Analysis of droplet evaporation on a superhydrophobic surface

The evaporation process for small, 1-2-mm-diameter droplets of water from patterned polymer surfaces is followed and characterized. The surfaces consist of circular pillars (5-15 microm diameter) of SU-8 photoresist arranged in square lattice patterns such that the center-to-center separation between pillars is 20-30 microm. These types of surface provide superhydrophobic systems with theoretical initial Cassie-Baxter contact angles for water droplets of up to 140-167 degrees, which are significantly larger than can be achieved by smooth hydrophobic surfaces. Experiments show that on these SU-8 textured surfaces water droplets initially evaporate in a pinned contact line mode, before the contact line recedes in a stepwise fashion jumping from pillar to pillar. Provided the droplets of water are deposited without too much pressure from the needle, the initial state appears to correspond to a Cassie-Baxter one with the droplet sitting upon the tops of the pillars. In some cases, but not all, a collapse of the droplet into the pillar structure occurs abruptly. For these collapsed droplets, further evaporation occurs with a completely pinned contact area consistent with a Wenzel-type state. It is shown that a simple quantitative analysis based on the diffusion of water vapor into the surrounding atmosphere can be performed, and estimates of the product of the diffusion coefficient and the concentration difference (saturation minus ambient) are obtained.     

Mean-field theory of liquid droplets on roughened solid surfaces: application to superhydrophobicity

We present calculations of the density distributions and contact angles of liquid droplets on roughened solid surfaces for a lattice gas model solved in a mean-field approximation. For the case of a smooth surface, this approach yields contact angles that are well described by Young's equation. We consider rough surfaces created by placing an ordered array of pillars on a surface, modeling so-called superhydrophobic surfaces, and we have made calculations for a range of pillar heights. The apparent contact angle follows two regimes as the pillar height increases. In the first regime, the liquid penetrates the interpillar volume, and the contact angle increases with pillar height before reaching a constant value. This behavior is similar to that described by the Wenzel equation for contact angles on rough surfaces, although the contact angles are underestimated. In the second regime, the liquid does not penetrate the interpillar volume substantially, and the contact angle is independent of the pillar height. This situation is similar to that envisaged in the Cassie-Baxter equation for contact angles on heterogeneous surfaces, but the contact angles are overestimated by this equation. For larger pillar heights, two states of the droplet can be observed, one Wenzel-like and the other Cassie-like.     

Dynamic Self‐Assembly Adhesion of a Paraquat Droplet on a Pillar[5]arene Surface

The adhesion of herbicide droplets on leaf surfaces plays an important role in the herbicide's adsorption by crops. How to control the adhesive binding which occurs through dynamic self‐assembly between the macroscopic droplet and the surface is a challenging task. We introduce a host onto surfaces that controls the binding of guests in the paraquat droplets. The pillar[5]arene‐functional surface showed the selective binding of paraquat droplets via the host–guest interaction. The work is promising for improving the efficiency of herbicides.     

Dynamic behavior of water droplets on solid surfaces with pillar-type nanostructures

In the present study, we investigated the static and dynamic behavior of water droplets on solid surfaces featuring pillar-type nanostructures by using molecular dynamics simulations. We carried out the computation in two stages. As a result of the first computational stage, an initial water cube reached an equilibrium state at which the water droplet showed different shapes depending on the height and the lateral and gap dimensions of the pillars. In the second computational stage, we applied a constant body force to the static water droplet obtained from the first computational stage and evaluated the dynamic behavior of the water droplet as it slid along the pillar-type surface. The dynamic behavior of the water droplet, which could be classified into three different groups, depended on the static state of the water droplet, the pillar characteristics (e.g., height and the lateral and gap dimensions of the pillars), and the magnitude of the applied body force. We obtained the advancing and receding contact angles and the corresponding contact angle hysteresis of the water droplets, which helped classify the water droplets into the three different groups.     

Enhanced hydrophobicity of rough polymer surfaces

Molecular dynamics simulations were used to study the effect of periodic roughness of PE and PVC polymer surfaces on the hydrophobicity. Pillars of different lateral dimensions and heights were derived from flat crystalline surfaces, and the results of nanoscale simulations on the structured surfaces were compared with theoretical predictions of the Wenzel and Cassie equations. Hydrophobicity increased on all rough surfaces, but the increase was greater on the structured PE surfaces because of the larger water contact angle on the flat PE surface than the corresponding PVC surface. Equally sized pillar structures on the two polymers resulted in different equilibrium wetting geometries. Composite contacts were observed on rough PE surfaces, and the contact angle increased with decreasing contact area between the solid and the liquid. Opposite results were obtained for rough PVC surfaces; the contact angle increased with the solid-liquid contact area, in agreement with Wenzel's equation. However, the composite contact was observed if the energies of the wetted and composite contacts were almost equal. Good agreement was obtained between the simulated contact angles and equilibrium droplet shapes and the theories but there were also some limitations of the nanoscale simulations.     

Thermodynamic analysis on wetting behavior of hierarchical structured superhydrophobic surfaces

Superhydrophobicity of biological surfaces has recently been studied intensively with the aim to design artificial surfaces. It has been revealed that nearly all of the superhydrophobic surfaces consist of the intrinsic hierarchical structures. However, the role of such structures has not been completely understood. In this study, different scales of hierarchical structures have been thermodynamically analyzed using a 2-D model. In particular, the free energy (FE) and free energy barrier (FEB) for the composite wetting states are calculated, and the effects of relative pillar height (h(r)) and relative pillar width (a(r)) on contact angle (CA) and contact angle hysteresis (CAH) have been investigated in detail. The results show that if the geometrical parameter ratio is the same (e.g., a:b:h = 2:2:1), the equilibrium CA for the composite of the three-, dual-, and single- scale roughness structures is 159.8°, 151.1°, and 138.6°, respectively. Furthermore, the nano- to microstructures of such surfaces can split a large FEB into many small ones and hence can decrease FEB; in particular, a hierarchical geometrical structure can lead to a hierarchical "FEB structure" (e.g., for a dual-scale roughness geometrical structure, there is also a dual-scale FEB structure). This is especially important for a droplet to overcome the large FEBs to reach a stable superhydrophobic state, which can lead to an improved self-cleaning property. Moreover, for extremely small droplets, the secondary or third structure (i.e., submicrostructure or nanostructure) can play a dominant role in resisting the droplets into troughs, so that a composite state can be always thermodynamically favorable for such a hierarchical structured system.     

Droplet motion on designed microtextured superhydrophobic surfaces with tunable wettability

Superhydrophobic surfaces have shown promising applications in microfluidic systems as a result of their water-repellent and low-friction properties over the past decade. Recently, designed microstructures have been experimentally applied to construct wettability gradients and direct the droplet motion. However, thermodynamic mechanisms responsible for the droplet motion on such regular rough surfaces have not been well understood such that at present specific guidelines for the design of tunable superhydrophobic surfaces are not available. In this study, we propose a simple but robust thermodynamic methodology to gain thorough insight into the physical nature for the controllable motion of droplets. On the basis of the thermodynamic calculations of free energy (FE) and the free-energy barrier (FEB), the effects of surface geometry of a pillar microtexture are systematically investigated. It is found that decreasing the pillar width and spacing simultaneously is required to lower the advancing and receding FEBs to effectively direct droplets on the roughness gradient surface. Furthermore, the external energy plays a role in the actuation of spontaneous droplet motion with the cooperation of the roughness gradient. In addition, it is suggested that the so-called "virtual wall" used to confine the liquid flow along the undesired directions could be achieved by constructing highly advancing FEB areas around the microchannels, which is promising for the design of microfluidic systems.     

Liquid nanodroplets spreading on chemically patterned surfaces

Controlling the spatial distribution of liquid droplets on surfaces via surface energy patterning can be used to deliver material to specified regions via selective liquid/solid wetting. Although studies of the equilibrium shape of liquid droplets on heterogeneous substrates exist, much less is known about the corresponding wetting kinetics. Here we present large-scale atomistic simulations of liquid nanodroplets spreading on chemically patterned surfaces. Results are presented for lines of polymer liquid (droplets) on substrates consisting of alternating strips of wetting (equilibrium contact angle theta0 = 0 degrees) and nonwetting (theta0 approximately 90 degrees) material. Droplet spreading is compared for different wavelength lambda of the pattern and strength of surface interaction on the wetting strips. For small lambda, droplets partially spread on both the wetting and nonwetting regions of the substrate to attain a finite contact angle less than 90 degrees. In this case, the extent of spreading depends on the interaction strength in the wetting regions. A transition is observed such that, for large lambda, the droplet spreads only on the wetting region of the substrate by pulling material from nonwetting regions. In most cases, a precursor film spreads on the wetting portion of the substrate at a rate strongly dependent on the width of the wetting region.     

Fabrication of super-oil-repellent dual pillar surfaces with optimized pillar intervals

Hierarchical dual pillar surfaces with optimized pillar intervals are fabricated by a novel combined process of the oblique angle magnetron sputtering deposition of Al-Nb alloys and their anodizing. The pillar intervals are controlled by the deposition angle and cell size of a scalloped substrate for oblique angle deposition. Anodizing of the deposited pillar surfaces develops a nanopillar oxide layer, producing the hierarchical dual pillar surfaces. After being coated with a fluoroalkyl phosphate layer to reduce the surface free energy, hierarchical surfaces with submicrometer pillar intervals greater than 400 nm show super liquid repellency even for hexadecane with a low surface tension of 27.5 mN m(-1), although the submicrometer pillar surfaces with smaller submicrometer pillar intervals and without nanopillars were not super-oil-repellent. In contrast, the dual pillar surfaces show superhydrophobicity regardless of the submicrometer pillar intervals. Thus, the present study demonstrates the importance of the pillar intervals (gap size between pillars) to realize the superoleophobicity.     

Analysis on wetting and local dynamic properties of single water droplet on a polarized solid surface: a molecular dynamics study

Molecular dynamics simulations of single water droplets on a solid surface were carried out in order to investigate the effects that the Coulomb interaction between liquid and solid molecules has on wetting behavior by appending vertical electric polarization on a solid surface. The water droplet became more wettable both on upward and downward polarized surfaces, although structures of the adsorption layer appearing near the solid surface were clearly different, and the relation between droplet contact angle and surface polarization was also different for upward and downward polarization directions. The probability density distribution of molecular orientation around the adsorption layer indicated that preferable water molecule orientations varied largely by the surface polarization, and the rotational mobility around the preferable orientations was also affected. The dynamic property due to this rotational mobility was clearly captured by means of distribution of rotational diffusion coefficient, which potentially corresponded to local viscosity distribution.     

Novel shape and placement definitions with retention modeling for solid microfabricated pillar columns for CEC and HPLC

A novel design approach for optimizing the shape of microfabricated pillar columns for LC is presented. 2-D flow simulations are performed with a focus on electrokinetically driven flow, in order to evaluate the performance of the new method. The proposed foil shape is compared with geometrical shapes known from the literature, for various arrangements. It yields a much more uniform velocity field distribution and a decrease in plate height values up to 25%. In addition to shape optimization, a new method for spatial arrangement of structures is presented. With the aim of conserving the hydrodynamic balance, the axial spacing of the pillars is adjusted according to the proposed equivalent width approach. When compared with a fixed interpillar spacing in all directions, it increases the flow uniformity and results in an 18% lower plate height. A new direct simulation approach is implemented to model both flow field and retention for solid microfabricated pillar structures in the 2-D domain. This model, which defines retention as inward/outward fluxes through the wall surfaces as first order reactions, enables monitoring of the time-dependent process and an evaluation of the parameters affecting performance. The meaning of the obtained results in a practical setting, with limitations in photolithography and microfabrication, will be highlighted.     

Molecular dynamics simulations of water droplets on polymer surfaces

Molecular dynamics simulations were used to study the wetting of polymer surfaces with water. Contact angles of water droplets on crystalline and two amorphous polyethylene (PE) and poly(vinyl chloride) (PVC) surfaces were extracted from atomistic simulations. Crystalline surfaces were produced by duplicating the unit cell of an experimental crystal structure, and amorphous surfaces by pressing the bulk polymer step by step at elevated temperature between two repulsive grid surfaces to a target density. Different-sized water droplets on the crystalline PE surface revealed a slightly positive line tension on the order of 10(-12)-10(-11) N, whereas droplets on crystalline PVC did not yield a definite line tension. Microscopic contact angles produced by the simple point charge (SPC) water model were mostly a few degrees smaller than those produced by the extended SPC model, which, as the model with lowest bulk energy, presents an upper boundary for contact angles. The macroscopic contact angle for the SPC model was 94 degrees on crystalline PVC and 113 degrees on crystalline PE. Amorphicity of the surface increased the water contact angle on PE but decreased it on PVC, for both water models. If the simulated contact angles on crystalline and amorphous surfaces are combined in proportion to the crystallinity of the polymer in question, simulated values in relatively good agreement with measured values are obtained.     

Methodology for calculating the volume of condensate droplets on topographically modified, microgrooved surfaces

Liquid droplets on micropatterned surfaces consisting of parallel grooves tens of micrometers in width and depth are considered, and a method for calculating the droplet volume on these surfaces is presented. This model, which utilizes the elongated and parallel-sided nature of droplets condensed on these microgrooved surfaces, requires inputs from two droplet images at ? = 0° and ? = 90°--namely, the droplet major axis, minor axis, height, and two contact angles. In this method, a circular cross-sectional area is extruded the length of the droplet where the chord of the extruded circle is fixed by the width of the droplet. The maximum apparent contact angle is assumed to occur along the side of the droplet because of the surface energy barrier to wetting imposed by the grooves--a behavior that was observed experimentally. When applied to water droplets condensed onto a microgrooved aluminum surface, this method was shown to calculate the actual droplet volume to within 10% for 88% of the droplets analyzed. This method is useful for estimating the volume of retained droplets on topographically modified, anisotropic surfaces where both heat and mass transfer occur and the surface microchannels are aligned parallel to gravity to assist in condensate drainage.     

Solid‐to‐Liquid Charge Transfer for Generating Droplets with Tunable Charge

Charged liquid droplets are typically generated by a high‐voltage power supply. Herein, a previously unreported method is used for charging liquid droplets: by transferring charge from an insulating solid surface charged by contact electrification to the droplets. Charging the solid surface by contact electrification involves bringing it into contact with another solid surface for generating static charge. Subsequently, water droplets that flow across the surface are found to be charged—thus, the charge is readily transferred from solid to liquid. The charge of the droplets can be tuned continuously from positive to negative by varying the way the solid surface is charged. The amount of charge generated is sufficient for manipulating, coalescing, and sorting the water droplets by solid surfaces charged by contact electrification. This method of generating charged droplets is general, simple, inexpensive, and does not need any additional equipment or power supply.     

Dynamic effects of bouncing water droplets on superhydrophobic surfaces

Superhydrophobic surfaces have considerable technological potential for various applications due to their extreme water repellent properties. Superhydrophobic surfaces may be generated by the use of hydrophobic coating, roughness, and air pockets between solid and liquid. Dynamic effects, such as the bouncing of a droplet, can destroy the composite solid-air-liquid interface. The relationship between the impact velocity of a droplet and the geometric parameters affects the transition from the solid-air-liquid interface to the solid-liquid interface. Therefore, it is necessary to study the dynamic effect of droplets under various impact velocities. We studied the dynamic impact behavior of water droplets on micropatterned silicon surfaces with pillars of two different diameters and heights and with varying pitch values. A criterion for the transition from the Cassie and Baxter regime to the Wenzel regime based on the relationship between the impact velocity and the parameter of patterned surfaces is proposed. The trends are explained based on the experimental data and the proposed transition criterion. For comparison, the dynamic impact behavior of water droplets on nanopatterned surfaces was investigated. The wetting behavior under various impact velocities on multiwalled nanotube arrays also was investigated. The physics of wetting phenomena for bouncing water droplet studies here is of fundamental importance in the geometrical design of superhydrophobic surfaces.     

液滴在超疏水植物叶面的沉积：实验和分子动力学模拟

农药液滴在靶标植物叶面的动态沉积对于提高农药利用率具有重要的意义,特别是在超疏水植物叶面的动态沉积。在本文中,我们利用生物基表面活性剂和甘油之间的氢键作用来增强液滴在超疏水植物叶面的有效沉积。在较低浓度的山梨醇-烷基胺表面活性剂溶液中,添加0.001%的甘油,可有效抑制液滴在不同超疏水/疏水植物叶片表面的弹跳和飞溅行为。结果表明,甘油的加入并没有显著改变山梨醇-烷基胺表面活性剂溶液的表面张力、粘度和聚集体的形态。核磁共振波谱(DOSY)显示,甘油加速了山梨醇-烷基胺表面活性剂分子的扩散速度。利用分子动力学模拟,对山梨醇-烷基胺表面活性剂/甘油体系的能量演化及表面活性剂相对于固体表面距离的分布进行了研究。这项目工作不仅为抑制液滴在植物叶面的弹跳飞溅提供了一种建设性的方法,而且为选择农用表面活性剂提供了理论基础。     

Equilibrium contact angles of liquid droplets on ideal rough solids

This work proposes a theoretical model for predicting the apparent equilibrium contact angle of a liquid on an ideal rough surface that is homogeneous and has a negligible body force, line tension, or contact angle hysteresis between solid and liquid. The model is derived from the conservation equations and the free-energy minimization theory for the changes of state of liquid droplets. The work of adhesion is expressed as the contact angles in the wetting process of the liquid droplets. Equilibrium contact angles of liquid droplets for rough surfaces are expressed as functions of the area ratios for the solid, liquid, and surrounding gas and the roughness ratio and wetting ratio of the liquid on the solid for the partially and fully wet states. It is found that the ideal critical angle for accentuating the contact angles by the surface roughness is 48°. The present model is compared with existing experimental data and the classical Wenzel and Cassie-Baxter models and agrees with most of the experimental data for various surfaces and liquids better than does the Wenzel model and accounts for trends that the Wenzel model cannot explain.     

Curvature modulates the self-assembly of amphiphilic molecules

In this work, we used lattice Monte Carlo simulations and theoretical model calculations to show how the self-assembly of adsorbed amphiphilic molecules is affected by the local curvature of solid surfaces. It is found that, beyond a critical curvature value, solid surface geometry governs the spatial ordering of aggregates and may induce the morphological transitions. The simulation results show how the curvature of solid surfaces modulates the distribution of aggregates: the anisotropy in local curvature along and perpendicular to the cylindrical surfaces tends to generate orientationally ordered cylindrical micelles. To account for the morphological transitions induced by the local curvature of solid surfaces, we constructed a theoretical model which includes the Helfrich bending energy, the deformation energy of aggregates induced by solid surfaces, and the adsorption energy. The model calculations indicate that on highly curved solid surfaces the bending energy for bilayer structure sharply increases with surface curvature, which in turn induces the morphological transition from bilayer to cylindrical structure. Our results suggest that the local curvature provides a means of controlling the spatial organization of amphiphilic molecules.     

Adsorption of polycyclic aromatic hydrocarbons at the air-water interface: molecular dynamics simulations and experimental atmospheric observations

Adsorption of benzene, naphthalene, anthracene, and phenanthrene at the aqueous surface is investigated by means of molecular dynamics simulations. Potentials of mean force, i.e., free energy profiles obtained when moving the studied molecules across an aqueous slab were evaluated. In all cases, deep surface free energy minima, corresponding to orders of magnitude of surface enhancement of the aromatic molecule, were located. This enhancement, which increases with the size of the solute, points to the importance of the aqueous surface for the chemistry of polycyclic aromatic hydrocarbons (PAHs). Supporting evidence in the atmospheric environment related to the heterogeneous chemistry of PAHs on water droplets and planar surfaces is summarized. There is good agreement between the hydration free energies computed from MD calculations and the experimentally determined values. Data pertaining to the importance of the air-water interface in the adsorption and transport of PAHs on micron sized water droplets are described. The relevant data on adsorption and reaction (ozonation and photochemical) at the air-water interface of planar surfaces and droplets are also summarized.