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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Modeling of contact theories for the manipulation of biological micro/nanoparticles in the form of circular crowned rollers based on the atomic force microscope

This article has dealt with the development and modeling of various contact theories for biological nanoparticles shaped as cylinders and circular crowned rollers for application in the manipulation of different biological micro/nanoparticles based on Atomic Force Microscope. First, the effective contact forces were simulated, and their impact on contact mechanics simulation was investigated. In the next step, the Hertz contact model was simulated and compared for gold and DNA nanoparticles with the three types of spherical, cylindrical, and circular crowned roller type contact geometries. Then by reducing the length of the cylindrical section in the circular crowned roller geometry, the geometry of the body was made to approach that of a sphere, and the results were compared for DNA nanoparticles. To anticipatory validate the developed theories, the results of the cylindrical and the circular crowned roller contacts were compared with the results of the existing spherical contact simulations. Following the development of these contact models for the manipulation of various biological micro/nanoparticles, the cylindrical and the circular crowned roller type contact theories were modeled based on the theories of Lundberg, Dowson, Nikpur, Heoprich, and Hertz for the manipulation of biological micro/nanoparticles. Then, for a more accurate validation, the results obtained from the simulations were compared with those obtained by the finite element method and with the experimental results available in previous articles. The previous research works on the simulation of nanomanipulation have mainly investigated the contact theories used in the manipulation of spherical micro/nanoparticles. However since in real biomanipulation situations, biological micro/nanoparticles of more complex shapes need to be displaced in biological environments, this article therefore has modeled and compared, for the first time, different contact theories for use in the biomanipulation of cylindrical and circular crowned roller shaped micro/nanoparticles. The results of models indicate that the contact model of Hertz achieves the largest amount of deformation for the DNA nanoparticle in cylindrical form and the contact model of Heoprich achieves the largest deformation for the circular crowned roller shaped DNA. Of course, this finding is not always true for the other nanoparticles; and considering the mechanical and environmental characteristics, different results can be obtained. Also, by comparing the deformations of different types of nanoparticles, it was determined that the platelet type nanoparticles display the highest degree of deformation in all the considered models, due to their particular mechanical characteristics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2024

Effect of Varying HUT Sizing on Human-Spacesuit Contact Patterns

Fit, comfort, and mobility of the spacesuit rely on the location, magnitude, and type of contact between the suit and wearer. Typically, spacesuits include the Hard Upper Torso (HUT) comprising the upper torso of the spacesuit. Potential injuries from hard contact between the wearer’s shoulders and the HUT are a concern; therefore, to investigate spacesuit-wearer contact patterns, data from a retrospective study was analyzed. This study had eight subjects wearing the Shuttle Extravehicular Mobility Unit (EMU) spacesuit in two configurations, one with a nominally sized HUT and another with an oversized HUT. The subjects were sized per the NASA standard suit fit procedure. The suit’s arms and lower body were also resized to provide nominal arm and lower body fit, accounting for the larger HUT. Subjects held various shoulder postures (neutral posture, and various maximum shoulder rotations) with the suit pressurized to 4.3 PSI. For each posture, subjects reported the intensity of their perceived contact with the suit on a Borg CR10 scale, 0 indicating a non-existent contact intensity, and 10 representing a maximal contact intensity. Ratings were recorded for 11 regions covering the upper body and these ratings were used to determine the impact of body shape and size on suit contact. Our preliminary findings suggest that oversized HUTs had less contact regions than compared to the nominal HUT; and the region of contact, contact patterns, and contact intensities varied from person to person with the oversized HUT. This variance could be linked to subjects’ body shape and size. The next goal is to establish a causal factor between body shape and size, pose, contact region, and the HUT size. The outcome is expected to help understand the overall contact trends and insights into the influence of HUT sizing on suit fit.

Will Green↗
DOE OSTI2025

Measurement of Contact Resistivity In Symmetric Polycrystalline Si/SiO x /Monocrystalline Si Test Structures Using Variable Light Illumination

While different methods exist to determine the contact resistivity in semiconductor devices, these methods are limited to measurement of the majority carrier contacts. The measurement of p‐ or n‐type contacts on n‐ or p‐type crystalline silicon, respectively, is challenging due to the blocking diode formed by the p–n junction. In this article, we address this problem for tunneling oxide passivating contacts used in high‐efficiency Si solar cells. We propose a universal method to extract contact resistivity on symmetric test structures with polycrystalline silicon on SiO x (poly‐Si/SiO x ) passivating contacts under illumination, both for p–n and high–low‐junction passivated contacts. In this method, we demonstrate that the total contact resistance of each cell grid finger to the base wafer is governed by its effective contact area, defined by the transfer length extending from both sides of the finger. Therefore, the grid contact resistance of a poly‐Si contact depends on the ratio of the doped poly‐Si sheet resistance to the tunneling contact resistivity.

14 SOLAR ENERGY↗
DOE OSTI2017

Stiffness of frictional contact of dissimilar elastic solids

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This study gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the friction coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations – adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. Finally, the correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Influence of axial self-magnetic field component on arcing behavior of spiral-shaped contacts

The transverse magnetic field (TMF) contact design is commonly used in vacuum interrupters. When arcing occurs between the TMF contacts, the contact structure can create a self-induced magnetic field that drives the arc to move and rotate on the contact, and thus local overheating and severe erosion can be avoided. However, TMF contacts could also create an axial self-magnetic component, and the influence of this component on the arc behavior has not been considered to date. In this paper, five different types of Cu-Cr spiral-shaped TMF contacts with three different structures are investigated in a demountable vacuum chamber that contains a high-speed charge-coupled device video camera. It was found that the contact structure greatly influenced the arc behavior, especially in terms of arc rotation and the effective contact area, while contacts with the same slot structure but different diameters showed similar arc behavior and arc motion. The magnetic field distribution and the Lorentz force of each of the three different contact structures are simulated, and the axial self-magnetic field was first taken into consideration for investigation of the TMF contact design. It was found that contact designs that have higher axial self-magnetic field components tend to have arc columns with larger diameters and show poorer arc motion and rotation performance in the experiments.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Electrical Analysis of Pulsed Laser Annealed Poly-Si:Ga/SiOx Passivating Contacts

High-efficiency single crystalline silicon (c-Si) solar cells require precise control of dopant diffusion profiles and highly active doping concentrations through thermal annealing. Conventional furnace annealing has been successfully employed for dopant diffusion in aluminum back-surface field (Al-BSF), passivated emitter and rear contact (PERC), and Topcon cells. However, furnace annealing limits some next-generation polycrystalline silicon (poly-Si) on SiOx passivating contacts. This limitation largely affects p-type passivating contacts by not being able to: 1) control the dopant diffusion accurately to prevent B segregation at the SiOx and c-Si interface; and 2) provide highly activated doping concentrations for low contact resistivity. In this contribution, we use a nanosecond excimer laser to examine the passivation quality and electrical performance of both B- and Ga-doped poly-Si/SiOx passivating contacts. The core of this method is to take advantage of the nonequilibrium nature of the anneal through rapid melting and recrystallizing the poly-Si in a short timescale and to achieve doping concentrations above the solid solubility limit. Simulations were performed on polished surfaces to visualize the doping diffusion profiles under different laser conditions, and secondary ion mass spectrometry (SIMS) was used to verify the experimental diffusion profiles post pulsed laser melting (PLM). The results show the dopant diffusion profiles can be tuned precisely through PLM. The electrical analysis using VdP-Hall measurements reveals that the active doping concentration reached 10^21 cm-3 for B and ~2×10^21 cm-3 for Ga in poly-Si, far exceeding their solid solubility limit in Si, with a nearly 100% dopant activation achieved for B, and 20% for Ga. This highly activated dopant profile results in a low contact resistivity of <15 mO·cm^2 for B-doped contacts and <40 mO·cm^2 for Ga-doped contacts. We demonstrate that the passivation quality of the laser annealed contacts shows a linear dependency with the laser energy density and the number of pulses. PLM was also performed on random pyramid textured samples, and we found that preferential melting exists for the tips of pyramids, which can be pursued further for selective pinhole opening. Additionally, we perform thermal stability tests of these hyperdoped passivating contacts and show that under certain laser conditions, the B-doped samples exhibit good thermal stability with near full activation for temperatures up to 800°C. Lastly, we transfer this technique to a larger area by overlapping laser spots and show uniform passivation quality and electrical performance. We are currently implementing this PLM annealed p-type passivating contacts into double-side back-junction poly-Si/SiOx passivating contact devices. Our results show that PLM can not only enable the next generation of high-efficiency c-Si photovoltaics technology but can also benefit the c-Si integrated circuit industry through hyperdoping other semiconductors with atoms that may otherwise have a low solubility.

doping diffusion profile↗
DOE OSTI2017

A revisited concept: Contact inhibition of growth. From cell biology to malignancy

In cell biology, contact inhibition refers to two different but closely related phenomena, contact inhibition of locomotion and contact inhibition of proliferation, exhibited by fibroblasts when in contact with one another. Normal fibroblasts migrate across the surface of a culture dish until they make contact with a neighboring cell. Further cell migration is then inhibited, and normal cells adhere to each other, forming an orderly array of cells on the culture dish surface. Tumor cells, in contrast, continue moving after contact with their neighbors, migrating over adjacent cells, and growing in disordered, multilayered patterns. Not only the movement but also the proliferation of many normal cells is inhibited by cell-cell contact, and cancer cells are characteristically insensitive to such contact inhibition. - Highlights: • Contact inhibition refers to contact inhibition of locomotion and of proliferation. • Normal fibroblasts migrate across a culture dish until they make contact with a neighboring cell. • Tumor cells, in contrast, continue moving after contact with their neighbors.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Comparative study on the formation of Cr and Ti ohmic contacts to (001) β -Ga 2 O 3

Here, a comparative study of Cr/Au and Ti/Au ohmic contacts on (001) β-Ga 2 O 3 was conducted. The electrical behavior from current-voltage measurements and the interfacial composition and microstructure as determined from high-resolution transmission electron microscopy (TEM) with energy dispersive x-ray analysis were compared for the different contacts at selected points in an annealing series (300–700 °C, 1 min. anneals in N 2 ). Cr/Au contacts became ohmic at temperatures (300–350 °C) approximately 50–100 °C lower than Ti/Au contacts (400–450 °C). Cr/Au and Ti/Au contacts demonstrated optimal ohmic behavior (lowest resistance) when annealed to 450–500 and 500–600 °C, respectively, with Ti/Au contacts yielding a lower total resistance than Cr/Au. Cross-sectional TEM images of Cr/Au contacts annealed at 450 °C revealed the presence of Au nanoclusters at the Ga 2 O 3 interface and CrO x layers at both the top of the contact and the Ga 2 O 3 interface. Whereas TiO x also formed at the top and bottom interfaces in 450 °C-annealed Ti/Au contacts, the TiO x surface layer appeared to be variable in thickness and/or discontinuous, unlike the CrO x surface layer. Au nanoclusters were not detected at the interface in the Ti/Au contacts. The interdiffusion and oxidation observed in both contact metallizations point to the need for diffusion barriers that may allow these contacts to be used in future Ga 2 O 3 -based devices that operate at elevated temperatures.

36 MATERIALS SCIENCE↗
NASA NTRS1983

Ohmic contacts for laser diodes

Requirements for ohmic contacts to laser diodes are discussed, and properties of Schottky barrier tunneling contacts are reviewed. A procedure is described for measuring contact resistance on fabricated laser material without the need for specially constructed samples and contact configurations. Measurements of contact resistance and estimates of specific contact resistance are given for Ti/Pt/Au contacts to surfaces with three different doping levels. It was found that below a p-type carrier concentration of 1 x 10 to the 19th per cu cm the contact resistance is likely to be too high for good device performance. At higher doping levels, a specific contact resistance as low as 2 x 10 to the -6th ohm sq cm was obtained. Oxide stripe lasers provided with the type of contact discussed in this paper have been operated without failures for periods up to 7 years at a current density at the contact of 6-8 kA/sq cm. It appears therefore that these contacts satisfy the need for low resistance and durability and that, at the same time, they do not cause any obvious material degradation.

Ladany, I.↗
NASA NTRS1989

Contact solution algorithms

Two algorithms for obtaining static contact solutions are described in this presentation. Although they were derived for contact problems involving specific structures (a tire and a solid rubber cylinder), they are sufficiently general to be applied to other shell-of-revolution and solid-body contact problems. The shell-of-revolution contact algorithm is a method of obtaining a point load influence coefficient matrix for the portion of shell surface that is expected to carry a contact load. If the shell is sufficiently linear with respect to contact loading, a single influence coefficient matrix can be used to obtain a good approximation of the contact pressure distribution. Otherwise, the matrix will be updated to reflect nonlinear load-deflection behavior. The solid-body contact algorithm utilizes a Lagrange multiplier to include the contact constraint in a potential energy functional. The solution is found by applying the principle of minimum potential energy. The Lagrange multiplier is identified as the contact load resultant for a specific deflection. At present, only frictionless contact solutions have been obtained with these algorithms. A sliding tread element has been developed to calculate friction shear force in the contact region of the rolling shell-of-revolution tire model.

Tielking, John T.↗
NASA NTRS2012

Techniques for Solution- Assisted Optical Contacting

A document discusses a solution-assisted contacting technique for optical contacting. An optic of surface flatness Lambda/20 was successfully contacted with one of moderate surface quality, or Lambda/4. Optics used were both ultra-low expansion (ULE) glass (Lambda/4 and Lambda/20) and fused silica (Lambda/20). A stainless steel template of the intended interferometer layout was designed and constructed with three contact points per optic. The contact points were all on a common side of the template. The entire contacting jig was tilted at about 30 . Thus, when the isopropanol was applied, each optic slid due to gravity, resting on the contact points. All of the contacting was performed in a relatively dusty laboratory. A number of successful contacts were achieved where up to two or three visible pieces of dust could be seen. These were clearly visible due to refraction patterns between the optic and bench. On a number of optics, the final step of dropping isopropyl between the surfaces was repeated until a successful contact was achieved. The new procedures realized in this work represent a simplification for optical contacting in the laboratory. They will both save time and money spent during the contacting process, and research and development phases. The techniques outlined are suitable for laboratory experiments, research, and initial development stages.

DeVine, Glenn↗
DOE OSTI2016

Thermal contact conductance as a method of rectification in bulk materials

A thermal rectifier that utilizes thermal expansion to directionally control interfacial conductance between two contacting surfaces is presented. The device consists of two thermal reservoirs contacting a beam with one rough and one smooth end. When the temperature of reservoir in contact with the smooth surface is raised, a similar temperature rise will occur in the beam, causing it to expand, thus increasing the contact pressure at the rough interface and reducing the interfacial contact resistance. However, if the temperature of the reservoir in contact with the rough interface is raised, the large contact resistance will prevent a similar temperature rise in the beam. As a result, the contact pressure will be marginally affected and the contact resistance will not change appreciably. Owing to the decreased contact resistance of the first scenario compared to the second, thermal rectification occurs. A parametric analysis is used to determine optimal device parameters including surface roughness, contact pressure, and device length. Modeling predicts that rectification factors greater than 2 are possible at thermal biases as small as 3 K. Lastly, thin surface coatings are discussed as a method to control the temperature bias at which maximum rectification occurs.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Lattice Boltzmann Modeling of Drying of Porous Media Considering Contact Angle Hysteresis

Drying of porous media is governed by a combination of evaporation and movement of the liquid phase within the porous structure. Contact angle hysteresis induced by surface roughness is shown to influence multi-phase flows, such as contact line motion of droplet, phase distribution during drainage and coffee ring formed after droplet drying in constant contact radius mode. However, the influence of contact angle hysteresis on liquid drying in porous media is still an unanswered question. Lattice Boltzmann model (LBM) is an advanced numerical approach increasingly used to study phase change problems including drying. In this paper, based on a geometric formulation scheme to prescribe contact angle, we implement a contact angle hysteresis model within the framework of a two-phase pseudopotential LBM. The capability and accuracy of prescribing and automatically measuring contact angles over a large range are tested and validated by simulating droplets sitting on flat and curved surfaces. Afterward, the proposed contact angle hysteresis model is validated by modeling droplet drying on flat and curved surfaces. Then, drying of two connected capillary tubes is studied, considering the influence of different contact angle hysteresis ranges on drying dynamics. Finally, the model is applied to study drying of a dual-porosity porous medium, where phase distribution and drying rate are compared with and without contact angle hysteresis. The proposed model is shown to be capable of dealing with different contact angle hysteresis ranges accurately and of capturing the physical mechanisms during drying in different porous media including flat and curved geometries.

36 MATERIALS SCIENCE↗
DOE OSTI2015

An analytical elastic plastic contact model with strain hardening and frictional effects for normal and oblique impacts

Impact between metallic surfaces is a phenomenon that is ubiquitous in the design and analysis of mechanical systems. We found that to model this phenomenon, a new formulation for frictional elastic–plastic contact between two surfaces is developed. The formulation is developed to consider both frictional, oblique contact (of which normal, frictionless contact is a limiting case) and strain hardening effects. The constitutive model for normal contact is developed as two contiguous loading domains: the elastic regime and a transitionary region in which the plastic response of the materials develops and the elastic response abates. For unloading, the constitutive model is based on an elastic process. Moreover, the normal contact model is assumed to only couple one-way with the frictional/tangential contact model, which results in the normal contact model being independent of the frictional effects. Frictional, tangential contact is modeled using a microslip model that is developed to consider the pressure distribution that develops from the elastic–plastic normal contact. This model is validated through comparisons with experimental results reported in the literature, and is demonstrated to be significantly more accurate than 10 other normal contact models and three other tangential contact models found in the literature.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Fabrication methods for high reflectance dielectric-metal point contact rear mirror for optoelectronic devices

The patterned dielectric back contact (PDBC) structure can be used to form a point-contact architecture that features a dielectric spacer with spatially distributed, reduced-area metal point contacts between the semiconductor back not recognized contact layer and the metal back contact. In this structure, the dielectric-metal region provides higher reflectance and is electrically insulating. Reduced-area metal point contacts provide electrical conduction for the back contact but typically have lower reflectance. The fabrication methods discussed in this article were developed for thermophotovoltaic cells, but they apply to any III-V optoelectronic device requiring the use of a conductive and highly reflective back contact. Patterned dielectric back contacts may be used for enhanced sub-bandgap reflectance, for enhanced photon recycling near the bandgap energy, or both depending on the optoelectronic application. The following fabrication methods are discussed in the article: PDBC fabrication procedures for spin-on dielectrics and commonly evaporated dielectrics to form the spacer layer; methods to selectively etch a parasitically absorbing back contact layer using metal point contacts as an etch mask; methods incorporating a dielectric etch through different process techniques such as reactive ion and wet etching.

14 SOLAR ENERGY↗
DOE OSTI2014

Sheet resistance under Ohmic contacts to AlGaN/GaN heterostructures

For the determination of specific contact resistance in semiconductor devices, it is usually assumed that the sheet resistance under the contact is identical to that between the contacts. This generally does not hold for contacts to AlGaN/GaN structures, where an effective doping under the contact is thought to come from reactions between the contact metals and the AlGaN/GaN. As a consequence, conventional extraction of the specific contact resistance and transfer length leads to erroneous results. In this Letter, the sheet resistance under gold-free Ti/Al-based Ohmic contacts to AlGaN/GaN heterostructures on Si substrates has been investigated by means of electrical measurements, transmission electron microscopy, and technology computer-aided design simulations. It was found to be significantly lower than that outside of the contact area; temperature-dependent electrical characterization showed that it exhibits semiconductor-like behavior. The increase in conduction is attributed to n-type activity of nitrogen vacancies in the AlGaN. They are thought to form during rapid thermal annealing of the metal stack when Ti extracts nitrogen from the underlying semiconductor. The high n-type doping in the region between the metal and the 2-dimensional electron gas pulls the conduction band towards the Fermi level and enhances horizontal electron transport in the AlGaN. Using this improved understanding of the properties of the material underneath the contact, accurate values of transfer length and specific contact resistance have been extracted.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Passivated Contacts for Direct Wafer Product (Final Technical Report)

This TCF project developed a thin-oxide (SiO 2 )/polycrystalline silicon (poly-Si) passivated contact solar cell on CubicPV's (formally 1366 Technologies, Inc.) Direct Wafer® Product (DWP) kerfless wafers. The project used two NREL-developed technologies described in U.S. Patent No. 9,911,873, Hydrogenation of Passivated Contacts and U.S. Patent Application Serial No. 15/890,172, Doped Passivated Contacts . The project was motivated by a potential higher efficiency cell (compared to a PERC cell) using passivated contacts on the ultra-low cost kerfless wafers grown using the Direct Wafer process. The hope was to accelerate market adoption of the cell and wafer by delivering the lowest LCOE in the PV industry. The project tested both n-type and p-type SiO 2 /poly-Si passivated contacts grown by thermal oxidation and plasma enhanced chemical vapor deposition (PECVD) of the poly-Si layer on DWP with varying wafer resistivities. Both deposition techniques are industry standards and thus economically viable methods for commercializing the contacts. The results indicated that both n-type and p-type poly-Si passivated contacts can be formed on polycrystalline DWP wafers, but implied open-circuit voltages (i Voc ) were limited to below 0.65 mV (compared with ~ 730 mV on n-Cz wafers). Diffusion of H to the Si/SiO 2 /poly-Si interface was key to obtaining high i Voc values. In this study, H was diffused from a high-temperature SiN x layer deposited over the poly-Si layer during a high-temperature firing step, similar to one used for screen printed metals. The study concluded that poly-Si passivated contacts on DWP wafers passivated the surface of the wafers as well as PERC passivated surfaces, which use a less expensive dielectric layer stack. The project showed that Direct Wafer Product wafers grown by CubicPV could produce high i Voc values (~0.647 mV), which could produce a cell over 20% efficient with proper processing and metallization. These cells, though not economically viable in 2024 as a stand-alone cell, could be integrated with a wide-bandgap top solar cell to form a two-junction tandem cell that could be viable under certain circumstances. This is because the bottom cell of a 30%, two-terminal tandem only needs to be a 20% cell under one-sun conditions. Thus, the DWP could be an ideal low-cost wafer for tandems. The project also revealed that a TOPCon type cell could be formed on a p-type DWP wafer using a P-diffused emitter and a p-type poly-Si contact. In fact, the p-type version of the poly-Si contact out-performed the n-type version for a variety of wafer resistivities, from highly doped to lowly doped. This curiosity requires more work to understand because on Cz wafers, the n-type poly-Si contact is of much higher quality than the p-type version.

14 SOLAR ENERGY↗
DOE OSTI2017

Beyond-Cassie Mode of Wetting and Local Contact Angles of Droplets on Checkboard-Patterned Surfaces

Droplet wetting and distortion on flat surfaces with heterogeneous wettability are studied using the 3D Shan–Chen pseudopotential multiphase lattice Boltzmann model (LBM). The contact angles are compared with the Cassie mode, which predicts an apparent contact angle for flat surfaces with different wetting properties, where the droplet size is large compared to the size of the heterogeneity. The surface studied consists in a regular checkboard pattern with two different Young’s contact angles (hydrophilic and hydrophobic) and equal surface fraction. The droplet size and patch size of the checkboard are varied beyond the limit where Cassie’s equation is valid. A critical ratio of patch size to droplet radius is found below which the apparent contact angle follows the Cassie mode. Above the critical value, the droplet shape changes from a spherical cap to a more distorted form, and no single contact angle can be determined. The local contact angles are found to vary along the contact line between minimum and maximum values. The droplet is found to wet preferentially the hydrophilic region, and the wetted area fraction of the hydrophilic region increases quasi-linearly with the ratio between patch and droplet sizes. We propose a new equation beyond the critical ratio, defining an equivalent contact angle, where the wetted area fractions are used as weighting coefficients for the maximum and minimum local contact angles. This equivalent contact angle is found to equal Cassie’s contact angle.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗