from the macroscopic stationary pinning. Particularly, we found that the speed of the contact line may be not only affected by the intrinsic energy barrier between the two adjacent stripes ( ũ) but also relevant to the evaporation rate. Generally speaking, the larger the intrinsic energy barrier, the slower the movement of the contact line. At the specified temperature, when ũ is less than a critical energy barrier ( ũ*), the speed of the contact line would increase with the evaporate rate. When ũ > ũ*, the speed of the contact line is determined only by ũ and no longer affected by the evaporation rate at different stages (the first stick and the second stick).

Wetting Transition at a Threshold Surfactant Concentration of Evaporating Sessile Droplets on a Patterned Surface

Wetting transitions induced by varying the components in a solution of a drying droplet can lead to its evolving shape on a textured surface. It can provide new insights on liquid pattern control through manipulating droplet solutions. We show the pronounced transitions of wetting for surfactant solution droplets drying on a micropyramid-patterned surface. At low initial surfactant concentrations, the droplet maintains an octagonal shape until the end of drying. At intermediate initial surfactant concentrations, the early octagon spreads to a square, which later evolves to a stretched rectangle. At high initial surfactant concentrations, the droplet mainly exhibits the "octagon-to-square" transition, and the square shape is maintained until the end. The octagon-to-square transition occurs at similar temporal volume-averaged surfactant concentrations for the various initial surfactant concentrations. It results from the dependence of the surface energy change of spread over the micropyramid structure on the temporal volume-averaged surfactant concentration. At high initial surfactant concentrations, the accumulation of the surfactant near the contact line driven by outward flows could raise the local viscosity and enhance the pinning effect, leading to the great suppression of the "square-to-rectangle" transition.

Equilibrium Drop Shapes on a Tilted Substrate with a Chemical Step

We calculate the equilibrium shape of a droplet sitting on a tilted substrate with a "chemical step", that is, different lypophilicity at the two sides of the step. This problem can be generalized to that of a droplet experiencing a body force, pushing it from the lyophilic part to the lyophobic part of the substrate. We present phase diagrams, in which we show for which droplet sizes there are dynamically inaccessible equilibrium shapes. We also identify what determines the threshold volume. While this given system was studied previously in the literature using contact angle hysteresis laws, we present the full static thermodynamical solution of the interfacial energy including the contact energy, while omitting the hysteresis effects from the contact line.

In situ reversible underwater superwetting transition by electrochemical atomic alternation

Materials with in situ reversible wettability have attractive properties but remain a challenge to use since the inverse process of liquid spreading is normally energetically unfavorable. Here, we propose a general electrochemical strategy that enables the in situ reversible superwetting transition between underwater superoleophilicity and superoleophobicity by constructing a binary textured surface. Taking the copper/tin system as an example, the surface energy of the copper electrode can be lowered significantly by electrodeposited tin, and be brought back to the initial high-energy state as a result of dissolving tin by removing the potential. Tin atoms with the water depletion layer inhibit the formation of a hydrogen-bonding network, causing oil droplets to spread over the surface, while copper atoms, with a high affinity for hydroxyl groups, facilitate replacing the oil layer with the aqueous electrolyte. The concept is applicable to other systems, such as copper/lead, copper/antimony, gold/tin, gold/lead and gold/antimony, for both polar and nonpolar oils, representing a potentially useful class of switchable surfaces.

Materials with in situ reversible wettability have attractive properties for switching applications, but are a challenge to use especially for the inverse process of liquid spreading. Here, the authors propose an electrochemical strategy enabling in situ reversible superwetting conversion between underwater superoleophilicity and superoleophobicity by constructing a binary textured surface.

Controlling Octagon-to-Square Wetting Interface Transition of Evaporating Sessile Droplet through Surfactant on Microtextured Surface

Producing and maintaining specific liquid patterns during evaporation holds great potential for techniques of printing and coating. Here we report the control over the evolution of surfactant solution droplets on the micropyramid substrates during evaporation. The polygonal droplet shape is achieved during the drying rather than solely at the beginning. As the initial surfactant concentration is 0.04 mM, the droplet maintains its initial octagonal shape throughout the lifetime. Interestingly, the initial octagonal shape transforms into a square during the evaporation as the initial surfactant concentration reaches 0.8 mM. These findings can shed light on wetting pattern control for complex solutions required in various applications.

Open Fluidics: A Cell Culture Flow System Developed Over Wettability Contrast-Based Chips

Biological tissues are recurrently exposed to several dynamic mechanical forces that influence cell behavior. On this work, the focus is on the shear stress forces induced by fluid flow. The study of flow-induced effects on cells leads to important advances in cardiovascular, cancer, stem cell, and bone biology understanding. These studies are performed using cell culture flow (CCF) systems, mainly parallel plate flow chambers (PPFC), and microfluidic systems. Here, it is proposed an original CCF system based on the open fluidics concept. The system is developed using a planar superhydrophobic platform with hydrophilic paths. The paths work as channels to drive cell culture medium flows without using walls for liquid confinement. The liquid streams are controlled just based on the wettability contrast. To validate the concept, the effect of the shear stress stimulus in the osteogenic differentiation of C2C12 myoblast cells is studied. Combining bone morphogenic protein (specifically BMP-2) stimulation with this mechanical stimulus, a synergistic effect is found on osteoblast differentiation. This effect is confirmed by the enhancement of alkaline phosphatase activity, a well-known early marker of osteogenic differentiation. The suggested CCF system combines characteristics and advantages of both the PPFC and microfluidic systems.

Breath-Taking Patterns: Discontinuous Hydrophilic Regions for Photonic Crystal Beads Assembly and Patterns Revisualization

Surfaces patterned with hydrophilic and hydrophobic regions provide robust and versatile means for investigating the wetting behaviors of liquids, surface properties analysis, and producing patterned arrays. However, the fabrication of integral and uniform arrays onto these open systems remains a challenge, thus restricting them from being used in practical applications. Here, we present a simple yet powerful approach for the fabrication of water droplet arrays and the assembly of photonic crystal bead arrays based on hydrophilic-hydrophobic patterned substrates. Various integral arrays are simply prepared in a high-quality output with a low cost, large scale, and uniform size control. By simply taking a breath, which brings moisture to the substrate surface, complex hydrophilic-hydrophobic outlined images can be revisualized in the discontinuous hydrophilic regions. Integration of hydrogel photonic crystal bead arrays into the "breath-taking" process results in breath-responsive photonic crystal beads, which can change their colors upon a mild exhalation. This state-of-the-art technology not only provides an effective methodology for the preparation of patterned arrays but also demonstrates intriguing applications in information storage and biochemical sensors.

A Computational Scheme To Evaluate Hamaker Constants of Molecules with Practical Size and Anisotropy

We propose a computational scheme to evaluate Hamaker constants, A, of molecules with practical sizes and anisotropies. Upon the increasing feasibility of diffusion Monte Carlo (DMC) methods to evaluate binding curves for such molecules to extract the constants, we discussed how to treat the averaging over anisotropy and how to correct the bias due to the nonadditivity. We have developed a computational procedure for dealing with the anisotropy and reducing statistical errors and biases in DMC evaluations, based on possible validations on predicted A. We applied the scheme to cyclohexasilane molecule, Si₆H₁₂, used in "printed electronics" fabrications, getting A ≈ 105 ± 2 zJ, being in plausible range supported even by other possible extrapolations. The scheme provided here would open a way to use handy ab initio evaluations to predict wettabilities as in the form of materials informatics over broader molecules.

Sessile Nanodroplets on Elliptical Patches of Enhanced Lyophilicity

We theoretically investigate the shape of a nanodroplet on a lyophilic elliptical patch in lyophobic surroundings on a flat substrate. To compute the droplet equilibrium shape, we minimize its interfacial free energy using both Surface Evolver and Monte Carlo calculations, finding good agreement between the two methods. We observe different droplet shapes, which are controlled by the droplet volume and the aspect ratio of the ellipse. In particular, we study the behavior of the nanodroplet contact angle along the three-phase contact line, explaining the different droplet shapes. Although the nanodroplet contact angle is constant and fixed by Young's law inside and outside the elliptical patch, its value varies along the rim of the elliptical patch. We find that because of the pinning of the nanodroplet contact line at the rim of the elliptical patch, which has a nonconstant curvature, there is a regime of aspect ratios of the elliptical patch in which the nanodroplet starts expanding to the lyophobic part of the substrate, although there is still a finite area of the lyophilic patch free to be wetted.

Contact-angle hysteresis on periodic microtextured surfaces: Strongly corrugated liquid interfaces

We study numerically the shapes of a liquid meniscus in contact with ultrahydrophobic pillar surfaces in Cassie's wetting regime, when the surface is covered with identical and periodically distributed micropillars. Using the full capillary model we obtain the advancing and the receding equilibrium meniscus shapes when the cross-sections of the pillars are both of square and circular shapes, for a broad interval of pillar concentrations. The bending of the liquid interface in the area between the pillars is studied in the framework of the full capillary model and compared to the results of the heterogeneous approximation model. The contact angle hysteresis is obtained when the three-phase contact line is located on one row (block case) or several rows (kink case) of pillars. It is found that the contact angle hysteresis is proportional to the line fraction of the contact line on pillars tops in the block case and to the surface fraction for pillar concentrations 0.1-0.5 in the kink case. The contact angle hysteresis does not depend on the shape (circular or square) of the pillars cross-section. The expression for the proportionality of the receding contact angle to the line fraction [Raj et al., Langmuir 28, 15777 (2012)LANGD50743-746310.1021/la303070s] in the case of block depinning is theoretically substantiated through the capillary force, acting on the solid plate at the meniscus contact line.

Microchannel Wetting for Controllable Patterning and Alignment of Silver Nanowire with High Resolution

Patterning and alignment of conductive nanowires are essential for good electrical isolation and high conductivity in various applications. Herein a facile bottom-up, additive technique is developed to pattern and align silver nanowires (AgNWs) by manipulating wetting of dispersions in microchannels. By forming hydrophobic/hydrophilic micropatterns down to 8 μm with fluoropolymer (Cytop) and SiO2, the aqueous AgNW dispersions with the optimized surface tension and viscosity self-assemble into microdroplets and then dry to form anisotropic AgNW networks. The alignment degree characterized by the full width at half-maximum (FWHM) can be well-controlled from 39.8° to 84.1° by changing the width of microchannels. A mechanism is proposed and validated by statistical analysis on AgNW alignment, and a static model is proposed to guide the patterning of general NWs. The alignment reduced well the electrical resistivity of AgNW networks by a factor of 5 because of the formation of efficient percolation path for carrier conduction.

Pinning of the Contact Line during Evaporation on Heterogeneous Surfaces: Slowdown or Temporary Immobilization? Insights from a Nanoscale Study

The question of the effect of surface heterogeneities on the evaporation of liquid droplets from solid surfaces is addressed through nonequilibrium molecular dynamics simulations. The mechanism behind contact line pinning which is still unclear is discussed in detail on the nanoscale. Model systems with the Lennard-Jones interaction potential were employed to study the evaporation of nanometer-sized cylindrical droplets from a flat surface. The heterogeneity of the surface was modeled through alternating stripes of equal width but two chemical types. The first type leads to a contact angle of 67°, and the other leads to a contact angle of 115°. The stripe width was varied between 2 and 20 liquid-particle diameters. On the surface with the narrowest stripes, evaporation occurred at constant contact angle as if the surface was homogeneous, with a value of the contact angle as predicted by the regular Cassie-Baxter equation. When the width was increased, the contact angle oscillated during evaporation between two boundaries whose values depend on the stripe width. The evaporation behavior was thus found to be a direct signature of the typical size of the surface heterogeneity domains. The contact angle both at equilibrium and during evaporation could be predicted from a local Cassie-Baxter equation in which the surface composition within a distance of seven fluid-particle diameters around the contact line was considered, confirming the local nature of the interactions that drive the wetting behavior of droplets. More importantly, we propose a nanoscale explanation of pinning during evaporation. Pinning should be interpreted as a drastic slowdown of the contact line dynamics rather than a complete immobilization of it during a transition between two contact angle boundaries.